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MECHANICS' AND ENGINEERS'
POCKET-BOOK
OF
TABLES, KULES, AND FORMULAS
PERTAINING TO
MECHANICS, MATHEMATICS, AND PHYSICS:
INCLUDING
AREAS, SQUARES, CUBES, AND ROOTS, ETC. ;
LOGARITHMS, HYDRAULICS, HYDRODYNAMICS, STEAM AND
THE STEAM-ENGINE, NAVAL ARCHITECTURE,
MASONRY, STEAM VESSELS,
MILLS, ETC. ;
COMPRESSED AIR, GAS. AND OIL ENGINES;
LIMES, MORTARS, CEMENTS, ETC.;
ORTHOGRAPHY OF TECHNICAL WORDS AND TERMS, ETC., ETC.
Seventy-eighth Edition. 152d Thousand
BY CHAS. H. HASWELL,
»»
SITIL, MASINB, AND MKCHANICAL BNUI.NBKR; HO.NOKAKY MKM8RR OP THK AM. 80C. OF NAVAI. ARCHI
AND MaKINK K.NUINKIItS, BUSTON SUCIBTY OK CIVIL ENGIXEKKO, AND THK BNUINKBRS'
CLUB OP PHILADBLPHIA; LirB MBHBBK Or THB AM. 80C. OK CIVIL KNUINBKUS AND
OP THB INHTITUTIONS OP CIVIL BNQINBBBS AND OF NAVAL ARCHITBCTS OF
BNOLAND ; UBMBBR OF THB N. Y. ACADBMY OF SCIBNCK8 ; FBL-
LOW OF THB AM. OBOOHAPHICAL SOCIETY; CORRB8POND1NG
MBUBBB OF THB AM. IN8TITDTB OF ARCHITBCTS, AND
^ A880CIATB MBMBBR OF THB NBW YORK Mt«
CEOSCOPICAL SOCIETY, BTC., BTC.
An examination of facts is the foundation of science.
A resultant effect, physical or mechanical, cannot be renewed without an
expenditure of power in addition to that which originated it.
NEW YORK:
HARPBR & BROTHERS, PUBLISHERS,
FBANKLIM BQUABX.
Mechanics' and Engineers' Pocket-book
Copyright, X884, 1887, 1890, 189J, 1893, 1894, 1895, 1896, 1897, 1898, 1899. 1901,
1903, 19 1 8, by Harper & Brothers
Copyright. 191 2. 1919. by Gouverneur Kemble HaswelL
Copyright, 1920, by Julian B. Haswell
Printed in the United States of America
a-u
357193
MAY 2 3 1930
•A-
IJtfaCRIBEU
TO •
CAPTAIN JOHN ERICSSON, LL.D.,
AS A SLIGHT TRIBUTE TO HIS GENIUS AND ATTAINMENTS,
AND IN TESTIMONY OP THE SINCERE REGARD
AND ESTEEM OF HIS FRIEND,
THE AUTHOR
PREFACE
To the Kortsr-fiflh. Kdition.
Thb First Edition of this work, consisting of 284 pagea»
was submitted to the Mechanics and Engineers of the United
States by one of their number in 1843, who designed it for
a convenient reference to Rules, Results, and Tables con-
nected with the discharge of their various duties.
The Twenty-first Edition was published in 1867, consisted
of 664 pages, and, in addition to the original design of the
work, it was essayed to embrace some general information
npon Mechanical and Physical subjects.
The Tables of Areas and Circumferences of Circles have
been extended, and together with those of Weights of Metals,
Balls, Tubes, Pipes, etc., of this and some preceding editions
were computed and verified by the author.
This edition is a revision and an entire reconstruction of
all preceding, embracing amended and much new matter, as
Masonry, Strength of Girders, Floor Beams, Logarithms, etc.,
etcJ
To the young Mechanic and Engineer it is recommended
to cultivate a knowledge of Physical Laws and to note re-
sults of observations and of practice, without which eminence
in his profession can never be attained ; and if this work
shall assist him in the attainment of these objects, one great
purpose of the author will be well accomplished.
V<fn i.—iHechaniccd and Phyticai tuit^eds, eomnuneing at p. 437 and ending at
p. 870. are given in aiphabetuxU order.
3. — Tont are given and computed cU 3240 lbs.
y.— Degree* qf temperature are given by the Scale of Fahrenheit.
INDEX.
A. Ftg*
Abctmkiits AMD AR0HS8 {See Arches
and Abutments) 604-605
AccsLKRATBD BoDT, Distances, Ve-
locities, and Acceleration of. .921-922
Adds 188
Acreage, To CompiUe. 337
Adulteration in Metals, Proportion
0/ Two Ingredients in a Compound. 216
Aerodynamics 614
ASROMBTBT 673-676
{See also Pneumatics.)
" Course of Wind, etc '. 675
" Cyclones, Direction of. 675
" Degree of Rar^action 673
" Discharge Pipes, Diameter of. 676
*' Distance of Audible Sounds... 674
♦ ' Force of Wind on a /Sur/ace.674-675
" Height of a Column of Mer-
cury to Induce an Efflux of
Air, To Compute 675
" Resistance of a Plane Surface
to Air, To Compute 675
" Resistance to a Steam Vessel in
Air or Water 911
Weight or Pressure of Air
under a Given Height of
Barometer and Temperature
Discharged in One Second. '. 675
Wind, Velocity and Pressure
of. 674,911, 924
Volume of Air discharged
Through an Opening, etc.,
into a Vaaium 674
AiROSTATics 427-431, 614
" Clouds, Classijlcation of. 430
" Distances, by Velocity of Sound 428
*' ElewUions,by a Barometer. ^^^-^2()
" " Thermameter.. 429
" Lightning, Classi^fication of . . 430
Velocity of Air flowing into
a Vacuum, To Compute. 428
" of Sound 428
Weather Glasses and Barom-
eter Indications 430-431
Age of Horses, To Ascertain 186
Ages of Animals 192, 196
Air, Atvosphrric 431-43^? Qi'
'^ and Steam, Mixture of. 737
Carbonic Acid Exhaled by Man. 432
Compressors 940
Consumption of by Candle 432
Decrease of Temperature by Al-
titudes. 522
Discharge of. Coefficients of Ef-
flux 674
Expansion of 520
FUxw of, in Pipes, Loss of. . 745, 909
Head of, to Resist Friction in
Long and Rectilineal Pipes. . 925
Pressure of,inRear of a Projectile 648
K
(t
((
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it
(I
((
It
(t
i(
(I
(I
It
II
. Paffa
AiB, Atmobphkrio, Pressure,Velocity,
and Resistance of a Plane Sur-
face,To Compute 648
" Pressure of a Weight of, or other
Gas at 62° and 14. 7 Lbs. Press-
ure, with Constant Volume fvr
a Given Temperature 522
" Proportion of Oxygen and Har-
bonic Acid at Various Loca-
tions 432
" Rarefaction of. 430
" Resistance of different Figures
in, at different Velocities, and
to Falling Bodies. . . .646-647, 949
" Specif^} Heat of, and Other
Oases. 505-506
<* Temperature, for a Given Lati-
twie and Elevation 676
" Volume qfa Weight of, or Per-
manent Gas for any
Pressure, To Compute. . 520
• ' • » and Weight of Vapor in . 68-69
" •« of a Weight of, or Perma-
nent Gfasfor any Pressure
and Temperature. . .521-522
« « of and G<u in a Furnace.. 760
<( (* ^ Enclosed, at o* that may
be Heated by One Sq.
Foot of Iron Surface. . . 925
" " of, or Gas' Discharged
through an Opening and
under a Pressure above
that of External Air. . . 676
" " Pressure, and Density of
at Various Tempera-
tures. 521-522
" *• Required per Hour, for
ecuh Occupant in an
Enclosed Space 525
Ajutage, Cylindrical 549
Alcohol. .' 194
^' Elastic Force and Tempera-
ture, of Vapor of. 707
" Proportionof,inLiquors.igj,904
A\6 And Beer MeoMtres 45
♦♦ Water in 201
ALCffiBRAIO STXBOLS AND FORMULAS, 22-^5
Alimentary Principles 200
Alligation 106
Alloy, Expands in Cooling 952
Alloys and Compositions 634-637
♦» Bronze 637
*' Cf*mpounds,Fusible and Solders 634
" OfSt^el 643
" Soldering Fluid and Fluxes. . . 636
" Solders 636
" Welding Cast Steel 634
Almanac, Kpacts and Dominical Let-
ters, i9oo io iqpi .....,,..,. 73
Vlll
INDEX.
Almahac, Altitude of Sun at New
York
Page
932
Altitudes, Decrease of Temperature by 522
^*"";>°«™ iS5,93S,976
Amalgam 634
Ammeters and Voltmeters. 961-962
Analysis of Organic Substances.. 190
" of Foods and Fruits 201
*' ofJlleat,Fish,andVegetables,etc. 2cx>
Anchors and Kbdgks and Units,
2 o Determine Weight and
Number of U. S.N... 174-175
" Number ' and Weight of
U.S.N. 174
Cables, Chains, etc., for a
Given Tonnage, Am. Ship
M. Ass^n '73~*74
Experiments on and Compar-
ative Resistance to Dragging 175
Proof Strain of. 175
\ Ancient and Scripture Lineal Meas-
ures and Weights 53
Anglss {See also 2Vi^ono»i«<ry). .385-389
and Distances Corresponding
to Opening of a Rule of
Turn Feet 160
Chord of to Plot and Compute. 359
Critical and Visual 669
Stn<M of To Compute 402
To Describe, etc 222
To Plot wit/tout a Protractor^ 359
Ahtm AL and Human Sustenance.. . . . 303
** Food 200-207
Power anil Work. 432-440
Birds and Insects. .438, 440
Camel and Crocodile. . 438
Coursing and Chasing. 440
Day^s Work 434
D09 438
£ror««. 435-437, 439-440,918
Llama and Ox 438
^^ 433-435, 438-439
Mule and A ss 437, 918
on Street Rails ^r Tram-
ways 435
Stage Coaching 440
Animals, Proportion of Food for. . . . 205
•* Agesofexxi!. 192,196
Annealing. 786
Annuities i lo-i 1 1
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it
it
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it
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it
tt
tt
Paift
Arc, To Describe 225, 227-228
Arch, Radius of To Compute 604
' • Depth of To Compute 605
Arches and Abutments 604-605
(See atso Masonry, 604-605.)
** Chords, etc. , Safe Weight of 776
" Minimum Thickness fjf, for
Bridges. 605
" and Walls. 602-603
Area and Population of Divisions
and Countries 188
Arenes 589
Areas of Circles by 8ths. 231-236
" " and Circumferencss of Cir-
cles by loths 243-252
** and Circumferences Greater
than in Table, To Compute 252
by i2tfis 253-257
by Birmingham Wire Gau^e 236
by Logaritlim^ 236,^252
Greater than in Table.. 225, 252
*' In Feet and Inches 235-236
" When Diameter is composed
of an Integer and a Frac-
tion, To Compute 236
OF Segments op a Circle.. 267-269
OF Zones of a Circle 269-271
" To Compute 271
Arithmetical Progression 101-103
Artesian Well ^g ,q8
Asbestos
it
it
tt
tt
it
it
it
ti
it
it
tt
tt
it
tt
tt
Felting, Cement, etc.
Ash, Proportion of in Woods.
913
1032
482
it
it
it
it
Amount of To Compute. .. no
" at Compound
Interest m
Present Worth of.....j lo-i 1 1
Yearly Amount, that will
Liquidate a Debt.. . . i lo-i 1 1
Anti-attrition Metal, BabbitVs 636
Antidotes for Poisons 185, 935
Anvils, Weight of. 918
Apartments, Buildings. Ventilationof 524
Apothecaries' or Fluid Measure. ... 46
Weight 32
Appold'i Pump and Whed. , . , , ,579*580
APPINDIZ 9i9"-955» X024-X029
Asphalt 481, 515, 689-690
" and Pavement 944-945
" Composition ^q^
" Mortars and Concrete 913
Astronomical Day ^q
Atlantic and Pacific Oceans. ....*.".*' 007
" Tides of. ', ,gi
Atmosphere g^^
Avoirdupois Weight ,2
Ax]e,Compound,or Chinese Windlas.^, 627
{See also Wheel and Axle, 626-627.)
B.
Babbitt's Anti-attrition Metal 636
Bacteria in Earth soil g^g
Baking of Meats, Loss by ..'. 206
Balances, Fraudulent ^c
Balks and Battens, Dimensions of. '. . 62
Balloons. Capacity and Diameter of. 218
Balls, Cast Iron and Lead 153
Balls, liCad, Weight and Dimensions of 501
Barbed Wire Fencing q^-
Barker's Mill .' tyi
Barley, Value of Compared to ioo
Lbs. of Hay 203
Barometer {See also Aerostatics), ^^j-^-^i
" Elevations by Readings . 429
♦' Height of, To Compute.. 429
' ' Indications 420-4^0
♦' Weather Glasses. ....... Aq
*' Weather Indications.. . 431
Barrel, Gimwsiow of ,,,..,, 30
IHDBX.
XI
BRjkss Castings, WeigM ofy To CompuU 155
" TuheB, Weight of 142
" WeigfUof. 136
" yv ire. Weight of. 120-121
Braziers' Sheets and Sheathing 155
" " Copper...,, 131
Bread, Wheats Water Lost ^ Drying. 207
Breakwaters 181
Breast-wheel 568-570
" Proportions and Ejfe<^., 569
Brick Walls, ThickMSS of. 603
Brickwork. 595, S97-598> 6oo> 8o»
" Masonry 595
Brick or Compressed Fuel 907
Bricks 598-600
" Stones, etc 800
" Crushing Resistance of. 908
** Volume of and Number in a
Cube Foot of Masonry. , 599-600
Bbidob, Britannia Tubular 178
Highest 907
Iron over Kentucky River. . 178
N. Y. , Erie, and W. Railroad 178
Hew York and Brooklyn . . , 178
overOxus 930
Resistance offrom a Model. 645
Suspension, Elements of,.,, 842
Plates and Rivets. 830
t<
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It
t*
BRID0B8 178, 930, 936
Lengths and Spans of. . . 181-182
(t
t(
Suspension and Length of
^ans oj. 178, 199, 842
Bridles or Stirrups, /or Beams 838
British and Metric Measures, Com-
merciai Equivalenis qf. 906
Broccoli, Value of 207
Bronzb 637
" MaUeabU. 907
" Manganest 832
*' 1ofav,Yacht Shaftmg,Plates,
and Pump^ Piston Rods. , . 929
Browning or Bronzing Liquid 874
Builders* Measure 46
Building Department, Requirements
of ; -907
BuiLDuro Stonbs, Expansum and
Contraction of 184
Buildings, WaUs of English 189
" Protection offrom Lightning 907
Bums and QiXufp,, Application for, , . 196
Bushel, Poumb «n 34
Buttermilk^ Sugar and Water in. ... 201
Buttress and Cotmter/br^ 696^
C.
Cabbage. Fa2ti« oy 207
" Water in 201
Cablkr, Ropes, IJ[awsbrs, Anchors,
AND Chains. 163-175
'•' Chain 169, 930
Diameter of for a Given
Weight of Anchor. 175
Oalvanued Steel, Strength
and Weight of, 163
Hawsers, Hemp and Wire
Mope, Comparison qf. 169
Paf«
Cablbs, Ropes and Hawsers, Circum-
ference of, To Compute. . 171
" " Weights of To Compute. . 173
" Ropes and Hawsers 170
" *» Strain Borne with Sc^e-
ty. To Compute. 171
Calculus 24
Calendar, Rcclesiastical 70
*' Gregorian or N. S 70-71
Calorie 504) 614
M Engine, Ericsson^ s 903
Camel, Load of and Travel 438, 918
Canal, Suez, and Via 277, 183, 912
' ' or Conduit, To Discharge a Given
Volume of Water, and To Compute
FcUl of. 920
Canals, Dimensions, etc z8i
" Flow of WoUer in 550 .
•* Locks and Capacities of, To
Compute 183, 553-555
•* Power of a Horse on 848
*' Traction on 848
" Transportation of. 193
Candles, Lamps, Fluids, andGas. Light
0/, etc 583-584
Cane Sugar or Sa^xharose 207
Cannon Ball, Flight of. 49s
Capillary Tube. 358
Cargoes, To Ascertain Weight of. . 176-177
" Umts for Measurement of. , 176
Carrot Ratio of Flesh-formes. 207
" Vatue of. Compared to 200 Lbs.
of Hay 203
Cascades and Waterfalls 184
Case Hardening 644, 786
Cask Gauging 377
Casks, Buoyancy of. 193
»* Ullage, To Compute Vobim^ of 378
Cabt and Wrought Iron of a Given •
Sectional Area, Weight of,,.,, 136
" Weight of , To ComptUe 155
*t
u
*■
Cast Iron. 131, 637-638^65, 783-786, 798
andLeadBaJlls,Weifihtof.,,, 153
BaHs, Weight and Diameter of, 153
Bar or Rod, Weight of. 131
Bars, Experiments on 780
Characteristics of 637
Columns, Weight Borne Safely
by 768
Malleable Castings 639
of a Given Sectional Area,
Weight of 136, 149
Pipe, To Resist Oxidation 927
Pipes and Tubes, Dimensions
and Weight of, 147
" Weight of. 132-133
Plates, Weight of a Sq. Foot ., 146
Ultimate Strength of 781
Castings, Shrinkage of 218
*' Holes in 873
" Weight of, by Pattern 317
Citcnary. To Delineate 230
Cathedra], St. Peter's 179
Cattle and Horses, Transportation of 193
Dressed Weight of To Com-
puU 35
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INDBX.
Pagt
BoiiiKR, ComumpHon of Fud in a
Furnace^ To Compute. . .725-726
*» Draught 739, 744-74^
** " and Blasts, ('ompar-
aiive Effect of..,. 746
« " Velocity of 746
" lifficiency, NominaZ and IIP
and Economy of. 758, 976
** Kvapora/bive Capacity of TiLbes 742
*• EvaporaMfie Effects of for
Differemt Rates of Combus-
tion and Surface BaHos. . . 743
** Evaporation, Power of.... 757-758
* * Eyes, Stays, Bods, etc 754
** F^t thai may be Consumed
per Sq. Foot of Orate 74a
" Girders for Furnaces 754
** GrcUe, Heating SurJace,Waierf
Fuel, etc., To Ctmpute. .741, 927
*' Heating Surfaces and Rela-
tive Value of. 740
" Mean Strength of Riveted
Joints Compared to Plate.7 51-7 52
•' Minimum Volumes of Fuel
Consumed per Sq. Foot of
Grate. 74o>74x
" Plates and Bolts 749-750
" *' Thickness of for a Given
Pressure and Pit(^,eUi. 753
♦* Power and W of. 526,760
** Proportion and Capacities
of, and Firing 739-740
** Bate of Combustion 760
** Relation of Grate, Heating
Surface, and Fuel. 741
•• Besults of Operation of and
under Varying Proportions
of Grate, Surface, Draught,
Combustion, etc 743, 924
'•• Besults of Operation of vor
rious Designs of Boiler and
Varying Ptoportionsof Area «
of Grate Surface, etc. 744
** Return TubtUar, Elements of
a Test 726
«• Biveting, 755-757»907
** " General Formulas and
Illustrations 757
" Sitfety Valves 746-747
** Saline Saturation in 726
•• Scale, Removal of Incrusta-
tion of. 726
'* Stay Bolts, Diameter and Pitch
of. To Compute 754
" " Tensile Strength of. 753-734
** Steam Heating. 526, 957-958
** Steam Room 748
•• Tubes, Evaporating Capacity
of Various Lengths. . . . 742
•• *' Lap-welded Charcoal, Di-
mensions of. 139
»• Volume of Water per Lb. of
Coal, 7b Compute 725
" Weights ofandwith Water. 759,929
BoiLBM, Area of Grate per Lb. of
CoaL ..o.. 7481
Paffc
BoiLBBS, Blowing off, To Compute
Loss of by. 727
" Bottoms of. To Preserve. 878
" Corrugated Flues 941
** Cylindrical jS/wM*. ...751-752, 913
" Elements of 958
•* Flued, Arched, or Circular
Furnaces, U. 8. Law. . ..754-75^
" SheU Plates, Pressure and
Thickness of, U. S. Zraw. 750751
• •* Horse-Power of. 914,936
" Incnutation or Scale, To Re-
move 726
" Magnesia Covering 0/ .... 918, 921
" Plates, Straps, and Stays. 753
♦* Proportion of Grate and Heat-
ing Surfaces, Result of Ex-
periments 926
** SaUne Saturation in 726
** ** Matter, Prcportionate
Volumes Of. 727
** Smoke Pipes and Chim-
neys 748-749
•* Steam in Foreign Countries . . 935
" Steam Water Tube, Sufficiency
and Results of ^ 947
** Volume of Furnace Gasper Lb. •
of Coal 760
«* " of Water Blowed off to
that Evaporated 727
*♦ Water Tube and Efficiency of,
926, 947
BoiUNO - Points of Various Siib-
stance^. 517
** " at Different Degrees of
Saturation. 815
Bolts, Adhesion of Drifted 949
" and Plates, U. S. Test . . . .749-750
' " Rods of Copper, Weight of,... 148
** Bound and Square, Relative
Driving Resistance of Steel. 970
*' Tenacity and Resistance of,
Round, Square, and Screw. . 970
" Wro't Iron, Experiments on. . 783
*< AND Nuts, Dimensions and
We^/hts of and ofTobin
Bronze 1 56-1 59, 929
I* " English and French Stand-
ard. 158
" " In Wood, Tenacity of. 198
** " of WroH Iron as effected by
the Thread..,. 916
** ^* Square Heads 159
Boring and Turning Metal 197
" Instruments, Tempering of. . 197
« Well 197
Boyden Turbine 574
Brain, Relative Weights of, 192
Brakbs, Locomotive 923
Brass 636
*' qfaGivenSection^Weightof.i26,i4g
" Ornaments, To Clean 877
" Plates, Weight of. 118-119, 146
" *' Thickness of 121
*■*■ Seamless Pipes. 14a
'* *Sbeet, Weightof. 143
INDEX.
IX
Pag*
Babs, WroH Iron^ Square and RoUed,
125-128
• ' Steel, Plat and Rolled 134-135
BSAMS, Bars, OR Gikdxrs, Tratuverie
atrengUi of. &02-81 1, 813-820
{See also Girderg, Beams, etc.)
** Box, Plate and Bars. . 806, 817, 827
** Comparative Strength and De-
flection of Cast Iron 809
" Comparative Value of Bars,
Oirders, or Tubes 824
" Common Centre of Gravity, etc. 8ig
" Cylinder and Cylindrical, Di-
ameter and Weight, To Com-
pute 805
" Cylindrical, or Tubes, Trans-
verse Strength of. 810
• ' Deflection of. 770-782, 840-8 41
•• Depths and Weight, etc., of Steel 134
" Dimensions and Weigh t of Roll-
ed Steely and To CoMpute. 134, 644
'* Rolled Steel Beams and Bulb
Angles 807,808
** Elliptical Sided, To Determine
Side or Curve of. 826
" Factors qf Safety 821,841
" Flanged, Dimensitms and Pro-
portions of WroH Iron 809
" Floor Beatns, Headers, Trim-
mers, etc., To Compute. . .835-^38
" Formulas for TransverseStress,
To Compute 801, 816
" General Deductions 824-825
" Inclined, Formula for ■. 811
•' Lintels, etc 822-823
** Moments and Stress of..., .621-622
** " of Resistance 818
- ** Rectangular, Girders or Tubes. 809
" Scarfs, Resistance of. 841
** Shearing Stress 623
" Solid Cylinder, Diameter of,
To Compute 804-805
** Symmetrical Forms and Sec-
tions, Conditions of. 825-826
" Trussed, Notes on 823-824
** Une(^uaUy Loaded. 810
** Various Figures and Sections,
Dimensions of. . 147, 805, 813, 814
'« Wrought Iron Rolled. 809
BSAMS, Inertia and Resistance, Mo-
ments of and Neutral Avis,
To Compute 818-820
" Circular or Elliptic 815
** Hollow or Annular. 815
" Miscellaneous lUiutrations. . . 826
" of Unsymmetrieal Section, and
Ultimate Strength of. 817, 820-821
♦' OR TuBRS, Elliptical 810, 815
Bearings, for Propeller Shaft 473
Beef, Lean., Water in. 201
Beer and Ale Measure 45
" ♦* Water in aoi
Beet Root, Ratio of Flesh -formers
and Sugar, Analysis of. 907
Beevefl and Beef, Weights of 35
BeR Ringing. 433
Phf*
Bella, Weight of. 180, 936
Belt, Equivalent, and Wire Rope 167
Belting, and Destructive Stress of, 907, 935
" or Hose, To Preserve 877
Belts and Bxltixg,44i-443,877,96o,zoz8
^' Adhesive Compound jor Rubber. Sj J
" Dressing for 878
'* Dynamo and Link Leather 960
" General Notes and Memoranda,
.. . .. «... 442-443.872,877,989
" India Rubber 442
" Width of. To Compute 441-443
Bench Marks 85, 1035
Beton or Concrete 593
Bibliotfieque National 936
BiTdB,Flying 440
'■^ Incubation of 192
** and Insects 196,438
Bissextile or Leap Year 70
Blacking. 877
Blast Furnace 539
" Pipe of a Locomotive . . 907
Blastiso 443-445, 9»3, 916
*' Borxng Holes in Granite. . 444
" Charge of Gunpowder for,
and EffecU of. 444
*' Weight of Explosive MaU-
ruUs in Holes 444
" Gelatine, Composition of... 916
" Paper, Composition of..... 912
'* Tunnels and Shq^, Cost of. 444
" Drilling and Mining 445
Blasts and Draughts, CorfiparaUve
EffecU of. 746
Blower and Exhausting Fan 898
Blowers, Fan 447-448, 898, 1015
" Elements of. To Compute. . . . 448
" Memoranda 448-449
" Power of a Centrifugal Fan. 448
" Pressure of Blast, To Compute ^^j
Blowing Evoinb, Friction of Air in
Long Pipes, etc 925
Enqines 445-440. 898, ioz8
Dimensions of a Driving
Engine, To Compute 446
Elements of To Compute. . . 447
Memoranda 448
Power of, and Power Re-
quired to Dnve 446
'' RooVs Rotary 449
" Volume of Air transmitted. 447
Blowing Off of Steam 726-727
Board and Timber Measure 61
Boards, Volume that can be sawed
from a Round Log 947
Boiler, Steam 526, 739-745
*' and Ship Plates 828
" AbtU Straps and Stays. . . 753-754
' ^ A reas and Ratio of Grate and
• Healing Surface, Volume of
WaterandWeightnfFuel.74t^j^a
^' Coal, Utilization of, in a Ma-
rine 726
Comparative Result of Experi-
ments with a Steam Jet. . . . 746
it
ti
((
(I
Xll
INDEX.
u
«t
t(
(»
1(
tt
Cauliflower, Value of. 207
Cave, Mammoth, of Kentucky 936
Cement Mortar 595
" Cloth, elc, /or Covering Steam
Pipes. 956
ClMKNTS-SIS, 589-590,871-873,907,956,958
(See Limes, Cements, Mortars, and
Concretes, 588-597. )
CsMTKAL Forces 449-454
" " Formulas for Variotu
Elements 450
Cbmtrb or Gravity 605-608
and Vertical Distance be-
tween Centre* of Crush-
ing and TensiUStrength
of a Oirder or Beam, . . 819
Centre of amy Plane Fig-
ure, To Ascertain. .605-606
of Displacement of a
Vessel 653,658
Ckmtrx of Gyration 609-61 1
" '^ Elements and Centre of 610,611
Ckntrss or Oscillation and Pbr-
cuB8iON,and 7V)Compute.6i2-€i4
*' " Centre ofin Bodies of
Various Figures. . , 613
CiNTRiruoAL FAS,ElementsandPOw-
erofa Fan Blower, e^jo. 448
(See Fan Blowers, 447-448. )
Forge of any Body 450
Forces. 499
Formulas, to DetermineVa-
rious Elements 450
Pumps 579. 9". 9*7
Chain, To Set out a Right Angle with. 69
" Cable, Diameter and Length
for a Given Weight of Anchor,
** CABhEa,Breaking Strain, Proof
and Strength of. . 1^, 930
" Anchors, etc. , for a Given
Tonnage, Am. S. Ass^n. 173-174
" Length of for Anchors. ... 175
" Stud - Link, WeiglU and
Strength of. 168, 930
" '* Stowage of 913
Cbaining over an Elevation 69-1034
Chains and Ropes/ot Cran««, Weight
of and Proof. 457
*' " of Equal Strength 165
* < Safe Working Load of. 168
Characters and Symbols. . . . .21-22, 973
Charcoal. 33, 194. 480-481, 485
" Produce of from Woods. . . 481
Cheese, Composition of Different
Countries 205
Chemical Composition of some Com-
pound Combustibles 461
" FormuUis, To Convert 190
Chimney Draught and Chimneys. ^7, g 18
" Velocities of Current of A ir
in One of 100 Feet 749
CHiMNSTp 179-180, 904, 916, 918, 935
' * and Smoke Pipes 748-749
" Height of and Commercial
Wfor a Given Diameter of Flue. . 935
it
ti
i(
Chinese Wall 179, 936
*» Windlass, To Compute 627
" or Indian Ink 907
Chronological Eras and Cycles. ... 26
Chronolooy 70-74
" To Ascertain Years of Coinci-
dence of a Given Day of the Week,
«tc 74
Churches, Opera-Houses, and Thea-
tres, Capacity qf. 180
Circular ARC8,^m i* to 180'' 262
" " LengUis of up to a
Semi-cirde 260-261
" " Length of, To Ascer-
tain 261
" Motion 618
** Measure of an Angle 113-114
Circulating Pumps. . . : 749
Circle, to Ascertain Square that has
the Same Area of. 259
*' Sides of a Square Equal in
Area to 258-259
Circles, Areas of, by Sths, ic>ths, and
i2ths 231-257
" " by Logarithms 236
" " by Wire Gauge. 236
CiBCUMrxRKNCE of a Circle when
Greater than Contained in
Tables,To Compute. 241-^42, 252
" of Birmingham Wire Gauge. 24a
" When Diameter consists of an
Integer and a Fraction. . . . 242
CiRCUMrSRKNOES OF CIRCLES by Bths,
2yi-^42
" " and Area ofbyi oths. 243-252
" " " " by Incites and
1 2t/(5.... 252-257
" " 6y Logarithms 242, 252
'( t( In Feet and Inches.. 241-^42
Cisterns and Wells, Excavation, Lin-
ing^nd Capacity of, 63
Civil Day .' 37, 70
" Year. 70
Cloth Measure 27
Clouds, Classification of. 430
Clover, Value of. Compared to 100
Lbs. of Hay 203
Coal, Anthracite. . . . ^^3, 480, 483, 485-486
" Composition of Average 485
" Fields of U. S., Areas of 191
CoAJA^ Average Composition of and
Fuels, Heat of Combustion
and Evaporative Pouter of . . 486
' ' Bituminous .... 33, 479, 483, 485-486
" " and Natural Goa, Relative
Water Evaporating Powers 913
" " Calcing, Splint or Hard.
Cherry or Soft, and Cannet 479
" " Classijfication, Chemical
Composition and Varieties
of 479
' ' Consumedper Hour, to Heat 100
Feet of Pipe 527.528
" Effective Value of 908
I Coals, Elements of Various American 48a
' " Fields, Areas of U.S. 191
INDEX.
Xlll
Page
Coals, £feu 4^4
" Japan. 909
" LigniU 479> 481
" Measures 33, 46
" Mine 936
" Miscellaneous Experiments 487
" Production and Consumption
of the World. 955
Coast and Bay Service and Scour. . . 908
Cocks, Composition, and Copper
Pipes, Dimensions of. 150
Coffee and Tea^ WcUer in 4. 201
Cohesion. 614
" Modulus of 763-764
ColnSj Br\i\sh Standards 38
" To Convert U. S. to Bi-Uish
Currency, and Contrariwise 39
" Tolerance of. 38
" U. S., Weight and Fineness of. 38
** Value of To Compute 39
«• Foreign Silver and Oold, and
Weighty Fineness^ and Mint
Value of 39, 43
CoKS, Evaporative Povoer of etc 480
Cold, Extremes of in Various Coun-
tries and Snow Line 191-192
** Greatest, Artificial. 908
CoDege, Oxford X79
CoLUSioN OB Impact 580-582
" " Velocities of. sSi-sS2
Color Blindness. 195
Clolors for Drawings. 913
'•* Proportion of for Paints. .... 66
Oolamns, Towers^ Domes, Spires, etc. ,
180, 936
" Crushing and Safe Load of. . . 766
** Lona Solid, Comparative Value
of. 769
•• of Cast Iron 768-769
•* ^*' Weight Borne with Safety,
768-769
CJOMBINATION 1 1 2-1 1 3
tJOMBUBTION 458-466
** Chemical Composition of some
Oompound Combustibles. . . 461
" Composition and Equivalen ts
of Oases Combined in Com-
hustion of Fuel 460
" Consumption of Fuel to Ileal
Air, To Compute 466
*• Evaporative Power of i Lb.
of a Given Combustible. . . 462
•• Heat of. 463
** Beating Powers of Combus-
t£bles,and To Compute. ^61-^62
« Of Fuel, Ratio, etc 463-465
** Products of Decomposition in
Ou Fumade 458-459
*• Bate of in a Fumade 760
*• BelaUve Evaporation of Sev-
eral Combustibles. ... 465
«« *• Volumes of Gases or
Products of per Lb.
of Fuel 465
* Temperature of To Ascer-
tain. 463-463
Paf«
CoicBUsnoiv, Volume of Air Chemical-
ly Consumed in Complete
Combustion of 1 Lb. of Coal 459
" Volumes of Air Required for
Combustion 464-465
" Weight and Specific Ileal of
Products and Temperature
ofCombttstion,etc 462-463
" Weight andVolume of OoMous
Products of 1 Lb. Fuel 460
Compass, Degrees, d: Graduation. 54, 1023
Coif POSITION Cocks, Dim,ensions of... 150
Composition /or Welding SteeL 634
Compositions and Alloys 634-637
(See Alloys and Compositions.)
Composition Sheathing Nails 135
Compound Axle or Chinese Windlass 627
»» Ixtbrest 108-109
Proportion 95-96
Weights of Ingredients... 218
Concbetb 588-597
{See Limes, Cements, Mortars,
and Concretes.)
*>* CoigneVs 914
*' Compositions of 593
" or Beton. 593
Concretes, Cem,ents, eta 800
Conks. 353-354
Condensation, Surface. 967
♦' " Experiments on. 911
Condenser, Results of an Operation
of 967
Conic Sections 379-380
* ♦ Conoid and Ellipse, Elements of 2!^
'* "To Describe, ami Area, Or-
dinate, Absciss(e, Diam-
eters, Circumference, Seg-
ment,and LengUi of Curve,
To Compute 380-382
" General Definitions 379
" Hyperbola, To Describe, and
Abscissce, Diameters, Length
of an Arc, and Area, To Com-
pute 379-380
" Parabola 379-380, 382-383
It ** 2V> Describe Ordinate,
Abscissa, Curve, Area,
and Segment of... 382-383
Constructions and Satural Forma-
tions, Largest 936
Contractility and Elasticity 614
Cooking of Meats 206
Copper, Tensile Strength nf 750, 788
" and Iron Riveted Pipes, Weight
of 148
" Braziers^ and Sheathing 131
•' '' Rods or Bolts, Weight of . 148
' ' Given Sectional A rea. Weight of 1 36
' ' Plates, Thickness of. 121
" " Weight of. 1 18-119
" " " per Sq. Feet. . 146
*' Seamiest Drawn Tubes, Weight
of. 140-142, 144-145
*' Sheathing and liraziers' . . . 131-1 55
" Sheet, Weight of a Sq. Foot. . . 135
XIV
INDEX.
Page
GOPPBR, Weight o/, and To Compute,
136, 155
" Wire, C0rd 123
" ' ' Weight of. 120-121
Copying, Wordn in a Folio. .., 29
Cord, CopjM'r Wire 123
CoKUAUK, Friction andRigidity 0/472-473
Com Measure 198
*' Value, of, Compared to 100 Lbi.
of Hay 203
Corrotrive Effect* of Salt-water on
ateel and Iron 916, 971
CO-BKGANTB AND SECANTS 403-4I4
" " To Compute, etc. 4^14
Cosines and Siner 390-402
" *' To Compute, otc. 401-402
CO-TANQBNTS AND TaNQKNTS 415-426
" " To Compute, etc. 426
Cotton Factories 899
Cou])lo, Comtitution of. 614
Couftliiig or Sleeves of Shafts. 796
('oijr8ing and Chasing 440
Ckank, Railroad 962
" Steam Dredgers, Elements of
and Dredging 890-900
Cranes 179, 433, 455-45/, 962
" Chains and Rnj)esfor. 457
" l>imensionsofPost,To Compute 456
" Machinery and Proportion of. 457
•* Post, Stress and Conditions of. 455
•' Stress on Jib, Stay, or Strut,
o u m. . 455-457
Crank, Turning 433
Cream, Percentage of, in Milk 205
Creosoting, Effects o/. 869
Crwodtle, Power of. 438
Chops, if inera^ Constituents A bsorbed
or Removed from an Acre of Soil. . 189
Cross-ties, Railroad, Duration of. . . 970
Croton Aqueduct 178, 939
Cruslier, Ore and Stone Breaker. . . . 957
Cki'shinq Strength 764-769, 1021
{See Strength of Materials.)
Cube Measurea 30-31
Cube Root, To Extract. 97
" AND Sqcark Root of a Sum-
ber consisting of Integers
and Decimals, To Ascer-
tain 301-302
•* ** of Decimals alone, To As-
certain 302
•• " of any Number over 1600,
To Ascertain 301
•• ** or Square Root of Roots.
Whole Xumbers and of
Integers and Decimals, To
Ascertain 97-98
** ** ofaHigherSumberthanis
Contained in Table 301
CuBBS, Squarks, and Roots 272-302
{See Squares, Cubes, and
Roots. )
" " To Compute and to As-
certain, etc 300-302
Cucumber, Water in 207
'Currency, To Convert U. S. to British 39
Current Wheel 570
" of Rivers 193
Curvature and Refraction of Earth. . 55
Curves, Caustic, or Lines 669
Cut Nails, Tacks, Spikes, etc 154
Cutters, Vacfits, Pilot Boats, Launches 895
Cycle, Dominical or Sunday Letter. . 70
'' Lunar or Oolden Kumber. ... 71
" of the Sun, To Compute 70-71
Ctclss and Chronological Eras. .... 26
Cycloid, To Describe 228
Cyclones, Direction of. 675
Cylinders, Flues, and Turks, HoUow 827
" Solid and Hollow, of Various
Metals. 8or
D.
Dams, Embankmbnts, and Walls {See
Embankments, etc.) 700-703
Day, A stronomical, Marine or Sea. . 37, 70
•' Sidereal, Solar, and Civil 37, 70
Day^s Work 434
Dead Sea and Valley of the Jordan. . 934
Deals and Local Standards of. 62
Decimals 92-94
Deer Park, Copenhagen 179
Deflection [See Strength of Mate-
rials.) 770-781
Delta Metal 384, 913
Departures, Table of. 54
Deptfis, Sea 184
Derrick Guys 163
Desert of Sahara 936
Desiccation 513
Detrusivb or Shearing Strength
(SeeStrength of Materials, 782-783. )
" and Transverse, Comparison of. 782
" Strength of Woods 782
♦* Wood, Surface of Resistance of. 782
Dew Point, and To Ascertain 68
Diamond Weight 32
Diamonds, Weight of. 193
Diet, Daily, of a Man 202, 207
'* " (fan Esquimau 914
Differentiation, Integration,and Cal-
culus. 24-25
Digkstion of Food, Time Required
for 206-207
Discount or Rebate 109
Displacement of a Vessel 653
Distances, Steaming 86
" and Angles, Corresponding to
Opening of a Rule of 2 Feet . 1 60
" between Cities of (7. S. 184
" '♦ " East and West. . 187
" " Principal Ports of World 87
" " " " of U.S.. 88
•' " Various Ports of Eng-
land, Canada^ and U. S. , and
X T. and London 86
" Velocities and Acceleration of
a Body. To Compute 921-922
" Oeogrnphic, and Measures 54
Distemper (Coloring) 593
Distillation 514
" of Fresh Water 955
INDE2.
XV
P»ge
DittiUers and Evaporators, Capaci-
ties of. 950
Dog^ Power of, Courting and Charing,
438, 440
DoMKS and Towers^ Diameter and
Heights of. 179-180, 932
Domestic Remediais 938
DominicaJ. Letters and Epacts 73
" or Sunday Letter 70
D0VBTAIL8, Tenacity of. 948
"DRAiNAORor Landm by Pipes 691
Drains, Diameter and Grade of to
Discharge Rainfall 906
•' and Sewers, Velocity and Orade
of 692
Draught, A rtificial 745-746
" Natural 739-74°, 744
" Steam Jet and Blast, Com-
parative Effects of and Result
of Experiments ufith 746
Drawing and Tracing Paper 29, 964
'* or Pushing 433
Drawings, Colors for 196, 913
" Dimensions of for U. S- Patents 198
Dredger, Steam Hopper, and Ma-
chines 899-900
Drxdgiko, and Cost of 197
'' Machines and Crane 899
Drilling in Rock 445, 940
*' in Metals 477
Drills, Mountings, etc 940
Drowning Persons, TreatvMnt of. . . 187
Dry Mkasurrs 30, 31
DuAUN 503
Ddodbcimals 94
Dtnamitb aaid Celltdose 443-444
Dtmamicb 614, 616-620
" Circular Motion 618
" Decomporition of Force 620
*' Motion on an Inclined Plane 619
" Uniform Motion 617-618
*< Work A ccumulated in Moving
Bodies,and To Compute 619
•* " By Percusrive Force.... 620
Dynamo Leather Belts ^. 960
E.
Earth, Diameters and Density. , . z88, 198
^ and Rock Excavation and
Embankment 192
Area and Population of 188
Boring and Heat of Mines. . . . 955
" Conductivity of Temperature in 914
•* Curvature and Refraction of. 55
" Elements of Figure of 6m
" Influence of the Rotation of on
Moving Bodies 942
" Mrdion of 70
" Weight of per Cube Yard. . . . 468
" Weights of 33
Eabthwork 467-468
" Bulk of Rock, etc., Original
Excavation Assumed at t.. 468
' * Number of Barrow and Horse-
" cart Loads and Shovelling, and
Volume of Transported per Day. . 908
4(
Easter Day. «,. 71
Ecclesiastical Year 70
Egg, Fowls', Composition of 207
Egyptian and Hebrew Measures 53
Elastic Fluids, Specific Gravity of. 215
Elasticity and Strength. 195, 614, 761-763
" Coefficient of 761
" Modulus of and To Compute 762-763
'* Relative, of Materials 780
Elkctric and Gas Light 198
'* Dynamo Engine 954
" Elevators, P^mer Required. . . 959
" Launch 900
" Light, Candle Power of. 908
♦' Fans, Uotohs, Power, Pumps. 959
** WiRBS AND Cables, Tele-
graph, Telephone, and Light Wires
and Cables 960
Electrical Engineeriug, Units in. Re-
sistance and Expressions. gbj-^HB, 1033
Elementary Bodik^, with their Sym-
bols and Equivalents 190
Elephant, Power and Weight of.. ... 918
Elevations by a Barometer 428-429
" and Heights of VaHous
Places above the Sea 183,1035
Ellipse, To Describe and Construct,
etc 226-227, 380
(See Conic Sections, 379-380.)
Elliptic Arcs, Lengths up to a Semi-
ellipse of. 263-266
To Ascertain Length of 266
Embankments, Walls, AND Daub, Ele-
ments of. 700-703
{See also Revetment Walls, 694-
699, and Stability, 69^-703. )
" " Equil'U>rium, StaJ)iUty and
Moment, To Compute 701
" ^^ Form of a Pier, 7^0 Determine "joo
'* " High Masonry Dams 703
** *' Materials, Weight of a Cube
Foot of. 694
'* " Surcharged Revetments 699
" " Various Elements, To Com-
pute and Determine. . . . 702-703
Endless Ropes 167
Enoinxs and Machines, Elements
and Cost of 898-904
*' and Sugar-mills, Weights of. 908
Engravings, To Clean Soiled 875
Ensigns, Pennants, and Flags, U. S . 199
Epacts, and Dominical Letters. ... 73
Equation of Payments 109
Equilibrium, iln^2«« of, at which Va-
rious Substances will Repose 694
" Of Forces 616
Ericsson's Caloric 903
Esquimau, Daily Food of 914
Establishment of the Port for Several
Locations in Europe 85
Ether, Elastic Force of Vapor 707
Evaporation 747-748, 1024
" of Water per Sq. Font 514
" "per Month of Year gt6
It
XVI
INDKX.
t(
t(
t(
u
u
u n
Evaporative Power of Tubes per De-
gree of Heat, etc 513
Evaporators and Distillers, Capaci-
ties of. 955
EVOLDTIOW 96
" To Extract Square and Cube
Roots. 97
any Root 97-98
Excavation and Embankment, Ele-
ments of etc 466-468
" Bulk of Rock, Earthwork,
etc., OriffincU Excavation
Assumed as 1 468
*• Cost of per Cube Yard. . . . 467
** Earth, Rocks, etc., Weight of 468
** •* Eartiiwork by Carts and
Barrow Loads Removed
by a Laborer per J>ay. 467^468
" Labor and Work upon and
Estimate of Cost o/. 466-467
" in Blasting and Hauling
Stone or Earthwork,eic. 468
'• " Load.wr Tripsin Cube Yards
per Cart per Day 466-467
" " of Earth and Rocic 192
Expansion 614
'* and Contraction of Building
Stones, etc 184
Expenditures in Englandfor Various
Purposes and of Articles, compared
with Spirituous Liquors 938
Explosives, Relative Strength of.
Fired under Water. 946
" High, Firing Point and Rela-
tive Strength 953)966
F.
Falling Bodies, Resistance of Air to, 949
Family of .Mechanics, Costof,inPrance,^oS
Fan Blowers 447-448
** Elements of, and Power of 448
" Exhausting and Blower. 898
" Memoranda 448
Farms, Sustaining Production of,., 207
Fascines 690
I'KLLOWBHIP 99
I'Kr.TiXG. Covering. Lagging, etc. . . . 1032
Fence Wire, Strength and Weight of
Single Thread and Cable Laid. . . . 164
fKNciNo, Barbed Steel Wire. 947
y/ff. Value of. 207
Files, Repair of 878
Filter BeAls. 851
Filtering Stone 909
Filters ^r Waterworks. 1 84
Fire Bricks 515, 600
" Clay. 597
Fire- Engine, Steam 004, 909
FIsli, Mfoi, and Vegetables, Analysts oj 200
Flag.'i, Ensigns, and Pennantu, U- S.. 199
Flax Mill 476
Floating Bodies, Velocities of 909
Flexible Paint/or Canvas 915
Flood Wave of Ohio River 912
->R Beams, of Wrought Iron, and
^^mces fi^om Centres 931
P«g«
Floors and Loads, Factor of Safety,
and Weights of and on. 841
(See StrengOi of Materials, 795-841.)
Flour, Consumption and Tests of. 206-207
"■ Mills Qoo
Flues, Tubes, and Cylinders. . . .747, §27
Arclied or Circular FumaA:es. 754
and Fuma/x, Corrugated, and
Formulas for. 909, 941
Fluid and Liquid Measures 30, 46
Fluids, Candles. Lamps, and Qas. ... 584
*♦ Percussion of 579
Fluttbr Wheel 571
Fluxes /or Soldering or H elding. . . . 636
Fly Wheel, Weight and Dimensions
of Rim, To Compute. 451
Flying of Birds 440
Fontaine Turbine 574
Food, Animal 200-207
*' Comparative Values, for Sheep. gj^B
" Daibf. of an Esquimau zo6, 914
" Digestion of, and Time Re-
quired for 200
" Milk, Relative Richness of. 207
" Nutrient Value and Ratio of
100 Parts 203
" " Equivalents of from Ammmt
of Nitrogen in,when Dried 205
* * Proportion of. Appropriated and
Expended by Animals. . . . 305
" " q/' Starch in Sundry Veg-
etables 205
" Ratio of Flesh •fbi'mers from
Tubers 207
" Tliermometric Power and Me-
chanical Energy of, when Ox
idized in the Animal Body. . 205
Foods and Fruits, Analysis of. 201
" " in Reference only to Heat
and Strength 203
" Elements of Various 207
" MiUe, Nutritive Values and Con-
stituents of. 203
' * Nutritious Properties of Differ-
ent Vegetables and Oil-cake
Compared 204
Relative Values of. 202. 204
** ** to make an Equal
Quantity of Flesh in
CcUtle or She.ep 202
" " Comparedwith 100 Lbs.
of Hay. 203
" " as Productive of Force
when Oxidized in the
Body. 204
" Required by a Man 207
Volume of Oxygen to Oxidize
as Consumed in the Body. . . 204
Weight of, to Develop Power in
Human System 204
* * to Fum ish 1 2 20 Gra ins of
Nitrogenous Matter . . . 202
Foot-pound 947
Force, Decomposition of. 6fo
Forces, Composition and Resolution
</" 615
C(
it
((
u
((
INDEX.
XVll
Page
PoRCKS, DiviHon of. 614-616
" Equilibrium of 616
" Inertia of a Revolving liody. 616
*' Perciutsive, Work by 620
F0RKI6N Measitkes and Weights. .48-52
B'ormcUions, Natural^ and Construc-
tions, Largest 936
Formulas and Algebraic Symbols.. 22-22
Fortress Monroe 179
Foundation Piles 198, 909
Fonnd&t'ions, Pressur'', a. Lock/. 781-1040
FSAOTION'8 89-gi
Fraudulent Balances 65
J^reeboard of Vessels 666, 913
Freezing, Effects of to the Resistance
of Stones, etc 184
Frbsh Water, DistUlation'of 955
Friction, Elements of, etc . .469-478, 571
" and Delivery in Hose 922
" and Rigidity of Cordage. 472-473
*' Application of Results 474
" Bearings for Propeller Shafi. 473
" Coefficients of Axle 471
•* ** o/" Masonry on Masonry^
Clay, and Earths 696
** ^^ of Motion and Hepcee^,^, 470
*• " To Determine 471
** Elements of 469-470
** Grain Conveyers 478
" in Launcli ing of Vessels. 478
" Mechanical Effect of..., 471-472
" of A ir in Jjong and Rectilineal
Pipes, Head of in Lbs. 925
" of Bottoms of Vessels 909
•* of Engines and Propellers . 662-663
** of Journals or Oudgeons of a
Water-wheel 571
" of Journals of a Water-WheeL 571
" of Machinery, Results of Ex-
periments upon. . .475-478, loto
" of a Non-condensing Engine.^7B,gi&
" of Pivots and Relative Value
of Angles of. 472
»* of Planed Brass Surfaces. . . . 009
«• of Roads 847
" of Steam- Engines. . , . 475, 478, 918
" of Screw Steamer. 478
** of Tools. 476
" of Water in Pipes 925
" of Winding Engines, Shearing,
FUtx Mill, Tools, Planing,
Molding, Slotting^ Turnings,
Grindstones, etc 476-478
»' of Wall and Earth. 698
♦' Relative Value of Unguents. .. 471
*■ Results of Experiments on Sev-
eral Instruments 474
'• Rolling , 473
" Wood-saunng 477
Frictional Resistsince of a Hail way
Train 916
Frigorific Mixtures. 193, 516
FsriTS, Analysis of. 201
" ProportionofAeid and Sugar 202
Fr«L. Elements of , 479-487
Pag*
FiJJtL,Area of Orate and Consumption
of To Comjnite 513
" A^h, Peat, and Tan ^82
** Asphalt 481
" Average Composition of. Heat,
and Evaporative Power ^>/' 48 5-486
*' Bituminous Coal 479-487
" Brick or Compressed 907
" Charcoal and Coke 480, 483
" Classijication of Coal. 479
'* Comparative Value of, and
Weights. 484
" Elements of 486
" Lignite and Wood. 481-482
** Liquid, Petrol/um, Coal Ga.<i.
and Oils 484
" Miscellaneous *. .483. 485-487
" Produce of Charcoal 481
" Relative Values of. 483
" Uni*s of Heal in... 927
" Valves, Weights, and Evapora-
tive Power of per Balk 483
Furnaces 528-529, 754-755
Fusible Compounds. 634
G.
Galvanized Sheet Iron, Thiclcness
and Weight of. 124, 129
" Charcoal Iron 163
** Iron Wire Riggmg and Guys
and Steel Cables 162-163
" Iron Wire and Diameter of... 123
Galvanizing 786
Gas, Elements of etc 585-587, 676
and Electric Liqht, etc 198. 969
A tniospheric Engine and Engines,
587,912,990
CandUts, Lamps, Fluids, etc 584
Coal, Composition of. 484
Diameter and Length of Pipe to
Transmit Given Volume of.... 586
Flow of in Pipes 586
Ligfu,, intensity of , equal Volumes
from Differnii Burners 585
Mains, THmensions of, etc 587
Natural- and Bituminous Coal,
Relative Evaporating Powers. 913
Pipe Threads 160
" Elements of and Weight. ... 123
Steam and Hot-air Engine.^ 909
Tubing, and Xumber of Burners,
Regulation and Length of. .... 586
Volume of per Lb.ofCoal and Air 760
" of a Weight of Air,or Perma-
nent Gas for any Pressure. 520
of Discharged through a Pipe 587
of per Hour under Pressure . 58 7
" froinaTonof(^oal,Re.nn,etc. 586
Weight of a Cube Foot of. 215
Gases. Expansion of and Volume ofi
Lb. at 32*5 undrr One Atmosphere 520
Permanent, Volumes of 103
•' Temperature of. 587
" *' of Soiid.'fcation 5x6
Gauge, MfrcuriaX , 910
Qauget, Wire.n ««<«««t-<«>*ii8-ia3
(<
XVIU
INDEX.
Qadoinq Cfuk and Varieties of,.,,, 377
*' 0/ Weirs. 922
Oear, Spur 911
Gelatine, Blasting 916
Gkographio Mkasdres and Dis-
tances and Levellings 54-5^
Geographical and Nautical Measures 26
Gbomktkical Progression 103-105
Okometry, Elements of, etc 219-230
** Angles 2C2
*' " and Distances 160
*' Arcs 225-227
** Catenary. 230
** Circles. 224-225
*' Cycloid and Epicycloid. . . . 228-229
" Definitions 219-220
" Ellipse 226-227
*' Gnomon. 219
" Hexagon 223
*' Hyperbola and Spiral 230
" Involute 229
** Length of Elements and Lines,
221-222
" Octagon and Polygon 223
*' Parabola 229-230
'^ Rectilineal Figures. ...... 222-224
*' Scales 221
Oeostatics and Geodynamics. 614
Gestation, Periods of and Number
of Voung of Animals 192
Girder, Dimensions of and Greatest
Load, To Compute 839-840
" Bowstring 812
Girdbrs, Beams, etc., General Deduc-
tions from Experiments. . 824
{See Beams,Bars,or Girders,8o2-S2o. )
•* *' and Beams, Destructive
Weight of, of Various
Figures and Sections .Zo^-ZdS
•* »* CevUre of and Vertical Dis-
tance of Centres of Crush-
ing and Tensile StreM. . . 819
*• " Comparatiw Value of Bars,
Tubes, etc 824
«» " Deflection of 840-841
** " Factors of Safety 821, 841
" " Lintels, Beam>s, etc 822-826
** ' ' Moments of Stress 62 1-622
" " PlcUe 811-812
** " Shearing Stress Deduced by
Graphic Delineation of. , 623
» " Trussed 823
" " Tubular 775
" " " Deflection and Weight qfyj 5
Glass Globes and Cylinders, Resist-
ance to Internal Pressure and Col-
lapse 831
Glass, Window, Thickness, etc 124
Glazing 197
Glues, Mucilage, etc 874
Gold Sheet, Thickness of 119
" Value of from 1501 to 1880. . . . 934
Golden Number or Lunar Cycle, To
Compute 71
Oooseberry^ValMt of. % 907
607BRN0RS. 452
" Revolutions and Elements of , 452
Grade, Reduction of, to Degrees 359
Grain, and Roots, Weights of 34
" Conveyers, Operation of, etc. . 478
'' Standard Weights per Btuhd. 32
Granite Masonry 595
Graphic Operation, ^Udion by 905
Graphite and Pencils 978
Gravel 690
*' or Earth Roads 688
Grates of Boilers, To Compute Areas, 927
Gravitation 487-496
*' Accelerated and Retarded Mo-
tion. 49A
Action of, by a Body Pro-
jected Upward or Down-
ward, To Compute. . .490-491
Average Velocity of a Moving
Body, Uniformly Acceler-
ated or Retarded 495
Formula for Flight of a Can-
non Ball 495-496
Formulas to Determine the
Various Elements of 490
** to Determine Varimu
Elements cf on an
Inclined P^ne.. 49 3-494
** of Retarded Motion... 492
General Formulae for Ac-
celerating and Retarding
Forces 495
Gravity and Motion at an
Inclination 492-493
Miscellaneous lUustrations . . 496
Relation of Time, Space, and
Velocities 488-492
" Retarded Motion 490
Space Fallen y/irem^A. .489, 491
Velocity of a Falling Stream
of Water, To Compute 496
** due to a Given Height
of Fall and Height
due to Given Velocity 488
Gravity, Action of To Cowymte. 488-489
'* at Various Locations at Level
of Sea 487
" Centre of. 605-608
•* OF Bodies 208
*' Promiscuous Examples o/. 489-490
' ' Various Formulae for 488-489
Grease, Anti-friction 877
*♦ from Stone or Marble, To Re-
move 878
Grecian Measures and Weights 53
Gregorian Year and Calendar 70-71
Grindstones and Friction of. 478
Grouting 593-594» 59^
Gudgeons, Diameter of, To Com-
pute 795
Gun Barrels, Length of. 198
" Browning 875
'^ Cotton 443
•' Steel, KruppU 913
GMn-meiaA, Weight of, and of a Given
Sectionai Areci. 136, 149
It
(t
it
tt
it
Ci
ft
t(
tt
ti
tt
tt
l(
INDEX.
XIX
Page
QumotRT, Elements of, etc 497-503
** Charge, Ranges Elevation^ and
Velociiy,and To Compu^gy, 499
" Comparison of Force of a
Charge in Various Arms. . 502
'* Experiments unth Ordnance
and Penetration of Shot
and Shells. 498, 500
" Initiai Velocity and Ranges
of Shot and Shells 498-499
*' Lead BaUSj Weight and Di-
mensions of. 501
" Number of Percussion Caps
corresponding to BOauge 502
" " ofPeUeU in an Oz. of Lead
Shot of all Sizes. 50Z
** Penetration of Lead Balls in
Small Arms 500
" Ranges for Small ,4»-ma 502
" Report of Board of Engineers,
ir.S.A., Fortifcations, etc. 499
♦' Summary of Practice in Eu-
rope with Heavy Guns. ... . 5cx>
" Time of Flight, Rule fw. 497
" Velodtyofa Shot or SheU... 497
** Windage and WaddingSjZ^ss
andEffect of 501
Gunpowder 443, 502
" Charges of, and To Compute. 444
*' HeaJt and Explosive Power
of 503
" Mant^acture of. 503
" Proof of 503
" Properties and Results of, De-
termined by ExperinurUs. . ■ 503
" Proportion of to Sliot 502
" Relative Strength of Different,
for Use under Water 503
Guntbr's Chain 26
Ouys, Derrick, Strength, etc 162-163
Gwynne's Pump, Centrifugal 579, 917
Gyration, and Centres of 609-611
" Centre of, of a Waler-wheel. . . 6n
" General Formulas 611
" Moment of Inertia of aReimlv-
ing Body, To Compute. . . . 609
" RadiuSj To Compute 609
H.
Hammbrs. Steam 179
Hancock Inspirator 90X
Hand-cars and Portable Railroad. . 908
Hawsbbs, Wire, and Hbmp Ropes
Am> Cablks, Comparison of. 169
{See Cables, Ropes, etc , 163-178. )
" and Warps, Length of. 173
" Cables and Ropes 170
" Circumference of. To Ckrmpute 171
" Units for Computing Se^fe
Strain Borne by and for
New Ropes and Hawsers,
170-171
" Weight qf. To Compute. 172
Hat, Relative Value of Foods com-
pared with 100 Lbs. of. 912
** and Straw, Weights^ etc. 298
Pag*
Heat, Elem^ents of, etc 504-529
*' Absolute Temperature 504
" Absorption of, in Generation of
I Lb. Steam at 212° 705
" Altitudes, Decrease of by 522
" Available Expended per IIP 909
" Boiling- Points of Pure Water,
etc., Corresponding to Alti-
tudes of Barometer 518
«* Capacity for. 505, 507
" Communication and Transmis-
sion of, and Relative Power
of I of Various Substances. ... 510
" Ck)NOENSATioN and of Steam in
Cast-iron Pipes 51S-516
•* " ofSteamper Sq. Foot amdper
Degree per Hour 516
" Conducting Powers,Relative, of
Various Substancea and De-
ductions from Results 514-515
" Conduction or Convection of. . 514
" Congelation and Liquefaction 516
" Degrees of Different Scales, To
Reduce, and Contrariwise. . . . 523
" Densities of Some Vapors 521
" Density of Water, To Compute. . 520
** Desiccation 513-514
•* Distillation 514
" Effect upon Various Bodies by. 518
" Evaporation or Vaporization,
Elements of, etc. .512-513
" '• Area of Grate and Fuel
for, To Compute 513
" " of Water per Sq. Foot of
Surface per Hour. . . 514
«* « To Evaporate 1 Lb. of
Water 512
" Evaporative Power of Tubes per
Degree of Heat, etc 513
*' Expansion of Water, Liquids,
Gases, aiM Air. 519-520
" Extremes of and Cold in Fo-
rious Countries 191-192
" Fluids, Expansion of, in Vol-
ume, To Compute 523-524
" Frigorijic Mixtures 193, 516
* ' Heating and Evaporating Water
by Steam in Pipes and Boilers 511
" Height Corresponding to Boil-
ingPoint of Water 519
" Latent, and To Compute. . .508-509
*' " ofFusionofSolids,andqfa
Non- Metallic Substance. 509
" " qf Steam, To Compute 707
" Length of 4-Inch Pipe to Heat
1000 Cube Feet of Air 526
" Linear Expansion or Dilatation
qfa Bar, Prism, or Substance. 519
*' Liquids, Volume of Several at
their Boiling- Point. 518
" Mean Temperatures of Various
Localities. 192
" Mechanical Equivalent (joules). 504
" " '* of, Contained in Steam. 705
" Melting and Boiling Points of
Various Substances 517
" of Mines. «**
XX
INDEX.
Paee
Hkat, ofth£ Sun. Z93
" Proper Temperatures qf Enclosed
Spaces 526
" Radiation of. 509-510, 1027
" Radiating or A bsorbent and Re-
flecting Powers of Substances,
and in Units of. 509-510
" Reduction of, by Surfaces 525
" Rbflbctiom of. 510-512
" Refrigerator, Surfase of. 512
" Relative Capacities of Various
Bodies for 507
" Required to EvaporcUe i Lb. Wa-
Ur Below 212.° fi'om Air at 32°. 512
" SaturcUed Vapors, Pressure of,
under Various Temperatures 518
•^ ^'' Steam, Total of 705>707
'* Sbnsiblk 504, 507
^ Sensible and Latent, Sum of,
and Latent of Vaporization. . 508
' * Snow Line, or Perpetual Con-
gelation 192
* Sfbgifig, To Ascertain, etc. . 505-507
* " for Equal Volumes ofOas
and Air, To ComptUe — 507
' Temperature by AgitcUion 524
•* *^'of a Mixture of Like and
Unlike Substances. 506
« " of Solidification of Several
Gases 516
« " to which a Substance q^ a
Given Length must be Sub-
mitted or Reduced to Give it
a Greater or Less Length or
Volume by Expansion or
Contraction 522-523
** Transmission of, through Glass
of Different Colors 511
•* " Quantities Transmittedfrom
Water to Water through
Metals and other Solid
Bodies i Inch Thick, per
Sq. Foot. 511
" " Units of, To Compute.... sii-512
" Underground. 519
" Unit. 504
" Units of in Fuels 927
" Vegetation, Limit of. 192
" Vi^ume of Water Evaporated in
a Given Time, To Compute. . .513
HBATiHO,iltr, Length of Pipe Required
to Heat A ir in an Enclosed
Space by Water 525
" by Steam, Illustration of. 527
" 6jr Hot-air Furnaces, Stoves, or
or Open Fires 528-529
" by Hot Water 524, 1028
•' by Steam 527, 913, 1027
" Coal Consumed per Hour to
Heat 100 Feet of Pipe. . . .527-528
" Length of Pipe Required to Heat
Air by Steam at 5 Lbs. per
Sq. Inch 527
" Temperature of Enclosed Spaces 526
" Ventilation of Buildings,
Apartments, etc 5*4-525
Pafo
Hkatino, Volume of Air by i Sq. Foot
of Iron Surface 925
" " of Air Heated by Ra-
diators, Fuel, Grate,
and Heating Surfaces 528
* ' Warming Buildings, etc. . . 524-529
Hebrew and Egyptian Measures, etc. 53
Height Corresponding to Boiling-
Points of Water. 519
Heights and Elevations of Various
Places Above the Sea 183
" Measurement of 60
Hkkp and Wire ^ov^,Circumference
of, for Rigging, U. S. N.... 172
** " Circumfei-ence and Breaking
Weight of, U.S.N. 168
" " General Notes 167
" " Hawsers and Cables, Com-
parison of. 169
" " Weight and Strength of. ... . 172
" " Weight of 166
" Rope, Iron and Stekl, Safe
Load and Strength of. 164-165
" " Iron and Steel, Relative Di-
m,ensions of. 172
" " Safe Strain Borne by. Units
for Computing. 170-171
" Shrouds and Wire 173
" Tarred, Destructive and Break-
ing Strength of. 171
" RoPRS {See Ropes, Hawsers, and
Cables) 166-173
Hewing and Sawing Timber, Loss in. 62
High Water, Time of. To ComptUe. .74-75
Hills or Plants in Area of an Acre. . 193
Historical Events and Notat}le Facts. 939
Hitches, Knots, etc ^972
Hoggin '690
Hoisting Engines, Details 0/, etc 901
Honey, Analysis of. 207
Hoop Iron, Weight of. 129,131
Hopper Dredgers, Steam 899-900
Horizon, Dip of. 60
Horizontal Wheels 572
H0R8B 435-437
" Cart, Volume of Earth Trans-
ported 908
" Transportation 918
" Power 4^1, 733-734, 1028
" " British Admiralty Rule. 734
" ' ♦ Cost of, by Steam 950-95 1
" " Notes on 758
" " of Boilers 914
" " OnaCanal 848
" " Transmission of 188
" Team, Tractive Power of. 436
Horses, Age of. z86
" Labor of, etc 435-437
' ' Performance of. 439-440
" and Cattle, TransportcUion
of 192
" Weightof 35
Horseshoe Nails, Length of. 153
Horseshoes and Spikes 152
Hose, Delivery and Friction in 922
*' ToPieserve 877
INDEX.
XXI ,
Pag*
Hot-air Furnaces or Stovei. 538
** Gas, and Steam Engines, Rel-
ative Cost of. 909
Human and Animal Sustenance 203
Hydraulic Radius or Mean Depth. . 552
" Cement 958
" *' or Turkish Plaster. 591
" Faint 872
" BjM^Elements andEfficien-
cyof- 561,9171923
" " per Cent, of Volume of
Water Expended^ To
Compute. 917
Htdraulics, Elements of etc. . . . 529-557
" CanaX Locks., and Times of
Filling and Discharg-
ing, To Com.p\Ue..sS3-SSS
" " MisceU.IUustrations.ss(>-SS7
" Circular Bent or Angular.,
Circular or Cylindrical
Curved Pipes, Valve €kUe.s
or Slide Valves, Throttle,
Clack or Trap Valve Cock,
or Imperfect Contraction,
Coefficients ofResistancc^^ssij
" Circular Openings or Sluices^
Coefficients of 536
" Circular Sluices, etc 537
" Circular, Triangular, Trape-
zoidal, Prismaiic Wedges,
Sluices, Slits, etc 538
" Curvatures. Radii of 544
" Curves and Bends 545
" Cylindrical Ajutage 549
* * Deductions from Experiments
on Discltarge, from Reser-
voirs,Conduits,or Pipes. 529-531
** Depth of Flow over a SHI tiuU
will Discharge a Given Vol-
ume, To Compute 534
** Discharge from a Notch in
Side of a Vessel. 541
" "from Conduits or Pipes,
and Friction of. . . 530-531
<• ^^from Irregular - shaped
Vessels, as a Pond,
Lake, etc. , Time, FlmOy
Fall, Velocity, and VoU
ume Discharged. 542
•* "from Vessels not Receiv-
ing any Supply ... 538-539
" "from Vessels of Commu-
nication 541
*• " ofinPipesfor any Length
and Head, etc.. and
Elements of, To Com-
pute 547-548
«* " of under Variable Press-
ures, and Time, RisCy
Fall, and Volume. . . . 540
** "of ufhen Form and Di-
mensions of Vessel of
JBfffiux are not Known 539
•* "or tiffiux for Various
Openings and Aper-
tures, and Relative Ve-
locity under like Headt 53a
((
(I
Pag*
Hydraulics, Distance of a Jet of
Water, Projected from an
Opening in Side of a Vessel,
549-550
Fall of a Canal or Conduit
to Conduct and Discharge
a Given Quantity of Water
per Second, To Compute. . . 920
Flow and Velocity in Rivers,
Canals, and Streams,
and To Compute Ele-
ments of 55«>-553
and Velocities at which
Materials will Move 916
in Lined C/iannels. . . 551-552
of Water in Beds, Fall
and Velocity of, as in
Rivers, Canals, Streams,
etc., and Coefficients of
Friction of. 542-543
Flowing Water, Head of. To
Compute 552
Forms of Transverse Sections
of Canals, etc 543
Friction in Pipes and Sewers,
and Head Xecessary to Over-
come, To Compute 543-544
" of Liquids through Pipes. 531
' ' of Water in Beds, as Rivers,
etc., Coefficients of . . 543
Head and Discharge in Pipes
of Great Length 920
"from Surface of Supply to
Centre of Discharge. . . . 544
Height of a Jet in a Conduit
Pipe, To Compute 919
Inspirator, Hancock 901
Jets d^Eau, and Formulas
for 550
Journals or Gudgeons, Fric-
tion of. 571
Miner^s and Water Inch 557
Obstruction in Rivers 551
Pipe, Inclination of, and Ele-
ments of Long, To Com-
pute 548
Fi^smalic Vessels 539-540
" Fall of in a Given Time,
To Compute.. 540
557
W under Different Heads.
Rectangular Notches or Ver-
tical Apertures or Slits. 534
" Openings or Sluices or
Horizontal Slits, and
Discharge, To Compute. 535
" Weir, Volume of Diverge,
To Compute 532-534
Relative Velocity of Efflux,
through Different Apertures
and under Like Heads. . . . 532
Reservoirs or Cisterns, Time
of Filling and Emptying,
To Compute 541
Short Tubes, Mouthpieces, and
Cylindrical Prolongations
or Ajutages,and Coefficients
for Discharge of. 536-537
XXll
INDEX.
Page
"BrDRAViAca^Sluice Weirs or Sluices. 535
" '" Impeded or Unim-
peded Discharge of. ... 535-536
" Submerged or Drovmed Ori-
fices and Weirs. 553
" Variable Motion of Water in
Beds of Rivers or Streams. 543
«*. Velocity in Profile of a
Navigable River, To Com-
pute 551
" Velocity ofWater or of Fluids,
Coefficients ofDisdiarge.sz^S'i^
** Vena Contra^ta 529
" Vertical Height of a Stream
Prcfjecied from Pipe of a
Fire- Engine, To Compute. . 549
" Volume of Water Flowing in
a River, To Compute. . 543
** Weirs, Oatiging of. 922
" " or Kotches. 539
flVORODTNAMICS AND HYDROSTATICS,
Elements of 610.558-580, 614
" " Appold's Wheel 580
" " Barker's MUl 577
" *' Boyden Turbine 574
♦* " Breast Wheel, Proportion,
Effect, and Power of. 569-570
" " Centrijugal I\imps....5j()-$So
" " Current Wheel 570
" " FltUter or Saw-mill Wheel 571
" '* Fontaine Turbine 574
it i( Horizontal Wheels.... 572-577
«* ** Hydraulic Ram, Elements
of and Operation.. . . 561-562
»* ** Hydrostatic Press 561, 901
«♦ « '^ Thickness of Metal... s6i
** * ♦< Motors, Effective Pow-
er of Water 563
** " Impact and Reaction Wheel. syS
" " Impulse and Resistance of
Fluids. 577-578
** •* Inward - Flow Turbines,
Description of. 575
** " Jonval Turbine, Elements
and.ResuUs 575
•' " Low-Pre.>sure Turbines. . . 575
** " Memoranda on Water-
Wheels 571-572
** " Overshot Wheel, Elements,
Power of, etc. . 563-566
•* " " Power and Effect of ,
To Compute. . . 565-566
** " Percussion of Fluids 579
« " IHpes.ElementsandWeight
of etc.. To Compute. 560-561
•* " PonceleVs Wheel, Propor-
tion and Power of. 567-568
** " ^^ Turbine,Eleme7Us of . 574
" " Power of a FaXl of Water,
To Compute 562
" " Pressure and Ce^itre of ^l%-e,Co
u ii i^ofa Fluid upon Bottom
of Vessel, Vertical, In-
clined, Curved, or any
Surface, and also on
aSluice 559-5^
Pai^
Htdrodtnahios and Htdrostatios,
" " Pressure of a Column of
a Fluid per Sq. Inch . . . 560
" " Rankine Wheel 580
" " Ratio of Effect to Power
of Several' Turbines. . . . 577
" " Reaction Wheel 576
" " Swain Turbine 575-576
" " TangentiaJ, Wheel 576
" •' Tremoni Turbine 576
" " Turbineand Water Wheels,
Comparison Between. . . 579
{( (( Turbines,Elements,Poioer,
and Results... 5y2-5yy
" " " High Pressure and
Downward Flow. 574
" " Undershot W heel, PouKr of 566
" " Victor Turbine 576
" " Water Power 562
" «* " FaUof...... 563
" " , " Motors, Ratio of Ef-
fective Power 563
ti It it Pressure Engine 579
" " " Wheels, Dimensions
of Arms, etc 571
«* " " Wheels, Divisions of,
etc. 563
" " WhiUlaw's Wheel. .... 576-^77
Hydrometers 67
'' Strength of or Volume of a Spirit,
To Compute, etc. 67
Hydrostatic Rail or Slip Railway,
Power Required to Draw a Vessel. 910
Hydrostatic Press 561, 901
Hygrometer 68
'' Dew-point, and to Ascertain
Volume of Vapor in Atmos-
phere 68
»* Existing Dryness, To Ascertain 68
" Vapor, Weight of, in Air 69
" Volume of Vapor in Air..... 68
Hyperbola. To Describe. 230
Hypkhbolic LoGARiTiiMa . . .331-334, 712
I.
ICB, Strength of, etc 195, 012, 939, 943
" and Snow, Weight and Volume. . . 849
" Boais and Speed of. 896, 909
" Making and Refrigeration. g^2} 9^5-9^^
" Manufacture of. 943, 967
Impact and Reaction Wheel 576
" OR Collision 580-582
•' Velocities of Inelastic Bodies
after. To Compute 581-582
Impenetrability 195
Inclined Plank, Motion on 619
*' Elements of. To Coinpute.ti$-6y>
Incubation of Birds, Periods of. 192
India- Rubber, To Cut 877
Indicator, To Compute Pressure by. . 724
I X Kr.Ti A , Moment of a Revolving Body. 609
*' Moment of Approximately to
A sextain 659
" " of a Solid Beam 819
^^ of a Revolving Body, To Com-
pute 6f$
INDEX.
XXlll
Ii^lector, Steam 736
*^ Stu of, To Compute 736
" Volume of WcUer required per
IIP per Hour, To Compute 736
" " of Feed Water required per
IH* per Hour 736
Ink, Chinese or India. 907
" Stains, To Remove 035
Inks, Indelible, etc 875
Insects and Birds 196
Inspirator, Hancock's 901
Integration. 24-25
biTKRBST, Simple and Compound. 107-109
IirvKNTiONS, Origin and Period of
Great 937
Involute, To Describe 329
Ikyolutiok. 96
Iron, Elements of, etc. 637-640
(See Wrought-iron, 130-136, 6391-640,
765, 768, 773, 780, 785-786. )
" and Steel, Corrosion of. 908
" Bolts in Wood, Tenacity of. 198
** Bridges, and Iron Pipe Bridge .. 1 78
" Mold, To Remove. 871
OR Stbbl, Corrosive Effects of
SaU Water on 916
" Pig, Ton of. Requirement of Air. 445
*• Preservation fy. 955
" Rust, To Remove 935
Iron Steamer, First BuilJ 915
Irregular Body, Volume of, To Compute 870
IRRIOATIOM, Cost qf^ per Acre 952
J.
Jarrah Wood 913
Jets d^Eau 550
Jewish Measures 53
Jonval Turbine 575
Jordan, Vafley of, and Dead Sea. . . . 934
Joules' Equivalent 504
Julian Calendar. 70
Jumping, Leaping, etc, by Men 439
K.
Kbdoks and Anchors, Weight and
Number of. Units to Determine .... 174
Kerosene Lamps, etc 872
Khorassar, or Turkish Mortar 592
Knot 27
Knotty Hitches, etc 9go
Labor, Man and Horxe. 433-434, 436, 468
Lacqwsrs. 875
Laitance 593
Lake, Highest Elevation of. 968
Lakes, Areas of in Europe, Asia, and
African, and DeiMis and Heights of
OreaJt Northern of U. S. 181-182
lAinps, Candles, Fluids, and Ctas. . . 584
lAnd Measure 29
Larrying 598
Latbs, Dimensions, etc.. 603
LATirrDE, Length of etc 198
** and Longitude of Principal
Looationt and Otoerva<ioiu.76-8o
Pag«
Latititdb N. reached by Explorers. . . 931
Launching Vessels, Friction of 47
Lb AD, Sheet, Caxt or MiUed 640
'' Balls, Weight and Dimensions
of' 50X
" Encased Tin Pipe, Weight of. . . 151
" Given Sectional Area, Weight
of. 136
" Measure 32
" Pipe, Resistance, Thickness,
Weight, and Bursting Press-
ure of. To Compute 831
" Pipes and Tin-lined, Weight of,
per Foot and Thickness. . 137, 150
" Plates, Weight of per Sq. Foot. 146
*• " Thickness of. 121
" Sheet,Weight qf. 151
" Shot, Number of Pellets in an
Ounce 501
" AND Cast iron Balls, Weight
and Volume of 153
*' Weight of. To Compute 155
Leap or Bissextile Year 70
Leaping, Jumping, etc 439-440
Leaves, Value of, etc 207, 481
Lee-w.'iy or Drift of a Vessel 910
Legal Tenders 38
Lknsesand Mirrors, £r2em«nteo/:67o-67 1
I^evel, Apparent, of Objects at or upon
Surface of Land or Sea 56
Levelling, Geographic 55-57. >o35
" by Boiling - Point of Water,
Table of, etc '"SS-S?
** Height o/Above or Below Level
qf Sea, To Compute 55
Lbvbr, Elements of To Compute. . 624-626
Lifting by Men 439
Light, Elements o/) etc 583-587
" Sun's Rays. 195
" Candles,Lamps, Fluids, and Gas 584
^' Consumption and Comparative
Intensity of of Candles 583
'* Decomposition of. 583
" Electric, Candle Poxoer of. 908
" Crox and Electric 198
" *' Consumption, Volume, and
Flow of 585-587
" Intensity of wUh Equal Volumes
of Gax from Different Burners 585
" Ta)SS of by Use of Glaxs Globes. 584
*' Penetralion of, in Water 915
" Refraetum, Mean Indices of.... 584
" Relative Intensity, Consumption,
Illumination, and Cost of Va-
riotu Modes of Illumination . . 584
•' Services for Lamps 587
** Standard of. 910
" Volume of Gas from a Ton of
Coal, Resin, etc 586
Lighting Power in Streets, To Deter-
mine Coefficients of 969
Lightning, Classifcation of 430
* ' Protection of Buildings . 907 -9^,0
Lignite 479, 481
Lime, Hydraulic ofTeil 589
XIV
IKDKX
Paffo
GoppBR, Weight of^ and To Compute,
136, 155
" Wire, 0»rd 123
tt » I \yeight of. 120-121
Copying, Words in a Folio. .., 29
Cord, Ctjtpper Wire 123
CoKDAGK, Friction andRigidity 0/472-473
Corn Measure 198
" Value of, Compared to 100 Lbs.
o/Hay 203
Corrosive Effects of Salt-water on
Steel and Iron 916, 971
CO-SKGANTS AND SECANTS 403-4I4
" ** To Compute, etc. 414
Cosines and Sines 390-402
" " To Compute, otc.401-402
Co-tangents and Tangents 415-426
"■ " To Compute, etc. 426
Cotton Factories 899
Couple, Constitution of. 614
Coupling or Sleeves of Shafts. 796
Coursing and Chasing 440
Ckang, Railroad. 962
*' Steam Dredgers, Elements of
and Dredging 890-900
Cranes 179, 433, 455-457» 962
" Chains and Ropes for. 457
" DimensionsofPost,To Compute 456
** Machinery and Proportion of. 457
" Post, Stress and Conditions of. 455
" Stress on Jib, Stay, or Strut,
455-457
Crank, Turning 433
Cream, Perceida^e of, in Milk 205
Creosoting, Effects of. 8'
Crocodile, Power of.
CR0PS,ifinera2 Constituents A bsorbed
or Removed from an Acre of Soil. . 189
Cross-ties, Railroad, Duration of. . . 970
Croton Aqueduct 178, 939
Crusher, Ore and Stone Breaker.. . . 957
Crushing Strength 764-769, 1021
(iSVe Strength of Materials.)
Cube Measurea 30-31
Cube Root, To Extract 97
♦♦ AND Square Root of a Sum-
ber consisting of Integers
and Decimals, To Ascer-
tain 301-302
•* ** of Decimals alone, To As-
certain 302
•• ** of any Number over 1600,
To Ascertain 301
•* ** or Square Root of Roots,
Whole Xumbers and of
Integers and Decimals, To
Ascertain 97-98
** ** of a Higher Number than is
Contained in Table 301
"GuBBfi, Squares, and Roots 272-302
(iS'e« Squares, Cubes, arid
Roots. )
(i «« To Compute and to As-
certain, etc 300-302
Cucumber, Water in 207
Currency, To Convert U. S. to British 39
»^j
^
Current Wheel 570
" of Rivers 193
Curvature and Refraction of Earth. . 55
Curves, Caustic, or Lines 669
Cut Nails, Tacks, Spikes, etc 154
Cutters, Yaclits, Pilot Boats, Launches 895
Cycle, Dominical or Sunday Letter. . 70
'' Lunar or Golden Number. ... 71
" of the Sun, To Compute 70-71
Cycles and Chronological Eras 26
Cycloid, To Describe 228
Cyclones, Directum of. 675
Cyunders, Flues, and Tubes, Hollow 827
" Solid and /Hollow, of Various
Metals. 8oy
D.
Dams, Embankments, and Walls {See
EmlHznkments, etc.) 700-703
Day, Astronomical, Marine or Sea. .37, 70
'' Sutereal, Solar, and Civil 37, 70
Day^s Work 434
Dead Sea and Valley of the Jordan. . 934
Deals and Local Standards of. 62
Decimals 92-94
Deer Park, Copenhagen 179
Deflection {^e Strength of Mate-
rials.) 770-781
Delta Metal 384, 913
Departures, Table of. 54
Depths, Sea 184
Derrick Guys 163
Desert of Sahara 936
Desiccation 513
Detrusive or Shearing Strength
{SeeStrengtfi of Materials, 782-783. )
" and Transverse, Comparison of. 782
" Strength of Woods 782
" Wood, Surface of Resistance of. 782
Dew Point, and To Ascertain 68
Diamond Weight 32
Diamonds, Weight of. 193
Diet, Daily, of a Man 202, 207
" " (^an Esquimau 914
Differentiation, Integration,and Cal-
culus .24-25
Digestion of Food, Time Required
for 206-207
Discount or Rebate 109
Displacement of a Vessel 653
Distances, Steaming 86
" and Angles, Corresponding to
Opening of a Rule of 2 Feet . 1 60
" between Cities of U. 8. 184
" " " East and West.. 187
" " Principal Ports of World 87
" " " " of U.S.. 88
" " Various Ports of Eng-
land, Canada, and U. S. , and
N. Y. and Ijondon 86
" Velocities and Acceleration of
a Body. To Compute 921-922
" Geographic, and Measures 54
Distemper (Coloring) 593
Distillation 514
" of Fresti Water 955
INDE^t.
XV
P»ge
DisHHers and EvaporalorSf Capaci-
ties of. 950
Dog, Power of, Coursing and Charing,
438, 440
Domes and Towers^ Diameter and
Heights of. 179-180, 932
Domestic RemediaLs 938
Dominical Letters and Epacts 73
*' or Sunday Letter 70
Dovetails, Tenacity of 948
^DrainaOe or Lands by Pipes 691
Drains, Diameter and Grade of to
Discharge JiainfaU 906
»* and Sewers, Velocity and Grade
of 692
Draught, A rtifidal 745-746
" Natural 739-74o> 744
" Steam Jet and Blast, Com-
parative Effects of and Result
of Experiments roith 746
Drawing and Tracing Paper 29, 964
'* ■ or Pushing: 433
Drawings, Colors for 196, 913
" Dimenrions offer U.S. Patents 198
Dredger, Steam Uopper, and Ma-
chines 899-<)oo
Dredging, and Cost of 197
' ' Machines and Crane 899
Drilling in Rock 445» 94°
" inMetals 477
Drills, Mountings, etc 940
Drowning Persons, Treatment of. . . 187
Dry Measures 3o> 3^
DuAUN 503
Duodecimals 94
Dynamite and Celluhse 443-444
Dynamics 614, 616-620
" drcidar Motion 618
Decomposition of Force 620
Motion on an Inclined Plane 619
Uniform Motion 617-618
Work A ccumulated in Moving
Bodies,andTo Compute 619
" By Pereusrive Force. .. . 620
Dynamo LeaJther Belts 960
E.
((
it
it
it
i(
t<
Earth, Diameters and Density. , . 188, 198
and Rock Excavation and
Embankment , 192
Area and Population of. 188
Boring and Heai of Mines. . . . 955
Cmductivity ofTemperature in 914
Curvature and Refraction of. 55
Elements of Figure of 6*
Influence of the Rotation of on
Moving Bodies 94*
Motion of 70
Weight of per Cube Yard 468
Weightsof 33
IC
if
u
tt
if
ti
t(
l(
Easter Day. , ...<.. 71
Eccleriastical Tear 70
Egg, Fowls\ Composition of. 207
Egyptian and Hebrew Measures 53
Elastic Fluids, Specific Gravity of. 215
Elasticity and Strength. 195, 614, 761-763
" Coefficient of 761
" Modulus of and To Compute 762-763
" Relative, of Materials 780 ,
Electric and Gas Light 198
" Dynamo Engine 954
Elevators, Powei- Required ... 959
Launch 900
Light, Candle Power of. 908
Fans, Motors, Power, Pumps. 959
Wires and Cables, Tele-
graph, Telephone, and Light Wires
and Cables ; 9^0
Electrical Engineering, Units in, Re-
sistance and Expressions. gfij-g&S, 1033
Elementary Bodies, with their Sym-
bols and Equivalents 190
Elephant, Power and Weight of. 918
Elevations by a Barometer 428-429
" and Heights of Various
Places above the Sea 183,103s
Ellipse, To Deserve and Construct,
etc 226-227, 380
{See Conic Sections, 379-380.)
Elliptic Arcs, Lengths up to a Semi-
»» *' ellipse of. 263-266
« ' » To Ascertain Length of 266
Embankments, Walls, and D/MB,Ele-
menis of. 700-703
[See also Revetment Walls, 694-
699, and Stability, 693-703.)
*' Equilibrium, Stability and
Moment, To Compute 701
" Form of a Pier, To Determine 700
'* High Masonry Dams 703
" Materials, Weight of a Cube
Foot of. • 694
" Surcharged Revetments 699
" Various Elements, To Com-
pute and Determine. . . .702-703
Endless Ropes 167
Engines and Machines, Elements
and Cost of. 898-904
*' and Sugar-mills, Weights of. 908
Engravings, To Clean Soiled 875
Ensigns, Pennants, and Flags, U.S . 199
Epacts, and Dominical Letters 73
Equation op Payments 109
Equilibrium, ilngrk* of at which Va-
Hous Substances will Repose 694
" Of Forces 616
Ericsson's Caloric 9^3
Esquimau, Daily Food of 914
tt
ti
tt
tt
Rarthwork ■ .' * .'.'!.'*.!" ^467-468 Establishment of the Port for Several
^Bulk 'of 'hock, etc. , Original Locations in Europe.. ._._ 85
tt
Excavation Assuvied at t.. 468
yumber of Barrow and Horse-
cart Loads and Shovelling, and
Volume of, Transported per Day. . 908
707
Ether, Elastic Force of Vapor
Evaporation 747-748, 1024
" of Water per Sq. Foot 514
tt t» per Month of Year 916
XXVI
INDEX.
Page
MiNSURATioN OF ARIA8, eta, Any
Figure of,ReiH)lution. . . .358, 376
" Arc and Chord, etc. ,ofa Circle,
343-345
" Area Bounded by a Curve. . . . 342
" " of any Plane Figure... 359
" Capillary Tube 358
" C<uk Gfauging and UUaging,
377-378
" Chord of an Angle, To Compute 359
" Circle 342
* ' " Sector and Segment of. 346-347
" Circular Zone 349
" Cones 353-354i 363, 365
" Cubes and Parallelopipedon. . 360
*' Cycloid. 352
" Cylinder. 350, 363
" " Sections 357
" Ellipsoid, Paraboloid, or Hy-
perboloid of Revolution,
, _ 357.375-376
" Onomon * 335
*' Helix [Screw) 354-355
*' Irregular Bodies 377
" " Figures 341.358
" ^wfc 353, 370
" Lune 352
" Parallelograms 335
" Plot Angles without a Pro-
tractor 359
" Polygons. 338-341
" Polyhedrons. 362
" Prismoids 351, 361
" Prisma 350, 360
" Pyramids 354, 365-366
" Reduction of Ascending or De-
scending Line to Horizontal
Measurement. 359
** Regular Bodies. . .3^^.0-341, 362-364
" Rings, Circular and Cylin-
drical 353, 368
*' Side of Greatest Square in a
Circle 343
" Sj^iere 347-348, 367-368
" " Segment of 347
*' Spherical Sector. 370
♦« " Triangle 387
" " Zone 368
" Spheroids or Ellipsoids,
348-349. 368-369
" Spindles 355, 370-374
•• Spirals 355
" To Plot Angles without a Pro-
traction 359
" Trapezium 337-33°
" Trapezoid / 338
" Triangles 335-337
(see Trigonometry y 385-389. )
" Ungulas 35 » -352. 366-367
*' Usefid Factors 343
" Volume of an Irregular Body . 870
** Wedge 350, 361-362
" Zone, Spherical and Circular,
348-349
Mercurial Gauge. 910
Meta-Centre of Hull of a Vessel. .659, 919
Metal Products of U.S 910
Tufet
Metals, AUoys and Compositions . 634-637
" Adulteraiion in^ To Discover. .. 210
" and Elements of. 637-644
" Comparative Quality of Various 821
" Lustre, Degrees of. 194
" Values of some Precious 938
" Various Weight of. 155
" Weight of. To Compute 131
" " by Pattern, To Compute 217
'■^ of a Given Sectional Area,
Weight of. 149
MKTKR,and Ko/ue of. 27, 934
Meters, Water. 942
Metric Measures 27-33» 1013
" Fa/Hors 923
Milk, Nutritive Values and Constit-
uejits of. 202
" Percentage of Cream 205
" and Relative Richness of, of Sev-
eral Animals 207
" To Detect Starch in 196
Mineral Constituents Absorbed from
an Acre of Soil 189
" Waters, Analysis of, etc. . 850-851
Minerals, Relative Hardness of. 193
Miner's Inch 557
Mines, Temperature of 918, 955
Mining, for Blasting 445
' ' Engines and Boilers 901
" Flat Ropes 165
Mirage 195, 669
Mirrors and Lenses 670
Miscellaneous Elements. 188-198
" Mixtures, Cemints, Glue, Inks,
Lacquers, Soldering, Varnish^
Staining, etc 871-879
" Operations and Illustrations,
879-885, 935
Mississippi River, Silt in 910
Models, Strength of. 644-645
" Bridge, Resistance of, from.. . . 645
" Dimensions of a Beam, etc,which
a Structure can Bear. .... 644-645
Molasses, Analysis of. 207
" Sugar and Water in 201
Molding and Planing 476
Molecules, Velocity, Weight, and Vol-
ume of. 194
Moment, Quantity of, etc 614
Momentum 195
Monoliths 179
Month, Mean Lunar 70
Months, Numbers of. 74
Moon's Agk, To Compute 74-75
Mortar 590-592. 95i, 97'
" Sugar in 951
Mortars, Limes, Cements, and Con-
cretes 588-597
Motion, Accelerated, Retarded^ and
Uniform Variable. . .494-495, 6x7
" of Bodies in Fluids 645-648
" Pressure, Velocity, Time, etc.. . . 648
" Resi. stances of Areas and Dif
ferent Figures in- Wafer or Air.. . 646
Motive Power 910
»' of the World 935
INDEX.
XXVll
Hoton, Experiments on, for Street
Bailtoays. 915
MountaiDS, Volcanoes, and Passes,
Heig'its of. 182-183
Mowing 433
'^ Machine 910
Mule, Load and Work of. 437, 918
Mural Efflorescence 593
N.
Nails, Length and Number of. . .153-154
*' cmd Spikes, Retentiveness of.... 159
" Composition Sheathing. '135
" Tacks, Spikes, etc 154
National Roaid, 178
Natural Formations and Construc-
tions, Largest 936
'* Powers 198
Nautical Mkasurr 3°
Natal Architecturi! 649-667
*' Angles of Course and Sails. . . 665
" BfMom, Side, and Immersed
Surface of Hull 653
•* Centre of Gravity of Bottom
Plating of a Vessel 638
«« " " Common of Hull, Ar-
mament, Engines,
etc, To Compute. . 656
** " *^ Depth of or Buoyancy
below Meia- Centre,
andApproximately.6s6-^57
" " ofEffoH, and Lateral Re-
sistance, Relative Posi-
tions of. 659
" Centres of Lateral Resistance
and Effort, To Compute. 658-659
" Dead Flat 2a
** Displacement, and its Centre
of Gravity, To Compute,
65^-655
** " Approxim>cUely, and Coeffi-
cients of. To Compute. . . 655
" *' Coefficients of 655,657
** " Curve of. To Delineate, and
Coefficients of. 657
" Elements of a Vessel, To Com-
pute 653-660
** " of Capacity and Speed of
Several Types of Steam-
ers of R.N 660
" " ofaSteamFrigcUe,Weight,
Moments of, etc 656
** Eameriments upon Forms of
Vessels, Results of. 649
" Freeboard 666, 913
'* Heel and Steady Heel, An-
gles of. To Compute. . . .664-665
*' Lee-way, Angle, Ardency and
Slaaeness 666
" Length of Vessel 909
" Masts and Spars 667
" *' Location of. 664
** Memoranda of Weights and
Elements 667
•« Meta-Centre of Hull of a Ves-
idjTo Compute. 6591919
Pug*
Naval Arohitbcturb, MetaUing,
Loss of Weight per Sq. Foot
of on a Vessel's Bottom. . . . 667
'* Moment of Inertia Approx-
imately, To Ascertain. . . 659-660
<* Pitch of Screw Propeller and
Slip of Side Wheels 662
" Plating Iron HuUs 667
" Proportion of Power Utilized
in a Steam Vessel and Fric-
tion of Engines 663
'* Resistance of Bottoms of Hulls. 662
• ' " of Air to a Vessel 666
" " to Wet Surface of IIulL 653
" Rudder Head 667
" Sailing Power and Careening
Power of a Vessel 665
" " Ratio of Effective Area
of Sails, etc., and of
VesseVs Speed to Wind. 663
" Sails, Propulsion and Area of 663
" " Area and Trimming of. 664-665
" Screw Propeller, Experiments
upon Resistance of at High
Velocities, etc 666
" Slip of Propeller and Side-
wheels 666
*' Speeds, Relative of Forms of
Vessels 649
" Stability, Elements of etc. 649-653
" " and SpeM of Models of
different Sections, etc. . 650
*• ♦* Elements of Power Re-
quired to Careen a Body
or Vessel, To Compute,
652-653
" " Power Required in a
Steam -vessel, Capacity
of another being given. 66z
" ** Resutts of E^qperiments
upon Bodies 649-650
" " Statical, Statical Surf a/ic
and Dynamical Surface
Stability, To Compute,
651-652
" " Measure of, of HuU of a
Vessel, ToDetermine.6so-^52
** Steam Vessels, Approximate
Rule for Speed and H* of
To Compute 662-663
" Trim, Change of. 655-656
" Weight, Curve of 657
" TTtnd, EJfective Impulse of. . . 665
" *' Course and Apparent
Course of. 666
Needle, Magnetic, Variation of. 1035
" Decennial Variation of. 58
" Variation of it in U. S and
Canada 59
Needles, First Introduced 72
Neutral Axis of a Beam, To Compute 820
New and Old Style 37» 70
Niagara, FaMs, Height of, etc. 198, 930, 952
" Volume of Water and Power. . 952
Nitro-Glycerine 443
Non-conductibility of Materials. .911, 914
" -condensing Ef^ne, Friction qf. 9x8
r
XXVlll
INDEX.
Page
Non-conductors o/TfempcrcrfMr*, and
Comparative Efficiency of. 933
NOTATIOX 25
Number of Direction 71
Numbers, Properties and Powers of. 98
" 4th and sth Powers of. 303, 304
*' 4<A, 5</i, and 6th Power ^ and 4<A
and 5</i Root of, To Compute. 304
Nutritive Equivalents, Compu^ed/rom
am/)unt of Nitrogen in Human Milk
at I..... 205
O.
Oats and Oat Straw, Value of com-
pared to icx> Lbs. of Hay 203
Obelisks, Egypt and Nexo York 179
Objective Glasses, Diameter of the
Principal 942
Observatories, LcUitude and Longi-
tude 80
Ocean, Depth of 912
Oceans and Seas, Depths and Areas. 182
" Atlantic and Pacific. 937
Oflfal, Weight of, in a Beef and Sheep. 35
Oil, Yield of from Seeds 189, 939
" Cake and Vegetables, Nutritious
Properties of Compared 204
" -Engine Launch 893
" Proportions of, in Air-dry Seeds. 203
" To Remove from Leather 878
»' Watchmakers^ 878
Oils, Petroleum, Schist, and Pine-
wood 484
Old and New Style 37> 70
Omnibus, Weight, etc , 844
Onion, Proportion of Gluten, and Ra-
tio of Flesh-formers 207
Opera-Glasses, Telescopes, etc. 671
'* -Houses 180, 936, 954
Operations, Miscellaneous 879-885
Optics, Elements, etc 668-671
" Critical and Visual Angles, Mi-
racle and Caustic Curves or
Lines. 4 669
" Elements of Mirrors and Lenses,
To Compute 670
** Focus and Focal Distance, etc.. 668
" Refraction, Index of and Indices
of. To Compute 668-669
" Dimensions or Volume of an
Image, To Compute 668
Ordnance, Energy of. 910
Ore and Stone Breaker .003, 951
Organic Substances, Analysis of by
Weight 190
Orthography op Technical Words
AND Terms 1042-1052
OSOILLATION AND PERCUSSION, Centres
of 612-614
" *' Centre of in Bodies of Va-
rious Figures 613
" " Centres of To Compute.(n2-6i4
*♦ " " of Experimentally,
To Ascertain. 613
OvxBaHOT Whskl. 563
Oxford College. 179
Oxidation of Cast-iron Pipe^ To Retiit 927
P.
Poci/Ec and Atlantic Oceans. ... . 937
Paint, Flexible for Canvas. 915
" for Window-Glass. 879
" Hydraulic 872
" To Clean and Remove 878
F8L\nt\ng, and Proportion of Colors for 66
" Iron Rods 956
Paper^ Blasting. 912
'^ Drawing, Tracing, Profile,
Photo-printing, Cloths, etc 29, 964
Parabola, To Describe 229
Park, Deer 179
Parsnips, RaMo of Flesh-formers 207
Paste, Durable. 878
" Preservation of. 878
Passages of Steamboats 896
" Ice-boals 896
" Steamer and Sailing Vessels. 897
Passes, Mountains, and Volcanoes. . . 182
Pastils for Fumigaling 879
Pavement, AsphaU. 690, 944-945
* ' Block Stone. . . . .689-690, 944-945
" Comparative Merits of 945
" Granite 690
'' Macadam and Brick 944
" Miscellaneous Notes 690
*' Neufchatel. '. ... 945
" Rubble Stone 689
" Telfn-d. 688
" Voids in a Cube Yara of Stone 690
" Wood 689,690,944
Pavements, Roads, and Streets. . .686-690
Payments, Equation of. 109
Peat 482
Pendulum Measure 27
Pendulums, Elements of, etc 452-454
" Centre of Gravity of. 453-454
" Conical, Number of Revolu-
tions of To Compute 454
" Lengths and Number of Vi^a-
tions of To Compute. . . .453, 454
" Vibrations, Number and Time
cf To Compute 454
Pennants, Ensigns, and Flags, U. S. . 199
Percussion and Oscillation, Centres
of {see Oscillation and Per-
cussion) 612-614
' ' Caps, Number of, Correspond-
ing to Birmingham Gattge. 502
Performances o/'ilf«n,£r(M»e5,etc.438-44o
Perimeter of a Figure. 912
Permutations. 100
Perpetuities 112
Petroleum, Elastic Force of Vapor. . 707
" Evaporative Effects of. 910
Physical and Mechanical Elements,
Construction and Results. 907
Pile Driving 433, 671-673. 902, 97a
" Coefficient of Resistance of Earth 972
" Pneumatic 673, 972
" Resistance of Formations. ..... 673
INDEX.
XXIX
FtLi DRimro, Ringing J^ngine 972
" 8afs Load, To Compute 672
" Sheet Piling 672
" Sinking. 673
" Weight of Ram 972
PiLSS, Foundation 198, 781, 909
" Extreme Load a Pile wiU Bear 912
" Retaining WalU of Iron 196
PiuHo OF Shot and Shklls 65
PiUar at Delphi 179
Pillart or Columtu 936
PiDit, First in Use 915
Pipes, Dimensions, etc 747
" and Tubes, Weight of. 147-148
" Copper, Dimensions of. 150
** Gas, Thickness of 123
« " Threads 160
" Lead, and Tin-lined^ Weight of. . 137
" " Encased 151
»* «' Weight of. 150
" Metal, and Weight of. 147
** of Cast-iron to Resist Oxidation. 927
" or Cylinders of Cast-iron. . . .132-133
" Riveted Iron and Copper, Weight
of One Foot in Length 148
" Steam, Gas, and Water. 138
" Tin,Weightof. 151
" Thickness of. To Compute 560
»' Water, Standard of Cast-iron. . . 147
Pisfi. 593
Pivots, Friction of. 472
Planing, Cast-iron and Molding. .476-477
Plask Road& 688
Plants or Hills, in an Acre. 193
" Weather Foretelling. 185
Plaster, Turkish 591
Plastirino, MeoMiring of 197
** Volumes Required, Materials
and Labor for 100 Sq. Yards of. . . 604
Platb Binding, Iron 476
Platks and Bolts, U. S. Test of, etc 749-753
** of Metals, by Gauge. 121
" Thickness of. To Compute. 751
" Wrought-iron Shell 750
Platino Iron Hulls 667
Ploughing. 433
PnUMATICa.— AXROMBTBT 673-676
{See also Aerometry.)
PoiNTiNO in Masonry. 598
^o\uovB,Antidotes and Tr€atment.iZs, 935
PoLBS AND Spars 62
Poncblst's Whkbl 567-568
** Turbine 574
PoruuknON, and Area of Divisions
and Countries. x88
*' Comparative Density of, and
Number of Persons in a
House in jHfferent Cities. . 910
" of Principal Cities. 187
Position. 98-99
JPbtxuoUoML, Elements of 589
Potato, Anii • Scorbutic Power and
Ratio of Flesh-formers 206-207
PowDBB, Smokeless. 952
" Forcite 966
** GtmfPropartionMqftoShot,, 50a
(I
((
Pafc
Power and Work, Metric 36
'* Motive. 910
" " of the World 935
'* Movers and Transmitters of.... 797
^^ of a Quantity, Value of. 359
" Ordinary Distribution of, in a
Propeller Steamer. 911
' ' Required to Draw a Vessel up an
Inclined Plane. 910
'* Thermometric and Mechanical
Energy of 10 Grains of Va-
rious Substances when Oxi-
dised in Human Body 205
" To Stutain a Vehicle on an In-
clined Road, To Compute.. 845-846
" Transmission, Elements of..... 176
Powkrs, Natural 19S
4th, sth, and 6th of a Number. 304
of first 9 Numbers 98
of^th and $th Numbers. . . .303-304
" of 6th Number 304
Precious Metals, Values of some... 938
Pressures and Weights, Metric 36, 923
Probability and Illustrations. . . 11 4-1 17
'^ Odds between Results and
Chances, etc 117
Progression 101-105
Proof of Spirituous Liquors. 218
Propeller Steamers, Ordinary Distri-
bution of Power in on
PROPELLBR& 730-731, 886-891
Properties of Numbers 98
Proportion 94-96
Pullet 433
" Compound, etc 633-634.
" Power, Weight it will Raise, and
No.of Cords to Sustain Lower Block 632
Pump, Working.ofa 433
" Appold^s and Gwynne^s 570
" Steam,Elements and Capacities of 738
" Water, First in Use 932
Pumping 433
" Engines. . . 738, 902-903, 954, 963
Pumps, Direct Acting. 738
" Centrifugal. . sjg-sSo, 911, 917, 1031
" Circulating 749
'* Water and Vacuum. 932, 963
'* Worthington 738
Pushing or Drawing 433
Pyramids, Statues, etc. 178, 936
Quartermasters, Service Train of. , . 198
R.
Race-Courses, English, Length of... 930
Rack and Pinion, Power of, 628
Radius Vector 449
Rail, Weight of. To Compute. 679
Railroad Crane 962
" Horse, First in Use 915
" Portable, and Hand-Cars... . . 908
Signals and Significations.... 954
tt
** Speed 969
" ^'' in England 93O} 951
II
Tleit, Duration of. 968
INDBX.
XXXI
PfefpB
BoAM,ete.f Difeftef 686
' Bnglith 689
" Gf iters, Fillers j and Wheelers^
Proportion of, in Different
Soils 688
'♦ Grade of. 686
" GranUe and Hoggin, 690
" Gravel or Earth 688
** Macadamited 687-690
** Metalling and Metalled. 690
" MisceUane&us Note* 6
" Plank. 6
" Besistance to Traction of a Stage
Coach 848
** .RuJbbU Stone 689
^ Ruts and Stone-breaJcing. 687
** Sweeping, Sprinkling, Watering^
Rolling, Washing, aaid Fas-
cines 690
" Telford. 688
" Voids in a Cube Yard of Stone. 690
Roadway, Central Width of, in CiU. 917
" Constmction of. 687
Roadways, Relative Resistance to
Traction 945
Rock, Weight and Volume of. 467
" AND EARTu,&BcavalionandEm'
bankment cf 192
8
it
ii
ti
.... 101
. ... 46I
** and Bulk of, and Earthvoork
** Drilling. ,...* 940
" Weight of per Cube Yard 468
VUoVitkVi Calendar 71
" Indiction 71
" Long Measures 53
Roof Plates, Corrugated, Weight of. . . 131
Roops of RuHdings 179, 952
" Stress on. To Compute 952
'* Weights and Pressure on. . .952, loao
" Wooden 189
Root, of an Even Power Greater than
Contained in Table 98
*• To Extract any whatever 97
Roots and Grains, Weights of. 34
** Sqdarbs, axd Curbs 272-302
" 4<A, 5M, and 6thy To Compute. 302-304
Ropbb, Working Load 782
" akd Cablis, Measure of. 26
*' and Chains of Equal Strength, . 165
*^ aian Inclination, Stresi of...,, 166
*' Cablbs, Ghaivs, etc 161-175
" Circumference of Wire, etc., To
Compute. 169
" " of, and of Hawser or Cable
for a Given Strain of.,,, 171
** Endless. 167
** Hawsers and Cables 170-172
" *' Circumference of, To CompiUe 171
" *' Weight of To Compute 172
" Hemp and Wire, General Notes. 167
" ''and Wire, WeightamdStrengthofiyz
»» ''Iron, and Steel 164
** Iron, Wire, and U. S. Hemp .... 168
" Mining, Flat 165, 1029
** Qf Corresponding Strength to
ffemp^and of Hemp to Circum-
StTtmot qf Wire Regfs 169
Pagf
ROPBS, Stren, Ttmtion, and D^eHon
of. To Compute 166
" Tarred Hemp and Wire,Circum-
ftrence of 169
'* •' " and Destructive and
Breakii g Strength of. 171
" Transmission of Poioer 167
" Units for Computing Safu Strain
for New, Hawsers, and Cables,
U. o. N. I7^'i7'
VViRK, Elements of etc 161-173
'' and Equivalent Belt 167
*' Experiments on, U. S. N. . . 166
" and Hemp, Circun\ference
of for Standing Rigging 172
" Iron,Steel,andHemp.Rel-
ative Dim£nsions of, *
^^ €/» o. iV •..••..«•.• 172
" White, DurabUity of 17c
Rotation of the Earth, Influence of. . 942
Rowing 433
Rubble-Stone Pavement 689
RCLB OF TURBB 95
Running, Men and Horses 438-440
Rye Straw, Relative Value of com-
partd with zoo Lbs. of Hay 203
Saccharose, or Cane Sugar 207
Safbty Valve, Adjustable Pop 986
« " ,.T^^^^ 746,931,933
Sago, Value of 207
Saiuno, Area of Sails and Vessel's
■ Speed 663
" Vessels, Iron 894-895
Sails, Propulsion and Area of 663
" To Preserve 870
** Trimming of 665
Saline Saturation. 726
' ' Proportional Volumes of Matter
in Sea-water 727
Salt Water, Corrosive Effects of on
Steel or Iron 916
Sand, Composition, etc 599
Sandstones 193
Saw- Mill, Elements of. 904, 913
Sawing and Hewing Timber, Loss in, 62
"• Stone and Wood 196,904
Saws, Circular 197, 477, 911-912
" Vertical and Band 477
Scale or Sediment, Removal of Incrus-
tation in Boilers 726
Scalbs, To Divide a Line, etc. 221
'* Weighing without 66
Scarfii Resistance of 841
Screw, Length, Power, Weighty Pitch,
etc. , To Compute. 630-631
*• Bolts, /\7W«r 0/ 968
*' Cutting. '. 477
" Compound .631
" Differential 63a
•♦ Propeller, Pitch and Speed of . . 669
" " Friction of Enginet .... 663
" *' Elements of, To Compute gij
Scripture and Ancient Measures. ... 53
Sea Depths. • »•»».. • sJU
xxxu
INDEX.
Seas and Oeeam, Vep&it and Area
of. 182
8£CANTS AND COSECANTS 403-414
" ^^ Degrees^ Minutes, etc. J of,
To ComptUe 414
Sbeds, Number of, in a Bushel, and
per S^. Foot per Acre.. . . . 193, 938
** Proporium of Oil in Air-dry . 203, 939
" Yield of Oil in Several. 189
Segments of a Cirolk, Area of. .267, 269
" '* Areaof, To Compu^«. 268-269
Sewage, Volume o/f etc 692, 1029
Sewers, CUtssification of. 691, 692
** Drains. Diameter and Grade of
0 to Discharge RainfaU 906
** Drainage of Lands by Pipes. . . 691
" Material per Lineal Foot of Egg-
shaped, Dimensions of 692
" Minimum Velocity and Grade
of 691
** Sewer Pipes. 692
** Surface, which will Discharge
a Volume of an Inch and also
of Two Inches per Hour, etc. . 692
Shaft, Bearings for Propeller 473
Shafting ybr Lathes and Mills. .948, loio
Shafts 778, 793, 794-797. 9*4
{See also Torsion, 790-797.)
*' and Gudgeons. 790
" Deflection of Shajts 778-779
" Diameter and Journal of, Stress
Uniformly along its Length,
To Compute 571
•• JoumaZs or Bearings of, etc . . . 796
** Loaded Transversely and Jour-
nals of 914
Shbabino or Detrusive Strength. 7S2-JS2
" Experiments in Cast-iron,Steel,
Treenails, and Wood 783
•* Power to Punch Iron, BrasSf or
Copper, To Compute 782
** JUsuUs of Experiments on, vrith
a Punch 782
" •* " with Parallel Cutters,
WroH-iron Bolts, Riveted Joints,
and Various Materials 783
Sheathing and Brasiers* Sheets 155
** " Copper..., 131
" Nails, FWpWo/. 135
StiMi-lrou,BlackandG€UvaniMed. 124, 129
** Weightof. 129
Sheet Pilwg « 672
Shells and Shot, PUing of. 65
Shingles 63
Shoemaker's Measure. 27
Shot and Shells, Piling of. 65
" Chilled and Drop 906
** No.^ Diameter, and Numbers of, 906
" Number ofPdlets in anOt. 501
Shrinkage of Castinga ai8
Shrouds, Hemp and Wire 173
Side Lights, Visibility of a VesseVs, 918
" WjiXJtiA,AreaofBladesand8lip 66a
** Friction of Engines. 66a
Sidereal Day and TeaT' .•• 37
Pag*
Sides of Squares, Equal in Area to a
Circle 258-259
Signals, Night, U.S. N. 199
'^ Railroad, and Significations.. 954
Silt, in Mississippi River 910
Silver Sheet, Thickness of. 119
Simple Interest 107
Simpson's Rule, ^rra,' TV) Compute.. 342
" " Volume of an Irregular Body 870
Sines and Cosines 390-402
" Number of Degrees, Min-
utes, etc. , of, To Compute 402
Siphon, Steam xoio
Sixth Power of a Number 304
Skating Performancf^ ' 439
Slackwater, Canal, etc., Traction on. 848
Slaking of Lime 594
Slate, Surface of, and Number of
Squares, To Compute 64
Slati ng, Weight of One Sq. Foot 64
Slates and Slating. 64
*' Dimensions of. 64
*• English 64
" Weight per 1000 and Number
Required to Cover a Square 64
SuDB Valves, Elements, etc 731-733
Smelting of Iron Ore 445
Slotting 477
Smoke Pipes and Chimneys 748-749
Snow, Pressure of, on Roofs 952
*' and Ice 849
" Flakes. 195
" Line or of Perpetual Congela-
tion 193
" Melted, Volume of. 195
Solar Day and Year. 37, 70
Solders 634-636
Soldering 875
Sound, Velocity of 195
" Distances by Velocity of. To Com-
pute 428
'* Velocity of in Several Solids. . . 428
Soundings, to Reduce to Low Waler. 60
Spars and Poles 63
Spbgifio Gravity and Weight. . .208-215
" Given Weight of a Body, To
Compute. 215
" of a Body Soluble in Water. 209
" ofa Body Heavier or Lighter
than Waler. 209
" of Elastic Fluids 215
*-^ of a Fluid 209
" of Liquids 214-215
" of Miscellaneous Substances 314
" of Solids 210-214
" or Density of Steam 706
" Proportions of Ttoo Ingre-
dients in a Compound, or
to Discover Adtdteralion. 316
" Weight of Ingredients, that
of Compound being Given,
To Compute 2x8
** Weights and Volumes of Va-
rious Substances in Ordi-
nwryUse,
,916^17
INDEX.
XXXlll
Pige
Speed of VeueU. ^71, zoto
Spikxs, Ship, Boat, and Railroad. 1 52, 1 54
'* and Horseshoes 152
" and NaUs, JRetentiveness of..., 159
** Chmeral Remarks 159-160
" Ship and Railway -970
" WroH-iron Nails and Tacks. . . 154
Spiral, 2b Describe 230
Spires, Towers^ Columns, etc 180, 932
Spirits, Strength of To Compute 67
Spirituous Liquors, Dilution per Centj 191
*' Dilution. To Reduce 191
" Proof of. 2i8
. " Proportion of Alcohol .... 191
Springs, Deflection of 779
Spur Gear 911
Squarb and Cube RooT) Square or
Cube, and when Number is
an Odd Number 300-302
" of Decimals alone,To A scertain^yxi
** ^a Higher Number than con-
tained in TaJfle, To Compute 301
•* of a Number consisting ^In-
tegers and Decimals^ To As-
certain 30X-302
•* Root, To Extract 97
" " or CuBK Roots of Roots,
WhoU Numbers, and of
Integers and Decimals,
To AKertain. 97-98
" To Ascertain One that has
Same Area <u a given Cirde 259
Squares, Cubes, and Square and
Cube Roots 272-302
" Sides of Equal in Area to a
Circle. 258-259
&r ABILITY, Elements, etc 693-703
** Angles of Equilibrium of..,., 694
'* DynanUccU and Statical 651
" Earthwork^ Centre of Pressure
of. 696
" Equilibrium and Stability, To
Compute. 701
** Mem4>randa 695-696
** Moment of, and To Compute. 693, 701
*^ of a Body on a HorizonUU
PUme or on an Indination,
694-695
** of a Fixed or Floating Body. , 693
" qfHuU of a Vessel or Floating
Body, To Determine 650
** of Varying Models. 649
** Statical and Dynamical, To
Compute. 651
'* Weight of a Body, To Sustain a
Oiven Thrust 693-694
Staging, Coach 440
Staining. Wood and Ivory. 876
Stains, To Remove. 878
Starcb, Proportion of in Vegetables. 205
Stars, Velocity of. 198
Statics 615-616
** Composition and' Resolution of
ForcM t 615
Pag*
Statics, Equilibrium of Force 616
** Inertia of a Revolving Body. , . 616
" Spherical TriangUs 387
" Specific Heal 505-507
" '* of Air and Oases.. 505
Statues, Pyramids, etc. 178
Stay Bolts, Diameter^ Pitch, etc. ... 754
Steam, Elements of, etc.. 640-643, 704-727
'* and Air, Mixture of 737
*' Blowing of, Saluraled Water, Loss
of Heat by, To Compute. . 726-727
" '* Volume Blown off to that
Evaporated, To Compute. , . 727
" Clearance, Effect of 715
" Coal, Utilization of in a Boiler. 726
** Combined Ratio of Expansion
and Final Pressure in 2cl Cyl-
inder, To Attain 723
'' Condensation of, in Cast-iron
Pipes 515-516
" Condensed per Sq. Foot and per
Degree per Hour 516
** " of Expanded, per W of Ef-
fect per Hour 716
" Consumption of Fuel in a Fur-
, nace. To Compute 725-726
" Cutting Off, Paint of, for a Given
Ratio of Expansion. .. . jtx
" " Point of, to Attain Limit
of Expansion 7x0
*' Cylinder, Net Volume of for
Given Weight of Steam, etc.,
To Compute 715
*♦ Density or Specific Gravity of. . 706
" Effect for One Stroke and a
Given Combined Ratio of
Expansion 723-724
" ** Relative,of Equal Volumes. 7x4
" " Totalof I Lb. of Expanded,
714-7x5
" Effective Work in One Stroke as
Given by an Indicator Dia-
gram, To Compute : . . 714
" Efficiency, Actual, Conclusions on 724
" Elastic Force and Temperature
of Vapors of Alcohol, Ether,
Sulpkuret of Carbon, Petro-
leum, and Turpentine 707
" Expanded, Consumption of per
H» of Effect per Hour 716
" Expansion, Points of 712
" " Effectsof. 713
" '' Point 0/ Cutting off, Actual
Ratio of. Pressure at any Point
of. Mean or Average, and Final
Effective or Initial, To Com^
pute 710-7x1
" Expansive Force of 704
" Feed Water, Gain in at High
Temperature, To Compute 7x9
" " Gain in,andIniti€U Pressure,
when Acting Expansively,
compared with Non-mpan-
sion or Full Stroke 725
" Gaseous, Total Heat, and Veloc-
ity of To Compute 710
XXXIV
INBKX.
Page
Strax Hfoting Co. of N. T. 904
•' " and 5oi7er». 013,957, 1025, 1027
** IncruitoHon qf Scale or Sedi-
ment, To Remove 726
♦* Indicator, Mean Pressure by, To
Compute. 724
" -Injector 736
'* Mean Pressure by Hyperbolic
Logarithms, To Compute.. 7 12-7 13
" Mechanical Equivalent of....;. 705
" Notes of. 936, 954
*' Pipes and Casing. 5x5
** Pipes, Gas^ etc., Dim^juions and
Weights of. 138
•* Plant, Cost of Coal and Labor in
Operation of 1000 "EP. 951
" Pressure in Ins. of Mercury., . . . 706
•« " Weight of a Cube Foot,
Pressure and Temperor
ture. To Compute 705
^ •• in a Cylinder, at any Point
of Expansion, or at End
of Stroke, To Compute,, 711
" Pressures, Mean, Final, Effective,
Initial, or Total Average, To
Compute 7x1
" Saline Matter, Proportion of in
Sea-toater 727
*« ** Saturation in Boilers 726
•• Specific Gravity of. 704, 706
** " of compared voith Air, 2b
Compute 706
** Surface Condensation, Experi-
ments on 911
•* VelocUyof 704. 913*936
** ** of into a Vacuum 704
'•' Volume of Cylinder for a Given
Effect, etc 715
•• "of Water at any Given
Temperature Mixed wUh
it, to Raise or Reduce
Mixture to any Required
Temperature, To Compute 707
•• " of Water Evap&rated per
Lb. of Coal, To Com-
pwfe 725
•• ■ ** of Water in a Given Volume
of and of a Cube Foot of
To Compute 706
•• " of to Raise a Given Volume
of Water to any Given
Temperature. 706-707
•* Weight and Effect of, for other
IVessures than 100 Lbs., Multi-
pliers for 719
•* Wiredrawing of 7x8
■^ Vaehls, Relative Velocities of
from Elem,entt of their Con-
struction, To Compute 928
** GoMrouND Expansion, Elements
of, etc 7>3, 720-724
^ " Combined Ratio of and Final
Pressure in ad Cylinder,
To Attain 723
* '* ComparativeEfectinReoeiv-
er oimI Woolf Engine 724
Stsax, CoMPOtnm Expansion, Wocl
for One Stroke and a Q*ven
Ratio of in ist Cylinder,
To Compute 721-729
" " Effect for One Stroke and a
Given Combined Actual
Ratio of, To Compute. .783-724
** " Eafpansian in a Comp^iund
Engine, To Compute. . 721
a {( ** From Receiver 720-724
" " Final Pressure 720-72X
•* " Wodf Engine, Ratio of Ex-
pansion, etc 722
*' Satubatbd, Total Heat and Ab-
sorption of. *.. 705
•* ** Energy and Efficiency of.
To Compute. 716-717
<• *'- Latent and Total Heat of
To Compute 707
** " Pressure, Tentperature, Vol-
ume..and Density..., -/oS-jog
** " Properties of, of Maximum
Density 717
" " Vapors, Pressure of 518
" SUPBRHEATBD, Energy and Effi-
ciency of To Compute. 717-718
" ** Expansion, Effects with
Equal Volumes and One Lb. of
100 Lbs. Pressure 718-719
Stkaxboat, Iron, First buiU. 915
Steamboats, Ritbb, and Engines. 892-893
** Passages of 896
" Wood and River Side-wheels. 892,919
** " Ferry, Passenger, Team,and
Tow-Boats 890
" " Passenger and Deck Freight. 893
" " Stem-u^ieels 892-893
Stbam-bnoinb, Elements of etc. .727-760
*' and Sugar-Mill, Weights of... 908
** -Boilers in Foreign Countries. 935
" and Boilers, Cost of Operating
per Day of 10 Hours 904
" Circulating Pumps,Volumeof
etc. , 749
" Condenser or Reservoir, Tem-
perature of Water in, To
Compute 707
" Dimentions of Cylinder, Grate,
and Heating Surfaces, To
Compute 927, 1024
" Distance of Piston from End
of Stroke, when Lead pro-
duces its Effect, and when
Steam is AdmiUed for Re-
turn Stroke. 732-733
*' Feed Pump, Area tyT, To Com-
pute 736
" Fire, Elejnenis, etc 9.>4
" General Rules for 728-730
" H» of To Compute 733-734
" " AdmirtUty and French. . 734
" If^ection Pipe, Area of, To
Compute. 735-73^
" Not^qf. 936,954
Pag*
9nA]|-BNOiini, PortdbUj Standard
Operation of, and Elements
of 737
*' Propeller Slip and Thrwty To
Compute 730-731
•' Proportion of Partt, Condens-
ing and yon-condensing. 727-729
" Beeeiver 721
" Resultt of BxperimetAs on
Operatton of, 933
** Hcreio, I'*riction oj 478
** Steam- Irtfector and Volume of
Water Discharged per Hour 736
'* " -Pumps, EUmefntB and Ca-
pacities of. 738
" Vertical Beam, Jet Condens-
ing, Weight of, To Compute. . 759
** Volume of Water Jiequtred to
be Evaporated in.. .734-735
" Volume of Circulating Water
Required in 735
" Volume of Feed Water and In-
jection Water Required
per IP per Hour 736
" " of Flow through an Ii\jec-
tionPipe.. 735
** Water -wheeUs, Radial and
Feathering, and Elements of. 730
** SuDK Valves, To Compute and
Ascertain Lap and Breadth
of Ports 731
•• Distance cf Piston from End
of Stroke given, To Compute
Lead, eta 732-^33
*^ Lap and Lead of Locomotive
valves 733
" Part qf Stroke any Given Lap.
uHll Cut off. To ComvUle. ... 731
** Stroke at which Exhausting
Port is Closed, etc. .... 732
" •' of, To Compute. 732
ShrsAM-EvoiNBB, Results of Operation
of' 737i 924. 933» 954
'' and Boilers, Weights of with
Water 929
** " RestUts of Performances
of 9241927
*' Duty of and Relative Cost of
for Equal Effects 757
" Practical Efficiency of. 737
" 8ide-wheds,PropMer and Ma-
rine, Weights of. 758-759
" Weights of. 758-759. 9"
SraAMVESBBL, Pofwer Utilised in... 662
*^ Resistance to, in A ir and Water 911
" -Pkopkllbr, Ordinary Distri-
bution of Power in 9x1
" Vdociiyof. xozo
Steamer "Great Eastern'* 173
SnuvKRs 478
" Iron, First Built 915
" Rflative Velocities of TachU,
from Elements oj Cat^rwUion,
and Large 928
RtOTiiitng Distances : 86
Steel 640^3^ 750^ 783, 787-788, 827
" and Iron, Corrosion of, 908
" and Iron, Corrosive Effects of
Salt Water 916
" Ouns 913
" Hemp,Iron and Steel Wire Ropes,
RekUive Dimensions of... 172
" *' and Iron Rope, Round and
Flat and Safe Load. . . 164-166
" " Iron and Steel Wire Rope. . . 164
" Hexagonal, Octagonal, and Oval 135
'* Locomotive Tubes 138
" Manufacture of. Remarks on.... 642
*^ofa Oiven Section, Weight of.i^S, 149
' ' Plates 750, 830
" " Thickness of. i2x
** ''Weight of ;.ii8-ii9, 146
*' and Iron, Rolled Bart^ arid
Weight of. . . 125, ia6j 128, 134, i3«i
" Wire, Weight of. 120-iaf
Sterling, Pound, etc 38
Stings and Burns, Application for. . . 196
Stirling's Mixed Iron 785
Stirrups or Bridles, /or Beams 838
Stone and Ore Breakers and Crusher,
903) 957
*• Dressed, Modes of. 603
" Hauling 468
" Load per ^. Foot 915
" Masonry, Elements of. 595-600
'* '^ Ashlar and Rubble. . . .600-601
'' Resistance of, to Freezing 184
'' Satoing. 196, 904
•' *' and Dressing, Cost of..... 949
*' Voids in a Cube Yard of. 690
Stones, Cements, etc., Crtuhing of. . 766
(See Crushing Strength, 764-769.)
" Building, EsqMinsion and Con-
traction of. 184
Straw and Hay, Weif^ of. 198
Streams, Rivers, and Canals, Flow of
Water in 550
Street Rails oliTRAinrATS.435, 915, 918
*' Raiiaoabb, Experiments on Mo-
tors, Result of 915
" " Cost of Maintenance 918
" Roads and Pavements 686-690
Strimoth of Materials, Elements
of. i 761-841
'* Elasticity and Strength, Co-
hesion and i{M<{ienc«. 761-763
*' Coefficient of. 761-762
** Modulus, Height of, Weight
of. Various Materials.'jb2-j6-i
*• *' q/1 3\) Compute 763
♦» »* of Elasticity, Height of To
Compute 763-764
" ** Resilience, Comparative, of
Woods 763
♦« " Weight a Material will Bear
without Permanent Alter-
ation of its Length 763
'' Ck)HBBioN, Modulus of and
Weight, To Comj^te. .963-^
ti
it
XXXVl
INDEX.
SlBKNGTB OV iffATKUALS, GRUSHINO,
Elements of, etc 764-769
'• ** Bricies 908
*» " Casi ind WroH Iran, Woods
and Various Metals 765
" " Columns of Iron and Steely
Sa(f'e Load of and Coeffi-
cients of To Compute. . . 769
<« <* Columns, Arches, Chords,
etc , of Cast Iron, Safe
Load of 766-767
* " '' Weight of To CompuU. ^(i()
«« « Cylinders and Rectangular
Tubes of WroH Iron 767
** " Elastic Limit compared to 764
** " Granite, Limestone, Marble,
and Sandstone 767, 1039
** " HoUow Columns or TuJbes,
8afk Load of. 768-769
" " lee 912
** " Long Solid Columns, Com-
parcUive Value of 976
" " Notes and Effects, Season-
ing, etc 764
" *^ of Cements and Mortars. . . 596
** " Relative Value of Woods,
Strength and Stiffness
Combined 976
** *^ Sandstones,Stones,Cements,
Masonry, etc 765-766
" " Various Materials 765-769
" Dbflbction, Elements of, etc..
770-781
<^ " and Weight Borne by a Bar
or Beam of WroH Iron. . 773
** " Bars, Beams, Girders, etc,
770-771
" ** Beams of Rectangular Sec-
tion, Formulas far. . 77 1-773
" " ^*and Comparative Strength
of Flanged 778
M ** * » arid Girders. 840-841
" " " Elastic Strength of of
Unsymmetrical Section 778
" " ''Flanged, and Weight of
that may be Borne by
One of Cast Iron. .777-778
u ti ii qf Cast and WroH-ir<m,
and Woods. 772-774
«« (i (t Of, Qirders, Continuous. 772
** ** Bearings, Admissible Dis-
tances between 778
** " Cast Iron Flanged Beams
andCgmparcUiveStrength
of ,809
*• •* General Deductions — 779-780
•• *' Girders, Tulndar, of WroH
Iron 775, 809
" " Rails, Flanged, Iron and
Steel 775-776
** " Rectangular Beam of Iron
and Woods, Load that
may be Borne by 773
* •* " Bars and Beams of Cast
Iron and Various Sec-
UanStBio. 777
Pa^r
Strbngth op Materials, Results of
Experiments on Subjec-
tion of Cast-iron Bars to
Continued Strains 780
" " Riveted Beams of WroH
Iron and Weight of. . 774-775
'* ''Rolled Beams of WroH
Iron 774
" " Shaft from iU Weight alone 778
" "Shafts and Distributed
Weight for Limit 778
" " " MiU and Factory, and
To Compute. ..:.... 779
♦• " Springs, Carriage and In-
dia-rubber 779
" " WorHng Strength or Fac-
tors of Safety. 781-782
" Dbtrusivb OR Shearing, ^fe-
menls of, etc 782-783
" " Comparisonbetween Trans-
verse. 78a
•' "Lengthof Surface of Wood
to Horizontal Thrust. . . . 789
" •* of Metals with a Fundi. . . 782
" •• of Riveted Joints, Cast Iron,
Steel, Treenails, and Woods 783
" " of Rivets and Memoranda. 830
" " of Various Metals by Par-
allel Cullers 783
" " of Woods 783
" " of WroH-iron 783
♦• " " BoUs, Experiments
on and by U. S. N. 783
" " Pov)er to Fundi Iron, Brass,
or Copper, To Compute. . 782
" Tbnsilb, Elements of etc. .784-790
" " Average Elasticity of Steel
Bars and Plates 788
" " Cast Iron, StirUng's Mal-
leable, and Wrought. . 784-785
" " Ductility and MaUeabilUy
of Metals, Ratio of 787
" " Elements connected with
Various Substances 786
" " Manganese Brome 832
" " Memoranda on Rehealing,
Temperalure, Annealing ^
Cold Rolling, Hammer-
ing, Welding, Cutting
Threads, Case Harden-
ing, and Galvanizing. . . 786
" "of Various MetaU, Woods,
and Miscellaneous Sub-
stances. 788-790
" "of Wood in Various Posi-
tions 870
" ** Result of Experiments on
by Soc. ofC.E. 787-788
" " Riveted and Welded Joints
of WroH-iron Plates 828
'* ♦' Steel, Crucible, Bessemer,
Fagersta''s and Siemen^s
Experiments on 787
<i ii WroH Iron Tie-rods,Exper-
imetUs on..t 787
INDEX.
xxxvii
(( ((
(( ((
ct
Page
Stbbioth or Materials, Relative
Besistcmce of WroH-iron
and Copper to^ and Com-
pression 787
" ToRSiONALjBfewiento 0/ etc 790-797
** *' Shafts and Gudgeons. .790-792
«* " Cast Steel and Coefficients
of. •.-. 795
" " Gvdgeons, Diameter of To
Compote 79s
" * » Hollow, Round,and Square
Shafts and Cylinders^ To
Compute. 792-794
** ^^ Shafting, Coefficients for
Ultimate Resistance of. . 797
" " Shafts of Oak or Pine, To
Compute. 793-794
•* " " Couplings or Sleeves,
and Supports for. . , . 796
u «4 tt Diameter of to Resist
Lateral Stress, To
Compute 791-792
" ^^ and Journal, of for
a Water-wheel. ... 571
" ^^ofa WroH Iron Cen-
tre Shaft 794
" " " of to Resist Torsion
and Weight. ...... 792
u «( it Hollow, Diameter of to
Sustain its Load, etc. 792
«* «* " Journals of, etc 796
" " " MM and Factory, For-
mtUoJsfar 797
<( ci 4t 0^ \ifrroH Iron for Ma-
rine En{fines, For-
midas for Diameter. 796
«i i« »* Round and Square, Ul-
timate Strength of To
Compute 795
«* " " toResistLateralStressofjgy
« ^* of Various Metals, Woods,
andTohin Bronze, 793-794» 9^9
" Transverse, Elem^ents of, etc. ,
798-841
" " Coefficient or Factor of
Safety of Materials 802
** " Bar or Beam,Fixed or Sup-
ported, hears Weights
at Unequal Distances. 803
»* " Bars of Steel, To Compute,
817, 827
" ii u HoUowGirdersor Tubes,
Comparative Value of. . 824-825
«• " Beam or Girder of any Sec-
tion or Material, For-
mulas for. 817-818
u u <t Qf. Shaft, Rectangular,
Diagonal, etc., For-
mulas for 817
" »* Beams of Various Woods.
Safe Statical Load of ana
Corffidentsfor. 834-835
•• " B(^tom Plate Area and De-
structive Weight of 810
<* " BowstringGirder, Diameter
cf Tie-rodj To Compute. . 812
Strength of Materials, Cast Iron
Beams or Girders of Va-
rious Figures, To Com-
pute 81^-821
« <c Uf,f yarious Figures of
798, 800, 813-817
" " Centres of Gravity and of
Crushing and Tensile
Strength of a Girder or
Beam, To Compute 819
•• *' Concretes, Cements, etc. . . . 800
" " Cylinders, Flues, and Tubes,
Elements ofwiUUn Elas-
ticity, To Compute... 827-828
" " Cylindrical and Elliptical
Beams or Tul)es of WroH
Iron 810
*' " Diameter of a Cylinder to
Support a Given Weight,
804-805
" " Depth of Beam to Support
a Uniform Load 808
" " Elastic of WroH Iron Bars. 808
" ^^ Elliptical-sided Beams,Side
or Curve, To Determine. . 826
" *♦ Equilateral Triangle or T
Beam, To Compute 804
" " Flanged Beams of Cast Iron,
Comparative Strength
and Deflection of.... 809
" " *' Dimensions and Pro-
portions of. 809
" »' •' Hollow or Annidar
Beams of Symmetri-
cal Section. 815
♦' " Floor Beams, Girders, etc.,
of Wood, Capacity and- El-
em,ents of, To Compute.S^S-B^S
" FormiUa^andRtdes for Rec-
tangular Bars, Beams,
or Cylinders. 801-803
" '^for Destructive Weight
of Solid Beams ofUn-
symmetrical Section,
816-819
" " General Deductions from
Experiments 824-825
*' " GirderorCylindricalShaft,
Lower Flange of, Sec-
tion to Sustain a Safe
Load in its Middle, To
Compute 817
" " " Beam, etc., Factors of
Safety 821
*' Dimensions of and Load
on, To Compute. . .839-840
" Graphic Delineation of
Stress 840
•* " Girders and Beams of Va-
rious Figures and
Sections, Symmetrical
and Unsymmetrical,
JromExperiments.Si^-%ij
«« «« "Beams, Lintels, etc.,
Elements of 822-823
" *« " or Beams of Unsym-
metrical Section. .8xo-9mi
t(
u
C( i(
II il
xxxvui
INDBX.
u
t(
It
Strhtoth of Uatkbjajjl Girders of
WroH-ircn^ PI<Ue 811-812
'« " GUus QUtU* and Cylin-
ders, Resistance to Inter-
nal I^essurt and Collapse 831
*' " Headers and Trimmers or
Oarriage Beanu, EUmenU
of, To Compute 836-838
** " Homogeneous Beams of Un-
symmetrical Section, Ul-
timate Strength <{/*, To
Compute 820-821
" " Inertia of Beams, Moment
of. 818-819
** '* Inclined Beams, etc, of
Wro t Iron, 811
" ** Lead Pipes, Resistance to,
Thickness qf, Weight, and
Bursting Pressure, To
Compute 831
** *^ Manganese Bronze 832
" ' ' Memoranda on Joints, etc . 830
•' •' ''onMetaU. 832
" ''Metals 798
" " MisceUaneous lUustrations 826
" '• Neutral Axis of a Beam of
Unsymm^rical Section,
To Compute ^ 820
*' of a Beam in an Inclined
or (Mique Position. . 799, 804
*• ''of Brickwork 801
*♦ "of Woods. 798-799,800
" PUUe Joints, Double Rivet-
ed and Strapped, Experi-
mjerUs on 829
" Pressure on Ends or Sup-
ports of a Bar, Beam.etc. 803
** " Rails, Iron and Steel, To
Compute 812
" " Bectaimular and Cylindri-
cal Beam^, Formulas
and Coefficients for. . 805
" " " Girders or 7Yibe« 809
" *' Resistance, Moment and
Work of, To Compute. . . 818
*• " Riveted Joints, Compara-
tive Strength of 828
" " Rivets, Pitch, Lap, and Di-
ameter of 829
" MoUed Beams and Channel
Bars, Safe Load and
Weight 0/. 807-808
'* and Girders or Riveted
Tubes of WroH Iron,
of Various Figures
and Sections, Destruc-
tive Weight, To Com-
pute 805
" " " " and Channel Bars of
WroH Iron of Various
Sections. 8o6.A>8
" •• " iiteH Beams ■147, 808
" " Scarfs, RelaHve Resistance
of. 841
•* ** SeoMning, 7nr.rease in
Strength of Woods 800
** " SMid C^Hsmr^ To Compute 804
tt
t< (I
Strinotb of Uatvri aim. Solid Cylin-
der and Hollow Cyl-
indtrsof Various Ma-
terials. 801
« li tc Diameter of to Support
a Given Weight. . .804-805
'^ " Statical, Deador Live Load,
Factors of Safety 841
" " Steel and Bridge Plates and
Rivets 830
'* " " Bars, To Compute 827
♦• **Stifness of Materials 798
* * " Stirrups or BrifUes, Dimen-
sions of To Compute. . . . 838
" " Symmetrical Girder or
Beam, Conditions of
Forms, etc 825-826
" " Tobin Bronte 029
" Trussed Beams or Girders, §23
" " UnequaUy Loaded Beams,
etc 810
'* " Various Materials and of
tl K
Various Ftps. .708-801, 1029
"Metals, Comparative
(Qualities of. 8si
" " Woods, Large Timber, To
Compute. .% 833
" «• WroHii-on Joints, Propor-
tion of Single Rivets. 829
8TBKN0TH OF MoDVLfi 644-645
"■ Dimensions of a Beam whidi a
StrwAure will Bear, To Com-
pule 644
" Resistance of a Bridge from a
Model, To Compute 645
Stress, Moment of, and on Rods. 621-1041
Street RalirondB or Tramways, and
RjuuU of Experiments on
Motors for 915
" CostqfMainteHaitee. 918
Stucco 591-593
Sues Canal, Via. 912
Sugar Cane, and Beet Root 207
" and Acid in Fruits 203
" and Water in Various Products 201
" in Mortar, 951
" Mill Rollers 911
*' '}l\lls, and Engines, Weights of,
759, 903, 908
Sulphuret of Carbon, Elastic Force
and Tempera/ture of Vapor of.... 707
Sun, Heat, Diameter, etc 188
" Heatof. 193
Sunday Cycle or Cyele of the Sun. . . 70
" or Dominical Letter 70
Sun-dial, To Set. 69
Sunstroke Remedy 938
Surveying, Useful Number in. 69
ScjsPKNSion Bridoks 178, 199, 842
** " Elements, Stress, and
Pressure, To Compute 842
". " Horisontal Streu and
Vertical Pressure on
PierSs To Compute . . 84a
'* "StulOMstM «63
INDEX.
. XXXIX
Pftg*
SuarcMsiOH Briik»8, BaHo ofStreu
an Chaim or Cabla at I\>int ofSus-
peruion Bean to whole Weight of
Structure and ijoad, To Compute. . 842
SustenaDce, Human and Anim.al. . . . 203
" RequiremenU of a Workman 207
Sweet Potato 307
Swimming 439
Symbols, a Ig^n'aiCy and FormtiUu. 22-23
" and Characters 21-22
^' and Equivalents 190
'' for Elements and Formulas. . . 981
Symbolic Hatching and Designa-
tions 93a
T.
Tttcks, Nails, Spikes^ etc., fTro'i Iron 154
Tan, Elements of. 482
Tangential Wbeel 57^
TAMOKlTTa AND CO-TAMOXNTS 41 5-426
u (( Xo Compute 426
" " '' Degrees, Minutes,
etc., 0/ fifteen 426
Tannin, Quantity of, in Substances. . 190
TofM Ltne or Chain, to Set out a Eight
Angle with 1 69
TscHincAL TsBMS, Orthography of. 1042-51
" " in if onmry.... 597-599
Tee and Angle Iron, Weight of. 130
Teeth of WheelB 850-862
" Dim/emions of a Tooth, etc.. To
Compute 860-861
" W and Stress of. To Compute. . . 861
" Involute 859
Telegraph Wire, Span of. 179, 936
'■*■ Telephone,Wires and Cables.. 960
Telescopes, Opera-Glasses, etc. . .671, 942
telford Roads 688, 690
TucPKRATiTRi and Extremes of. .914, 952
*' Absolute 504
" Artifieial and of Earth 195
*' by Agitation 534
^ Decrease of, by Altitude 522
** Extremes of. 952
'* JVon-conductOrs of. 933
*' ofJSnclosed Spaces 526
♦* of Mines. 918
<* q^ SiUurated Steam, Latent
and Total Heat of.
To Compute. 707
** of Steam, To Commute 705
** of Various Localities 192
** To Reduce Degrees of Differ-
ent Scales, 523
** Transmission or CoTiductiv-
, *^of. 9x4
** Underground 519
Temperatures, Metric 37
Tempering Bmn£ /n«irufn«nte 197
Tenacity of Iron Bolts in Woods 198
TnrBaa STRKiraTH {See Strength 4/
Materials) 784-790
Teme Platea 124
Terra Cotta. 602
teaHA, Simple, of Water. 928
Pttm
Theatres and Opera-Housea. 180
Thermometers, Reduction of. 533
Throwing Weights by Men 439
Thrust, Weight of a Body, to Sustain a
Gityen. To Compute 693
Tidal Pbouomeuu una i iirreui. .75-1010
Tide Table fw Coatt ofU.S 84-8 c
T1WS8 84, 198
'' of Atlantic and Pacific 191, iq8
'' of Pacific Coast 85
' ' Rise and PaU of, Gulf of Mexico. 85
" Time of High Water 74-75
Tie- rods. Experiments on 787
Timber and Boakd Mbasurk. .^. . . 6z
*' AND Woods, Elements, iflk«>
Treatment, etc .^65-870
«♦ C<mparative Weight of Green
and Seasoned 217
(See Wood and Timber, 865-870.)
" Measure, and Volume of. To Com-
pute 61-62
*» Strength of 870
*' Volume of Sijtiared,To ComptUe 6a
" Waste in Hewing or Sawing. .. . 6a
TncB, qfter Apparent Noon, before
Moan next passes Meridian ... 75
** Civil and Marine 37
*' Difference in 81-83
" "of, betv>een New York and
Greenwich, and any Location,
To Compute.^ 83
" Meaxures of and New Style 37
^^ Sidereal and Solar 37
" To RedMce to Longitude 54
Tin, Plate and Block 644
" Lined, and Lead Pipes, Weights of
per Foot. , 137* '5"
'* Pipes, Lead Encased, Weight of., 151
»* Plates, Marks and Weights. 137
ToBiN Bhonzb, } acht Shafting^ etc. . 920
Tolerance, of Coins 38
Tonite, or Cotton Powder 443
Tonnage, of Vessels, To Compute. 175-177
" Approximate Rule 176
" Builder^ s Measurement. 176
** Corinthian, New Thames, and
Royal Thames Yacht CltUts. . 177
" English Registered. 175-176
" Freight or Measurement 177
" of Suet Canal 177
" To Compute 173
*' Units for Measurement, and
Dead-weight Cargoes 176-177
" Weight of Cargo, To Ascertain. 177
Tools, Friction of. 476
Tornado, Pressure of. 911
ToRPKDOKS, St^bmarinie. 946
Torsional Strrnoth (See Strength
of Materials) 790-797
Towers, Spires, and Donus 180, 933
Towing, on Erie Canal arwl Hudson
River 193
Traction, Elements of, etc 843-S49
" and Statical Resistance of Ele-
vations 846
" Co^fflcitnts of , for Roads 845
xJ
INDEX.
«
u
It
u
it
((
Paffe
Traction, Friction of Roads and
Coefficients of in Propor-
tion to Load 847
Maximum Power of a Horse on
a Canal 848
ofOmnUms and Speed 844
on Canaly Slack-water, Rioer^
and on Street Railroads 848
on Various Roads and of Va-
rious Vehicles 845. 847-848
Power Necessary to Sustain a
Vehicle on an Inclined Road,
To Compute 845-846
'* Power Necessary to Move and
Mtustain a Vehicle Ascending
Wr Descending an Elevation,
To Compute 846
" Resistance of a Car 849
" " of Gravity and Grade., 847
on an Inclined Road 846
on Paved, Rough, and
Common Roads 843-844
to on Ormmon Roads. 843-845
' ' Results of Experiments of on
Roads and Pavements 843
Tramways or Street Railroads,
435i 848, 915
Transportation, Canal. 193
" of Horses and CatUe 192
Travsversb Strength {See Strength
of Materials) 798-841
Trass or Terras. 580
Treadmill 433
Treenails, Strength of etc 783
Trees, Large, in California 184
" " in Australia 971
Trigonometrical Equivalents 387
Trigonometry, Plane, AngUs, Sides,
etc, To Compute 385-389
Distances of Inaccessible Ob-
jects, To Ascertain 388-389
Height of an Elevated Point,
To Compule 389
Tripolith, Composition of. 198
Troops, Marine Transportation of... 914
Trotting 430-440
Troy Measure 3a
Truss, Iron and Stress on. 1 78-1041
Tubers, Ratio of Flesh-formers 207
Tubes, and Flues 747, 827
* ' and Pipes, Weight of To Compute,
147-148
Brass and Seamless Brass, Weight
„^f' 142
Copper, Seamless Drawn, Weight
o/' 140-142, 144
English Wro'tlron, Weight of i^-^,i^^
Evaporative Capacity 'f Varying
Length *. 742
Lap-toelded Iron Boiler 139
or Girders, Dimensions and Pro-
(i
(t
(I
<t
(1
tt
li
Turbines [See Hydrodynamics). .572-5^
" and Water- Wheels Compared. 579
Turkish Plaster and Mortar soi-soa
Turning, FHction of ^ 47,
•' and Boring Metal .* jAy
Turnips, Ratio of Flesh-fDrmers 207
Turpentine, Elastic Fwce and Tem-
perature of Vapor of 707
U.
Underground Temperature 519
Undershot- Wheel (See Hydrody-
namics) 566-571
Vug\xenV8, Relative Value of. 471
Units for Computing Safe Strain of
New Ropes, Hawsers, etc 170
V.
Value of Coins. To Compute 39
' ' and Weight of Foreign Coins . 40-45
* ' of Uie Metre in terras of the Brit-
ish Imp. Yard. 934
Vapor in Atmosphere, Volume and
Weight of To Compute. 68-69
" Elastic Force of of Alcohol,
Ether, Sutphuret of Carbon, Petro-
leum, and Turpentine 707
Vapors, Relative Density of Some... 521
Variation of Magnetic Needle. . . 57-1039
" Decennial, of Needle 58
" of, in U. S. and Canada 59
Varnishes 876
Vegetable Marrow, Composition of. . 207
Vegetables, Analysis of Meat and
Fish and Foods 200-201
and Oil-cake, Nutritious Prop-
erties of Compared 204
Elements of Various. 207
Proportion of Starch in 205
" Tubers, RcUio of Flesh-formers 207
Vegetation, Limits of. 1^2
Velocities, Metric. 37, 923
" Acceleration and Distance of a
Body, To Compute 921-922
" of Different Figures in Air,
Resistance of 646-648
Velocity Lost by a Projectile, T» Com-
pute 648
" and Tim4i, To Compute 648
" and Volume of Molecules 194
*' of Current of a Bay or River. . 97 j
Ventilation, Buildings, Apartments,
((
ti
etc.
524
portions of. 809
" Steel and Semi-Steel Locomotive 138
" Thickness of B W G 748
Tubular Bridge. Britannia. 178
Tunnels, Lengths of. 179, 936
Length of Iron Pipe required
to Heat A ir, To ComjMt^e.525-526
of Mines 449
Proper Temperatures of En-
closed Spojces 526
Volume of Air Discharged
through a Ventilator. 524
*' of Air per Hour for
each Occupant of a House.
Vernier Scale
i(
((
((
525
27
Vessel, Elements of, To Compute. . . 653
" HuUs of Iron, Thickness of
Plates and Rivett » , . i . 830
(I
INDEX.
xli
P»»ce
VeueVs Side Lights, Visibility of.,,, 918
Vessels, Mean Speed of. 971
Veterinary, Treatment in 186
Victor Turbine 57^
Volcano, Power of. 910
Volcanoes, and Heights of. 182, 936
Voltmeters and Ammeters. 961-963
VoLUXB AND Wkioht of Various Sub-
stances in Ordinary Vse 216
" of Molecules 194
VoLUMKS, Mensuration of. 360-378
W.
Walking 433> 438
Wall, Chinese 179
Walls and Arches, Elements of. .602-603
(See WaUs, Dams and Embank-
mentSj 700-703. )
and Earth, Friction of To Ascer-
tain and Compute 698
»♦ M<mient of To Compute — 701
»' " of Pressure, Point of
To Ascertain 698
of Buildings, Thickness of .iSg, 1020
or Dams, Centre of Gravity of . 702
Retaining, of Iron Piles 196
or Dam StabUiCy of, To
Determine 702
(C
(t
(4
i(
ii
ii
it
ii
ii
ii
ii
Revetment, Elements of. 694
Warehoases, Brick Wcdls for 603
Wabmiko Buildings 527-528
by Hot-air Furnaces or Stoves 528
by Hot Water 524
by Steam 527
Coal Consumed per Hour. ... 527
Furnaces and Open Fires. ... 528
Illustrations of Heating 527
Volume of Air Heated by Ra-
diators, Consumption of Coal, Areas
of Orate, and Heating Surface of
Boiler, etc., per 100 Sq. Feet 528
Warps and Hawsers 173
Washington Aqueduct 178
Watches, First Constructed 915
Watbr, Elements of 849-852, 916
Ajpproximale Bottom Velocities
of Flow of in Channels, at
which Materials are Moved. . . 916
BoiHng- Points of, at Different
Degrees of Saturation 851
Column, Height of 849
Density of. To Compute 520
Deposits of at Different Degrees
of Saturation and Tempera-
ture 852
Evaporation of. 916
it
tf
14
it
ii
ii
ii
ii
it
ii
ii
ii
i(
it
it
it
ii
ii
tl
it
tl
it
ii
ii
ii
ii
ii
it
tl
it
ii
ii
It
Expansion of 5^9
Freik and Sea 849-851
" DistiUationof. 955
Friction of in Pipes 925
Head and Discharge of in Pipes 920
Inch, Miner^s 557
Motors, Ratio ofEffectine Power 563
Pipe, Dimensions and Weight of,
from. 275 to s Inches i37-'38
Water and Metal Pipes, To Compute
Weightof. 147
Power and of a Fall 0/ 562
" Cost of on Driving Shajt . . 950
Pressure Engine 579
Rainfall and Volume of. 850
Resistance of to an Area of One
Sq. Foot Moving through, or
Contrariwise 646
Saline Contents of 852
Salt, Corrosive Effects of, on Steel
or Iron 916
Sea, Composition of. 851
Tests, Simple 926, 974
Vdocity of a Falling Stream
of 496
Volumes of Pure, and at 32°. . . 849
Weights of, and To Compute. 852, 923
-Meters, Worthington^s. 94a
-Raising, Cost of. 949
•Tube Boiler, Elements, Tests,
and Average Results of. . 926
" Efficiency of. 947
-Wheel, Centre of Gyration... 611
*' Diav^ter and Journal of a
Shaft, etc 571
" Dimensions of Arms. 571
-Wheels, of Steamboats. 730
" Compared wiih Turbines. . 579
{See Hydrodynamics and
Hydrostatics, 563-579.)
Waterfalls and Cascades 184
Watermelon, Water in 207
Waterproof To Render, Wood, Iron,
Walls, Paper, etc 875
Waters, Mineral^ Analysis, etc. . .850-852
Waterworks, Filters for 184
Wave, Flood 912
Waves of the Sea 852-853
" Height of, in Reservoirs, etc. , To
Compute 853 >
" Tidal, and Length of 853
" Velocity of To Compute 853
Weather- Foretelling Plants 185
" Glasses 430
" Indications 43'
Wedge, and To Compute Power. .... 630
Weighing without Scales 66
Weight, Diameter and Volume of, oj
Ca^t-iron and Lead BaUs.. .. 153
Aluminum^ i55
Anchors, Cables, Chains, etc. . . 173
and Diviensions of Lead Balls'. 501
*' of Gas and Water Pipe. . 138
" of Water Pipe 137
and Fineness of U. S. Coins. . . 38
and Mint Value of Coiwt 4<>-43
and Mint Value of Foreign
Coin, 1888 40-43
and Specific Graviti/ 208
and Strength of Wire, Iron. etc. 124
of Stiui-iink Chain Cable
per Fathom 168, 930
of Hemp and Wire Ropes 172
Angle and T Iron and Steel,
125, 126, 130
ii
it
it
tl
<i
(t
i(
it
i(
it
it
tt
it
it
xlii
INDEX.
(t
It
_ Pme*
VfEiQETf Ap<ahecarie9* 47
" Brass and Various Metals
per Cube Inch and Foot^
and Wire 125
** and Oun- Metal of a Given
Sectional Area 136, 149
u a Wro't and Cast Iron and
Steely Lead, Copper, and
Zinc Plates per Sq. Foot.. 146
«* «» Cast and WroH Iron, Steel
and€fun-Metal,ofaOiven
Sectionai ArecL 149
" «' Castings 155
«« " Copper, Wro't and Cast
Iron, and Steel, of a Qiioe/n
BtdtiofMA Area 136
" " »* /ron, etc, If ire... I30-I3I
«» " ofShteU X4a
«« «« Pipes correspojidin^ to Iron
and Iron I^pe Fittings.. 14a
« ** Wrought Iron, Steel, and
Copper PlaUt 1 18-1 19
<' Cables, Oalvanised Steel, for
Bridges. 163
" CaUle, To CompuU Dressed
WtiahJtof. 35
** Centr\fugaJL Pump. 917
" Crane Chains and Ropes. ..... 457
*' Diamond, and qf Diamonds, ^a, 193
*' Earth 33
*' 'EkctricaJLRstistanoc ;... 34
" Fire-Engine. 904
" Oun-Metal.,*, 155
" Hay and Straw xo8
** Hemp and Wire Bf^ x6a, z66
** Lead,and qf, To Compute. 33, 151, 155
*' Pipes i37«i50|83i
«* PUUes,WeightqfSq.Foot. 146
" " Sheet 151
** Length and Oauge of Iron Wire 17a
** of Anvils. 918
" of Articles of Food Consumed
in Human Sj(Stem to Develop
Power of Reusing 140 Lbs. to
a Height of 10,000 F^ 304
*^ of a Body or Substance when
Specific Gravity is given. To
Compute ai5
" of Beeves and Be^^Comparative 35
" of Bolts and Nuts 156-157, 159
** qf Cast and Wrought Iron Bar
or Rod, To Compute... . 131
*f " Pipes or Cylinders. . . 133-133
•' of Cast Metal by Weight of Pat-
tern ai7
** of Composition Sheathing Nails 135
*• of Copper, Casland WroHIron,
and Lead, To Compute.. 155
** of Copper, Braziers^ and Sheath-
ing. 131
** *^ PipesandComposition Cocks 150
M '' Rods or Bolts. 148
** ** Seamless Tt^M. . . . 140-143, 144
" " Sheet per Sq. Foot. 135
i(
n
'* of Corrugated Roof Plates. ... . 131
^* of a Cw>e Foot qf Oak and
Yellow Pine. 870
Paf*
WuoHT of a Cube Foot of Steam, To
Compute 705
^^ofa Solid or Liquid Substance
or an Elastic Fluid, To Ascer-
tain 317
" of Cube Foot ofGojtes at 33°.. . 3x5
" of Embankments, Walls, and
Dams, per Cube Foot 694
" of Fence Wire 164
*' ^ Flat Mining Ropes 165
'* of Flat Rolled Iron and Steel,
and Steel Angles. . . .X36, xay, xaS
" of Food, Articles of. 304
" of Foods, to Fumi^ Nitroge-
noy>s Matter. aoa
" of Galvanized Iron Wire. . . xda, 163
" *■'■ Sheet Iron. . . 124, 139
" of Gaseous Products of Comhw-
iion. To Compute 460
" of Gun-Metal qf a Given Sec-
tionoU Area, and per Cube
Inch or /bo< 149, 155
" qfHemp, Iron, and Steel Rope. 164
" of Hoop and Sheet Iron. . . . 139, 131
'* of Horses 35
** ^Ingredients,thatof Compound
being given. To Compute 318
** qf Iron and Steel, Bound RoUed 126
" " •' Square Rolled 135
*' '* Wire and Strength of. 134
** of Lead and Tin4ined Pipe.. . X37
** of Men and Women 35
** qf Metals of a Given SeUional
Area, per Lineal Foal.. . 136, X49
" of Molecules^ Volume and Ve-
locity 194
" of Oak and Yellow Pine 870
" ^ Offal in a Beef and Sheep. . 35
** of Products of Combustion. .. . 463
" <ir Riveted Iron and Copper
Pipes. X48
" qf Ropes, Hawsers, oMd Cables,
To Compute 172
** cf Silver and Tin 155
" of Steam- Engine, Vertical Beam,
Condensing, To Compute. . . . 759
" qf Steel, Round, Hexagonal,
Octagonal, and Oval 135
« " qf Stud-link Chain Cables 168
" of Timber, Green and Seasoned 217
" ^ Tin Pipes 151
'* " Plates and Marks 137
" qf Tube4 of Copper, Brass, and
Iron 140-147
" ^ of Brass, To Compute 1^2
** qf Various Materials 763
" of Various Substances per Cube
Foot in Bulk. 3x7
" of Volume of Air Consumed per
Lb. of Combustible 46X
" of Water-Pipes, To Compute. . . 561
'« qf Wire and Wire Rope. 163
'* ** Length and €fauge 163
" " Iron, and Steel 164, 173
" of Wro't and Cast Iron per Sq.
Foot Z46
** qfZinc, RoUed ••-••uSxSS
INDEX.
xliii
WnoKt ^Wrwght and CMt It^n
Tubei. 143-145
»» " " Steely Copper^ and
Bran PUUei, per
Sq. Ft. per Qaugt^
1x8-119
** on Floort and of Strwsturti.. . . 8iz
♦• iioclbs, Earth, eto : 467-468
»* Silver. 155
" Special, Locomotive 138
'* Steel, Copper, Iron, and Brau. 136
<* *' CV»pp«r, BroM, Afui Wro't
Iron Hates 118-119, 155
u " Copper, BraUf and Iron
Wire zao-z3i
" Teme Plates, and Thickness. . . 124
" Tin Cast 155
** U. S. and Standard Measures. . 934
•♦ Water Pipe 137
'* Wrought and Cast Iron, Steel,
Copper, Lead, Brass, and
Zinc Plates, per Sq. Fool. 146
** *^ Steel, Copper, and Brass
Wire, X20-I3Z
" ^^ Wire, and Strength Z24
" Zinc Sheets 123, Z51-Z52
" *^ Plates and Dimensions of. 1^6,151
•* ''Boiled 146,155
WliOHTB, Various Materials zz8-z75
*' ANP MSASUBM, U. S. stand-
ard 26-36, 934
" Ancient and Scripture 53
♦* and Pressures, Meti-ic 923
** and Volumes of Various Sub-
stances in Ordinary Use,. . . 316
" Apothecaries* 32
** Avoirdsmois 32
" Bushel^ Pintnds in 34
" Coal, Earth, and Wood 33
*' Engine and Sugar Mill 908
** Enf^sh and French 44* 47
•* Foreign Countries. 48-53
** Grain, Lead, and Tn/g. 32, 47
" Orecian. 53
** Hebrew, Jewish, and Egyptian. 53
" Measures of.. 33-47
" ** and Pressures, Metric. . 36
" Metric. . . .37-33. 36-37» 46-47. 9*3
** Miscellaneous Articles and
SiAstanees. 33. 46, 2Z4-3Z7
" ofBdU. z8o
** of Boilers. 759
** of Brain, Bidative z93
** of Chains and Anchors Z74
** ifFuds, Coalt and Woods,
483-484, 486
** of Ouns {Ordnance) 498
** of Lead Balls, and Shot... $oo-yyi
»• " Pipe, To Compute. 83Z
** of Rope, Hempy Iron and
Steel 164-166, 173
** •/ Slating per Sq. Foot. ..... 64
** of StMoan-Enginu,
758-759. 9".^29. 954
** of Steam- Engina and Batters 939
^ ** tfStoamers* Engines ^ii» 954
WBiasTC ^ steamers. Steamboats,
Engines, Boilers, Launches,
Tachts, Cutter, Pilot -Boat,
Sailing Vessels,and Dredgers,
888-895, 900
" ^f Substances in BtUk. 317
" ofSugar-MiUs 903,90s
'' of U.S. Coins 38
♦' ^Wire, Iron Z63-Z64
** onBoi^ 053
" on Structures per Sq. Foot. . . 84X
" Pipes, Steam, Gfas,and Water,
Standard Dimensions. Z38
" " Ca^-iron Z32-Z33
<( t( Iron and Copper ^Riveted Z48
u tt Lap-welded, Steam, Oas,
and Water Z38
" '* Lead and Tin... 1^7^ 150-X5Z
" *« Metal, To Compute... i47~i^S
" " Seamless Brass, to Corre-
spond vrith Iron Z42
*' Roman. 53
" Tubes,Lap-u>elded,Steel,Semi-
Steel, Special Locomotive,
and Boiler 138-139
*' " Charcoal Iron, Boiler Z39
" U. S. Old i£ New, Approximate,
EquivcUents, dt To Compute. 33, 36
" Water. 853
" Fiat, Square, and Hound Boil-
ed Iron and Steel Z85-138
Weirs, Ouaging of 922
WeldiDg. 786
'* Cast Steel, Composition for . . . 634
** or Soldering, Fluxes for 636
Well, Artesian. Z79, Z98
" Boring. Z97
Wells or Cisterns, ExcavaJtwn of eto. 63
Whales, Length and Weight of 918
Whkat, Yearly Consumption of..... 206
'* Straw and Bran, Relative V'^alue
of, Compared urith zoo Lbs.Hay 303
Whkkl and Axlk 626-627
^' and Pinio^ Combinations or
Complex wheel-work 627-628
*< Okarino, Elements of. 854-862
'^ General Illustrations of. 858
''"B^ofa Tooth, To Compute 86z
" PUch,Diameter,Number of Teeth,
Velocity, Circumference of. Rev-
olutions, eic. To Computo.. 855-858
'* Spur Gear. 9zz
Whsils, TtnOhexl, Proportions of... 863
" Depth, Pitch, Breadth, Propor-
tions,and Resistance to Stress,
To Compute 859-863
" Teeth, Elements of, To Compute,
859-863
Wbitelaw's Wheel 576
Whitewash or Grouting 594
Wind, Coum qf. 675
" ^ective Impulse of 665
" Force of. To Compute. 674
" Pressure of 9iz,zo35
*' Velocity and Pressure of, . .674, 934
xliv
INDBX.
Page
Winding Engines 476, 862-863
" Diameter of a Drum and RoU^
and Number of Revolutions,
To Compute 862-863
Windlass. 433
" Chinese, Elements of To Com-
pute 627
" Power of. 433
Windmills, Elements of^... .863^865, 924
*' Deductions arid Results of
from Experim^ents on Effect
and of Operation. . .864-865, 924
" Elements of To Compute 864
Wmdovf-G\asSfThickness and Weight 124
Wine and Spirit Measures. 45
Wire Gauge, French 123
" " Area of Circles by. 236
'' " Circumference of Circles by 242
" ^^for Galvanized Iron 123
'• '* Standard of Great Britain 122
" Gauges 122-123
' ' Iron. Gauge, Weight and Length
of. 163
WiRE^Lengths of 100 Pounds. 124
^^ Rope, Hbup, Iron, and Steel,
Dimensions, Safe Load, and
Strength of. 164
" Rope 161-162, 948
" '* and Equivalent Belt 167
" " Elem,ents of Standing and
Running 162
" " Rssults of an Eseperiment
with Galvanized. . . . z6i
tt t( u f^jr Experiments on, at
U. S. Navy- Yard 169
" " Rolling Friction of 473
* ' and Hemp Rope, Iron and Steel,
Relative Dimensions of. 172
*' and Hemp Ropes, Weight and
Strength of. 172
" and Tarred Hemp Rope, Haw-
sers, and Cables, Comparison
of 169
" and Hemp Ropes, General Notes 167
" " '* Weight of. 166
*' and TT. S. Navy Hemp Rope,
BreaJcing Weight of. 168
" Brass,Weight of ^ 155
" Cables, Galvanized Steel 163
*' Diam£ter and Weight of.,.. 1 20-1 21
" Fence, Weight and Strength of. 164
" Galvanized Iron 162-163
" Iron Chmge, Weight and Length 163
•' Rope, Circumference of with
Hemp Core ofCorrespond-
ing Strength to Hemp^
and of Hemp to Circum-
ference of Wire, To Com-
pute 169
" ^^ for Standing Rigging, Cir-
cumference of. To Compute. . . 172
'* Ropes Endless, Transmission of
Power of. 167
*' Shrouds 173
" Steel,Weightof 155
" Weight and Strength of 124
Pac«
Wises and Gables, Tdegraphic, Tele-
phone, Electric, etc 960
Wood, Elements, etc 48
^' Bituminous or Lignite. 479
' * EvaporcUive Power of. 482
'* Floor Beams. 835
" Measure 47
'' Pavem,ent 689-690
" Tensile Strength of 870
" Working Strength, or Factors
of Safety 781
Wood and Timber, Elements 0/. .865-870
(See also Timber and Wood^
865-870.)
" and Stone Sawing. 196
*' Creosoting, Effect of. 869
" Decrease by Seasoning 869
" Defects of. 866
" Impregnation of 868-869
" Jarrah 913
" Seasoning and Preserving,
866-868
" Selection of Standing Trees., 865
" Transverse Strength of Large,
To Compute 833
" Weight of Oak and Yellow
Pine per Cube Foot 870
Woods 765, 769, 780, 782-783, 986
" Absorption of Preserving Solu-
tion by. 869
" Coefficients for Safety. 781, 835
" Composition of 485
" Detrusive Strength of 782
' ' Durability of Various. 934, 969
*' Extension of by Water. 952
" Proportion of Water in 869
*' Relative Value of their Crush-
ing Strength and Stiffness
combined 769
" Safe Statical Loads for Beams. 834
" Strength of. 833, q86
" Weightsof. 33
" " and Comparative Values
of Various 484
Woolf Engine 722
Work, Animal Power 432, 440
" Accumulated in Moving Bodies. 619
" and Potoer, Metric 36, 923
Works of Magnitude, Miscellaneous,
178-179, 936
Wrought-Iron, Elements of . ...130-136,
639-640, 765, 768. 773, 780, 785-786
*' and Cast, Weight of. 155
" Angle and T, Weif/ht o/". 125, 130
'* Bolts, as Affeded by the
Thread 916
" " and Nuts, Dimensions
and Weights. . . . 156-159
" Corrosion of. 955
♦ ' Crushing "Weight of Columns 768
" Deflection of Bars, Beams,
Girders, etc. . . .773-77S
" " of Rails 775-776
" FUURoUed 126-128
INDEX.
xlv
Pag*
WHOuaHT-lRON of a Oi-oem Sec-
tional Area, Weight of,
136, 149
" Plates, Weight of a Sq.
Foot 146
" Plate* and BoUs, Strength
and Test of. 749
" " Thickness of. 121
" " Weight of. 118-110,146
*' JBope, Hemp, jnd Steel,
Strength and Safe Load
of 164-165
*^ Round Rolled. 126
** Sheet and Hoop, Thickness
and Weight of 129, 131
" Shell Plates, Pressure and
Thickness {U. S. Law). . . . 750
*' Square Rolled, and To Com-
pute Weight of. 125
*' Weight of To Compute 155
»* Wire, Weight of 120-121
Y. P«g«
Yachts, Steam, Relative Velocities^
fi'om EUments of their Constribc-
tion. To Compute 928
Yam, Ratio of Flesh-formers 207
Year, Biiseztile or ^Leap, Civil, Ec-
desiastical « . 70
" Solar 37i 70
Years of Coincidence, To Ascertain. • 74
Zenith aitd Mkridian Distances and
Altitude of Sun at New York 932
ZiMC, Elements of. 644
" Malleability of 644
" Plates, Weight of per Sq. Foot . . 146
" Sheets, Thickness and Weight of
123, 151
" Foil in Steam Boilers 912
Zones of a Circle, Areas of — 260-271
" " '* To Compute Area of . 271
ADDENDUM.
P«K*
Absorptive Power of Charcoal 986
Acetylene Formula 1036
Air., Dryness of. Dew- pointy and Hu-
midity, To Ascertain. 10x1-1013
Air Puxps. Of Condensing Steam
Engines 1041
Almanac, Perpetual loxs
Aluminum 976
Area of a Circle or Volume of a Cube,
Increase of, To Compute 988
Beams, Headers and Trimmers 1021
Bearings ufWunU Luinricants.,.,.. 974
Belt Driving 1038
Bi-sulphide of Carbon Engine, Rela-
tive Efficiency of and a Steam-En-
gine 982
Bi«AST AND Exhaust Fan Blowers. 1019
** Dimensions of Fan 1019
<* Loss of Pressure of Flow
of Air for Varying Di-
ameter of Pipe, etc..,, 1020
Blast Draught in a Marine Boiler., 974
Boiler Setting 976
BoUs in Slone, Anchorage of 974
Brass, Copper, etc.. To Color 97s
Cast Iron, Strength of. loiz
Cement, Portland and Cement Mor-
tar 983
Cement and Mortar, Rdative Hard-
ening in Fresh ami Salt Water, , 1035
Centrifugal Pump. Required Veloc-
ity of Edge of Blades, To Compute 953
Chimney, Height and Draught of
To Ascertain Z014
Coke and Coal, Ewyxtrative Pouter
of Z035
Columns, £to/e Crushing Strength of 10 iz
** Computations of 1022
Compass, to Graduate, a Tnmsit'
Theodilite 1023
P«g«
Compression op Air. Flow, Opera-
tion, Effect, Power of
Pressure, Temperature^
and Compression 994
" Volume, Mean Pressure and
Temperature of. 995-966
" To Compute J IP 997
** Friction of, in Long Pipes 997
" J^fficiency qf Engine of
Operation 997
" Loss of Head, To Compute 998
" Loss of Pressure per Mile
of Pipe 998
" Heating Compressed Air. , 999
" Loss of Efficiency 999
" Efficiency of Cooling 999
'* Air Receivers 1000
** Efficiency 2f Engines. 1000
" Adiabatic Expansion zooo
" " Compression, Z007-Z008
" Bardie Motor. Operation
of, and Mean Results.. . . zooo
•* Power required to Com-
press Air zooa
" J^low of Compressed Air
through Pipes zooz
»* Volume of Free Air Re-
auired in a Motor per
IIP per Minute Z002
•* Loss of Pressure by Fric-
ton in Pipes 1002, Z005
** Dimensions and Elements
of Air Compression Z003
" H* Required to Compress
one (htbe Foot of Air per
Minute, etc Z003
** Mean and Terminal Press-
ures of Compressed
Air Z003
** Heat procured by Com-
pression of Dry Air. . . . Z004
*^ Efficiency of an Engine, , , 1004
xlvi
INt>fiX.
JumtltfliQir OF Air. Work Lett
byHeatofOompretsion., zcx>4
" SteoM Preuure and Point
of Cutting offy To Com-
pute 1006
** Volumt ofOnePound of Dry
Air in Cube Feet, Weight
of etc.. To Compute, .... xoo6
" Sinjgle and Compound
Compreuion^ Compari-
ton of. 1006
" Mean Effective Prenuret
in Compreuing and De-
livering of Air. etc 1005
•* Work per Pound of Air in
Compretting i<, To Com-
pute. 1007
•• Stean. Pressure required in
the Steam Cylinder^ To
Compute X007-1008
" Weight of Air per MinuU
for a Oiven Amount of
Work, To Compufe. 1008-X009
** Isothermal Compreasion . Z007
** Dimenfions of Valves,
Pipes, and Clearance of
Air in Cylinders 1009
«< Compound Air Cylinder. . icx>7
** Work vfkich may be At-
tained in a Motor by One
Cube Foot of Stored Air,
To Compute 1009
CRUSHiNa andTransvkrsk Strength
and Coefficients of St^ety ;. 1022
Depths and Heights, Qreatest 983
Draught, Blast 1036
Earth, /iepofe of 982
Eddy Valve 975
Elbotrioal, Units in Klectrlcal
Engineering 987
" British Association. 988
Electrical H*, Cot< 0/ 983
Elevation of Localities in Upper
Mississippi, etc 982
EirsRaT AND Motion 989
Floor Biaks, ComputcUious of..,,, zo2z
Flume, To Compute Elements of..,, 984
Food Substances, Composition of,,, 34
FooTiNOB of Buildings • . . . • 1020
Foundations, Computation of Z022
'' Safe SUtic I^ad of. . Z040
Freestone, Broumstone, Tests of.., 982
Friction of Engines and Gearing. . , 976
Gas and Steam Engine, ComparUon
of 953
Oas Enqinbs 990-992
" " Results of Trials. . .991-992
** " Pressures produced by
Explosion ofOaseous
Mixtures. 992
Gate Valves 975
Geological Strata, Absorption (^.^7^101$
Girders and Floor Beama, Capacity
of 984
** Computations of , zo2z
Glue 976
Ground, Consolidaiion nf Loose •r
Made ...••...••••• Z037
Hand Brakes, Hffidencv qf. Z036
Heat, Coefficients of Radiation qf. . Z014
** Radiated per Sq. Ft per Hour 1014
" Relative Effmency qf Non-
conductor Z023
Heights and Depths, Greatest 983
Hydrants, Eddy 975
Hydraulics of a Fire-Engine Z035
Hydro-Geology 983
Iron and Steel, Effects of a lAno
Temperature Z035
Kiln Drying, Effects of, on Pine and
Hemlock Z037
Kinetics, Force and Mass. 989-990
Lightest Known Substance Z036
Lightning Conductors 907, 956
Liquid Fuel Z040
Long-leaf Pine. Effect of Tapping. , 985
Magnalium Z037
Magnesium 976
Marine Boiler, To Compute Weight
of 985
•* " Forced Draught in. zois
Masonry, Execution of, during Se-
vere Frost Z038
" Mortar for, below Freez-
ing-point 982
Maximlte 1037
Memoranda {additional),
974i 9761 979' 982-985. xo«4. »<»5
Metal Bearings, Lubncation of..,. Z038
Metric Measures, Reduction of. Z0Z3
Mill Race, Ratio between Surface
and Mean Velocity. Z036
Mines, Temperature in Z038
Monolith 982
Mortar, Portland and Cement, 983
Nails and Drift Bolts, Tenacity
of. 1038
** Cut and Wire, Tenacity of, . . 983
Oil Engines 1019
Oil or Tallow in a Steam Boiler,
Effects cf. lo- •
Paint, Estimate of (Quantity required 984
Pier, Computation of. 1022
Piers, Stress of etc 1020
Piles, Dimensions of xosc
Piling, Computation of. zob2
PtTMPS, ReUUive Efficiency of, and a
Siphon. X038
Railway, Highest, in Europe
INDBX.
xlvii
Pag*
Rlile, JIfiuxfe r«toe% </. 1036
RiTKTfl, Besitt€Mce o^to a Lap, . . • 1036
Ropes, To Comfmfo £p </. 979
Sand and Clay, SupporHng Power
fif 979
SAW^Effectof a Diamond-edged..,, Z036
Shaft 3b Compute B? </ 983
ShAMng, Nickel SteeL 986
Slates, JSBoq/Sn^. 979
Soath Point, To Determine^ by the
HandofaWatch 983
Spirally Riyeted Iron Pipes 977
SUiff. 976
Steam Boilers and Pipes, Insulation
of. ZO40
Stsam-Enoinks, Cylinder RaJtioe for
Compound and Triple. 1037
Steam-Launcb, Pirtt. 974
Steam-Power, Relative Cost of per
W xoa3
Stbam Vkssels. Resistance of., ,,, 10x4
Steel Springs, ^/«m«n<« q/*. 973
Stonks, TetUng of 1036
Stream of Water, To ComptUe EP
of 984
TireCement \ 10x3
To Determine the Eiist and Weal
Meridian. 988
Train Rksistahck, a New FomuUa 103^
Trees,^^<2^. 983
Vegetation, Absorption by. 34
Walls, Width of. ' loao
Water, Friction and Flow of, in
Smooth M^al Pipes and
Loss of Heady To Com-
pute X016
Friction and Flow of, in
Cast-iron Pipes xox6
Flow of,/rom a GivenHead,
To Compute 1016-ZOX7
Velocity of Flow, Dis^arge^
and Loss of Head due to
Friction of Flow j etc.^ To
Compute. X0X7
• Tests for. 983
Water Pipes of Cast Iron, Thickness
of To ComptUe 10x5
WiEs RoPB, Test of. ; 1037
Wrought Iron, Effect of Repeated
Stresson. ...*. zo^c
M
M
NoTS. — Tons are given and computed ak «a4o lbs.
Degree! of (emperatare are given by the scale of Fahrenheit
EXPLANATIONS OF CHAEACTBES AND SYMBOLS
Used in FormulaSj Computationa, etc.^ etc.
^ Equal to, signifies equality ; a» 12 inches = i foot, or 8 X 8 = 16 X 4.
+ PitUy or More, signifies addition ; as 4 + 6 + 5 = 15.
— Minus, or Less, signifies subtraction-, as 15 — 5 = 10.
X Multiplied by, or Into, signifies multiplication ^ as 8 X 9= 72. axd^
a.d,oT ad, also signify that a is to be multiplied by d.
-^ Divided by, signifies division ; as 72 -4- 9= 8.
'.hto,:: 80 is, : To, signifies Proportion, as a . 4 :: 8 : 16 ; that is, as 2 is
to 4, so is S to 16.
.*. signifies Therefore or Hence, and v Because.
Vinculimi, or Bar, signifies that numbers, etc., over which it is
placed, are to be taken together; as 8 — 2 + 6= 12, or 3 x 5 + 3 = 24-
. Decimal point, signifies, when prefixed to a number, that that number
has some power of 10 for its denominator ^ as .1 is j^ .15 is ^, etc.
CO Difference, signifies, when placed between two quantities, that their
diflference is to be taken, it being miknown which is greater.
V Radical sign, which, prefixed to any number or symbol, signifies that
square root 01 that number, etc., is required ; as V9^ or Va-\-h. The degree
of the root is indicated by number placed over the sign, which is termed
index of the root or radical; as / , v^, etc.
> T » < L signify Inequality, or greater, or less than, and are put between
two quantities ; as a 1 ^ reads a greater than h, and a Ij 6 reads a less than 6.
( ) [ ] Parentheses and Brackets signify that all figures, etc., within them
are to be operated upon as if they were oa^y one ; tiius, (3 + 2) x 5 = 25 ;
[8 — 2] X5 = 30-
± If signify that the formula is to be adapted to two distinct cases, as
c =f V ^ a, either diminished or increased by v. Here there are expressed
two values : first, the difference between c and v ; second, the smn of c and v.
In this and like expressions, the upper symbol takes preference of the lower.
poT irla used to express ratio of circumference of a circle to its diameter
= 3.1416; -i-p=.7854,and^p = .s236.
° ' " '" signify Degrees, Minutes, Seconds, and Thirds,
' " set superior to a figure or figures, signify, in denoting dimensions, F«ef
and Inches.
a' a" a'" signify & prime, a second, a third, etc.
z, 9, added to or set inferior to a symbol, reads sub j or sub 9, and is used
to designate corresponding values of the same dement, as h, hi, Ih, etc.
', 3, \ added or set superior to a number or symbol, signify that that num-
ber, etc., is to be squared, cubed, etc. ; thus, 4' means that 4 is to be multi-
plied by 4 ; 43, that it is to be ctAed, as 4^ =: 4 x 4 X 4 = 64. The pcnoer,
or numoer of times a number is to be multiplied by itself, is shown by the
nvmber iwided, as *, 3, ♦, s, etc.
22 ALGEBBAIC SYMBOLS AND FORMULAS.
", ^f etc., set superior to a number, signify square or cube root, etc., of the
number ; as 2* signifies square root of 2 ; also * * *, ', etc., set superior
to a number, signify two ttiirds power, etc., or cube root of square, or square
or cube root of 4th power, or cube root of sixth power ; as 8^ ^ "/P or
= (^8)'.
1-7, 3*6 etc., set superior to a number, signify tenth root of 17th power, etc
•03, 0:7, set superior to a number, signify hundredth root of 2d power, or
thousandth root of 59th power, the numerator indicating power to which
quantity is to be raised, and denominator indicating root which is to be ex-
tracted.
GO signifies Infinite, as - or a quantity greater than any assignable quan-
tity. Thus, - = oo signifies that o is contained in any finite quantity an in-
finite number of times : - = a. — = loa, etc.
cc signifies Vcaries as. Thus, M oc D x V signifies that mass of a body in-
creases or diminishes in same ratio as product of its density and volume, or
S oc <^, signifies S varies as t'.
^ signifies Angle, -l Perpendicular, A Triangle, D Square, as Q
inches; and' GO cube, as cube inches.
N0TB8.— Degrees of temperature used are those of Fahrenheit.
g is common expression for gravity = 32. 166, 2 j;r = 64. 33, V^ i7 = 8.09 feet.
)S signifies Detid Flat, denoting dimensions or greatest amidship section
of hull of a vessel.
breadth.
c
' u
chord,
h
((
h sub,
depth.
a
u
area,
sin.
i(
sine^
height.
r
it
radius,
9
it
graioiiy
ALGEBBAIC SYMBOLS AND PORMXTtAS.
I representing length, h' representing h pritne, v representing versed sine,
d
h "
l-\-h
-J- =. sum of length and breadth divided by depth.
lb
-j^ product of length and breadth divided by depth.
-^ = difiTerence of length and breadth divided by depth.
^ &3 = product of square of length and cube of breadth.
-^.-, = square root of length divided by cube root of breadth.
— ^ =: square root of sum of length and breadth divided by depth.
a
j/-^iJ = cube root of difference of h prime and h sub, divided by
square root of ag.
Va-|-(c— r)' = a;. Add square of difference between the chord and ra-
dius to the area, and extract the square root ; the result vrill be equal to x.
NoTK— It is fVeqaenUy advanta^pegiii to begin interpretation of a formula at its
right ban4, as in the above case.
ALGJCBSJUC SYMBOLS AND FOJEUtfULAS. 23
'n/^P^=
9, Divide flqnare of sum of x and y by square of y )
subtract wUty from quotient ; extract square root of result ; multiply it by
length, and product will be equal to z,
2 (sin 7K^)'
\ .' '^ '. Divide twice square of sine of the angle of 75° by square
i+(sm.75°)'
of sine of the angle of 75° added to uaity,
~4^^SV^(V&-v^A)+».303c.% 52^^ [==:<. Multiply
S by the V of 9g^ and this product by difference between square roots of k
and h prime; add this to 3.303 times common logarithm of quotient arising
from dividing product of S into Vagh diminished by b by product of S
into y/Ugh prime diminished by d, and midtiply this sum by the quotient
of 2a divided by square of product of S into v^2^ which will be equal to t.
2a + 3 COS. 98° = 2a — 3 COS. 82° ^ twice a diminished by three times
cosine of 82®.
Cosine of any angle greater than go^ and less than 370*^ Is always — or negative,
but IS nwnericaHy eqml to cosine of its supplement, i. e., remainder after subtract-
ing angle flrom 180°.
39.127 — .099 82 COS. 2 L = 2. Assuming L less than 45O as 42^^ this equation
becomes 39.137 — .09983 co& {2 X 430=84°) = ^; and also, L greater than 450, as
50°, It becomes 39. 137+099 83 cos. (180° — 3 X 50° = 80°) = I.
L — 10*^ N =: L -f- 10° S, as a negative result furnished by a formula in*
dicates a positive result in an opposite direction.
_(B-fe) p-f 2BV_^ Minus, the fraction B minus J, times », plus
B -f-6
2 times BV, divided by B plus 6, is equal to y.
Sin. ~* «, tan. ~' a?, cos. ~' «, signifies the arc, the sme, tangent or cosine
of which is «. Thus, if »=.s, this is 30^, as 30<» is the arc, the sine of
which is .5.
^ ' sin. a; o 0 * c^ r r
Raise r to nth power, i. c, multiply r by itself and this result by r, and so
on, until r appears in result as a factor, as many times as there are units
in n. Multiply this result by /, diminish this by I; divide remamder by r
raised to the nth power, diminished by r raised to a power whose exponent
ia n dimirdshed by i, and quotient = or is value of 8.
^/L:^r. Divide I by a and extract that roet of the quotient, index
of which is n duninished by i, and this root ia =; or value of r.
Logarithm of a Number is exponent of the power to which a particujal
constant quantity must be raised in order to produce that number.
Corutani Quaniity is termed the base of the system.
Cbmmon (or Brigg't) Log. is the logarithm the base of which is la
HfipeiMic Log, is the logarithm the base of which is 2.718 2&
Com, Log, = Hyp. log. X -434 394*
Mffp, Log,^Cwu\Qg. X 2.302 585053 994, o'dinwily a-303 or 2.309^
24 DIFFEBBNTIAL AND INTSGBAL CALCULUS.
Illttstratiox.— When a number, hyp. log. of which = a given figure or numbes
is required.
M ultiply figure or number (hyp. log. ) by . 434 394 (dmkIuIus of com. log. ) = com. log.
of figure.
Thus, Required the number, hyp. log. of which = .03. .03 X . 434 394 = .00 868 588,
com. log., and 1.020a = number.
Log. ioo-°»=.o59 X log. of 100 = .059 X 3 = .118; the number corresponding to
log. .n8, is X.3ZS3; bence, ioo°S9= 1.3122. That is, if 100 is raised to 59th power,
and the zoooth root is extracted, the result will be 1.3x33.
DifTerexxtial axxd Integ;ral Caloulus. — In Equation, u= 2^" -"
2 x, u is termed a function of x. If it is desired to indicate the fact that u
thus depends for its value upon value of a;, without expressing exact value
of tt in terms oi a;, following notation is used :
U =f (X), U=.F(x)y OTU=.<f> (x).
Each of these notations is read, k is a function of x. If in such function
of X value of x is assumed to commence with o and to increase uniformly, the
notation indicating rate of increase is dx, and is read *' the differential of x."
Differentiation, d is its symbol, and it is the process of ascertaining the
ratio existing between the rate of increase or decrease of a function of a
variable and the rate of increase or decrease of the variable itself. If
y^3a5*,y or its equal 3a:' is the function of x, and x is the independent
variable, while the exponent of the variable or the primitive exponent is 2.
B^ the operation 01 Calculus, such expressions are differentiated by di-
minishing toe exponent of the variable by unity, multiplying by the prim-
itive exponent, and attaching the dx.
Hence, c{y = 2 x 3xdx=:^6xdx, This indicates the relation between
the differential of ^, the function of x, and the differential of x itself.
Assume that x increasing at rate of 3 per second becomes 4 ; that is, a; = 4,
and d a; ^ 3 ; hence dy = 6 x 4 X 3 = 72. That is, if x is increasing at
rate of 3 per second, at the time that x := 4, the function itself is increasing
at rate of 72 per second.
To differentiate an expression of two or more terms, it is necessary to
differentiate them separately and connect the results with the signs with
which the terms are connected.
Thus, differentiating u =3 a:^ — 2 X, we have dM = d (3ar* — 2x) ^6xdx
— 2dx:=(6x — 2) dx.
Assuming x=4 and dx^^ we have <iM=:(6x4 — 2) x 3=66. This
indicates that when x = 4, and is increasing at rate of 3 per second, the func-
tion u, or 3 x' — 2 X, is at same instant increasing at rate of 66 per second.
Integration, Its symbol / was originally letter S, initial of mm, the
symbol of an operation the reverse of differentiation ; and when the oper-
ation of integration is to be performed twice, thrice, or more times, it is
written//, ///,etc
By the operation of Calculus, expressions are integrated by increasing the
exponent of the variable by unity, dividing by the new exponent, and de«
tacning thedx.
Hence, integrating the differential 6 x d x, we have f6xdx:=$x'. This
result is the ninction, the differential of which is 6x e^x.
To integrate an expression of two or more terms, it is necessarv to inte*
grate the terms separately and connect the results with tiie signs with which
the terms are connected.
Thus, integrating (6x— 2) <ix, we have /(6x— 2) dx=: f(6xdx—2dx)
= 3a:' — 2X. This result is the function the differential of which is (620
— 2) dx or (6x — 2 x°) dx.
Non.— A quantity with the exponent o, as «<> or 30, is equal to unity.
NOTATION. 25
The operation of summation may also be illustrated in use of the sym-
bol /. Assuming 07 = 4, the former of the preceding results becomes
/6a;dx = 3ar'^48, the latter /(6x — 2) dxzrjor* — 2a?:=4a
Here x is assumed to commence at o and to continue to increase by in-
finitely small increments of dx until it becomes 4. The summation is the
addition of all these values of x from o 10 4.
Arithmetically. — The first formula may be written
6 {x + x" -\- x'" -H etc.) d X, If then a: is to advance from o to 4 by in-
crements of I, we have 6 (0-1-1 + 2 + 3 + 4) X 1=60, which exceeds 48.
If dx is assumed to be .5, the result is 54. The correct result is obtained
only when dxia taken infinitely small. By Arithmetic this is approximated,
but it is reached by the operations of Calculus alone.
The second formula may be written
(6 [x' + x" + ic"' + etc.] - 2 lx°' -j- a;°" + a;°'" etc.] ) dx. Assuming x =
4, and da? = I, we have (6 [i + 2 + 3 + 4J — 2 [i + i + 1 + i] ) x i = 52,
which exceeds 40. ltdx=: .25, the result would be 43, and if .125 it would
be 41.5, ever approaching but never reaching 40, so long as a finite value is
assigned to dx.
A, DeUay when put before a quantity, signifies an absolute and finite in-
crement of that quantity, and not simply the rate of increase.
S, Sigmct, signifies the summation of finite differences or quantities. Thus,
Xy^ Ax= (y'^ + y "' + y""" + etc.) A x. Assume y = 6, y" = 8, y" = 4, and
A X the common mcrement of a; =: 5, then 2y* A a; ^ (36 + 64 + 16) X 5 =
580.
NOTATION.
1=1.
20 = XX.
1 000 = M, or CIO.
3 = 11.
30^ XXX.
2 000 = MM.
3 = 1".
40 = XL.
5 000 = V, or 100.
4=IV.
50 = L.
6ooo = VI.
5 = V.
6o = LX.
ioooo = X,orCCIOO.
6 = VI.
70 ^^ LXX.
50 000 = L, or 1000.
7 = VII.
8o=LXXX.
60 000 = LX.
8 = VUI.
9o=XC.
100 000 _ C, or CCCIOOO.
9 = IX.
100 = C.
I cx)o 000 = M, or CCCCIOOOO.
10 = X.
500 =D, or 10.
2 000 000 — MM.
As often as a character is repeated, so many times is its value repeated,
lis CC = 2CO.
A less character before a greater diminishes its value, as IV= V — I.
A less character after ft greater increases its value, as XI =: X + 1.
For every 0 annexed to 10 the sum as 500 is increased 10 times.
If C is placed on left side of I as many times as 0 is on the right, the
number is doubled.
A bar, thus , over any number, increases it 1000 times.
lUuttration i.— 1880, MDCCCLXXX. 18 560, XVIITDLX.
2. — 10 = 500. CIO =: 500 X 2 = 1000. 100 = 500 X 10 = 500a
CCI00 = 5oooX2=ioooo. 1000 = 500x10x10=50000. CCCIOOO
^ 50000 X 2 = lOOOOO.
26 CHBOXOLOGICAIi SBAS. — ^ICBASUBES AND WEIGHTS.
CHRONOLOGICAL ERAS AND CYCLflS FOR 1906.
Vhe year 1906, or the lyoth year of the Independence of fht United States of America,
ccrre$pond» to
Tht year 7414-15 of the Byzantine Era;
*i 6619 of the Julian Period;
** 5666-67 of the Jewish Era;
** 2071 of the Olympiads, or the second year of the 67181 Olympiad, com-
mencing in July (1802), the era of the Olympiads being placed at
775.5 years before Christ, or near the beginning of July of the
3938th year of the Julian Period ;
** 2659 since Uie foundation of Rome, according to Varro;
** 2218 of the Grecian Era, or the Era of the Seleucidas;
" 1622 of the Era of Diocletian.
The year 1323-24 of the Mohammedan Era, or the Era of the Hegira, begins on
the 26th of July, 1906.
The first day of January of the year 1906 is the 2,412,115th day since the eom-
mencement of the Julian Period.
Dominical Letter G I Lunar Cycle or Golden Number 7
Epact 5 1 Solar Cycle 11
Roman Indiction 3. was a period of 15 years, in use by the Romans. The precise
time of its adoption is not known beyond the flict that the year 313 A.D. was a first
year of a Cycle of Indiction.
Julian Period is a cycle of 7980 years, product of the Lunar and Solar Cycles and
the Indiction, and it commences at 4714 years B.C.
6513 -|- (given year — 1800) = year of Julian Period, extending to 3267.
MEASURES OP LENGTH.
Standard of measure is a brass scale 82 inches in length, and the
yard is measured between the 27th and 63d inches of it, which, at tem-
perature of 62°, is standard yard.
Inches. Feet. Tarda. Rods. Furl.
36= 3-
198= 16.5= 5.5.
7920= 660 = 220 = 40.
63360 = 5280 =1760 :=320=.3.
Xiineal.
12 inches ^i foot.
3 feet s= I yard.
5.5 yards := i rod.
40 rods := I furlong.
8 furlongs^ I mile.
Inch is sometimes divided into 3 harleycomg, or 12 linet.
A hair^s breadth is .02083 (48th part) of an inch.
I yard =.000 568, and i inch = .000015 8 of a mile.
Grunter's Oliaixi.
7.92 inches ^ i link. | 100 links := i chain, 4 rods, or aa yards.
80 chains = i mile.
I^opes and Cables.
I fithom = 6 feet. | i cable's length = lao fathoms.
Gtooorapliioal and IN'autioal.
I degree, assuming the Equatorial radius at 6967 459.893 yards (3958.784
mUea), as given by IT. S. Coast Survey, =: 69.094 Statute miles.
X mile ^2026.7566 yards or 6080.27 feet
X leai^e = 3 Nautical miles.
HBABUKBS AND WBIGBTB.
2;
Hiog Hiixies.
Estimating a mile at 6080.27 feet, and using a 30" glass,
I knot ^ 50 feet 8.03 inches. | i fathom = 5 feet .08 inch.
If a 28" glass is used, and 8 divisions, then
I knot ^ 47 feet 5 inches. | i fathom ^5 feet 11.25 inches.
The line should be about 150 fathoms long, having 10 fathoms between chip and
first knot for stray line.
NoTB. — This estimate of a mile or knot is that of U. S. Coast Sarvey, assuming
Equatorial radius of Earth to be 6967459.893 yards and a Met-er to be 39-370433
inches of the Troughton scale at 62°.
Clotli.
I nail = 3.25 inches. | i quarter = 4 nails. | 5 quarters := i eU.
FendoalTiin.
6 points ^ I line* | 12 lines = i inch.
Slioeixiakers'.
No. 1 is 4.125 inches, and every succeeding number is .333 of an inch.
There are 28 numbers or divisions, in two series or numbers — viz., from i
to 13, and I to 15.
M!isoellaiieous.
12 lines or 72 points := i inch.
I palm = 3 inches.
I hand := 4 inches.
I span =9 inches.
I cubit = 18 inches.
"Vernier Scale.
Vernier Scale is f^, divided into 10 equal parts ; so that it divides a scale
of loths into looths when two lines of the two scales meet.
M:etrio, T^y ^ct of Congress of Jiily S8, 1866.
Vnit of MeasurevMtU is the Meter, which by this Act is declared to be 39.37 ins.
DanomioMioDs.
Millimeter. .
Centimeter.
Decimeter. .
Meter
Dekameter .
Hektameter
Kilometer..,
Uyriameter
Meters.
.001
.ox
.X
X.
10.
xoo.
looa
xoooo.
Inches.
•0394
•3937
3-937
39-37
393-7
Feet.
.328083
3-28083
32.80833
328.083 33
328a 833 33
Yards.
1.093 61
xa936xx
109.361 IX
1093.6x1 XX
Miles.
.62137
6.2137
In Mbtkic system, valaes of the base of each measure^viz., Meter, Liter, Stere,
Are, and Gramme— are decreased or increased by following prefix. Thas,
Milli, xoooth part or .oox.
Cent!, xooth *
.ox.
Deci, lotb part or . i.
Deka, 10 times valae.
Myria, xoooo times value.
Hekto, xoo times value.
Kilo, 1000 "
NoTB.— The Meter, as adopted by England, France, Belgium, Prussia, and Russia,
is that determined by Capt A. R Clarke, R.E., F.R.S., x866, which at 32^^ in terms
of Imperial standard at 62° F. is 39*370432 inches or X.0Q362311 yards, its legal
equivalent by Metric Act of 1864 being 39.3708 inches^ the same as adopted im
France.
Captain Kater^s comparison, and the one formerly adopted by the U. S. Ordnance
Corps, was = 39.3707971 inches, or 3. 280 899 76 /ee^ and the one adopted by the
U & coast Survey, as above noted, is = 39-37° 43' 35 inches.
28
MEASURES AND WEIGHTS.
E: 0.1x1 valent Values in DVHetrio Denoxxiinations of* XJ. St
DenominatioiM.
Vklue in Meters.
DenominatioBi.
Valaea in Meters.
Inch
•'^54 ^
.3048006
.914401 8
Rod
5.0202099
201.168396
1609.347 168
Foot
Furlong
Yard
Mile
I Furlong . . . := 200 "
5 Furlongs . . . = i kilometer*
^Approximate ISq.xiivalen.ts of Old and. Aletrio U. S*
.^dCeasures of* J-jengtli.
I Kilometer . . . . = .625 mile. i Chain = 20 meters,
I Mile = 1.6 kilometers,
I Pole or Perch . = 5 meters.
I Foot =: 3 decimeters or 30 centimeters,
I Metre :=3.28o833ycc<=:3y*w^ 3 ins, and 3 eighths.
II Meters ^12 yards, \ i Decimeter ... =4 inches,
1 Millimeter . . ^ i thirty-second of an inch.
To Convert Meters into Ittches. — Multiply by 40; and to Convert Inches
into Meters. — Divide by 40.
Approximate rule for Converting Meters or partSj into Yards, — Add one
eleventh or .o^b9.
Inches Decimally = Millimeters,
Milli-
meters.
Milli-
Milli-
Milli-
Milli-
Inches.
meters.
Inches.
meters.
Inches.
meters.
12.2
Inches.
meten.
Inches.
.01
.25
.2
5.08
.48
•7$
19. 3
2
.02
•51
.22
5-59
•5
12.7
.78
19.8
3
•03
.76
^
6.1
•52
13.2
.8
20.3
4
.04
1.02
.26
6.6
•54
>3-7
.82
20.8
5
•05
1.27
.28
7.11
.56
14.2
.84
21.3
6
.06
1-52
•3
7.62
.58
14.7
.86
21.8
7
.07
1.78
•32
8.13
.6
15-2
.88
22.4
8
.08
2.03
•31
8.64
.62
15-7
•9
22.9
9
.09
2.29
•3S
9.14
.64
16.3
.92
234
10
.1
2.54
.38
965
.66
16.8
•94
239
IX
.12
305
•4
10.2
.68
>7-3
.96
24.4
12
^i
356
•42
ia7
•7
17.8
.98
24.9
m I
.16
4.06
•44
II. 2
•72
18.3
I.
25-4
.x8
4-57
.46
11.7
•74
18.8
50.8
76.2
XOI.6
127
152.4
177.8
203.2
228.6
254
2794
304.8
foot
Inches
in Fractions =
Millimeters.
4
■2
•a
u
^l
I
sic
9
•a
^1
as
•
"1
H
17
if
■a
^1
•79
9
7.14
135
I
3
1.59
2.38
5
II
7-94
8.73
9
>9
'4-3
15- 1
13
I
■"
5
3-17
3-97
3
"
13
952
10.32
5
^""*
21
iS-9
16.7
7
^^
3
7
4.76
5.56
7
15
II. II
11.91
II
23
I7-5
18.3
15
9
—
—
6.35
4
—
—
127
6
—
—
19
8
—
• J
.
h
25
19.8
—
20.6
27
21.4
—
22.2
29
'^0
—
23.8
3«
24.6
—
25-4
By means of preceding tables equivalent values of inches and millimeters,
equivalent values of inches in centimeters, decimeters, and meters, may be
ascertained by altering position of decimal point
Illustration.*— Take i millimeter, and remove decimal point successively by one
figure to the right; the values of a centimeter, decimeter, and meter become
In. Ins.
X millimeter 0394 I x decimeter 3-94 i '32 inch = 8.13 millimetera
X centimeter 394 1 1 meter 39.4 | 3.2 inches = 81.3
(i
MSASUBES AND WEIGHTS.
29
MEASUBES OV SUBFACB.
144 square inches ^ i square foot. | 9 square feet =: i square yard.
Architect's Measure^ loo square feet ^ i square.
Xjaxid.
30.25 square yards = i square rod.
40 square rods =: i square rood.
4 square roods }_jacre
10 square chains j
640 acres = i square mile.
Yards.
I2IO.
RodB.
Roods.
4840 = 160.
3097600=102400 = 2560.
43 560 square feet, or 208.7x0326 feet square, or 220 x 198 feet = i Acre.
Faper.
14 sheets = I quire. | 20 quires^ i ream. | 21,5 quires = i printer's ream.
2 reams = I buudle. | 5 bundles ^ i bale.
Dra-wing.
Cap 13 X 17 inches.
Universal 14 X 17
Demy 15 x 20
Medium 17 x 22
Royal 19 X 24
Super-royal .... 19 x 27
Imperial 22 x 30
Elephant 23 X 28
(1
u
u
tc
t(
((
((
Columbier 23 x 34 inches.
Atlas 26 X 34
Theorem 28 X 34
Doub. Elephant. 27 X 40
Antiquarian ... 31 X 53
Emperor 40 X 60
Uncle Sam .... 48 X 120
Peerless 18 X 52
Double Crown 20 x 30 inches.
Double D. Crown . . 30 X 40 "
Double D. D. Crown, 40 x 60
T'racin.g.
Grand Royal 18 x 24 inches
Grand Aigle 27 x 40 "
Vellum Writing, iB to 28 ins. in width
Mounted on cloth, 38 ins. in width.
Afiscellaneous.
I sheet ^ 4 pages.
I quarto = 8
I octavo := 16
4(
I duodecimo = 24 pages.
I eighteemno := 36 "
I bundle =: 2 reams.
I piece wall-paper, 20 ins. by 12 yards.
I " " " French, 4.5 sq. yards.
Boll of Parchment =: 60 sheets.
Copying.
100 Words = I Folio.
metric, by Act of* Congress of July S8, 1866.
Unit of Surface is Are or Square Dekameter.
A square meter (39-37') = ' 549- 99^9 ^' ^^^^ ^^^ ^y ^his Act is declared to be
1 550 sq. ins.
Denominationt.
Centimeter ...
Decimeter ....
Centareor
Square Meter
Are.
Hectare.. f ...
g • • • •
Sq. Meters.
.oooz
.oz
z.
zoa
lOOOO.
Sq. Inches.
•'55
15-50
1550.
Sq. Feet.
.Z07638
za 763 888
ZO76.38888
Sq. Yards.
Z.Z96
ZZ9.6
ZZ960.
Acres.
.02471
2.471
30
MJfiASUBES AND WEIGHTS.
Ejq.iilvalent Values in I^etrio Denominations of TJ. S.
DenomiDationi.
Sq. luch .
" Foot.
" Yard.
" Rod .
Sq. Meter*.
.00064516
.09290323
.836 12907
25.292904
DenomiDationt.
Sq.
Chain . . .
it
Rood
((
Acre ....
((
Mile
Sq. Maten.
404.68647
1011.716175
4046.864699
Sq. Hectares.
.404686
258.99934
Sq. Ares.
4.046 865
10. 1 17 162
40.468647
25899-934074
.A.pproxixnate Equivalents of* Old and Aletrio U. S.
iSq.uare Aleasures.
6. 5 square centimeters =s i sq. inch. I i acre = 1.16 per cent over 4000 tq. meten.
I '•'■ meter =iio.'jssq.fBet\ x square mile = 259 Atfctor^x.
MEASURES OP VOLUME.
Standard gallon measures 231 cube ins., and contains 8.3388822
avoirdupois pounds, or 58 373 Troy grains of distilled water, at temper-
ature of its maximum density (39.1°), barometer at 30 ins.
Standard bushel is the Winchester^ which contains 2150.42 cube ins.,
or 77.627 413 lbs. avoirdupois of distilled water at its maximum density.
hts dimensions are 18.5 ins. diameter inside, 19.5 ins. outside, and 8
ins. deep ; and when heaped, the cone must not be less than 6 ins. high,
equal 2747.715 cube ins. for a true cone.
A struck bushel contains 1.24445 cube feet.
Xjiqnid..
4 gills ^ I pint.
8 pints ^ I quart
4 quarts = i gallon.
I>ry.
a pints
4 quarts
3 gallons
4 pecks
quart
I gallon.
I peck.
I DusheL
Cube Ins.
28.875
57-75
231.
Cube Int.
67.2006
268.8025
537.605
2150.42
Ollla. Plata.
8.
32 = 8.
Pinto. Qomrte. G«lk.
8.
16= 8.
64 = 32 = 8.
Cu"be,
1728 cube inches = i foot I inches.
27 cube feet ^ i yard. J 46656
KoTX.— A cube foot contains 2200 cylindrical inches, or 3300 spherical inchea
iriuid.
60 minims
8 drams
16 ounces
I dram.
I ounce.
I pint
8 pints ^ I gallon.
Minims.
480.
7680=128.
61 240 = 1024
Dnuna. Ooiioaai
= 128.
IN'autioal.
X ton displacement in salt water =35 cube feet
((
(i
««
registered internal capacity ^40
Dimensions of a Sarrel.
Diameter of head, 17 las. ; bung; 19 ina ; length, 28 ina ; volume, 7689 cube Uuk
: 3.5756 bushela
MBASUQBS AND WBIOETS*
31
Misoellaneou*.
I cube foot 74S05 gallons.
I bushel Q'JOQ 18 ^alloni,
I chaldron = 316 biuhels, or 57-244 cube feet
I cord of wood 128 cube feet.
I perch of stone 24.75 cube feet.
I quarter = 8 bushels. | i load hay or straw s= 36 trusses.
OtlU.
I Barrel 38
I Tierce ^. 4a
Butt of Sherry. 35X 50. . . . 108
Pipe of Port 34X58.... 115
Pipe of Teneriffe 100
Butt of Malaga. 33X53. . * • 105
GalU.
Puncheon of Scotch Whisky, .xxo to 130
Puncheon of Brandy 34X53.. ixo to x2o
Puncheon of Rum xoo to xio
Hogshead of Brandy 28X40.. 55(0 60
Pipe of Madeira 9a
Hogshead of Claret 46
A Hogshead is one half, a Quarter ca^ is one fourth, and an Octave is one eighth
of a Pipe, Butt, or Puncheon.
Mietric, by -A.ot of Congress of Jiily 38, 1©66.
Unit or Base of Measurement is a cube Decimeter or Liter, which is declared to be
61.033 eulbt inf.
Oube IMeasures.
DenotninatfoM. Value*. Cab« Inche*. Cube Feet. ' Cube Yards.
Cube Centimeter
" Decimeter.
"* Meter
.001 cube milliliter
X cube liter
Kiloliteror stere..
.061 022
6x.022
•035313657
35-3«3657
Dry MieasTires,
Donominatione.
Milliliter
Centiliter
"Deciliter
Liter
Dekaliter
Hektoliter....
Kiloliter \
or Stere j ••*
Valnee.
X cube centimeter.
xo
X
xo
t(
i(
tt
«(
decimeter. .
* .
meter
(I
Cube Ins.
Quarts.
Pecks.
Bushels.
.061
__
.^^
^.^
.6x03
-.
..
—
6.I023
..
..
—
61.032
.908*
•"35
—
—
9.08
i'>35
•28375
—
—
"•35
2837 5t
—
—
—
38.375
X.308
Cube Yards.
.1308
x.308
• Or .337 ^Jkm, t 3«53i 3^5 7 ctAefut.
None. —In practice, terra cube Centimeter, abbreviated to cc, is used instead of
Milliliter, and cube Meier instead of Kilometer.
Sqixivaletxt Values in. Afetrio Denoxninatioxis of XJ. S.
Dry nVfeasures.
Denominations.
CmUUtsrs.
DsciUtsrs.
Liters.
DsksUtors.
Inch ,
•3524
.xxoxa5
.4405
.881
3524
X. 10x35
4405
8.81
3524
Pint
Quart
IX 0x35
Gallon
Peck
Bariiel
352-4
XiiquicL IVXeasures.
Dwomlaatloiis.
MiUiliter
Centiliter
Dariliter.
Lii- •
Oekaliter
Hektotlter
Kiloliter )
or Store/ "••••
Liters.
Drams.
Ounces.
.oox
.37
___
.ox
3.7
•338
.1
"7 ;
3.3*
I
^ I
33.8
10
—
WiW
xoo
—
—
xooo
—
—
PlBta.
Quarts.
Gallons.
' _
..
__
^
—
—m
.8X134
a.xx34
ax.X34
X.0567
XO.567
.864X7
a. 641 7
36.4x7
—
—
364. X7
32
MEASUBES AND WEIGHTS.
A.pproxixnate SquivalentB of Old. and "NLetrio TJ. S.
!N£ea8U,re8 of* Voliuxie.
z Gallon =4-5 liters-
I Liter = .26 gallon.
I cube foot =28.3 liten.
I cube meter = x.33 cube yards
«c
yard.
= .75
ii
meter.
kiloliter = 2240 lbs. nearly of water.
MEASURES OP WEIGHT.
Standard avoirdupois pound is weight of 27.7015 cube inches of die
tilled water weighed in air, at (39.83^) barometer at 30 inches.
A cube inch of such water weighs 252.6937 grains.
Avoirdupois.
16 drams = i ounce.
16 ounces = i pound.
112 pounds = I cwt.
20 cwt. ^ I ton.
OonoM. Poandu
Drams.
256.
28 672 = I 792.
573 440 = 35 840 = 2a4a
I pound = 14 oz. II dwts. 16 grs, Troy, or 7000 grains,
I ounce := 18 dwts. 5.5 grains Troy, or 437.5 grains,
I dram = i dwt, 3.343 75 grains Troy, or 53.5 grains.
I stone := 14 pounds.
Dwt.
I
I
20 grams
3 scruples
8 drams
12 ounces
45 drops
Troy.
Orafna.
480.
5760 = 2401
= I lb. avoirdupois.
= I oz. "
= I dram "
= 144 lbs. "
= 192 oz.
=1480 grs.
:= .822 857 lb.
avoirdupois pound = 1.2x5 278 lbs. Troy,
Apotlieoaries.
=: I scruple. Grains. Scniplst. Drwn.
:= I dram. 60.
= I ounce. 480 = 24.
5760 = 288 = 96.
24 grains =: i dwt.
ao dwt. =: I ounce.
12 ounces ^ i pounds
7009 Troy grains
437.S " "
27-343 75 Troy grains
175 Troy pounds
175 " ounces
I " ounce
pound
u
ti
t(
= I pound.
= 1 teaspoonful or a fluid dram.
2 tablespoonfuls =: i ounce.
The pound, ounce, and grain are the same as in Troy weight
IDiaznoxid.
I grain = 16 parts. | 4 grains = 3.2 Troy gnum.
16 parts = .8 iroygrain.! i carat =4graiQ8.
1 50 carats := i Troy ounce.
Xjead.
A Fodder of lead = 8 pigs.
Sheet lead rolls = 6.5 to 7.5 feet in width and from 30 to 35 feet in lengtfs
Grrain.
Standard "Weiglits por Bushel.
LW. I Lbi. I
Wheat.... 60 I Com £6 and 58 I Rye..
Ltw.
56 I Oats.
Lbs. I Lb»
32 I Barley.... 48
HBASUKBS AND WEIGHTS.
33
^Ciscellaneous.
3?er Cu."be Tf"oot ii\ Sulk and.
For additional f see page 217.
Mats RIALS.
per
a?o
11.
t(
u
u
u
u
u
Coal, Anthracite ,
Bituminous
Cannel ,
Cumberland ....
Newcastle
Scotch
Welsh
li. N. allowance.
Charcoal, hardwooil. . ,
" pine
Clay, loose
Coke, Newcastle
Gravel, coarse
" fine
Marl, loose
.Sand, river.
Wood, Virginia pine. .
Southern
u
PeT Cube Foot.
In Lbs.
Cub« Feet.
In Tons.
50 to 55
41 to 45
44 " 50
45 " 51
■50-3
44.5
42.2
53.8
50
45
52
43
52
46.6
18.5
43
48
121.8
18
80
124.4
28
23 to 28
80 to 97.4
97
23
109
80
20.5
28
107
21
21
26
107
86
NoTB.— ThcM weights are eonuncrcial, not cooiputed from the specific grHvity of the material.
Mietric, by A.ot of* Congress of July S8, 1866.
Unit of Weight is the Gram, which is weight of one cube centimeter of pure water
weighed in vacuo at temperature of 4^ C, or 39.3O F., which is about its tem-
perature of maximum density = 15.432 grains.
Valoea. Orains. Dances. Lba. Ton.
]>eaoiniaationa.
Milligram
Centigram
I>ecigram
Gram
Pekagram
Hektogram
Kilogram or Kilo . .
Myriagram
Qu'ntal
M iliier or Tonneau .
cube millimeter
(I
I
10
.1
I
10
I deciliter . . .
I liter
10 "
I hektoliter. .
X cube meter
centimeter
Grains.
Dances.
__
, .
15432
—
1-543 2
—
15-432
.03527
—
•3527
—
3527
■~.
35-27
_-
_
Kilogram = 2.679 17 lbs. Troy, or 2 U>s. 8 oz. 3 dwts.
.23046
2.2046
22.046
220.46
2204.6
3072 grain.
.098419
.984 196
£lQ.uivalen.t Valuea in 3V£etrio l^enomiiiatioiis of TJ. S.
Denominalions.
Grain
Scruple
Pennyweight
JDrachm
" (Apoth.)
Grams.
.0648
1.296
1-555 2
1. 771 87
3.888
DckafH'ama.
17.7187
38.88
Denominations.
Ounce
'* Troy
Pound
Ton
Troy
Grams.
28.3502
31.1041
453.6028
3732504
Kllofrrams.
.02835
.03x1
•4536
•37325
1016.057 28
A.pproxitnate Equivalents of Old and Ne-v^r XJ, S.
]M[eaeiitr<>s of WeiprKt.
The ton and the grsLxn are at nearly equal distances above and below the
kilogram. Thus,
I ton ....== 1 016057.28 grams. | i kilogram = 1000 grams.
I gniin is nearly 15.5 grains (about .5 per cent. less).
I kilogram about 2.2 pounds avoirdupois (about .25 per cent. more).
1000 kilograms, or a metric ton, nearly i £ngL ton (about 1.5 per cent, less)
MBASDKES AND W BIO UTS.
Abvorption by V«efltatioii.
tify VonnanpHm of Water bg Vigetatim.
C^.
iBcWofW.ur.
''^ Jm^
.'™.'
';!
■^4
{M.l
Si;™.-;:::::: ■
Lu<:en,go.Bs
*Jt:;
r«.
VyJl;
B^SS"!?'::;
"^5
FBcnL
9"
"^Ts
Bo tier.
Bultermllk. ,
= '
Kunwii:::::
'V
no» Kood
SHba
unoes
tlE:- 1 '-■
m',^
*!J^":::::
■9 5
,*"
M*
Oatmeal
BirlaymeaL.
5.>6
66. 7J
&S« do.
<6
fJC™w,M,.«
K welfe'hla have been fixed by alatnle in nisiiv of tlic Slatesj and
rtiese wnghts govern in buying and BeDing, luileas a specific ajjrcemcnt te
the contcuy luia been nmde.
Pounds 111 a Bushel.
HKASUBBS AND WBIOBTS.
35
'Weislit of Mieix and "Women.
Average weight of 20000 men and women, weighed in Boston, 1864, was
— men, 141.5 lbs.; women, 124.5 lbs. Average of men, women, and chil-
dren, 105.5 1^8. A mass of people, densely packed, weighs 85 lbs. per sq. foot,
each occupying .8 of one sq. foot of area':= 54 450 per acre.
Weight of Horses.-CXJ. S.)
Weight of horses ranges from 800 to 1200 lbs.
WEIGHT OF CATTLE.
To Compute Dressed TVeiglit of Cattle.
Rule. — Measure (is follows in feet:
1. Girth close behind shoulderB, that is, over crop and under plate,
imroediately behind elbow.
2. Length from point between neck and body, or vertically above
junction of cervical and dorsal processes of spine, along back to bone at
tail, and in a vertical line with rump.
Then multiply square of girth in feet by length, and multiply product
by factors in following table, and quotient will give dressed weight of
quarters.
Condition.
Haifer, StMr,
or Ballock.
BuU.
Condition.
H«lfer, St«6r,
or Bullock.
Ball.
Half fat
336
3 5
3-36
3-5
3.64
Very prime fat . . .
Extra fat
364
3.78
3-83
4.06
Moderate fat
Prime Ikt
Illustration.— Girth of a prime fat bullock is 7 feet 2 ins., and length measured
as above 4 feet 5 ina*
7'. a" = 7. 17, and 7.17'=^ 51.4, which x 4' 5" and by 3- 5 = 794- 5 *«• Exact
weight was 799 lbs.
NoTS.~i. Quarters of a beef exceed by a little, half weight of living animal
3: Hide weighs about eighteenth part, and tallow twelfth part of animal.
Comparative AVeiglita of X-iive Beeves and of Beef.
Lb*.
Per eant.
BallockR
Heifers ,
2800
3600
2600
2400
2400
2100
9IOO
1800
72 to 78
J 70 to 76
66 to 70
64 to 68
63 to 66
Bullocks
Heifers
Bullocks
Heifers
Bullocks
Heifers
LiM.
Per rent.
Bullocks
1550
1550
1260
1200
1050
X050
980
950
61 to 64
58 to 61
} 57 to 58
50 to 56
Heifers
Bullocks
Heifers
Bullocks
Heifers
Bullocks
Heifers
'Weight of Ofikl in a Beef and Sheep.
BKVP.
Lbe.
Hide and Hair.... 56 to 98
Tallow. 42 ** 140
Head and Tongoe . a8 " 49
Feet
31
i(
35
8H1KP.
BBKP.
simp.
Lbe.
Lbs.
Lb«.
8 to 16*
S" M
Kidneys, Heart,)
Liver, etc. . . . f
31 to 62
6toxo
6 " lit
Stomach, Entrails, etc.,
126 " 196
9 "18
a " 3
Blood '.
. 4a " 56
4" 6
f Ipcludioff 3 to 6 lb*, for fleece.
i lQcl«4isK 3 (o 5 lb*, for homa.
36 MEASURES, WEIGHTS, PRESSURES, BTG.
To Compute ICq.-uivalen.ts of Old. and New U. S. and
of AXetric X>exiomiiiatiou8.
Bi/ Act of Congress^ July 28, 1866.
Rule. — Divide fourth term by second, multiply quotient by first
term, and divide product by third term.
Or, Ascertain relative ratio of firat and second terms, and multiplj
result by ratio of third and fourth terms.
Note. — When resalt is required in French or other Metric denomiDations thav
those of U.S., use exact aenominations, as, 61.025 3^7 ^^^ 61.022, 39- 370 432 for 39.37
etc.
Example i.— If one gallon (ist), per sq. foot, yard, acre, etc. (2d) ; how many liter^
(3d), per sq. foot, yard, acre, etc. (4th) ?
— X 231 -i- 61.032 = 3.7851 litei'i or 3. 7848 liUn.
m
Or, — = 1.604, and —^^^^= 2.3598; hence, 1.604 x 2.3598 = 3.7851 liters.
144 01.022
NoTK.— In computing ratios, first term is to be dividcdby second, and fourth by third
Example 2.— If one ton per cube foot, how many kilograms per cube decimeter?
61 022
— ^— r-X 2240 -r- 2.2046 = 35.881 liters^ or 35.882 litres.
1728
MEASURES.
By Ad of Congress of U, 8. By Metric Computation
I Liter per sq. foot, etc. = .2642 Gallon per sq.foot^ or .264 2 gallon.
1 Liter per sq. meter . = .0245 Gallon per sq.foot, or .024 5 galbm.
J (iallon per sq. foot . =; 40.746 Liters jter sq. meter^ or 40.745 4 llttes.
I Sq. foot per acre . . . = ,22^^ Sq.vieters per hectare, or 2.2^ og metres.
*
WEIGHTS AND PRESSURES.
By Act of Congress of U. 8. By Metric CompiUation
Per sq. inch. Per sq. inch.
I Centimeter = -3937 ^»». or -393 704 32 Ins.
I Atmosphere . . . , = 6.6679 Kilo^'amSf or 6.667 8 kiUtyrainme^,
I Inch mercury . . = 2.54 CentimeteiSy or 2.54 centirnefres.
I Pound = 453.6029 Grams, or 453.592 6 grammes.
I Kilogram = 317.4624 Lbs. per sq.foot, or 317.465 lbs.
Note.— 30 ins. of mercury at 62° = 14.7 Ws.per sq. inch ; hence, i lb. = 2.0408 ins
and a centimeter of mercury = 30-r- .3937 for U. S. computation,, and 30 -i- .393 704 3
for French or Metric.
POWER AND WORK.
I Horse - power := Cheval or Cheval-vapeur = 4500 kx mz=, 33 000 t
(4500 X 2.2046 X 39.37 -i- 12) = 1. 013 88 chevaux.
I Cheval or Cheval-vapeiir (75 i X >» per second) =; horse-power.
(4500 X 2.2046 X 39.37 -r- 12) -A- 33000 = .9863 horse-power.
Bv A ct of Congress ofU»8. By Metric Computation.
Kilograiumeter k X m=^'j.2;i^ foot-lbs. ; hence,
1-^(2.2046x3.280833)=: .13826 Kilogr ammeter, or .13825 kilofpammetrc
I Cube foot per IP . . . . = .0279 Oibe meter per cheval, or .0279 cheval.
J Pound " " . . = .447 38 Kilogram per cheval. or .447 38 h'logrummei
T. Cube meter per cheval = 35-80,^8 CvbeJ'eel per IP, or 35.8058 ft'.
PBESSUEB8, ETC. — MEASURES OF TIME. 37
TEMPERATURES.
I Caloric or French unit s? 3.968 Heat-wiits^ and i heat-unit = i -i- 3.968
=^ .35a caloric.
I U. S. Mechanical equivalent ( 772 foot -lbs. ) = 772 ~ 7.233 = 106.733
Kilofframmeters and 106.7;^^ kilogrammefres.
I French Mechanical equivalent (423.55 k x m) :=• 3.280 833 X 2.2046 x
423.55 = 3063.505 /oo^-/&#., or 3p63.566foot-lbs. Metric,
I Heat-unit per pound = .5556 Kilogram^ or .5556 kilogramme,
I Heat-unit per sq. foot = .2715 Caloric per sq. meter^ or .27i3per sq. metre
VELOCITIES.
I Foot per second = '3047 Meter per secondj or .3047 metres.
I Mile per hour =. .447 " " ** or 447 '*
MEASURES OF TIME.
60 thirds = I second.
60 seconds ^ i minute.
60 minutes = i degree.
30 degrees = i sign.
360 degrees = i circle.
True or apparent time is that deduced from observations of the Sun^
and is same as that shown by a properly adjusted sun-dial.
Mean Solar time is deduced from time in which the Earth revolves
c n its axis, as compared with the Sun ; assumed to move at a mean
r: te in its orbit, and to make 365.242218 revolutions in a mean Solar
or Gregorian year.
Sidereal time is period which elapses between time of a fixed star
being in meridian of a place and time of its return to that place.
Standard unit of time is the sidereal day.
Sidereal day := 23 h. 56 m. 4.092 sec. in solar or mean time.
Sidereal year, or revolution of the earth, 365 d. 5 h. 48 m. 47.6 sec. in solar
or mean time == 365.242 218 solar days.
Solar day, mean = 24 A. 3 m. 56.555 sec. in sidereal time.
Sol'tr year (Equinoctial, Calendar, Civil or Tropical) = 365.242 218 solar
days, or 365 (2. 5 A. 48 m. 47.6 sec.
Civil day commences at midnight. Astroiumiical day commences at
noon of the civil day, having same designation, that is, 12 hours later
than the civil day.
Marine or sea day commences 12 hours before civil time or i day
before astronomical time.
yew Style was introduced in England \\\ 1752.
NoTS. — In Russia days are reclconed by Old Style, and are consequently 12 days
behind Gregorian record.
38
MBASUBES OF VALUB.
MEASTTBES OF VALUE.
10 mills = I cent. I lo dimes = i dollar,
lo cents = I dime. | lo dollars = i eagle.
Standard of gold and silver is q/oo parts of pure metal and loo ol
alloy in looo parts of coiii.
Fineness expresses quantity of pure metal in looo parts.
Remedy of tite Mint is allowance for deviation from exact standard
fineness and weight of coins.
Nickel cent (old) contained 88 parts of copper and 12 of nickel.
Bronze cent contains 95 parts of copper and 5 of tin and zinc.
Pure Gold 23.22 grains = |i 00. Hence value of an ounce is
I20.67.183+.
Standard Gold, $1^ 60.465+ per ounce.
WEIGHT, FINENESS, ETC., OP U. 8. COINS.
G-old.
DenomiiMtion.
Dollar
Quarter Eagle. .
Three DoUur . . .
Weigh
of Coin.
t
of Pure
MeUl.
Os.
•053 75
•134375
.i6i 25
Gra.
25.8
645
77-4
Gra.
23.22
58.05
69.66
Denomination.
of Coll
Weight
1.
Half Eagle
Eagle
Oz.
.26875
•537 5
J-075
Gra.
129
258
5.6
Double Eagle...
Dime
20 Cent
Quarter Dollar .
.080375
.16075
.2009375
38.58
77.16
96.45
Silver.
Half Dollar. .
Trade Dollar.
Silver Dollar
34.722
69.444
86.805
.401 875
•875
•859375
192.9
420
412.5
of Pore
Metal.
Gra.
116.1
232.2
464.4
I73.6f
378
37I-2S
Copper and Niclcel.
One Cent . . . .
Two Cents . . .
Weight.
Graina.
48
96
Copper.
Per cent.
95
95
Tin and
Zinc.
Per cent.
5
5
Weight.
Copper.
Tin and
Zinc.
Three Cents.
Five Cents. .
Graina.
30
77.16
Per cent.
75
75
Per cent.
25
25
Tolerance. — Crold^ DoUar to Half Eagle, .25 srrains. Eagles, .5 grains.
— Silver^ 1.5 grains for all denominations. — Copper^ i to 3 cents, 2 grains ;
5 cents, 3 grains.
Hiegal Tenders. — Gold, unlimited. — Silver, Dollars of 412.5 grains
unlimited ; for subdivisions of dollar, $10. (Trade dollars [420 grains] are
not legal tender.) — Cofyper or cents, 25 cents.
NoTK. —Weight of dollar up to 1837 was 416 grains, thence to 1873, 412.5. Weight
of $1000, ® 4I2-5 gr. = 859.375 <w.
British standards are : Gold, {} of a pound,* equal to 11 parts pure gold
and I of alloy ; Silver, ffj of a pound, or 37 parts pure silver and 3 of alloy
:= .925 fine.
A Troy ounce of standard gold is coined into £3 i^3. lod. 2/*., and an
ounce of standard silver into 58. 6d, 1 lb. silver is coined into 66'shilliiigs.
Copper is coined in proportion of 2 shillings to pound avoirdupois.
£ Sterling (1880) $486.65; hence 7^ of this = value of i penny =
2.027 708 33 centa.
* A pound 18 assumed to be divided into 24 equal p9.tU* or carats, hence the pro
portion is equal to 22 carats.
FOBBIGN MEASUBBS OP VALUB. 39
To Compute Value of Coins.
Rule. — Divide product of weight in grains and fineness, by 480
(grains in an ounce), and multiply result by value of pure metal per
ounce.
Or, Multiply weight in ounces by fineness and by value of pure metal
per ounce.
RxAMPLB I.— When fine gold is $20.67.183+ per oz., what is value erf a British
sovereign? ^
By following tables, p. 40, Sovereign weighs .2567 oz., and .2567 x 480 = 123.816
grains, and has a fineness of .9165.
_ i23.2i6x Q165 , « . A „^
Hence, — ^ -—2 — ^ x 20.67.183+ = $4.86.34.
400
Example 2.— When fine silver is $1. 15. 5 per oz., what is value of U. S. Trade dollar ?
By table, p. 38, Dollar weighs .875 oz. and has a fineness of .90a
Hence, .875 x 900 X 1-15.5 = 90.95625 cents.
EzAMFLK 3.— A 4-Florin (Austrian) weighs 49.92 grains and has a fineness of .900.
What is its value ?
4Q.Q2X.0OO
^^^g^ X 20.67.183+ = $i.93-49-
To Convert XJ. S. to BritisH Currency and Contrari-
"v^^ise.
Rule i. — Divide Cents by 2.027 71— (2 027 708 33), or, Multiply by
.493 12— (.493 118 26), and result is Pence.
2. Multiply Pence by 2.02771— , or divide by .49312—, ^nd result
IS Cents.
EzAJiPLB.— What are 100 cents in pence?
100 X 493 12 — = 49.312— peiMe = 4«. 1.312(1.
3. What is a Pound sterling in cents?
36 X 12 = 240 pence, which x 2.027 7* — = $4 86.65.
POEEIGN MEASURES OF VALUE.
"VST'eiglit, Fineness, and. ]Mint "Values of Foreign
Silver and. Grold Coins,
By laws of Congress, Regulations of the Mint, and Reports of its Directors.
Current Value of silver coins is necessarily omitted, as the value of
silver is a variable element. Hence, in order to compute current value
of a silver coin, the price of fine or a given standard of silver being
known,
Proceed as per above rule to compute value of coins.
The price of silver should be taken as that of the London market for
British standard (925 fine), it being recognized as the standard value,
and governing rates in all countries.
ExAMPLB.— If it is required to determine value of a Mexican dollar in cents.
Weight 867.5 oz. .903>In«. Value of Silver in London 52.75 pence per ounce =>
106.9616-4- eenti.
nien 7-5Xy>3 _^ g^^ ^^__ ^^ J06.9616 x . 846 867 = 90, 5822 cents.
925
40
FOREIGN MEASURES OF VALUE.
"W^eiglit and IMint "Values of IHoreign Coin.
(Value is bused on their Value on April, iqoiJ
Countries given in Italics Itave not a National Coinage.
V ALOB.
Gold.
U.S.
Coontry tod Denomination.
Arabia.
Piastre or Mocha Dollar. ....
Argentine Republic.
Dollar = loo Centisimos. . . .
Peso , , .
Australasia.
Same aa Britlah.
* Australia.
Sovereign, 1855
Pound, 1852
Austria.
Kreutzer (copper)
Florin, new
Dollar, "
4 Florins.
Ducat
Souverain
Belgium.
Same aa France.
Bolivia.
Centena
lloliviano
Doubloon, 1827-36
Brazil.
Rei
Milreis
Double Milreis
20 Milreis, 1854-56
Moidore, 4000 Reis
Canada.
Mil, sterling.
Cent "
2o Cent, currency
25 *'
Penny
Shilling
Dollar, sterling
4 " :^2o killings, currency
Pound '•
Cape of (jood Hope.
Same as British.
Central America.
4 Reals ,
Colon
2 Escudos. ,
Doubloon ante 18^4
Chili. ^
Centaro
Dollar, new
10 Pesos
Doubloon
China.
Cash, Le
jZoCents, I^eang. ,..
Tael Hankow
Cochin China.
Mas, 60 Sapeks
xo Mas, I Quan
u
n
Weight.
Oz.
•256.5
.281
•397
•596
.104
.112
.363
.867
.028.8
.83
•575
.261
•15
.1875
.027
209
869
•492
867
.087
Fine-
ness.
Thous's.
916
916.5
900
900
900
986
900
870
916.66
918.5
917-5
914
925
925
875
853-1
833
900
870
901
Pure
Silver
or
Gold.
Current
or
Nominal.
Grains.
CenU.
—
8314
•^—
50.69
•
—
—
171.47
257-47
-456
—
"*■*
362.06
•75
12.67
393-6
•547
66.6
8325
.1
1. 014
I 52
—
.^_
"~
—
IX. 34
3798
14
- 6.75 -
% c.
•96s
4-85.7
5- 32. 37
345
I- 93- 49
2.28.3
6.75.4
•451
15-59-3
■54-59
zo.90.6
4.92
British.
iC a. d.
— I
3- 97- 43
3-99-97
•46s
3.68.8
14.96.39
•365
9.15.4
X5-59-3
19 11.5
X I 10.5
711
9 4.6
7 9'i
37
3 4 I
4
o
26.92
9.84
2.63
•05
•5
4
z6
z6
•75
2
4
S.25
.682
15
X
» «7
3 4
- I 67.5s I
X.88
5-97
7-45
I
■07
3-33
9-33
40
FOREIGN MEASURES OF VALUE.
Weigh-t and IVIint "Values of IHoreign. Coin.
(Value is based on their Value on April, igoij
Countries given in Italics iiave not a National Coinage.
Country «i)d DenomlBation.
Arabia.
Piastre or Mocha Dollar. . . . .
Argentine Republic.
Dollar = icK> Centisimos. . . .
Peso
Australasia.
Same as British.
* Australia.
Sovereign, 1855
Pound, 1852
Austria.
Kreutzer (copper)
Florin, new
Dollar, «
4 Florins
Ducat
Souverain
Belgium.
Same at France.
Bolivia.
Centena
Boliviano
Doubloon, 1827-36
Brazil.
Rei
Milreis
Double Milreis ,
20 Milreis, 1854-56
Moidore, 4cnx> Reis
Canada.
Mil, sterling. ,
Cent " ,
20 Cent, currency
25 "
Penny-
Shilling
Dollar, sterling
Welgbt.
((
—20 killings, currency
Pound
Cape of Good Hope.
Same as British.
Central America.
4 Reals
Colon
2 Escudos
Doubloon ante 1834
Chili.
Centaro
Dollar, new
10 Pesos
Doubloon
China.
Cash, Le
jioCents, Leang. ...
Tael Hankow
Cochin China.
Mas, 60 Sapelcs
xoMas, I Quan
Oz.
.256.5
.281
•397
•596
.104
.112
.363
.867
.028.8
.83
.575
.261
15
.1875
.027
209
869
.492
867
.087
Flne-
uesa.
Thous's.
Pure
Silver
or
Gold.
Graint.
Current
or
Nominal.
916
916.5
900
900
900
986
900
870
916.66
918.5
917-5
914
925
925
171.47
257-47
362.06
12.67
393-6
66.6
8325
875
853.1
833
900
870
901
"•34
3798
CenU.
8314
50.69
■456
•75
■547
.1
1. 014
I 52
14
6-75
67.52
V A L U B.
Gold.
U.S.
> c.
British.
•965
4-85-7
5-32-37
34-5
1.93-49
a. 28. 3
6.75.4
•451
15-59-3
•54-59
ia9o.6
4.92
£ ■. d.
397- 43
3-99-97
•465
3.68.8
14-96-39
.365
9.15-4
15.59-3
.682
1911.S
I 10.5
9 4-6
7 9->
37
341
4
o
26.92
9.84
2.63
•05
•5
4
16
z6
•75
2
4
5. 25
15
I
I X7
3 4
X.88
5-97
.45
7-45
z
.07
3-33
9-33
FOREIGN MEAStJEES OP VALUE.
41
"Weiglit and IMint Values.
Coantry and Denomination.
Cuba.
Same B8 Spain. Peso
Ck)lombia.
Centaro '.
Peso, new
4 Escudos
Doubloon, old
Gofita Rica.
Sanaa aa Mexico.
Denmark.
Mark, 16 Skilling
Crown
2 Rigsdalcr
10 Thaler
East Indies.
See Hindostan and Japan.
Ecuador.
Centaro
Sucre
England.
Penny
Groat
Shilling, new
*' average
Half Crown
Florin
Sovereign or Pound, new . . .
" " average.
Egypt
Piastre, 40 Paras % . .
Guinea, Bedidlik
Pound
Purse, 5 Guineas
France.
Centime
Sou, 5 Centimes
Franc, 100 Centimes
5 Francs
20 Francs, Napoleon, new . . .
35 Francs 20 centimes =£1 Stg.
Germany.
Groschen, 10 Pfenning
Mark, zo Groschen
10 Marks
Thaler
Ducat
Greece and Ionian Islands.
Same a« France.
Drachma, 100 Lepta
5 Drachmaa ,
20 Drachmas.
Pound
Guatemala.
Sam* as Mexico.
Chiiana, British, French, and
Dutch.
Same ac that of tbeir Countries.
Hanso Towns.
Mark
Holland.
Cent
Weight.
Oz.
•433
.867
.025
.927
.427
.304
.060.4
.182.5
.178
•454-5
.363-6
.256.7
.256.2
.04
.275
.275
1375
.032
.161
.i6x
.804
.207.5
.012.8
.128
•595
.112
.010. 4
.719
185
.012.8
Fine-
ness.
Thous's.
844
870
900
877
895
92s
26.82
924.5
80.99
925
79-03
925
2or.8
925
161.44
916.5
—
916.5
—
755
875
875
875
900
900
900
900
986
900
900
900
900
Pure
Silver
or
Gold.
Grains.
390-23
14-5
6955
347-76
25704
310.61
Current
or
Nominal.
Cents.
I. ox
8-94
1. 01
2.024-"
.2
1. 01
2.38
Value.
Gold.
U. S.
$ c.
.926
.451
7-55-5
15- 59- 3
26.8
7.90
.451
4.86.6s
4.85.1
4-9
5. 0.52
4-94-3
25. 2.6
»9-3
9645
3.85-8
23.8
2.38.24
2.28.38
iy-3
.344.2
5. 6.11
British.
£ B. d.
I II 0.58
3 4 I
439
13.22
I 12 5.6
100
100
I o 6.84
I o 5.3
5 2 ia2
.1
•5
15 10.26
1.175
IX. 74
9 9-5
9 4-63
14 1-75
X o 9.6
■405
23.8
1 1. 7,
.3
• a.027 71 cents.
42
FOREIGN M£ASUA£8 OF VALUB.
"Weiglit -and Miint Valiies.
CooBtry Mid DenominaUoo.
Holland.
Florin or Guilder, loo cents.
lo Guilders
Hindostao.
Rupee
Honduras.
Siim« as Mazico.
Italy.
Saroa as France.
Lira, loo Centimes
Scudo
Indian Empire.
Pic, nominal
Anna '•
Rupee,* i6 Annas
lo Rupeesj and 4 Annas ....
Mohur, 15 Rupees
Japan.
Yen
Itzebu, new
Yen, 100 Sen
it tt
Cobang, old
*' new
20 Yen
Java.
Same aa Holland.
Liberia.
U. S. Cnrrency.
Malta.
X2 Scndi = I Sovereign
Mexico.
Peso, new
*' Maximilian
Doubloon, new
30 Pesos, Republic
Morocco.
Ounce, 4 Blankeels
xo Ounces, Mitkeel
Naples.
Scudo
6Ducati
Netherlands.
Same aa Holland.
New Brunswick.
Same aa Canada.
Newfoundland.
Same aa Canada.
New Granada.
Dollar, 1857.
Doubloon, Popayan
Norway.
Alike to Denmark.
Mark, 24 Skillingen
Nova Scotia.
Same aa Canada.
Persia.
Keran, 20 Shahis
10 Keran, Toman
Paraguay. Foreign coins.
* .093 76 of a £
Weight.
Fine-
neaa.
Pure
Silver
or
Gold.
Current
or
Nominal.
V ALOS
G(
U.S.
Oz.
Thoa8»».
Grains.
Cents.
♦ c.
.021.6
•215
899
—
—
40.2
3- 99- 7
•374
916.5
164.53
—
-^
.16
.864
835
900
65.12
37324
^
19.3
•375
•375
916.5
916.5
i67
.25
3-03
32.9
4.86.65
6.84.36
.279%
.866.7
.053.6
.289
.362
1.072
890
900
900
572
568
900
119. 19
374-4
I
75-3
99.72
3- 57- 6
4.44
19.94.4
_
__
^.^
■
4-8665
.861
.867.5
1.081
902.5
870.5
873
37298
—
49.0
15. 6.x
19- 51- 5
.844
•245
830
996
336.25
—
5- 4^4
.803
.867
896
858
-_
.
15378
—
—
—
a 1. 63
—
^ ^
^_^
.
.083
""
""
~
•83
dritiah.
JC 8. d.
X 8
x6 5.ti
X xa5
.125
15
o o
8 X.5
.498
4 1.18
14 8.35
18 2.96
4 X XX.6
X o o
3 4 J-88
4 o a.4
X o 8.75
3 3 3-39
xa66
Stg., nominal raJoe = 3 shillings sterling.
FOEEIGN MKASUBBa OF VALDE.
43
Weigh.! and TVIint "Values.
Country and Denomination.
Peru.
Dollar, 1858
Sol
Doublooo, old
P0rtug.1L
Corda, 1838, loooo Reis . . . . ,
xoo Reis
Roamania.
2 liei •. . . .
Russia.
Ck>pek
xoo Ck>pek, Rouble
5 Roubles
Sandwich Islands.
U. S. Currency.
Sardinia.
Lira
Spain.
Centimo
xc» Centimo, Peseta
Dollar, 5 Peseta
100 Reals
10 Escudos
3oRealsvellon8=i U.S. Dollar.
Sweden.
Riksdaler, 100 Ore
Rlxdollar
Carolin, 10 Francs
Switzerland.
Sam« aa Franca.
St Domingo.
Gomdes, 100 Cents.
Tunis.
Piastre, 16 Kanibs ,
5 Piastre
25 Piastre.
Turkey.
Piastre, 40 Paras
20 Piastre
xoo Piastre, Me<Uidie
Tuscany.
Zecchino, Seqain
Tripoli.
20 Piastres, Mahbnb
Uruguay.
Dollar, 100 Centimea
West Indies, British.
SaaM aa England.
Venezuela.
Cenlbro.
BoliTar, i Franc. '....,
Weight.
Oz.
.766
.867
.308
•095
•322
.667
.21
.16
.16
.8
.268
.270.8
•273
1.092
.104
•5"
.161
•77
.231
.112
Fine-
new.
Thous's.
900
868
912
912
835
500
875
916.6
835
83!
900
896
896
750
750
900
898.5
900
830
915
900
Pure
Silver
or
Gold.
Grains.
341.01
129.06
277-73
65.12
6413
345-6
98.28
393- 12
220.38
306.77
!MCetn oreind.a«
Current
or
Nominal.
CenU.
77
.193
6-33
11.83
74.8
V AI. VI
G
U.S.
old.
Britlah.
% c.
.487
15- 55-7
xo.81.78
Z0.8
51-5
2.90
19-3
99.6
4.96.4
5- >-5
I- 93- 5
2.99.5
.044
.88
4-36.9
2-3»-3
-76
»-03-4
19.3
£ s. d.
3 3 11.29
2 4 5S
38
10.14
.09s
I o 4.8
I o 7.32
7 "42
3-125
_5-83
12 3.7
18 o
9 6.1
3 0-89
9-5
Frahck. — Bronze coins 9.5 copper, 4 tin, and x zinc.
Hansi Towns. —Monetary system same as that of German Empire.
SwiTZERLAVD. — The Centime is termed a Rappe.
Spain. — 25 Peseta piece is i9». 9.5^. Stg. ; Real vellon was 2.5(1 Stg.
Italy. — All coins same weight and fineness as those of France.
Malta. — 7 Tari and 4 Grani = i Shilling Sterling.
BoYPT.— A Para = .061 sd. Sterling, and 97. 22 Piastres = i Sovereign.
tsfj>wx Empiimj.— X Lac Rupee8=£xo 000 Sterling. In Ceylon, Rupw=: 109 ^^w
44
ENGLISH AND FRENCH MEASUBES AND WEIGHTS.
ENGLISH AND FRENCH MEASURES AND WEIGHTS.
MEASURES OF LENGTH.
English. — ^Imperial standard yard is referred to a natural standard,
which is a pendulum 39.1393 ins. in length vibrating seconds in vacuo
in London, at level of sea ; measured between two marks on a brass
rod, at temperature of 629,
NoTc - In consequence of destroctlon of standard by fire in 1834, and difflcuiUy
of repIacAg it by measarement of a pendulum, the present standard is held to be
about I part in 17 230 less than that of U. 13^. equal to 3.67 ina in a mile
Miiscellajieous.
Land. — ^Woodland pole or perch or Fen ^ iS/eet.
Forest pole = 21 ''*
^rish mile = 2240 yards. \ Scotch mile = 1984 yards.
Sea. — ID cables, or 1000 fathoms, or 6080.27 feet, or x.1516 Statute miles.
I A dmiralty or Nautical mile or knot ^ (>d8ofeet.
3 mil&t^= I league. 60 Nautical or 69.094 Statute miles or 20 Leagues
= I degree.
Mean length of a minute of Latitude nt mean level of the sea=: 1.1451
Hatule miles.
Nautical mile is taken ap length of a minute z± the Equator.
Nautical fathom is loooth part of a nautical mile, and averages about
x>i25 l(Miger than the common fathom.
French. — Standard Metre or unit of measurement is defined as the
ten millionth part of the terrestrial meridian, or the distance from the
Equator to the Pole, passing through Paris. Actual standard is a plat-
inum metre, deposited in the Palais des Archives, Paris.
I^etrio XjengtU ixx InoUes, ITeet, etc.
Denominntioo.
Hetrw.
Inebw.
Feet.
Yards.
Mile*.
I Millimetre
.cox
.039 37
—
__
_^
I Centimetre
.ox
•393 7
—
__
_„
I Decimetre
.X
3-93704
—
—
— _
X Mbtrb
f
39-37043
3.28087
32.80869
1.09362
xa93623
X Dekametre
xo
_„
X Hektometre
ICX3
—
328.0869
109.36231
— _
I KlLOMSTRB
xooo
—
328a 869
X 093.623 1
.62x38
X Myriametre
10 000
—
—
xo 936. 231
6.2x377
Non.— For length of metre see p. 27.
Old ACeasure.
I Toise = 1.949 metres.
I Mille = 1.949 kilometres.
I Noeud (knot). ^ 1.855
u
1 Terrestrial league = 4.444 kilometres.
I Nautical league . = 5.555 "
I Arpent ^900 sq. loists.
MEASURES OP SURFACE.
English. — Same as that of United States of America.
JVIisoellaixeoiis.
Builders, 1 superficial part = 1 square inch,
12 parts = 1 inch.
12 mches = square foot,
^oarei^.— Boards 7 inches io width are termed battens, 9 mches deals, and
13 inches planks.
AKGLISH AND FBENOH MEASURES AND WEIGHTS. 45
French.
IMetrio Sixrfkoea izx Sq^uare Inolxes, Feet, etc.
Daaomination.
I Square millimetre
I
z
X
z
X
X
z
tt
((
(t
tl
((
H
centimetrd
decimetre
Metre or Centiare ....
dekaroetre or are. ....
hektometre or hectare
kilometre
myriametre* i
* Equal 98.6x0 908 *g. m*I«$.
Sq. InchM.
.00155
.155003
15.500309
1 550030 916
Sq. Feet.
. 107 641
10.764104
1076.410358
Sq. Yards.
1.196 01
119.60115
1x960.11509
Sq. Aeraa.
.094711
2.471 098
247. 109 8x6
24710.98x6
I square inch
I toise
I arpent (Paris)
I arpent (woodland)
Old SyBtexxx.
■ i'i35 87 inches,
• 6-394 6/ec<.
= 900 square toises ^ 4089 s^are yards.
= 100 square royal perches = 6108.34 ^^
6108.34 square yardi.
MEASURES OP VOLUME.
Imperial galhn measures 277.123 cube ins., but by Act of Parliament
1825 its volume is 277.274 cube ins., equal to 10 lbs. avoirdupois of
distilled water, weighed in air, at temperature of 62^, barometer at 30
inches. 6.2355 gallons in a cube foot.
Imperial bushel^ 18.5 his. internal diameter, 19.5 external, and 8.25
in depth, contains 2218.192 cube ins.j and when heaped in form of a
right cone, at least .75 depth of the measure, must contain 2815.4872
cube ins. or 1.6293 ciAefeet.
Grain. — i quarter = 8 bushels or 10.2694 cube feet.
Vessels. — I ton displacement = 35 cube feet; 1 ton freight by measure-
ment = 40 cube feet.
I ton internal capacity := 100 cubefeet^ and i ton ship -builders = 94
cube feci.
English standard No. 5 is .008 grain heavier than the pound, and U. S. pound U
<x>x grain lighter than English.
Wixie aiicl Spirit IMeasures. *
4 quarts (231 cube ins.) = .8333 Imperial gallon,
10 gallons =1 anchor.
18 ** (15 imperial) =1 runlet,
31.5 " 26.25 " , . . = 1 barrel.
43 " 35 ** t . . = I tierce.
63 " 52.5 ** =1 hogshead.
84 " 70 *• =1 puncheon. .
Z26 ^ 105 *^ ^ I pipe or butt,
apipesor 1
3 puncheons/
A.le and. Seer Aleasures.
Imp'l gall's.
4 -quarts (38a cube ins.) . . = 1.017
9 gallons = I firkin = 9.153
3 firkins^ I kilderkin . . . = 18.306
Imp'] call'*
3 kilderkins = I barrel =r 36.613
54 gallons = I hogshead =: 54.9x8
108 " =1 butt . . . . = 109.836
46 ENGLISH AKD FBENCH MEASURES AKD WEIGHTS.
J^potlieoaries* or Fluid Mieasixres.
I drop = 1 grain.
60 drops ^ I drachm.
4 drachms =: i tablespoon,
3 ounces (875 grains) = i wineglass.
Coal Afeas-urea.
50 pomids ....
00 . . . . '
9 bushels . . . . :
80 or 84 pounds :
90 or 94 "
93 pounds . I . . :
3 neaped bush. :
10 sacks :
; I cube foot,
: I bushel.
I vat,
f I London or
( Newcastle bushel,
1 ConUsh "
I {Velsh bushel,
I sack.
I ton.
12 sacks :
J chaldron :
5.25 chaldrons . . :
I London chaldron :
I Newcastle "
I ton :
I room :
21 chaldrons :
I barge or keel . . :
; I chaldron.
58.6548 cube ft.
: I room,
: 26.5 cwts.
S3 "
44.5 cube feet,
; 7 tons.
I score,
\ 21.2 tons.
M!iscellaTieou.s.
X last com
I ton water
I dicker hides . . .
I last hides
I barrel tar
6 bushels wheat .
I clove .*.
X score ....
I sack flour .
X truss straw
-.^Inuhds,
. ^5.g cube feet.
: 10 skins.
: 20 dickers.
; 26^5 gcUlons.
I sack flour.
; T pounds,
:20
28.3
= 36
35.9 cube feet
11
1 truss old hay
X " new " ,
X bushel oats . ,
X " barley
X " wheat ,
X cube yard new hay
X " " old
X quintal
I boU
I sack wool . . .
I ton water.
t(
: 50 ponn /j?.
; 60
40
47
60
84
126
100
X40
364
4.
t(
(I
(•
4i
(i
U
(*
Liquid.
I wine gallon
X beer "
X litre
I gallon ....
I cube foot . .
I anker ....
23X cube ins,
282 " "
.220 og gallon.
4.544 litres.
6.232X gallons.
8.333
(t
X hogshead wine . .
X " beer . . .
X puncheon wine . .
X pipe or butt wine
X " " " beer
X tun
52.5 gallons.
54.918
70
105
X09.836
3IO
n
u
u
I ton water 62° = 224 gallons.
Builders.
I solid part
X2 *•'' parts
X2 "inches"
X load timber, rough
X " " hewn
I " lime
I " sand
X2 cube ins,
1 *' inch."
1 cube foot.
40 " feet.
50 " ' "
32 bushels.
36
14
X square
X bundle laths . . .
X rod brickwork .
X rood masonry .
Batten, in section
Deal, * "
Plank, " "
:= xcx) itq.feet.
= 120 laths.
= 306 cube feet.
= 648 " "
^ 7 X 2.5 ins.
= 9X3
= 11 X 3
IMetrio Volumes in Cube Iiiclies, ITeet, etc.
D«noRiin«tloiia.
Centilitre . ,
Decilitre..,
Litre*
Dekalitre.,
Hectolitrei ,
Kilolitre..,
Litres.
OilU.
PlDto.
QaarU.
Galloni.
BQshcU.
01
.0704
.0176
—
—
.1
.7043
176X
—
—
I
7.0429
1.7607
o'S^l
.2201
—
10
—
—
&8036
2.3009
.27511
100
—
—
—
22.0091
2-751 «3
1000
—
—
r—
220.0908
27-5" 35
Qunrton,
* Eoaal 6Z.03S 24 crUn ina.
ENGLISH AND FRENCH MEASUBBS AND WEIGHTS. ^J
"Wood. M!ea8xire.
I Stere or cube metre := 35.3150 cube feet or 1.308 cube yards.
I Voie de bois (Paris) :x 70.6312 cube feet ; i voie de charbon (charcoal)
: 7.063 cube feet ; i corde = 4 cube metres = 141.26 cube feet.
MEASURES OF WEIGHT.
British.— I Troy grain = .003 961 cube inches of distilled water.
I Troy pound =22.815 689 cube inches of water.
I Avoir, drachm = 27.343 75 Troy grains.
16 drachms, or
437-5 grains
16 ounces, or
7000 grains
^ I ounce.
> = 1 pound.
A.voix*d.upois.
8 pounds
14
28
112
20 hundredweiorhts = 1 ton
= I stone (for meat).
= I stone.
= I quarter.
= I cwL
The ffraiuy of which there are 7000 to the pound avoirdupois, is same as
Troy grain, of which there are by the revised table 7000 to tne Troy pound.
Hence Troy pound is equal with the Avoirdupois pound.
In Wales, the ir(m ton is 20 cwt. of 120 lbs. each.
Troy.
24 grains = i dwt.
20 pennyweights, or)
437.S gnuns j
16 ounces = 1 pound.
25 pounds = 1 quarter.
4quarters, or 100 pounds := i cwt.
By this are weighed gold, silver, jewels, and such liquors as are sold by
weight. ■
The old Troy ounce to the Avoirdupois ounce was as 480 grains, the
weight of the former, to 437.5 grains, weight of the latter ; or, as i to .9115.
.A^potlxecar ies . *
437.5 grains = i ounce. | 16 ounces = i pound.
French.
Aletrio "Weiffhts in A-voirdupols.
Deoomlnatioiia.
Milligramme ..
Centigramme. .
Decigramme ..
Oramme.
Dekagramme..
Hektogramme.
Kilogramme^ . .
Myriagramme .
Quintal
Millier or Ton. .
GramoiM.
001
01
.1
Graint.
OuncM.
01543
—
.15432
—
I 543 23
J 5- 432 35
154-32349
•3527
» 543234 87
35274
X5 432. 348 74
352739
..^
—
Poands.
X
10
100
1000
lOOOO
100 000
1000 000
t Kilogramme = 3 26*. 3 oc. 4 draekmMf 10.4734 graint.
. 220 ^6
2.20462
22.04621
220.462 12
2204.621 25
Ton.
.9842
NoT& — For the values of the prefixes, as Milli, Cent), etc., see p 27.
Old. System.
z grain . . =: 0.8188 grains Troy.
1 gross . . = 58.9548 "
I ounce ^ 1.0780 oz. Avoirdupois,
I livre = 1.0780 lbs.
* As by revised PharmacopoBia.
48
FOBEIGN MEASURES AND WEIGHTS.
A-raloia, Bassora,
!N£oolia.
Foot, Arabic i.
Covid, Mocha. 19
Guz, " as
Kassaba 12.
Mile, 6000 feet 2146
Baryd, 4 farsakh 21 120
Feddan 57 600
Noosfla, Arabic 138
Gudda 2
Maund 3
Tomand 168
Other Measures like those of
FOBEIGN MEASURES AND WEIGHTS.
It being wholly impracticable to give all the denominations of measures
and weights of all countries, the following cases are selected as essential and
as exponents.
With parent countries, as England, France, etc., their denominations ex^
tend to their colonies and dependencies. Thus, the denominations of England
extend to Canada, a large [M)rtion of the East ^nd West Indies, and parts of
South America, and those of France to a part of the West Indies, Algiers, etCr
A.'byssinia.
Pic, Stambouili 26.8 ins.
" geometrical 30.37 "
Madega 3.466 bush.
Ardeb 34.66 "
" Musuah 83.184 "
Wakea. 400 grains.
Mocha X Troy oz.
Rottolo 10 " **
Also^ same as in Egypt and Cairo.
.A.fVioa, A^lexandria, Cairo,
and Ifigypt.
Cubit 2a65 in&
Derah 25.49 "
Pic,cloth. 26.8 •»
'^ geometrical ^9- 53 '*
KaRsaba,4.73PicB 11.65 ft
Miie 2146 yds.
Peddan al-risach 553 48 acre.
Roobak 1.684 gails.
Ardeb 4.9 bush.
Rottol , .98211b.
Distances are measured by time.
A Maragha= 15 D^rcghd or i hour.
A.leppo and. Syria.
Dra Mesrour 21-845 >°8.
Pic 26.63 "
Boad Measures are computed by time.
iVlgeria.
Jlob, Turkish 3. 11 ins.
Pic, " .,...24.92 «*
" Arabic 18.89 '*
Also DecimaX System.
A.lioaute.
Palmo 8.908 ins.
Vara.. 35632 "
A.znsterdaxn.
Voet 1 1. 144 ins.
Ei 21.979 '^
Faden 5- 57 ft.
Lieue 6.383 yds.
Maat 1.6728 acrea
Morgen 2.0005 **
Vat 40 CUD, fu
Also Decimal System.
and
.0503 t^
ins.
3 ft.
yda
sq. ft
cub. ina
galls.
lbs.
((
Egypt
A.rg;entine Con federation,
Paraguay, and Uruguay.
Fanega 1.5 bush.
Arroba. 35-35 1^
Quintal 101,4 *'
Also Decimal System in Argentine Con-
federation and Para^iuay.
.A.ustralasia.
Land Section 80 acrea
Other Measures same as English.
i\.ustria.
Zoll 1-0371 iQ&
Fuss xo37ifL
Meile. 24000 ft.
Klafter, quadrat. 35-854 sq. yd&
Jochart 6.884 "
Cube Fu8S...« I-II55 cub. (t
Achtel 1.692 galls.
Eimer X2.774 "
Viertel 3- "43 "
Metze Z.6918 bush.
Unze 8642 graina
PAind (1853, 500 grammes), 1-2347 lbs.
Centuer 123.47
Also Decimal System.
t(
AntAverp.
Fuss 11-275 ins.
EUe, cloth 26.94 "
Ck>rde 24.494 cub. ft.
Bonnier 3-2507 acres.
Also Decimal System,
Babylon.
Pachys Metrios 18. 205 ins
Baden.
Fus& Z1.81 Ins.
Klafter 5-9055 ft^
Kuthe 9-8427 "
Stunden 4860 yds.
Moi^eo 8896 acre.
Stutze 3. 3014 galla
Malter 4. 1268 bush
PAind z. Z023 lb&
Also Decimal System.
FOBEION MBASUBES AND WEIGHTS.
49
((
14
ti
3agdad,.
Gas 31.665 in&
Bafbary States.
Pic, Tunis linen 18.62 ins.
" " cloth .....26.49 "
** Tripoli 8i'75
Batavia.
Foot 12.357 ins.
CoTid.... 27
El 27.75
Savaria.
Fuss 1 1'49 ii^s*
Klafler 5-74536 ft
Ruthe 3.i9i8yd8.
Heile 8060 "
Ruthe, quadrat 10. 1876 sq yds.
M orgen or Tagwerk 8416 acre.
Klafter, cube 4.097 cub. yds.
Eimer 15.05856 galls.
ScheffeL 6.119 ''
Metze. 1.0196 bush.
Fnind 8642 grains.
Also Decimal System,
Selgiuxu.
Heile 2.132 yds.
AUo Decimal System.
Benares.
Yard, Tailor's. 33 ins.
Bengal* Bom'bay, and Cal-
outta.
Moot 3 ins.
Span 9 "
Ady, Malabar 10.46 ins.
Hath 18
Guz, Bombay 27 *'
'* Bengal ....36 **
Corah, minimum 3>4i7 ^
Ck)ss, Bengal 1.136 miles.
'' Calcutta Z.2273 '^
Kutty. 9. 8x75 sq. yds.
Biggab, Bengal .3306 acre.
*' Bombay 8x14 '^
Seer, Factory 68 cub. ins.
Covit, Bombay. 12.704 cub. ft
Seer, Bombay. i. 234 pinta
Parah 4.4802 galla
Mooda 112.0045 '^
Liquids and Cfrain measured by weight.
Boliexuia.
Foot, Prague xz.88 in&
^ Imperial 12.45
Aiso same as Austria.
n
Bolivia, Cliili, and Fern.
Vara 33-333 ins.
Fanegada x.5888 acres.
Gallon 74KaU-
Fanega x.572 "''
Libra... 1.014 lbs.
Arroba 25-36 ''
Originally as in Spatn ; now Decimal
Syitem in Chili and Peru.
Brazil.
Palmo, Bahia. 8. 5592 ins
Vara 3. 566 it
Braca 7' 132 ''
Geira 1.448 acrea
Aluo same (U Portugal^ and sometimes
as in England.
Buenos .Ayres.
Vara 2.84 ft
Legua 3.226 mUe&
Suertes de Estancia .... 27 000 sq. varas.
Also same as Spain.
Burmali.
Paulgat X inch. .
Dain 4.277 yd&
Viss 3.6 Iba
Taim. 5.5 "
Saading 22 **
Also same aS England.
Canary Isles.
Onza 927 inch.
Pic, Castilian xi.128 ina
Almude 0416 acta
Fanegada. 5 "
Libra X.0X48 lb&»
Also same as Spain.
Cape of" Ghood Hope.
Foot X1.616 ina
Morgen 2. 1 16 54 acrea
Also same as in England.
Ceylon.
Seer i quart
Parrah 5.62 galla
Also same a« in England.
China.
Li 486 inch.
Chih, Engineer's 12.7X ina
*' orCovid '3-125 "
" " legal 14.X "
Chang 131-25 "
*■*■ legal..... X4X "
Pu 4.05 ft
Chang, fathom 10.9375 ft
Li 486 yds.
P6orKuDg 3.32sq. yda
King, xoo Mail 16.485 acrea
Tau X.13 galla
Tael 1.333 oz.
Catty i.333lba
Cochin China.
Thuoc or Cubit 19.2 ina
Sao 64 sq. yda
Mao r 1.32 acrea
Hao. 6. 222 galla
Shita 12.444 "
Nen 8594 lb.
Coloinhia and Venezuela.
Libra 1. 102 lbs
Oncha 25 *'
Also Decimal System.
so
FOBSIGN MBA6UBSS AND WEIGHTS.
Denmarlz,* Ghreenlaiid, Ice-
land, and Norway.
Tomme 1.0297 ing
Fod 1.0297 ft
Favn, 3Alea 6.1783''
Mil 4.680 55 miles.
" nautical 4.61072 ''
Anker 8.0700 gall&
Skeppe '.478 bush.
Fjerdingkar 9558 ''
Pand 1. 1023 Iba
Lispand 17-367 *'
Centner 110.23 "
* Also Decimal System.
Bonador.
Decimal System.
C}-exioa, Sardinia, and
Turin.
Palmo 9.8076 ins.
Piede, Manual, 8 oncie. . . 13.488 ''
♦' Liprando, 12 " ...2a23 . "
Trabuco or Tesa 10. 1 13 ft.
Miglio 1-3835 miles.
Starello 9804 acre.
Giomaba 9394 ''
Ghermany.
The old measures of tiie different Stales
differ very malenaUy ; generally^ how-
ever.
Foot. Rhineland ia-357 ins.
Meile 4603 miles.
Decimal System made compulsory in 1872.
G}-reeoe.
Stadium 6155 mile.
Also Decimal System.
Ghuinea.
Jachtan 12 ft
JrLamtyvLVfs,
Fuss II. 2788 ins.
Klafter 5.6413 ft.
Morgen 2.386 acres.
Cube Fuss 831 1 cub. (t
Tehr 99-73 "
Viertel 1-594 7 galte.
Pftind (500 grammes) ... 1. 102 32 lbs.
Ton 2135.8 lbs.
Also Decimal System.
Kanover.
Fuss ii.Slns.
Morgen 6476 acre.
Hindostan.
BojreJ 1.2II ins.
Gerah 8.387 "
Haut 19.08 '♦
Kobe 29.065 ♦'
Cobs 3.65 mile&
Tuda i.i84cub. ft.
Candy 14.909 «'
Hungary.
Fass 13.445 Ina
Elle 30.67 "
Meile 9-139 y^
Also as in Vienna.
Indian ISxnpire.
Guz 27. 125 ins.
Cowrie x sq. yd.
Sen 61.025 39 cub. iD&
" , 2.204737 Iba
Uniform, standard of multiples of the Sen
adopted in 1871.
Italy.
IVHilan and Venice.
Decimal System.
The Metre is termed Metra ; the Are, An;
the Stere, Stero; the Litre, Litro; the
Gramme, Gramma, and the TouueaU;
Tonnelata de Mure.
Naples and T-wo Sicilies.
Palmo 10.381 ins.
Canna 6.921 ft.
Miglio 1. 1506 miles.
Migliago. 7467 acre.
Moggia 86 *'
Pezza, Roman 6529 **
Homan States.
Old Measure.
Foot "-592 Ina
" Architect's 11.73 •♦
Braccio 30-73 "
Palmo 8.347 '*
Miglio 1628 yds.
Quftrta X.1414 acres.
ILiucoa and Tnsoany.
Pie « 1X.94 ins.
Palmo X1.49 "
Braccio aa.98 "
Passetto 3.829 ft.
Passo 5.74 '•
Miglio t.0277 milea
Quadrato 8413 acre.
Saccate i. 324 «»
Japan.
Sun, . 303 03 Metre — 1. 193* Ins.
Shaku, 3.0303 Metros.... 11.9305* in&
Jo, 30.303 " — 9.9421* ft.
Ken, 5.5 " .... 5-9653* "
Ri, 11880 '• .... 2.4403 miles.
Kai-rl 6080 feet t
Hiro 4.971* feet
Momme 3-756 521 7 grammes Fr.
Hiyaku me 828 17 lbs.
Kwam-me 8.28171 "
Hiyakkin 132-50732 "
Man's load 57972 "
Koku 331-26831 *'
Hiyak koku 33126.8308 "
* These are m eqnUalent m they are praett
cable of reduction.
t Admiralty knot.
FOKEIGN MBASUBES AND WEIGHTS.
51
Java.
Dalm X.3 ins.
Ell 27.08 '•
Djong 7-015 acres.
Kan 328 galls.
Tael 593.6 grains.
Sach 61.034 lbs.
Pecul 122.068 "
Catty 1.356 "
Aladrae.
Ady ia46 ins.
Covid 18.6 "
tiuz 33 "
Culy 20.92 ft.
League 3472 yds.
Vnddy 338 galls.
Marcal 2-704 ''
Tola 180 grains.
Seer 625 lbs.
Viss 3.086 *'
Maund 24.686 ''
A£alabar.
Ady xa46 ins.
I^alaooa.
Hasta or t'ovid 18. 125 ins.
Depa 6ft.
Orlong 80 yd&
^Calta.
Pftlmo 10.3125 ins.
Pie 11.1^7 '*
Canna 82. 5 *'
Salma 4.44 acrea
Also <u in Sicily.
IMLoldavia.
Foot Sins.
Kot, silk. 24.86 ins.
Fathom sa
Aloluooa Ifllaxids.
Covid 18.333 ins.
Alorooco.
Tomin 2.81025 in&
Cadee. 20.34 '^^
Cubit 21 "
Muhd. 3.081 35 gall&
Kula,oll 3.356 "
Rotal or Artal 1. 12 lbs.
Liquids other than oil are sold by weight.
Affysore.
Angle 3. 12 ins.
Haut 19. 1 "
Guz 38.2 "
Candy 500 lbs.
^Netherlands.
Elle 39.370432 ins.
Decimal System since 1817.
Persia.
6«reh 2.375 ins.
Guezm common 25 '^
•' Ifonkelrer 37.5 "
Archin, Schah 31.55 ins.
" Arish 38.27 "
Parasang 6076 yds.
Chenica 80.26 cub. ins
Artaba 1.809 bush.
Miscal 71 grains.
RateL 2.ii361ba
Batman MauLd 6. 49 ''
Liquids are measured by weight.
Ir'olande
Trewice 14.03 ins.
Precikow 17 ins.
Pretow 47245 yds.
Mile, short 6075 yds.
Morgen 1-3843 acres.
FortuQal and ^lozazn'biq.ue.
Foot 13 ins.
Milha X.2788 miles
Almiide 3.7 galls.
Fanga 1.488 bush.
Alguieri ^ 3.6 "
Libra i. 01 2 lbs.
Also Decimal System.
Prussia.
Fuss ; 12.358 ina
Ruthe , 4. 1 192 yda
Meile 24 000 feet
Quadrat Fuss 1.0603 sq. ft.
Morgen 631 03 acra
Cube Fuss 1.092 cub. fL
SchefTel i. 5121 bush.
Anker 7. 559 galls.
Pound 7217 grains.
Zollpfund 1. 1023 lbs.
Centner "3.43 Iba
liussia.
Vershok z.75 in&
Foot 12 ins.
Arschine 28 **
Rhein Fuss 1.03 ft
SiO^ne 7 ft.
Verst 3500 "
Mila 5-5574 miles
Dessatina 2.4954 acres.
Vedro 2.7049 galla
Tschel-werha 1-4424 "
P«Oak 1.4426 bush.
Tschetwert 57704 "
Pound 6317 grains.
Funt 902 85 Iba
Decimai System adopted in 1872.
K'up 9.75 in&
Covid. 18 ins.
Ken 39 "
Jod 098 48 mile
Roiineng 2.462 milea
Silesia.
Fuss II. 19 ins.
Ruthe 4-7238 yds.
Meile 7086 yds.
Morgen 1-3825 acres
52
FOKEIGN M£ASUB£S AND WEIGHTS.
Singapore.
Hasta or Cabit i8 ina
Dessa. 6 ft.
Orlong 80 yUs.
Sxiiyrxia.
Pic 26.48
Iodise 24.648
Berri 1828 yda
1D&
4(
Spain., CulDa, !M!alaga, AdCa-
xiilla, O-uateznala, l^ondu-
raH, and. ]V£exioo.
Pie 11.128 ins.
Vara 33-384 *'
Milla 865 mile.
Legua, 8000 varas 4* 2x51 miles.
Fanegada x>6374 acres.
Vara, cubo 21.531 cub. ft
Cuartilla. 888 galL
Arroba, Castile 3. 554 galls.
Fanega 1-5077 bush.
Libra. 1.0144 lbs.
Tonelada 2028.2 lbs..
Also Decimal System.
Stettin.
Fuss 1 1. 12 ins.
Foot, Rhincland 12-357 '^
Kile 25.6 in&
Morgen i'5729 acres.
Sumatra.
Jankal or Span o ins.
Elle 18 "
Hailoh 36 "
Fathom 6 ft.
Tung 4 yds.
Sxxrat.
Tnssoo, cloth x. 161 ins.
Guz, " 27.864 "
Hath 20.9
Covid 18.5
Biggah 51 acre.
Tunnland 1.2x98 acres
Anker 8.64X gaU&
Spann x.962 bush.
Centner 1 12.05 ^^^
Also Decimal System.
S'witzet'land .
Fuss, Berne 11.52 ins.
'< 11.54 "
Vaud. ii.8x "
Klafter 5-77 ft-
Meile 4.8568 miles
Juchart, Berne 85 acre.
Maas 2.6412 pints.
Eimer. 8.918 galls.
Malter 4.X268 bush.
rfund X. X023 lbs.
Also Decimal System.
Tripoli.
Pik, 3 palmi 26.42 ins.
Almud 319-4 cub. ins.
Killow 2023 " "
Barile X4.267 galla
Temer 7383 bush.
Rottol 7680 graina
Oke 3.8286 lb&
Turkey.
Pic, great 27.9 ins.
'^ small ..27.06*'
Berri 1.828 yds.
Alm^ X. 154 galla
Also Decimal System.
AViirtena"berg.
Fuss XX.29 ins.
Elle.' 2.015 ft.
Meile 8146.25 yda
Morgen 7793 acre.
Cube Fuss 83045 cub. ft.
Eimer 64.721 galla
ScheflTel 4.878 bush.
Pound 7217 graina
Zurioli.
Fuss XX.812 ins.
Elle 23.625 "
Klafter 5.0062 ft.
Meile 4.8568 miles
Jachart 808 acre.
Cube Klafter X44 cub. ft.
S'^vedell..
Foi 11.6928 ins.
Ref 324703 yda
Faden 5-845 ft.
\/eague 3- 3564 m ilea
Meile 6.6417 "
IXollq,xid.
Denominations corresponding to the French are as follows:
Length. — Millimetre, Streep; centimetre, Duim; decimetre, Palm; metre, El;
decametre, Roede; kilometre, Mijle.
Surface. — Square millimetre, Vierkante Streep; square centimetre, Vierkante
Duim; and so on. Hectare, Vierkante Bunder.
Cube Measure. — Millistere, Kiibicke Streep, and so on.
Capacity. — Centilitre, Vingerhoed; decilitre, Maatje; liquid litre, Kan; dry litre,
Kop; decalitre, Schepel; liquid hectolitre. Vat or Ton; dry hectolitre. Mud or Zak;
30 hectolitres = i Last = 10. 323 quarters.
Weiglit. — Decigramme, Korrel; gramme, Wigteje; decagramme, Lood; hecto-
gramme, Onzc; kilogramme, Pond.
Belgium.
Metric system.— The term Litore is substituted for kilogramme, Litron for litrCj
and Anne for iiiotre. -
^
SCBIPTUBE MEASUBBS. — AJfClKNT WEIGHTS.
53
t(
SCRIPTURE AND ANCIENT LINEAR MEASURES.
Scripture.
Digit...... 912 inch. I Span, 3 palms 10.944 ins
Palm, 40 digits..; 3.648 ins. | Cubit, 2 spans 2i.§88
Fathom, 4 cubits 7 feet 3. 552 ina
Hebrew awd Sgjrptian.
Nabud cubit 1.475 feet.
Royal ♦' 1.7216 "
Egyptian finger 06145 '*
Hebrew sacred cubit
Babylonian foot 1. 140 feet
Hebrew "
" cubit '..[
• 2.002 feet
1. 212
1.817
^ Q-reoian.
Digit 7554 inch,
Pous (foot) 1.0073 feet
Cubit 1. 1332 "
Pythic or natural foot 814 foot
Attic or Olympic " 1.009 *®6t
Ancient Greek foot >
(16 Egyptian fingers) J 9841 foot
Arabian foot ,.095 feet
Stadium 604.0375 "
Olympic stadium 606.29 "
Ai A ■ *IJu®i ? stadium 4835 feet
Alexandrian or Philetenan stadium (600 Phil, feet) = 708.65 feet
F(irfu»uj.-Keramion or Metretes 8.488 gallona
Cubit
Sabbath day's journey.
Jewish,
. . . 1.824 feet I Mile, 4000 cubita 7296 feet
3648 " I Day's journey 33. 164 milea
Itoxnan. Xjong Pleasures.
Digit .725 75 ina | Cubit 1-4505 feet
Uncia (inch) 967 " Passus 4835 '*
Pe8(foot) 11.604 " Mile, milliarium 4842
u
ANCIENT WEIGHTS.
Hebre">w and S^g^srptian.
Attic
Troy grains.
obolus I ^-2*
1 9- it
<(
drachma
Lesser mina 3-892
Greater mina 5.46
Egyptian mina 8.326*
Ptolemaic '* 8.985*
Alexandrian " 9.992*
Obolus 4.63
Troy graina,
Denarius, Roman ( 5i-9*
I 62. 5T
92.62
Nero
Shekel.
Ounce .
Drachm 146. ■
Libra 4086. i
Pound 12 Roman ouncea
Talub 581.71 ouncea
Talent (60 minae) 56 lbs. avoirdupoia
Grecian.
Troy fp-ains.
Obelus, ancient 8.33
(t
»i'57
Gramme 23. 15
Drachma. 50.01
" great 69.47
- ,. Troy ounceii
Mina — ; 10. 41
*' great 14.47a
Talent 625. 19
" Attic 868.33
Ounce.
!R.oznan.
416.82 grains. I Pound
Z0.41 ounces
•ChristlaiiL
t Arbttthnot.
E*
tPaacton.
54
GEOGBAPUIC MEAiSUKES AND DISTANCES.
GEOGRAPHIC MEASURES AND DISTANCES.
To iReduce Xiongitude into Time.
Rule. — Multiply degrees, minutes, and seconds by 4, and product is
the time.
Example.— Required time corresponding to 50° 31'. 50** 31^ x 4 = 3%- 32m. 4*.
To Reduce Time into Xjongitude.
Rule. — Reduce hours to minutes and seconds, divide by 4, and qucv
tieut is the longitude. Or^ Multiply them by 15.
ExAKPLE.— Required longitude corresponding to $h. 8m. 11. 2t.
5ft. 8in. ii.2«. = 308m. 1 1. 2*., which -^ 4 = 77° 2' 8".
Or, multiplying by 15: 5A. 8»i. 11.2*. x 15 = 770
2' 8".
Table of IJeparttxros Tov a X>istauoe run of 1 Afile.
Course. Departure. Coarse. Departure. Course. Departure.
3.5 polnta.
4 "
.773
.707
Coarse.
Departure.
Course.
4.5 poiuls.
5 "
•634
•556
5.5 points.
6
■471
•383
Thus, if a vessel holds a course of 4 points, tlmt is without leeway, for distance
of I mile, she will make .707 of a mile to windward.
Or, a vessel sailing E.N.E. upon a course of 6 points for 100 miles will make 38.3
(icx} X -383) miles of longitude.
IDesrees, JV^iiiutes, and Seooxids of eaoli Point of tlie
Coxxipasfii -svitli HMCeridian.
North. South. PolnU. o / n Siu. A.» | Cos. A.» Tan.A.*
N.
N.by K..
N. by VV.
N.M. Bi .
N.N.W
N.EbyN. ..
N.VV. byN...
N.E.
N.W.
' i
S.by E
&by W
o. o. Ci. .......
O'O. W. ......
S. E. by S.
S.W.byS.
2 48 45
5 37 30
8 26 15
" 15
14 3 45
16 52 30
19 41 IS
30
1845
7 30
22
25
27
N. E. by E. . .
N.W.byW...
E.N.E
W.N.W.
E.byN..
W. by N.
S.E.
S.W.
S.E. by E..
S.W. by W.
E.S.E. .
W.S.W.
E. by S.
W. by S.
45
East or West. East or West . .
30 56 15
33 45
36 33
39 22 30
42 II IS
45
47 48 45
50 37 30
53 26 IS
56 15
59 3 45
61 52 30
64 41 IS
67 30
70 18 45
73 7 30
75 56 15
7845
81 33 45
84 22 30
87 II
15
90
.0489
.098
.1467
•195
.2429
.2903
.3368
.3827
•4275
.4714
•514I
•5556
•5957
•6344
•6715
.7071
•7404
•773
.8032
•8315
.8819
.904
•9239
•941S
•9569
•97
.9808
.9891
•9952
.9988
9988
9952
9891
9808
97
9569
941 5
9239
004
8819
8577
831S
8032
773
7409
7071
67 IS
6344
5957
5556
5141
4714
4275
3827
3368
2903
2429
>95
J467
098
0489
0000
.0401
.0985
•1484
.1989
.2504
•3034
.3578
.4142
.4729
•5345
•5994
.6682
.7416
.8207
.9063
z
1. 103
Z.218
1.348
1.497
1.668
X.871
2.114
a. 414
3.795
3.296
3941
5-027
6.74X
10153
20.55s
00
* A| Tepres«nttng coane or point* f^om the meridian.
GBO6BAFHI0 LBVELLIKG.
55
GEOGBAPHIC LEVELLING.
C"arvatiire and. Xiefraction.
Correction for Curvature of Earth, to be subtracted from reading of
a leTelling-Btaff, is determined as follows :
Divide square of distance in feet from level to staff, by Earth's Eaua
torial diameter — ^viz., 41 852 124 feet.
Or, Two thirds of square of distance in statute miles equal the cur-
vature in feet.
Correction for Befraction is to be subtracted from reading, and as a mean
may be taken at about one sixth o2 that for curvature.
Correction for Curvature and Refraction combined, is to be iadded to
reading on staff.
Formulas of Capt, T. J. Lee^ U, S. JiM^ineen.
D* D^ . .
— =r = correction for cwrvcUure^ -^ r:, = correction for refraction^ and
3 R K
D"
(1—3 m) — =T = correction for curvature and refraction, D representing
distance, R radius of earth, and m a coefficient of refraction = .075, ufi
infeet.
Illustratiox. —A distance is 3 statute miles, what is correction for curvature
and refhicUon?
2
(1-3 X .075)^^^ = .8S X 5-996 = 5-097.A«t
Approximately, -^ D* = curvature infeet
3
Xjevellins T>y Boiling Point of "Water.
To Compute Kelglit A-lsove or Selow I^evel of Sea.
517 (212° - T) -f (212° - T)* = Height.
Illustration. — What isheighiof an elevation, when boiling point of water is i82<'f
517 X 212° — 182° + 212° — 182° = 517 X 30 -t- 3o» = 16 410/frf.
Corrections for Temperature to he made in Connection with Formula,
Corr«e<
tlon.
CJorwc-
_
Correc-
Correc-
Correc-
Correc-
Tnnp.
tion.
T«mp.
tion.
Temp.
tion.
Temp.
tion.
Temp.
tion.
Temp.
0
.936.
•
18
.972
36
1.008
e
54
1.046
72
1.083
■
90
a
•94
90
.976
38
1. 012
56
1.05
74
1.087
92
4
•944
32
.98
40
1. 016
58
1.054
1.058
76
Z.091
94
6
.948
24
.984
42
1.02
60
78
1.096
96
8
•952
26
.988
44
1.024
62
J. 062
80
l.i
98
10
•956
28
.992
46
1.028
64
1.066
82
1.104
TOO
X3
.96
30
.906
48
1.032
66
1.071
84
X.108
102
X4
•^A
32
I
50
1.036
68
I 075
86
1.112
104
x6
.968
34
1.004
52
1.04 1
70
1.079
88
1.I16
T06
1. 12
1. 124
1. 128
1.132
1. 136
I.I4
1.144
1.148
1.153
iLLUsntATioif. — AsBume temperature in preceding illustration to have been 80*,
Then 16 410 X 1. x = 18 051 feet
56
GEOGRAPHIC LEVELLING AND DISTANCES.
9
u
b
9
ID
O
0
h
9
•P
9
U
eS
P.
ft
:^
ON tN m tN,oo »*■ r>. M
CO \o ■♦00
moo ON f>vo
. m ON 00 m -^
8 00 CO ov coco «
S f*«oo CO d^ ON d M M e* covd o6 ci>o ONCi uSK-onm
g HHMHMiiHMetcicnrococo^
M en ■♦ ON
ONOO I/) CO C\
d^ ci CO fo co\d dN
m r>.co ov O ♦ t>.
a
2
'•S
aas
•
•
0\ CO •♦ CO On covO
00 '«• On -4-00 CO M
t>oo 00 dN dN o M
M M
com CO COVO
g^v^
5?^
M moo M
CO CO CO N 00
CO
NO
includ
and
•a
s
OvvO
M M
CO cooo
covdod
H H M
oovontH MvOOcOCt
ONCi mr^o ci dNcO"*-'"}-
(« CO en CO ♦ ♦ m t».oo On
M
M
M
M
M
l>i et 00 On CO ■♦vo
NO
CO
00 vo
n v5
NO Oni^ rx r>.
•
t^ 0 c« looo o m
M m
HNO «
moo 00 w 00
m«
cntnoo
m
•o
S
«
6\ '*-od ci >d M dNOO \d
m r^ d
m d
m 0 m MOO
« CO ♦NO r^ M
^
NO
5
03
,•
« CO CO ■♦ ■♦ lo io>o t^oo « t^ in •*•
M M ONOO vo
m o
♦ o moo
♦
■ .
EX4
M H
« CO
•♦ m mNO ^.oo fs m ♦ «
M
com
2^
M
M cn^-m 0
m
M
M
M ro m M c« On CO
On m w
rovo
mvo m t>.vo
0 CO
^«
io tN. o\ « ♦mo
moo
CO m tx o VO
r* coNO w H
00 CO (O On
H
"O
dNcot>>ci\d d d^txin ti-vd od
CO tx
• • • • •
HI vo o mvo
♦00
MVO 0 NO
♦ o
o
0
,1
« CO CO •*■ ■♦ «n inNO t^oo n vo
m CO w 0 ON r>. m ♦oo
CO rx c«
CO 1^ CO
S
^
M H
M CO ♦ m mvo t^oo vo
m CO «
M
M
•♦
M
« CO ♦ m o
m
a
M
M
u
•
vo « moo 00 n
t*\5 so vo m ♦ ♦
♦ d\ -i- dN -i- d\ dN
CO CO ♦ ♦ m m\o
I^COOO
a
.,|2
•
a
otf
•
1
CO c« M tx ♦vo •««• m On M m
didN dNodoo t^i^mm-4-cococi mt^o «
o
M
ON
o *S
r>.oo
On^OnOnOnOnOnOnOvOn
ONOO
rot^vo
♦
*8
M
B-
Ix
M H
« CO ♦ mvo r«.oo
Ov Ov On On On O
M
0 "
M
W CO ♦vo
MOO
M M
o
e
o
s
«
o
^mOmomQOOOOOQOQQQOQQ
« CO ♦ ♦ m mvo t^w ONOmOOOOdOQQ
* M M « CO ♦ mNO t>.oo ov
S
I
i
♦ ♦ MVO
MVOOOOO^mM^OVM OvlxOvOvCOCOnvONQ ♦OO « ON ♦
t^ « vo O ♦ « ONNO en Ov CO « ♦ CO ON COVO t^rxt*.© ♦mmo ♦
5 *^ t^oo 00 d\<>6 d M ei ♦K.m ♦t^dNci ♦vd od ♦ tv »s.vd w\h\h
g MMMMMMdMCicicocococo mvo txoo Ov co<o
M « CO -^s:
it
•si
« o
« B
.S 0
« •
«8
^ s
'Sg
I"
Apparent I^vel
induaing Curvature
and Refraction.
1
• 00 MOO ONmt^mM moo Ot o«oo no ♦ no ci oo cooo n vo cono
JS 0 cooo wvo ovw mtvONM ♦mis.ONM co ♦vo tx Ov o « CO mvo «
g M M M ci ci « cococncO'4- + ^--+'i-mmm»om mvo vd vo <> no r^
•6
3
8 ON CO Ov M r«.oo rx en r^ « m o m ovvo co NOMvoMmovcots.
^S 0 cooo covo On « m J«» m ♦vO oo On m to mvo 00 On m « to mvo co
g H M M ei e» « cncofo* + 4-^'i"vi"«ommmm thsd no vd vd vd t^
G HT
of Curvature and
Refraction.
1
00 N
Uvo^ mMvo NO mnvoMmMNO^cn ^vo to. ct i^ m t«.
« moo rx m ♦ et M onoo no m co m 0 Ov tN,vo ♦comooo r^^mcoci m
U« ' ' M « CO ♦ m mvo t^oo dv d m m ci co ♦ *h\o t^ t>.o6 dt d m m
mmmmmmmmmmmmSc«C(
73
CO m
.* vo fo Ov fooo CO tx M ♦oo cooo «mMm« NOQNMCtm cooo fs
J moo vo mcop» 0 Ovt^m^c* m ovoo no mcoM ONONtN.m^M0 m
Vn ' * w ci en + m *n<'0 is.od dvddMcico^-m mvo tvod dv d m m
mmmmmmmmmmmmC«NCI
H E I
of
Curvature
above
Zjaad.
4J vo cvoo 00 tx iwo mcoNMM ^sO^^HONncoMoocoMH^sOve«
{NO OvOvONOvOvON On ON ON On Ov OtOO OOQOOOOOOOOOOOOOOOOONO t>.t«>
Ixt ' ■ M ci CO ♦ mNO iNod d. d h ci co ♦ v^\o ti.od 6\6 m ei r?) ^ dv
l|
I?
• ,2
o
*ivO
I •
cS
SCci
H « en ■♦ m>o »^oo ON o H « CO ♦ mvo isoo on o
O M « CO '♦m o
N M CI M « M en
m
♦vo !>. t>iVO ♦ M 00 ♦ ♦ON cooo M ♦ tvOO N
« ♦NO 000«^m»«»0>OMto ♦'O h»09 On M t>
M hi c< e( c« coeocococo'i-^-'>i--^'i-'*'mmmmmmm mvo vd
w en «
« tS. M
tl
(i
u
II
t(
(t
(t
li
(i
6E0GBAPHIC LEVELLING. — MAGNETIC VARIATION. 57
Illdstration. — Curvature of Earth independent of refhiction is computed At
.667 foot =8.004 ^^^- 'or I geographical wile, and as refraction on land is talcen as
.104 foot or 1.248 ins., and on ocean at .099 foot or i.z88 ins., relative visible dis-
tances of an object, including curvature and refraction, for an elevation of
.667 foot is 1.09 miles on land, and 1.08 miles at sea.
I " *' 1.33 " " " *' 1.32
9 feet " 4 " " »» " 3.98
I mile " X04.03 " " " • ** X03.54
Difference between two levels in feet is as square of their distance in
miles.
iLLcsTSATioir. —At what elevation can an object be seen, at surface of ocean, when
It 18 2 miles distant?
i'' : 2' :: .667^ — .099 : 2.272 feet :z= 2 feet 3 2S-\-ins.
DifTcrence between two distances in miles is as square root of their heights
in feet.
Illustration i. —At an elevation of 9 feet above letel of sea, at what distance
can an oLJcct be seen upon its surface?
V-667 —.099 = .754 : I :: v''9 : 3-98 miles.
2.— If a man at the fore-topgallant mast-head of a vessel, 100 feet from water, sees
another and a large vessel *' hall to,''' how far are the vessels apart?
A large vessers bulwarks are at least 20 feet from water.
Then, by table. 100 feet =13.27! ,g,^ rniles distance.
50 = S-93) '
When an observation for distance is taken from elevation, as a light-house,
a vessel's mast, etc., of an object that intervenes between observer and hori-
zon, or contrariwise, observer being at a horizon to elevated object, distance
of observer from intervening object is determined by ascertaining or esti->
mating its ele\'ation from horizon, and subtracting its distance from whole
distance between observer and point from which observation is taken, and
remainder is distance of object from observer.
Illustration. — Top of smoke pipe of a steamer, assumed to be 50 feet above sur
face of water, is in range with borizon from an elevation of 100 feel; what is dib
tance to steamer from elevation ?
100 feel,
so " .
= 'q ^81 3" ^9 miles distance.
MAGNETIC VARIATION OP NEEDLE.
America. — Needle reached a Westerly maximum in 1660, and then varied to East
until 1800, when it reversed to West.
London (Eng.).— From 1576 to 1815 variation ranged from 11° 15' East to 24° 27'
West, when It receded gradually to 21° in 1865.
Jamaica {W. I.). — No variation from year i66a
Diurnal Variation.— There is a small diurnal variation, being greatest in'sum-
mer (15') &iid least in winter (7' 30"), added to which a change or temperatura
affects a needle.
Variation in U.S. — Professor l/oomis concludes that the Westerly variation is
increasing and Easterly diminishing in every part of United States ; thnt thiji
cbaog* occurred between 1793 and 1819, and that present annual change is about
2' in Southern and Western States, from 3' to 4' in Middle States, and 5' to 7' ia
Eastern Stales.
NoTK.— Rules for computation of variation are empirical, except in each par-
ticular locality, as annual and diurnal variations of needle, added to local allniC'
lion, render it altc^ether unreliable.
58
MAGNETIC VARIATION OF NEEDLE.
XDeoennial IVIagxxetic Variation, in. tlie XJ. S. and.
some i^oreign Countries. From, January^ 1820, to January, 190CX
If. S. Coast and Geodetic Survey. Chaa. A. Sdiott.
Location. 1820. 1830. 1840. 1850. i860. 1870. 1880. 1890. 1900.
EAST.
Acapulco, Mex
Austin, Tex
Charleston, S. C
Chicago, 111
Cincinnati Obs'y, 0
Cleveland, O
Denver, Col
Detroit, Mich
Duluth and Superior, Minn
El Paso, Tex
Erie, Marine Hos'l, Peun
Fernandina, Fla
Florence, Ala
Galveston, Tex
Havana, ColPe de Belen, Cuba.
Milwaukee, N. P't, Wis
Mexico, Ast'lObs'y, Mex
Mobile,^ Ala
Monterey, Cal
Nashville, near Van't U'y, Tenn.
Newborn, N. C
New Orleans, I^a
Olympia, Wash
Omaha, Neb
Pensacola, Fla
Portland, C. House, Ore
Port Townsend, Wash
St. Louis, Mo
Salt Uke City, T'mple B'k, Uuh
San Antonio, Tex
San Diego, C'y Park Obs, Cal. .
Sau Francisco, Presidio. Cal. . . .
Savannah, Hutch'n Is'd, (ia. . . .
WEST.
Albany Obs'y, N. Y
Baltimore, F't McH., Md
Bangor, Tlio's Hill, Me
Boston, Mass
Bullalo, N. Y
Burlington U'y, Vt
Cambridge, CoIPe Obs'y, M.iss.
Charleston, St. M. Ch ,S. C...
Cleveland, 0
Detroit, Mich
Erie, Pa
Halifax, N. S
Harrisburg, Pa
Hartford, C. Hill, Conn
Ithaca, N. Y
Montreal, Can
New Brunswick, N. S
New Huveu, Coun
New York, C. Hall, N. Y
Philadelphia, Gi'd Coll'e, Pa...
Pittsburg, Pa
Portland, Bram'l Hill, Me
Portsmouth, N. H
Providence, near B. \]"y^ R. I..
Quebec, Can
Toronto, Can
Washington, N. Obs'y, D. C...
o
8j
4- OS
6.12
5
1-43
2.84
•39
6.58
6.2
8.2
4.6
13-4
6-7
1.66
7.96
18.8
12.64
7.42
18
19.04
9.8
11. 79
14.6
4-7
6.02
•93
12. 1
7.84
.41
778
8.12
'7
5
2.
8
3
5
4
4
8
58
7
43
04
61
2-44
9,46
8-3
6-95
12.3
o
,8.7
II
3-59
6.28
4.82
I.I
2.49
.09
6.54
6!^8
8~S
703
'3-93
6.9
1.23
8.25
19.4
12.56
18.8
20.06
8.9
Id
12.27
15- 1
4-5
6.49
1.29
12.9
8.42
•79
8.29
8.7
18.2
1-4
6 02
2.8
8.7
4.02
5-44
4.98
2.91
10. 1
7.67
12.9
.8
.6«;
o
8.9
10.7
3-03
6.25
4^5i
.66
2.04
•5
6-37
8.8
5-77
8.6
7-^
H-45
6^
7
8.16
20.1
12.33
7-4
19.S
20.67
8.6
10.28
12.67
'5-43
4.2
7.07
1.77
»3-7
9.6
1-35
8.9
932
.36
18.4
21
6-59
3^1
9 5
4.66
5-97
5.61
3.46
.18
10.82
955
8.49
13.8
1.32
1. 17
O
8.88
10.2
2-39
6.04
4.08
.16
1-55
9.8
12.14
6. 1 1
8.9
5.39
7-4
8.62
6.99
1^.91
6.7
20.65
11.96
7- 14
20.3
21.22
82
15.8
10.31
12.99
15.8
3.78
773
2.35
24.48
9 73
2.05
958
9-97
•94
19.4
2.9
7.24
3-5
10.5
5- 32
6-59
6.31
4.07
.68
19.56
10.28
9.06
14.9
1.6
1.77
o
8.75
9-74
1-73
5-67
3-57
15-14
•93
10.02
12.34
3I
5-74
8.8
4-95
6.9
8.55
6.71
15.32
6j
7.66
21.17
11.47
6.73
21
21.71
7 7
16.27
KX17
13.21
16. II
325
8.44
2.99
15.24
10.38
2.84
10.27
10.6
•39
1.6
19.9
3 7
7-93
4.1
1 1.6
598
7.28
6.91
4-73
1.26
12.29
1103
9.67
16
2.17
2.43
o
8.5
9.27
1.07
5-15
2.99
14.88
•34
laii
12.38
3.2
5.3
8-55
tt
8.39
6.27
»5^65
5.78
7.18
21.63
10.89
6.19
21.5
22.15
7-»
16.54
9.87
13-32
16.36
2.65
9.17
365
15.92
10.99
3-67
10.96
11.18
.96
2.3
20.3
4.46
8.62
4
12
6
7
7
5
I
12.97
11.75
10.23
16.9
2.66
c
8.12
8.8
•45
452
2.39
88
6
59
99
4
44
87
^ »
1452
10.06
12.23
2.5
4.81
8.16
3-97
5.4
8.13
5.71
»5-89
5.13
6.59
22.01
10.23
5-55
22
22.4
6.4
16.61
9 44
'3-32
16.57
2.01
9.87
4-3
16.48
"•53
4-51
11.58
11.68
1.52
•23
2.99
20.6
5.12
9.24
5-71
»3-7
7.12
8.69
7-9
6.2
2.49
'3-58
12.4
10.85
17.4
3 62
3.72
7.64
8_34
3.81
1.8
14.06
9.9
"•93
1.9
4.28
7.62
346
4.5
7.77
506
16.04
4-4
59'
22.29
956
4.8s
22.3
22.58
5.6
16.46
8.9
132
16.64
137
10.52
4.89
16.89
11.96
5-3
12-11
12.08
.09
2.05
•74
3- 62
20.7
5^64
9.89
6.58
14.6
7-55
933
8.49
6.97
3.06
14.08
12.94
11.48
12.5
4.12
4.28
o
7-9
3-1
13
9-5
11.5
12
3.8
6.9
3
3
7
4 _
16.1
3^6
2
5
9
M
5
7
5
22
8
4
22.
22
5
16. 1
8.3
»3-7
16.7
.8
II. z
5-4
17.1
12 3
6
12.5
12.4
.05
2.5
12
4.2
20.7
6
10.4
7-5
15-4
7-9
9.9
9.1
7-7
35
14.4
»3-3
12
17.5
4-8
6.3
MAGNETIC VARIATION (
K^IaKiietiti Vai-iation of Needle at Xjooationa in
United states and Canatia, 1800.
U. S. CViosI and Otodetic Hunx). Clias. A. SchoO.
Loc.no..
"^^
LM.tIO,.
''.^:-
Loc.Tmi..
iKJ^
AHceB, S.C
Astoriai, Ore...... .
BatcnKouge.La:;!!
h
I w.W
) ., cJi"
I iia,::
3-3
Natcbai, Mlas.......
toktan'i'"™'!''!'.!*
Pansacota. Fla
'SacrainBDloG.G.,Cat
Sa'ltlAkeT., UtaV;:
Sao Antonio Ob,,TBi,
SanBlaa, Hei
Sbd [•iego.C. Fk.,Cal
Santa Barbara, CI..
SanlaFc.F.M'r'y.N.M
SeatUs, Wash.
5S:,;iwi:.::
aiL"a'iffiG'Ai^i;;
.1
D«rl8ii.(Ja.
S:a:W~:::::
FortUowl., AMI....
Fort Garland, CaL...
Fort Gil>«D7[Dd. T
'e-3
eilwa, lU
iTuscaloou, Ala
VickBburgC.H..Mies
S-6
Aubum,N. Y.
8.5
S^^ro''.'!^::
HBnllngi™, I......
S-b
JlhiH!a,KY
UlUs Kails. N. Y. ..
Iwego, N, Y
M«lKb,nrCap-|,Rc!
Saginaw, HIcb
Sandusky, 0
"iibrook, Conn
ibenecudy, H. Y..
Sou lb B«lUlB)ieni,Fa.
- igfleHl. Mass....
i^, Conn
Stobtngton, Conn...
Tapnanhl"['iles,N.Y.
Toledo M'uLiiH.O..
't1^™:y: :'.:::::
Co GEOGRAPHIC LEVELLING. — BASE LINE. — ^SOUNDINGS.
Dip of IHIorizson.
Approximate, 57.4 VHzs,dip in aecondsy varying with temperature of
air. H representing height ofooterver's ejfe injeet.
.667»'=H: .498#*=Hr i.43V'H = *; 1.113 v^H = f».
ft representing distance in geographical miles and s in statute.
INleasuremeiit of Heiglxts -with a Bextant.
Malti-
plier.
I
1-5
3
Angle.
Multi-
plier.
Angle.
MhUI-
plier.
Angle.
Malti-
plier.
ABfle
Multi-
plier.
0 »
45 0
56 18
63 36
2-5
3
3-5
68 IX 4
71 34 4-5
74 4 U 5
• »
75 58
77 29
78 41
5-5
6
7
• •
79 42
8c 33
8x 53
8
9
xo
Angle.
• t
82 53
83 40
84 17
Operation Set sextant to any angle in table, and height will equal distanca
multiplied by number opposite to it
Illustration. — When sextant is set at 80® 32', and horizontal distance from ob-
ject in a vertical line is 100 feet, what is its height ?
100 X 6 = 600 ^i.
By Trigonometry: x : xoo :: 5.997 (ton. angle) . s^ 7 feet.
To Reduce a Soiindins to X-iotv "Water.
- [ I :p COS. — - — j = A', h representing rertical rise oftide^ and k sound-*
ing or depth at low water, both in feet ; t time bettoeen higJi and low wafer , and
t timsfrom time of sounding to low water, in hows. — cos. when — — <90°
and + COS. when >9o*^.
Illustration. — Low water occurring at 3.45, and high water at 10.15 p.m., a
soundipg taken at 5.30 p.m. was 18.25 ^^^^\ what was depth at low water, vertical,
risebemg 10 feet?
h r= xofeet ; t^ = $h. 30m. — sfe. 45m. = ifc. 45m. = x. 75 hours,
t = xo^ xsm. — 3^. 45m. = 6h. ym. = 6. 5 hours.
Then — f i qicos. '^Xi-75\ _j (,_cor 48© 37' 4x")=5)<(x-.663 i«4)=i.68438,/teft
2 \ 0.5 / V
Sounding i8.25/e«t — Redirction i.68407/r<< = i6.56593yfe«t
.rjengtlis of a "Degree of Iuonf(ltude on paraUAlff> of Uatl-
tvide, for each, of its Degrees fronx £g.uator to £*ole.
Lat.
Miles.
Lat.
Miles.
Lat.
Milet.
Lat.
Milee.
xO
59-99
16O
57-67
31°
51-43
46O
41.68
3
59-96
17
57-38
32
5a 88
47
40.93
3
59-92
18
57-06
33
50.3a
48
40.15
4
59-85
19
sf-^i
34
49-74
49
3936
38.57
5
59-77
20
56.38
35
49-15
48.54
SO
6
59-67
3X
56.01
36
S«
37-76
7
59-55
32
5563
37
47.93
5«
36.94
8
59-42
23
55-23
38
4728
53
36.11
9
59.26
24
54-81
39
46.63
54
3527
10
59-09
25
54.38
40
45.96
55
34 4«
XI
58.89
26
53-93
41
4528
56
33 45
X2
58.69
^l
53- 46 .
42
44-59
43-88
57 ,
32.68
13
58.46
28
5297
43
58 '
31 79
14
58.32
29
52-48
44
43- 16
59 .
309
15
57-95
30
51-96
45
4243
60
30
Lat.
Milee.
6jO
30.09
38.17
6a
63
3774
64
36.3
6S
35.36
66
24-4
67
»3-44
68
33.48
69
215
70
3053
71
1953
18-54
72
73
1754
74
>6-54
75
1553
Ut.
Milee.
76°
"4-52
77
«3-5
78
13.4B
P
11.45
80
10.43
81
038
8-35
83
83
731
84
6.37
«S
5-23
86
4.18
87
3-J4
88
3
89
1.05
90
.00
NoT«. — Degrees of longitude are to each other in length as Cosines of their
Uitudea
FIGUBE OF EAETH. — BOABD AND TIMBER MEASUEB. 6 1
Bjlexneiits of* F'isure of tlie Kartli.
CapL A. B. Clarke^ 1866.
Feet. Mile*.
MiOor semi-axis of Equator (longitude 15O 34' E.) 20926 350 3963.324.
Minor " " " '* ( " io5°34'E.) 20919972 3962.115.
Polar " " 20853429 3949-513.
Equatorial sem i-axfs 20 926 062 3 963. 269.
Circumference, mean 24898.563.
Diameter, " 7916.
BOARD AND TIMBER MEASURE.
BOARD MEASURE.
In Board Measure, all boards are assumed to be i inch in thickness
To Compute Mieasnre or Surface.
Wkefi all Dimetisions are in Feet.
Rule. — Multiply length by breadth, and product will give surface in
square feet.
When eiiher of Dimensions are in Indies.
EzAMPLR. — What are number of square feet in a board 15 feet in length and i€
inches in width? *
15 X 16 = 240, and 240 -r- 12 = 20 sg. feet
When all Dimensions are in Inches,
Rule. — ^Multiply as before, and divide product by 144.
TIMBER MEASURE.
To Compute Volume of Round Tim'ber.
When all Dimetisions are in Feet,
Rule. — Add together squares of diameters of greater and lesser ends,
and product of the two diameters ; multiply sum by .7854, and product
by one third of length.
Or,a + a'-f a" x - = f,and c' + c" -|- c x c' x .07958 X - = V. a and
3 3
a' represeniing areas of ends, d' area of mean propoi'tiotial, I ler^th, and c
and c' circumference of ends.
Non.— Mean proportional is square root of product of areas of both ends.
IixcsTRATioN.— Diameters of a log are 2 and 1.5 feet, and length 15 feet
15
(a^+i.s^+aX i.5) = 9-25> which X .7854 and ^=-.36.3245 c^befeet
When Length in Feet, and Areas or Circumferences in Inches.
Rule. — Proceed as above, and divide by 144.
When all Dimensions are in Inches.
Rule. — Proceed as before, and divide by 1728.
Note. — Ordinary rule of Button, Ordnance Manual of U. S., and Molesworth, of
i X c-i- 4, giv. s a result of about .25 less than exact volume, or what it would be
if the ioff was hewn or sawed to a square, c reprezcniing mean circumferences
F
62
BOABD ATSTD TIMBER MEASUBS.
To CoixipTite Volume of Squared. Tim'ber.
Wheii all Dimeiwions are in Jf'eet.
Rule. — Multiply product of breadth by depth, by length, and product
will give volume in cube feet.
When either Dimentsion is in Inches.
Rule. — Multiply as above, and divide product by 12.
When any tioo Dimensions are in Incha».
Rule. — Multiply as before, and divide by 144.
ExAMPLK.— A piece of timber is 15 inches square, and 20 feet in length; required
its volume in cube feet
15 X 15 X 30 ^ ^ t
-^ = 31.25 cube feet
144
Allowance Is to be made for bark, by deducting from each girth from
.5 inch in logs with thin bark, to 2 inches in logs with thick bark.
100 superficial feet > „„„„.«
of pUking ( = ^ »^"^'^
120 deals = 1 hundred.
!M:ea8vires of *I^iTxx\yer. -—{English.)
50 cube feet of squared ) 1 j,
40 feet of unhewn timber = i load.
600 superficial .feet of inch planking = i load.
X)ea,ls.
Deals. — Boards exceeding 7 ins. in width, a!id if less than 6 feet in
length, are termed deal ends.
Battens are similar to deals, but only 7 inches in width.
Balk. — Roughly squared lo^ or trunk of a tree.
Planks are boards 12 ins. in width.
LaOOBl iStaudards.
Country.
Country.
Long.
Broad.
Thick.
Volume
Russia and
Prussia . .
Sweden . . .
Ft,
12
14
Ina.
II
9
Ins.
1-5
3
Cub. ft.
1.375
2.625
Norway . .
Christiana
Quebec. . .
100 Petersburgh standard deals equal 60 Quebec dcais.
Long.
Broad.
Thick.
Volam*.
Ft.
Ina.
Ina.
Cub. ft.
12
9
3
2.25
II
9
1.25
.859
12
II
2.5
2.293
SPARS AND POLES.
Pine and Spruce SparSy from 10 to 4.5 inches in diameter inclusive,
are to be measured by taking their diameter, clear of bark, at one third
of their length from abut or large end.
Spars are usually purchased by the inch diameter ; all under 4 inches
are termed Poles.
Spars of 7 inches and less should have 5 feet in length for every
inch of diameter, and those above 7 inches should have 4 feet in length
for every inch of diameter.
I^oss or '^Vaste in
Oak, English 200 per cent
" AfVican 100 '• "
«♦ Dantzic 50 " "
" American ip "
iHe-w-ins or Sa^wing of Xixn"ber.
(C. Mackrow.)
Yellow Pine from planks. . jo per cent
Tealc 15 " •'
Elm,Engli.sh 200 " **
" Awericaft 15 " ♦♦
ti
CISTERNS. — SHINGLES.
63
CISTERNS.
Capacity of* Cisterns in Cnbe I^eet and G-allons.
For each 10 Jnclien in Depth.
Diatn. I Cnb. ft. I Oallona
Diam.
Feet.
2
2-5
3
35
4
4-5
5
5.5
6
6.5
7
7-5
8
8.5
9
Cub. ft
2.618
4.091
S.89
8.018
10.472
13-254
16.362
19.798
23.562
27.652
32.07
36.816
41.888
47.288
53014
Gallona
Diam.
Cab. ft
Gallons.
Feet.
19.58
9-5
59.068
441.8
30.6
10
65.449
489.6 '
44.07
10.5
72.158
53978
59.97
II
79.194
5924
78.33
"5
86.558
647.5
99.14
12
94.248
705
122.4
12.5
102.265
764.99
148. 1
13
110.61
827.4
176.24
13.5
1 19.282
892.29
206.84
14
128.281
959.6
23988
14.5
137.608
102938
275.4
15
147.262
1101.6
313.33
15.5
157.243
1176.26
353-72
16
167.552
1253.37
396.55
16.5
178.187
1332.93
Feet.
17
17.5
18
19
20
21
22
23
24
25
26
27
28
29
30
189.15
200.432
212.056
236.274
261.797
288.632
316.776
346.23
376.992
409.062
442.44
471-13
513.126
550.432
589.048
1414.94
1499.33
1586.28
1767.45
1958.3
2159.11
2369.64
2589.97
2820.09
3059.8
3309.67
3569.17
3838.44
4117.51
4406.08
Kxoavation and X^iniiig of* AVells or Cisterns.
For each 10 Inches in Depth.
m
•
1
Bricki.
Masonry.
J
8
Num-
Uid
8 inches
I foot
Q
iS
ber.
dry.
thick.
thick.
Feet.
Cob. ft.
Cub. ft.
Cub. ft.
Cub. ft.
3
12.29
126
5.24
6.4
10.47
3-5
15.29
147
6. II
7-27
11.78
4
18.62
168
6.98
7.85
8.14
13.09
4-5
22.27
z88
9.02
14.4
5
26.25
209
8.73
9.89
15.71
5-5
39-56
230
9.6
10.76
17.02
6
35-2
251
10.47
11.64
18.33
6.5
40.16
272
"•34
12.51
19.63
7
45-45
293
12.22
«3.3«
20.94
l'^
51.07
314
13.09
14-25
22.25
8
57.02
335
13.96
15.13
23.56
i
«
•
§
Bricks.
Masonry.
1
Num-
Uid
8 inches
I foot
Q
rt
ber.
dry.
thick.
thick.
Feet.
Cub. ft.
Cub. ft.
Cub. ft.
Cub.ft.
8.5
63.29
356
14-83
16
24.87
9
69.89
377
15-71
16.87
26.18
9-5
76.81
39«
16.58
17-75
27-49
10
84.07
419
17-45
18.62
28.8
10.5
91.65
440
18.33
19.49
30. IX
II
9956
461
19.2
20.36
31.42
12
116.36
503
20.94
22.11
3403
13
134.46
545
22.69
23.85
36.65
14
153-88
586
24-43
25.6
39-27
15
174.61
628
26.18
27-34
41.89
16
196.64
670
27.92
29.09
44-51
Number of bricks and width of curb are taken at dimensiiHis of ordinary
brick — viz., 8 by 4 by 2.25 ins. = 72 cube ins.
In computing number of bricks required, an addition of 5 per cent, should
be added for waste. It is to be considered, also, that diameter of excavation
necessarily exceeds that of masonry.
SHINGLES.
Usually of white Cedar and Cypress ; 27 inches in length and 6 to 7
inches in width, dressed to light .25 inch at point and .3125 inch at
abut.
Laid in three thicknesses and courses of about 8 inches, so that less
iban .33 of a shingle is exposed to air, or about 2.25 shingles are re-
quired per square foot of roof.
Shingles, alike to SUtes, are laid upon boards or battens.
64
SLATES AND SLATING.
SLATES AND SLATING.
A Sqtiare of Slate or Slating is loo superficial feet.
Gaitffe is distance between the courses of the slates.
Lap is distance which each slate overlaps the slate lengthwise next
but one below it, and it varies from 2 to 4 inches. Standard is assumed
to be 3 inches.
Margin is width of course exposed or distance between tails of the
slates.
Pitch of a slate roof should not be less than i in height to 4 of length.
To Compixte Surface of a. Slate -wlien. laid, and Num-
ber of Sq.uares of Slating.
Rule. — Subtract lap from length* of slate, and half remainder will
give length of surface exposed, which, when multipUed by width of
slate, will give surface required.
Divide 14 400 (area of a square in inches) by surface thus obtained,
and quotient will give number of slates required for a square.
Example. —A slate is 24 X 12 inches, and lap is 3 inches; what will be number
required for a square?
24 — 3 = 21, and 21 -i- 2 = 10.5, which x 12 = 126 indie* ; and 14 4c» -4- 126 =
1x4.29 tlaUi.
IDixxiensions of Slates.
[American.]
Int.
Ins.
Ins.
Ins.
Ids.
Ins.
Ins.
14X7
14 X 8
14X9
14 X 10
16 X 8
16 X 9
16 X 10
18 X 9
18 X 10
18 X II
18 X 13
aox 10
aox II
20 X 12
32 X II
22 X 12
22 X 13
24 X 12
24 X 13
24 X 14
24 X 16
English.
Doubles
Small doubles
Plantations . . \
Viscountess . . .
Ins.
13X10
13X 7
iiX 6
lox 5
12x10
13x10
18x10
Ladies
Countess
Ins
I2X 8
14X 8
14X12
15X 8
i6x 8
16x10
20X10
Marchioness
Duchess . . .
Imperial . . .
Rags
Queens . . . .
Empress . . .
Princess . . .
Ins.
22X22
24X12
30X24
36X24
36X24
26X15
34X14
Thickness of slates ranges from .125 to .3125 of an inch, and their weight
varies from 2 to 4.53 lbs. per sq. foot
"^Veiglit of One S<inare Koot of Slatingr.
. 25 in. thick on laths 9. 25 lbs-
" " " " 1 in. boards.. 11.25 "
.3125 in. thick on laths ix.15 "
" «' " " I in. boards, 14. 10 "
125 in. thick on laths 4.75 lbs,
" " " " I in. boards.. 6.75 "
1875 In. thick on laths 7 "
" »' " " I in. boards. 9 "
Slate weighs from 167 to 181 lbs. per cube foot, and in consequence of
laps, it requires an average of nearly 3.5 square feet of slate to make one of
slating.
Weights per 1000 and Number Required to Cover a Square.
Doubles 13 X 6
Ladies 15 x 8
J.U.
No.
1680
480
Countess . .
. ao X 10
3800
340 1
Duchess . .
. 24 X 12
6730
4480
No.
171
"5
* Length of* slsts Is taken from nail-hole to tall.
SBOt AKD SHELtS.^— ^SAUI>UL:KKT BALANCES. 6$
PILING OF SHOT AND SHELLS.
To Compute NumlDer of Sh,ot.
Triangular Pile, Rule. — Multiply continually together, number of shot
in one side of bottom course, and that number increased by i, and again by
2, and one sixth of ]uroduct will give number.
EzAMrLB.— What is number of shot in a triangular pile, each side of base contain-
ing 30 shot?
30X30+- X30-h» =, £9|6o ^ ^^^^^
0 6
Square Pile. RuLE.-^Multiply continually together, number in one side
of bottom course, and that number increased by i, double same number in-
creased by I, and one sixth of product will ^ve number.
ExAMPLK.— How many shells are there in a square pile of 30 courses?
30 X 30+1 X 30 X 2 + 1 _ 56730 ^,„.juwi.
^ — — g — = 9455 smUs.
Oblong Pile. Rule. — From 3 times number in length of base course sub-
tract one less than number in breadth of it ; multiply remainder by number
in breadth, and again by breadth, increased by i, and one sixth of product
will give number.
Example. — Required number of shells in an oblong pile, numbers in base course
being 16 and 7 ?
'6X3 — 7 — 1X7X7 + 1 _ 2352 _ ,^^ ^fc,,;.
g = —^ = 392 shelU.
Ina}mplete Pile, Rule. — From number in pile, considered as complete,
subtract number conceived to be in that portion of pile which is wanting,
and remainder will give number.
FRAUDULENT BALANCES.
To Detect Them. — After an equilibrium has been established between
weight and article weighed, transpose them, and weight will preponder-
ate if article weighed is lighter than weight, and contrariwise if it is
heavier.
To Ascertain True Weight. Ru i.e.— Ascertain weight which will produce
equilibrium after article to be weighed and weight have been transposed ;
reduce these weights to same denomination, multiply them together, and
square root of their product will give true weight
ExAMPLa. —If first weight is 3a lbs., and second, or weight of equilibrium after
transposition, is 24 lbs. 8 oz., what is true weight?
24 Iba 8 oz. = 24. 5 lbs.
Then 3a X 24. 5 =784, and y/jB^ = 28 lbs.
Or, when a reprewntt longest arm, I A greatest weighty and
b " shortest arm, \ B least weight.
Then WassAft^and W6 = Ba; multiplying these two equations, W=afc = ABa6,
or W» = AB, and W = VAB.
Illustbatiok. — a = 32 ; B = 24. s ; W = 28. Assume length of longest arm = la
Then 32 : 28 :: 10 : 8.75^
Be«oe, a = 10, 6 = 8.75, or 28* = 32 X 24. 5, and V32X24.5 = 2&
V*
66
WBIGHING WITHOUT 6CALSS. — ^PAINTING.
"Weieliiiis -witlxo-at Scales.
To i^Boertaixi l^eiglit or a Sar, Beaxn, etc., bjr Add. ot
Opbration. — Balance bar, ete., over a fulcrum, and note distance between
it and end of its longest arm. Suspend a known weight from longest arm,
and move bar, etc., upon fulcrum, so that bar with attached wei^t wiU be
in eqnilibrio; subtract distance between the two positions of fulcrum from
longest arm first obtained ; multiply this remainder by weight suspended,
divide product by distance between f ulcrums, and quotient will give weight.
ExAMPUL— A piece of tapered timber 24 feet in length is balanced over a ftilcrum
when 13 feet from less end; but when the body of a man weighing 210 lbs. is sus-
pended tram extreme of longest arm, the piece and weight are balanced when ful-
cmm is 12 feet Arom this end. What is weight of the timber?
13 — 12 = I, and 13 — 1 = 12 feet Then 12 X 2xo-r- 1 = 2520261.
PAINTING.
I pound of paint will cover about 4 square yards for a first coat and about
6 yards for each additional coat.
I*roportions of Colore for ordinary Paiiit8.--B3r '^Teiglit.
COLOKS.
White
Black.
Green
•2 c'
Hi
100
i»5
100
—
—
75
CoLOKS.
Lead
Chocolate. .
5 .
N
1-32
2
Red
Lead.
Red
Ochre.
1 .
>-6
•Sn
c 0
«COQ
98
—
—
— .
__
—
—
50
50
—
4
—
_^
^
96
These are the colors alone, to which boiled linseed oil, litharge, Japan varnish,
and spirits turpentine are to be added according to the application of the paint
Lamp-black and litharge are ground separately with oil, then stirred into the
lead and oil.
Thus for black paint: Lamp-black 25 parts, litharge i, Japan varnish i, boiled lin-
seed oil 72, and spirits turpentine i.
T'ar Faiut.— €k>al tar 9 gallons, slaked lime 13 Iba, turpentine or naphtha 2
or 3 quarts.
A GaLLOH or pAtRT WILL COTSB
On stone or brick, about .
On composite, etc, fh>m ,
On wood, from
SnperficiAl
ftet.
190 to 225
300 " 375
375 " 525
A Oalloiv or Paimt will cotbb
On well-painted surfkee or iron
One gallon tar, fiist coat
" " '• second coat . . .
Superficial
tmi.
600
90
160
Boiled Oil. — Raw linseed oil 91 parts, copperas 3, and litharge 6.
Pot litharge and copperas in a cloth bag and suspend in middle of a kettle. Boil
oil four hours and a half over a slow fire, then let it stand and deposit the sediment
"White Paint.
Inaida work. OnUid« work.
White lead, in oil . . 80 80
Boiled oil 14.5 9
Iiwid* work. Oateide work.
Raw oil — 9
Spirits turpentine. 8 ..... 4
New wood- work requires i lb. to square yard for three coats.
Imidb.
Priming . . . .
2d coat
3d "
Coats for 100 Square Tarda New White Pine.
OCTBII>C>
Priming...
ad and 3d )
coats I
White
le«l.
Raw
oil.
Tnrpen-
tine.
Drier.
Lb*.
16
«5
>3
PU.
3-5
2-5
Pte.
6
x-5
x-S
Lbe.
•25
.25
•as
White
lead.
Lh».
18.5
Raw
oil.
Pt«.~
2
Boiled
oil.
Pt».
9
tS
2
9
Tarpen-
tine.
Ptfc
. I lb. of drier with priming and coating for outside.
HTDBOMETEBS. 6/
HTDROMETERa
U. 8. Hydrometer (Trailers) ranges from o (water) to loo (pure spirit) ;
it has not any subdivision or standard termed " rroof ," but 50, upon
stem of instrument, at a temperature of 60°, is basis upon which com-
putations of duties are made.
In ooDDection with this instrament, a Table of Corrections, for differences in tem-
perature of spirits, becomes necessary; and one is Airnished by the Treasury De-
partment, from which all computations of value of a spirit are made.
Illdstkation. — A cask contains 100 gallons of whiskey at 70^^, and hydrometer
sinks in the spirit to 35 upon its stem.
Then, by table, under 70^ and opposite to 35, is 32.99, showing that there are 33.99
gallons of pure spirit in the loa
Commercial Hydrometer (Gendar's) has a "Proof" at 60*^, which is
equal to 50 upon U. S. Instrument and its gradations, run up to 100
with it, and down to 10 below proof, at o upon U. S. Instrument ; or o
of the Commercial Instrument is at 50 upon U. S. Instrument, from
which it progresses numerically each way, each of its divisions being
equal to two of latter.
In testing spirits. Commercial standard of value is fixed at proof ;
hence any difiFerence, whether higher or lower, is added or subtracted,
as case may be, to or from value assigned to proof.
A scale of Corrections for temperature being necessary, one is fur-
nished with a Thermometer.
ApfUicatian of Thermometer.— EleWiUon of the mercury indicates correction to
be added or subtracted, to or ftom indication upon stem of hydrometer.
When elevation is above 6o<^, subtract correction ; and when below, add It
Illustration. — A hydrometer in a spirit indicates upon its stem 50 below proof,
and thermometer indicates 4 above 60^ in appropriate column.
Then 50 — 4 = 46 = strength below prooj.
To Coxxxpute Strengtli of a Spirit, or Volutxie of* its Pure
Spirit, by Coxnxxieroial Hydrometer, and Convert it to
Indication of a TJ. S. Hydrometer.
When Spirit is above Proof. Ruut.~Add xoo to indication, and divide sum by 3.
When Spirit is below Proof Ruu. —Subtract indication flrom 100, and divide
remainder by 2.
Example. —A spirit is 11 above proof by a Commercial Hydrometer; what pro-
portion of pore spirit does it o<Hitain f
II -f- loo-T- 3 = 55.5 j>er oCTit
To Ooxnpnte Strengtli, etc., "by a U. S. Hydrometer.
When Spirit is above Proof. Rulm.— Multiply indication by 3, and subtract xoa
When Spirit is behw Proof Rdli. —Multiply Indication by s, and subtract it
firom loa
ExAMPLB.— A spirit is 55.5 ; what is its per centage above proof?
55'5X 2 — 100 = 11 per cent
Commercial practice of reducing indications of a hydrometer is as follows:
Multiply nnmber of gallons of spirit by per centage or number of degrees above
or below proof, divide by xoo, and quotient will give number of ^Ulons to be added
or subtracted, as case may be.
iLLraTEAnoH.— so gallons of whiskey are n per cent, above proof
TIWB 50 X XI -r 100= 5.5, which added to 50 = 55.5 gaUons.
68
HTGBOMETEB.
HYGROMETER.
Dew-point. — When air is gradually lowered in its temperature at a
constant pressure, its density increases, and ratio of increase is sensibly
same for the vapor as for the air with which it is combined, until a point is
reached at whicn the density of the vapor becomes equal to the maxinmm
density corresponding to the temperature.
This temperature is termed dew-point of given mass, and any further re-
duction of it will induce the condensation of a portion of the vapor in form
of dew, rain, snow, or frost, according as temperature of surface is above or
below freezing point
nVTason's or like Hygrometer.
Xo Ascertain. De-w-point.
RoLB. — Subtract absolute dryness from temperature of airland remainder is
dew-point •
Example. — ^Temperature of air 57°, and absolute dryness 70.
PIcucc 57° — 7° = 50° dew-point.
To Asoertaixx Absolute }£xistiu£> Dryness.
Rule.— Subtract temperature of wet bulb IVom temperature of air, as indicated
by a dry bulb, add excess of dryness fVora following table, multiply sum by 2, and
product will give absolute dryness in degrees.
Example.— Temperature of air 57O, wet bulb 540*
Then 57O — 54O = 3° and 30 4- -5° (^oni table) X 2 = 7° absolute dryness.
Obaerved Exc«u of |
Observed
Dryness.
Dryness.
Dryness.
•
e
•
•5
.083
5
I
.166
5-5
1-5
.2495
6
2
•333
6.5
9-5
•4*65
' 7
3
•5
7-5
3-S
.583
8
4
.666
8.5
45
•7495
9
Dryness.
•833
.9165
I
1.083
1. 166
1.2495
1-333
1.4165
1-5
Observed 'Excess of
Dryness. | Dryness.
:i
9-5
10
10.5
II
11.5
12
12.5
13
135
1.583
1.666
'•7495
1.833
1.9165
2
2.083
2.166
2.2495
Observed
Dryness.
14
145
15
155
16
16.5
17
17-5
18
Excess of
Dryness.
8-333
2.4165
2-5
2.583
2.666
2.7495
2833
2.9165
3
Observed
Excess 01
Dryness.
Dryness.
18.5
3-083
19
3- 166
19.5
3^2495
20
3.333
2a5
3.4165
21
3.5
21.5
3.583
23
3.666
22.5
3.7495
To Compu-te "Volume of "Vapor in -A^tmospliere.
By a Hygrometer.
When temperature 0/ atmosphere in shade, and of dew-point are given. — If temper-
ature of air and dew-point correspond, which is the case when both thermometers
are alike, and air consequently saturated with moisture, then in table* opposite to
temperature will be found corresponding weight of a cuDe foot of vapor in grains.
Illustration.— Assume temperature of air and dew-point joP. Then opposite
temperature weight of a cube foot of vapor = 8.392 grains.
But if temperature of air is different trom dew-point, a correction is necessary to
obtain exact weight
Illustration.— Assume dew-point 70^ as before, but temperature of air in shad*
80°, then the vapor has suffered an expansion due to an excess of lo^, which re-
quires a correction.
In table of corrections for 10° is 1.0208. Then divide 8.392 grains at dew- point-
viz., 70O by correction corresponding to degrees of absolute dryness— viz., lo^.
"^ - = 8.221 grains of existing vapor, which, subtracted trom weight of vapor
I.OSOO
corresponding to temperature of 80°, will give number of grains required for satu-
ration at that temperature.
11.333 grain* At temperature of 80° —8.221 contained in the air = 3.Z12 required
for saturation.
* For table, see Muon's as poblished by Pi|ce ^ 89n>i I^^w York, and oompvod with Sir Join
Leslie's «pd Professor Duiiel's.
HTGBOMETEB. — ^SUN-DIAL. — CHAINING. ' 6q
To ascertain relations of these conditioDB on natural scale of humidity (complete
saturation being looo), divide weight of vapor at dew-point by weight at tempera-
ture of air, and quotient will give degrees of saturation.
Illustration. — Dew-point = 70°, weight = 8.392.
Then 8.393-7-11.333 (at So°) = .7405 degrees of humidity; saturation = looa
To Compute Weight of Vapor in a Cube Foot of Air.
See Pressures, Temperatures, Volumes, and Density of Steam, p. 708.
Thus, Required weight of vapor in a cube foot of saturated air at 212''.
At a temperature of 213° density or weight of i cube foot of air = .038 lb.
If density is required for any temperatures not in table, see rule, p. 706.
irt<fns(2t(y.~~Condition of air in respect to its moisture involves amount of
vapor present in air and ratio of it to amount which would saturate it at its
temperature, and it is this element which is denoted by term humidity^ and
it is expressed as a per centage ; thus, if weight of vapor present is .7 of that
required for saturation, the humidity is 70.
Dt'y A ir is air, humidity of which is below zero, bnc it is customary to
term it dry when its humidity i^ below the average proportion.
NoTK.— Air In a highly heated space contains as much vapor (when weight of it
is equal) as a like volume of external air, but it is dri^r as its capacity for vapor
is greater.
SUN - DIAL.
To Bet a Sun-dial.
Set column on which dial is to be placed perpendicular to horizon. Ascertain by
spirit level that upper surface is perfectly horizontal ; screw on plate loosely by means
of centre screw, and bring gnomon as nearly as practicable to its proper direction.
On a bright day set dial at 9 a.m. and 3 p.m. exactly, with a correctly regulated
watch ; observe difference between them, and correct dial to half difference. Fro
oeed in same manner till watch and dial are found to agree perfectly. Then fix
plate firmly in that situation, and dial will be correctly set.
This is obvious; for, if there wore any defects, the Sun's shadow would not agree
with time indicated by watch, t>oth before and after he passed meridian. Take
care, however, to allow for equation of time, or you may set dial wrong. Best day
in the year to set a dial is 15th of June, as there is no equation to allow for, and no
error can arise from change of declination. A dial may be set without a watch, by
drawing a circle around centre, and marking spot where top of shadow of an upright
pin or piece of wire, placed in centre, Just to iches circle in a.m., and again in p.m.
A line should be drawn (Vom one spot to the other, and bisected exactly; then a
line drawn fh>m centre of dial through that bisection will be a true meridian line,
on which the XII hours' mark, should be set.
CHAINING OVER AN ELEVATION.
/ C = L, and 0 = con, angle.
I representing length of line chained, C cos. angle of elevation with horizon,
and L length ofHne reduced to horizontal.
iLLUSTBATioK.— Length of an elevation at an angle of 30^^ xf Is 100 feet; what is
horizontal distance ?
By liable of Cosines, 30© 17' = . 863 54. Hence, 100 X . 863 54 = 86. 354 feet
To set out a RisKt A^nele xvitli a Chain, Tape-line» eto.
Take 40 links on chain or feet of line for base, 30 links or feet for perpendicular,
aiiU 50 for hypothenuse, or in this ratio for any length or distance.
USKFUL NUMBKRS IN SURVEYING.
For ConT«rtln(r Mnltiplter. ConverM.I For Convertiog
Mnltiplter.
CoDverM.
1-515
4-545
.66
.33
Feet into links.. 1.5x5 .66 Square feet into acres.
Yardb '' *' .. 4.545 .33 Square yards '' '* ..
Multiplier.
.0000339
.0003066
Coovcntk
43560
4840
/^
70
CHBONOLOOT.
CHRONOLOGY.
Solar day is measiired by rotation of the Earth upon its axis with respect
to the Sun.
^ Motion of the Earth, on account of ellipticity of its orbit, and of perturba-
tions produced by the planets, is subject to an acceleration and retardation.
To correct this fluctuation, timepieces are adjusted to an average or mean
solar day {jnean time)^ which is divided into hours, minutes, and seconds.
In Civil computations day commences at midnight, or A.M., and is divided into
two porticos of 12 hours each.
In Aitronomical computations and in Nautical time day commences at M., or
la hours later than the civil duy, and it is counted throughout the 24 hours.
Solar Tear, termed also Equinoctial^ Tropical, Civil, or Calendar Tear, is the
time in which the Sun returns from one Vernal Equinox to another; and its average
time, termed a Mean Solar Tear, is 365.342218 solar days, or 365 dayt, 5 hourt, 4S
minuta, and 47.6 tecondt.
Tear is divided into 12 Calendar months, varying from 38 to 31 daya
Mean Lunar Month, or lunation of the Moon, is 29 days, xa hours, 44 minutes,
s seconds, und 5.24 thirds.*
BiMMcxlile or Leap Tear consists of 366 days; correction of one year in four is
termed Julian ; hence a mean Julian year is 365.25 days.
In year 1582 error of Julian computation of a year had amounted to a period of
10 days, which, by order of Pope Gregory VIIL, was suppressed in the Calendar, and
5th of October reckoned as 15th.
Error of Julian computation, .00776 days, is about i day in 128.79 y^r^t *^^ adop-
tion of this period as a basis of intercalation is termed Gregorian Calendar^ or New
Style^i Julian Calendar being termed Old Style.
Error of Gregorian year (365.2425 days) amounts to i day in 3571.4386 years.
New Style was adopted in England in 1752 by reckoning 3d of September as 14th.
By an English law, the years 1900, 2100, 3200, etc, and any other looth year, ex-
cepting only every 400th year, commencing at aooo, are not to be reckoned bissex*
tile years.
Dominical or Sunday Letter is one of the first seven letters of alphabet, and is
UMd for purpose of determining day of week corresponding to any given date. In
Rxletiattical Calendar letter A is placed opposite to ^8t day of year, January ist;
li to second: and so on through the seven letters; then the letter which falls oppo-
site to first Sunday In year will also foil opposite to every following Sunday in that
year. See table, p. 73.
Nora.— In bissextile years two Dominical letters are used, one before and the other
after the intercalary day.
In Ecdftiattical Tear the intercalary day is reckoned upon 24th of February;
hence 24th and 35th days are denoted by same letter, the dominical letter being set
back one place.
In Civil Tear the intercalary day is added at end of February, the change of letter
tak I ng place at ist of March.
Dominical Cycle is a period of 400 years, when the same order of dominical letters
and days of the week will return.
Cydf of the Sun, or Sunday Cycle, is the 28 years before same order of Dominical
loiters return to same days of month, and it is considered as having oommenoed o
years before the era of Julian Calendar.
To Compute Cycle of tlie Sun.
RrLR.— Add 9 to given year; divide sum by 28; quotient Is number of cycles that
Dave elapsed, and remainder Is number or years of cycle.
NoTj.— rso of this computation Is determination of dominical letter for any given
year of J ulian Calendar for each of the 38 years of a cycle.
* f crivMa. t Now adopM in •▼«7 Chrlitiaa cooBlry «n:«pt RoMla and Gnwe.
CHBONOXiOGY. 7 1
Bj adoption of Gregorian Calendar^ order of the letters is necessarily interrupted
by suppression of Uie century bissextile years in 1900. 2100, eto.^ and a table of Do-
minical letters must necessarily be reconstructed for following Ciantury.
Lunar Cycle, or Golden Number, is a period of 19 years, after which the new
moons fall on same days of the month of Julian year, within 1.5 hours.
Year of birth of Jesus Christ is reckoned first of the Lunar Cycle.
To Compi:ite Lunar Cycle, or Q-olden Nxiijatoer.
RuLB.— Add I to given year; divide sum by 19, and remainder is Golden Number
NoTB.— If o remain, it is 19.
ExAUPLK. —What is Golden Number for 1879 ?
1879-)- 1 -^ 19=98, and remainder = 18 = Golden Numben
Epaet fbr any year is a number designed to represent age of the moon on ist day
of J anuary of that year. See table, p. 73.
fI?o Compute tlie Roman Indiotion.
RuLS.— Add 3 to given year; divide sum by 15, and remainder is Indlction.
NoTK.-^If o remain, Indiction is 15.
Number of Direction is the number of days that Easter-day occurs After 9tst of
11 arch.
Easter-day ia first Sunday after first ftill moon which occurs iipon or next after
2i8t of March; and if full moon occurs upon a Sunday, then Caster-day is Sunday
after, and it is ascertained by adding number of direction to sist of March. It is
therefore March N-j- 21, or April N — la
Illustration. — If Number of Direction is 19, then for March, 19-f ai 1=40, and
40 — 31 = 9 = 9* 0/ -^pra ;
again for April, 19 — 10 = 9 = 9^ of April.
NoTB.— Moon upon which Easter immediately depends is termed Paschal Moon.
FuU Moan is 14th day of moon, that is, 13 days after preceding day of new moon.
X>a9r0 of tbie Roman. Calendar.
Calends were the first 6 days of a month, Nones following 9 days, and Ides remain-
ing days.
In Maroh, May, July, and October, Ides fbll upon 15th and Nones began upon 7th.
In other months Ide* commenced upon 13th and Nones upon 5th.
For Roman Indiction and Julian Period see p. 96.
Clironology.
4004. Creation of World (according to Julius Africanus, Sept i, 5508 ; SamarlUn
Pentateuch, 4700; Septuagfnt, 5B72 ; Josephus, 4658 ; Talmudists, 5344 ; Sca-
liger, 3950; PetaviuB,3984; Hales, 541 1).
2348 Deluge (according to Hales, 3154)- 1 576. Money coined at Rome.
3247. Bricks made and Cement first used
Tower of Babel finished,
9903. Chinese Monarchy.
aoQo. First Egyptian Pyramid and CaAal.
1920. Gold and Silver Money first intro-
duced.
1891. Letters first used in E@rpt
1832. Memnon invents the Egyptian Al-
phabet
1 400. Crockery introduced.
4340. Axe, Wedge, Wimble, Lever, Masts
and Sails invented by Daedalus
of Athena.
1180. Troy destroyed. ^ ^ ^
ix3(x Mariner's Compass discovered in
China.
753. Foundation of Roma
640. Tbales asserU Earth to be spherical
605. Geometry, Maps, etc., first intro
569. First Comedy performed at Athena
480. First recorded Map by Aristagoras.
420. First Theatre built at Athens.
336. Calippus calculates the revolution of
Eclipses.
32a Aristotle writes first work on Me-
chanics.
310. Aqueducts and Baths introduced in
Rome.
306. First Light-house in Alexandria.
289. First Sundial
367. Ptolemy constracts a Canal from tha
Nile to the Red Sea.
334. Archimedes demonstrates the Prop-
erties of Mechanical Powers and
the Art of measuring Surface^ Sol-
ids, and Sections.
219. Hannibal crossed the Alp&
219. Surveying first introduced.
duced. ' I 203* PriQting introduced in China.
72
CHBONOLOGT.
B.G.
198.
170.
168.
162.
Books with leaves of vellum first
iDtruduced by Attalus.
Paper invented in China.
An eclipse of the Moon which was
predicted by Q. S. G alius.
Hipparcbus locates the first degree
of Longitude and the Latitude at
Ferro.
A.D.
69.
79-
214.
622.
Destruction of Jorusalera.
Destruction of Ucrculaneum and
Pompeii.
Grist-mills introduced.
Year of Hegira, commencing i6th
July; Glazed windows first intro-
duced into England in thiscent'y.
Glass discovered.
Stone buildings introduced into Eng-
land.
I^nda first enclosed in England-
Printing said to have been invented
by the Chinese.
Arabic Numerals introduced.
Battle of Hastings.
Mariner's Compass discovered.
Mariner's Compass introduced in
Europe.
Chimneys first introduced Into
Rome fk'om Padua.
Cannon introduced.
Woollens first made.
Printing invented at Mayence.
Wood-engraving invented and First
Almanac.
Printing in England by Caxton.
Watches first introduced at Nurem-
berg.
America discovered.
Vasco de Gama discovers passage
to India.
Variation of Mariner's Compass ob-
served.
F. de Magellan circumnavigates the
Globe.
Incas conquered by Pizarro.
Needles first introduced.
Potato introduced into Ireland from
America.
Telescopes invented by Jansen and
used in Ix)ndon in 1608.
Tobacco first introduced into Vir-
B.O.
159.
146.
70.
51-
45-
&
Clepsydra, or Water - clock. Invent
ed.
Carthage destroyed.
First Water-mill described.
C»sar invaded Britain.
First Julian Year by Csesar.
Augustus corrects the Calendar.
667.
670.
842.
933-
X066.
IIIX.
X180.
1368.
1383.
1390-
1434-
X460.
1471.
M77-
1492.
1497-
1500-
1522.
'530-
X545-
7*586.
X59a
x6x6.
ginia.
1620. Thermometer invented by Drebcl
X627. Barometer invented.
X629. First Printing press in America.
1639. First Printing office in America at
Cambridge.
1647. Otto Van Gueriche constructed first
electric mnchino.
x65a Railroads with wooden rails intro-
dticed near Newcastle.
1652. First Newspaper Advertisement
1704. First Newspaper in America.
1705. Blankets first made at Bristol, Eng-
land.
*WltaeM«l
A.D.
X752. Beujamin Franklin demonstrated
identity of the electric spark and
lightning, by aid of a kite.
1752. New Style, introduced into Britain:
Sept. 3 reckoned Sept 14.
1753. First Steam-engine in America.
1769. James Watt — First design and pat-
ent of a Steam-engine with sepa-
rate vessel of condensation.
1772. Oliver Evans— Designed the Non-
condensing Engine. X792. Ap-
plied for a patent for it x8oi.
Constructed and operated it
1774. Spinning Jenny invented by Robert
Arkwright
1776. Iron Railway at Sheffield, England.
1783. First Balloon ascension,and Vessel's
bottoms coppered.
179a Water-lines first introduced in mod-
els of Vessels in the U. S.
1797. John Fitch — Propelled a yawl-boat
by application of Steum to side-
wheels, and also to a screw-propel-
ler, upon Collect Pond, New York.
1807. Robert Fulton — First Passenger
Steamboat
1824. Compound marine steam-engines
first introduced by James P. Al-
lan, New York.
1825. Introduction of steam towing by
Mowatt, Bros. & Co.,of New York,
by steam- boat " Henry Eckford,"
New York to Albany.*
1826. Voltaic Battery discovered by Alex.
Volta, and First Horse-railroad.
1827. First Railroad in U. S., from Quim y
to Neponset
X829. First Lucifer Match and first Loco-
motive in America.
1830. Liverpool and Manchester Railroad
opened. Firat Steel Pen and first
Iron Steamer.
X832. S. F. B. Morse invents the Magnetic
Telegraph.
1836. Robert L Stevens first burned An-
thracite Coal in flimace of boiler
of steamboat *' PassaJe."
X840. First steam-boiler constructed for
burning Anthracite Coal in steam-
boat "North America," N. Y.
X844. Telegraph line ft-om Washington to
Baltimore, Md.
1846. First complete Sewing-machine.
Elias Howe, inventor.
x866. Submarine Telegraph Inid {torn
Valencia to Newfoundland, N.S.
by Aothor.
SHd* AKI> SHELLS. — ^I*BAtrr«JLENl? BALANCES. 6$'
PILING OF SHOT AND SHELLS:
To Corapute Nnixxber of* Sliot.
Triangtdar Pile, Eut.B.--Multiply continually togetho*, number of shot
in one side of bottom coarse, and that number- increased by i, and again by
2, and one sixth of product will give number.
ExAMPLK-— What is number of shot in a triangular pile, each side of base contain-
ing 30 shot?
30X30+1X30+^ ^,29760 ^ ^^ ^^^
6 6
Square Pile, Rule. — Multiply continually together, number in one sid«
of bottom course, and that numl)er increased by i, double same number in-
creased by I, and one sixth of product will give number.
ExAMPLK.— How many shells are there in a square pile of 30 courses?
6 o
Oblong Pile. Rulb. — From 3 times number in length of base course sub-
tract one less than number in breadth of it ; multiply remainder by number
in breadth, and again by breadth, increased by i, and one sixth of product
will give number.
Example.— Required number of shells in an oblong pile, numbers in base course
being 16 and 7 ?
.6X3-7-. X7X7 + .^»a;=3y,rtrit..
6 0
Incomplete Pile, Rule.— From number in pile, considered as complete,
subtract number conceived to be in that portion of pik which is wanting,
and remainder will give number.
FRAUDULENT BALANCES.
To Detect Them. After an equilibrium has been established between
weight and article weighed, transpose them, and weight will preponder-
ate if article weighed is lighter than weight, and contrariwise if it is
heavier.
To Ascertain True Weight RiTLK.—Ascertain weight which will produce
equUibrium after article to bei weighed and weight have been transposed ;
reduce these weights to same denomination, multiply them together, and
square root of their product will give true weight.
EXAMPLB. -If first weight is 3a lbs. . and second, or weight of equilibrium after
transposition, is 24 lbs. 8 oa., what is true weight?
24 lbs. 8 oz. =r 24. 5 Iba
Then 32 X 24. 5 = 784, and V784 = 28 lbs.
Or when a represents Umgest arm, I A greai^t joeight, and
b " shortest arm, \ B least wetght
Then Wa = A&, and W6 = Ba; multiplying these two equations, W^afc = ABa6,
or W» = AB, and W = VAB.
Illustration. -A = 32 ; B = 24. 5 ; W = 26. Assume length of longest arm = la
Then -^2: 28 :: 10: 8.75.
Heftce, a = 10, 6 = 8.7s. or 28* = 32 X 24. 5, and 1^32X24-5 = 28-
V*
go PBACTIONS.
To K.6d.rioe a A^ixed Fraction to its HSquivalezit, an. Izxx*
proper fraction.
Rule. — Multiply wbole number by denominator of fraction and to product add
numerator; then set that sum above denominator.
ExAHPLK I.— Reduce 21I to a fraction. — — , ' ° = i4? = Z?.
*'* 663
3.— Reduce ^|^ inches to its value in feet 133 -h 6 = 2o| = i JM 8^ int.
To K.educe a Complex ITraotion to a Simple one.
Rule.— Reduce the two parts both to a simple fhtction, multiply numerator of re-
duced Auction by denominator of reduced denominator, and denominator of numer-
ator fVactiou by numerator of denominator firaction.
2I 2|= 4 8X 5=40 s
Example.— Simplify complex firaction -f. A^£l .,n/« ~~ == —
4 J 4f = T^ 3X24 = 73 y
To Rednce a "^Vliole NunxToer to an Equivalent B'raction
liaving a given IDenominator.
Rule.— Multiply whole number by given denominator, and set producit over said
denominator.
Example.— Reduce 8 to a fraction, denominator of which shall be 9.
8 X 9 = 72 ; then ^^ resuU required.
To Reduce a Compound ITraotioxx. to an Ifiq,uivalent
Simple oii(*.
Rule.— Multiply all numerators together for a numerator, and all denominators
together for a denominator.
Note.— When there are terms that are common, they may be cancelled.
Example.- Reduce ^ of } of { to a simple fraction.
|^x|x| = T^ = ^. Or, Jxf xf = J, 6ycanc««in^2'B»nd3'8.
To Reduce Fractions of* diiTerent Denominations to
Eq.uivaleuts h.avinis a Common X>enominator.
Rule.— Multiply each numerator by all denominators except its own for new nu-
merators; and multiply all denominators together for a common denominator.
NoTK. — In this, as in all other operations, whole numbers, mixed or compound
fractions, must first be reduced to form of simple fkactiona
2. When many of denominators are same, or are multiples of each other, ascertaii#
their least common multiple, and then multiply the terms of each fk-action by quo-
tient of least cuiumou multiple divided by its denominator.
Example. — Reduce \^ |, and Jtoa '^3^*~"/_i8 le
common deuomiuaior. 2X2X4— '6/ —1^1=;^^ = |^,
3 XO<3=i8 ) ^^ « 8 and A.
2X3X4 = »4
i\.dd.ition..
Rule.- If fractions have a common denominator, add all numerators together,
and place sum over denominator.
Note. — If fractions have not a common denominator, they must be reduced to
one. Also, compound and complex must be reduced to simple fractions.
Example i.— Add J and J together. J + i = } = I-
2.— Add J of } of ^jf to 2J of }.
Th«°» i* + 14 = ttiX + AW = ItIJ' '•«*"«^ ^ equivaknt fractions hamn^
cf common denamincUar qnd thence to its lotvest termt.
FBACTIOKGU 9 1
Snlitraotioii.
RuuL ^Prepare flractions same as for other operations, when necessary; then
sabtract one numerator from the other, and set remainder over common denom-
inator.
ExAMPLK.— What is difference 6X9 = 54) .
between I and 4? 3X8 = 24} = ^f — ff = f|:i=f| = ^.
• • 8X9 = 72*
!Multiplicatiozi.
RuLB. — Prepare fractions as previously required; multiply all numerators to-
gether for a new numerator, and all denominators together for a new denominator.
EzAMPLB I.— What is product of | and {? |xf = |^ = }.
2.— What is product of 6 and fofs? ^xfof5 = *x^ = y = 20.
Division.
RcLK.— Prepare fractions as before; then divide numerator by the numerator,
and denominator by the denominator, if they will exactly divide; but if not, invert
the terms of divisor, and multiply dividend by it, as in multiplication.
ExAMFLB I — Divide V by J. y -r- f = | = 1}.
2.-Divide f by ^. {-A = fxV^ = Vx4 = ff = V = 4i-
-A.pplioatioii or Reclu-ction of Fraotions-
Xo Compute "Value of a ITrewstion. iu I*arts of a Whole
Numtoer.
RuLB. — Multiply whole number by oumerator, and divide by denominator; then,
if anything remains, multiply it by the parts in next inferior denomination, aud
divide by denominator, as before, and so on as far as necessary; so shall the quo-
tients placed in order be value of firaction required. '
ExAJCPLK I. — What is value of i^ of | of 9 ?
lof{ = i,andfx^ = V = 3.
a. — Reduce 4 of a pound to an avoirdupois ounce. 4) 3 (o ^^'^
16 ounces in a lb.
4) 48 (i3 ounces.
To Recluoe a Fraction. fVotici one IDenoiiiinatipn to
anotlxer.
RuLB.— Multiply number of required denomination contained in given denomina-
tion by numerator if reduction u to be to a leu name, but by denominator ^to a
greaier.
EzAXPLB I.— Reduce ^ of a dollar to fk^ction of a cent
Jxioo=JL^ = ^.
3.— RedBCe 1^ of an avoirdupois pound to fraction of an ounce.
3.— B«dace } of } of a mile to the fraction of a foot
fof} = AX5a8o = *JjV^=:14^.
tot RaU of ThTM la Valpur FrMtiona, mo Decimalt, pax* 94.
92 DECIMALS.
DECIMALS.
A Decimal is a fraction, having for its denominator a tTNiT with
as many ciphers annexed as the numerator has places ; it is usually ex-
pressed by writing the numerator only, with a point at the left of it. Thus,
Y% is .4; ^\ is .85; iViy^r Js .0075 ; and tVwtt ^^ -^^25. When there is
a deficiency of figures in the numerator, prefix ciphers to make up as many
places as there are ciphers in denominator.
Mixed numbers consist of a whole number and a flraction; as, 3.25, which is the
same as 3 y^q, or *^^
Ciphers on right nund make no alteration tn their value; for .4, .40, .400 are deci-
mals of same value, each being j^, or |. *
A-dd-ition.
Rule. —Set numbers under each other according to value of their places, as in
whole numbers, m which position the decimal points will stand directly under each
other: then begin at right hand, add up all the columns of numbers as in integers,
and place the point directly below all the other points.
ExAXPLB.— Add together 25.125 and 293.7325. 25.125
2937335
318.8575 sum.
Subtraction.
RxTLK. — Set numbers under each other as in addition; then subtract as In whole
numbers, and point off decimals as in last rule.
Example. — ^Subtract 15. 15 trom 89. 1759. 89. 1759
15- 15
74.0359 remainder.
]VI\iltiplicatioii.
Rule.— Set the foctors, and multiply them together same as If they were whole
numbers; then point olTin product just as many places of decimals as there are
decimals in both factors. But if there are not so many figures in product, supply
deficiency by prefixing ciphers.
Example.— Multiply 156 by .75. 1.56
'75
780
X092
i.iyoo product.
By Contraction.
To Contract tlie Operation bo as to retain, only as many
i:>ecimal plaoes in I^rodnct as may be required.
Rtlb. —Set unit's place of multiplier under figure of multiplicand, the place of
which is same as is to be retained for the last in product, and dispose of the rest of
figures in contrary order to which they are usually placed.
In multiplying, reject all figures that are more to right hand than each multiply-
ing figure, and set down the products, so that their right-hand figures may foil in a
column directly below each other, and increase first figure 13.574 01
in every line with what would have arisen (Tom figures f 50264
omitted; thus, add 1 for every result flrom 5 to 14. 2 flpora — ^ — '~
15 to 24, 3 from 25 to 34, 4 firom 35 to 44, etc., and the sum H^^l^ j-
of all the lines will be the product as required. li 144 gP-- 2 jor 18
Example.- Multiply 13. 574 93 by 46.2051, and retain only '^J ^^^ "^ i> L
four places of decimals in the product. 14- -x « 5
627.23 II
Note.— When exact retuU it raquired, increate Uit figure with what woald have ariaan from all tha
figures omitted.
DECIMALS. 93
Division.
RuLB. — Divide as in whole numbers, and point off in qaotient as many places for
decimals as decimal places in dividend exceed those in divisor; but if there are not
so many places, supply deficiency by prefixing ciphers.
Example. Divide 53 by 6.75. 6.75) 53.00000 (==7.851-!-.
Here 5 ciphers are annexed to dividend to extend division.
By Contraotion.
Role.— Take only as many figures of divisor as will be equal to number of figures,
both integers and decimals, to be in quotient, and ascertain how many tfmes they
may be contained in first figures of dividend, as usual
Let each remainder be a new dividend; and for every such dividend leave out
one figure more on right-hand side of divisor, carrying for figures cut off as in Con-
traction of Multiplication.
Non. — When there »re not wo many fiff^res In divisor •• there are required to b« in qaotient, con-
tinae first operation until namber of figures in divisor are equal to those remaining to be round in quo-
tient, aftar which bagin the contraction.
ErAMPLB.~>Di vide 3508.93806 92.410315)2508.928106(27.1498 13.849 012
by 92.41035, so as to have only 1848 207 -}- i 9241 832 -|- 4
four places of decimals in quo- "660721 ^608 "80
*'®'*^- 646872 -|- 2 3696 ^.+ 2
13 849 912 6
Red-uction of IDecimals.
Xo Redxioe a Vulgar I^raotiou. to its ISqixivaleut Deoiiual.
Rule.'— Divide numerator by denominator, annexing ciphers to numerator to ex-
tent that may be necessary.
ExiXPLB.— Reduce { to a decimal. 5) 4.0
To Compute Value of* a Decimal in Terms of* aii lufferior
X>enomiuatioii.
Rule. — Multiply decimal by number of parts in next lower denomination, and
cut off as many places fof a remainder, to right hand, as there are places in given,
decimal.
Multiply that remainder by the parts in next lower denomination, again cutting
off for a remainder, and so on through all the parts of integer.
Example l— What is value of .875 dollars? .875
100
CenH^ 87.500
10
Jf t7te, 5.000 = 87 ctnXM 5 miXLi.
a.— What is volame of . 140 cube feet in inches?
X .140
1728 cube inches in a cube foot
24i.92ocu5etn«.
3.— What is value of .00129 ^^ ^ ^'^^ ^ •01548 ins.
To Reduce a Deoixnal to an Equivalent IDeoixnal or a
Kiglier X)enomination.
Rota. — Divide by number of parts in next higher denomination, continuing op^
eration as fiir as required.
Example l — Reduce i inch to decimal of a foot i2|i. 00000
I -08333-1-/001
s.~B«dace 14'' la''^ to decimal of a minuta 14" 12"'
60
60
60
852.
Hf
X4.2"
.23666'+ mifittfe.
94
DECIMALS. — ^DUODECIMALS. — MEAN PROPORTION.
When there are several numbers^ to be reduced all to decimal of highest,
RuLB.-> Reduce them all to lowest denominatioii, and proceed as for one denomi-
nation.
Example.— Reduce 5 feet
barleycorns to decimal of a yard.
ncbes and 3
Feet. Ine. Be.
5 10 3
12
70
3
3
12
3
213.
71-
5.9166
1.9722-H yatris.
TlvilG of Three.
Rule. — Prepare the terms by reducing vulgar fractions to decimals, compound
numbers to decimals of the highest denomination, first and third t«rms to same
denomination, then proceed as in whole numbers.
Example.— If . 5 of a ton of iron cost .75 of a dollar, . 5 : .75 : : .625
wha( will .625 of a ton cost? .625
-S) 46875
.9375, dollar.
DUODECIMALS.
In Daodecimals, or Cross Multiplication, the dimensions are taken in feet,
inches, and twelfths of an inch.
Rule. — Set dimensions to be multiplied together one under the other, feet under
feet, inches under inches, etc.
Multiply each term of multiplicand, beginning at lowest, by feet in multiplier, and
set result of each immediately under its corresponding term, carrying i for every
12 fh)m one term to the other In like manner, multiply all multiplicand by inches
of multiplier, and then by twelfth parts, setting result of each term one place farther
to right hand for every multiplier. And sum of products will give result.
Example. — How many square inches are Feet. Iiu. Twelfths,
there in a board 35 feet 4. 5 inches long and 12 35 4 6
feet 3^ inches wide? '" 3 4
424
8
6
xo
IX
o
X
9
6
6
434
II
Value or IDuodeoixnals in
Sq. Ft. Sq. Ins.
X Foot = I or 144.
I Inch = "A" " '*•
Twelfth = yjj-
Sq.uare ITeet and tnolies.
Sq. Ft. Sq. Ins.
^ of I twelfth = -p^^ or .083 333, etc.
^of^of" =
lijTIT" 006 944, etc-
Illustration. —What number of square inches are there in a floor xoo feet
6 inches long and 25 feet 6 inches and 6 twelfths broad?
2566 yee< IX ins. 3 twdJVisr=2^fBet 135 tiM.
MEA.N PROPORTION.
Mean Proportion is proportion to two given numbers or terms.
Rule.— Multiply two numbers or terms together, and extract square root of their
product
Example.— What is mean proportionate velocity to 16 and 81 ?
x6 X 8x = 1296, and y/12^ = 36 mean velocity.
HVhK OF THB^US,— COMPOUND PBOPOBTION. 95
BXTLE OF THBEB.
Rule of Three. — It is so termed because three terms or numbers are
given to ascertain a fourth.
It is either Direct or Inverse.
It is Direct when more requires more, or less requires less ; thus, if 3 bar>
rels of flour cost $z8, what will 10 barrels cost?
In this case Proportion is Direct, and stating must be,
As 3 : 10 : : 18 •- 60.
It is Inverse when more requires less, or less requires more; thus, if 6 men build
a certain quantity of wall in xo days, in how many days will 8 men build like quan-
tity ? Or, if 3 men dig 100 feet of trench in 7 days, in how many days will 2 men
perform same work?
Here the Proportion is Inverse, and stating must be,
As 8 : 6 :: 10 : 7.5, and 2 : 3 :: 7 : 10.5.
The fourth term is always ascertained by multiplying 3d and 3d terms together,
and dividing their pruduct by ist term.
Of the three given numbers necessaiy for the stating, two of them contain the
supposition, and the third a demand.
RcLB.— State question by setting down in a straight line tbe three necessary
numbers in following manner :
Let third term be that of suppatUUmy of same denomination as the result, or 4th
term is to be, making demanding number 2d term, and the other number ist term
when question is in Direct Proportion, but contrariwise if in Inverse Proportion;
that is, let demanding number be ist term.
Multiply ad and 3d terms together, and divide by ist, and product will give re-
sult, or 4th term sought, of same denomination as 2d term.
. NoTB.— If flnt and third tertni are of different denominatloiu, reduce them to aame. If, after divis-
ion, there ia any remidnder, reduce it to next lower denemlnation, divide by diviaor a* before, and
quotient wil! be of tiiis laat denomination.
Sometimes two or more statings are necessary, which may always he known by
nature of question.
EXAMPLB I.— If 20 tons of iron cost $225, what will Tons. Tona. DoUs.
500 tons cost? 20:500:: 225
500
2|o) II 250I0
5 b25 dollars.
2. — A wall that is to be built to height of 36 feet, was raised 9 feet by 16 men in
6 days; how many men could finish it in 4 days at same rate of working?
Days. Days. Men. Men.
4 : 6 :: 16 : 24
Then, if 9 feet requires 24 men, what will 27 feet require?
9 : 27 :: 24 : 72 mm.
COMPOUND PROPORTION.
Compound Proportion is rule by means of which such questions as
would require two or more statings m simple proportion (Rule of Tlif^e)
can be resolved in one.
As rule, however, is but little used, and not easily acquired, it is deemed prefer-
able to omit it here, and to show the operation by two or more statings in isimple
Proportion.
lUtUflnunoH LxHow many men can dig a trench 135 feet long in 8 days, when
16 men can dig 54 feet in 6 days?
Feet. rbet. Klen. Men.
first As 54 : 135 :: 16 ; 40
Days. Days. Men. Men.
Second. ...As 8 : 6 :: 40 ; 39
102 AHlTHMJSTtCAL t>BOGB£SSlO^.
rro Compute Common X>ifierenoe.
When Number of terms and Extremes are ffiven. Rulk.— Divide diffennca ct
extremes by i less than number of terms.
aS — 2an l4-axl — a _.2nl — aS
Or, — ; ; — 1- — J ; and — ; r = *
' n(n— i) ' aS — l—a ' n(n — i)
Illustration.— Extremes are 3 and 15, and number of terms 7; what is commop
diffei-ence?
15 — 3-r- (7—1) = ^, and ^ = 2 am.(iif.
o o
rro Compute Suxn of* tlie Series or of* all rPerms*
When Extremes and Number of terms art given. Bulx. — Multiply number of
terms by half sum of extremes.
. T-. ^. l-\-ay,(l — a) , 1 4- a
Or, 3 a+d (n-i) X .5 ♦»; -^ ^ + -^;
andaf — (clxn— z)X.5n = S.
Illustration.— How many times does hammer of a clock strike in 12 hours t
12X134-1 = 156, and 156 -f- 2 = 78 timesl
7*0 Compute any dumber of* A.ritIxm«tioal Cleans or
rrerms Iset^^een t-wo Sxtremes.
RuLS. — Subtract less extreme fVom greater, and divide difference by 1 more
than number of means or terms required to be ascertained, and then proceed as
in rule.
To Compute T-wo A.rith.metical ACeans or Terzns beti^een
t-%vo given Sxtremes.
RuLB Subtract less extreme trom greater, and divide difference by 3, quotient
will be common difference, which being added to less extreme, or taken f^om great-
er, will give means.
ExAMFLS L— Ck>mpute two arithmetical means between 4 and x6w
16 — 4-5-3= 4Com.dif.
4 -{- 4 = 8 one mean.
16 — 4 = 12 sewnd mean.
3.— Compute four arithmetical means between 5 and 3a
30— 5 = 25, and 25-T-4-|-x = 5 = com. dif.
54-5 = io=i«tmMfk i5-j-s = 2o=3dmeaik
io4-S = i5 = ad " 2o+5 = 25 = 4«* "
IVfisoellaneous Illustrations.
X. A Steamer having been purchased upon following terms— viz.: $5000 upon
transfer of bill of sale and balance in monthly instalments, commencing at $4500
for first month, and decreasing $500 in each month, until whole sum is paid.
ist. How many months must elapse before final payment?
2d. What was amount of purchase- money, or sum of series ?
Here are first and last (emu — viz., 500 and 5000, and common difference^ 50a
Hence^ To compute number of terms and amount of purchase,
5000 — 500 -r- 500 = 9, and 9 -{- X = xo = nu'n^>er of terms or months^ and 10 X
^^^ — = xo X 2750 = $27 SCO, ammmt of purchase.
2
3- If 100 Stones are placed in a right line, one yard apart; how many srards maal
c. person walk, to take them up one at a time and put them into a basket, one yard
fbom first stone?
First term 2, last term 200, and number of terms loa
200-^ 3
Hence, 100 x ■ — = xo xoo yards.
SIMPLE INTSBBST. lO^
SIMPLE INTEREST.
7o Compute Interest on. axxy d-iven Sum Tor a PeriocI
of* One or xnore Years.
RuLR.— Multiply given sum or principal by rate per ceut. and uuinber of years:
point off two figures to right of product, and result will give interest in dollars and
cents for the period.
' ExAMPUB.— What is interest upon $ 1050 for 5 years at 7 per ceut. Y
X050 X 7 X 5 = 36750» «"»d 367.50= $ 367.5a
When Time is leu than One Fear Rule.— Proceed as before, multiplying by
number of months or days, and dividing by following units— viz., 12 for mouths,
and 365 or 366, as the case may be, for days.
EzAMi'UL— What Is interest upon $1050 for 5 months and 30 days at 7 per cent.?
5 months anjl 30 days = 183 days. ~^^—l — ?_? = 3685, and 36. 85 = $ 36. 85.
The operation of computing interest may be performed thus :
AGBnming interest upon any sum at 6 per cent. = i per cent for 3 montlia
Interest at 5 per cent Is |th less than at 6 per cent
Interest at 7 per cent is Jth greater than at 6 per cent
Taking preceding example— a months = i per cent = 10.50
2 ** = I " 10.50
. " =i " 5.25
todays =1 month = 5.25
31 50
Add ( for 7 per cenL= 5.25
N<yR.— DUTertuM between tbie smonnt and preceding «riMs from 183 days being taken In one GaM«
aod balf a year, or 182.5 dayt, In the other.
In every computation of interest tbere are four elements— viz., Principal, Time,
Rate, and Interest or Amount, any three of which being given, remaining one can
be ascertained.
To Compute Principal.
When Time, Rate per Cent., and Interest are given. Ruut.— Divide given interest
by interest of $1, etc., for given rate and time.
ExAXPLB.— What sum of money at 6 per cent will m 14 months produce $ 14?
14 -7- .07 = aoo dollars.
To Compute Rate per Cent.
When Principal^ Intere^, and Time are given. Ruul— Divide given interest by
interest of given sum, for time, at i per cent
ExAMPU. — If $ 32.66 was discounted flrom a note of $ 400 for 14 months, whal
was that per cent t
iBterMt on 400 for 14 months at x per cent = 4.66.
Then 32.66 -r- 4.66 = 7 per cent
To Compute Time.
When PHne^xUf BaU per Cent , omd Interest are given. Ritlb. —Divide given m
tereat by intereal of sum, at n^ per cent for one year.
ExAMFLa.>-lB wbai time will $ 108 prodace $ ix. 34, at 7 per cent f
lolMPeaC on 108 for one year is 7.56.
"■ 34 -J- 7- 56 = «• 5 years.
Illcst&atkui r. —If an amount of $2175 is returned for a period of 15 monthk
ttt0 of Interest liaving been 7 per cent. , what was principal invested f $ 2000.
s.— If $ sooo tn 18 months will produce $ 1090, what is rate ? 6 p^ > jcnf
io8
COMPOUND INTEREST.
COMPODND INTEREST.
If any Principal be multiplied by number (in following table) oppositi
years, and under rate per cent., sum will be amount of that principal at com*
poimd interest fur^ime and rate taken.
Example. — What is nmount of $500 fur 10 yeans at 6 per cent ?
Tabular number. . . . la 790 84, and 1.790 84 x 500 == 895a 42 dollars.
m
e
r
3
4
5
6
i
>*
3
4
5
6
>*
Percent. Per Cent.
Per Cent. Per Cent.
Per Cent.
Per Cent.
Per Cent.
Per Cent.
I
1.03
1.04
1.05
1.06
»3
1.46853
1.66507
1.88564
2.13293
2
1.0609
1.081 6
1. 102 5
1. 123 6
14
1.51529
1.73167
1-97993
2.078 92
2.2609
3
1.09273 1. 124^6
1.15762
1. 191 01
15
'-557 97
1.80095
2.39655
4
1. 125 51 ; 1. 169 86
I-2I5 5
1.26247
16
1.604 71
1.87298
2. 182 87
2.5403s
5
1.15927 1.21668
1.276 28
1.33822
"7
1.65285
1.94709
2.02581
2. 292 01
2.69277
t
1. 194 05 1. 265 32
134
1.41851
18
1.70244
2.40661
2-85433
. 7
1.22987 1.31593
1.407 I
1.50363
»9
1-753 5
2. 106 84
2.52695
302559
8
1.26677 ' 1.36857
1-477 45
1-59384
20
1.80611
2.191 13
2.65329
3207 13
9
1.30+77 1. 423 31
^•55»32
1.68947
21
1.86029
2.27876
3.78596
3-39956
10
1.34392 1.48024
1.62889
1,79084
22
1.916 I
2.36992
2.92526
3603 53
II
1.38424 1.53945
1-71033
1.89829
23
19736
2.46421
3.071 52
381974
12
1-42576.
1. 601 03
1-79585
2.012 19
24
2.03379
25633
3.22509
4.04873
For any other RiUe w Period. — Multiply logaritbm of rate 4- » ^y period, and
Diiinbor Tur logarithm will g.ve tabular amount as above.
Illustration.— What is tubular number for 4 per cent for 10 years?
Log. of 1.04 = .017033 3, which X 10 = .170333, and number for log. = 1.48024.
Time in Years in >vliieli a Sum of !M!oney ■wrill "be
clonbled at S«^veral Ftates of* Interest.
Rate. Time.
Per cent.
I
2
3
69.68
35
2344
Rate.
Time. 1
1 Rate.
Time.
Rate,
Tlm«.
Per cent.
4
5
6
17.67
14.21
11.88
Per cent.
I
9
10.34
9.01
8.04
I'er cent.
10
20
30
7.27
2.64
Value of^la etc.. Computed Semi-annup,lly fbr a Period
of IS Years.
6
Per Cenb
3
4
5
6
Years.
Per Cent.
Per Cent.
Per Cent.
Per Cent.
•5
1.015
1.02
1.025
1.03
I
1.0302
1.0404
Z.0506
1.0609
i-S
10457
I.o6l2
1.0769
1.0927
2
1. 0614
1.0824
1.1038
<-i25S
a-S
10773
I.I04I
I.1314
I- 1593
3
1-0934
1. 1262
1. 1597
1.1887
1.1941
3-5
1. 1098
1. 1487
4
1.Z205
1. 17 17
1.2164
4-5
I- 1434
1.1951
1.2489
1.3048
5
1.1604
1.219
1.2801
1-3439
1.3842
5-5
1.178
1.2434
1.3121
6
1. 1956
1.2689
1-3449
1.4258
'|Year».
3
Per Cent
6-5
1.2134
7
I.2317
V
1.2502
1.269
8.5
X.28§
9
9-5
10
10.5
11
"•5
1-3073
1.3269
1-3469
1. 367 1
1.3876
1.4084
12
1.4295
4
5
Per Cent.
Per Cent.
1.2936
1.3785
I-3195
1-413
1-3459
1.3728
1.4483
1-4845
1.4000
X.5216
1.4283
1-5597
1-5987
1.4568
1.486
1.6386
1-5157
I 6796
I 546
1.7216
1-5769
1.7606
1.6084
1.8087
Illustration.— What is amoant of $500 at semi-annaal interest of 5
compounded for 10 years?
Tabular number 1,6386. Then, 500 x 1.628 89 = $ 814.44.5.
1.4684
I 5102
1558
1.6047
i.65a8
i-7o«4
1-7535
X.80OX
X.8603
x.9i^i
1-9736
2.0356
per cent
For a Period of t^rs. P (i -f- r) " = A ;
To Coixip^vkte Interest on anjr G}<iven Sum.
A »/X __
(,-fr)»- ' V p '-*'•
, log.' A — log. P^ _ ,. ... . , .
niKl — 1 r /I -u u' ~^' representing principal, r rate per cent. -r- 100 per annum^
n number of year 8 ^ and 4 ftROwnf ofj^rincipa^ g^v-^ interest.
OKOMETBICAL PB06BBSSI0N.
105
Illustration i.— First term Is 2, ratio 2, and number of terms 13; what is sum
of senes?
3'3_|=8i92 — x = 8i9x, »nd8i9i-4-(a — i) = 8i9i, and 8191 X 3 = 16382.
3. — If a man were to buy 12 horses, giving 2 cents for first horse, 6 cents for
second, and so on, what woufd they cost him ? $ 5314.4a
Xo Compute Ratio.
When First Term, Lmt Term, and Numbers 0/ Terms are given. RuLS. — Divide
last term by first, and quotient will be equal to ratio raised to power denoted by z
leas than number of terms; then extract root of this quotients
^ S-a
Illustration.— First term is 2, last term 4374, and number of terms 8; what Is
ratio?
^^=2187, and ^^2187 = 3, ratio.
l^isoellaneous Illustrations.
X. What is 9th term in geometrical progression 3, 9, 27, 81, etc.? and what Is
sum of terms?
I St term = 3, number of terms 9, and ratio 3.
Hence, by rule to compute last term, ist term and ratio being equal—
Indices, 1234
Terms, 3,9,27,81.
Then, 3->- 3 + 4 = 9 =«»m of indices, and 9 X 27 x 81 = 19683 = last term.
By rule to compute sum of terms—
^'— I 10683 « «.
i X 3 = — 9841 X 3 = =9 5a3» «*»» of terms.
3 — I a
a. First term is i, ratio 9, and last term 131 072 ; what is sum of series?
131 073 X a — I = 262 X43, and 263 143 -1-2 — i = 262 143.
3. What are the proportional terms between 2 and 2048 ?
4 -f- 2 = 6, and 6 — x = 5, and
■5/2048
V— =■
Hence, 2 : 8 : 32 : 128 : 512 : 2048.
4. Sum of series Is 6560, ratio 3, and number of terms 8; what Is first termf
6560 X \~' = 6560 X 2^ = 2,/rrt term.
38 — 1 •' 6560
Oeometrioal I>rogreBsions.
Whereby any questions of Geometrical Progression and of Double Ratio may 6s
solved by Inspection, number ^ terms not exceeding 56.
z
X
«5
a
2
16
3
4
t
:i
5
x6
19
6
32
20
i
xti
2X
23
9
256
23
to
51a
24
zx
1024
2048
25
za
26
«3
4096
1 27
«4
8Z93
1 28
X6384
89
33768
30
65536
3«
X31072
202 144
33
33
524 288
34
z 048 576
35
3097x53
36
83I8608
37
38
x6 777 3x6
39
33 554 432
40
67 108 864
4«
X34217738
42
268435456
536870912
1 073 74» 824
2147483648
4 294 967 296
8589934592
17x79869184
34359738368
68719476736
»37 438 953 472
274877006944
5497558x3888
X 099 511 627 776
2199023355552
43
44
45
46
47
48
49
50
51
52
53
54
55
S6
4 398046 5XXX04
8796093022308
X7 592 1860444x6
35 '84 372 088 8m
70368744177664
140737488355328
fe8i 474 976 7x0 656
562049953431 313
X 135 899 906 842 634
3 351 799-813 685 248
4503599627370496
9007190254740993
180x4398509481984
36 028 797 0x8 963 968
Illustbatiovs.— i2th power of a = 4096, and 7th root of X28 = a.
I06 ALLIGATION.
ALLIGATION.
Alligation is a method of finding mean rate or quality of different ma-
terials when mixed together.
To Compute 2VIean JPrioe of* a Alixture.
When Prices and Quantities are known. Rule. —Multiply each quantity by its
Ate, divide sam of products by sum of quantities, and quotient will give rate of the
composition.
Example. — If lo lbs. of copper at 20 cents per lb., i lb. of tin at 5 cents, and i Ih'
of lead at 4 cents, be mixed together, what is value of composition?
xo X 20 = 200
IX 5= 5
_2X 4= 4
12 ) 209 (17.4x6 cents.
To Coxnptite Quantitsr or eaoli i\.rtioIe.
Wlwn Prices and Mean Price are given. Rule. —Write prices of mgredients, one
under the other in order of their values, beginning with least, and set mean price
at loft. Connect with a line each price that is less than mean rate with one or more
that is greater.
Write difference between mixture rate and thai of each of simples opposite price
with which it is connected; then sum of differences against any price will express
quantity to be taken of that price.
Example.— How much gunpowder, at 72, 54, and 48 cents per pound, will compose
a mixture worth 60 cents a pound ?
12, at 48 cents.
1 34\/ X2> at 54 cents.
(72/ i2-|-6 = x8, at72 cente.
Here, 73 — 60 = 131^48, 72 — 6o=:x3at54i 60 — 48 = 12, and 60— 54 = 6 =
12-^6 = 18 at 72.
Then 12 X 48 + 12 X 54 + 18X72 = 3520, and 252o-f-x2 + i2+i2 + 6=6ocentt.
NoTB. — Shoald it be required to mix a definite qnantitj of any one article, tbe qnantitlee of each,
determined by above mle, must be increased or decreased in proportion they bear to defined quantity.
Thus, had it been required to mix 18 pounds rt 48 cents, result would be x8 at 48,
z8 at 54, and 27 at 72 cents per pound.
When the tohole Composition is limited. Rctlb —As sum of relative qnanlities,
as ascertained by above rule, is to whole quantity required, so is each quaD,tity so
ascertained to required quantity of each.
Example.— Required xoo pounds of above mixture
Then, 12 + X2+ x8=42. Then, 42 : xoo :: 12 : 28.57X pounds.
42 : xoo :: 12 : 28.571 pounds.
42 : xoo :: 18 : 42.857 pounds.
When Price of Several A Hides and Quantity of one of them u given. Rdlb. — As-
certain proportionate quantities of ingredients by previous rule.
Then, as number opposite ingredients, quantity of which is given, is to given
quantity; so is number opposite to each ingredient to quantity required of that In-
gredient
Example. — Having 35 Iba of tobacco, worth 60 cents per pound, how much of
other ({ualities, worth 65, 70, and 75 cents per pOund, must be mixed with it, so as to
sell mixture at 68 cents per pound?
By previous rule, it is ascertained there must be 7 lbs. at 60. 2 at 65, 3 at tq, and
8 at 75 cents; but as there are 35 lbs. at 60 cents to be taken, other quantities and
kinds must be increased in like manner.
Hence, 7 : 35 : : 2 : xo = xo at 65 cents.
7 • 35 : : 3 : "5 = 15 " 70 cents.
7 : 35 : : 8 : 40 = 40 '* 75 cents.
6o|54\)
ANNUITIES.
ill
(x + .05)* per table, page xo8, loox -05 (i + -o5)^ _ SX x.34 _ 6. 7 _ ^
— ■ — —— — — — ^10. JO.
— '•3^ (x-f.o5)6— I 1-34 — X 34
When AnnwUiet do not commence till a certain period of time, they are mid to be
in Reversion.
To Coxnpute Present "Wortli of* an Annnity in Reversion*
Rule.— Take two amounts ander rate in abave table— viz., that opposite sum of
two given times and that of time of reversion ; multiply their difference by an*
unity, and product will give present worth.
Example. — What is present worth of the reversion of a lease of I40 per anaum,
to continue for 6 years, but not to commence until end of 2 years, at mte of 6 per
cent, f
6 -f- 2 = 8 years 6.209 79
3 " X. 833 39
4.37640 X 40 = $i7505- 6.
' .A.znoant of A-nnuity of* Si, etc.. Compound Interest,
f*rozn 1 to SO Years.
X
2
3
4
5
6
7
8
9
10
4
Per Cent.
X.
2.04
3.12x6
4. 246 46
5-4>632
6.63297
7.89829
9»3X433
xo. 582 79
x2.oo6xx
5
Percent.
X.
a. 05
3- 152 5
4.310x2
552563
6.801 91
8. 142 ox
9-549"
IX. 026 56
12.57789
6
Per Cent.
X.
2.06
3-1836
4.37462
5.63709
6.97532
8.39384
9.89747
1 1. 491 32
X3. 18079
7
•
Percent.
>< '
X.
II .
2.07
12 1
32149
13
4-439 94
14
5-75074
15
7-15329
16
8.65402
17
xa259 8
18
11.97799
13.8x645
19
20
4
Per Cent.
13-48635
15.0258
16.626 84
18.291 91
20.023 59
21.82453
23.697 51
25.645 4X
27.671 23
29.77808
S
Per Cent.
14.206.79
15-917 "3
X7.71298
19.59863
21-57856
2365749
25.84037
28. 132 38
30-539
33-06595
6
Per Cent.
14-971 64
16.86994
X a 882x4
21.0x507
23.27597
25-672 53
28.2x288
30.90565
33-75999
36.78559
7
Per Cent.
15.7836
17.88845
201 140 64
22.55049
25.12902
27.88805
3a 840 22
3399903
37.37896
140.99549
iLLrsTRATioN.— What is amount of $ 1000 for 20 years at 5 per cent.?
5 per cent, (br 20 years = 33*065 95 ; hence, 1000 x 33-065 95 = 1 3306. 595.
Xo Compute A.mount of an A^nnuit^r for an3r Period
and. Rate.
Rule.— From table for Compound Interest, page xo8. take value for rate per cent,
for X year, and raise it to a power determined by time in years. fh>m which subtract
x, divide remainder by rate, and quotient multiplied by annuity will give amount
required.
Example.- What will an annuity of $ 50^ payable yearly, amount to in 4 years, at
5 per cent ?
By table, page 108, 1.054 = 1.2x55.
1.2x55 — x-r-(x.o5 — x) =4.31, and 4.31 x 5o = $2i5.5a
P'or Half-yearly and Quarterly Payments.
Multiplf annuity for given time by amount in following table:
Bete per cent.
Helf-Tearly-
QoArteriy.
Rate percent.
Hftlf-yesrly.
Quarterly.
3
3-5
4
45
5
>-oo7 445
X.008675
1.009903
X.OXI X26
X.OX2348
i.oxx i8x
1.01303X
1.0x4877
1.016729
x.ox8 559
5-5
6
6.5
7
7-5
X.013567
X. 014 781
X. 01 5 993
X. 01 7 204
1.0x84x4
x.020395
1.022227
X.024055
x.025 88
X.027 704
Illustration i.— Annuity as determined in previous case=$2i5.5a
Hence, 2x5.50 x 1.0x2348 flrom above table =r $2x8. 16 ybr ha^ yearly payments.
3. A person 30 years of age has an annuity for xo years, present worth of it being
liooo, provided he may live for xo years. What is annuity worth, assuming that
60 persons out of every 3550, between the ages of 30 and 40, die annually ?
3550 — 600 (60 X xo) = 2950 would therefore be living.
Andf 3550 : 2950 :: xooo = $83o.98.
no
▲imUlTIBS.
ANNUITIES.
170 Coixipute A-xnoniit of* A.iixi'ultsr.
When Time and Ratio of Inlereist are Given. Rulk — Raise the raiio to a power
denoted by time, from which subtract i ; divide remainder by ratio less i, and quo-
tient, multiplied by annuity, will give amount
NoTK.— $ X added to given rate per cent, to ratio, and pracsdlng table in Gk»mpoand Interest to a
table of ratios.
Example.— What is amount of an annual pension of $ioo, interest 5 per cent.,
which has remained unpaid for four years?
1.05 ratio; then 1.05* — 1 = 1.21550625 — i =.21550625, and .21550625-7- (1.05
— i) 05 = 4.310125, which X 100 = $431.01. 25.
To Compute Present "Wortb, of an A-nimity.
When Time and Rate of Interest are Given. Rulk.— Ascertain amount of it for
whole time; divide by ratio, involved to time, and result will give worth.
ExAMPLK. — What is present worth of a pension or salary of $500, to continue xo
years at 6 per cent, compound interest f
1 5oo> by last rule, is worth $6590.3975, which, divided by x.o6'*^ (by table, page
108, is 1.79084) = $ 3680.05.
Or, Multiply tabular amount in following table by given annuity, and product
will^ive present worth.
Illustration l — As above; 10 years at 6 per cent. =7. 360 08, and 7.36008 x 500
— 3680.04 dollar g.
2. What is present worth of $150 due in one year at 6 per cent interest per annum i
•943 39 X 150 = $141. 5a 85.
Present Wortli of an A.iinnity of ^1, at 4, 6, and G
Per Cent. Compound. Interest for Periods under S3
Years.
Years.
4 Per Cent.
5 Per Cent.
2
.96154
1.88609
•95238
1.859 41
3
27751
2.72325
4
3.6299
3.54595
5
f- 452 03
432948
6
5242 > 5
507569
7
6.00203
5-78637
8
6.731 76
6.46321
9
74364
7. 107 82
xo
8. 1 10 85
7.72173
XI
8.76044
8.30641
xa
938505
8.86325
6 Per Cent.
Years.
•943 39
>.83339
13
>4
2.67301
15
3465 «
16
4.21236
17
4.91732
18
5-58238
19
6.20979
20
6.80169
7.36008
21
22
7.88687
23
8.38384
24
4 Per Cent. I 5 Per Cent
9.98562
10.56307
11.X1843
II. 651 28
12. 166 26
12.65926
13-13388
13.59029
14.02912
H-45I 12
14.85682
15.24695
9-393 57
9.89864
XO.37966
X0.83778
XI. 27407
11.68958
12.08532
12.46221
12.821 15
13.163
13.48807
13.79864
6 Per Cent.
8.85268
9.29498
9.71225
10. 105 89
10.47726
10.8276
IX. 158 II
11.46992
11.76407
12.041 58
12.303 38
12.5503s
For a Rate of Interest and Term of Tears not given in either Tal>le.
— I : — - = A. Notation as preceding.
r I (i + r)»J
Illubtratiox. — ^Take $ i at 4 per cent for 24 years.
Log. 1.04 = .017 033, which X 24 = .408 799. log. .408 799 3= 2.5633 = ratio raited
to power of 24.
Then, — x(i ^-r—) = 25 X i — 390 122 =s $ 15.24. 695.
04 \ 2.5633/
To Compntv* Yearly Amount tliat Avill IL<iq[uidate a IDe'bt
in a Oiven P^^umlser of Years at Compound Interest.
p ,- (i -i-r)*
— - ' - = A. Illustration. —What is amount of an annual payment that
(i-f-r)«— I
will liquidate a debt of $ 100 in 6 years at 5 per cent compound interest?
PBOBABILITT. 1 1 5
Namb«r of cases which favor drawing of a white ball fyom both bags is 5 X 7 = 35,
for every one of the 5 white balls in one bag may be drawn in combination with every
one of the 7 in the other For a like cause, namber of cases which favor drawing of
a white ball ttom ist bag and a black one from 2d is 5 x 3 = xs ; a black ball from ist
bag and a white ball fh)m 3d is 7 X 2 = 14; and a black ball nnom both is 3 x 2 =6.
Probability, therefore, of drawing is as
^^= — ==— = xtoi,att»At<e6ottyrom6o</i6<v». l^li == !5 ^ _3, ^ .^^ ^
70 70 2 "^ ^ 70 70 14 ^ '
a vihite ball from ist, and a black from 2d. - — - = — = — = it0 4, a black
70 70 5
ball from i«f, and a white from 2d - — - = — = — = 3t0 32, a black ball from
70 70 35
both. - — ^^ = -^ = 29 to 41, a white ball' from onCy and a black from other.
70 70
for both 2d and 3d cases favor this result : hence, JL -f- A = ??. 5X74-5X3+2X7
5 x4 70 70
= — = — = 32 to 3, a< Ucut one white balL for the ist, sd, and 3d cases favor this
70 35 " "^ J 1 J
result; hence, _ 4- -^ 4. -L — H.
a 14 5 35
Again, if number of white and black balls in each bag are same, say 5 white and
9 black, 5 + 2X5 + 2 = 49, then |m>bability of drawing is as
5211 — ?5_. jQ 24,awhiU baUfrom both. ^2Ll^ll— ,© to 39, a whiU baU
49 49 49 49
from ift, and a black from 2d. = — = 10 to 39, a black baUfrom i<<, and a
white from 2d. - — ^ = -^ = 4 to 45, a dZocfc 6aWyro« fcott.
49 49
4.— When two dice are thrown, probability that sum of nambers on upper sides
is any given number, say 7, is as follows:
As every one of the six nambers on one die may come up alike to, or in combi-
nation with the other, number of throws is 6 x 6 = 36.
1 1 and 6 )
Number 7 may be a combination of ] 2 ** 5 1 ; and as these numbers may be
^ (3 " 4)
upon either die, there are 3 x 2 =:6 throws in fkvor of the combination of 7 ; hence
6 I
probability of throwing 7 is -g = -r-, or as i to 5.
5. —Probability of a player's partner at Whist holding a given card is as follows :
Number of cards held by the other 3 players is 3 x 13 = 39; probability, there-'
fore, that it is held by partner is — , but it may be one of the 13 cards which he
holds; hence probability Is — x 13 = ~ = — , or as 1 to 2.
39 39 3
6.— Probability of a player's partner at Whist holding two given cards is as follows:
Namber of combinations of 39 things, taken 2 and 2 together, is ^^ ^ = 741 ;
therefore, probability that these 2 cards are in partner's hand is 39 x 38 = — ^ —
= ~ = z to 740; but they may be any 2 cards in partner's hand; therefore, since
74 X
namber of combinations of 13 cards, taken 2 and 2 together, is ^ — — = — = 78,
X X 2 2
78 s
vrobability reqaired is -^—= —, or as 2 to 17.
74X X9
Similarly, probability that he holds any 3 given cards Is as — , or as 2a to 68z.
703
Il6 PROBABILITY.
PrubabilitiBs at a game of Whist upon following points are :
9 to 7, tficU one hand has two honoi's^ and two hands one ;
9 to 55) ^^' two hands have each two honors ;
3 to 29, that each hand holds an honor;
3 to 13, that one hand has three honors, and one hand one;
I to 63, tftaijbur honors are held by one hand.
7.— If 3 half dollars are thrown into the air, probability of any of the possible com
binatioos of their falling is determined as follows :
Eenco", f — J = .125 = i to 7 in favor of 3 heads.
~ ( — J — . 375 = 3 to 5 " " 2 Jieads and i tail
^^(^V=. 375 = 3^5 " " 1 head and 2 tails.
\y ^ [— ) =.125=1 t0 7 " " ^taiU.
1X2X3x2/
i\nd in like manner, if 5 were thrown up, probability of any of their possible
<:ombination8 woald be determined as follows :
/ i + i_y= ^-V+i- /lV-Li2l4 (L\^4, 5X4X3 /»\5 5X4X3X2 A \5
U ^ 2/ \2/^ I V2y ^iX2\2/ "^1X2X3 \2/ 1X2X3X4 \2/
,5X4X3X2X1/1X5
"^1X2X3X4X5X2/
Hence, f — j = .031 35 = 1 to 31 in favor of 5 heads;
— f-j j = . 156 25 = 5 to 27 " " 4 heads and t tail;
f^ l^j = -3" 5 = 10 to 22 " " 3 heads and 2 tails;
5X4X1/1 \5 '
0<Tx"3 \T/ = -3" 5 = 10 to 22 " '» 2 heads and 3 taHs;
5X4X3X2/1 \5
rxTxTx"^ W = • ^56 25 = 5 to 27 *' " I head and 4 taOs;
' 5X4X3X2X1/1X5
xX2X3X4X5W=°3''^ = '*^3' " ■ 5'«t^.
All Wagers are founded upon the principle of product of the event,
and contingent gain, being equal to amount at stake.
iLLUSTBATioN I.— Supposo 3 borscs, A, B, and C, are entered for a race, and X
wagers 12 to 5 against A, n to 6 against B, and 10 to 7 against C.
If A wins, X wins 6 + 7 — 12 = 1.
"B - X " 5l;_x, = x.
'«C *' X » 5-1-6-10=1.
Hence, X wins i, whichever horse wins, fh)m having taken field against each
horse at odds named. . *
*°* ~ + — + 7^ = — = «o6 = i-o6toi in Jitvor qf taker iff <tdd8.
COMBINATION. — CIRCULAR MEASURE. IIJ
Cozn'biiiatioiiB -^vith. Repetitioxx0.
In this caee the repetition of a term is considered a new combination. Thus,
I, 2, admits of but one combination, if not repeated; if repeated, however, it admits
of three combinations, as i, z ; i, 2; 2, 2.
Rule.— To number of terms of series add number of class of combination, less i ;
multiply sum by successive decreasing terms of series, down to last term of series;
then divide this pr^uct by number of permutations of the terms, denoted by class
of oomblBElion.
E^MPLK.— How many different combinations of numbers of 6 figures can be
made out of 11 ?
1x^(6— x) = i6=zium 0/ number of tenns^ and number of class, less i .
16 X 15 X 14 X 13 X 12 X II = 5 765 76o=productofsumf and successive terms to
Uisl term.
1X2X3X4X5X6 = 720 ptrmutaiions of class of combination.
^5765760^8^ .
720
"Variations -witli Repetitions.
Every different arrangement of individual number or things, including repeti-
tions, is termed a Variation.
Class of Variation is denoted by number of individual things taken at a time.
RuLB.— Raise number denoting the individual things to a power, the exponent
of which is number expressing class of variation.
ExAMPLK I. — How many variations with 4 repetitions can be made out of 5 fig-
ures? 54 = 625.
2. — How many different combinations of 4 places of figures can be made out of
the 9 digits?
, , , . I2X 11X10X9 "880
Coxzil>in.ation w^tliout Repetitions.
RuLK. —From number of terms of series subtract number of class of combination
less I ; multiply this remainder by successive increasing terras of series, up to last
term of series; then divide this product by number of permutations of the terms,
denoted by class of combination.
EzAMPLK 1.— How many combinations can be made of 4 letters out of 10, exclud-
ing any repetition of them in any second combination ?
10 — (4 — i) = 7 = number of terms — number of class, less i,
7X8X9X10 = 5040 = prod, of remainder 7, and successive terms up to last term. .
1X2X3X4= 24 = permutations of class of combination.
Then, 5212 = «o.
24
2.— How many combinations of the 5th class, without repetitions, can be made
of 12 different articles?
Z2 — (5 — i) = 8, and 2 = 2_ = 702.
1X2X3X4X5 120 ^^
CIRCULAR MEASURE.
Unit of Circular Measure is an angle which is subtended at centre of a circle
by an arc equal to radius of that circle, being equal to
180O
^ = 57.296°.
3. 14x6 "'^ ^
Circular measure of an angle is equal to a fhiction which has for its numerator
the arc subtended by that angle at centre of any circle, and for its denominator the
radius of that circle.
114 CIKCULAB MEASUBB.-^PKOBABIT>lTT.
Xo Cozxipute Ciroular Pleasure of* an i\.iigle.
Rdlb.— Multiply measure of angle in degrees by 3.1416, and divide by 180.
Example.— What is circular measure of 24° 10' 8"?
24O 10^ S" X 3-1416 _ 87008 X 3i4'6 _
180 ~ 180X60X60 °** •
To Coxxip-ute I^easure or an .A^iigle, its Oiroular ACeasure
l>eing Chiven.
RuLB.— Multiply circular measure of angle by 180, and divide l>y 3.1416.
PROBABILITY.
Probability of any event is the ratio of the favorable cases, to all the
cases which are similarly circumstanced with regard to the occurrence. If
an event have 3 chances for occurrmg and 2 for failing, sum of chances
being' 5, the fraction | will represent probability of its occurring and is taken
as measure of it. Thus, from a receptacle containing i white and 2 black
balls, the probability of drawing a white ball, by abstraction of i, is ^ ; prob-
ability of throwing ace with a die is I : m other words, the odds are 2 to i
against first, and 5 to i against second.
If m -f- n = whole number of chances, m representing number which are favorable^
tn
and n unfavorable. Therefore — r — = probability of event
m-f-n
Probabilities of two or more single events being known, probability of their oc-
curring in succession may be determined by multiplying together the probabilities
of their events, considered singly.
Thus, probabihty of one event in two is expressed by | ; of its occurring twice in
succession, i X J, or J; of thrice m succession, ij X -J X !» or J, etc.
Illustration l— If a cent is thrown twice into the air, the probability of its fall-
ing with its bead up, twice in succession, is as i to 4. Thus, it may fall :
1. Head up twice in succession. ^
2. Head up ist time and wreath 2d time, f „ i _ _ i ,. ^.
3. Wreath up ist time and head 2d time, f ^ence, j-— _ .25 — — = 4 times.
4. Wreath up twice in succession. )
These are the only results possible, and being all similarly circumstanced as to
probability, the probability of each case is as i to 4, or odds are as 3 to i.
Probability of either head or wreath being up twice in succession is as i to i, or
chances are even, because ist and 4th cases favor such a result; probability of head
once and wreath once in any order is as i to 2, because 2d and 3d cases favor such a
result; and probability of head or wreath once is as 3 to 4, or odds are as 3 to i, be-
cause ist, 2d, and 3d, or 2d, 3d, and 4th cases favor such a result
NoTV.— I to 2 it an equal chance, for i out of 2 chances = i to x, being an equal chance ; afcain, i to
S ia 4 to I, for I oat of 5 chances la i to 4.
2.— If there are 4 white balls and 6 black in a bag, what is the chance of a person
drawing out 2 black at two successive trials?
This is a combination without repetition. Hence, 6 — (2 — i) = 5,
. 5 X 6 30 15 , . , - . X . 1 'S3
and = — = r-^, which x 2 for successive trials = — or — .
I X 2 2 I 2 15
3.— Suppose with two bags, one containing 5 white balls and 2 black, and the other
7 white and 3 black.
Number of cases possible in one drawing f^om each bag is (5-)- 2) x (7 + 3) =7
X xo = 70, because every ball in one bag may be drawn alike to one in the other.
WBIGUI'S OF IBON, STEEI^ COPPXB, BTC.
119
'Wroueb.t Ix*oii, Steel, Copper, and Srass Plates.
{JBirmingham Gaitge.)
No. of
Gauge.
0000
oco
00
o
I
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
23
24
35
26
27
28
29
30
31
32
33
34
35
36
Thicknesa
i light
Inch.
•454 or ^^ f uU
.425 .
.38 or f full
•34 or J *'
•3
.284
.259 or 4 full
.238
.22
.203 or \ full
.18 or y\ light
.165 or i "
.148 or \ full
.134
.12 or
.109
•095 or ^ Ught
.083
.072
.065
.058
.049 or -^ light
.042
•035
.032
.028
.025 or ^
.022
.02
.018
.016
.014
.013
.012
.01 or
.009
.008
.007
<x>5 or
.004 or
Iron.
or A
xiv
Lbs.
18.2167
17.0531
15-2475
13.6425
12.0375
11.3955
10.3924
9.5497
8.8275
8.1454
7.2225
6.6206
5.9385
5.3767
4.815
4.3736
3-8119
3.3304
2.889
2.6081
2.3272
I.9661
1.6852
1.4044
1.284
I.I235
1. 0031
.8827
.8025
.7222
.642
•5617
.5216
.4815
.4012
.3611
.321
.2809
.2006
.1605
Pkr Squaks Foot.
Steel. I Copper.
LIm.
18.4596
17.2805
154508
13.8244
12.198
".5474
10.5309
9,6771
8.9452
8.254
7.3188
6.7089
6.0177
5-4484
4.8792
44319
3.8627
3<J748
2.9275
2.6429
2.3583
1.9923
1.7077
1.4231
1.3011
1.1385
1. 0165
.8945
.8132
.7319
. .6506
.5692
.5286
.4879
.4066
.3659
.3253
.2846
.2033
.1626
Lbs.
20.5662
19.2525
17.214
15.402
13-59
12.8652
11.7327
10.7814
9.966
9.1959
8.154
74745
6.7044
6.0702
5-436
4-9377
4.3035
3.7599
3.2616
2.94*5
2.6274
2.2197
1.9026
1-5855
1.4496
1.2684
1.1325
.9966
.906
.8154
.7248
.6342
.5889
•5436
.453
-4077
.3624
•3171
•2265
.1812
Brass.
No.
Inch.
No.
7
Inch.
No.
13
Inch.
I
.004
x>is
.036
2
.005
8
.016
14
.041
3
.008
9
.019
15
.047
4
.01
10
.024
16
.051
5
.013
II
.029
n
•057
6
X)i3
12
.034
18
.061
No.
19
20
Inch.
.064
.067
21
.072
22
•074
23
24
.077
.082
No.
25
Inch.
•095
26
.103
27
."3
28
.12
29
.124
30
.126
Tliiclzness of* Sheet Silver, O-old, etc.
By Birmingham. Gauge for these Metals.
Lb«.
19.4312
18.19
16.264
14.552
12.84
12.1552
11.0852^
10.1864
9.416
8.6884
7.704
7.062
6.3344
5.7352
5-136
4.6652
4.066
3.5524
3.0816
2.782
2.4824
2.0972
1.7976
1.498
1.3696
1.1984
1.07
.9416
.856
.7704
.6848
•5992
.5564
.5136
.428
.3852
•3424
.2996
.214
.1712
31
32
33
34
35
36
•133
.143
.145
.148
.158
.167
I20 WEIGHTS OF IBOX, STEEL, COPPER, ETC.
^^ro-uglit Iron, Steel, Copper, and Srass "Wire.
American Oauge, f. full, I. light
No. of
Gauge.
Diameter.
oooo
ooo
. oo
o
I
2
3
4
5
6
7
8
9
lO
II
12
13
14
15
i6
I?
i8
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Inch.
46 or j\ f .
40964
,364 8 or f 1.
.324 86 or y«y f .
2893
257 63 or J 1
229 42
20431 or Jf.
181 94 or Y»y 1.
16202
14428
128 49 or J £.
"4 43
loi 89 or ^jj £.
,090742
.0S0808
,071 961
064084
057068
050 82 or ^ 1
045 257
.040 303
03589
031 961
028462
025347
022 571
O2oiory\^f.
0179
01594
014 195
012 641
^11 257
oioo25or 1 f.
.008928 ^°°
00795
00708
006304
005 614
005 or ^1^
004453
003965
003 531
.003144
Iron.
Per Linbal Foot.
Steel. Copper.
Lb«.
.56074
.444683
.352 659
.279 665
.221 789
.175888
.13948
.110616
.08772
.069565
.055 165
.043 751
.034699
.027 512
.02182
.017 304
.013 722
.010886
.008631
.006845
.005 427
.004304
.003413
.002708
.002 147
.001 703
.00135
.001 071
.0008491
.0006734
.000534
.0004235
.0003358
.0002663
.000211 3
.000 167 5
.000 132 8
.000 105 3
.00008366
.00006625
.000 052 55
.000041 66
.00003305
.0000262
Lbi.
.56603
.448 879
.355986
.282 303
.223 891
•177 548
.140 796
.III 66
.088548
.070 221
•055 685
.044 164
.035026
.027 772
.022026
.017 468
.013851
.010989
.008712
.006909
.005 478
.004344
•003445
.002734
.002 167
.001 719
.001 363
.001 081
.000 857 I
.000-679 7
.0005391
.0004275
.000 338 9
.0002688
.000 213 2
.000 169 I
; .000 134 1
' .000 106 3
.00008445
. .00006687
.000 053 04
.000 042 05
.000 033 36
.00002644
Lbt.
.640 513
•507 946
.40283
.319451
.253342
.200911
.159323
.126353
.1002
.079 462
.063013
.049976
.039636
.031426
.024924
.019766
.015674
.012 435
.009859
.007 819
.006 199
.004916
.003899
.003094
.002 452
.001945
.001542
.001 223
.ooo'9699
.0007692
.0006099
.0004837
.000 383 5
.0003042
.000241 3
.000 191 3
.000 151 7
.000 1204
.0000956
.0000757
.00006003
.000 047 58
.00003775
.00002992
Brass.
Lba.
605 176
479908
380666
301 816
239353
189 818
150 522
119376
094666
075075
059545
047 219
037437
029687
023549
01S676
014809
oil 746
009 315
007587
005857
004645
003684
00292
002317
001838
001457
001 155
0009163
000 726 7
0005763
000457
0003624
0002874
000228
0001808
0001434
000 113 7
00009015
000 071 5
00005671
.000044 96
00003566
00002827
Specific Gravities 7.774
Weights of a Cube Foot . . 485.87
Inch.. .2812
(i
it
7.847
8.88
8.386
490.45
554988
524.16
.2838
.3212
•3033
Specific Gravities to determine the computations of these weights were made b;^
author for Messrs. J. R Browne & Sbarpe, Providence, R. I.
PBOBABIIJTT.
117
3. —Odds given upoD tiirst seven favorite horses fbr Oujcs Stakes of 1828 were so
great, that probability iu favor of taker uf the odds wbeu reduced was as follows :
ist, 5 to 2 ; 2d, 5 to 2 ; 3d, 4 to i ; 4th, 7 to i ; 5th, 14 to i ; 6th, 14 to 1 ; 7th, 15 to i
i 4 X 3 X 16 = 19a
iX7Xi6 = ,ia
3X7 X 3= 63
7 X 3 X i6 336
8^15^x5^16
= 367 -J- 336 = 1.092 = 1.092 to I, in favor of taker of odds, yet ueither of the horses
upon which these odds were given won.
3.— If odds are 3 to i against a horse in a race, and 6 to i against another horse
in H second race, probability of ist horse winning is -^, and of other i^. '1 hercfore
probability of both races being won is -^g, and odds ugaiust it 27 to i,or xooo.to 37-037.
Odds tit»ou sach an event were given in 1828 at 1000 to 60, or 16.67 ^ '-
4.— Two persons play for a certain stake, to be won by winner of three games or
results. One having won one and the other two,' they decide to divide the sum,
propurtioaate to their interest. How much of it should each one receive?
OPKKATiozr.— If winner of two games should win game to be [dayed, he would be
entitled to the whole sum; if he lost, he w^ould be entitled to half of it. Now as
one event is as probable as the other, 1 = — , half of which = — , or ghare
13 2 4 •
of winner qf ttoo games.
When events are wholly independent, so that occurrence of one does not
affect that of the other, probability that both will occur is product of proba-
bilities that each will occur.
Nora.— It i* Indifferent whether erenta are to occar together or consecutively.
iLLrarTRATiON I Assume three boxes, each conUiining white and black balls as
follows :
6 white, 5 black : 7 white, 2 black ; 8 white, 10 black. What is chance of drawing
from them a white, black, and a white ball?
Probabilities are — , — , and -~t, product of which = -^-?-i— ^ 17.621; to i.
11' 9 18 297 ' ^
3.— A gives an answer correctly 3 times out of 4, B 4 times out of 5, and G 6 out
of 7. What is probability of an event which A and B declare correct and C denies?
Operation. — Compound probability that A and B answer correctly and C denies
12 _ 3
140 35'
Ck)m pound probability that A and B deny and C is correct .all 3 of which are
3_
70
Then correct, divided by sum _3_^/3j^3\_ -8714 ^» _ 3
of correct and incorrect, ~ ^ "~
(all 3 of which are in favor of event) I3 — x — X —
against event) is — X —
4 5
6^
7 ""140
_ _3_ ^ / JL I A\ = .
35 * \35 70/ •
35 70/ .857 14 + .428 57
= .68 or—.
Odds bet'weexi Results dr Ch.ai\oes, and bet'vp'een any
Number and Whole Numlaer, at various Odds against
eavh., also Valufe of eaolx Chance in parts of lOO.
Odde aK»inet
each.
Valae of
Chance.
Odds acpilnit
each.
Even
50
3 to I
XI to 10
47.63
3.5 "«
6 '* 5
45-45
3 "I
5 ;: ♦
44-44
3.5 "I
1^ :: J
75 " 4
42.1
40
38.1
36.36
34.78
45"*
5-5" I
6 "i
Value of
Chance.
33-33
88.57
85
22.22
20
18.18
16.66
1538
14.28
Odde
eac
Inst
Viilae of
Chance.
6.5 to
7 "
7-5
8
8.5
9
9-5
10
12
it
Ci
li
((
li
13-33
12.5
11.76
II. IX
ia52
xo
9-52
9.09
7-7
Odde
eac
nea
ich.
inat Value of
Chance.
IS to I
18 *♦
20 "
25
30
40"
50"
60 "
100
6.25
5.26
4.76
384
3.3a
1.90
X.64
•99
OpvRATioir. — Divide 100, or anit, as case may be, by sum of odds, and multiply
qnottont by lesser chance or odda
bujsnunov.— 6 to 4. 6+4 = xo, and too-r- xo x 4 = 4o,«aitt« ofehanee.
Il8 WEIGHTS OF IRON, STBICL, COPPER, AND BRASS.
WEIGHTS OP IRON, STEEL, COPPER, AND BRASS.
\v rouglit Iron, Steel, Copper, and Brass Plates.
C S. Law, March ^d. 1893.
Standard Oauge. Iron and StetL
No. of
Gauge.
»oooooo
000000
00000
0000
000
00
o
I
2
3
4
5
9
10
II
12
'3
14
15
16
17
18
»9
30
31
92
a3
a4
9S
26
27
28
29
30
31
3a
33
34
35
36
37
38
Thicknbbs.
Approxi- I Approzi-
mate
Deciinaii.
niHte
Fractions.
Inch.
1-2
15-32
7-16
13-32
3-8
11-32
5-16
9-32
17-64
1-4
15-64
7-32
13-64
3-16
11-64
5-32
9-64
1-8
7-64
3-32
5-64
9-128
i-i6
9-160
1-20
7-160
3-80
11-320
1-32
9-320
1-40
7-320
3-»6o
11-640
1-64
9-640
i-8o
7-640
13-1280
3-320
11-1280
5-^40
9-1280
17-2560
i-i6o
Inch.
5
46875
437 5
40635
375
343 75
3*2 5
28125
265 625
25
234375
2187s
203125
*87 5
X71 875
15625
140625
125
109375
09375
078 125
0703125
0625
05625
05
04375
0375
034 375
03125
028 125
025
021 875
01875
017 187 5
015625
0140695
0125
0109375
010 156 25
009375
00859375
0078195
007 031 25
006640625
00625
WlISRV.
Wro't Iron
Per Sq. Ft.
20.
18.75
17-5
16.25
15.
13-75
12.5
11.25
xa625
10.
9-375
8.75
8.125
6.875
6.25
5625
5-
4-
3-
3-
2.
375
75
"5
8125
5
25
75
5
375
25
125
.875
75
.6875
.625
.5695
.5
•437 5
.40625
•375
•34375
•3" 5
.381 95
.965 625
•«5
No. of
Gauge.
0000
000
00
O
I
2
3
4
5
6
7
8
9
10
II
12
>3
>4
15
16
"7
18
'9
20
21
22
23
24
25
26
3
3
39
30
3'
33
33
34
35
36
37
38
39
40
American GoMge.
Wbiout.
Thickn
A
pprozimate
t^xJuiala.
Inch.
46 or % t
40964
364 8 or K I.
324 86 or ^1.
2893
25763 or ^f-
22942
204 31 or Vs f.
181 94 or ^ I.
16202
14428
12849 or >^ ^^
"4 43
loi 89 or Vio r
090742
080808
071 961
064084
057068
O5o82or%of.
045 257
040303
03589
031 901
028462
025347
022571
0201
0179
015 94
01419s
012 641
01 1 357
010025
008928
00795
00708
006304
005614
005
004453
003965
003531
003 144
Pbb Squakc Foob
Copper.
Lbs.
20.838
18.5567
16.5254
14.7162
i3>o5 3
11.6706
'0.3927
9-2552
8.241 9
7-3395
6.5359
5.8206
5-1837
46156
4.1x06
3.6606
3-2598
903
5852
3021
0501
8257
6258
4478
1.2893
1. 140 2
1.0225
?io53
1087
.72208
.64303
•57264
.50994
•454 «3
•40444
.36014
.32072
•28557
•25431
.2265
.20172
.17961
•15995
.14242
BraM
2.
2.
2.
2.
I.
I.
I.
Lbs.
19.688
17-5326
15-6134
13-904
12.382
11.0266
9.8192
8.7445
7.787
6.934 5
6.1759
5-4994
4-8976
4- 3609
3.8838
3-4586
3-.0799
2.7428
4425
175 >
937
725
5361
3679
2182
t.0849
.06604
.86028
.76612
.68223
»6o7 55
•54>03
.4818
42907
.382 12
.34026
.30302
.26981
.24028
.214
.19059
.1697
.15113
•»3456
2.
2.
I.
I.
I.
I.
I.
In the practical use and application of the U. S. Gauge, a variation of
two and one-half per cent, either way may be allowed.
WrH Iron.
Specific Gravities 7^704
Weights of a Cube Foot 481 .75
" •* Inch 2787
steel.
Copper.
Brasa^
7.806
8.698
8.218
487.75
543-6
513-6
.2823
.3146
.29? a
WISS GAUOBS. — C^AS Pl^£S AKD WIBE CORD. 12^
Frenobi {Jaugea de FUs de Fer),
French wire-gauges, alike to the English, have been sabjected to vftriaitioii.
Following table contains diameters of the numbers of the Limoges gauge.
"Wire-GI-auge (Jattffe de Limoges),
Number.
Millimetra.
Inch.
N«mber.
MUUmetra.
Inch.
O
•39
.0154
9
1-35
.0532
I
•45
.0177
10
1.46
.0575
2
.56
.032I
II
1.68
.0661
3
.67
.0264
12
1.8
.0706
4
•79
.0311
13
1. 91
.0752
5
•9
•03S4
14 .
2.Q2
.0795
6
1. 01
.0398
15
2.14
.0843
7
I.I3
.0441
16
2.25
.0886
8
1.24
.0488
17
2.84
.112
18
19
20
21
22
23
24
Bfillimrtre.
Inch.
3.4
.134
3-95
.156
4-5
,177
51
.201
5.65
.222
6.3
•244
6.8
.268
For
Ghalv€iiiized.
Iron "Wire.
Number.
MiUimetre.
Incfa,
Number.
Millimetre.
Incb.
Number.
I
.6
.0236
9
1.4
•0551
17
2
•7
.0276
10
1.5
.0591
18
3
.8
•0315
II
1.6
.063
19
4
•9
•0354
12
1.8
.0709
20
5
I.
•0394
13
2.
.0787
21
6
I.I
•0433
14
2.2
.0866
22
7
1.2
•0473
IS
2.4
•0945
23
8
1.3
.0512
16
2.7
.106
Mililmetre. . Incb.
3-
3-4
39
44
4.9
5-4
S-9
118
134
154
173
193
213
232
F'or "Wire and Sara.
Mark.) Millimetre. Mark. Millimetre
P
I
2
3
4
5
6
5
6
7
8
9
10
II
7
8
9
10
II
12
12
13
14
15
16
18
Mark.
Millimetre.
13
20
H
22
15
16
24
27
17
18
30
34
Mark.
Millimetre.
Mark.
«
Millimetre.
19
39
25
70
20
44
26
76
21
49
27
82
22
54
28
88
23
59
29
94
24
64
30
100
Th.iokn.es8 of G-as Fipes.
Diameter.
i-5to3
4 "6
ThickneM.
.25
•375
Di(uneter.
8 to 10
"13
12
Thickness.
.5
.625
Diameter.
14*0 15
16 "48
Thickness.
•75
.875
Copper "Wire Cord.
Ciroixmrerenoe and Safe Xjoad.
_, - Inch. Inch. Inch. Inch. Inch. Inch. Ins. Ins
Circumference., 25 .375 .5 .625 .75 i 1.125 1.25
Safe load m Lbs 34 50 75 112 168 224 336 448
Zinc— sheets.
Thickness and "Weight per Square Tfoot.
Inch.
.0311 = 10 OZ.
/>457 = 13 oz.
loch.
.0534 = 14 OZ.
.0611 =: 16 OZ.
Inrh.
.0686 = 18 OZ.
.0761 ^ 20 OZ.
124 WBIG^T AND STBBirGTH OV WIBB^ IBOH, BTO.
WEIGHT AND STBENGTH OP WIRE, IRON, ETC.
"W^eigUt and Strength, of "Warrington Iron Wire.
Manufactttred by Inlands Brothers. (England.)
Weight per :
too Lineal Feet
^\t^amm»
Breaking Weight.
BrMkln«p Weight
No.
DfanM*
tor.
Tnch '
Weight
' Lbs.
An-
nealed.
Bright.
No.
Gauge.
Diameter.
Weight.
An-
nealed.
Bright.
Scuge.
Lbt.
LIHI,
Inch.
!'Lb..
LlM.
Lbe.
7/0^
^
64.46
3490
5233
9
.146
55
298
447
6/0
1
56.66
3066
4603
10
•133
4-43
247
370
5/^
4936
2673
4000
10.5.
.125
403
218
327
4/0
42.53
2303
3457
II
.117
3-53
191
288
3/0
%
36.26
1963
2945
12
.1
2.66
145
217
2/0
/!«
30.46
1653
2473
13
.09
2.1
"3
i6q
0
.326
27.36
I486
2226
14
.079
i6
87
130
I
•3
233
1257
1885
15
.069
1.23
66
99
2
.274
19.36
1046
1572
16
.0625
.96
53
77
3
•25
16.13.
«73
1309
17
.053
•73
39
59
4
.229
13-53
733
1098
18
.047
.56
31
46
5
.209
11.26
610
913
19
.041
.43
23
, 35
6
.191
9.4
509
763
20
.036
•33
18
27
7
.174
7.8
422
633
21
.031 25
.26
14
21
8
.159
6.53
353
519
22
.028
.2
II
16
To Compute ILiengtli of lOO Pounds of "Wire of a Q-iveu
I>ianieter.
Rule. — Divide following numbers by square of diameter, in parts of an
inch, and quotient is length in feet.
37.68. for wrought iron. I 33.42 for copper. I 28 for silver.
37.45 for steeL | 34.41 for brass. | 15.3 for gold.
13.64 for platinum.
Window Giass.
rrhiolzness and l^eiglit per Square lEToot.
No.
12
z6
Thickneas.
Inch.
•059
.063
.071
.077
Weight.
Ox.
12
16
No.
17
21
24
Thicknen.
Inch.
.083
.091
.1
.III
Weight.
Oz.
»7
19
21
24
No.
ThickneM.
Weight.
26
Inch.
•"S
Oi.
a6
36
42
.154
.167
.2
36
4a
Teme Plates.
Teme IHcUes — Are of iron covered with an amalgam of lead.
'PHiokness and. "Weiglit of Gralvaxiized. Slieet IroA.
Sheet Ti Feet in Width by from 6 tog Feet in Length {M, Lejjferts).
Weight
per
Sq. Footi
4
Weight
el
Welffht
£&
Weight
.&
Weight
Weight
•
0 M
per
Sq. Foot.
k
per
Sq. Foot.
No.'
per
8q Foot.
No.
per
Sq. Foot.
ij
per
Sq. Foot.
Ox.
^1
No.
No.
No.
Ot,
o«.
Oi.
No.
29
12
26
IS
23
20
30
27
17
36
14
28
13
25 16 1
22
22
19
30
16
42
13
27
'4 1
24
18 I
21
24
18
35
IS
46
12
Os.
53
6x
70
WEIGHTS OF lEON, STEEL, COPPER, ETC.
121
Wroixgh.t Iron, Steel, Copper,, and Srass TVire.
BiiTninfffiam Wire Oav^e. f. full, 1. light.
Pbr Lineal Foot.
Iron. I
No. of
Gauge.
Diameter-
f.
Steel.
Lbs.
.546207
.478 656
.38266
•30634
.2385
.213 738
.177 765
.150 107
.128 26
.109204
.08586
.072 146
.058 046
•047 583
.038 16
.031 485
.023 916
.018 256
.013 728
.011 196
.008915
.006363
.004675
.003246
.002714
.002078
.001 656
.001 283
.00106
.000 858 6
.000 678 4
.0005194
.0004479
.000 381 6
.000265
.000 214 7
.0001696
.0001299
.00006625
.0Q00424
Lbs.
•551 36
.483 172
.38627
.30923
.24075
•215 755
.179442
.151 523
.12947
.110234
.086667
.072 827
•058593
.048 032
.038 52
.031 782
.024 142
.018 428
.013 867
.011 302
.008999
.006423
.004719
.003 277
.002739
.002097
.001 672
.001 295
.001 070
.0008667
.0006848
.0005243
xx)0 452 I
.000 385 2
.0002675
.000 216 7
.000 171 2
.000 131 I
.00006688
.0000428
Copper.
LbB.
.623 913
.546 752
•437099
.349921
.272 43
.244 146
.203 054
.171 461
.146507
.124 74
.098075
.08241
.066303
.054353
•043589
.035964
.027 319
.020 853
.015692
.012 789
.010 183 .
.007268
.00534
.003708
•0031
•002373
.001 892
.001 465
.001 211
.0009807
.0007749
.000 593 3
.0005116
•0004359
.000302 7
.000 245 2
.000 193 7
.000 148 3
.000 075 68
.000 048 43
brass.
Lba.
.589286
.516407
.41284
.3305
.25731
.230 596
.191 785
.161 945
.138376
.117817
.092 632
.077 836
.062624
.051 336
.041 17
.033968
.025802
.019696
.014 821
.012 079
.009618
.006864
•005043
.003502
.002928
.002241
.001 787
X)oi 384
.001 144
.000 926 3
.000 731 9
.0005604 .
.000 483 2
.000411 7
.000 285 9
.000 231 6
.000 183
.000 140 I
.000071 48
.000 045 74
GDIiiokiiess of £*lates.
No.
Inch.
No.
Inch.
I
.3125
9
.15625
3
.28125
10
.140 625
3
•25
II
.125
4
•234375
12
.1125
5
.218 75
13
.1
6
.203 125
14
•0875
7
•1875
IS
.075
8
.171 87s
16
•0625
No,
Inch.
No.
Inch.
17
.05625
25
.02344
18
.OS
26
.021 875
19
•04375
27
.020 312
20
•0375
28
.018 75
21
.034375
29
.017 19
22
.031 25
30
.015 625
23
.028 125
31
.01406
24
.025
33
•0125
122
WIBS GAU6SS;
WIBE GAUGES. (S^nglisli.)
Warrififfton (Rylands Brothers).
No.
Inch.
No.
0
Inch.
No.
Inch.
No.
II
Inch.
No.
17
7/0
K
.326
6
.191
.117
6/0
/^
I
•3
7
.174
12
.1
18
5/0
S
2
.274
8
.159
13
.09
19
4/0
%
3
.25
9
.146
14
.079
20
3/0
%
4
.229
10
•133
15
.069
21
2/0
m
5
.209
10.5
.125
16
.0625
22
Sir Joseph Whittoorth d: Co,%
Inch.
No.
Inch.
No.
Inch.
No.
Inch.
No.
.001
14
.014
34
.034
85
.085
240
.002
15
.015
36
.036
90
.09
260
.003
16
.016
38
.038
95
.09
280
.004
17
.017
40
.04
100
.1
300
.005
18
.018
45
.045
no
•II
325
.006
19
.019
50
•05
120
.12
350
.007
2Q
.02
55
•055
135
.135
375
.008
22
.022
60
.06
150
•15
400
.009
24
.024
65
.065
165
.165
425
.01
26
.026
70
.07
180
.18
450
.011
28
.028
75
.075
200
.2
475
.01:2
30
•03
80
.08
220
.22
5CX)
.013
32
.032
Inch.
.053
.047
.041
.036
•0315
.028
Inch.
.24
.26
.28
•3
•325
•35
•375
•4
•425
•45
•475
•5
No.
I
2
3
4
5
6
7
8
9
10
II
12
13
Sir Joseph Whitworth, in 1857, introduced a Standard Wire-Gauge, rang-
ing from half an inch to a thousandth, and comprising 62 measurements.
It commences with least thickness, and increases by thousandths of an inch
up to half an inch. Smallest thickness, y^itu ^^ ^^ ^"^^^ ^^ ^^* ^ ' ^^' 2
is Yinrff' ^^^ ^ ^^i increasing up to No. 20 by intervals of j^j^ ; from
No. 20 to No. 40 by yuito ' *"^ from No. 40 to No. 100 by yj^^y. The
thicknesses are designated or marked by their respective numbers in thou*
sandths of an inch.
This gauge is entering into general use in England.
Ne^w Standard 'Wire Grange of Grreat Sritain,
No. Inch.
No.
Inch.
No.
Inch.
No.
loch.
7/0
.5
8
.160
22
.028
6/0
.464
9
.144
23
.024
5/0
•432
10
.128
24
.022
4/0
•4
II
.116
25
.02
.1/0
•372
12
^ .104
26
.018
2/0
•348
13
.092
27
.0164
0
•324
14
.08
28
.0148
I
.3
15
.072
29
.0136
2
.276
16
.064
30
.0124
3
.252
17
.056
31
.0116
4
.232
18
.048
32
.0108
5
.212
19
.04
33
.01
6
.192
20
.036
34
.0092
7
.176
21
.032
35
.0084
36
37
38
39
40
41
42
43
44
45
46
47
48
49
.0076
.cx)68
.006
.0052
.cx>48
.0044
.004
.0036
.0032
.0028
.0024
.002
.0016
.ooia
No. ^Q, .001 inch.
WEIGHTS OF MBTALS.
127
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73
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128
WEIGHTS OP MBTAXS.
0
u
M
H
M
H
QQ
0S
moo « «noo ^ »noo « moo
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w « CO m<o t^oo
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moo
tN.00
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m -^ m>o t>. o^ O H
t^oo
mvo
t^ o^ o « «
m ts.00 c«
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M fO
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mvo t«»
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ro m ts. o\ M fT> moo o « *vo oo O « •♦r^O^•H fo^-^
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I
fo ■♦ mvo 00
oo t>iVO m -^
CO «
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comt^Ovw Pomts.Ovw
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^vo 00
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m ^ CO « M ^ ONOO
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ts.vo m * fo M M ovoo txvo m •♦ CO « M
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jo CO ^h^ 00 d w CO m t«.od d « »*> "O t>oo d « •^mti.ONd w ^mt^dvHci •*
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t>. ^ hOO
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m CO N M
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t>HHVO MVO MVO MVO
Ov M « -4- m t««o6 d M CO ■^vd t»>
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CO
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VO CO 00 m CO 00
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m CO 00 >o fo 00
tNi O fo moo M ■♦vo
m CO 00 m CO oo
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m CO 00 m CO
M ^ t>. Ok « moo
« CO mvo t^oo o w « * mvo
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M M «
M
PI
mvo 00
N « M
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« cocococococof*)ro-*
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moo O covo 00
m M 00
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m M ho m M 00
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to Ov o M
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mwoo m«oo mej
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H
K
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J M* « CO -^ mvo t^od o^ ^ M ej CO ^ mv© rj oo g^ g 5 jj g jj> j g*^ jj-'g ^ ^
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m
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^ _ e* M ovoo o m CO « O Ov tsO ■♦ N m ovoo vo m co m O
J M* pi c<j + 1^ mvo ti.oo' o* 2 ^ j; 2 IT M M 'S *H Ji**S 2" « « ei N 5* ef «*"§«■
^ vO m CO e* O On toO
m
m m
w m t*.
m m
M m io.
m m
« m to.
m m
M m to
vt m
c« «A to
m m
et m t>
m m
c* m to
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3 2^ « J?) P; !? inmvo o i^oooo Ov O « ►^ « «?'?"t'?'?'*i^ *^'^"i ?*
WEIGHTS OF METALS.
125
Wrought Iron and Steel.
'^Veiglits of Square [Rolled. Iron and. Steel,
From .125 to 10 Inches, one foot in length.
Iron^ 485 lbs. Steely 489.6 lbs, pkr cube foot.
SiDK.
Inc.
.125
.1875
.25
.3125
.375
•4375
.5
.5625
.625
.6875
.75
.8125
.875
.9375
[
.125
.25
•375
.5
.5625
•75
875
2
.125
•25
•375
•5
.625
Iron.
Stksl.
SiDK.
Irox.
Stekl.
Si OK.
Ikox.
LiM.
Lbs.
Ini.
Lbs.
Lbs.
Ins.
Lbs.
.053
.053
2-75
25.47
25.71
6.25
131.6
.118
• .119
.875
27.84
28.1
.375
137
.21
.212
3
30-31
30:6
.5
142.3
•329
'333
.125
32.89
3.3-2
.625
147.9
•474
.478
•25
35-57
3592
.75
153.5
.645
.651
•375
38.57
38.73
•875
159.2
.812
.85
•5
41.26
41.65
7
165
1.066
1.076
.625
44.26
44.68
.125
171
1.316
1.328
•75
47-37
47.82
.25
177
1.592
1.608
•875
50.37
51.05
•175
183.2
1-895
1-9^3
4
53-89
54-4
.5
189.5
2.223
2.245
.125
57,31
57-85
.625
195.8
2-579
2.608
•25
60.84
61.41
•75
202.3
' 2.96
2.989
•375
64.17
65.08
•875
208.9
3368
34
.5
68.2
68.85
8
215.6
4263
4303
.625
72.05
72.73
.125
222.4
5263
5-312
•75
75-99
76.71
•25
229.3
6.368
6.428
.875
80.05
80.81
•375
236
7578
7-65
5
84.20
85
•5
243-4
8.893
8.978
.125
,88.47
893
.625
250.6
10.31
10.41
.25
92.83
93.72
•75
257-9
11.84
"•95
•375
97-31
98.23
.875
265.3
1337
13.6
•5
101.9
1028
9
272.8
15.21
15-35
.625
106.6
107.6
.25
288.2
17.08
17.22 .
•75
111.4
112.4
.5
304
19
19.18 1
.875
116.3
117.4
•75
320.2
21.05
21.25
6
121.3
122.4
•875
328.6
23.21
2343 i
.125
—
127.6
10
336.8
Stbrl.
Lbs. .
132.8
138.2
143.6
149.2
154-9
160.8
166.6
172.6
178.7
f84.9
191-3
197.7
204.2
210.8
217.6
224.5
231-4
238.5
245.6
252.9
260.3
267.9
2754
290.9
306.8
323^2
3316
340
Weiglit or ^xigle Iron,
From 1.25 fo 4.5 Inches, one foot in length.
Thickness meaaui^ in Middle of each Side,
L E<i|-AL SID8S.
Tkiek
Sides
fns.
1.25X1.25
1.5 X15
>.75Xi 75
2 X2
2.25 X 2.25
2.5 X2.5
3 X3
3-5 X3 5
4 X4
45 X4-5
4-5 X4-S
i.
Weljcht
L UxK
Side*.
Lbs.
Ins.
1-5
3 X2.5
^
3^5X3
3 1
3.5x3
35
4 X3
4.5 ;
4 X3^5
5
4 X3 5
7
45x3
9
5 X3
125
5 X3
14
5.5X3.5
16
5-5x5.5
JAL Si
rhick-
DSS.
oess.
Weljfht.
Inch.
Lbs.
375
6.25
4375
7.75
4375
9.6
5
II
5
"-5
5
"•75
5
"75
5
1265
5625
137
5
14-5
5625
156
Inch.
1875
1875
25
35
3125
3125
375
4375
5
5
5625
* II1U columD ifivei d«ptb of web added to the tbicko«sa of tmae or fluigc.
L*
L Unequal SiDsa
Thick-
Sides.
ness.
Weight.
Ins.
Inch.
Lbs.
6 X3.5
.625
18
6 X4.5
.625
20
T
2 X2 375*
.375
5.5
25x2.875
•375
6.5
35x3.5
•4375
10.5
4 X3.5 {
•4375
•75
13
4 X3.5
.75
13.5
128
WBIOHTS OF HETAI^.
«
1»
H
H
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OQ
O
moo M
moo
t>.oo
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m ^ rooo « to M so m on ♦
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3 2 m « ro P> '«i- m mo o tooo ooon 0««Nf^ro^m mo o t^oo oo ov
WEIGHTS OF METALS.
125
Wrought Iron akd Steel.
Weigh. ts of Sqnare Rolled. Iron. and. Steely
From .125 to 10 Inches, one foot in i.ength.
Irony 485 lbs. Steely 489.6 lbs. pkr cube foot.
fliDR.
lac.
.125
.1875
.25
.3125
.375
.4375
•s
.5625
.625
.6875
.75
.8125
.87s
•9375
[
.125
.25
•375
•5
.5625
'75
875
2
.125
•25
.375
•5
•625
Ibon.
Stkrl.
SlDK.
Iro.v.
Stskl.
SlDK.
Iitox.
Stkrl.
Lbs.
LbB.
Ins.
Lba.
Lb0.
Ins.
Lbs.
Lbs.
.053
.053
2.75
2547
25.71
6.25
I3I.6
132.8
.118
• .119
.875
27.84
28.1
■375
137
138.2
,ii
.212
3
3031
30:6
.5
142.3
143.6
.329
•333
.125
32.89
33-2
.625
147.9
149.2
.474
.478
•25
35-57
3592
•75
i53'5
154.9
.645
.651
•375
38.57
38.73
.875
159.2
160.8
.8X2
.85
•5
41.26
41.65
7
165
166.6
1.066
1.076
.625
44.26
44.68
.125
171
172.6
1.316
1.328
•75
47^37
47.82
•25
177
178.7
1.592
1.608
•875
50.37
51-05
.175
183.2
184.9
1.895
1-913
4
5389
54-4
.5
189.5
19T.3
2.223
2.245
.125
57,31
57.85
.625
195.8
197.7
2.579
2.608
.25
60.84
61.41
•75
202.3
204.2
• 2.96
2.989
•375
64.17
65.08
•875
208.9
210.8
3368
3-4
•5
68.2
68.85
8
215.6
217.6
4.263
4303
.625
72.05
72.73
.125
222.4
224.5
5.263
5.312
•75
75.99
76.71
•25
229.3
231.4
6.368
6.428
.875
80.05
80.81
•375
236
238.5
7578
765
5
84.20
85
•5
243.4
245-6
8.893
8.978
.125
88.47
893
.625
250.6
252.9
10.31
10.41
.25
92.83
93.72
•75
257-9
260.3
11-84
"•95
•375
97.31
98.23
.875
265.3
267.9
1337
13.6
.5
101.9
1028
9
272.8
275.4
15.21
15-35
.625
106.6
107.6
•25
288.2
290.9
17.08
17.2a .
.75
111.4
1 12.4
•5
304
306.8
19
19.18 !
.875
116.3
1 1 7.4
.75
320.2
323-2
21.05
21.25
6
121.3
122.4
.875
328.6
331.6
23.21
2343 i
.125
—
127.6
10
336.8
340
"Weiglit of ^ngle Iron,
From 1.25 to 4.5 Inches, one foot in length.
Thickness meatU7*ed in Middle of each Side,
L Gi^lAL SlDBS.
Tkiek
Sides.
Ins.
1.25X1.25
1.5 Xi-5
'-75 XI 75
2 X2
2.25 X 2.25
2.5 X2.S
X3
X35
X4
X4-5
X4S
3
3-5
4
45
4-5
Inch.
•1875
-1875
-25
-25
•3«25
•3125
•375
4375
5
•5
.5625
Weight
Lba.
1-5
2
3
3
4-
5
7
9
12.
14
16
5
•5
L UXSQUAL SlDBS.
Thick-
neu.
Sides.
Ins.
3 X2.5
3-5X3
3-5x3
4 X3
X3-5
X3 5
5x3
X3
X3
«5X35
4
4
4
5
5
5«
5-5 X 5^5
Inch.
375
4375
4375
5
5
5
5
5
5625
5
5625
Weight,
Lbs.
6.25
7^75
9.6
II
"5
"•75
"75
1265
137
14-5
156
L Unequal Sidk&
Thick-
Sides.
ness.
Weight
Ins.
Inch.
Lbs.
6 X3.5
.625
18
6 X4.5
.625
20
T
2 X2375*
•375
5.5
25X2.875
•375
6.5
35X3.5
•4375
10.5
4 X3.5 {
•4375
•75
13
4 X3-5
-75
135
11ti» coiump |;ivfll depth of treb added to the thickness of iMM Qr (Uui|[c.
126
WEIGHTS OF METALS.
Wrought Iron and Stkel.
W eiglits or liouxid. Rolled Iron and. Steel,
From, .125 to 10 Inches, onb foot in lbnoth.
IroUy 485 Ubs. Steely 489.6 lbs. pbr cubb foot.
Diameter.
Iron.
Stbkl.
Diameter.
Iron.
Stbbl.
Diameter.
Iro.v.
Strbl.
Ins.
Lbs.
Lb«.
Ins.
Lbs.
Lbs.
Ins.
Lbs.
Lbs.
.125
.041
.042
2.75
20.01
20.2
6.25
103.3
104.3
•1875
•093
.094
•875
21.87
22.07
•375
107.7
108.5
•25
.165
.167
3
23,81
24.03
.5
111.8
II2.8
•3125
.258
.261
.125
2583
26.08
.625
116.4
1 17. 2
.375
•372
•375
•25
27.94
28.2
•75
120.5
121. 7
•4375
.506
•5"
•375
30.13
30.42
•875
124.9
126.2
• 5
.66x
.667
•5
32.41
32.71
7
129.6
130.9
.5625
.837
.845
.625
34-76
35.09
.125
134-2
135-6
.625
I-033
1-043
•75
37-2
3756
.25
139 „
140.4
.6875
1.25
1.262
.875
39.72
4a I
.375
143-8
145-3
•75
1.488
1.502
4
42.33
42.73
•5
148.8
150.2
.8125
X.746
'•763
.125
45.01
45-44
.625
153-8
155-2
.875
2.025
2.044
•25
47.78
48.24
•75
158.9
i6a3
•9375
2.325
2-347
•375
50.63
51.11
•875
1 64. 1
165.6
I
2645
2.67
.5
53-57
54.07
8
169.3
171
•"5
3348
3.379
.625
56.59
57-12
• 125
174.6
176-3
•25
4.133
4->73
'P
59.69
60.25
•25
180.1
181.8
.375
5
5.049
.87s
62.87
63.46
•375
185.5
i87.3
.5
5-952
6.008
5
66.13
66.76
•5
191. 1
193
.625
6.985
7.051
.125
69.48
70.14
.625
196.6
198.7
•75
8.104
8.178
.25
72.91
73.6
•P
202.5
204.4
•875
9-3
9.388
.375
7643
77.16
•875
208.1
210.3
2
10.58
I0.68
•5
80.02
80.77
9
214-3
216.3
.125
11.95
12. 06
.625
!3^
!l*9
• 25
226.3
228.5
• 25
13-39
«3-52
•75
87.46
88.29
•5
238.7
241
•375
14.92
15.07
•875
91.31
92.17
•75
251-5
253-9
•5
16.53
16.69
6
95.23
96.14
.875
259^5
260.4
•625
18.23
18.4
•125
103-3
100. 2
10
264.5
267
Weiglit of Steel A^ngles.
From .75 to 7 X 3.5 Inches, one foot in lknotr.
Thickness measured in middle of each side.
Equal Sidbs
1.
SiDB.
Thick-
neas.
Area.
Weight.
Ins.
Ins.
Sq.Ins
Lba.
'P
•875
.125
-17
.6
.125
.21
-7
I
.125
•24
.8
1-25
.125
•30
I
1-5
.25
.69
^'i
'•75
•25
.81
2.8
2
•25
•94
3-2
2.25
-25
1.06
3-7
2.5
•25
1. 19
4-'
2-75
-25
1-3'
4.5
3
-5
2.75
9.4
3.5
•5
3.25
II. I
A
•5
3.75
13.8
4
•75
5-44
18.5
5
•5
4.75
z6.2
5
•75
6-94
23.6
5
I
9
30.6
6
•5
5.75
19.6
6
•75
8.44
28.7
$
"
37-4
Unbqual Sides.
SiDKS.
Ins.
1.375X1
2 X 1.37s
2.25 X1.5
2.25 Xi
2.5 X2
2.5 X2
3 X2
3 X2
3-25 X2
3-25x2
3-5 X2.
X3
X3
X3
X3
X3
X3
X3
X3
X3
•5
•5
Thick-
ness
Area.
Weigh t.
Sides.
Thick-
ness.
Ann.
Sq.Ins
Ins.
Sq.Ins
Lbs.
Ins.
Ins.
.25
-53
1.8
5X35
•5
4
.25
•7S
2.7
5X3.5
.625
4-92
.25
.88
3
5X3.5
•75
5.81
-5
1.63
5-5
5X3.5
• 875
6.67
.25
1.06
11
5X4
•5
4.25
-5
2
6.8
5X4
.625
5.23
25
1. 19
4
5X4
.75
6.19
'S
2.25
7-7
5X4
.875
7.11
.25
1.25
4-3
6X3-5
.5
4-5
•5
2.3«
8.1
6X3.5
.625
5-55
-25
'-44
4.9
6X3.5
■75
6.56
•75
4-3'
14.7
6X3.5
I
«5
•5
3.25
11
6X4
.5
4-75
•75
4.69
16
6X4
.625
5.86
•5
3.5
11.9
6X4
•75
6.94
.75
5.06
17.2
6X4
I
9
5
3-5
11.9
7X3.5
-5
5
.75
5.06
17.2
7X3.5
.625
6. 17
•5
3-75
12.8
7X3.5
•75
7-3'
-75
5.44
18.5
7X35
I
9-5
Weight
Lbs.
13.6
16.8
19.8
22.7
'4-5
17.8
21. z
24.2
'5-3
18.9
32.3
28.9
16.2
20
23.6
30.6
'7
21
24.9
323
WEIGHT OF SHEST AKD HOOP IBOK.
129
"WeigUt Qf Blieet Iron. {EngUsh. D. K. Clark.)
Per Squakk Foot {at 480 ibs.per Cube Foot).
As by Wire>gauge used in South StafTurdshire, England.
Tblcknett.
WeiKbt.
No.
Inch.
LlM.
32
.0125
•5
31
.0X41
.562
30
.0156
.625
29
.0172
.688
28
.0188
•75
27
.0203
.813
26
.0219
•875
25
.0234
•938
24
.025
I
23
.0281
113
22
.0313
125
Square
Feet
Thickness.
Weight.
in I ton.
No.
No.
Inch.
Lbs.
4480.
21
•0344
1.38
3986
20
0375
1-5
3584
19
0438
175
3256
18
■05
2
2987
17
•0563
225
2755
16
.0625
25
2560
15
•075^
3
2388
14
.0875
35
2240
13
.1
4
1982
12
.1125
45
1792
II
.125
5
Squ
F«
nare
eet
in I ton.
No.
1623
1493
1280
1 120
996
896
747
640
560
498
448
Thickness.
No.
Inch.
10
.1406
9
.1563
8
.1719
7
.1875
6
,2031
5
.2188
4
•2344
3
•25
2
.2813
I
•3125
Weight.
Lbs.
563
6.25
6.88
7-5
8.13
8.75
9.38
10
11.25
12.5
Sqn
Fe
loare
Teet
I in I ton
No.
398
358
326
299
276
256
239
224
199
179
"Weiglit of Koop Iron. {English.)
Per Lineal Foot.
Width.
W.G.
Weight.
Width.
W.G.
Weight.
Width.
W.G.
Ins.
No.
Lbs.
Ins.
No.
Lbs.
Ins.
No.
.625
21
.067
I.125
17
.21
1.75
14
75
20
.0875
1.25
16
.27
2
13
.875
19
.1216
1.375
IS
•33
2.25
13
X
18
.1636
1-5
15
.36
2.5
12
Weight.
Lbs.~
.484
•634
.714
.91
'Weiglit of Blaclt and. Gralvanized. Slieet Iron.
(Jforton'* liable, founded upon Sir Joseph Whihooi^fh ^ Co.'s Standard Bir-
mingham Wire^Gauge.) (D. K. Clark.)
Note.— 'Numbers on Holtzapffers wire gauge are applied to thiuknesses on Whit-
wortti gauge.
Gan
fee and Weight of
Black SbeeU.
ApnroxJniate nuoibc
of Sq. Ft. in z ton.
Black. iGalyaoizei
No.
Inch.
Lbe.
Sq.Ft.
Sq.Ft.
I
•3
12
187
185
3
.28
II.2
200
197
3*
.26
10.4
215
212
4
.24
96
233
229
5
.22
8.8
254
250
6
.2
8
280
275
7
.18
7.2
311
3<H
8
.165
6.6
339
331
9
•15
6
373
363
10
•135
5-4
415
403
II
.12
4.8
467
452
12
.11
4-4
509
491
13
•095
3.8
589
S66
14
.085
3-4
659
630
15
x>7
2.8
800
757
16
^S
2.6
862
813
Gaujre and Weight of
Black fiheeU.
No.
Inch.
Lbs.
17
.06
24
18
.05
2
19
.04
1.6
20
.036
1.4
21
.032
1.28
22
.028
1. 12
23
.024
.96
24
.022
.88
25
.02
.8
26
.018
.72
27
.016
.64
28
.014
.56
29
.013
•52
30
.012
.48
31
.01
•4
32
.009
.36
Approxin
ofSq.F
late naoiber
t. in I ton
Black.
1 Galvanised.
Sq.Ft.
Sq. Ft.
933
876
1120
1038
1400
1274
1556
1403
1750
1558
2000
1753
2333
2004
2545
2159
2800
2339
3111
2553
3500
2808
4000
3122
4308
3306
4667
3513
5606
4017
6222
4327
130
WBIGHT OF ANGLB AND T IBON.
'Weigh.t of English. .A^ngle and T Iron. {D. K. CUxrk.)
ONE FOOT IN LENGTH.
Note.— When base or web taiiera in section, mean thickness is to be measured.
Sum or Width ahd Dkpth in Imcbss.
Thick-
neac.
••5
Inch.
Lbt.
•125
•57
.1875
.81
25
1.04
3125
1.24
a.875
125
1. 14
.1875
T.68
25
2.19
•3125
2.67
•375
3-13
•4375
3-57
I 1.625' '-75 '-875
LlM.
.62
.89
1-15
1-37
LtM.
.68
.97
1^5
1-5
Lba.
•73
I. OS
1.36
1.63
3125 ' 325
1.25 1-3
1.84 1. 91
2.4 2.5
2.93 3-o6
3-44 3-59
3-75 1 3-93 4-"
1.2 1
1.76
2.29
2.8
328
Lbs.
.78
113
1.46
1.76
3-375
1875
25
3125
375
4375 j
5625'
25
3125
375
4375
5
5625
625
•375
•4375
•5
•5625
.625
•75
4-5_
2.7
3-54
436
5-i6
592
6.67
738
4-75
2.85
3-75
4.62
547
6.29
7.08
7.85
.625
•75
•875
I
7-25 . 7.5
3-OI,
396
4.88:
578
6.65
75
8.32
7-75
5.83 1 6.04 6.25
7.23; 7-49 7-75
8.59; 8.91 9.22
9.93 10.3 1 10.66
11.25 11.67 ii2.oS
12.54 13-01, 1348
3.16
4.17
5-14
6.09
7.02
7.92
8.79
8
1-45
1.99
2.6
3-19
3-75
4.29
5-5
2.125 I 2.25 I 2.375
Lbs.
.83
I.2I
1.56
1.89
3-5
6.46
8.01
9-53
11.03
12.5
1.41
2.07
2.71
332
3-91
4.48
5.75
332
4.38
5-4
6.41
7.38
8.33
9.26,
8.25
138 1 1432
10.5
24.74
13 29.37
14.84
13-28
154
17.5
19-57
21.61
6.67 6.88
8.27 8.53
9.84 10.16
11.39 11-76
12.92113-33
13.94 14.41 ; 14.88
15.36 15.89 16.41
3.48
4.58
566
6.72
7-75
8.75
9 73
8.5
•I 5
12
13.91 14.53
16.13 16.86
18.33 19-17
20.51 21.44
22.66 23.7
12.5
17-59
20
22.38
Lb«.
.88
1.29
1.67
2.02
3625
1.46
2.15
2.81
3-45
4.06
4.66
3-63
4-79
592
7-03
8.11
9.17
10.2
8.75
Llw.
•94
1-37
1.77
2.15
3-75
2.5
Lb*.
•99
1-45
1.88
2.28
3.875
1^51
2.23
2.92
3.58
. 4.22
4.84
6.25
3-79
5
6.18
7.34
8.48
9.58
10.66
1.56
2.3
3.02
3-71
4-38
5-02
6.5
3-95
5-21
6.45
7.66
8.84
10
11.13
925
7.08 7.29 7.5
8.79 9.05 9.31
10.47 10.78111.09
12.12 12.49 112.85
13-75 14' 17 14-58
15 35 15-82 16.29
16.93 17.45 17.97
•3
18.31
•3-5
'4
19.77
19.04
20.84 '21.67 '22.5
23.31 '24.25 '25.19
24.74 '25.78 126.83 1 27.87
25.63 26.88 28.13 29.37 30.63 31.88 33.13
13
• 35
14
27.87
15
29^95
16
32.03
25.78 26.83 . . ^
^ ,^. 30.63 i 31. 88 1 33. 13 35-63, 38^i3
32.45 3391 35.36 36-82 138.28 41.19 44.12
36.6738.3340 41.67 1 43^33 46.67150
NoTB.— American rolled is slightly heavier.
"7
18
34.12 36.2
2.625
Lbt.
1.04
1.53
1.98
2.41
1.62
2.38
3^13
3.84
4-53
5-2
6.75
4.1
5-42
6.71
7-97
9.21
10.42
12.6
95
7.71
957
X1.41
13.22
15
16.76
18.49
•45
2.75
Lb>.
1.09
1.6
2.08
2.54
4-25
1.72
254
3-33
4.1
4.84
556
4.26
5-63
6.97
828
9-57
10.83
12.07
9-75
7.92
9.83
IX. 72
1358
15-42
17.23
19.01
•5
aO.5 21.23
23^34 3417
26.12 27.06
28.91 '39-95
34-38 35.63
'9
20
38.28 40.36
40.63 41.13 43.63 46.13
47.02 49.95 52.87 55.78
53-3356.67,60 I63.33
IBON BOILER TUBES.
Standard Dimbkbiomb.
Ka/ionai 7Vi< Co.
'A
KoTB I. — For ilUinetara from 13 up to and including 30 ins. O. n,, detaili
«re in contormanm with (be circumstancea, as lliere is not a slandsrcl, the
thicknus Taiying.
NoTK 3, — In Mlimnting elTective heating or evaporating surface of Cubes'
perheating sleam, or Iraniifernng heat from
r, mean surface of tubes is to be cuaiputed,
132
WEIGHT OP CAST IRON PIPES.
""Weight of Cast Iron Fipes or Cylinders.
F^om I to 70 Inches in Infernal Diameter, '
ONE FOOT IN LENGTH.
IMameUr. 1 Tbickn.
Int.
I
1.25
1.5
1.75
2.25
2.5
2.75
3
325
35
3-75
4-25
4*5
Inch.
.25
375
25
3125
375
375
4375
5
375
4375
5
375
4375
5
375
4375
5
375
4375
5
375
4375
5
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
Weight.
Diameter.
Lbs.
Ins.
3.06
4-75
505
368
4 79 .
5.97 '
5
689
831
98
7.81 '
55
938
11.03
873
10.45
6
12.25
965
1
11.52
1
13.48
6.5
10.57
1
12.6
1
t
147
1
11.49
7 !
14.67
1593
12.4
1715
7-5
22.2
2757
13-32
18.38
8
2374
29.4
14.24
19.6
9
25.27
31.24
1516
20.83
9.5
26.8
33.08
16.08
22.05
10
28.33
34-92
17
23-28
10.5
29.86
36.76
17.92
23.88
ji
314
38.50
rhickn. WefKht. Diameter. Thickn
Inch.
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
75
375
5
625
75
5
5625
625
75
5
5625
625
75
5
5625
625
75
5
5625
625
75
5
5625
625
75
5
625
75
875
5
625^
75
875
5
62s
79
Lbs.
1884
25.72
3293
4043
1976
2695
3446
4227
21 59
294
3752
45 95
2343
31.86
4059
4962
25.27
3431
4365
53 3
36.76
41.7
4671
5697
39.21
44-45
49 77
60.65
41.66
47.21
52.84
64.32
46.56
52.72
58.96
71.67
49.01
55.48
62.06
75-35
51-45
65.09
7903
932:
53.91
68.15
82.7
9756
56.36
71.21
96.18
Ina.
II
"•5
12
12.5
13
13.5
14
14-5
15
15-5
16
16.5
17
I
17-5
Inch.
875
5
625
75
875
5
625
75
875
5
625
75
875
5
625
75
875
5
625
75
875
5
625
75
875
5
625
7*5
875
5
625
75
875
5
625
75
875
625
75
875
625
75
875
625
75
87s
625
75
Weight.
Lbs.
101.85
58.81
74.28
90.06
106.13
61 26
77-34
9373
1 10.42
63.71
80.4
97-4
114.71
66.16
8347
101.08
119
6861
8653
104.76
12329
71.06
89.6
108.43
127.58
7351
92.66
112. II
131.87
7596
9572
115.78
136.16
78.47
98,78
119.46
140.44
101.85
123.14
144-73
166.63
104.9
126.75
149.02
171-53
107.97
130.48
153-3
1 76-43
111.03
134.16
WBIGHT OF CAST IBON PIPES.
133
Diftinctor.
Ins.
17-5
18
19
20
21
22
23
24
25
26
27
28
39
Thickn.
Welfrht.
Diiim«t«r.
In.
Th
Inch.
LlM.
1
.875
157.59
29
•
I
181.33
.<
.625
114. 1
I
.75
137.84
30
•
.875
161.88
• 1
I
186.23
.625
120.23
x«
.75
145.19
31
•
.875
170.46
•
I
196.03
.625
126.35
A •
•75
152.54
32
•
•875
179.03
•
I
205.84
.625
132.48
X •
•75
159.89
33
•
.875
187.61
•
I
215.64
.625
138.61
X •
.75
16724
34
•
.875
196.19
•
I
22544
.625 j 144.73
1
A •
.75 174-59
1 35
•
.875 204.76
1
1
•
I
23524
1
1
.625 ' 150.86
1
x»
.75 1 181.95
; 36
•
•875 , 213.34
1
.i
I ] 245.04
.625 156.98
X 9
.75 1 189.3
A*
.875 221.92
'. 37
•
I i 254 85
i
•
.625 163 II
.75 ' 196.65
Jl •
.875 , 230.5
X •
1 ) 264.65
38
•
.625 , 169 23
•4
.75 1 204
'
.875 239.07
1
A •
" 274 45
« •
.625 175.36
39
•
.75 211.35
•
.875 247.65
I
284.25
1
X •
.625
181.49
1
X ■
ins.
•75
.875
125
75
.875
"5
75
875
125
75
875
125
75
875
125
75
.875
125
75
875
125
25
75
.875
125
25
75
.875
125
25
75
875
125
25
Weight. DlAHMter. Thickn. Weight
Lb*.
218.7
256.23
294.05'
226.05 '
264.8 i
303.86
343.22 i
233.41
273.38
3*3.66 ;
354.24
240.75
281.95 !
32346
36527
248 II
290.53
33326
376.29
25546
299.11
343.06
38733
262.81
30768
352.87
39835
270.16
316-26
362.67
409.28
45637
277.51
324.84
372.47
420.4
468.65
284.86
33341
382.27
431-41
48089
292.21
34197
39208
44244
493.14
Ins.
40
42
44
46
48
50
52
55
58
60
65
70
Int.
.87s
125
25
«75
125
25
875
125
25
875
125
25
875
125
25
875
125
25
875
125
25
875
125
25
125
25
375
125
25
375
125
25
375
35
Lbs.
350.56
401.86
453^46
505.41
367.69
421.45
472.52
529.87
384.88
441.1
497.58
554.43
402.01
460.07
519.64
578.88
419.17
480.29
541.69
603.44
436.43
499.89
563.75
627.93
453-49
519-5
585-81
654.42
47923
5489
618.91
689.21
578.29
651.96
725.93
800.22
59792
674.01
75045
827.17
646.93
729.18
811.73
894.6
69592
872.98
1051.25
JS^twcdeni Length of Pipe for a Socket.
7 H = /. d representinff diameter of pipe and I kngth in inches.
AddilionnI weight of two flanges for any diameter is computed equal to a lineij
fiMtoftbopipe.
KoTS.— These weights do not include any allowance for spigot and socket ends,
a.— For rale to compute thicknesses of pipes, flanges, etc , see page 56a
X34 'W'filGHT O^ StAlfDAftn ROLLlJD STEEL BEAMS.
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0 -^
•P J .g
oo IB
s <v
0
" (a 'e
5
■♦^ r
® 0
9 ^
■P
«
«
0
«
I ir
s 8
a
»9
•Ci
o
m
w
O
be
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o
s
00
w
8
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OO
p
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08
8
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0
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O
WEIGHT OF BOLLED STBBL, 8HBBT COPPBBy BTC. 1 35
'Weiglit of Round Rolled Steel.
From .135 Inch to 12 Inches Diameter, one foot in length.
DUun.
Inch.
125
1875
25
3"5
375
4375
5
.5625
.625
•6875
•75
.8135
Lbs.
.0417
•0939
.167
.26
•375
•5"
.667
.845
1.04
X.27
1-5
1.76
Diameter.
Weight.
Diameter.
Ins.
Lba.
.Ins.
.875 ' 2.04
1.625
•9375 , 2.3s
1.6875
I 1 2.67
1-75
1.0635 1 3
1.8125
1. 125
3.38
1.875
1. 1875
376
3
125
4.17
2.125
1.3125
4.6
2.25
1-375
5.05
2.375
14375
5.18
2.5
I 5
6.01
2.635
1.5635
6.52
2.75
Lbs.
7-05
7.61
8.18
8.77
9-38
10.7
12
13.6
15.1
16.7
18.4
20.3
Diam.
Weight
Ins.
Lbs.
2.875
33
3
34.1
325
38.3
3-5
327
3.75
34-2
4
43.7
4.25
48.3
4-5
54-6
4-75
60.3
5
66.8
5^25
73.6
5-5
80.8
Dlam.
WaiRht.
Ins.
Lba.
5-75
6
88.3
96.1
6.5
II3.3
7
7.5
13c. 8
136.8
170.8
8.5
193.3
9
318.4
9.5
10
341.3
367.3
II
323
13
384-3
"^^eielit of* Hexagonal, Octagonal, and Oval Steel.
ONE FOOT IN LENGTH.
HEXAGONAL.
1
OCTAGONAL.
Diam.
Diam.
Diam.
Diam.
ovar
Sidaa.
Weight
«w»r Weight
Sides, t *
over
Sidea.
Weight
Qver
Sides.
Ins.
Weight.
liich.
Lbs. !
Ins. Lbs.
.Inch.
Lbs.
Lbs.
% \ .414
I
2.94
%
•396;
1
3.82
K .736,
iK 3-73
%
.704
iK
356
H ^-"5 ,
iX ' 4-6
%
I.I
'H
4.4
k >i.66
iK : 5.57
%
1.58
I^
532.
%
2.25 1
iKl
6.63
%
3.16
IK
6-34,
OVAL.
Diam.
over Sidea.
Area.
Ins.
%xK
1 xK
13^ x^
iXx%
Sq. In.
.251
•344
.446
.697
.884
Weight.
Lbs.
.853
1. 17
152
2.37
3
V^eight of* a Square IToot of Sheet Copper.
Wire Gattge of Wm. Foster
Tbi^knaas.
Weight.
W.G.
I
3
3
Inrh.
.306
.384
.363
Lbs.
14
13
13
4
•24
II
5
.333
10.15
6
7
8
.303
.186
.168
93
8.5
7-7
9
ID
.153
7
6.3
Thl«lcneaa.
W.G.
Inch.
II
.133
13
.109
13
.098
14
.0S8
15
.076
16
.065
17
•057
18
.049
X9
.644
SO
.038
&Co,
Weight.
Lbs.
565
5
4-5
4
3-5
3
3.6
2,25
2
1.75
(England.)
Thickfaesa.
Weight.
W.G.
Inch.
Lbs.
31
.034
1-55
22
.029
1-35
23
.035
^•i5
24
.033
I
25
.019
.89
26
.017
•79
27
.015
•7
38
.013
.63
29
.013
.56
1 30
.611
•5
No.
I
a
3
"WeigHt of Composition Sheatlxins IQ'ails.
Langtli.
Natdbar
Poaod.
No.
Ltagth.
Ibch.
Ills.
•75
.875
^
4
5
1.125
1.35
I
9ia
6
I
Kamber
Ina
Pound.
aoi
199
igo
No.
7
8
LonRth.
Ins.
1.125
1.35
9 iX-5
Namber
Nnmber
In*
No. L«igth.
iaa
Pound.
Pound.
Ins.
184
lo 1,625
lOI
168
" 1.75
?^
no
13
9 j
64
136
WEIGHT OF IBON, STBEL, COPPBB, ETC.
VSTeiglit of Cast and. "WTroTxelxt Iron, Steel, Copper, and
Srass, of a given Seortional ^rea.
Per Lineal Foot.
Sectional
Area.
Wrougfat
Iron.
Cast Iron.
steel.
Copper.
Lead.
Brass.
Oan-metaL
Sq. Ins.
Lb«.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbe.
.1
•336
•313
•339
.385
.492
.357
.38
.2
.671
.626
.677
.771
.984
.713
•759
.3
1.007
.939
1. 016
1. 156
1.476
1.07
1.139
.4
1.343
1. 25 1
1.355
1.542
1967
1.427
1.519
.5
1.678
1.564
1.694
1.927
2.461
1.783
1.894
.6
2.014
1.877
2.032
2.312
2.953
2.14
2.279
•7
2.35 •
2.19
2.371
2.698
3445
2.497
2.658
.8
2.685
2.503
2.71
3.083
3.937
2.853
3.038
•9
3.021
2.816
3049
3.469
4.429
3.21
3418
I
3-357
3.129
3387
3854
4.922
3567
3.798
I.I
3.692
3442
3.726
4.24
5.414
3.923
4.177
1.2
4.028
3754
4.065
4.625
5.906
4.28
4-557
1-3
4364
4.067
4404
501
6.398
4.636
4-937
1.4
4.699
4.38
4.742
S.396
6.89
4.993
5.317
1.5
S035
4693
5.081
5-781
7.383
5.35
5696
1.6
5-37^
5.006
542
6.167
7.875
5.707
6.076
1.7
5.706
5-319
5759
6.552
8.367
6063
6.456
1.8
6.042
5632
6.097
6.937
8.859
6.42
6.836
1.9
6.378
5-945
6.436
7.323
9351
6.777
7.21S
2
6.714
6.258
6.775
7.708
9843
7133
7.595
2.1
7.049
6.57
7.114
8.094
10.33
7.49
7.97
2.2
7385
6883
7452
8.474
10.83
7.847
8.35
2-3
7.721
8.056
7.196
7.791
8.864
11.32
8.203
8.73
2.4
7509
8.13
9.25
11.81
8.56
9.11
2.5
8.392
7.822
8469
9.635
12.3
8.917
9.49
2.6
8.728
8:135
8.807
10.02
12.8
9.273
9.87
2.7
9063
8.448
9.146
10.41
13.29
963
10.25
2.8
9-399
8.76
9485
10.79
1378
9-98
10.63
2.9
9-734
9.073
9.824
11.18
1427 .
10.34
II.OI
3
10.07
9.386
10.16
11.56
14.76
10.7
11.39
31
10.41
9.699
10.5
11.95
15.26
11.06
11.77
3-2
10.74
10.01
10.84
12.33
15.75
II.4I
12.15
3-3
11.08
10.32 •
II. 18
12.72
16.24
11.77
12.53
3-4
II. 41
10.64
11.52
I3.I
16.73
12.13
12.91
3-5
"■75
10.95
11.86
13.49
17.22
12.48
13.29
3.6
12.08
11.26
12.19
13.87
17.72
12.84
13.67
3-7
12.42
".58
12.53
14.26
18.21
13.2
14.05
3.8
12.76
11.89
12.87
14.64
18.7
13.55
1443
3-9
13.09
12.2
13.21
15.03
19*19
1391
14.81
4
13^43
12.51
13.55
15.42
19.69
14.27
15.19
4.1
13-76
12.83
13.89
15.8
20.18
14.62
15.57
4.2
14. 1
13-14
1423
16.19
20.67
14.98
15.95
4-3
1443
13.45
14.57
16.57
21.16
15.34
16.33
4-4
14.77
13.77
14.91
16.96
21.65
15.69
16.71
45
15."
14.08
15.24
17.34
22.15
16.05
17.09
4.6
15-44
14.39
15.58
17.73
22.64
16.41
17-47
4-7
15.78
14.7
15.92
i8.li
23.13
16.76
17.85
4.8
16. 1 1
15.02
16.26
18.5
23.62
17.12
18.23
4-9
16.45
15.33
16.6
18.88
24.12
17.48
18.61
5
16.78
1564
1694
19.27
24.61
17.83
18.99
WEIGHT OF LEAD AND TIK PIPE AND TIN PLATES.
137
"^^eigh-t of Xj^ad and Tin. Xjined r*ipe per B^oot,
From .375 Inch to 5 Inches in Diameter, {Tatham Sf Bros.)
Weight.
WASTE-PIPK,
BLOCK-TIN PIPE.
Diam.
Weight.
Diam.
Weight.
Diam.
Weight.
Diam.
Weight. 1
1 Diam.
IllB.
Lbs.
Ini.
Lbe.
Inch.
Lb.
Inch.
Lbe.
Ins.
i-S
2
4
8
•375
•3594
.625
•5
1-25
d
3
4.5
6
.375
•375
.625
.625
1.25
3
3-5
45
8
•375
•5
•75
.625
1-5
3
5
5
8
•5
•375
•75
•75
1-5
4
5
5
10
•5
•5
I
'9375
2
4
6
5
12
.5
.625
I
1.125
2
Lbs.
1.25
1-5
2
2.5
2-5
3
WATER-PIPE.
Fiimi .yj$ Inch to 5 Inches in Diameter,
XHaiB.
Thick-
Dees.
Inch.
•375
•375
•375
•375
.375
•5
•5
•5
•5
•5
•5
•5
.625
.625
.625
.625
.625
.625
Inch.
.08
.12
.16
.19
.34
.07
.09
.II
•13
.16
.19
•25
.08
.09
•13
.16
.2
.22
Weight.
Lbe.
.625
I
125
^•5
2.5
.0545
•75
I
1.25
^•75
2
3
.0727
I
15
2
2-5
2.75
Diam.
Thick-'
Ins.
.625
•75
•75
•75
•75
•75
.75
I
I
I
I
I
I
I
1.25
1.25
1.25
1.25
Inch.
•25
.1
.12
.16
.2
.23
•3
.1
.II
.14
•17
.21
.24
•3
.1
.12
.14
.16
Thick-
Thick-
Weight.
Dtam.
ness.
Weight.
Lbe.
IMam.
ness.
Lbe.
Ids.
Inch.
Ins.
Inch.
3.5
1. 25
.19
4^75
2.5
•3125
1.25
1.25
.25
6
2^5
.375
1^75
1-5
.12
3
3
•1875
2.25
1-5
.14
3-5
3
•25
3
1-5
•17
425
3
•3125
35
1-5
.19
5
3
•375
4^75
^•5
•23
6^5
3.5
•1875
1^5
^•5
•27
8
3-5
•25
2
^•75
•13
4
3.5
•3125
9'S
^•75
.17
5
3-5
•375
3.25
175
.21
6.5
4
.1875
4
1-75
.27
8.5
4
•25
4.75
2
•IS
4^75
4
.3125
6
2
.18
6
4
•375
2
2
.22
7
4^5
•1875
2.5
2
.27
9
4-5
.25
3
2.5
•1875
8
1
5
•25
3-75
2.5
•25
'11
5
•375
Weight
Lbs.
14
17
9
12
16
20
9-5
15
18.5
22
12.5
16
21
25
14
18
20
31
JMai*ks and 'V/ eight of* Tin-plates, (EngUsh.)
Mask
om Dhawd.
iCori Com.
aC
k%:::::::.
HX.
xX
aX
3X
iXX
iXXX.
1 A A A A. . . .
I XXXXX..'
iXXXXXX
DC
DX
DXX
DXXX ....
Plates
per Box.
No.
aas
aas
aas
225
225
225
225
225
225
225
225
225
225
100
100
100
100
Dimenaions.
Ins.
375X10
3.25X 9.75
2-75X 9.5
375X10
3-75X10
375X10
3-25X 9-75
4-75X 9 5
375X10
3-7SXIO
3-75X10
375X10
375X10
[6.75X12
6.75X12 .
6.75X12.5
16.75X12.5
•5
•5
Weight
per Box.
No.
112
»05
98
119
>57
140
133
126
161
182
203
224
245
98
ia6
M7
168
Mask
Plates ,
OR Bband.
per Boz.i
No.
DXXXX
100
snc
aoo
aoo
SDX
SDXX
aoo
snxxx
aoo
SDXXXX. . . .
aoo
SDXXXXX.
aoo
SDXXXXXX.
aoo
Leaded IC...
iia
♦' IX...
iia
ICW
335
IXW
335
csnw
aoo
CIIW
100
XIIW
100
TT
450
450
XTT
Dimensions.
Ins.
16.75X12.5
IS Xii
Xii
Xii
Xii
Xii
Xii
Xii
X14
X14
13-75X10
13-75X10
15 Xii
16.75X12.5
16.75X12.5
13-75X10
13-75X10
15
15
>s
15
15
15
ao
30
Weight
per Box.
No.
189
168
188
209
330
251
272
293
112
140
112
140
168
105
126
112
ia6
When the plates are 14 by so inches, there are 1 12 in a boZi
■38
STEAM, QA8, AND WATER PtPBB.
^
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imftc
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—
ILap.wel(Ied Steel, Semi-Steel, Special I^ooi
and Eh^anlc Unite Boilei' ITubes.
Standard Dihessions. :^atioaul T<J>e Co.
DU
IdHc-
a
^1
EiHr-
Ibb^
Tr.
ii
1
95"
"■"■
'Sf
CS.
liJ^
ii>.
iji
IS"
i.
2
IDI.
1
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9.61,
s
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1
4.58
!-3p
r
IJS
Ek or tvpiperiiMu Hirffid* of LdIh. u
nCON BOILSB TUBES.
139
X^ap • -welded.
Ch.arooal Iron.
TulDes.
and Steel IBoiler
Standard Dimensions.
National Tube Co,
Dkwwlcr.
1
\
Circumfsr-
TransTerss Arsss.
ijen^iu per
Sqaare Foot
111
•
11
■S a
J
1^
•DCS.
of Snrfiiee.
Extar.
Inter.
n»l.
1
Ezter.
nsl.
Intsr-
nal.
Exter-^
nal. *
Inter-
nal.
Mefol.
Exter-
nal.
Inter-
nal.
?>l
&i
Ins.
Ina.
Ins.
No.
Ins.
Ins.
Sq. Ins.
Sq. In».
Sq.Ins.
Ft.
Pk
Lba.
Ina.
I
.86
.072
IS
3-14
2.69
3.08
.78
-57
.21
3.82
4.463
3.894
.71
• 0
1
1. 125
.98
.072
15
3^53
•99
.75
.24
3.396
1.125
1-25
I. II
.072
15
3.93
3-17
1.23
.96
.27
3^056
3-453
.89
1.25
1«3I2
1. 15
.083
14
4.12
3-S
'•35
1.03
.32
2. 911
3-333
1.08
I- 313
1-375
1. 21
.083
14
4 -.32
3.8
1.48
>.i5
•34
2.778
3.16
«.i3
1-375
1-5
1.33
.083
H
4.71
4.19
1.77
X.4
•37
2.547
2.863
1.24
J-5
1.625
1.43
-095
«3
5-'
4-51
2.07
1.62
•46
2.352
2.662
^•11
1.625
X.75
1.56
095
13
5-5
4.9
8.4^
X.91
•49
2.183
2.448
1.66
1-75
1.875
1.68
-095
13
5.89
5.29
2.76
2.23
•53
2.037
2.267
1.78
1.875
2
Z.81
•095
13
6.28
5-6o
6.08
3^i4
2.57
•|7
Z.91
2. II
x.91
2
3.125
1.93
•095
13
6.68
3-55
2.94
.6x
1.797
1.974
2.04
2.125
3.35
a. 06
.095
13
7-07
f-^z
3.98
3-33
.64
1.698
1.854
2.16
2.25
2.375
2.16
.109
12
7.46
6.78
4^43
3-65
•78
1.608
1. 771
2.61
2.375
2.5
2.28
.109
12
785
7.17
4.91
4.09
.82
1.528
1.674
2.75
2.5
2.75
3.875
2-53
.109
12
8.64
7-95
5.94
503
•9
1.389
1.508
3.04
2.75
2.87s
2.66
.109
12
9-03
8.35
6.49
5.54
•95
1.329
1.438
3.Z8
3
2.78
.109
12
9.42
8.74
7.07
6.08
,:?!
1.273
'•373
3.33
3
3-25
3.01
.12
IX
X0.21
9.46
H
7.12
J.I75
1.269
3.96
3.25
3-5
3.26
.12
IX
II
10.24
9.62
8.35
X.27
1. 091
1. 172
4.28
3.5
3-75
3.51
.12
>X
11.78
11.03
XX. 04
9.68
>.37
1.019
X.088
4.6
3.75
4
3-73
•134
10
12.57
11.72
12.57
X0.94
X.63
.955
1.024
5.47
4
4.25
3-98
-134
10
13.35
12.51
14.19
12.45
'•^3
.899
•959
5.82
4-25
4.5
4-23
•134
10
14.14
13.29
14.08
15.9
14.07
1.84
.849
.903
.852
6.17
4-5
4-75
4.48
.»34
xo
14.92
17.72
15.78
1.94
.804
6.53
4.75
5
4-7
.148
9
15. 7'
14.78
19.63
17.38
2.26
.764
.812
7.58
5
5- "25
4.95
.148
9
16.49
17.28
15.56
21. 65
19.27
2.37
.728
.771
I'^l
5.25
5. 25
5.2
.148
9
16.35
23-76
21.27
2.49
.694
.734
8.36
5.5
6
5.67
.165
8
18.85
17.81
28.27
25-25
3.02
.637
.674
10.16
6
7
6.67
.165
8
21.99
20.95
38.48
34^94
46 2
3-54
.546
.573
11.9
7
8
7.67
.165
8
25.13
24.x
?^:??
4.06
•477
.498
13.65
8
9
8.64
.18
7
28.27
27.14
58.63
4.99
.424
'442
16.76
9
10
9-59
.203
6
31.42
30-14
78.54
V,:%
6.25
.382
.398
20.99
10
zx
10.56
.22
5
34^56
33-17
95.03
7-45
•3^Z
.362
25.03
11
12
11.54
.229
.238
4-5
37-Z
40.84
36.26
113. X
104.63
8.47
.318
•33
28.46
12
X3
12.52
4
39-34
132.73
123.19
9-54
.294
•305
32.06
'3
X4
'3 5
.248
3.5
43.98
42.42
153-94
143.22
Z0.71
.273
.383
36
14
15
14.48
.259
3
47.12
45-5
176.71
164.72
11.99
.255
.2^%
40.3
15
16
15.46
.271
2.5
50.27
48.56
201.06
187.67
238.66
13 •39
•239
.247
45.2
16
18
17-43
.284
2
56-55
54-76
254-47
15.81
.212
.219
52.87
64.84
18
20
19.38
.312
•31
62.83
60.87
314.16
294.86
356.8
19.3
.191
.197
20
22
21. 31
•343
•03
69.11
66.96
380.13
23.34
.174
.179
78.5
22
24
83.25
.375
•37
75.4
73.04
452.39
424.56
27.83
.159
.164
93-37
24
26
»5.BS
-375
•37
81.68
79-32
530.93
500.74
30.19
.147
.151
1 03
26
28 >.
87.25
-375
-37
87.96
85.61
615.75
583.21
32.54
.136
.14
no
28
30 Ij
19.25
•375
•37
94-25
91.89
706.86
671.96
34.9
.X27
.131
u8
30
NoTB I. — For diameters from 13 up to and including 30 ins. 0. D., details
are in conformance with the circumstances, as there is not a standard, the
tiUckaess varying.
Note 2. — In estimating effective heating or evaporating surface of tubes*
as heating liquids by steam, superheating steam, or transferring heat from
0D« HQOid or one gas to another, mean surface of tubes is to be computed*
I40
WEIGHT OF COPPER TUBES.
"W^eigh-t of Seamless IDraTvn. Copper Tubes.
A.ixiericaii Tube "Worlis. (Boston.)
BY EXTEHNAL DIAMETER. ONE FOOT IN LENGTH.
Stubs' W. G. From .25 Inch to 12 Ins.—fjvil^ I light.
No. 20 19 18 I 17 16 I 15 14 I 13 | 12 11
Ins.
Diamet'r.
.25
•375
.5
.625
•75
•875
I *
1. 125
125
1-375
1-5
1.625
^•75
1875
2
2.125
2.25
2375
2.5
2625
2.75
2.875
3
3-25
35
3-75
4
4^25
45
4-75
5
525
5-5
5-75
6
6.25
6.5
6.75
7
7-25
7-5
8
8.5
9
95
10
10.5
zi
"5
la
V32/ 3/64/
Lbs.
.09
.14
.2
•25
•3
.36
•41
.46
•52
•57
.62
.68
•73
.78
.84
•89
•94
I
1.05
I.I
1. 16
1.21
1.26
137
1.48
1.58
1.69
1.8
1.9
2.01
2.12
2.23
2.34
2.44
2.55
2.66
2.76
2.87
2.98
3^o9
3-19
3-41
3.62
383
4-05
4.26
447
4.69
4.9
Lbs
.1
.16
•23
.29
.36
.42
.48
•55
.61
.68
•74
.8
•87
•93
.06
•13
.19
•25
•32
•38
•45
•51
.64
•77
•9
2.02
2.15
2.28
2.41
2.54
2.66
2.79
2.92
305
3-i8
331
3-44
356
369
382
4.08
433
4^59
4.85
5."
5-37
5.62
5.88
6.13
3/64 / 1 1/16 (
»/i6/i 5/64/
LbB.
.12
.19
•27
•34
.42
•49
•57
.64
•71
•79
.86
•94
.01
.09
.16
.24
•31
•39
.46
•54
.61
.68
•76
.91
2.06
2.21
2.36
2.51
2.65
2.8
2^95
3-1
325
3-4
3-55
3-7
385
4
4-iS
4-3
4-45
4-74
5-04
5-34
5-64
5-94
624
6.54
6.84
7^U
Lbs. I Lin.
•13
•23
.31
•4
•49
•58
.67
•76
.84
•93
.02
.11
.2
.29
•37
.46
•55
.64
•73
.82
•9
•99
2.08
2.26
2.43
2.61
2.79
3.14
C532
3-49
367
3.85
3.85
4.02
4.2
4.38
4.55
4.73
4.91
5.09
5.26
5.62
5^97
6.33
6.68
7^03
7-39
7^74
8.1
8.45
.14
.24
•34
•44
•54
.64
•74
.83
•93
•03
•13
•23
•33
•43
•53
.63
•73
.82
.92
2.02
2.12
2.22
2.32 I
2.52
2.72
2.92
3-II
331
3-51
371
3-91
4.II
4^3
4.5
4-7
4.9
5-1
5-3
5^49
569
5.89
6.29
6.68
7.08
7.48
7.87
8.27
8.67
9.06
9.46
Lbs.
•15
.26
•37
.48
•59
•7
.81
.92
1.03
1. 14
1.25
1.36
1.47
1.58
1.69
1.8
1. 91
2.02
2.13
2.23
2.34
2.45
2.56
2.78
3
3.22
3-44
366
3^88
4.1
432
4^54
4.76
498
5^2
541
563
5^85
6.07
6.29
6.51
6^95
7^39
7^83
8.26
8.7
9.14
9.58
10.02
10.4s
5/64/^
Lbs.
•17
.29
.42
•55
.67
.8
•93
.05
.18
•31
•43
.56
.69
.81
94
2.07
2.19
232
2.45
2.57
2.7
2.83
2.95
3.21
346
3^71
397
4.22
447
4^73
4.98
5.23
5-49
5^74
5-99
6.25
6.5
6.75
7.01
7.26
7-51
8.02
8.52
903
9-54
10.05
10.55
11.06
11.56
12.07
3/32/ 7/64
Lbs.
.18
•32
•47
.61
.76
•9
1.05
1. 19
134 j
1.48
1.63
1.77
1.92
2.06
2.21
2.35
2.5
264
2.79
293
308
3.22
3-37
3-66
3-95
4.24
4-53
4.82
5^"
54
569
598
6.27
6.56
6.85
7.14
7 43
7.72
8.01
8.30
8.59
9.17
975
10.33
10.91
11.49
12.07
12.65
1323
13-81
Lbs.
.19
•35
•52
.69
.85
1.02
1. 18
13s
1^52
1.68
1.85
2.02
2.18
2-35
2.51
2.68
2.85
3.01
3- 18
335
351
3.68
384
4.18
451
4.84
5.17
5.51
5.84
6.17
6.5
6.84
7.17
7^5
7.83
8.17
8.5
8.83
9.16
9-5
9^83
10.49
11.16
11.82
12.49
1315
1382
14.48
15-15
1581
»/8 /
Lbs.
,19
•37
.56
74
.92
I. II
1.29
1.47
165
1.84
2.02
2.2
2.39
2.57
2.75
2.93
3.12
3-3
3.48
3.67
385
4^03
4.22
4.58
4.95
5.31
5-68
6.05
641
6.78
714
7.51
7.87
8.24
8.61
8.97
934
91
10.07
10.44
10.8
"•53
12.26
13
1373
14.46
15-19
15-93
16.66
17.29
WBIOUT OF COP?4» TUBES.
141
No.
10
9
8
7
6
5
4
^ 3
2
1
lita.
9/64/
9/64/
"/64^
3/x6/
'3/64
7/32 / 13/64 /
V4/
9/32/
'9/64/
DUmet'r.
Lbt.
Lbs.
LlM.
Lbi.
Lbe.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
.375
•4
.41
.42
.44 —
—
—
—
—
—
•5
.61
.64
•67
.71 .73
.75
.76
—
—
—
.625
.81
.86
.92
.99 1.04
1.09
1. 12
iii3
1.18
—
.75
1. 01
1.09
I.I7
1.26 j 1.35
1.42
1.49
1.53, i-6i
163
.875
1.22
I -31
1.42
1.53 ! 1.66
1.76
1.85
1.92 1 2.04
2.09
I
1.42
1-54
1.67
1.81 1 1.97
2.09
2.21
2.32 ! 2.48
2.5s
I.125
1.63
1.78
1.93
2.08 2.28
2.43' 2.58
2.71 2.91
3
1.25
J.83
2
2.18
2.36 2.59
2.76: 2.94
3-11
3-34
3-46
1-375
2.03
2.22 2.43
2.63 2.9
31 1 3.3
3-5
3-77
392
1.5
2.24
2.44 2.68
2.91 3.21
3-43; 3-67
3-9
4.21
4-38
1.625
2.44
2.67 2.93
3.18
3-52
3-77' 403
4.29
4.64
4.83
1-75
2.65
2.89 3.18
3.45
3.83
411 1 4-39
4.69
507
5-29
1.875
2.85
3.12
3-44
3-73
4.14
4-44 476
5-o8
5-51
5-75
2
3.06
3-34
3-69
4
4-45
4.78 1 5.12
548
5 94
6.21
2.125
3.26
3-57
3.94
428
4-75
5.11 5.48
587
637
6.66
2.25
3-46
3.8
4.19
4-55
5.06
5-45 5-84
6.27
6.81
7.13
2.375
3.67
4.02 4.44
4.82
5.37
5.78 6 21
6.66
7.24
7-37
2.5
3.87
4.25! 4.69
5.1
568
6.12
6.57
7.06
767
804
2.625
4.08
4-47 1 4-95
5-37
6
645
6.93
7 45
8.1
849
2.75
4.28
4.7 5-2
5-65
63
679
7.29
785
854
895
2.875
4.48
4-92 5-45
5-92
661
7.12
766
8.24
8.97
941
3
4.69
5-15 5.7
6.2
692
7-46
802
8.64
94
987
3.25
5.1
56 [ 6.2
6.74
7-54
8.13
8.75
9-43
10.27
10.78
3-5
5.51
6.05 6.71
7-29
8.16
8.8
9 47
10.22
11.14
11.7
3.7s
5.91
6.5 1 7.21
7.84
8.78
9 47 ; 10.2
11.01
12
12.61
4
6.32
6.951 7-71
8.39
94
10 14]- 10.92
11.8
1287
1353
4.25
6-73
7-4
8.22
8.94
10.02
10 81
11.65
12.59 1 1373
14.44
4-5
7.14
7.85
8.72
9.49
1064
11,48
12.37
1338 14-6
15-36
4.75
7-55
8.3
9.22
10.04
11.26
12.16 1 131
14.17 15.46
1627
5
7.96
8.75
9-73
10.58
11.88
12.83 1 13 83
, 14-96 ' 16.33
17.19
5.25
8.36
9.21
10.23
11.13
1249
135
14.55
i 15-75 172
181
5.5
8.77
9.66
10.73
11.68
13. 1 1
14.17
1528
^ 16.54 ) 18.06
1902
5.75
918
10. 1 1
11.24
12.23 1 13.73
14.84
16
1 17-33 1893
1993
6
9-59
10.56
11.74
12.78
; 14 35
15-51
16.73
18.12 1 19.79
20.85
6.25
xo
1 1. 01
1 12.24
13.33
1 14-97
16.18
17.46
18 91
20.66
21.76
6.5
10.41
11.46; 12.75
^3-88
: 15.59
16.85
18.18
,19-7
21.53
22.68
6.75
10.82
II. 91
1325
14.42 ' 16.21
1752
18.91
20.49
22.39
2359
7
11.22
12.36
1375
14.97 16.83 1 18.19
1963
21 28 j 23.26
24.51
7.25
11.63
12.81
14.26
15-52
17.45 18.86
20.36
22.07 24.13
25-42
7.5
12.04
13.26
14.76
16.07
18.07 ; 1954
21.08
22.86 25
26.34
7.75
12.45
13.71
15.26
16.62
18.68 20.21
1
21.81
23.65 25.86
27-25
8
T2.86
; 14-17 ' 15-77
17.17
19.3 1 20.88
22.54
24.44
26.72
28. 1 7
8.25
13-27
14.62 16.27
17-71
1992 21.55
23.26
25-23
27-59
29.08
8.5
13-67
15.07 16.77
18.26
20.54 , 22.22
2399
26.02
28.45
30
8.75
14438
15.52 17.28
18.81
21.16 , 22.89
24.71
; 26.81
29.32
30.91
9
14.49
15-97 , 17-78
19.36
21.78 23.56 [ 25.44
27.6
30.18
31.83
9-25
14.9
\ 16.42 18.28
19.91
22.4 24.23
26.17
28.39 '31-05
32.74
95
15.31
' 16.87
1 18.79
20.46
23.02 24.9
26.89
29.18131.92
3366
9-75
15.72
, 17.32
1929
21.01
23.64 25.57 j 27.62
29.97 32.78
'34.57
10
16.12
17.77 ' 19.79
21.55
24.26 26.24 ' 28.34
30.76 33.65
' 35-49
10.5
16.94
! 18.68 20.8
22.65
255 27.59 29.79
32-34 3538
37.32
n
17.76
1958 21.81
23-75
2673 28.93 '31.25
3392 37.11
3915
"•5
18.57
20 48 22.81 1 24.84
27-97 30.27:32.7
355 38.84
40.98
12
19.39
21.38
23.82
'25.94
29.21
3161
'34-15
137.08
40.58
42.81
142 WEIGHT OF COPPBB AND BBASS TUBES, ETC.
JBy Internal X>iameter.
Add following Units to Weights for External Diameter in preceding tables.
No.
2.21
No.
•35
2
1.97
1.66
JL2^
.29
13
.22
4
5
6
7
8
9
10
1.38
1. 18
ix>i
.78
.67
•53
.43
14
15
16
17
18
19
20
•17
.13
.11
.08
.06
.05
•03
Illustration.— What is weight of a copper tube 6 ins. in internal diameter,
No. 3 gauge, and one foot in length ?
By preceding table 6 ina external, No. 3 gauge = 18.12, and 18.12 -f- 1.66 =
19. 78 lbs.
WEIGHT OF BRASS TUBES.
To Compu.te "Weiglit of Srass Tnbes.
jALxrierioaii Tti"be "Works. {Boston.)
Rule. — Deduct 5 per cent from weight of Copper tubes.
Example. — What is weight of a brass tube 6 ins. in external diameter, No. 3
gauge, and one foot in length?
By preceding table 6 ins. = 18.12, from which deduct 5 per cent =17.21 Iba
By Internal X>iameter.
Rule. — Proceed as above for internal diameter, and deduct 5 per cent.
Example. — Weight of a copper tube 6 ins. internal diameter, No. 3 gauge, and
I foot in length = 19.78 lbs.
Hence, 19.78 — 5 per cent. = 18.79 Ibg.
Note. — Diameter of Tubes, as for Boilers, is given externally, and that for Pipes
internally.
Weights of Enylish are essentially alike to the preceding. {D. K. Clark.)
Seamless Brass Pipe.
A-xiierioaii Tube "WorUs. (Boston.)
Made to correspond with Iron Pipe ami to fit Ir<,n Pipe fillings.
S -*i
Diameters.
gs.g
Same
Exact
M Iron
Pipe.
Inter-
nal.
Exter-
nal.
Ills,
IllK.
Ins.
Lbs.
%
.281
•40s
•25
K
■375
•54
43
%
.484
•67s
.62
X
.625
•84
•9
K
808 I. OS
1-35
I
1.062 1.315
I 7
Seui
nless C
opper F
Mpe of
Same
as Iron
Pipe.
Diameters.
Exact
Ins.
iX
2
2>^
3
Inter-
Exter-
nal.
nal.
Ins.
Ins.
1368
1.66
1.6
1.9
2.062
2375
2-5
2875
3.062
3-5
3-5
4
ll«
$^
Lbs.
2-5
3
4
5-75
8.3
10 9
Diameters
Same
as Iron
Pipe.
Exi
Inter-
nal.
Ins.
Ins.
4
5
6
4
45
5.062
6.125
i —
—
3 k. «>
ct
Exter-
nal.
.^3
Ins.
Lbs.
4-5
12.7
5- '563
6.625
13.9
«575
18.31
ike diameter is 5 per cent, heavier
"Weiglit of Sheet Brass.
ONE SQUARE FOOT. {Holtzapjjfd's Gaugc.)
Tbickness.
No.
Inch.
3
•259
4
.23S
5
.22
6
.203
7
.18
8
.165
Weight.
Thickness.
Weight.
Lbs.
No. Inch.
Lbs.
10.9
9 .148
6.23
10
10
•134
5.64
9.26
11
.12
505
8.55
12
.109
4-59
7.58
13
•095
4
6.95
14
.081
3-49
Thickness.
Weight.
Thickness. |
No. Ii)cb.
Lbs.
No.
Inch.
15 , .072
3-03
21
•032
16 1 .065
2.74
22
.028
17 1 .058
2.44
23
.025
18 .049
2 06
24
.022
19
.042
1.77
25
.02
20
'03S
1.47
Weight.
Lbs.
1-35
1. 18
1.05
.926
.842
WEIGHT OF WROUGHT IKON TUBES.
143
"Weight of Wrough-t Iron Tubes. {SnglUh.)
EXTERNAL DIAMETfiR. ONE FOOT IK LENGTH.
HoltzapJeVs Wire-Gauge. ffuUy I light.
No.
—
—
4
5
Int.
•3»25
S/16
Lbs.
21 9
235
^ 281
9/32
.238
«5/64/
.aa
7/32
Di«in.
7
75
Lbs.
19.8
21.3
Lbs.
16.9
18.I
Lbs.
15-6
16.8
8
85
25-2
268
22.7
24.2
193
30.6
17.9
19. 1
9
; 284
257
21.8
202
9-5
XO
1 301
1 31 7
27.1
•28.6
23,1
24-3
21.4
22.5
.148
9/64/
Lbs.
Lbs.
Lbs.
Lbs.
14.5
129
II.8
10.6
15.5
138
\ 12.7
II.4
16.6
147
13.5
12.3
17.6
157
14.4
12.9
18.7
166
153
13-7
19.8
17.6
16.1
14-5
20.8
18.5
17
15.3
No
Dlam
X
X 125
1-25
1-375
X.025
1-75
187.5
2
2 125
2 2S
2^375
25
2625
27s
2875
3
325
3 5
3-75
4
4-25
45
4 75
5
5-25
5-5
5-75
6
6.25
65
6.7s
7
725
7-5
7-73
%
7
8
« 9
10
1 1
12
18
165
148
•134
ta
.109
3/16/
"/64 /
9/64/
Lbs.
9/64/
«/8/
l.bs.
7/64
~ Lh*^
Lbs.
Llw.
Lbs.
155
1.44
1.32
1.22
I. II
1.02
1.78
1.66
i-Si
1-39
1.26
1. 16
202
1.88
I-7I
^•57
1.42
1-3
225
2.09
1.9
1.74
1.58
145
249
2.31
2.1
1.92
1-73
1-59
2 72
2 52
2.29
2.09
1.89
1-73
2.96
2.74
2.96
248
2.27
2.05
1.87
319
2.68
245
2.21
202
3 43
317
2.87
262
2.36
2>l6
367
3-39
3.06
2.8
2.52
2.3
39
36
3.26
2.97
2.68
2.44
4.14
3.82
3-45
315
2.83
2.59
437
4.04
365
332
2.99
273
461
425
384
3-5
315
287
4.84
4 47
403
3.67
331
302
5*^8
468
423
3.85
3-46
316
532
4.9
4.42
402
3.62
3-3
5-79
533
4.81
4 37
394
3 59
626
5-76
5-2
4.72
42s
387
673
6.19
5.58
507
4-57
416
72
6.63
5-97
5-43
488
4.44
7.67
706
6.36
5.78
52
473
8.14
7-49
6.45
6.13
5-51
501
861
7.91
713
6.48
5-82
53
9.08
8.35
7-52
683
6.13
5.58
9-56
8.79
7.91
7.18
6.44
5.8-
10
9.22
8.3
7-53
6.76
615
10.5
965
8.68
788
7.07
6.44
IX
10. 1
9,07
8-23
7-39
6.73
X1.4.
10.5
9.46
858
7-7
7.01
IX.9
109
9-85
8-93
8.02
7-3
xa.4
11.4
10.2
928
8.33
758
13.9
IX.8
lo.b
963
1%
7.87
13.3
13.2
II
999
8. IS
138
12.7
X1.4
10.3
9.27 ,
8.44
14-3
131
X1.8
10.7
9-59
872
14.7
'^•^
13.3
II
9-9
9.0X
13
•095
3/32/
083
5/64/
07a
5/64/
Lbs.
Lbs.
! Lb*.
9
•797
.7
1-3
.906
1 .794
1-15
1. 01
\ .888
1.27
1. 12
.983
1.4
1.23
1.08
1.52 .
1.34
1. 17
165
1-45
1.27
1.77
1.56
I..36
1.9
1.67
1.45
2.02
1.78
• 1-55
2.14
1.88
1.64
2.27
1.99
1.74
2-39
2.1
1.83
252
2.21
1.93
264
2.32
2.02
2.77
2.43
2.11
2.89
2.54
i 2.21
314
' 27s
, 2.4
3-39
2.97
2.59
364
319
2.77
3-89
3-4
2.96
413
3.62
315
438
3.84
3-34
463
4.06
3.53
488
4.27
372
513
4.49
3-9
538
4.71
4.09
5-63
4.93
4.28
5.87
514
4.47
6.13
5.36
4.66
6.37
S.58
4-85
6.63
5-79
5-03
6.87
6.01
5^23
7.13 ,
6.23
5-4X
7-37 1
645
5.6
7.63 '
6.66
5.79
786 i
6.88 1
5.98
144
WEIGHT OF COPPER TUBES.
Weiglit of Seaxxiless Dra^vn Copper Tn^bes. (Englith^\
For Diameters and Thicknesses not given in preceding Tables, (D. K, Clark,)
INTERNAL DIAMETER. ONE FOOT IN LENGTH.
HoUzapJeTs Wire-Gauge, yjuli, I light.
Specific Weight = i.i6. Wrought Iron = i.
No.
Ins.
Diani.
•75
•875
I
1. 125
1.25
1.375
1-5
1.625
1-75
1.875
2
2.125
2.25
2-375
2.5
2.625
2.75
3
3.25
3.5
3-75
4
4.25
4-5
475
5
5.25
5-5
0000
•454
29/64
Lbs.
000
—
—
8.02
736
8.71
8
9.4
8.65
10. 1
9-3
10.8
994
11-5
10.6
12. 1
11.2
12.8
11.9
13.5
12.5
14.2
13.3
14.9
13.8
15.6
14.5
16.3
151
17
15.8
17.7
16.4
19. 1
17.7
20.4
19
21.8
20.3
23.2
21.6
24.6
22.9
25.9
24.2
273
25.4
28.7
26 7
30.1
28
31-5
293
32.8
30.6
425
27/64^
Lbs.
00
.38
3/8/
Lbs.
5.79
6.37
6.95
7.52
8.1
8.68
9.26
983
10.4
II
11.6
12. 1
12.7
13.3
139
14.5
15.6
16.8
17.9
19. 1
20.2
21.4
22.5
23.7
24.8
26
27.1
.34
"/32
Lbs.
4-5
5.02
5-53
6.05
6.57
7.08
7.6
8.12
8.63
9-15
9.66
10.2
10.7
11.2
11.7
12.2
12.8
13.8
14.8
15.9
16.9
17.9
19
20
21
22.1
23.1
24.1
No.
Ids.
Diam.
5.75
6
6.5
7
7-5
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
23
24
26
28
30
32
34
36
0000
•454
29/64
Lbs.
34.2
35.6
38.4
41. 1
43.9
46.6'
52.1
57-7
63.2
68.7
74.2
79^7
85.2
90.7
96.3
101.8
107.3
1 12.8
1 18.3
123.8
129.3
134.8
146
157-2
168.4
179.6
190.7
201.9
000
.425
«7/64/
Lbs.
31.9
332
35.8
38.3
40.9
43-5
48.7
53.8
59
64.2
693
74.5
79.6
84.8
90
95.1
100.3
105.5
110.7
1 15-8
120.9
126. 1
136.4
146.7
157.1
167.4
177.7
188
00
38
3/8/
Lbs.
28.3
29.5
31.8
34.1
36.4
38.7
43-3
47-9
52.5
57-2
61.8
66.4
71
756
80.2
84.9
895
94.1
98.7
103.3
107.9
112.6
121.8
131
140.2
1495
1587
167.9
•34
"/3a
Lbs.
25.2
26.2
28.3
30.3
32.4
34-5
38.6
42.7
46.8
51
55-1
59-2
63.4
67.7
71.8
76
80.1
84.2
88.3
92.5
96.6
100.6
108.8
117. 1
125.4
133-6
141.9
1 50. 1
For Diameter
sfrom
13 (0 24 Inches.
No.
1
2
3
4
5
6
7
8
9
10
fna
•3
.284
•259
.238
.22
.203
.18
.165
.148
•"34
^9/64/
9/32/
Lbs.
V4/
^5/64/
Lbs.
7/32/
Lbs.
«3/64
3/16/
"/64/
9/64/
9/d4 /
OUin.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
13
48.5
45.8
41.7
38.3
35.3
32.6
28.8
26.4
23.6
21.4
H
52.1
49-3
44.9
41.2
38
35.1
31
28.4
25.4
23
15
55-8
52.7
48
44.1
40.7
37.6
33-2
30.4
27.2
24.6
16
59.4
56.2
51.2
46.9
434
40
35.4
32.4
29
26.3
17
63
59^6
54.3
49.8
46
42.5
37.5
34-4
30.8
27.9
18
66.7
63.1
57-4
52.7
48.7
45
39-7
36.4
32.6
295
19
70.3
66.5
60.6
55.6
51.4
47-4
41.9
38.4
34.4
31 .a
20
74
70
63.7
58.5
54
49.9
44.1
404
36.2
32.8
21
77.6
73.4
66.9
61.4
56.7
52.4
46.3
42.4
38
34-4
22
81.3
76.9
70
643
594
54-9
48.5
44.4
39-8
36
^3
849
80.1
73-2
67.2
62.1
57.3
50.7
46.4
41.6
37-7
34
88.6
83.8
76.3
70.1
64.7
59-8
52.9
48.5
43.4
39-3
WEIGHT OF COPPER AND WEODGHT IRON TUBES.
For Diamtttrt/ron 13 to 14 fneiti.
No,
11
H
IS
iG
.7
IS
.11
.IDtl
,=,5 .».,
.071
.06,
.0,8
.1.49 1 .04a
03s
Vj"/ ] V6,/
Wii,i
VM/.3/UI
1,1..
14
14.2
.S.98
■^-.i-a
ai.,t
'4-1
ia.7
II.T
"7
as
22.7
n.'i
-4
■Jf,.K,
■■■i-t
i4-.l
11.7
10.7 9.3
IQ
37-g
IVl
14.1
a7.i(
■M-^
31.1
I3.S 10.7
V-T
HA
:i^7
ai-.-t
351
3'-9
a4-3
"'-'
19
10.3
"Weiitht of "WrouBht In
I Tubes. (fBpiirtl
ol givea in prectding Tabia. {D. K. Clark.)
B<ilUapfftl'> Wire-Gai^. f/vU, I Hgbl.
) 93.6 80 66.S S3 S0.4
i 98.3I 83.9I 69.7 S5-6 52-9
i ica^S. 87.9' 73 58.3 55.4 _
76.3 60.9 57.9 . 53.4 (
I 144.7,138.31113 I
1.156-5 138.8 iai-i;i
I 168-3 149.3 1 130.3, 1
" "°" i59-7l'39'5;i
5 203.6 180,6 157-81 13s
146
WEIGHT OF IBON, ST££L, COPPER, ETC.
Weight of a Square IF'oot of "Wroiaglit and Oast
Iron, Steel, Copper, Lead, Srass, and Zinc Plates.
From .0625 to 1 Inch in Thickness,
Tbickneu
Ipcb.
.0625
.125
.1875
•25
•3x25
•375
•4375
•5
.5625
.625
•6875
•75
.8125
•875
•937S
Thick nesa.
Iiivli.
•05
.1
.2
.25
3
'35
•4
.45
.5
.55
.6
65
•7
•75
.8
.85
•9
•95
f
1.125
I.2S
1-3125
1-375
1-4375
1-5
1.5625
1.625
1-75
1875
Wrought
iron.
Lbs.
a.517
5.035
7552
1007
12.588
i5^io6
17.623
30 141
22.659
25.176
27.694
30-21 1
32.729
35-247
37.764
40.283
j Ca»t Iron.
steel.
Coppor.
Lba.
Lba.
Lb*.
3.346
2.541
2.89
4693
5081
5.781
7039
76«2
8,673
9.386
10.163
11.563
"•733 i "703
14-453
14 079 '5 244
17-344
16.426 17785
20.334
18.773 1 20.326
23-125
31.119 22.866
26.016
23 466 t 25 407
28.906
25.812
27948
31*797
28159
30488
34.688
30.505
33.029
37-578
32852 35.57
40.469
35-199 38."
43359
37-545
40.651
46.25
LnA.
Brau.
Gan-
inet«h
Zinc.
Lb».
L>>a.
Lba.
Lha.
3691
2.675
2.848
234
7.383
5.35
5.696
468
IX. 074
8.025
8.545
7.02
14-765
10.7
"-393
936
18.456
13-375
14.241
II 7
32.148
16.05
17.089
1404
25-839
18.725
19.938
16.34
2953
31.4
32.786
18.72
33.222
34.075
25-634
21.06
36.913
26.75
38.483
23.4
40.604
39.425
31-331
2574
44.396
32.1
34-179
2868
47.987
34-775
37.027
3042
51.678
36656
39.875
32.76
55-37
39-331
42.723
35-1
59»o6i
42.8
45-572
37-44
F)*om One Tiaeniieth Inch to TxDO Inches in T%ickne8s,
Wroaght
Iron
Lba.
2.014
4.028
6.042
8.056
10.071
12.085
14.099
16.113
18.127
20.141
22.155
24.169
26.183
28.197
30211
32.226
34-24
36.254
38.26S
40.282
45317
50.352
53.87
55387
57905
60423
6294
65458
70.493
75528
80.564
Caat Iron.
Lba.
1.877
3-754
5.632
7-509
9.386
11.264
13.141
15.018
1689s
18.773
20.65
22.527
24.409
26.281
28.154
30.035
31.912
33-79
35.668
37-545
42338
46.931
49.378
51.634
53.971
56.317
58663
61.011
65704
70.397
75-09
SteeL
Lba.
2033
4.065
6.098
8.13
10.163
12.195
14.228
16.26
18.293
20.325
22.358
24-391
26.423
28.456
30.488
32.521
34.553
36.586
38.628
40.651
45-732
50.814
53.354
55.895
58.436
60.976
63.517
66.058
71-^39
76.33
81.3
Copper.
Lba.
2.312
4.625
6.938
925
11.562
13875
16.187
18.5
20.813
23-125
25.437
27.75
30.063
32.375
34.687
37
39-312
41.625
43.937
46.25
52.031
57-813
60.703
63594
66.484
69-375
72.266
75 136
80938
86.719
93.5
Lead.
Braaa.
Lba.
2.593
5.906
8.859
II.8I2
14.765
17.718
20.671 j
23.624 1
26.577
2953
32.484
35-437
38-39 I
41-3431
44.3961
47.2491
50.202
53-154;
56.X08
59061
66.443
73.826
77.517
81.309
84.9
88.591
93.283
95-974
103.356
110.739
1X8.123
Lba.
3.14
4.28
642
8.56
10.7
12.84
14.98
17.12
19.26
2X.4
23-54
25.68
2782
29.96
32 1
34-24
36.38
3852
40.66
43.8
48.15
53-5
56.17
58.85
61.53
64.2
66 88
6955
749
80.35
85.6
Gun-
metal.
Lba.
3.379
4-557
6.836
9.114
11-393
13.672
15.95
18.229
20.507
22.786
25.065
27-343
39.622
31.9
34179
36.458
38.736
41.015
43293
45572
51.268
56.965
59813
62.661
65-51
68.358
71.206
74054
79-751
85.447
91.1^
Zinc.
Lba.
1.872
3.744
5616
7.488
9.36
X 1.232
13-104
14-976
16.848
18.72
20.592
22.464
24336
26.208
28.08
29.95
31.834
33696
35.568
37-44
42.13
46.8
49.14
51.48
53-83
56.16
58.5
60.84
65.52
70.3
74.88
WEIGHT OP ROLLED STEEL T. PIPES AND TUBES. 1 47
"Weigh.ts, etc, of Rolled Steel
Safe Load for One Foot Uniformly Distribute.
Load.
Dlmen-
•iotif.
Area.
Weight
per
foot.
Tensile Strength
per Sq. Inch.
Dimen-
sions.
Area.
Weight
per
foot
12500
16000
Ins.
Sq. Iiu.
Lbe.
Lb».
Lbs.
Ins.
Sq. Ins.
Lbs.
4-5X2.5
2.79
V
5220
6950
4X4
3-21
10.9
4-5X2.5
2.4
4520
6030
4X4
4.02
»3-7
4-5X3
3
10
7540
10050
4X4.5
3.36
II. 4
45X3
2.55
8.5
6490
8650
4X4.5
4.29
14.6
4-5X3.5
4<)5
15-8
17020
22690
4X5
3-54
12
5 X2.S
3-24
II
6goo
9 200
4X5
4.56
15.6
5 X3
3-99
13-6
9410
»2 550
—
T.
Load.
Tensile Strens^th
per Sq. Inch.
12500
l<bs.
13100
16 170
15840
20400
19410
24800
x6ooo
Lbs.
17470
2»55o
21 I20
27200
25880
33070
To
Compete Weigh-t of M^etal !Pipes,
D* — li" C. D and d rqjresenting external awl internal diameters in inches^
and C coefficient.
Cast Iron 2.45. Wrought Iron 2.64. Brass 2.82. Cop[)er 3.03. I^ai 3.86.
To Compu-te "Weight of IMetal Tubes aiici Fipes
per Xjineal IToot-
fh)m .5 fnch to 6 Inches fntemal Diameter.
Diam.
Area of Plat^.
[ Diam.
Ins.
Area of Plate.
Sq. Foot.
Diam.
Area of Plate.
Diam.
Area of Plata,
Ilia
1
Sq. Foot.
Ins.
Sq. Feet.
Ins.
Sq. Feet.
•5
.1309
1 1-3»25
•3436
|2.7S
.7199
4.5
1. 1781
•5625
•1473
1375
.36
12875
.7526
4625
I.2108
^5
1636
14375
•3764
,3
.7854
4 75
1-2435
.6875
.18
l'-5
•3927
3.125
.8181
4875
1-2763
•75
1964
i 1.625
•4254
325
.8508
5
1.309
^125
2127
i'Z5
-4581
3-375
.8836
5.125
1-3417
.875
.2291
187s
.4909
35
.9163
5.25
1-3744
•9375
.2454
I2
•5236
3625
•949
5375
1.4072
I
.2618
2.125
.5543
|3 75
.9818
5-5
14399
1.0625
.2782
I2.2S
.587
4
1.0473
5^625
1.4726
1 125
•2945
i 2.375
.6198
14.125
1.0799
5-75
1-5053
I 1875
.3105
2.5
•6545
:4.25
1.1126 1
5.875
1 5381
1-25
•3272
, 2.625
.6872
4-375
1-1454 1
6
1.5708
.A.pplicatioi\ of Taljle.
Wlieii Thichnew of Metal is given %n Divisions of an Jnch.
To internal diameter of tube or pipe add thickness of metal ; take
area of the plate in square feet, from table for a diameter equal to
Bum of diameter and thickness of tube or pipe, and multiply it by
weight of a square foot of metal for given thickness (see table, page
146), and again by its length in feet.
iLLrsTRATioif. — ^Required weight of 10 feet ot copper tube i inch ln> diameter and
zas of an inch in thickneta
t + . 125 = 1. 125 X 3- 1416 -^ It = . 2Q45 square feet for i foot of length.
Weight of I square foot of cop)>er .izsth of an inch in thickness, per table, page
135, s= 5.781 Iht. ; then, .3945 ((Vom table above) x 5-781 X 10 ^ 17-025 ^s.
When 7%ickne$8 of Metal is given in lumbers of a IHre- Gattge.
To internal diameter of tube or pipe add thickness of number from
table, pp. 120 or 121 ; multiply sum by 3.1416, divide product by 12, and
quotient will give area of plate in square feet. Then proceed as before
148 WEIGHT OF IRON AND COPPER PIPES, BOLTS, ETC.
Illi'stratiox. — Required weight of 10 feet of copper pipe 2 inches in diametei
and No. 2 American wire-gauge in thickness.
a-f •25763X3.1416-:- 12 = 2.257 63 X 3. 1416-=- 12 = .591 square fui; then, .591
X XI. 6706 (weight nroro table, iiage 118) =6.897 lb*.
'Weigh.t of Riveted. Iron and. Copper r*ipes,
Fi'om 5 to 30 Inc/ies in Diameter,
ONE l-XKJT IS LENGTH.
I>i:.Tn«t«r.
ThicknMt.
Inch.
Iron.
Copper.
Diameter.
ThkkneM.
Iron.
Lb«
Copper.
Int.
Lbs.
Lb«.
Ins.
Inch.
Lba.
5
.125
7.12
8.14
9
•25
2501
28.58
.1875
10.68
12 21
.25
2633
30.09
•25
14.25
16.28
10
•»s
2775
31-71
5-5
.125
7.78
8.89
10.5
•25
29.19
3322
.1875
11.66
^3-33
11
•25
30.49
34.85
•25
15-56
17.78
12
.25
3313
37-86
6
.125
8.44
9.64
13
•25
3588
41
.1875
12.65
14.46
14
.25
38^52
44.0a
.25
16.88
19.29
15
•25
41.26
47.15
6.5
.125
9.1
10.4
•3125
51^57
58.94
•1875
13-65
15.6
16
•25
439
50.17
•25
18.2
20.8
•3125
5487
62.71
7
.125
9.78
II.I8
17
•25
46.53
53.18
•1875
14.68
16.78
•3125
5817
66.48
.25
1957
22.37
18
•25
49.17
56.3
7-5
.125
10.49
11.99
•3125
6147
70.25
.1875
15-73
17.98
20
•3125
68.07
77-79
•25
20.89
23-87
24
•3125
81.33
929s
8
•1875
16.7
1908
25
•3125
84.57
96.65
.25
22.26
2544
28
•3125
9456
107.95
8.5
•25
23-59
26.96
30
-3125
101.14
"559
Above weights include la|)6 of sheets for riveting and calking
Weights of the rivets are not added, a's number per lineal foot of pipe depends
upon the distance they are placed apart, and their diameter and length depend
upon thickness of metal of the pipe.
"Weight of Copper Rods or Solts,
From .125 Inch to 4 Tnches in Diameter.
ONE FOOT IN LENGTH.
Diameter.
Weiffht.
Lbe.
Diameter.
Weiicht.
DiaineUr.
WeiRbt
Dtamater.
Wdghk
Inch.
Int.
Lbt.
Ins.
Lh«.
IM.
Lbs.
.125
.047
.8125
1.998
1.5
6.81 1
2-75
22.891
.1875
.106
.875
2.318
•5625
7-39
.875
25.019
-25
.189
-9375
2.66
.625
7^993
3
27^243
•3125
.296
I
303
•75
9.27
.125
29.559
•375
.426
1.0625
3.42
.875
10.642
.25
31.972
.4375
•579
.125
3-831
2
12.108
.375
34.481
.5
•757
.1875
4.269
.125
13^668
•5
37.081
-5625
•958
•25
4.723
.25
15.325
.625
39 777
.625
1.182
' -3125
5-21 !
1 .375
17-075
.75
42.568
.6875
1431
-375
5723
•5
18.916
•875
45455
•75
1-703
1 .4375
6.255
.625
20.856
4
48.433
WEIQMI' OF METALS.
149
^Veiglit of* Mietals of a Griven Sectional
AjC^B.i
FroTO .1 Square
Inch to 10 SqtMre Inches.
PER LINEAL
FOOT.
(D. K, Clark.)
!>«rT.
Wroagfat
Iron.
Cut
Iron.
Stoel.
BraM.
Gon-
iD«tat.
SCCT.
Wrottfrbt
Iron.
Cm!
Iron.
Sf.1. i Bru.. 1 O-L
A&IA.
t.
•937S-
i.oa.
Z.052.
1.092.
ASEA.
I.
•9375-
1. 03.
Lb*.
1.052. ' 1.09a.
Sq.lDB.
Lbs.
Lbs.
Lbs.
Lbt.
Lbt.
Sq.lM.
Lb«.
Lbt.
Lb*. Lbs.
.1
•33
•31
•34
•35
.36
t S.I
17
159
173
17.9 18.6
.2
.67
.62
.68
•7
.73
5-2
173
16.3 17.7
18.2 ! 18.9
3
I
.94
1.02
1.05
1.09
5-3
17.7
16.6 18 1 18.6 19.3
•4
1.33
1.35
1.36
1-43
1.46
5-4
18
16.9 18.4 ! 18.9 \ 19.7
.5
1.67
1.56
i'7
1-75
1.82!
5-5
18.3
17.2 18.7 19.3 20
.6
2
1.88
2.04
2.11
2.18
5-6
18.7
17.5 19 19.6 1 20,4
•7
2.33
2.19
2.38
2.46
2.55
5.7
19
17 8 19.4 20 1 20.8
.8
2.67
2.5
2.72
2.81
2.91 1
5.8
193
18.1 19 7 20.3 ' 21. 1
•9
3
281
3-o6
3.16
3.38'
5-9
19.7
18.4 20.1 1 20.7 1 21.5
I
333
315
34
351
3-64
6
20
18.8 20.4 ,21 1 21.8
I.I
367
344
3 74
3.86
4 i
6.1
20.3
19. 1 20.7 21.4 1 22 2
1.2
4
3 75
408
4.21
4-37,
6.2
20.7
19.4 21. 1 21.7 ; 22.6
1-3
4-33
406
442
456
4.73'
6.3
21
19 7 21.4 22.1 22.9
1.4
4.67
438
4.76
4.91
5-1 1
6.4
21.3
20 21.8 22.4 23.3
1-5
5
469
5.1
526
546
6.5
21.7
20.3 22.1 22.8 23 7
X.6
5-33
5
544
561
582
6.6
22
20.6 22.4*' 23 1 24
1-7
567
5.31
578
5.96
6.19
6.7
22.3
20.9 22 8 : 23 5 1 24 4
1.8
6
563
6.12
6.31
6.5s
6.8
22.7
21.3 23.1
23 9 ; 24.8
1.9
6.33
5.94
646
6.66
6.92:
6.9
23
21.6 23 s
24.2 1 25.1
2
6.67
625
6.8
7.01
7.28:
7
233
21.9 23.8
24.6
255
2.1
7
6.56
7.14
7.36
7.64'
7-1
237
22.2 24.1
24.9
258
2.2
733
6.88
748
7.72
8.01;
7.2
24
22.5 24.5
253
26.2
23
7.67
719
7.82
807
8.37!
7-3
243
22.8 24.8
25.6
26.6
2.4
8
75
8.16
8.42
8.74'
7-4
24.7
23.1 25.2
26
26.9
3-5
8.33
7.81
85
8.77
9.1 1
75
25
234 25.5
26.3
273
2.6
8.67
5'3
884
9.12
946;
7.6
253
23 8 25.9
26.7
277
2.7
9
8.44
9.18
947
983
7-7
257
24.1 ' 26.2
27
28
2.8
9-33
8.75
952
9.82
10.2
7.8
26
24.4 26.5
27.4
28.4
2.9
9.67
906
9.86
10.2
10.6
79
263
24.7 26.9
27.7
28.8
3
10
938
10.2
10.5
10.9
8
26.7
25 ' 27.2
28.1
29.1
3-1
10.3
9.69
10.5
10.9
"3
8.1
27
253 27.5
28.4
295
3-3
10.7
xo
10.9
11.2
11.7
8.2
273
25.6 ; 27.9
288
29.9
3-3
II
10.3
II.2
11.6
12
8.3
27.7
25.9
28.2
29>I
30.2
3-4
"•3
10.6
1 1.6
11.9
12.4
84
28
26.3
28.6
29-5
30.6
3-5
11.7
ia9
1 1.9
12.3
12.7
8.5
28.3
26.6
28.9
29.8
309
3-6
12
11.3
12.2
12.6
I3-I
8.6
28.7
26.9
29.2
30.2
31.3
3-7
12.3
11.6
12.6
13
135
8.7
29
27.2
29.6
30 5 '31.7
3-8
12.7
11.9
12.9
13-3
13-8
8.8
293
275 ! 29.9
30-9 32
3-9
13
12.2
133
137
14.2
8.9
29.7
278 30.3
31.2 32.4
4
13.3
13.5
13-6
14
14.6
9
30
28.1 30.6
31.6 ; 32.8
41
13-7
12.8
139
14.4
14.9
9.1
303
28 4 i 30.9
3191331
4.2
14
13.1
14.3
14.7
153
9.2
307
28 8 i 31.3
323 33 5
43
14-3
13.4
14.6
iS-i
15.7
9-3
31
29.1 31.6
326 33 9
4-4
14.7
13*8
IS
154
16
94
313
294 32
33 34-2
4-5
15
14.X
iS-3
15.8
16.4
95
317
297 323
33 3 : 34-6
4.6
iS-3
14^
15^
16.1
16.7
9.6
32
30 32.6
33-7 , 34.9
4-7
iS-7
14.7
16
16.S
I /.I
97
323
303 33
34
35-3
4.8
16
15
16.3
16.8
17s
9.8
32-7
30.6 33-3 '344
35.7
4^
16.3
15.3
16.7
17.2
17.8
9.9
33
30.9 33-7
347
36
5
16.7
15.0 1
«7
175
l8.2
10 1
33-3
31-3 34
35- » 364
\*
»
I50
LEAD PIPES. — COPPER PIPES AND COCKS.
^Veigh-t of Lead I»ipe. {EnglUh,)
ONE FOOT IN LENGTH.
DUun.
Thick-
neat.
Weight.
DlAin.
ThiclK-
JI«M.
Weight.
Diam.
Thick-
Weight.
Diam.
Thlck-
nea*.
Ineh.
Inch.
Lb*.
In*.
Ineh.
LU.
Id*.
Inch.
LU.
In*.
Inch.
•5
.097
•93
I
.136
2.4
1.75
.t66
5
3
.275
.112
1.07
.156
2.8
.199
6
35
.225
.124
1.2
.2
3-73
.228
7
•273
.146
1.47
.225
4.27
.256
8
4
•257
.625
.089
I
1.25
•139
3
2
.178
6
•3125
.101
I-I3
.16
3-5
.204
7
•327
.121
1.4
.18
4
.231
8
4.25
.3125
.14
2
•193
4.33
.266
9-33
4'5
.232
•75
.112
1.6
1-5
.156
4
2.5
.2
84
.295
.147
1.87
.179
467
.227
9.6
•3125
.181
2.13
.224
6
.261 1 II.2
4-75
.3125
.215
2.4
•257
7
3
.218
1 11.2
5
•3125
^- Weight
Lta.
14
13
16
17
20.5
22
22.04
17
22
23.25
24.45
25.66
I>i]xieii8ioiis of* Copper Kpes and Composition
Cooks.
From I Inch to 23 Inches in Diameter,
% •'i
l^
|»-|
Flange D
•
Pipe.
In*.
In*.
I
3-375
1.25
3.625
1.5
3.875
1-75
4.125
2
4.375
2.25
4.625
2.5
4.875
2.75
5.2s
3
6
3.25
6.125
35
6.375
3.75
6.625
4
6.875
425
7.125
45
7.375
4.75
7.625
5
8
525
8.25
5-5
8.5
5.75
9
6
9.2s
6.25
9-75
6.5
10
6.75
10
7
10.5
7.25
10.75
7.5
H.125
7.75
".375
8
11.625
8.25 1
12
»5
12.25
«-75 :
13.5
uneter.
Thick-
BolU.
nea*.
Cock.
No.
Diam
Inch.
In*.
Inch.
3-5
•375
3
.5
3-75
•375
3
•5
425
•375
3
•5
4-375
•4375
4
.5
4.75
•4375
4
.5
525
.4375
5
.5
5-5
.4375
5
•5
575
•4375
5
•5
6.25
.5
5
.625
6.625
•5
6
.625
6.875
•5
6
.625
725
•5
6
.625
7^375
•5
6
.625
7.625
•5
6
.625
8.25
•5
6
•625
8.5
•5
6 1 .625
9
•5
6 I .625
925
5
6 i .625
9-5
.5
6 1 .625
9875
.5
6
•625
.625
8
.625
.625
8
.625
.625
8
.625
.625
8 i .625
.625
8 i .625
.625
8 i .625
.625
8 .625
.625
8 ^
.625
.625
9
.625
.625
9 i 625
.625
9 -625
.635
9
•^51
In*.
9
9-25
9-5
9.75
10
10.5
11
11.5
12
12.5
13 •
13-5
14
145
15
15.5
16
16.5
17
17-5
18
18.5
19
19.5
20
20.5
21
21.5
22
22.5
33
Flange
Diam.
Pipe.
Int.
12.75
13-125
13-375
13.625
13.875
14.5
15
15.625
16.125
16.625
17.25
17-875
18.375
18.875
19.5
20
20.5
21.125
21.625
22.125
23.75
23.25
23.75
24375
24.875
25375
26
26.3
27
27.625
38.125
Thick-
oeae.
Inch.
625
625
6875
6875
6875
687s
6875
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
Bolts.
No.
IHam.
Inch.
9
.625
10
.625
10
.625
10
.625
10
.625
10
.625
10
.625
10
.75
10
.75
10
.75
10
.75
10
.75
10
.75
10
75
10
75
10
.75
10
.75
10
.75
II
•75
11
•75
11
•75
11
.75
12
•75
12
•75
12
.75
13
.75
13
.75
13
.75
13
•75
14
75
H
•75
W£I6BT OF 8HBST LEAD, LEAD AKD Till PIFXS, ETO. 1 5 I
"Weight of Slieet Hiead.
PER SQUARE FOOT.
ThUkBCM.
Weight.
ThicknflM.
Inch.
.017
•034
.051
Lba.
I
2
3
Inch.
.068
.08s
.101
Weight.
TbickneM.
Weight.
ThicknflM.
Lbs.
4
5
6
Inch.
.118
•135
.153
Lbs.
7
8
9
Inch.
.169
.186
.203
Weight.
I,b«.
10
II
12
AVeight of Tin Pipe.
ONE
FOOT IN LKXGTII.
Dism.
THtCKNBSS.
Diam.
THICKNBSS.
Diam.
tHiCKN.
Diam. -
Cxtemnl.
% inch.
Lb.
^ inch.
EzternaL
Ins.
% inch. 1 ^ inch.
External.
3^ inch.
Elzternal.
Inch.
Lbs.
Lbs.
libs.
Ins.
Lbs.
Ins. ''
•25
.148
—
1.25
1.095
I 417
2.25
5.04
3.25
.5
.384
.472
I-S
1.328
I 732
2-5
5.67
3.5
•75
.62
.787
1.75
1,564
2.047
^75
6.3
3-75
I
.856
1.103
2
1.802
2.362
3
6.93
4
THICKN.
3^ inch.
Lbs.
7.56
8.19
882
9-45
"Weigh-t of Xjead Encased. Tin. ^Pipes.
Diameter.
Light W«ighta.
Ina.
Lbs.
Lbs.
Lbs.
•375
I
1-5
2
•5
2
2.5
3
.623
3
3-5
4
•75
3-5
4
4.5
I
4-5
5
5-5
1.25
6.5
7
8
1-5
8
9
10
2
II
13
—
for Supply of Water HemI
.•
50 feet and nniier.
51 to 250 feet.
251 to
;oo feet.
Lbs.
Lbs.
Lba.
2.5 to 4
3 to 4-5
3-5
to 5
3.5 '' 5
4 •' 6
4-5
" 7
45 " 7
S.25" 8
6
'[ 9
5-5 " 8
6 « 9
7
" 10
7.25 " 10
8 "11
9
" 12
9 " I3.S
10 " 14
12
" 16
II '* 16
12 5 " 18
14
" 21
16 " 23
18.5 " 26 1
21
"30
* The extreme weights are for extra heavy pipe with lea> proportion of tin.
X>ixxLen8iozLS and. "Weiglit of Sheet Zino. {VieUe-Montagne.)
PER S<2UARlfi FOOT.
2X .5 metres;
aX .65 metres;
sX .8 metres;
area, i square metre.
area, 1.3 aq. metres.
area, 1.6
sq. metres.
*
No.
Thickness.
Weight.
6.56X1.64 feet; area,
6.56X2.13 feet; area,
656X2.62(1.; area,
Z0.76 square feet.
13.99 square feet.
17.22 sq
Kilom.
uare feet.
Millim.
Inch.
Kilom.
Lba.
Kilom.
Lbs.
Lbs.
Lbs.
9
.41
.0161
2.9
6.39
3.7
8.16
4.6
10.14
.589
10
•51
.0201
3.45
7.61
4 45
9.81
0-5
12.12
.704
XI
.6
.0236
4.05
8.93
5-3
6.1
11.68
6.5
14.33
.832
12
.69
.0272
465
10.25
1345
7-5
16.53
.96
13
.78
.0307
5»3
11.68
6.9
15.31
8.5
i8«74
1.088
14
.87
.0343
5-95
13.12
7.7 . 16.94
9-5
20.94
I.216
IS
.06
.0378
6.55
14.44
8.55 ' 18.85
10.5
23.15
1.344
16
I.I
^33
75
16.53
9'75 . 31.5
12
26.46
1.536
\l
1.23
.0485
8.45
18.63
10.95 i 24.14
13-5
29.97
1.74
1.36
.0536
9-35
20.6l
12.2
26.9
IS
3307
1.92
19
1.48
.0583
10.3
22.71
24.S
13-4
29-54
16.5
36.38
2. 112
20
166
.0654
11.25
14.6
32.19
18
39.68
2.304
91
1.85
.0729
12.5
27.56
16.25
35-82
20
44.09
2.56
22
2.02
•0795
13-75
3031
17.9
3946
22
48.5
2.816
23
3.19
.0862
15
3307
19.5 42.99
24
52.91
3073
24
2.37
•0933
16.25
35.82
21.1
46.52
26
57-32
3-329
25
2.52
.0992
17.5
38.58
22.75
50.15
28
61.73
3-585
96
2.66
.1047
18.8
41.44
24-4
53-79
31
68..^
3.060
152 SHIP AND BAILROAB SPIKES, UOBSESHOKS.
Railroad Splices.
(DUworfk, Porter <6 Co., PiUshurrf^ Pa.)
Dimentiont.
a.5X.3'25
3 X.3125
2-5X.375
3 X.375
3-5X.375
4 X.375
Inkevr
of 200
Lbs.
Weifcbt of
Rftil per
Yard.
No.
2230
1880)
1650 1
.380)
1250 1
1025
Lbs.
8 to 12
12 to 16
16 to 20
16 to 25
Dimensiona.
Ilia.
4-SX.375
3- 5 X. 4375
4 X.4375
4- 5 X. 4375
3-5X.5
4 X.5
In kflf(
of soo
Lba.
No.
780 I
8gof
780
690
670
605
WeiKht
Rnil per
Yard.
0(11
Lba.
16 to 25
20 to 30
24 to 35
i
Dimensions
In kes
of 200
Lbt.
Ins.
4.5X.5
5 X.5
4.5X.5625
5 X.5625
5«5X.s625
No.
518
475)
460}
405
360
Weiftbt of
Rail per
Yard.
Lbt.
28 to 35
35 to 40
40 to 56
45 to IOC
street Railvtray Spiltes.
From .25 to .625 Inch. Have CourUermnk Heads.
SqLuare Solt i^pikes.
.25 In.
Lenjrth.
Ins.
3 to 3.5
.25 In.
Length.
Ins.
4 to 8
.3125 In.
Lenprth.
Ins.
4to8
•375 In-
Ijon^th.
Ins.
4 to 12
•4375 In.
Ins.
6 to 12
.5 In.
I^englh.
Ins.
6 to 16
.625 l3.
Lenirtb.
Ins.
8 to 16
.752 In.
Length.
Ins.
12 to 24
Sh.lp and. ^Railroad Spikes.
DIMKNSIONS AND NUMBKK PKR POUND, (/\ C. POffCj MoSS.)
Sliip Spilses.
% In. Sq.
J^ In. Sq.
A^Ii
a. Sq.
% In. Sq.
^ In. Sq.
a "2
•
fi
•
•2
BT5
•
■5
B-a
~- a
. s
0 0
3
— a
B
Ins.
— a
J
Ins.
"51
Ins.
Ins.
3
19
3
XO
4
54
5
3-4
3-5
15-8
3-5
9.6
4.5
5
5-5
31
4
13.2
4
8
5
4.6
6
3
4-5
12.2
4-5
6
5-5
4.2
6.5
2.8
5
10.2
5
5.8
6
4
7
2.6
•
—
6
5.2
6.5
3-2
7.5
8
2.4
2.2
a
— a
Ins.
6
6.5
7
75
8
85
9
10
2.2
2
1.9
1.8
1-7
1.6
1-5
1.4
% In. Sq.
%In
•
.B
Ins.
■El
eg
•
Ins.
8
1.4
10
9
1.2
15
10
I.l
—
II
I
—
^^^^
^BIM
5 "5
5«£
.8
.6
Railroad Spikes
.5 inch square X 5.5 ins. 2
.5625 " " X 5.5 " 1.6
per lb.
Spikes and Horseslioes.
LENGTH AND NUMBKU PER POUND. (//. Burden, Troy, N. Y.)
•Boat Spikes.
Ship Spikes.
•
B .
— J3
a .
■
bo
•s«-
•
B .
— .a
s
d-J
B
diJ
g
oh)
B
i^
.2
5r.
JS
?5
»2
?;
»s
y.
Ins.
Ins.
Ins.
Ins.
3
17.5
6.5
4.78
4
8
7.5
3-5
3-5
14.68
7
3.62
4.5
6.5
8
1.74
4
12.57
7-5
3-37 1 5
4.37
8.5
1.63
45
9.2
8
2.95 5-5
4-3
9
1-55
5
7.2
8-5
2.9 ,6
4.2
lO
1.15
5-5
6.3
9
2.1 1 6.5
3-77
—
—
b
4-97
10
1.98
i7
2.75
—
—
Hook Head.
Lenfcth.
Ins.
4 X.37S
4-5 X.4375
5 X.5
5-5 X.5
5-5 X. 5625
6 X .5625
6 X .625
5-55
4.14
2.52
2.41
1.87
1.72
1.38
Horseshoes.
tc
a
2_
Ins.
I
2
3
4
5
a .
d^
.84
•75
.65.
.56
•39
CAST IBON AND LBAD BALLS. — ^NAILS.
153
WTeiglit and. "Vol-axne of Cast Iron and Lead Sails.
Prom I Inch to 20 Inches in Diametei\
Diunetor.
YolanM.
Cast Iron.
Lead.
Diameter.
Ins.
Cube Ina.
Lb*.
Lba.
Ina.
I
.523
.136
.215
9
1-5
1.767
.461
•725
9.5
2
4.189
1.092
\ 1-718
JO
2.5
8.181
2.133
3.355
10.5
3
14.137
3.685
5-798
II
3-5
22.449
5.852
9.207
".5
4
3351
8.736
13.744
12
4.5
47-7U
12.439
19569
12.S
5
6545
17.063
26.843
'3
55
87 114
22.721
35.729
14
6
"3097
29.484
46385
15
6.5
143793 37-453
58.976
16
7
179594 , 46.82
73-659
1 17
7-5
220.893
57.587
90.598
1 ^^
8
268.082
69.889
109.952
, ^9
8.5
321.555
83.84
131.883
1 20
Cube Ina.
381.703
448.92
523599
606.132
696.91
796.33
904.778
1022.656
1150.346
1436.754
1767.145
2144.66
2572.44
3053.627
3591.363
4188.79
Note. — To compate weight of balls of other metals, multiply weight given ia
table by following multipliers:
Volume.
Caat Iron.
Lead.
Lba.
Lba.
9951
156.553
117.034
184.I2I
136.502
214.749
158.043
248.587
181.765
285.832
207.635
326.591
235.876
371.096
266.647
419.512
299.623
471.806
374563
589-275
460.696
724.781
559.114
879.616
670.717
1055.066
796.082
1252.422
936.271
1472.97
1092.02
1717.995
For Wrought Iron 1.067.
Steel 1.088.
Brass 1. 12.
Gun-metal x. 165.
'Weish.t and IDiametex* of Cast Iron Sails.
Weigbt.
DUunater.
Weight.
Diameter.
Weight.
Diameter.
Weight.
Diameter.
Lba.
Ina.
Lba.
Ina.
Lbs.
Ins.
Lba.
lua. '
I
1.94
12
4-45
50
7.16
224
II.8
2
a.45
14
4.6S
56
7.43
336
13.51
3
2.8
16
4.89
60
7.6
448
14.87
4
3.08
18
5.09
70
8.01
560
16.02
5
332
20
5.27
80
8.37
672
17.02
6
3.53
25
5.68
90
8.71
784
17.91
7
3.72
28
5-9
100
9.02
896
18.73
8
3.89
30
6.04
112
9.37
1008
. 19.48
9
4.04
40
6.64
168
10.72
II20
20.17
Weight.
Lba.
1344
1568
1792
2016
2240
2800
3360
3920
4480
Diameter.
Ina.
21.44
22.57
23.6
24-54
25.42
27.38
29.1
30.64
32.03
Xjength. of- Horseshoe !N'ails.
Btf Numbers.
No. 5 1.5 Ins. I No. 7 ..... . 1.875 Ins*
1-75
8
No. 9 2;25 Ins.
10.
2.5
Ijen^lis of Irop. ^ails, and Nnm"ber in a Xils.
Sli*.
L'gih.
No.
420
270
Slie
5d.
16
L'gth.
No.
220
175
SiM.
L'gth.
No.
100
65
Siie.
L'gth.
No.
52
28
Siie.
L'gth.
3d.
4
iBft.
1.25
1-3
Ina.
1-75
2
8d.
10
Ina.
2.5
3
J 2d.
120
Ina.
3.25
3-5
40
Ina.
4
4.35
N©.
24
20
154
NAILS, SPIKES, TACKS, BTC.
"Wroiaglxt
Iron Cut IN'ails, Taoks, Spikes, etc.
(Cumberland Nail and Iron Co.)
Lengths and Number per Lb.
o
Ordinary. f
Kixxislxi
mg.
:
Shinffle.
sice.
Length.
Ins.
No. per Lb.
Sixe.
Length.
No. per Lb.
Size.
Lenf^h.
No. per Lb
Ins.
Ina.
2d
-87s
716
4^
1-375
384
5**
1-75
178
3 fine
1.0625
588
5
1-75
256
r ^
2.5
74
3
1.0625
448
6
2
204
9
2.75
60
4
1-375
336
8
2.5
102
10
3
52
5
1-75
216
10
3
80
TaolcB.
6
2
166
12
3.625
65
I oz.
.125
16000
7
2.25
118
20
3.875
46
1-5
•1875
10666
8
2.5
94
Core.
2
.25
8000
lO
2.75
72
6d
2
143
68
2.5
•3125
6400
12
3-5
50
8
2-5
2333
3-125
3-75
4-25
4-75
2.5
3
.375
5 333
20
3-75
32
10
60
4
.4375
4000
30
40
50
60
4-25
4-75
5
5-5
Light
20
17
14
10
12
20
30
40
WH
42
25
18
14
69
6
8
10
13
14
•5625
.625
.6875
•75
.8125
2666
2000
1600
1333
1143
4'*
1-375
373
WHL
2 2^
72
16
.875
1000
5
1-75
272
18
•9375
888
6
2
196
Olinc
U.
20
I
800
Brade
}.
6<i
2
152
Soat.
6d
2
2.5
163
96
7
8
2.25
2.5
133
92
Siic
1.
No. per Lb.
8
Ilia
10
12
2.7s
3-125
74
50
10
2.75
3
3.25
72
60
43
3-!
t
Spi
>
206
kea.
19
6d
2
96
Slat<
5.
4
IS
7
2.25
66
3'*
1.625
288
4-!
>
13
8
2.5
56
4
1 4375
244
5
10
10
2.75
SO
5
1-75
187
5-^
m
>
9
—
3
40
6
2
146
6
7
Lanfrtb.
No.
3 X .375
3.5 X .375
4 X .375
No.
930
890
760
X^ailroad Spikes.
Number in a Keg q/* 150 &8.
Length.
Ina.
3 5 X .4375
4 X .4375
4-5 X .4375
No.
Length.
Ina.
675
4X.5
540
4-5 X .5
510
5X.5
No.
Length.
N«,
450
400
340
Ina.
5 X .5625
5.5 X .5625
300
280
5.5 X -5625 standard for a gauge of 4 feet 8.5 ins.
Ship and Soat Spikes.
Number in a Keg of 150 Vbs,
Length.
Ina.
4 X.25
4.5 X. 35
5 X.25
6 x.25
7 X.2$
No.
Length.
1650
1464
1380
1292
ii6i 1,
tl.S.
5 X. 3125
6X.3125
7 X. 3125
6X.375
7X375
No.
Length.
Ina.
930
8X.375
868
9X.375
662 ;
10 X. 375
570
8Xu^375
482
9 X. 4375
No.
Length.
No.
laa.
455
IOX.4375
270
424
8X.5
256
390
9X.5
240
384
10 X. 5
223
300 i
JIX.5
303
TABIOCB MBTALS.
155
"Weiglit of "VaxT-ou-s Mietals.
Per Cube Inch and Foot.
Mbtals.
Wrought-iron
plates
" wire.
Cast iron ....
Steel plates. .
" wire . . .
CJopper, ( .
rolled \ .
Can- metal,
cast
}
Spec.
W'srht
Ins.
Weight 1
Gravi-
in an
in a
. in a
ty-
Inck.
Lb.
Foot.
Lbs.
Lb.
7734
.2797
3-57
48338
7774
.2812
3-55
485.87
7209
.2607
3-84
450-54
7804
• 2823
3-54
487.8
7847
.2838
3.52
490-45
•3146
3- 19
543-6
.3212
3"
555
8750
•3165
3.16
546-875
Mktals.
Wrought iron
Cast iron ....
Steel
Copper plates
Gun-metal. . .
7.698
.278
3.6
480
7.217
.26
.3-84
450
7852
.283
3-53
489.6
8.805
.318
3-15
549
8.404
•304
3.29
524
Brass, rolled.
'' cast, . .
I^ead, rolled .
Tin, cast
Zinc, rolled..
Alumini- )
um, cast I
Silver
Tobin Bronze.
English, (D, K. Clark.)
Tin
Zinc
LieaQ ........
Brass, cast. . .
wire..
Specific
Gravi-
ty.
vV'glit
in an
Inch.
Lb.
8217
8080
.2972
.2922
II 340
7 292
7188
.4101
.2673
.26
2560
.0936
10480
8379
•379*
.3031
(I
7.409
7.008
II. 418
8.099
8.548
.268
•253
.412
.292
.308
Ins.
in a
Lb.
Weight
in a
Foot.
1
Lb.
3-37
513-6
342
2-44
3-74
3-85
505
708.73
462
449.28
10.8
160
2.64
655
3.299
523.69
3-74
462
3-95
437
2-43
712
342
505
3-24
533
WROUGHT AND OAST IRON.
To Corja.pu.te "Weight of "Wro-ugflit or Cast Iron.
RuLK.— Ascertain number of cube inches in piece; multiply sum by .2816* for
wrought iron and .2607* for cast, and product will give weight in pounds.
Or, for cast iron multiply weight of pattern, if of pine, by from 18 to 20, accord-
ing to its degree of dryness.
Example. — What is weight of a cube of wrought iron 10 inches square by ij
inches in length?
10 X 10 X 15 X .2816 = 422.4 lbs.
COPPER.
To Compvite "Weiglit of Copper.
Rule. — Ascertain number of cube inches in piece ; multiply sum by .321 18,*
and product will give weight in pounds.
Slieatliing and. Braziers' Sheets.
For dimensions and weights see Measures and Weights, pages 118-121, 131, 142.
LEAD.
To Conaptite "Weight of I^ead.
Rule. — Ascertain number of cube inches in piece; multiply sum by .41015,*
ftnd product will give weight in pound&
Example. — What is weight of a leaden pipe 12 feet long, 3.75 inches in diameter,
and I inch thick 1
By Ride in MensureUion of Surfaces^ to ascertain Area ofOylindTtcal Rings.
Area of (3. 75 -f i -|- 1) = 25.967
" " 3-75 ="044
Difference, 14.923 (area of ring) x 144 (12 feet) = 2148.912
X -410 i5=B8i.376 lbs.
BRASS.
To Compute Vt^eight of Ordinary Brass Castings.
RiTLB. — Ascertain number of cube inches in piece; multiply sum by .2922,* and
iwoduct will give weight in pounda
* Weights of a cube inch as here (riven are for the ordinary metals; when, however, the epecific
wrtLrHkf Si the meUl tinder conalderatton U accurately known, the weight of a cobe inch of it uioold
Se eiiMtltated for the nits hare glran.
156 DIMENSIONS AND WJ5IGHTS OP BOLTS AND NUTS.
X>iziieiisioiis and. "Weiglits of "Wrotaglit Iron Solts
and N'nts.
SQUARE AND HEXAGONAL, HEADS AND NUTS.
R,o-ugli, and from, .25 Inch to 4 Inches in Diameter,
Sc|.xiare Jlead and Nnt.
Diameter
of Bolt.
Wid
Head.
Ith.
Nut.
Diagooal.
Head. Nut.
Depth.
Head. Nut.
Weight.
Head i Bolt
and Nut. Iper Inch.
Threads
per Inch.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
lus.
Lbs.
Lbs.
No.
.25
.36
•49
•SI
.69
.25
.25
.024
.014
20
•3125
.45
.58
•64
.82
•3
.3125
•043
.022
18
.375
.54
.67
•76
•95
•34
•375
.068
.031
16
.4375
.63
.76
.89
1.07
•4 '
•4375
.104
.042
14
.5
.72
.84
1.02
1. 19
•44
•5
•145
.055
13
.5625
.82
.94
1. 16
1-33
.48
•5625
.204
.07
12
.625
.91
1.03
1.29
1.46
.53
.625
.273
.086
II
.6875
I
1. 12
1. 41
1.58
.58
•6875
•356
.104
II
•75
1.09
1.21
1-54
1.71
.63
•75
•454
.124
10
.8125
1. 18
1-3
1.67
1.84
.67
.8125
•565
.145
10
.875
1.27
1-39
1.8
1.96
.72
.875
.696
.168
9
1
1.45
1-57
2.05
2.22
.81
I
1. 013
.22
8
1. 125
1.63
1.75
2-3
2.47
•9
1. 125
1. 416
.278
7
1.25
I.81
1.94
2.56
2.74
I
1.25
1.923
.344
7
1.375
1.99
2.12
2.81
3
I.I
1-375
2^543
.416
6
1.5
2.17
2-3
3.07
3-25
1. 18
1-5
3-234
•495
6
1.625
2.36
2.48
3-34
3-51
1.28
1.625
4.105
.581
5^5
1.75
2.54
2.66
3-59
3^76
1-37
'•75
5.087
•674
5
1.87s
2.72
2.84
385
4.02
1.46
^•875
6.182
•773
5
2
2.9
3.02
4.1
4.27
1.56
2
7.491
.88
4-5
2.125
3.08
3.21
4-35
4-54
1.65
2.125
8.936
•993
4^5
2.25
3.26
3-39
4.61
4-79
1.75
2.25
IO-543
1.113
4-5
2.375
3-44
3-57
4.86
5^05
1.84
2.375
12335
1.24
4.375
2.5
362
3-75
5-12
5-3
1.94
2.5
14-359
^•375
4^25
2.625
3.81
3-93
5-49
5.56
2.03
1 2.625
16.549
i^5i5
4
2.75
3.99
4. 1 1
5-64
5-8i
2.12
' 2.75
18.897
1^663
4
2.875
4.17
4.29
5-9
6.07
2.22
1 2.875
21-545
1. 818
3^75
3
4-35
4-47
6.15
6.32
2.31
'3
24.464
1.979
3-5
325
4.71
4.84
6.66
6.84
2.5
325
30.922
2.323
3-5
3-5
507
5-2
7.17
7-35
2.68
3-5
38.391
2.694
3-25
3-75
5-44
556
7.69
7.86
2.87
:3-75
47.168
3093
3
4
5.8
592
8.2
8.37
3.06
4
56.882
3.518
3
Finished. — Deduct .0625 from diameters of bolts and depths of alL heads
and nuts. For Steel BoltSf add z. 3 per cent.
Screws with square threads have but one half number of threads of those
wlUi triangular threads.
Note. — The loss of tensile strength of a bolt by cutting of thread is, for one of j. 25
ins. diameter, 8 per cent. The safe stress or capacity of a wrought iron boit and nut
may be taken at 5000 lbs. per square inch.
Preceding width, depth, etc., are for work to exact dim^isions, whether
forged or finished.
To Compute TVeiel^t of a Bolt and Nu-t.
Operation. — Ascertain from table weight of head and nut for given di
ameter of bolt, and add thereto weight of bolt per inch of its length, multi
plied by full length of its body from inside of its head to end.
Note. —Length of a bolt and nut for measurementy as such, is taken fVom inside
of head to inside of nut, or its greatest capacity when in position.
DIMENSIONS AND WEIGHTS OF BOLTS AND NUTS. 1 5/
Illustbatiov. — A wronght-iron bolt and nut with a square bead and nut is z incb
in diameter and lo inciies in length ; what is its weight?
bolt per inch of length .22
xio=;:r^ J 3.-3/6*
For Steel BoUs^ add 1.3 per cent
Sexagoixal IXead.
and Nut.
Dfaunetor
of Bolt.
wu
HMid.
Ub.
Nut.
DUgonal.
Head. Nut.
Head.
epth.
Nut.
Weig
Head
and Nut.
lbs.
lit
Bolt
per Inch.
Threads
per Inch.
lot.
Ins.
Ins.
Ins.
Ina.
Ii».
Ins.
Lbs.
No.
•25
•375
.5
.43
.58
•25
•25
.022
.014
20
•3125
•4375
.5625
.5
.65
.3
•3125
.037
.022
18
•375
.5625
.6875
.65
•79
.34
•375
.062
.031
16
•4375
.625
•75
.72
.87
.4
•4375
.094
.042
14
5*
•75
•875
.87
I
•44
5'
.134
-055
13
•5625
.8125
•9375
.94
1.08
.48
•5625
.18
.07
12
.625
.9375
1.0625
1.08
1.23
.53
.625
.249
.086
II
.6875
I
1. 125
I.16
1.3
.58
.6875
.318
.104
II
.75
1. 125
1.25
1.3
1.44
.63
•75
.413
.124
10
.8125
1.25
1-375
1.44
1-59
.67
.8125
.522
.145
10
.«75
1.3125
1-4375
1.52
1.66
.72
•875
•639
.168
^
I
1.5
1.625
1.73
1.88
.81
I
.931
.22
^
1.X25
1.6875
1.8125
1.95
2.09
.9
1.125
1.299
.278
7
1-25
1.875
2
2.17
2.31
I
1.25
1.759
.344
7
1-375
2
2.1875
2.31
2.53 i i-i
1-375
2.263
.416
6
1-5
2.25
2.375
2.6
2.74 1 1.18
1.5
2.958
.495
6
1.625
2.4375
2.5625
2.81
2.96
1.28
1.625
3.741
.581
5.5
1-75
2.625
2-75
3.03
3.18
1.37
1-75
4.654
.674
5
1.87s
2.8125
2-9375
3-25
3.39 ; 1.46
1.875
5675
•773
5
2
3
3.125
346
3.61 1.56
2
6.854
.88
4-5
«.I25
3-1875
3-3"5
3.68
383 1-65
2.125
8.163
.993
4.5
2.25
3-375
35
3.9
4.04 i 1.75
2.25
9.658
1. 113
4.5
2-375
35625
3.6875
4.11
4.26 1.84
2.375
11.263
1.24
4.37s
2-5
3-75
3-875
4.33
4-47 , 1-94
^•1
13149
1.375
4.25
2.625
3-9375
4.0625
4-55
4.69 2.03
2.625
15-15
1.515
4
2.75
4.125
4^25
4-77
4.91 { 2.12
2.75
17.285
1.663
4
2.875
4^3125
4-4375
4.99
5.12 2.22
2.875
19.751
1.818
3-75
3
4.5
4.625
5-2
5-34 2.31
3
22.378
1.979
3-5
3.25
4875
5
5.63
5-77
2.5
3.25
28.258
2.323
3-5
3-5
5.25
5.375
6.06
6.21
2.68
3.5
35.081
2.694
3-25
3-75
5.625
5.75
6.5
6.64 2.8/
3.75
43-178
3-093
3
4
6
6.125
6.93
7.07
i3-o6
4
51.942
3518
3
Finished. — Deduct .0625 from diameters of bolts and depths of all heads
and nuts.
For Wood or Carpentry,
Head and Nut- {Square)^ 1.75 diameter of bolt. Depth of Head^ .75, and
of Nut^ .9.
Washer. — ^Thickness, .35 to .4 of diameter of bolt, on Pine 3.5 diameter,
and Oak 2.5.
MoUtworth gives following elements of Tliread of Bolts :
A ngle of thready 55°. Depth of thread sz Pitch of screw.
Number of threads per Inch. — Square^ half number of those in angular
threads.
Depih of thread.— .6^ pitch for angular and .475 for square threads.
O
CjS DIMENSIONS AND WJSI6HTB OF BOLTS AND NUTS.
BYenoh. Standard. Solts and N"-ats. {Armengaud'§i
HEXAGONAL HEADS ANP NUTS.
EquUafei^cU Tnangular Thread,
Diameter
of Bolt.
Mm.
5
75
lO
12.5
15
175
20
22.5
25
30
35
40
45
50
55
60
65
70
75
80
Ins.
2
3
39
49
59
69
79
89
98
18
8
8
77
97
17
36
56
76
95
*5
er
II
Threads
per Inch.
Ina.
No.
.13 18.I
.22 16
.31 14.1
.39 12.7
.48 1 1.5
.58 10.6
66 9.8
.76 91
84 8.5
1.02 7.5
I 2 6.7
1.4 6
1-56 55
I 74 5.1
1.92' 4.7
2.08 4.4
2.26 4.1
2.44 3.8
26 35
2.78
3-4
Thickness.
Head.
Ins.
.24
3
•38
44
•5-2
58
.66
.72
8
94
1.08
1.22
1.36
1-5
1.64
I 74
1.92
2.06
2.2
2.34
Nat.
Ins.
.2
•3
39
•49
•59
.69
•79
.89
•98
1. 18
1.38
158
1.77
1.97
2 17
u
e
lllS.
.55
.68
.88
1.04
1.2
1.4
1-5
1.68
1.84
2.16
2.48
2.8
3-2
3-44
376
2.36 408
2.56 4.4
2.76 4.7
2-95 5
3-15 1 5-35
d.
Safe
Tensile
Streas.
Diameter
of Bolt.
Lbs.
Mm.
ina.
44
20
•79
99
25
.98
178
30
1. 18
277
35
1.38
400
40
1-57
545
45
1.77
713
50
1.97
902
55
2.17
X 120
60
2.36
1635
65
2.56
2218
70
2.76
2912
75
2-95
3674
80
315
4547
85
3-35
5288
90
3-54
6540,
95
3-74
7660
ICX)
394
8893
105
4-13
10 214
no
4-33
II 468
"5
4-531
Square Thread,
OH
I116.
n
•a *-
HS.
No.
072 6.57
081 '5.97
093
06
14
28
3
4
5
58
66
74
83
92
2
209
22
226
23
iS-4
4-93
4-53
4.2
3-91
3-65
3 43
323
3.06
2.92
2.76
2.63
2.51
2.41
2.31
2.22
2.13
2.06
2..
B a
Safe
•fas
Tansila
S's
Stress.
hu.
Lbs.
1.82
717
2.01
I 142
2.22
^(>:iS
2.41
2218
2.63
2912
2.85
3674
3.07
4547
33
5288
3-5
6540
3-7
7660
392
8893
4-13
10214
4-36
II 601
4.58
13 100
4.78
14794
5
16352
5.22
18 144
5-43
20CX)0
5.66
21950
5.87
23990
Knglisl:! IBolts and 3^^latB. {Whitwwth's.)
Hexagonal Heads and .N'uts, and Triangular Tlireads.
Diameter.
Bolt.
las
187s I
2187,
25 I
3125 i
375 I
4375
5
5625
62 s
.6875
•75
.8125
^75
•9375
I
1. 135
Inch.
•093
•134
.t86
.241
.295
.346
•393
•456
.508
•571
.622
.684
•733
.795
.84
.943
No.
40
24
24
20
18
16
14
12
12
II
II
10
10
9
9
8
7
Depth.
Width
of
Head
Head.
Nat.
and
Inch.
Nat.
Ins.
Ins.
.109
.125
.338
.164
.1875
•448
.219
•25
•525
•273
•3125
.601
.328
•375
.709
•383
•4375
.82
•437
•5
.919
•492
.5625
1. 01 1
•547
.625
I.IOI
.6oi
•6875
1. 201
.656
•75
I. 301
.711
.8125
1.39
.766
•875
1.479
.82
•9375
IS74
•875
I
1.67
.984
1. 135
1.86
Diameter.
Base
Bolt.
of
Thread.
Ins.
Ins.
125
1.067
1-375
1. 161
1-5
1.286
1.625
1.369
1-75
1.494
1.875
1-59
2
1-715
2.125
1.84
2.25
1-93
2.375
2.055
25
2.18
2.625
2.305
2-75
2.384
^•87S
2.509
3
2.634
3-25
2.84
3-5
3.06
M
Dei
>th.
Width
of
S 0
Head
No.
HMd.
Nut.
and
Nat.
Ins.
Ins.
Ina.
7
1.094
1.25
2.048
6
1.203
1-375
2.213
6
1.312
1-5
2413
5
1.422
1.625
2.576
5
1^531
1-75
2.758
4-5
1. 641
1-875
3.018
45
175
2
3.149
4-5
1.859
2.125
3-337
4
1.969
2.25
3.546
4
2.078
2.375
3-75
4
2.187
2.5
3-894
4
2.297
2.625
4.049
3-5
2.406
2.75
4.181
3-5
2.516
2.875
4346
3-5
2.625
3
4.53*
325
—
—
—
3.25
—
—
—
RETENtlON OF SPIKES AND NAILS.
'59
Square Keeds and Nnts. {WhUvMrth^i.)
Diameter.
Bolt
Base of
Thread.
Ina.
3-75
4
425
Int.
3-5
3-75
Tbrwidft
per loch.
No.
3
3
2.875
Diameter.
Bolt.
Bum of
Thread.
ins.
4-5
4-75
5
Ina.
3.875
4.0625
4.25
Threads
per Inch.
II
No.
2.875
2.75
2.75
Bolt
Diameter.
Ba«« of
Ins.
525
5-5
6
ThruaJ.
Il'S.
4-4375
4.625
4-875
Threada.
per Inch.
No.
2.625
2.625
2.5
Weiglit of Heads and Nuts iix l^lyn. {Motes 'cm-th.)
[LroffOiuU, 1.07 D3, Square, 1.35 D^ D repreierUing diameter ofboit
in inches,
Retentivenfess of Wrought Iron Spikes and. N"ails«
Deduced from Experiments of Johnson caid Bevan.
■ SPIKES.
SriKB.
Square
• • • •
^ • • • •
« *
• • • •
Flat narrow. .
ii t(
u
ii
ti
broad . .
ii
Square) ^^
Round and)
grooved. . j
Wood.
ii
i(
Ilejnlotkt
(!hestnut
Yellow pine
White oak
Locust
(Jbestnut
White oak
Locust
Chestnut
White oak
I..ocust
Heralockf
Chestnutf
L(x:u8tt
A»h
»i
White oak
* Barden'a patent.
Inn.
-39
-37
•375
•375
•4
•39
•39
•39
•539
•539
•539
•4
•4
Diam.
i(
it
5
§•
0
^8
Ins.
Ina.
•3
•38
3-5
3-5
•375
3-375
•375
3375
-4
3-5
•25
3-5
•25
3-5
•25
.288
.288
35
3-5
3-5
3-5
•39
3-5
•39
3.5
•39
3-5
•5
3-5
•5
.48
35
3-5
• » >
fc.fel
O 3 u
Lhii.
1297
1873
2052
3910
5967
2223
3990
5673
2394
5330
7040
1638
1790
3990
2052
2451
3876
o5«i
9t u V
2^ »
RlMAIlKS.
1.58
2.16
2.37
4-52
6.33
3-93 i
7-05
9-32 I
2.66 ;
5-71
7-84
1-75
1.81
4.17
2.21
2.41
3-2
Seasoned in part
Unseasoned.
Seasoned.
ii
ii
Unseasoned.
Seasoned.
Ik
Unseasoned.
Seasoned.
ii
Seasoned in part.
Unseasoned.
Seasoned in part
Seasoned.
li
it
t Soaked io water ai'ter the spike* were driven.
NAILS.
Depth of
iuMrtion.
Force required to draw it.
Nail.
Length.
Pine.
Hemlock.
Lbs.
Elm.
Oak.
Lbs.
BeerJi.
Ins.
Ina.
Lbs.
Lbs.
Lbe.
Sixpenny,
2
X
187
31^
327
507
667
it
2
1-5
327
539
571
675
889
ii
2
2
530
857
899
139*
1834
Pressure r«qnired
to force them
into Pine.
Lbs.
235
400
610
Oeuoral RexnarUs.
With a given breadth t»f face, a decrease of depth will increase retention.
In Mitt woods, a blunt-pointed spike forces the fibres downwardii an.i
backwards so as to leave the fibres longitudinally in contact witli the faces
of the spike.
S60 ANGLES AND DISTANCES. — ^DISTANCES AND ANGLES.
To obtain greatest effect, fibres of the wood should press faces of the spike
in direction of their length ; thus, a round bluut bolt, driven into a hole of
a less diameter, has a retention equal to that of any other form, when wholly
driven, as without boring. * •
The retention of a spike, whether square or flat, in unseasoned chestnut,
from two to four inches in length of insertion, is about 800 lbs. per square
inch of the two surfaces which laterally compress the faces of the spike.
When wood was soaked in water, after spikes were driven, order of their
retentive power was Locust, White oak, Chestnut, Hemlock, and Yellow Pine.
Diameter in Inches. .
Threads per Inch . . .
Gra£
.125
28
J I*ipe Tlireads.
•25 .375 -5 .75 I
19 19 14 14 II
1.25
II
1-5
II
1.75 2
11 II
ANGLES AND DISTANCES.
A.ngleB and J^i stances oorresponding to Opening of a
Rvile of Two Feet.
Angle.
DitUoce.
0
Int.
I
.2
2
3
4
.42
.63
.84
5
6
1.05
1.26
7
8
9
1.47
1.67
1.88
10
2.09
II
2-3
12
2.51
13
2.72
14
2.92
15
16
3-13
3-34
17
18
3-55
3-75
Angle.
DIetaBM.
Angle.
0
In*.
0
19
396
37
20
4.17
38
21
4-37
39
22
458
40
23
4.78
41
24
4-99
42
25
5.19
43
26
5-4
44
27
5.6
45
28
5.81
46
29
6.01
47
30
6.21
48
31
6.41 '
49
32
6.62
50
33
6.82
51
34
7.02
52
35
7.22
53
36
7.42
54
DUtwice.
Angle.
Distance.
Angle.
Dbtanee.
Ins.
0
Ins.
0
Ins.
7.61
55
11.08
73
14.28
7.81
56
11.27
74.
14.44
8.01
57
"•45
75
14.61
8.2
58
11.64
76
14.78
8.4
59
11.82
77-
14.94
8.6
60
12
78
15.11
8.8
61
12.18
79
1527
8.99
62
12.36
80
»5-43
9.18
63
12.54
81
1559
938
64
12.72
82
1575
9-57
65
12.9
83
»5»9
976
66
1307
84
16.06
995
67
13-25
85
16.21
10.14
68
13.42
86
16.37
»o-33
69
1359
87
16.52
1052
70
13-77
88
16.67
10.71
71
1394
89
16.82
10.9
72
14.11
90
16.97
Distances and A.ngle8 corresponding; to Opening* or a
R,nle of Two Feet.
[MsUnce.
Angle.
DisUnee.
Int.
0
Ins.
.25
1. 12
3
•375
1.48
3-25
•5
2.24
35
.625
2-59
3-75
.75
3-35
4
.875
4.12
4.25
/
4.48
4-5
125
558
475
1-5
71
5
1-75
8.22
525
2
934
5-5
2.25
10.46
5-75
a-S
11.58
6
2.75
I3-*
6.25
o
14.22
15-34 i
16.46
17-58,
19.11
20.24
21.37
22.5 I
24-4 j
25.16 I
26.3 I
27.44
28.58
30.12
DUUnce.
Angle.
Ins.
0
6.5
31.26
6.75
334
7
33-54
7^25
35-09
7.5
36.24
7-75
37-4
8
38.56
8.25
40.12
8.5
41.28
8^75
42.46
9
44.2
9-25
45-2
95
46.38
9-75
47-56
Distance.
Angle.
DIstMice.
Angle.
Ins.
0
Ins.
0
10
49.14
13.5
68.28
10.25
50.34
13-75
6954
10.5
51-54
14
71.22
10.75
5314
14.25
72.5
It
54-34
14-5
74-2
11.25
55-54
14-75
75-5
"•5
5716
15
77.22
"75
58.38
15-25
78.54
12
60
15-5
80.28
12.25
61.23
15-75
82.2
12.5
62.46 ,
16
83.36
1275 ,64.1
16.25
85.14
13 65.36 1
16.5
86. sa
13-25
67.03 1
16.75
88.3a
wots iu^M. iOi
WIRE ROPE.
Wire rom will run oyer sheaves of like diunflter to Hemp rope of same
stoength ; but larger sheaves reduce wear. Adhesion is the same as that of
kemp rope. Wear increases r;ipidly with speed. Short bends should foe
avoided. In substituting wire rope tar hemp, allow same weight per foot.
Kinking wire rope materially damage^ and often destroys it.
For transmission of power, wire rope can foe us^ up to distances of 3
miles. For distances lees than 100 feet, it is not advised for long trans-
mission; sheaves are placed at intervals, dividing it into a number of
shorter ones of 250 to 300 feet.
Strength per square inch of section of rope is about 50 p£r cent of an
equal section of polid metal of same strength per squMre inch.
Stationary wire fopes should be kept weU painted or taned to prevent
their oxidation. Running ropes should always be well lubricated and pro>
tected from grit with Unseed-oil, pine tar,gniphjlte grease, or any similar
non-acid substances.
Standard wire rope is made of 6 strands of 7, 12, or 19 wires each, with
hemp or wire centre. Wire centre adds 10 per ce^t. to streng^ and wejght
<tf rope, but reduces its flexibility proportionally.
tSafe working load for standing ropes is about one fourth tdtimate strength,
and for running ropes it is from one fifth to one seventh.
Ropes for hoisting are composed of 6 strands of 19 wir^ each around a
hemp centre.
Ropes for transmission of power, for guys and rigging, are <x>mposed of
6 stranda of 7 or 12 wires each.
The ultimate strength of wires of which wire ropes are made are for:
Iron wire. 70000 to 900Q0 lbs. per s^. Inch ; Bessemer steel wir^ 100 000 to
iio<xx) 1m.; Cwclfolfi cast "Steel wire, 150900 to 180000 lbs., itnd Special
plough-steel wire, 210000 to 300000 lbs.
Special ropes can be made ^f 4, 6, 8, etc., strands of varied construction.
Wire ropes are also made flat, composed of sei\'eral strands alternately
twisted to right and left, laid alongside each other, and sew^ together
with floft iron wire.
Wire hawsers of steel are made of 6 strands of i;» wires each with hemp
centre,~around a common hemp centre, and are as ^exibie as hemp liawsers
of equal strength.
Galvanized wire rope replaces hemp for rigging, becfuise /of its cheapneea,
durability, and resistance to stretch. It is one fifth bulk rfor equal strepgth
of Jmiii|) rope, and offers less surlaoe to wind.
TUler rqpes ^or vessel-steering gear are made of 0 smaller ropes around
a hemp centre, each small rope composed pf 6 strands of 7 wires each with
hemp oentfe— 253 wires in all in the rope, giving great flexibility.
Tacbt rigging oi galvanized castisteel rope is one third to one Wi weight
of Iron wire rope of eqnal strength.
1 62
WIBB BOPSS.
Kleznents of* Hoisting and Haulage "^^ire liope.
John A. Roebling^s Sons Co.^ Trenton, N. J.
HOISTING ROPE. 19 Wii'es in a Strand. Hemp Centre.
Swedish Iron.
Diameter.
Ins.
2.25
2
«-7S
1.625
1-5
1-375
X.25
1. 125
.875
.75
.625
.5625
.5
•4375
.375
.3125
•35
ApproZ'
miate
Circum-
ference.
lus.
7-125
•25
•5
Weight
per
Foot.
Tons of 20cx> Lbs.
Breaking ) Safe
Strain.
Strain.
Lbs. No.
8 78
6.25 6.31 62
5-5 4'85 48
5 4- IS 42
4.75 3-55 36
4.25 3 3*
4- 2.45 25
3-5 2 21
3 i-S8 17
2.75 i'2 13
2.25 .89
2 .62
>-75 -5
1-5 .39
I. 25 .3
I.Z25 .22
I .15
• 75 .1
Transmission
1:1
5-5
4-4
3-4
2.5
1-7
X.3
Least
Diameter
of Drum
or Sheave.
7 Wires in a Strand. Hemp Centre,
No. Feet. No. No.
X5.6 X3 X56 31.2
X2.4 X2 X24 24.8
9.6 xo 96 19.2
8.4 8.5 84 x6.8
7.2 7.5 72 X4.4
6.2 7 62 12.4
S 6.5 50 xo
4.2 6 42 8.4
3-4 ' 5-25 34 6.8
2.6 4.5 26 5.2
r.94 4 19.4 3.88
*'36 3'5 i3'6 2.72
x.x 2.75 IX 2.2
.88 2.25 8.8 X.76
.68 2 6.8 1.36
•5 1-5 5 I
• 34 I 3-4 -68
.24 -75 2.4 .48
and Hanlage Kope.
Brealiing
Strain.
Gast-Stkel.
Least
Diameter
Tons of 3000 Lbs.
Safe
Strain.
of Drum
or Sheavie.
Feet
85
8
7
6.
25
25
75
5
5-
5-
5
4-5
4
3-5
3
2.25
1.75
125
.667
•5
Noi-^.— Add 10 per cent, to weight for itibk cbnt&b.
SWKDIi
311 Iron.
Cast-Stbei..
Diameter.
Approx-
imate
Cirenm-
Weight
Foot.
Tons of 2
Breaking
000 Lbs.
Safe
Least
Diameter
of Drum
Tons of s
Breaking
looo Lbs.
Safe
Least
Diameter
of D)-|im
ference,
Strain.
Strain.
or Sheave.
Strain.
Strain.
or Sheave.
Ins.
Ins.
Lbs.
No.
No.
Feet.
No.
No.
Feet.
1-5
4-75
3-55
34
6.8
13
68
13.6
!'5
1-375
4.25
3
29
S-?
X2
58
XI. 6
8
1.25
4
2.45
24
4.8
10.75
48
9.6
725
X.125
3-5
2
20
4
2-5
40
8
6.25
X
3
1.58
x6
3-2
8.5
32
6.4
5-75
.875
2.75
1.2
X2
2.4
7-5
*4 .
4.8
5
•75
2.25
.89
9-3
X.86
6-75
t8.6
3-72
4-5
.6875
2.125
•75
Z'2
X.58
6
X5.8
3.16
4
.625
2
.62
6.6
1.32
5-25
13.2
2.64
3-5
.5625
"•75
•5
5^3
i.o6
4.5
X0.6
2.12
3
•5
1-5
•39
4.2
.84
4
8-4
X.68
2.5
•4375
1^25
•3
3-3
.66
3-25
6.6
1.32
2.25
.375
x.125
.22
2.4
•48
2.75
4.8
't
2
• 3125
X
.15
1.7
•34
2.5
3-4
.68
«-75
.28x3
•875
.125
X.4
.28
2.25
2.8
.56
1.5
Approx*
unate
Diam-
eter.
Gralvanized Charcoal Iron Wire Rope.
Vessels* H,iggiiig eind Derriolt Q-viyn.
7 or 12 Wires in a Strand. Hemp Centre.
Breaking'
Strain
in Tons
of 3000
Lbs.
lot. '
"•75
X.6875
1.625
'•5
'•4375
I.375
Breaking
Cirt-um.
Circum-
ference.
Weight
Strain
of Manila
Foot.
in Tons
of 2000
Rope of
Equal
Lbs.
Strength
Ina.
Lbs.
No.
Ins.
5.5
4.85
44
XX
5-25
4-4
40
X0.5
5
4 ^
36
xo
4.75
3-6
32
9-5
4.5
3-25
29
1.5
4.25
2.9
36
Approx-
imate
Diam-
eter.
Circum-
ference.
Weigiit
Foot.
Ins.
Ins.
Lbs.
1.25
1.1875
4
3.75
2.55
2.25
1.125
1.0625
3-5
3-25
1^95
'•7
X
•87s
3
2^75
x.44
X.3X
No.
23
20
18
15
13
xz
Circum.
of Manila
Rope of
Equal
Strength.
Ina.
8
5
5
75
as
WIEB BO PXS, HAWSERS, AND CABLES.
163
Gralvanissed Clxarooal Iron '^Vix*e Rope*
Vessels' Rigging and X>erriok &xiytt.
John A, Roebling^s Sons Oo.j Trenton^ N. J.
7 Wires in a Strand.
Approx-
imate
- Diam-
eter.
Ins.
.8125
•75
• 625
.5625
•5
•4375
Approx-
imate
Diam-
eter.
Circum-
ference.
Ins.
3-5
3.25
2
'•75
x.S
1.25
Weight
per
Foot.
Breaking
Circum.
Strain
of Manila
in Tons
Rope of
of XK»
Equal
Lba.
Strenirth.
No.
Ins.
9
5
7*1
5.8
4-75
4-5
4-4
3.75
3-2
3
2.3
a. 5
Lba.
X
.81
.64
•49
.36
.25
Gralvanissed Steel Hawsers.
S^or Sea and X^alse To-wiiig.
Breaking
Circum.
Approx-
Weight
Strain
ofManila
imate
Diam-
Circnm-
ference.
^t.
in Tons
of aooo
Rope of
Equal
eter.
Lba.
Strength.
Ina.
Ina.
Lbs.
No.
Ins.
•375
1.125
.2
1.8
3.25
•3125
X
.x6
1^4
3
.28x2
.875
.123
x.x
«.75
•^5 .
•75
.09
1^5
1-5
.2188
.625
.003
I56
1-25
.1875
•5
.04
•36
X.X25
Ins.
X.75
1.6875
1.625
1.5
Circum-
ference.
Ina.
5-5
5^25
5
4-75-
Breaking
Circnm.
Breaking
Circnm.
Weight
Strain
ofManila
Approx-
Weight
Strain
ofManila
fQt.
in Tons
Rope of
imate
(Hrcnm-
foot.
in Tons
Rope of
of aooo
Equal
Diam-
ference.
of aooo
Equal
Lba.
Strength.
eter.
Lbs.
Strength.
Lbs.
No.
Ina.
Ins.
Ins.
Lbs.
No.
Ins.
3.25
6x
'3-5
>-4375
4-5
3.18
42
11-5
2.95
57
«3
1-375
4-25
1.94
39
XI
2.7
53
12.5
X.25
4
1.72
32
10
2.43
45
X2
1-1875
3-75
1.51
29
9-25
G^alvanized Steel Cables for Suspension Sridges.
Diam-
eter..
Weight
J^t.
Ins.
2.75
2.625
2.5
Lbs.
XI. 6
,xo.5
Breaking
Strain in
Tons of aooo
Lbs.
No.
310
283
256
Diam-
eter.
Weight
^ol.
Ins.
2.375
2.25
2.125
Lbs.
7.6
Breaking
Strain in
Tona of aooo
Lba.
Diam-
eter.
Weight
^t.
No.
232
. 208
185
Ins.
1.875
1-75
Lbs.
6.73
5.9
5-1
Breaking
Strain in
Tona of aooo
Lbs.
N^l
164
144
124
Graujge, Weiglit, and X^engthi of Iron 'Wire.
i
9
Diam.
m
0
No.
Inch.
6/0
■46
5/0
.43
4/0
•393
3/0
.362
2/0
•331
1/0
.307
1
.383
2
.263
3
-244
4
.335
5
.307
6
.193
7
.177
8
.163
9
.148
xo
•»3S
XX
.12
12
.X05
»3
14
T
«S
.073
Weight
Weight
per 100
of one
Feet.
Mile.
Lbs.
Lbs.
56.1
3963
49.OX
3588
40.94
2163
34.73
1834
29.04
1533
37.66
1460
21.23
1 131
18.34
€
15.78
13.39
707
11-35
599
9-73
8.03
514
439
6.96
367
1.08
,06
4.83
255
3.82
203
3.93
'5*
3.34
118
1.69
89
«-37
73
63 lba.
Bnndle.
Area.
0
Diam.
Feet
Sq. Inch.
No.
Inch.
XI3
.x66 19
x6
.063
129
•14522
17
.054
'i^
.121304
18
•047
x8x
.102921
19
.041
217
.086049
20
•035
228
.074023
31
.032
296
.062 90X
23
.028
343
•054325
23
.025
399
.046759
24
.023
470
.03976
25
.03
555
•033653
36
.018
647
.038952
27
..0x7
759
.024605
28
.016
90s
.030612
29
.0x5
1086
.017203
30
.014
1304
.0x4313
31
.0x35
1640
2158
.ox I 309
32
.0x3
.008659
33
.oxz
2813
.006647
34
.ox
3728
.005026
35
-0095
4598
.004071
36
.009
Weight
per 100
Feet.
Lbs.
X.05
.58
•45
•32
•27
.31
•17s
.1x6
.003
.083
.074
.o6x
.054
.040
.037
-03
.025
.03X
Weight
of one
Mile.
Lba.
55
41
3«
24
17
14
XI
9.24
739
6.124
4.91
4.382
3907
3.22
2.851
3.64
3.428
«-953
1.584
1.32
1. 161
63 lba.
Bundle.
Feet.
6000
8182
10862
14000
19687
23333
30000
36000
45000
54310
67742
75903
85135
X03 278
X 16 666
126000
136956
1 70 370
2IOOOO
252000
286 363
Area.
Sq. Inch.
003x17
.00229
001 734
.oox 32
• 000962
.000804
.0006x5
000491
000415
000314
000254
000227
.000201
.000 176
000154
000x33
000x33
000095
000078
000071
1.000064
I64
IBON, STESJjy AND HBMP BOPB.
'Weight and Strenetli of* Single Strand and Cable
laid :F'enoe 'Wire. {F. Mortomi Co.)
StraadA.
No.
No.
3
2A
4
2
7
I
7
O
flgl
or«qaal
Diametar.
No.
8
7
6
5
Inch.
•159
.174
.191
.2C9
Lcoftih
per xooo lbs.
Ofa
Of
Strands.
No.
Strand.
Rop«.
Feet.
Feet.
No.
20090
15270
7
00
14730
12790
7
3/0
13 125
JO 580
7
4/0
10446
8928
7
5/0
Sinffle Wire
of equal
Diameter.
No
4
3
2
I
Inch.
.229
•25
.274
•3
Length
per 1000 Ibc.
Ofa
Of
Strand.
Rope.
Feet.
Feet.
8300
1:^
8036
6228
7SOO
5156
5090
4286
No. and diameter of wire is that of Ryland^s Bros., pp. 122-4.
Hemp, Iron, and Steel. {B. S. NewM A Co,)
ROUND.
HXMP.
Clrcainfereaca.
Fns.
3.75
3-75
4.5
5.5
6
6.5
7-5
8
8.5
9-5
xo
XX
19
4 X
5 X
5-S X
5-75 X
6 X
7 X
8.25 X
8.5 X
9 X
9-5 X
10 y
VT f 1- A
HON.
nr 1 \-M.
8TIBL.
ATeight
Foot.
Circumference.
Weight
Circamference.
Lbi.
In».
Lbs.
Ins.
•33
I
.16
—
1-5
.25
X
.66
1.625
.33
—
i^75
,42
1^5
.83
1.875
.5
—
3
.58
1.625
1.16
2.125
.66
1-75
2.25
-75
—
1-5
2-375
.83
1.875
1
2-5
.92
...
1.66
2.625
I
2
2-75
1.08
2.125
2
2.875
1. 16
3.25
J
1.25
—
^•33
3-125
1-33
2-375
325
1. 41
—
2.66
3-375
1.5
2^5
3-5
1.66
2.635
3
3^625
1.83
2.75
3-75
a
—
3^66
3.875
2.l6
3-25
4-33
4
2-33
—
4-25
2.5
3-375
5
4375
2.66
—
4-5
3
3.5
5^66
4.625
3-33
3-75
FLAT.
.5
3-33
i-aS
4
1-375
4.33
1-5
4-66
1-5
5
1-875
6
3.125
6.66
a.35
7.5
2-5
8.33
2-375
916
10
a-S
DlinensioiM.
2.35
2.5
2.75
3
3-35
3-5
3.75
4
4.2s
4-5
X.5
1.85
X.5
2.16
X.625
2-5
X.625
2.66
X.625
3
X.625
3-3^
X.6875
1.66
X.6875
4.16
X.75
4.66
X.75
5-33
X.75
S.66
DlmensloiM.
2 X.5
a.25X.5
2.25 x.5
2.5 X.5
2-75 X. 375
3 X.375
3.25 X. 375
3.5 X.375
Weight
TensiM 2
Safe
Boot.
. Lowl.
Lbs.
Lba.
—
672
.16
1008
—
?344
.25
1680
2016
•3.1
235a
.42
2688
—
3024
•5
3360
—
3696
•58
4032
.66
4368
•75
4704
—
5040
•83
5376
-^—
5672
.93
6048
I
6720
1.08
739»
—
8064
1-33
8736
^^^
9408
1-5
10080
—
10752
1.66
12096
3
13440
—
4928
—
5824
—
6720
1.66
7168
1.83
8064
2
8960
2. 16
9850
2-5
II200
2^
13 544
3
14336
3^23
15 332 1
UltimaU
Strength.
Lh«.~
4480
6720
8960
xiaoo
13440
15680
17930
20160
22400
24640
366S0
29120
31360
33600
36840
38080
40320
44800
49280
53760
58240
62720
67300
71680
80640
89600
44800
51530
60480
62 720
71680
80640
89600
100800
112 OQO
125440
134409
RdPES AND CHAINS.
165
Ultimate Strengtlx and Safe ILioade of* IXemp, Iron,
and Steel.
Hemp .
Iron . . .
DIUmaU
Strongth
per Lb. Weight
per Foot.
Lbg.
15000
22000
Safc Load
per Lb.
Weight
per Fw>t.
Lbs.
4550
5000
per Square
of Circum.'
in Inebea. I
Lb*. •!
100
600
Steel
Ultimate
Strength
per Lb. Weight
per Foot.
{
Lhfl.
30000
45SOO
Safe Load
per Lb.
Weight
perFwt,
Lba.
C60OO
(5000
pe/Square
ofCircnm.
in Inches.
Lba.
1000
1300
PLOUGH 8TEKL FLAT MINING ROPES.
John A . Hoebling's Sons Co.^ New York,
width.
TUekneaa.
Ids.
Ina.
2
•375
3.5
•375
3
•375
3-5
.5
4
•375
4
•5
4.5
•375
4-5
.5
5
•375
5
•5
Weight
per Foot.
Ultimate
Strength.
Lbs.
1. 19
1.86
2.32
2.97
2.86
3-3
3.12
4
3-4
4.27
For CaBt-Steel Flat Ropes
Hopes and
Width.
Thiclcn'wa.
Weight
per Foot.
[JItimaU
Strength.
Ins.
Ina.
Lbs.
Lba.
5^5
•375
3-9
156000
5-5
•5
4.8
193000
6
•375
4-34
173000
6
•4375
4^5
160000
6
•5
5.1
210000
6.5
•5
5^5
224000
7
.5
5-9
238000
1 7.5
•5
6.25
250000
8
.5
6.75
270000
Lba.
63000
74000
93000
118000
II4OOO
130000
125000
160000
125000
170000
see page 1029.
Cliaiiis or £j<iu.al Strength,
Diameter
of
Iroa Chain.
Ins.
.218 75
•25
.281 25
•3125
•375
•437 5
.46875
•5
.625
•6875
•75
.875
•937 5
1^)625
1.125
1.25
'•375
1-5
1.625
'•75
CIRCUM PBRSNCK.
Heinp
Rope.
t
Ins.
2.75
3
3-5
4.25
45
5
5.5
575
6.75
7^75
875
9-75
10.5
"•75
12.75
H-75
15-25
15.75
1775
195
Crucible
Steel
Rope.
Charcoal
Iron
Rope.
WEIGHT PER FOOT.
Ina.
I
1.26
1^45
1^57
1-77
1.96
2.36
2.75
2.95
3^i4
353
3-93
432
4.71
4.81
5^1
5.8
6.35
Ilia.
I
1.18
139
1-57
1.77
1.97
2.19
2.36
2.75
314
3.53
3-93
432
4.71
5-1
5-5
5.89
6.28
7.07
7.85
steel
Rope.
II
Lbs.
.17
.25
•3
•35
•45
•59
.85
I.I
1.28
M5
1.83
2.33
2.98
3.58
365
4.04
565
6.S
Hemp
Rope.
Lba.
•34
.46
.67
•75
.83
1.16
1.2
1.6
2
2.65
335
4.6
4.92
5.83
6.2
8.7
9
10. 1
137
16.4
Iron
Chain.
Lbe.
•5
.65
.81
.96
1.38
1.76)
2.2
2.63
4.21
483
5.75
7.5
9.33
10.6
1 1.9
145
17.6
20
22.3
24.3
Safe
Load.
By ezperimeDte of U. S. Navy, hemp rope of this circun^ference ha* a
Vftif^ 0/71 309 lbt.f and a wire rope 0/5-^ in§. ha^s eqttiwi^t iirffW^
Tons.
•3
•4
•5
.6
.8
I
1-3
1.5
2.3
3-1
38
4.8
5.9
7
8.2
9-5
II
12.5
15.9
19.6
breaking
i66
WEIGHT, STBESS, AND TENSION OF BOPES.
"WeigUt of Hexup and "Wire Rope. (Molesioorth,)
In Lbs. per Fathom,
Circum- Hbmp.
Good.
Lbs!
6
7 26
864
10.14
11.76
1536
1734
1944
24
3456
54
Xo Compute Stress upon, a Ftope set at an Inclination.
Rule. — Multiply sine of angle of elevation by strain in lbs., add an allow-
ance for rolling friction and weight of rope, and multiply by factor of safety.
Factor of safety.— 'E or standing rope 4, for running 5, and for inclined
planes from 5 to 7.
Illustration. — Inclination of rope 02.5 feci in 100, velocity 1500 feet per minute,
and strain 2000 lbs. ; what should be diam. of iron rope, 7 wires to a strand ?
Angle of ^2.5 feet in 100=430, and sine of 43° = . 682. .682 X2ooo= 1364, to
which is to be added rolling friction and weight of rope, assumed to be 11 ; hence,
1364-4-11 = 1375.
Factor of safety assumed at 6, consequently 1375 X 6 = 8250 lbs. , capacity or break-
ing weight or stress of rope.
By table, page 162, 8200 lbs. is breaking weight of a wire rope of 7 strands, .625
tncA' in diatn.
Clrcnm-
Hbmp. |
WlRB. \
Circum-
Hb
tiar«nc«.
Conunon.
Good.
Iron.
Steel.
ference.
Common.
IDB.
Lbs.
Lbs.
Lbs.
Lbs.
Ins.
Lbs.
I
.18
.24
.87
.89
5
4.5 '
1-5
•41 .
.54
. 1.96
2
55
5-45
I 75
•55
.74
2.66
2.73
6
6.48
2
.72
.96
348
3-56
6.5
7.61
2.25
•91
1.22
4.4
4-51
7
8.82
2-5
113
I -5
5-44
5-56
7-5
10.13
2-75
1.36
1.82
6.58
6.73
8
11.52
3
1.62
2.16
7.83
8.01
8.5
130S
325
1.9
2.54
9.19
9.4
9
14.58
3-5
2.21
2.94
10.66
10.9
10
18
3-75
253
338
12.23
12.52
12
26
4
2.88
3.84
13.92
14.24
15
40.52
Xo Compute Tension of a Hope.
W
— = ^. 9 representing velocity of rope in feet per minute^ H* horses* power,
and t tension in lbs.
Illustration.— Assume wheel 7 feet in diameter, revolution 140 per minute, and
H* as per preceding table, 29.6.
^^ .9.6x33°°° ^97gjgg^ a^
7X3- 1410 X 140 3079
To Compute Operative Defleotion of a Rope.
= rf. D representing distance between centres of wheds or drums in
feet, w freight of rope in feet per Ib.^ t tension^ or poroer required to produce
required power or tension of rope when at rest., and d deflection in feet,
Illdstration.— Take elements of preceding case: diam. of wire rope of 7 strande
=7,5625 inch, and by table, page 162, 10 = .41 lb. , and D = 300 fidet
Then y^^-^^ = ,0.87 feeL
10.7 X 317-3
Capacity,^-A.t the Falls of the river Shine there is a wire rope in operation
that trangmits the power of $90 horses for a diijtftnce exceeding ope toUo,
TRANSMISSION OP POWJKE AND EQUIVALENT BELT. 1 6/
Sndless Hopes.
Wire Ropes, when practicable and proper for application, can be used for
transmission of power at a less cost than belting or shafting.
51
Feet.
4
4
4
4
5
5
5
5
6
6
6
6
► S a
Transmission, of* I'o'wer.
8o
lOO
I20
140
80
100
120
140
80
100
120
140
80
1^
M
|1
0 _ 0
SS.S
5"S
x^
5*8
Feet.
OS -IS
Ins.
.375
3.3
7
100
•375
4.1
7
140
.375
5
8
80
•375
5.»
8
100
•4375
6.9
8
140
.4375
8.6
9
80
.4375
10.3
9
100
•4375
12.1
9
140
•5
10.7
10
80
.5
13.4
10
100
.5
16. 1
10
140
.5
18.7
II
80
.5625
16.9
1 "
lOp
'' Ins.
.5625
.5625
.625
.625
.625
.625
.625
.625
.6875
•6875
■6875
.6875
.6875
TVire Rope and Eqnivalent Selt.
Horse
Power.
Feet.
Revolu-
tions per
Minute.
Diameter
of Rope.
Ins.
21. 1
II
140
.6875
29.6
12
80
•75
22
12
100
.75
27.5
12
140
.75
38.5
13
80
•75
41.5
13
100
.75
51.9
13
120
•75
72.6
14
«n
.875
58.4
H
100
•875
73
14
120
.875
102.2
15
80
.875
75.5
15
100
.875
94.4
15
120
.875
Kta
132-1
99-3
1 24. 1
173.7
122.6
153.2
183.9
I4«
176
222
217
259
300
In substitnting wire rope for an ordinary flat belt, the diameter is aeter-
mined by rule in practice for estimating power transmitted by a belt — \iz^
One horse power for every 70' square feet of running belt surface per
minute. Thus, a belt 15 inches wide running at rate of 1400 feet per min-
ute, its power would be equal to (1400 X 15) -r- (70 X 12) =r 25 horses' power.
The same result is obtained by the use of a wire rope .5625 inch in diam«
eter, nmning over a wheel 6 feet in diameter, making 130 revolutions per
minute.
Average life of iron wire rope with good care is from 3 to 5 years^ and
that of steel rope is greater. Wear increases rapidly with velocity/
General Notes. — Henap and Wire Ropes.
White Rope, a inches in circumference, of different manufactures, parted at
a stress of from 4413 to 6160 ibs.
Specimens of Italian,. Russian, and French manufacture parted with an
average stress of 5128 lbs. =: 1633 lbs. per square inch of rope.
Bearing capacity of a hemp rope is proportional to its thickness, number
of its strands, slackness with which they are twisted, and quality of tht
hemp.
ffemp and Wire Ropes, — Ultimate Stt^ength is 2240 lbs. per lb. per fathom
for round hcmi^, 3300 lbs. for iron, 7000 lbs. for cast-steel, and 10 000 lbs. for
plough-steel.
Working Load is 336 lbs. per lb. weight per fathom for round hemp, 660
lbs. for iron, 1400 lb.9. for cast-steel, and 2000 lbs. for plough-steel.
Or, .83 times square of circimiference in mches for round hemp, 5 times
square of -circumference for iron, and 9 times square of circumference for
steel. (Z>. K. Oark.)
Steel Ropes may be one half less in wei^t than iron or hemp for lik«
working loada.
i68
BOPSS A2n> CHAINS.
IBON WIBB AND U»ir«l> STATBll HAVT HEMP ROPBL
Wire 6 8trcmd9^ Hemp Core» lUpe 4 Sh'trndt,
CIrcainf«reiic«.
▲«twd.
Nominal.
In|.
tat.
7
6
I
4-937
4.9
4-375
3-5
3-187
2-75
4-5
3-36
3>98
2-5
3.4s
2-375
2
3-^
3.06
WIRE.
COTK
WiMft
Breaking
Ins.
No.
Lto.
2-35
108
187400
2.25
106
104050 '
1-57
114
65409
1-57
114
55316
1.27
114
34480
1.17
114
38606 1
.78
"4
21846 '
.7»
114
15692
.78
42
15718
•39
114
10925
Circnmferene*.
IlB.
12
II
10.5
10
95
9
8.5
8
7-5
7
Ins.
13-25
12.25
11.875
"•375
10.5
10.312
9-437
-8^12
8437
7.812
Yanu.
BraaktDg
Weight.
No.
Lbe.
1X68
75966
1036
77633
928
76933
876
70533
800
58766
712
56466
640
42866
560
40000
484
35500
436
, 32166
Weislkt and Streiie;t]:i of Stud-link CliaixL Cable.
{BngUsh.)
DimimoNB.
INmi.
ofeMh
uyb
Side.
Link.
Ine.
Ins.
.4375
2.625
.5
3
.5625
3*375
.635
375
'6875
4-125
.75
4.5
.875
525
I
6
1.125
6.75
1.25.
7-5
»'375
8.25
Widtk
Weight
AdminltT
Preof-atrMs
of
Unk.
FatEom.
(adopted by
Li<^ds').
Ins.
Lbs.
Toas.
1.575
11-3
3-5
1.8
134
4.5
2X>35
17.2
5-5
2.25
21
7
2.475
-25.4
8.5
2.7
30.3
10.135
3-15
41.3
13-75
3-6
53.8
18
405
69
22.75
4-5
84
28.125
4-95
101.6
34
DlMBMStOIfa.
Diaaa.
of «»ach
SMe.
Length
Link.
Ins.
1-5
1.625
1.75
1.875
3
3.135
3.35
?-375
2.5
2.75
Ins.
9
9-75
10.5
11.25
12
1275
135
1425
15
16.5
Width
of
Link.
Weight
per
Fatbom.
Ins.
54
5.85
6.3
675
7-2
7-6s
8.1
8-55
9
9.9
LU.
121
142
164.6
189
215
242.8
276.2
3032
336
406.6
Admiralty
Proof-stress
(adopted by
Uoyds*)L
Tons.
40.5
47.5
55-125
6325
72
81.25
91-125
101.5
112.5
136.125
Note tSafe Working-itreu is taken at bair Proof-siress, 3.82 tona per sq. inch
of section.
i.—Proaf-tAtti» and SafB WMetng ' ttreu ft>r cloeelink chains are respectively
two-thirds of those of stud-link chains.
■^.—Proof-stress averages 72 per cent, ultimate Strength, and UUiiMie' Strength
averages 8 tons per square inch or section of rod or one side of a Itnk.
Weight of close-link chain is about three times weight of bar from which
it is made, for equal lengths.
Karl voM Ott^ comparing weight, cost, and strength of the tliree materials^
hemp, iron wire, and chain iron, concludes tliat the proportion between cost
of hemp ^rope, wire rope, and chain is as 3 : 1 : 3 , and that, therefore, for
eaual resistances, wire rope Is only half the cost of hemp rope, and a tliird
01 cost of chains.
Safe 'WorkiniT I^octd of Chains. (Moletworih).
Diameter
of Iron.
Load.
Piameter
of Iron.
Load.
Ins.
.375
•5625
.635
Lb«.
2240
3800
49OQ
6270
Ins.
.6875
.8125
.87?
Lbs.
7390
8960
10280
W32O
Diameter
of Iron.
I.oad.
Diameter
of Iron.
Load.
lus.
.9375
1
1.0625
1.125
Lbs.
13700
15680
17920
20160
int.
1.1875
1.25
I-3125
1^75
Lbe.
22400
24640
26680
30240
BOPES AND CHAINS.
169
Sreaking Strain, and Proof* of Cliain Cables.
Diam.
Breaking
Diam.
Breakinp
Diam.
Breaking
Diam.
Breaking
of Chain.
Strain.
of ChHin.
Strain.
Lbs.
of Chain.
Strain.
of Cliain.
Strain.
Ins.
Lbs.
Ins.
Ins.
Lbs.
lUB.
Lbs.
I
67 700
I.1875
92940
1-5
143 100
2
243180
1.0625
75640
1.25
102 160
1.625
165920
2.125
272580
X.I25
84100
1-375
121 840
1-75
216 120
2.25
303280
Proof-stress is 50 per cent, of estimated strength of weakest link and 46
per cent, of strongest.
Comparison of '^Vire Ropes ancl rrarred. liieznp Rope,
Ua'^vsers, and Cables.
Diam-
eter.
Ins.
25
3"5
375
5
5625
6875
75
875
25
375
5
625
COARSE LAID.
riNK LAID.
Ropes.
HawB'rs.
Cables.
Ropes.
Haws'rs.
•
Safe
Load.
if
CO
CO
^1
Diam-
eter.
Safe
Load.
si
CO
Ins.
Lbe.
Ins.
Ins.
Ins.
Ins.
Ins.
Lbs.
Ins.
Ins.
•78
I
1.25
'•375
'■75
425
690
825
i6cx>
2800
1-25
2-43
2.68
2.87
3.81
2.25
2-375
2.62
3-5
332
387
5.18
—
•5
.5625
625
-75
'.875
1875
2420
2900
4320
5700
3.12
3-56
3-93
4.81
5-5
2.87
3-25
3.62
4-37
5
2.125
3800
4-75
4-25
6.12
^—
I
8200
7-25
6.25
2-375
2.625
3
4400
6150
8400
5-25
6.12
6.62
4.87
5-75
6.12
I
8.62
8
8.62
1. 125
1.25
1-5
10 100
13600
17500
8.18
8.81
10
7
8.06
9-75
3-75
13400
8.81
8.5
10.93
10.93
1.625
21800
11.18
10.93
4-25
16800
9.87
956
12.25
12.12
I 75
27OGO
12.5
12.12
4625
20160
IO-75
10.5
13
13.12
1875
32500
—
—
5
24600
—
11.87
II 56
"•75
2
37000
Gables.
1-3
OQ
Ins.
4.87
5-25
6.37
7- 25
8.7%
9-5
II
12.5
based upon
one fourth,
In above table, determination of circumference of rope, etc., is
Breaking Weight or Tensile resistance of wire being reduced by
and ultimate resistances of rope, etc., are reduced one third.
Result of* Experiments -Upon Wire Rope at XJ- S. Navy
Yard, Washinigton. {J A Roebling^s Sons.)
Circnmfe
Actoal.
rence.
Nom-
inal.
Wire
^ In each
strand.
Ins.
Ins.
4.9375
4-9
19
4.375
4-5
19
3-9375
3-5
3.1875
3-91
3-36
2.98
19
19
19
2-75
2.6875
2.68
2.56
19
7
2.5
245
19
"^-d
Weight
Breaking
Circamference.
Fw)t.
Weight.
' Actual.
Nom-
inal.
No.
Lbs.
Lbs.
lus.
Ins.
II
3-14
65409
2.375
2.4
13
2.15
55316
2.1875
2.12
14
2.0875
44420
2
2.06
14
I-I525
34840
1-9375
1.9
15
1.09
28606
1.75
1.85
17
1.0275
21846
1-4375
1.45
13
1.0225
18 810
1.3125
1.31
18
.14
15692
1. 125
I. II
e
•^■9
No.
7
7
19
7
7
19
7
7
•^
No.
13
14
19
14
17
20
18
19
Breaking
Weight.
Lbs.
Lbs.
.14
.11
15718
14478
.1
.1
10925
10 118
.07
.06
•05
7880
5687
4428
.035
3729
To Conapute Circu.mference of Wire Rope with. Xlexnp
Core, of* Corresponding Strengtli to Hemp Rope, and
of* l^em-p Rope to Circumference of Wire Rope.
Rule i. — Multiply square of circumference of hemp rope by .223 for iron
wire and ,1^ for steel, and extract square root of product
3.-~Multiply square of circumference of hemp-core wire rope by 4.5 for
iron wire and 8.4 for steel wire.
ExAMPLS. — ^What are the circnmferences of an iron and steel wire rop0 corre-
sponding to one of hemp-core, having a circumference of 8 ina ?
V82X.233 = 3. 78 im. iron, and V8*x.i2 = 2. 77 tn#. Oed.
170
BOPES, HAWBEBS, AND CABLES.
ROPES, HAWSERS, AND CABLES.
Ropes of hemp fibres are laid with three or four strands of twisted fibres,
and are made up to a circumference of 12 ins., and those of four strands up
to 8 ins. are fully 16 per cent, stronger thdn those of three strands.
Hawsers are laid with three or four strands of rope. Cables are laid with
but three strands of rope. Hawsers and Cables, from having a less propor-
tionate number of fibres, and from the irregularity of the resistance of their
fibres in consequence of the twisting of them, have less strength than ropes,
difference var3ring from 35 to 45 per cenUy being greatest with least circum-
ference, and those of three strands up to 12 ins. are fully 10 per cent, strong-
er than those having four strands.
Tarred ropes, hawsers, etc., have 25 per cent, less strength than white
ropes ; this is in consequence of the injury fibres receive from the high tan-
perature of the tar, viz. 290°.
Tarred hemp and Manila ropes are of about equal strength, and have from
25 to 30 per cent, less strength than white ropes.
White ropes are more durable than tarred.
The greater degree of twisting given to fibres of a rope, etc., less its
strength, as exterior, alone resists greater portion of strain.
Ultimate strength of ropes varies from 7000 to 12000 lbs. per square inch
of section, according as thev are wetted, tarred, or dry. One sixth of ulti-
mate strength is a safe working load = 1 166 to 2000 lbs. per square inch.
Units fbr coraiyuting: Safe Strain. tUat may "be "borne "by
Nexv fiopes, Hawsers, and. Ca'bles^ {U. S. Navy.)
Tirred.
3 ttT'dl.
R0PE8.
Hawsibs.
Cai
Descrip-
CircomfereDce.
White.
Tarred.
White.
Tarred.
White.
tion.
3>traDds.
4 Btranda.
Sstr'ds.
4str'da.
"LbT
3 strMa.
3 Btr'da.
3 str'da
Ina.
Lb*.
Lbs.
Lbs.
Lbs.
Lbs.
Lb«.
White
2.5 to 6
1 140
1330
—
—
600
—
—
t(
6 " 8
1090
1260
—
—
570
—
510
({
8 " 12
1045
880
—
—
530
—
530
§1
12 " 18
wmmmm
—
—
—
550
—
550
It
18 " 26
—
—
—
—
560
Tarred
2.5" 5
—
855
1005
—
460
ti
5 " 8
—
—
825
940
—
480
—
i.
8 " 12
—
—
780
820
—
505
—
i(
12 " 18
——
—
— .
^^
__
<(
18 " 26
—
_
"^^
■
^^^
.^^,
^^^
Manila
2.5 " 6
810
950
—
—
440
-_
—
ii
6 " 12
760
83s
—
—
465
_
Sio
(I
12 " 18
—
—
— >
535
(i
18 " 26
—
—
_
—
—
560
Lbs.
505
525
550
Ii^LUSTBATioir.^What weight can be borne with safety by a Manila rope of 1
strands, having a circumference of 6 inches ? (Set Rule, page 167. )
6^ X 760 = 27 360 Ws.
Whm it is required to asceHain weight or strain (hat can be borne by
ropes, etc, in general use, preceding Units should be reduced from one third
to two thirds, in order to meet their condition or reduction of their strength
by chafing and exposure to weather. Mdesworth's table is based upon a
reduction of three fourths.
Illustration.— What weight can be borne by a tarred hawser of 3 strands, lo
inches in circumference, in general use f
«o" X (50s — 505-^3) = xoo X 336.57 = 33 667 fe*
UOPES, HAWSERS, AND CABLES.
171
Destructive Strezi^tlx of Xarred Hemp Ropes.
(Z). K. Clark.)
lUgittor.
Clreiun.
DUm.
RflgUtor.
Common RomIui
Cold. Warm.
IDI.
3
3-5
Int.
•95
I. II
LiM.
7390
II200
Lb«.
86ao
II 760
4
45
5
1.27
1-43
1-59
13 100
16330
19580
15340
19440
23990
Circam.
Int.
5.5
6
6.5
7
8
Diun.
Ini.
1-75
1. 91
2.07
2.24
2.54
Common
Cold.
Lbs.
24800
28985
34030
40320
52480
RuuUn
Warm.
Ltw.
29120
33150
40550
47041
61420
Specimens furnished by National AssocicUion of Rope and Tioine Spinners^
• As tested by Mr. Kirkaldy.
Ron.
Russian rope ... 48 thr*ds.
Machine yam. . , 50 **
Hand-spun yam, 51
(i
Cirenm-
ferenee.
Ins.
526
5-37
5-39
W«iffht
per Lb.
Lb«.
.926
.891
1.006
Extreme
Strength.
Lb*.
II088
"514
18278
Breakiae
Weifcht <
?)rlli.per
athom.
Lba.
1933
2152
3024
Extension in so ina. Length
at Streaeper lb. Wei^t
Fathom of
per
1000 Ibe.
Ins.
529
4-53
4.46
aooolbe.
Ins.
6.56
5-91
3000 lba.
Ina.
6.63
Breaking Strength, of* Tarred Irlexxip H.opes. (Mr. Olynn.)
•
i
0
•
Ins.
Ins.
3
•95
3.5
i.ii
4
1.27
4-5
^•43
5
1-59
Old Method.
Common I Best
Hemp. Rnaaian.
Lbs. ' 'Lbs.
5056 6248
74661 8668
8780 10460
10300 12432
13328 15859
By Re{(ister.
Cold.
Warm.
Lbs.
Lbs.
7392 8624
II200 II 760
13 104 17 810
16330 19443
20496
23990
Ins.
5.5
6
6.5
7
8
Old Method.
Common
Hemp.
Best
Russian.
Ins. Lbs. I<bs,
1-75 15456 18 414
1.91 18 144 21 610
2.07 20518 23610
2.24 '22938 '27462
2.54 '26680 132 032
By Register.
Cold.
Lbs.
24797
28986
34630
40320
52483
Warm.
Lbs.
29120
33150
40544
47040
61420
To Compute Strain tb.at may "be "borne -w-itlx safety lay
new Ropes, Ha-vtraers, and Cables.
Deduced from experiments of Russian Government upon relative strength
of different Circumferences of Ropes, Hawsers, etc.
U. 8. Navy test is 4200 lbs. for a White rope of three strands of best Riga
hemp, of 1. 7 5 inches in circumference (= 17000 tbs.per square invh ofjibre),
but in preceding table, (page 166) 14000 lbs. is taken as unit of strain that
may be borne with safety.
Rule.— Square circumference of rope, hawser, etc., and multiply it by
Units in table.
To Ooxnpute Ciroumferenoe of a Rope, Hawser, or Cable
fbr a Gl-iven Strain.
RuLS. — Divide strain in pounds by appropriate units in preceding table,
and squai« root of product will give circumference of rope, etc., in ins.
ExAMPLB L— Stress to be borne in safety is 165 550 lbs. ; what should be circum-
ference of a tarred cable to withstand it?
165 55« -r 550 = 301, and v^3oi = 17. 35 ins.
2.— What should be circumference of a Manila cable to withstand a strain, in
general use, of 149 336 lba ?
AMumiBg circumference to exceed 18 ius., unit = 56a
149 336-5- (5C0 - 560-^3/ 5i; 4cx^ and y 400 =s ao tUf.
172
ROPES, HAWSERS, AND CABLES.
To Compute '^Veigll.t of Ropes, Ha-wsers, and Cables.
Rule. — Square circumference, and multiply it by appropriate unit in
following table, and product will give weight per foot in lbs. :
HAWSBSS.
BOPE^. CABLBB
3-8trand Hemp 032 .031 .031
3- strand tarred Hemp, .042 .041 .041
3-straDd Manila 032 .031 •031
HAWSERS.
BOPSB. CABLES.
4-8trand Hemp 033 — —
4-Btrand tarred Hemp, .048 — —
4-strand Manila 035 .034 .034
Units for Thread Ropes is same as that for Ropes of like materiaL
ExAUFLE.— What is weight of a coil of lo-iuch Manila hawser of 4 strands of 120
fathoms?
io2 X .034 = 3,4, and 120 X 6 X 3.4 = 2448 lbs.
Weiglit and StrengtU of Hemp and '^Vi»e Ropes.
{Molestuorth.)
C'y = W; 'C=;fc = L; C«a; = S; andy^ = C.
C representing circumference in ins., W weight of rope in lbs, per fatkomy
L working load in tons, and S destructive stress in tons,
VALUES OF y, X, AND k*
BOPKS.
9
»
Hawser, hemp
•131
Cable "
.117
Tarred hawser, hemp.
•235
.22
'* cable, " .
.207
•15
Cold register, . " .
—
.6
■037
•025
.1
BOPSB.
Warm register, hemp '
Manila hawser. ...
" cable
Iron rope
Steel "
y
X
•7
—
.177
.27
•155
.J9
.87
1.8
.89
2.8
.116
•045
•033
.29
•45
To Compute Cirouxnfference of Hemp or ^Wire Rope
for Fore or Alain Standing Rigging. {U. S. Navy.)
Rule. — To length of mast between partners and deck, add half extreme
breadth of beam of vessel and divide sum by half extreme breadth. Mul-
tiply quotient by half square root of tonnage (OM) and extract square root
of product.
For Mizzen, take .74 of Fore and Main.
Example. — Required circumference of hemp rope, for main - mast of a vessel
having a breadth of beam of 45 feet and a burden of 3213 tons ?
Extreme length of mast 94.4 feet
Depth of hold, or total bury of mast, 21.4 feet
Head 15 " 36.4 "
Breadth of beam, 45 feet 58 *'
58 -f ^ ^ ~ = 3. 58, and V (3.58 X ^^^) = Vioi.46.= 10.11 ins.
Then if circumference for a wire rope is required, see table, page 164.
Thus, a hemp rope xo ins. in circumference has equivalent strength of an inm
wire rope of 4 ins. and a steel rope of 3.25-I- in&
Oalvaniud Iron Wire. — Experiments at Navy Yard, Washington, gave for flex-
ibility a moan loss of 30 per cent, and for tensile strength a like loss of 13.5 per
cent
Relative Dimensions of Hemp Rope and Iron and Steel
'Wire Rope. (U. S. Navy.)
Circumference in Inches.
Hemp. 2.5 3.125 4 4.5 525 6-5 7-75 8.5 9.5 ti 11.75 13.5 16.5
Iron.. 1.25 1.625 a 9.125 a.5 3 3*5 4 4-5 5 5-5 ^ 7
Steel.. .875 Z.I35 z.5 1.635 ^-^79 ^.iss 9.5 9.75 3.35 3.5 4 4.375 5.35
ANCHORS, CABLES, ETC.
173
ANCHORS, CABLES, ETC.
^zicliors, Cliaitis, etc, for a Griven. XoxiiiE^se.
{American Shipmasters* Association.)
.3*.
Ill
-"* c »•
• 8*
75
100
125
150
175
2CX>
250
400
600
700
800
900
1000
1200
1400
1600
xSoo
2000
2500
3000
Anchoks
•
1
Bowen.
loeludlng Stock.
With-
Admi-
_^»
out
Stock.
ralty
Twt.
Stream.
Kedffe.
ad
Kedge.
LlM.
Lbt.
Toms.
Lbs.
Lba.
616
7
168
84
—
728
8
196
112
—
840
9
224
112
—
952
10
280
140
—
1036
II
336
168
—
II20
12
392
I9t>
—
1288
13
448
224
112
1456
14
504
252
126
1624
15.5
560
280
140
1848
17
616
308
154
1904
18.5
672
336
168
2016
20
784
392
196
2352
22
896
448
224
2688
24
1008
504
252
3024
26
1120
560
280
3248
28
1232
616
308
3584
295
1344
672
336
3808
31
1456
738
364
4032
32.S
1568
784
392
4256
34
1680
840
420
4480
35-5
1792
89b
448
4704
37
1904
952
504
5040
39
2128
1120
560
5376
41
2353
1232
616
SAILS.
Diameter.
t Brown,
Ina.
.8125
.875
•9375
I
2.0625
1. 125
1. 1875
1.25
1-3125
1.3125
1-375
1-4375
1-5
1.5625
1.625
1.6875
1-75
1.875
1-9375
2
2
2.0625
2.125
2.1875
Lennox, &
Chain Cablb.— Stdo.
Weight per Fathom.
be
a
FathB.
90
05
05
20
20
20
35
35
50
50
65
65
80
80
80
80
80
80
80
80
80
80
80
80
Admi-
ralty
Test.
Tons.
II
13
15
175
20
22.5
25
28
31
3^
37
40
44
47
51
55
59
63
67
72
72
81
86
96
stud.
Lbs.
40
44
51
59
66
75
82
91
100
100
"5
120
132
145
156
16;
175
189
205
219
240
Short
Link.
Eng.
lUh.f
Lbs.
42
48
55
63
.35
48
54
70
79
88
68
98
106
84
106
—
X18
102
—
122
143
—
166
._
191
—
217
—
244
— —
^—
Co.
To Coxxipute 1'oxinase.
Take dimensions as follows * Length, — From after-side of stem to for-
ward-side of stem-post, measured on spar or upper deck in vessels having
two decks and under, and on main deck in vessels having three or more
decks. BrecuUh. — Extreme at widest point. Depth. — At forward coaming
of main hatch, from top of ceiling at side of keelson to under side of deck.
Then multiply these dimensions together, divide product by 100, and
take .75 of quotient
All vessels to have 2 bowers and i each stream and kedge anchor, and for
a tonnage exceeding 1400 a third bower is recommended.
Hawsers and Waips to be 90 fathoms in length.
SUroricls,
Square-riooed. Hemp.—s.TS ins. in diameter for a tonnage of 75, in>
creasing progressively up to 12.75 ^^^' ^^^ 3<3oo tons.
Fore-and-aft rigged. From .25 to i inch in diameter progressively
greater than for square-rigged.
IVire. — One half diameter of hemp, increasing very slightly as tonnage
increases. Thus, for 3000 tons, 12.75 ins. for hemp and 6.875 i"s- ^°' ^^'*
174
ANCHORS, CABLES, ETC.
{American Shipmaster i Associatioti.)
STEAM.
lOO
150
2CX>
250
300
400
500
600
700
800
900
1000
1200
1400
i6(X)
i8cx>
2000
2300
2600
30CX)
3500
4000
4500
50CX)
Archorb.
Bowen. Inclading Stock.
LlM.
336
448
616
672
812
924
• II20
1344
: 1512
i;o8
1 1876
jao26
3352
2632
'2856
3108
3360
, 3584
3808
4088
4256
4480
4592
4816
5040
5264
Tona.
4.9
6.4
7.6
8.2
9-5
' 10.4
12
J39
15.2
16.7
18
19
21 6
25.2
26.9
28.6
301
01.6
33-4
34-5
35-7
37
38
392
41
§
s
Lba.
112
196 I
224 I
280
308
336
532
560
672
738
784
896
1008
IZ20
II76
1232
1344
1456
1512
1568
1624
1680
1792
I96O'
2128
2352
Lbs.
c
5 *^
• •
Lba.
252
280
336
364
392
448
504
560
Diam-
eter.
2241
252.
280'
Ins.
•6875
.8125
.875
•9375
I
1.0625
1. 125
1.1875
1.25
1-3125
1-375
1-4375
1-5
1.5625
Chain Cablc — Stod.
WeiKbtperFatk
t
588 308; 1.625
616
672
738
766
784
812
840
308
3361
364
364I
392;
392 1
420,
896 476
952 504
1064 532
1 120 560
1.6875
1-75
1.8125
1-875
1-9375
2
2.0625
2.125
2.1875
2.25
2-3125
Fatba.
105
120
120
120
120
120
135
135
150
150
165
165
180
180
180
180
180
180
I 180
. 180
I 270
270
i 270
270
I 270
270
28
Tona.
8.1
1 1.9
13.8
15-8
18
20.3
22.8
254
28.1
31
34
37-2
40.5
(44
'47.5
I 51.2
55.1
591
633
676
72
76.6
81.3
861
91. 1
96
Diam.
Stream.
Ins.
5
5625
5625
625
625
687s
6875
75
75
8125
8125
875
875
9375
9375
1 1
• I
11 0625
1.0625
1. 125
1.125
1.1875
1.1875
1.25
1-25
1-3125
t
a
(A
CAi
•^a
Lba.
40
44
51 !
59
661
75'
82 <
911
■ 100
"5
1 120
1132
145
156
162
175
189
1205
'215
240
Lba.
B-3
Us
25
35
42
48, -
55 I 48
63 54
70 —
79: 68
88' —
98
106
118 104
84
— 1 122
— 143
~ '166
— ' 191
217
244
* Brown, Leanojc, A Co,
ANCHORS AND KEDGES.
iU, 8. Nary.-)
To Compnte "^^eiglit of a Bo-virer A.nolior fbr
of* Bk given CUaraoter axid Rate.
Rule. — Multiply approximate displacement in tons, by unit in following
table, and product will give weight in lbs., inclusive of stock.
a "Vessel
Units to determine
Diaplncement
01 Vessel In
Tons.
'Weiglits and.
or liledges.
Number of iViicliors
Over 3700
2400
1900
.tj
•
1
§
1
B
&
.A
W
2
.^
&
1-75
2
I
4
2
2
2
1
3
2.25
2
2
I
3
Displacement
of Vessel in
Tons.
Over 1500 . .
" 900 . .
900 and under
•
2!
•
i
b
2
2
2.5
2.75
2
I
3
2
I
btf
3
3
2
ExAMPLB.— Tonnage of a bark-rigged steamer is 1500.
1500 X 2. 5 = 3750 lbs. , weight of anchor.
Bower and Sheet Anchors should be alike in weight.
Stream Anchors and Kedges are proportional to weip:ht of bowers. Thus,
Stream Anchor .25 weight. Kedges, — If i, .125 weight; if 2, .16 and .i
weight; if 3, .16, .125, and .1 wei'iht.
ANCHOBS. CABLBH, BTC— TONNAGE.
175
T'o Coxnpute Diameter of a Ch.ain. Cal^le oorrespondiug
to a Ghiveix "Weiglit of Anolior.
{U. 8. Navy.)
RuLB. — Cut off the two right-hand figures of the anchor's weight in lbs.,
multiply square root of remainder by 4, and result will give diameter of
chain in sixteenths of an inch.
EXAMFLB. — The weight of an anchor is 2500 lbs.
V25'Oo X 4 = 20 sixteenths = 1.25 ins.
NoTK.— Diam. of a messeDger should be .66 that of the cable to which it is applied.
X^engtlis of Glxaiix Cables for eaolx i^iolior. -
{U. 8. Navy.)
Weight of Anchor.
Llw.
Under 800
Over 800
" 1200
" 1600
Bower.
Sheet
Stream.
F«th«uu.
Fathonu.
Fathoms.
60
60
60
90
90
60
• 90
90
75
los
105
75
Weight of Aiu^or.
Lbs.
Over 2000
" 3000
(t
it
5000
7500
Bower.
Sheet.
Stream.
Fathoms.
Fathoms.
Fathoms.
120
120
90
120
120
90 .
I2Q
J20
J05
135
135
105
ANCHORS.
From Experiment of a Joint Commiiiee of Representatives of Ship-
owners and Admiralty of Great Britain.
An anchor of ordinary or Admiralty pattern, Trotinan or Porter's im-
proved (pivot fluke), Honiball, Porter's, Aylin's, Rodgers's, Mitcheson's, and
Lennox's, each weighing, inclusive of stock, 27 000 lbs., withstood without
injury a proof strain of 45 000 lbs.
Breaking weights between a Porter and Admiralty anchor, as tested at
Woolwich Dock-yard, were as 43 to 14.
Comparative Resistance to Dragging.
Trotman's dragged Aylin's, Honiball's Mitcheson's and Lennox's ; Aylin's
and Mitcheson's dragged Roidgers's ; and Kodgers's and Lennox's dragged
Admiralty's.
TON^^AGE OF VESSELS.
To Compiate Tonnage of "Vessels.
For Laws of United States of America, with amendments of 1882 relative
to Steam-vessels, see Mechanics' Tables, with rule and illustrated diagrams,
by Chas. H. Haswell, 3d edition. Harper & Bros., New York, 1878.
Snglisli Registered Tonnage. {New Measurement.)
Divide length of upper deck between after-part of stem and .fore-part of stem-
post into 6 equal parts, and note fbremost, middle, and aftermost points of division.
Measure depths at these three points in feet and tenths of a foot; also depths fVom
under-side of upper deck to ceiling of limber-strake; or in case of a break in the
upper deck, ftom a line stretched in continuation of the deck. For tn'eadths, divide
each depth into 5 equal parts, and measure the inside breadths at following points,
vix. : — At .2 and .8 f^om upper deck of foremost and aftermost depths; and from
.4 and .8 from upper deck of amidship depth. Take length at half amidship depth
from after-part of stem to fore-part of stem-post.
Then, to twice amidship depth add foremost and aftermost depths for sum of
depths^ and add together foremost upper and lower breadths, 3 times upper breadth
with lower breadth at amidship, and upper and twice lower breadth at after division
for sum ofhrtadths.
MnUipfy together sum of depths, sum of breadths, and length, and divide product
by 3500, which will give number of tons.
If the vessel has a poop or half-deck, or a break in upper deck, measure inside
mean length, breadth, and height of such part thereof as may be included within
the bulkhead; multiply these three measurements together, divide product by 92.4,
and quotient wlU give number of tons to be added to result as above ascertained.
176
T0KNA6E OF YSSSELS.
For Often VesseU. — Depths are to be taken Arom upper edge of upper strake.
For Steam VesgeU. — Tonnage due to engine-room is deducted from total tonnage
computed by above rule. To determine this, measure inside of the engine-room
from foremost to aftermost bulkhead; then multiply this length by amidship depth
of vessel, and product by inside amidship breadth at .4 of depth from deck, and
divide final product by 92.4.
The volume of the poop, deck-houses, and other permanently enclosed spaces,
available for cargo or passengers, is to be measured and included in the tonnage,
but following deductions are allowed, the remainder being the Register tonnage.
Deductions. — Houses for the shelter of passengers only; space allotted to crew
(12 square feet in surface and 7a cube feet in volume for each person); and space
occupied by propelling power.
A.p proximate Hiale.
Orots Register.— Tonnage of a vessel expresses her entire cubical volume In tons
of 100 cube feet each, and is ascertained by following formula :
* Li B D L B D
=: Oross tonnage, and ■ c =. Register tonnage. L representing length
of keel betvjeen perpendicidarSy B breadth of vessel, and D depth of hold, all in feet.
Builders' ]Vd[easu.rexxient.
(L — .6 B)XBX .5 B _
i '-^ — ^^—2 — = TonncMc.
94
Fore-perpendicular is taken at fore-part of stem at height of upper deck.
Aft-perpendicular is taken at back of stern-post at height of upper deck.
In three-deckers, middle deck is taken instead of upper deck.
Breadth is taken as extreme breadth at height of the wales, subtracting differ-
ence between thickness of wales and bottom plank. Deductions to be made for
rake of stem and stern.
Iron Vessels.
x8 / Girth -f- Breadlhy
/ Girth +BreadthY , ,, ^ ,
( ■ j X length = Gross tonna^ge.
lOOOO
Length measured on upper deck, between outside of outer plank at stem and
the aflorside of stern-post and rabbet of stem-post, at point where counter-plank
crosses it. Girth measured by a chain passed under bottom from upper deck at
extreme breadth, on one side, to corresponding point on the other.
L V B X D
Register tonnage = X C. C representing a coefficient for vessels a*
follows :
Ships of usual form 7
Clippers and Steamers |^ flecks.. . .65
Yachts above 60 tons 5
Small vessels { ^^^P:c:il 45
(very sharp 4
Units for Measurement and Dead-'weigh.t Cargoes.
(C. Mackrow, M. S. N. A.)
To Comjnde Approximately fnr an Averaqe Lenfffh of Voyage the Measure-
meut CaryOj at 40 Jcet per JVm, which a Vessel can carry.
RiTLR. — Multiply number of rep^ister tons by unit 1.875, ^^^^ product will
give approximate inoasurement cargo.
To Compute Ajiproximatety Dead-weight Cargo in Tons which a Vessel can
cany ofi an Average Lew/th of Voyage,
RuLK.— Multiply number of register tons by 1.5, and product will give
approximate dead-weight cargo required.
With regard to cargoes of coasters and colliers, as ascertained above, about
10 per cent may be added to said results, while about 10 per cent, may be
deducted in cas^ of larger vessels on longer voyages.
TONNAGE OF VESSELS. 1/7
In case of measurement cargoes of steam-vessels, spaces occupied by ma-
chinery, fuel, and passenger cabins under the deck must be deducted from
space or tonnage under deck before application of measurement unit thereto.
In case of dead-weight cargoes, weight of machinerj', water in boilers, and
fuel must be deducted from whole dead weight, as ascertained above by
application of dead-weight unit.
The deductions necessary for provisions, stores, etc., are allowed for in
sdection of the two units.
To Ascertain Weight of Cargo for an A verage Length of Voyage, (Moorsom.)
Deduct tonnage of spaces of passenger accommodations from net register
tonnage, and multiply remainder by 1.5.
Average space for each ton weight of cargo on such a voyage 67 cube feet,
Freight Tonnage or ^Ceasnrement Cargo.
Freight Tonnage or Measurement Cargo is 40 cube feet of space for cargo,
and it is about 1.875 times net register tonnage less that for passenger space.
Royal Tliames Yaolit Clxxb.
Measure length of yacht in a straight line at deck ft-om forepart of stem to after-
part of stern-post, (Vom which de<luct extreme breadth (measured from outside of
oatside planking), both in Teot; remainder is length for tonnage. Multiply length
for tonnage by extreme breadth, that product by half extreme breadth, divide re-
salt by 94, and quotient will give tonnage.
If any pan of stem or stern-post projects beyond length as taken above, such
projection or projections shall, for purpose of computing tonnage, be added to length
taken as before mentioned.
All fractional parts of a ton are to be considered as a ton.
Measurements to be taken either above or below main walea
L-BxBxs B
94
= Tons. L representing length and B hreadUi^ infect.
Corintlxian and New TlianleB Yacht Club.
Measure length and breadth as in foregoing rule, and depth to top of covering
board; multiply length, breadth, and depth togeUicr, divide result by zoo, and quo-
tient will give tonnage.
LxBxD _
= Tons.
300
Suez Canal Tonnage.
Gross Tonnage. — Spaces under tonnage deck, below tonnage and uppermost deck,
all covered or closed - in spaces, such as poop, forecastle, officers' cabins, galley,
cook, deck, and wheel bouses, and all inclosed or covered- In spaces for working the
vessel
From which are to be deducted berthing accommodations for crew, not including
spaces for stewards and passengers' servants; berthing accommodations for officers,
except captain; galleys, cook-houses, etc., used exclusively for crew, and inclosed
spaces above uppermost dock, designed for working the vessel. In none of these
spaces can passengers be berthed or cargo carried, and total deduction under all of
these spaces roast not exceed 5 per cent of gross tonnage.
Id steamers with standing coal-bunkers, Knglish rule may be followed, or owner
may elect to have tonnage of his vessel computed by ''Danube rule," which is an
allowance of 50 per cent, above space allowed to machinery in side- wheel steamers
and 75 in screw steamera
In no case, however, except with tow-boats, must deduction for propelling power,
exceed 50 per cent, of gross tonnage.
178
WOBKS OF MAGNrrUDB.
WORKS OF MAGNITUDE.
A.zn.ericaii.
A.qued.uots, JEioads, and Railroads.
Orcton Aqua^i^/tcty N. Y. — Has a section of 53.34 square feet and capacity of
loooooooo to 118000Q00 gallons per day, and firoin bam to Receiving Reservoir is
38. 134 miles in length.
AquedMc% Washington. —Cylinder of masonry 9 feet in diameter. Stone arch
over Cabin John's Creek, 220 feet span, 57.25 feet rise.
National Road.— Over the Alleghany Mountains, Cumberland to Illinois Town
65a625 miles in length, and 80 feet in width. Macadamized fur a width of 30 feet
Illinois Central Railroad. — Chicago to Cairo, length 365 miles, Central ia to Dun
leith 344 miles, total 709 miles.
Sridgea.
Siupmsion Bridge^ Niagara River. —Wire, Span 1042 feet 10 ins.
Suspension Bridge, New York and Brooklyn. — lAngih of river span 1595 feet 6
ins. ; of each land span 930 feet; length of Brooklyn approach 971 feet; of N. Y.
approach 1562 feet 6 ins. ; total length of bridge 5989 feet; width 85 feet; number
of cables 4; diameter of each cable 15.5 ins. ; each consisting of 6300 parallel steel
wires No. 7 gauge, closely laid and wrapped to a solid cylinder; ultimate strength
of each cable 11 200 tons; depth of tower foundation below high water, Brooklyn,
45 feet— New York 78 feet; towers at high water line 140X59 feet; towers at roof
course 136x53 feet; total height of towers above high water 277 feet; clear height
of bridge m centre of river span above high water, at 50°, 135 feet; height of floor
at towers above high water 119 feet 3 ins. ; grade of roadway 3 feet in 100; anchor-
ages, at base 129X1x9 feet, at top 117X104 feet; weight of each anchor-plate 23 tons.
Iron Pipe Bridge over Rock Creek. — 200 feet span, 20 feet rise. Arch of 2 lateral
courses of cast-iron pipe, 4 feet internal diameter, and i inch thick. These pipes
conveying the water not only sustain themselves over the great span, but support
a street road and railway.
Iron Bridge over Kentucky River near Shakers' Ferry, Md.— 3 spans, each 375
feet, and 275.5 feet above low water.
Bridge on line of New York, Erie, and Western Railroad across the KinttuL-^
Of iron; length 2060 feet; central span 301 feet in height.
Iron TViMf.— Cincinnati and Southern Railway, over Ohio River, 519 feet
Foreisn.
Pyramids, Statues, etc.
Pyramid of Cheops, Egypt— Length of side at base 762 feet; height to present
summit 453.3 feet; to original summit 485.2 feet; inclined length 568.25 feet; angle
of side 5i<' 51' 14"; area of each face = square of height; weight 5273600 tons;
built 2170 years B.C.
Peter the Great, St. Petersburg, Russia. — Bronze; height of horse 17 feet; of man
II feet; base of rock 42 feet at bottom, 36 at top, 21 wide, and 17 high, weighing
zioo tons.
Liberty, New York Harbor —Bronze; no feet in height ft-om head to foot and
151. 1 feet to flambeau ; including base, 305.6 feet Weight of statue 225 tons.
Daihuisu, of stone, Japan. —Sitting posture, height 44 feet, circumference 87
feet; fece 8.5 feet; circumference of thumb 3 5 feet
Colossus of Rhodes.— lSLe\g\ii, 105 feet
D ridge.
Britannia Tubular Bridge — Ot iron, with a double line of Railway, 964 feet iD
length, with two approaches of 230 feet each. Weight 3658 tons.
WOBKS OF MAaNITUDB.
179
l^oiiolitlis.
Obelisk at Kamak^ Egypt— Of granite, 108 feet xo ins. ; pedestal 13 feet. 2 ina;
weight 400 tons.
Obelisk in Central ParAr, N. T.— Of granite, 68 feet 11 ins.-, weight 168 tons.
U. S. Treasury^ Washington. — Some stones of, are heavier than any in the Pyra-
mids of Egypt
Bteazxi X^ammers.
At workshops of Herr Krupp, at Essen, there is a steam hammer weighing 50 tons
having a fall of 3 metres; and at Creusot there is a hammer weighing between 75
and 80 tons having a fall of 5 metres.
Crane.
. At Greasot there is a steam crane having a capacity to J i ft 1 50 tons.
Cliixnnesrs.
J. Townsend's chemical works, Glasgow, diameter at foundation 50 feet; at top
12 feet 8 in^ ; height from foundation 488 feet; from ground 47*4 feet
Metropolitan Traction Company, N. Y., diameter at base 85 feet; at top 25 feet,
and height 353 feet
P»illar.
At a gate near Delhi is a wroagbt-iron pillar having diameters of 16.4 ms. at 32
feet in its height above ground and 13 ins. at its top. It is estimated fh>m the re^
suit of excavations at its base to be 60 feet in length or height and to weigh 17
tons. Its period of structure is assigned to the 3d or 4th century A.O.
Roofb.
Midland Railway Station, London. 240 ft.
Imperial Kidiog-School, Moscow. 235 "
Union Railway Station, Glasgow. 195 ft
Grand Central Station, N. Y 300 ''
DOMSS.
Capitol, Wash ington
Glasgow W. Railway
JDiaraeters of Domes.
Fe«t. f DuaiKfl. Feet.
124.75
198
St Paul's, London .
St Peter's, Rome. .
X12
139
DOMU.
Midl'ndRaily.liOn.
Great North'n, Eng.
Feet.
240
210
TOHKIU.
Blaizy
Blue Ridge.
Hoosac
Hiengtlis of Tunnels.
Feet. TuNNRL*. Feet.
13455
4280
25031
Gunpowder, Md..
Sutro
Semmering
36500
30028
5630
TdrHKLS.
Nerthe
Nochistongo....
Riquivel
Feet.
'5 153
21659
18623
Thames and Med way, n 880 feet Weehawken, 4000 feet
Mont Cents 7.5 miles 243 yards, rises i in 45, and descends i in aooo.
St Gothard Tunnels and Roads a miles 477 yards in length ; tunnels 1 16 156.5 feet,
and rises i in 233 in whole lengtn; 26.5 feet in width; 19 feet 10 ios. in height
Maximum grade 2.7 feet per 100. Schemnitz, 10.27 miles in length, 9 feet 10 ins.
in height by 5.25 feet in width
Mliscellaneous.
Fortress Monroe, Old Point Comfort, Va.— Largest fortress.
Telegraph Wire.— Spaa, over river Kistnah between Bezorah and Sectanagran,
6000 feet in length.
Deer Park, Copenhagen. — 4200 acres.
Oxford College, England. — Largest University; said to have been founded by
Ain-ed.
Cathedral. SL Peter^s, Rome.^Width of front 216 feet; of the cross 251 feet; total
height 469. 5 feet
Steamer Great Eastern.— OT iron, 680 feet in length ; 83 feet width of beam ; 60
feet depth of hold; 22927 tons; built at Millwall, England, 1857.
Chinese Wall.— 2$ feet at base; 15 at top; height, with a parapet of 5 feet, 30 feet:
length 1250 milea
Artenan WeU^ Perth.— 3050 feet in depth; temperature of water 99^); volume
of discharge 18000 gallons per day.
l80 BELLS, CHUBCHBS, COLUMNS, TOWEBS, BTO.
TVeiglits of Bells.
Bkixs.
• ■ • • •
PekiD....
Lewiston, Me
Montreal, Can
Moscow, Russia. . .
ErAirt, Saxony —
Notre Dame, Paris
Lba.
I20 000
10233
28560
443 772
30800
28670
Bells.
Lbs.
Kells.
Oxford, "Great
Tora,"Eng
01m ntz. Bohemia.
Sac'd Heart, Paris
St Paul's, Eng, . .
St. Ivan's, Moscow
17024
40320
55 o<^
42000
127 830
St. Peter's, Rome
Vienna....
Westm'ster, "Big
Ben,'* England.
York "
State House, Phila.
Lb*.
1800C
4020c
35620
24080
13000
Rangoon, Burmab, 201 600 lbs.
Capacity of Principal Ch.urcUes and. Opera Houses.
Estimaiing a person to occupy an Area of 19.7 Ins. Square.
Cliurclies.
St. Peter's. 54000
Milan Cathedral 37 000
St Paul's, Rome 32000
St Paul's, London 25 600
St Petronio, Bologna 24 400
Florence Cathedral. 24 300
Antwerp Cathedral 24 000
St Sophia's, Constantinople 23000
Opera Houses
Carlo Felice, Genoa 2560
Opera House, Munich 2370
Alexander, St. Petersburg 2332
San Carlos, Naples 2240
Imperial, St Petersburg 2160
La Scala, Milan 2113
Academy of Paris 2092
St John, I^teran 22 900
Notre Dame, Paris 21 ooo
Pisa Cathedral i3cxx2
St Stephen's, Vienna. 12 400
St Dominic's, Bologna 12000
Tabernacle, London 7 cxxt
" Brooklyn ,.. 5500
St Mark's, Venice 7 000
and. rriieatres.
Teatro del Liceo, Barcelona 4000
Covent Garden, Ix)ndon 2684
Opera House, Berlin 1636
Now York Academy 2526
Metropolitan Opera, N. Y 5000
Philadelphia Academy 3124
Chicago " 3000
Heights of Coliamns, Towers, Doraes, Spires, eto-
L0CAT10N8. Feet. Locations. i Feet.
CHIMNEYS.
Townsend's Glasgow . .
StRollox
Musprat's liiverpool .
Gas Works Edinburgh
New England Glass Co. Boston
Steam Heating Co. . . .New York.
Metropolitan Tract Co.
u
COLUMNa
Alexander St Peters'g
Bunker Hill Mass
City London . . .
July Paris
Napoleon "
Nelson's London . . .
Place Vendomo Paris
Pom|)cy's Pillar Egypt
Tnij.'in Rome
Washington Wash'gton
York London . . .
TOWERS AXD DOMES.
Babel
Balber
Capitr»l Wtt.sh'gton
St Peters Rome
Cathedral Cologne . . .
*• Cremona..
** .....Escurial. ..
474
455-
406
34'-
230
220
353
175
221
202
157
132
171
136
"4
145
555
138
680
500
287.5
469.5
524-9
392
200
TOWERS AND DOMES.
Cathedral Florence . .
" Magdeb'rg
" Milan
" Petersburg
T^eaning Pisa
Porcelain China
St Mark's Venice
3t PaaPs .London . . .
SPIRES.
Cathedral New York .
" Strasburg .
♦* Antwerp..
Grace Church New York.
Freiburg
Salisbury
St John's New York.
St Paul's "
St Mary's Ijftbeck . . .
Trinity Church New York.
Balustrade of Notre
Dame. Paris
Towers of ditto "
H<Hel des Invalidos. . . *'
St Nicholas Hamburg. .
St Stephen Vienna
Stmsburg.
Utrecht
Votive Church Vienna. . . .
390-5
339 9
438
363
188
200
328
355- «
325
465-9
404.8
2X6
410
450
9XO
200
404
2S6
216
232.9
344
473
443 8
486
464
3'4-9
BBIDGES, CANALS, BEKAK WATERS, ETC.
i8i
i\.r€tas of Liakes in Evirope, A^aia, and Africa.
LAXta.
beoAva
Tcbad, Africa .
Sq.
Miles.
400
11600
L.AKK9.
Sq.
Miles.
Dembia, AbyssiDia.
Loch liOmood
13000
27
Lakes.
Lough Neagh,Irel'U
ToutiDg, China....
ILiengths of Bridges.
Bkidom.
Feet.
Avignon. . . ,
Bad^oz ..,.
Belfast
HIackfriars ,
Koaton ....
Lioudon
J710
1874
2500
995
3483
950
Bkiugkb.
Liou, China
Menai
N. Y. and Brook- )
lyn spans undS
approaches.. . . )
Pont St. Esprit. . .
Feet.
6600
1050
5989
3060
Bbidgrh.
Potomuc
Riga
St Lawrence Riv'r
Strasburg
Vauxhall
Westminster
Sq.
Miles.
80
1200
Feel.
Hiengtlis or Spans of Bridges.
Bbidobi.
Britannia,
Conway. . .
Menai . . . ,
Feet.
460
400
580
BSIPGEB.
Niag'a at the Falls
*^ at Queens-
town
Feet.
X26S
Z040
Briiigks.
Schuylkill.
Southwark.
Wheeling. .
5300
2600
9M4
3390
860
1223
Feet.
340
240
XOIO
Canals.
Lengths.— lake Erie to Albany 352 miles; Chesapeake and Ohio 307; Schuylkill
X08; Delaware and Hudson 109; Kideau 132; London to Liverpool 265; Caledonia
85: Liverpool and Leeds 127.5; Rhone to Rhine 203.
Capacity of Locks of Erie 240 tons, and of Welland 1500.
Welland 26.77 miles. Lake Erie to Montreal via Canal 70.5; Lake and River
375 miles.
Montreal to Kingston.— Canai 120 miles; River 126.25. Suez, see page 183.
Breakwaters.
Delaware.— Average depth of water 29.4 feet below low- water level ; range of tide
6.66 feet; Outer slope 45°; Inner slopes z.5, 5, 3, and 1.3 to i ; length of base 172.12
feet.
P/ymou/A.— Outer slopes 1.75 to z fVom bottom to 7 feet 6 ins. below low- water
line; 4 to z to low- water line; z6 to z to 4 feet 6 ins. above low- water line; 5 to 1
to high water; Inner slope z.5 to z above low water line; 2 to z below low- water line.
Depth of water at high tide 46.5 feet; at low tide 30 feet
Body of breakwater rased w^ith I'lrge squared stones cramped together
Portland. — Depth of high water 58 feet; of low water 51 loet , Outer slopes z to z
firom bottom to 20 feet 'below low water; 2 to x to 12 A^t below lo>\ water; 6 to z
to low-water line; 4 to z to high water line; Inner slope 1.25 to z.
Body of breakwater, rubble, with crest wall of ashlar.
Dover. — Depth of high-water line 6z feet; of low-water line 42 feet.
Body of breakwater, concrete blocks fkced with granite; batter 3 inches to the
<bot, stepped up in each course.
Martedles. —Depth of water 33 feet ; Outer casing of beton 25. 5 tons each ; average
thickness of casing fk-om Z4 to 20 feet; slope z to z i^om bottom to water line; 2.5
to z above water-line; all other slopes .33 to z; Inner casing of first-class rubble
(of stones 2 to 5 tons weight), about z2 feet thick: Hearting, second-class rubble
(of stones 5 to 2 tons weight), about 6 feet thick; Nucleus, of quarry rubbish.
Algiert. — Depth of water 50 feet; rubble base carried up to 33 feet from surface of
water; the remainder composed of large beton blocks 25. 5 tons each ; slopes of rubble
base z to z ; Outer sIoi)e of l)eton blocks z.25 to z ; Inner slope of beton bbcks z to z.
Port Said (Suez Canal).— Concrete blocks, zo cubtc metres each, composed of z
of hydraulic lime to 13 of sand, mixed with sea water; 4 days in the mold and dried
for 4 months before being put in position. In some instances the composition of
beton blocks is .33 lime or cement to .66 sand and broken stone, about the size of
ballasting.
Rubble or Mock i^h'ni^.— Proportion of interstices to volume of breakwater fin-
ished: First-class rubble of 2 to 5 tons, .25; second class rubble of .5 to a tons, .a:
third-class rubble, quarry chips, etc., .x6; beton blocks, 15 to 25 tons, .33.
Man.— For force of water, see Waves of the Sea, page 853.
Q
1^2
LAKES, OCEANS, SEAS, MOUNTAINS, ETC.
Areas, IDeptlis, and Xleiglxts of G}-reat T^ortliern ILialses
of United States.
Lakes.
Erie
Huron
Michigan..
Ontario. . . .
Superior*.
Length.
Mile*.
250
200
360
180
400
Breadth.
Milee.
80
z6o
Z09
65
160
Mean Depth.
Feet.
2CX>
I20
900
500
288
Height
above Sea.
Feet.
564
574
587
234
635
Area.
Sq. Miles.
9000
23800
22000
7200
32000
* GreHtest depth 5400 feet.
Elevation Above Tide-tocUer at Albany. — Lake Erie 57a 6 feet; Hudson Rivei
2. 46 feet.
I^ean X>eptlx8 an.d .A^reas of tb.e Oceans and Seas.
{Herr Krummel.)
Fathom*.
Atlantic ' 2013
Archipelago | 487
Azof
Baltic Sea.
Black Sea
BehriDg's Struits. . . .
Caspian Sea.
China (East) Sea. . . .
Dead Sea.
English Channel, etc.
_36
550
66
47
Area
Sq. Miles.
29514275
3046600
8800
159690
150000
864555
120000
472 210
370
78416
Gulf of Mexico . .
" *' St. Lawrence
Indian
Japan
Mediterranean . .
North Sea
North Ice Sea. . .
Persian Gulf....
Pacific
Red Sea
Fathom*.
Arwi
Sq. Miles.
lOOI
I 765 910
160
101 075
1829
2836959s
1200
383 205
'4I
110923c
210505
84s
5264600
20
90100
3887
60343690
243
17082c
Mean depth of Ocean surrounding land 1877 fathoms = 2. 19 miles.
In his subsequent computations he estimates ocean area at 143 703 000 square
miles and determines area of land to water as i to 2.75, and that mean height of
land = 1377 feet, or one eighth that of Ocean.
Heiglits of IVtountains, "Volcanoes, and. Passes
above Level of Sea.
Mountains.
BITROPE.
Azores Pico
Barth(^lemy, France
Ben Lomond
Ben Nevis
Elbrus, Caucasus. . .
Guadarama, Spain. .
Hecla
Ida
Jungfrau, Switz'd. .
Mont Blanc
" Cenis
Mont d' Or, France.
Mulahaa8en,Gren'a.
Nephin, Ireland....
Olympus
Parnassus
Plynlimmun, Wale&
The Cylinder, Pyr. .
Wetterhom
ASIA.
Ararat
Caucasus
Dhawalagheri
Oeta, Java.
Mount LAbanon. . . .
1 Feet.
7613
7365
3240
4380
17776
8520
5147
4960
13725
>5797
6780
6510
1x663
2634
6510
6000
2463
10930
12 154
17 100
16433
28077
8500
Z3000
Mountains.
MountEverest(Him
alaya, highest) . . .
Mount Libauus. . . .
Sinai
AFRICA.
of
Atlas
Compass, Cape
Good Hope
Dianai Peak, St He-
lena
Kilimaojaro
Ruivo, Madeira....
Teneriffe Peak
AUBRIOA.
Aconcagua (highest
in America)
Blue Mount, Jam'a.
Catskill '
Chimborazo
Correde, Potosi ....
Crows' Nest, High-
lands, N. Y
Great Peak, New
Mexico
Mauo* Loa, Hawaii
Feet.
29003
9523
X5000
7496
ZO400
10 000
2700
20000
5160
12300
23910
8000
3804
21 441
16036
1370
19788
13805
Mountains.
Mount Pitt
Mount Washington.
Nevado de Sorata. .
Orizaba
Potosi
Sierra Nevada
Tahiti
White Mountains . .
VOLCANOES.
I Cotopaxi
i Etna
I Hecla
I Popocatepetl
Sahama
St. Helen's, Oregon.
Vesuvius
Feet.
PASSES.
I i Cordilleras ...
"Mont Cenis.,
" Cervis.
I Pont d' Or
St. Bernard, Great. .
" Little. .
St. Gothard
Simplon. . ,
9549
6426
25248
18879
18000
15700
10895
623c
18887
X0874
5000
17784
22350
13320
3930
13525
677S
IZ xoo
9843
817s
719a
6808
6578
CANAL LOCKS, BLBVATION8, AND BIVEBS. 1 83
Dimensions of Oanal XjooIcs.-^CZT. S.)
Cahal.
Albemarle and
Chesapeake. .
Black River,
Crook'd L'ke,
ChenaDgo,
Chemung,
and Genesee
Valley
Chesapeake and )
Delaware ....]
•3
M
a
Feet.
220
90
330
s
Ft.
No
=4
a
Ft.
6
Length of
Caual.
Miles.
14
77
8
97
33
L"3-75
14
ClIfAL.
Champlain
Cayuga and )
Seneca )
Delaware and i
Raritan. ../..)
Dismal Swamp. . .
Erie
Falls of Ohio, Ky.
Oswego
Welland, Canada. .
•
-3
J
Feet.
1
ft
0
Feet.
Feet.
1 10
18
5
1 10
18
7
220
24
7
90
17-5
• 5-5
no
lU
7
350
80
2-60
no
18
4
270
45
14
Leocib
CiwaL
Miles.
66.75
a4-7S
43
44
353
38"
28
Length of vessel that can be transported is somewhat less than lengths of lock&
Suez Canal.'
Length 99 miles.
Width 196 to 328 feet at surface, 72 at bottom, and 26 deep.
Heiglits oro'btaineci IKlevatioiis, and. various I'laoes
and. I*oin.ts above tlie Sea.
Locations.
Aconcagua, Chili . .
Antisana, highest
established eleva-
tion (Prtrmhouse) . .
Balloon (Gay Lussac)
" (Green, 1837)
" (Glaisher and
Coxwell)
Braail, Qaito, and (
Mexico plains. . (
Condor's flight
Eagle's "
Everest, Himalaya.
Feet.
23910
13434
22900
27000
37000
6000
8000
29500
16500
29003
Locations.
Geneva city ....
Greneva Lake...
Gibraltar
Humboldt's highest
elevation
Isthmus of Darien.
Jungfrau, Switz'd. .
La Paz, Bolivia. . . .
LagunajTenetitlb. . .
iiOndon, city
Madrid.
Mexico, city of
Mont Blanc, Alps. . .
Feet. ]
I 220
1096
M39
19400
645
i37»5
12225
2000
64
2200
7525
15797
LocAtioxs.
Mont Rosa, Alps . . .
Mount Adams
Mount Katahdin...
Mount Pitt
Mount Washington.
Paris, city.........
Pont d' Oro, Pyr's. .
Posthouse, Ap. , Peru
Potosi, Bolivia. . . . .
Quito
St. Bernard's Mon'y
Vegetation
White Mountain . . .
Feet.
>5i55
5930
5360
9549
6426
"5
9843
14377
13223
13500
8040
17000
6230
BtTBBS.
BUROPS.
Danube
Dnieper. .....
Douro.
Dwina
Elbe
Garonne
Loire
Fo
Rhine
Rhone
Seine
Shannon
Tagus
niamea
Tiber
Vistula
Volga, Russia
AAA.
Amoor
Euphratfes....
Uenstlis of* !Rivers«
Mtlfls. RxTKRs. Miles.
1800
"43
400
1035
780
442
543
420
760
510
450
B50
510
220
190
630
2400
2500
X786
Ganges
Hoang Ho
Indus
Jordan
Ijcna
Tigris
Yenesei and Se-
lenga
Yang-Tse
AFRICA.
Gambia.
Niger
Kile
NORTH AMERICA.
Arkansas
Colorado
Columbia
Connecticut
Delaware
Hudson and Mo-
hawk.
1514
3040
1800
176
2762
1160
3580
3314
700
2400
4000
2070
1050
1200
410
420
335
RiTCBS.
Kansas
Ia Platte
Mackenzie
Mississippi ...,
Missouri
Ohio and Allegheny
Potomac
Red
Rio Bravo
Rio Grande
St. Lawrence
Susquehanna
Tennessee
Miles.
SOUTH AMKRICA.
Amazon . . . .
Essequibo . .
Magdalena. .
Orinoco
Platte
Rio Madeira.
Rio Negro. . .
Uruguay....
1400
850
2440
3160
3030
1480
420
1520
2300
1800
3173
630
790
4000
530
900
1600
2300
2300
1650
ZIOO
l84
8EA DEPTHS, BUILDING STONES, ETC.
Xjarge Trees in Caliibrnia,
" Keystone State.'''' — Calavera Grove, is 335 feet in height
'^Father of the Forest ^^—Felledj is 385 feet in length, and a man on horseback
can ride erect 90 feet inside of its trunk.
*^ Mother of the Forest. *'— Is 315 feet in height, 84 feet in circamference (26.75 feet
in diameter) inside of its bark, and is computed to contain 537 000 feet of sound i
inch lumber. t
Sea X>eptlis.
Feet.
Feet.
Baltic Sea.
Adriatic
English Channel...
Straits of Gibraltar.
Eastward of *'
Z20
130
300
3000
Coast of Spain
West of St. Helena.
Tortugas to Cuba . .
Gulf of Florida
Off Cape Florida...
Estimated depth of Atlantic 26cxx> feet
" " PaciQc 29000 "
250 miles off Gape Cod, no bottom at 7800 feet
Off Cape Canaveral .
'* Charleston
*' Cape Hatteras. .
" Cape Henry
" Sandy Hook. .. .
Feet
3400
4300
3120
4200
2400
Cascades and. W aterfklls.
Location.
Arve, Savoy. .
Cascade, Alps
Cataracts of the Nile.
Chachia, Asia
Foyers, Scotland . . . .
Garisha, India
Gavarny, Pyrenees . .
Feet.
1600
2400
130
34
40
362
197
1000
1260
Location.
Feet.
Genesee, N. Y ' 100
Lidford, England .... 1 100
Lulea, Sweden ' 600
Mohawk 68
Missouri
(50
}8o
Montmoronci I 250
Nant d'Apresias | 800
Location.
Niagara
Great Fall
Passaic
Potomac
Ribbon, Yosemite)
Valley J
Ruican, Norway . . . .
Staubbach, Switz'd. .
Tendon, Franco
Yosemite Valley 2600 feet
Fflel.
"lei
15a
74
74
3300
800
798
135
E^xpansioii and. Coxitraotion, of Building Stones fbr eaoli
Degree of Temperatvire. {Lieut. W. H. C BarUett^ U. S. E.)
For One Incb.
Granite 000004 825
Marble 000005 668
For One Inch.
Sandstone 000009 533
Whitepine 000002 55
fiesistaixce of Stones, etc., to thie Bfieots of Freezing.
Various experiments show that the power of stones, etc, to resist effects of freez-
ing is a fair exponent of that to resist compression.
Miagnetio Bearings of Ne-w York.
The Avenues of the City of New York bear 28° 50' 30" East of North.
Filters for 'Watev'worls.a.
I square yard of filter for each 840 U. S. and 700 Imp'l gaflons in 24
hours ; formed of a.5 feet of fine sand or gravel and 6 inches of common
sand or shells.
Led off by perforated pipes laid in lowest stratum.
Distaiaces between New York, Boston, Fliiladelplila,
Baltimore, and "Western Cities of TJ. S.
Assuming Boston as standard, New York averages 12 per cent nearer to these
cities, Philadelphia 18 per cent, and Baltimore 22 per cent
Between New York and Chicago the line of the Pennsylvania Railroad is 47 miles
shorter than that by the Erie and its connections, 50 miles shorter than that by the
N. Y. Central and Hudson River and its connections, and 114 miles shorter than that
by the BHltimore and Ohio and its connections.
For Distances between these and other cities of the U. S., see page 88.
WBATHBB-PLANT8, ANTIDOTES, ETC. iSj
"Weatlier-fbretelliiiK Il*laiits. {Hanneman.)
If Rain is imminetU. — Chickweed,* Sfellaria media ; its flowers droop
and do not open. Crowfoot anemone, Anemone ranunculoides ; its blossoms
close. Bladder Ketmia, HUnscus trionum ; its blossoms do not open. Thistle,
Carduua acaulia ; its flowers close. Clover, Thifolium pratensSj and its allied
kinds, and Whitlow ^rrass, Draba vema; all droop their leaves. Nipple-
wort, Lampsana communii ; its blossoms will not close for the night. Yel-
low Bedstraw, Galium verum ; it swells, and exhales strongly ; and Birch,
Betula cUb€L, exhales and scents the air.
IndicaHfMU of Rain. — Marigold, Calendula pluvialis ; when its flowers do
not open by 7 A. M. Hog Thistle, Sonchua arvensis and oUraceus ; when it6
blossoms open.
Rain of shoii duration. — Chickweed, Stellaria media ; if its leaves open
but partially.
If chudy. — Wind-flower, or Wood Anemone, Anemone memorasa; its
flowers droop.
Termination of Rain. — Clover, Trifolium praiense ; if it contracts its
leaves. Birdweed and Pimpernel, CbniWt^zc/tM and AnagcUlis arvensis; if
they spread their leaves.
Unifirm Weather, — Marigold, Calendula pluvialis ; if its flowers open early
in the A. M. and remain open until 4 P. M.
Clear Weather. — Wind-flower, or Wood Anemone, A nemone memorasa ;
if it bears its flowers erect. Hog Thistle, Sondius ai^vensis and oleraceus ;
if the heads of its blossoms close at and remain closed daring the night.
Treatxnent and. A.ntid.oteti to Severe Ordinary Poisons.
Antidotes in very smaU doses.
Chloroform and Eihet.—ColA afi^usions on head and neck, and ammonia
to nostrils. Antidote. — Camphor, petroleom, sulphur.
Toadstools, — (Inedible mushroom). Antidote.— S&me as for chloroform.
Arsenic or F^ Powder, — Emetic; after free vomiting give calcined ma^
nesia freely. If poison has passed out of stomach, give castor oil.
Antidote. — Camphor, nax vomica, ipec^caanfaa.
Acetate of Lead (Sugar of lead). — Mustard emetic, followed by salts,
Large draughts of milk with white of eggs.
Antidote. — Alum, sulphuric acid alike to lemonade, belladonna, strychnine.
Corrosive Sublimate (Bug poison). — White of eggs in 1 quart of cold
water, give cupful every two minutes. Induce vomiting without aid of
emetics. Soapsuds and wheat flour is a substitute for white of eggs.
Antidote. — Nitric acid, camphor, opium, sulphate of zinc.
Phosphorus Matches. — ftai Paste, — Two teaspoonfuls of calcined magne-
sia, foUowed by mucilaginous drinks. Antidote. — Camphor, coffee, nux vomica.
Carbonic Acid (Charcoal fumes). Chlorine^ Nitrous Oxide, or Ordinary
Gas. — Fresh air, artificial respiration, ammonia, ether, or vapor of hot water.
Antidote. — Otmphor, coffee, nux vomica.
Belladonna (Nightshade). — Emetic and stomach pump, morphine and
strong coffee. Antidote. — Camphor.
Ojnum, — Stomach pump or emetic of sulphate of zinc, 20 or 30 grains, or
mustard or salt. Keep patient in motion. Cold water to head and chest
AntidMe.—%irojig coffee fireely and by iigection, camphor, ether, and nux vomica.
Strychnine (Nux vomica). — Stomach pump or emetic, chloroform, cam-
phor, animal charcoal, lard, or fat.
Antidote.— Yl\ne,, coffee, camphor, opium freely, and alcohol in small doeea
Vef/etable fbiions.— As a rule, an emetic of mustard and drink freely of
warm water.
* Spreads its leavat about 9 A. M., and they remain open until noon.
i88
MISCELLANBOUd SLBMENTS.
MISCELLA^NKOtrS ELEMENTS.
Kartli.
Polar diameter 7899.3 miles. Mean density or specific gravity of mass 5.672. Maai
5 272 600 000 000 000 000 000 tons. Apparent diameter as seen fh)m Sun 17 seconds
Sun.
Heat of Sun equal to 322 794 thermal units per minute for each sq. foot of ph»
tosphere or solar surface.
Diameter of Sun 882000 miles, tangential velocity 1.25 miles per second or 4.41
times greater than that of the Earth.
Distance fh)m Garth 91.5 to 92 millions of miles.
^£asoxi Etild Dixon's Uixie.
39<> 43' 26.3" N. mean latitude. 68.895 miles.
DlTttiont.
A.rea and
Anm.
America.
Europe . .
Asia
Africa . . .
Sq. MilM.
14 491 000
3760000
16 313000
10936000
I'opulation. {Behm and Wagner.)
Po|Hilation.
95 495 500
315929000
834 707 000
205 679 000
DlTitloiu.
Aim.
PojpolatioB.
Oceanica.
Greenland )
Iceland J '•*
Sq. Mile*.
4500000
4031000
82000
Total
50000000
1455933500
Austria ) ,0 ,««,«««
Hungary) 38000000
China. 434 626 000
France. 37000000
India. British . .240298009
Canada 3 839000
Mexico 9485000
Brazil n 106000
Countries.
Germany 43 900000
Great Britain.. 34 000 000
{Russia 66000000
Territories . . .22000000
(United States.... 50 000 000 I (Turkey 8866000
(Indians 300000 | ( ** in Asia. .16320000
About one thirtieth of whole population are bom every year, and nearly an equal
number die in same time; making about one birth and one death per second.
Earlier authority estimated population at x 288000000, divided as fbllovre:
Caucasians 360000000
Mongolians . . . .552000000
Ethiopians. ... .190000000
Asiatics 60000000
Malaya and )
IndoAmer's} '77 000000
Protestants.... 80000000
Israelites. 5 000 000
MohammedanB . 190 000 000
Pagana 300000000
Catholics ) ,e««^oo«
Rom. & Greek} ^Soooo 000
Descent of "Western 'H.ivers.
Slope of rivers flowing into Mississippi fW)m East is about 3 inches per mile;
and trom West 6 inches.
Mean descent of Ohio River Orom Pittsburgh to Mississippi, 975 miles, is about 5.2
inches per mile; and that of Mississippi ta Gulf of Mexico, 1180 miles, about 2.8
inches. '
Transmission of* Horse Fo-wer.
Largest, and perhaps most successAi], wire rope transmission is one at SchaflT
hausen, at Falls of the Rhine. Here, power of a number of turbines, amounting
to over 600 IP, is conveyed across the stream, and thence a mile to a town, where it
is distributed and utilized.
At mines of Falun, Sweden, a power of over 100 horses is transmitted in like
manner for a distance of three miles.
A-oids.
Acetic Acid (Vinegar), acid of MaU beer, etc. Tartaric Acid, acid of Orape wint.
Lactic Acidy acid of MiUCy Millet beer^ and Cider.
"NLan-xi-rem,
Relative Fertilizing Properties of Various Manures.
Peruvian Guano . . . . i I Horse 048 I Farm-yard 0298
Human, mixed 069 | Swine 044 | Cow 0259
Or, I lb. guano = 14.5 human, 21 horse, 22.5 swine, 33.5 farm-yard, and 38.5 cow.
Relative Value, Covered and Uncovered, on an Acre of Ground,
Covered 11 tons 1665 lbs. potatoes, 61 lb& wheat, 2x5 lbs. straw
Uncovered 7 •• 1397 " " 6j.ft " " w6
({
<t
PerCflnt.
Poppy. . 56 to 63
MISCBLLANBOUB ELEMENTS.
Vleld of* Oil of* Several Seede,
I Percent.! Per Cent. I Per Cent. I
I Castor . . 25 I Sunflower. 15 I Hemp. 14 to 25 I
189
Percent
Lineeed. xi to 2a
T'hiokness of 'Walls of* Buildings. (Engluk.) iMole9tvmrt/L)
Odtkb Walls.
ist class dwelling.
2d " "
3d "
4tli
«i
II
Pabtt Walls.
ist class dwelling,
ad " **
3d " " '
4tb " "
If walls are more
by half a brick.
Warehouses ^Jfimum
1st Class. of Wall.
For a height of 36 feet from itM.
topmost ceiling 17.5
Maziniam
Width
Mi
Height
of Wall.
of
Ground
ut
Footin|{fc
Floor.
Floor.
Feet.
Ine.
Ina.
Ins.
8S
38.5
21.5
21.5
70
305
17.5
17.5
52
30.5
17.5
13
38
21-5
13
13
85
38.5
31.5
31.5
70
3P-5
X7-5
17.5
5a
30.5
17-5
13
38
31.5
»3
8.5
than 70 U
set in lei
Qgtb, those of
Minimam Width of Welte.
9d
Floor.
Floor.
4th
Floor.
Ins.
Ins.
Ins.
17-5 175
17.5
17.5 13
13
13
8.5
13
8.5
13
17-5
17-5
17.5
175 13
13
13
8.5
13
1 8.5
8.5
th I 6th
Floor. I Floor.
rj
Ins. ' Ins.
13 ; 13
13 —
13
13
13
ITTarehouses *wi*dth"
ad Class. ofWaU.
For a height of 22 feet below ins.
topmost ceiling 13
For a height of 40 feet lower. . 21.5 For a height of 36 feet lower . . 17.5
24 feet lower . . 26
For footings 43.5
3<i Class.
For a height of 28 feet below
topmost ceiling 13
For a height of 16 feet lower . . 17.5
8 feet lower.. 21.5
For footings 34.5
4tla Class.
For a height of 9 feet below
topmost ceiling 8.5
For a height of 13 feet below . . 13
For footings. 30.5 . For footmgs 21.5
'Wooden lioora. (Bngtish.)
in^S.
Pfinei|Md
Beam.
Tie Beam.
Kin^
Poeta
Pwie.
Scoan
Qneens.
Siniiniag
Beam.
StraU.
20
4X4
9X4
4X4
—
—
—
3 X3
35
5X4
10 X 5
5X5
•—
—
—
5 X3
JO
6X4
II X 6
6X6
—
.—
—
6x3
35
5X4
11 X 4
—
4X4
ft
7X4
4 X3
45
6X5
13 X 6
—
6x6
7X6
5 X3
50
8x6
13x8
—
8x8
8X4
9X6
5 X3
55
8X7
14x9
—
9x8
9X4
10 X 6
5-5X3
60
8X8
15 X 10
"~~
10 X 8
10 X 4
II X 6
6x3
M[ineral Ooxistltnents al>0orl>«id or removed fVoxxi an
A.care of* Soil by several Crops. (Johruon.)
CKon.
Lime
Magnesia . . ; .
<telde of Ironi
FlMwphorlc )
H
58
•
Lba.
Lbe.
Lbfc
Lbs.
39.6
>7S
^•'
38.2
3
5-a
8.3
12
12.9
17
29.9
44-5
10.6
9.2
19.7
^I
2.6
3.S
7.1
,6
3a6
25.8
46.3
iS.|
CBon.
Sttlphuric I
Acid. ..] '
Chlorine....
Sitica
Ahimina —
Tatal.
a i
^ 1
n
^1
Lbt.
Lie,
Lba.
10.6
2.7
133
3
16
3.6
118. t
1295
247.8
— ~
3-4
■^"
210
2x3
423
Lbf.
9-a
4>
78.9
190
MlSCSLLAK£OITS BLEMBNT6.
Arverage Quantity of* rTaniiizi in. Several Substances*
{MorJU.)
Catechu. per Cent.
Bonibay 55
Bengal 44
Kino 75
NutgaUs.
Aleppo 65
Chinese 69
Oak.
14.2
21
Old, inner bark |
Oak. Per Cent.
Sumac. Per Ceat
Young, inner b'k 15.2
Sicily and Malaga
16
♦' entire b'k. 6
Virginia
10
" spring- )
cut bark J ^'
Carolina
5
WUlow.
*' root bark. 8.9
Inner bark
16
Chestnut.
Weeping
16
Ainer. rose, bark 8
Sycamore bark. . . ,
16
Horse, " 2
Tan shrub " ....
'3
Sassafras^ root bark 58
Cherry-tret
24
Alder bark 36 per cent
To Convert Cliemioal ITormiiloB into a I\£ath.eniatioal
Bxpressiou.
KcLE. — Multiply together equivalent and exponent of each substance, and product
will give proportion in compound by weight. Divide 1000 by sum of their products,
and multiply this quotient by each of these products, and products will give re-
spective proportion of each part by weight in 1000.
ExAMPLK. — Chemical formula for alcohol is (74 fT^Os. Required their propor-
tional parts by weight in 1000?
C4 Carbon = 6. 1 X 4 = 24. 4 ) ( 525. 82 )
fl6 Hydrogen = 1X6= 6 [ X 21.55 (129.3 > by weight
O2 Oxygen = 8X2 = 16 ) (344-8 )
zooo-i-46.4 =21.55 999-9^
Klein eiitary Bodies, -with tlieir Sym"bols and.
!Eq.u. i val en ts .
Body.
Aluminium.. .
Antimony
Arsenic
Barium
Bismuth
Boron
Bromine
Cadmium. ...
Calcium
Cju'bon
Clilorine
Chromium...
Ccibalt
Coliimbium..
Copper
Fluorine
(ilucinum
I Symb.
Eqolv.
1 AI
137
1 Sb
64.6
As
37-7
Ba
68.6
Bi
71-5
B
ZI
Br
78.4
Cd
55-8
Ca
20-5
C
6.1
CI
35-5
Cr
26.2
Co
29-5
Ta
184.8
Cu
31-7
F
18.7
a
6.9
Body.
Symb. Equtv.
Gold.... Au
Hydrogen H
Iodine.! I
Iridium Ir
Iron Fe
Lead Pb
Lithium L
Magnesium . . - Mg
Manganese... Mn
Mercury j Hg
Molybdenum! Mo
Nickel ; Ni
Nitrogen N
Osmiam 1 Os
Oxygen
Palladium....
Phosphorus. .
O
Pd
P
196.6
I
126.5
98.5
28
103-7
7
12.7
26
200
47-
29.
14.
99.
8
53-
IS-
Body.
Platinum . . . .
Potassium . . .
Rhodium . . . .
Selenium . , . .
Silicon
Silver
Sodium
Strontium
Sulphur
Tellurium. . . .
Tin
Titanium....
Tungsten . . . .
Uranium ....
Yttrium
Zinc
Zirconium...
Symb.
Pt
K
R
Se
Si
Ag
Na
Sr
S
Te
Sn
Ti
W
U
Y
Zn
Zr
EqaW.
98.8
39-2
52.2
40
22
108.3
23-5
43-8
z6. 1
64.2
58-9
24-5
32
32:3
34
A^nalysis of oertain Organic SuTastanoee "by "Weight.
Body.
Albumen....
Alcohol
Atmospheric uir
Camphor . . .
Caoutchouc .
Casein
Fibrin
Gelatine
Gum
Hordein
Lignio
Car-
Hydro-
Oxy-
Nltro-
bon.
52.9
Kon.
gen.
23.9
gen.
7-5
'5-7
52-7
12.9
34-4
—
—
77^
23
73-4
ia7
15.6
•3
87.2
Z2.8
— .
59-8
7-4
11.4
21.4
53-4
7
19.7
19.9
47-9
7-9
27.2
17
42.7
6.4
50.9
—
44-2
6.4
47.6 1.8 II
52.5
5-7
41.8 1
- II
Boov.
Morphine
Narcotino
Oil, Castor.
Linseed. . . .
Spermaceti.
Quinine
Starch
Strychnine
Sugar
Tannin
Urea
Car-
Hydro-
Oxy-
bon.
Ren.
gen.
72-3
6.4
16.3
65
5-5
27
74
10.3
15-7
76
«i-3
12.7
78
II. 8
10.2
75.8
75
8.6
44.2
6.7
49.1
76.4
6.7
ii.i
42.2
6.6
51-2
52.6
3.8
43-6
18.9
9-7
a6.a
Nitro-
gen.
- ■ ■ — ^
5
2-5
45-«
UtSC£LLANBOtrs BLBMSKTS.
191
X>il\itioxi Per Cent. Necessary to Recluoe Spirituoua
IL«iquor8.
Water to be added to 100 volumes of spirit when of following strength:
Sirengtb
Reqairad.
90
85
80
75
70
65
60
ss
50
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent
85
5-9
—
—
—
—
—
—
—
—
80
12. s
6.3
—
—
—
—
—
—
—
75
20
»3-3
6.7
—
—
—
—
—
—
70
28.6
21.4
14.3
7-1
—
—
—
—
65
38.5
30.8
23.1
154
7-7
—
—
—
—
60
50
417
33-3
25
16.7
8.3
—
—
—
55
63.6
54-5
45.5
36.4
27.4
18. 2
9.1
—
—
50
80
70
60
50
40.
30
20
10
—
40
125
112.5
ICO
875
75
62.5
50
37-5
25
30
200
1833
166.7
150
133-3
116.7
100
83:3
66.7
Illustration.— 100 volumes of spirituous liquor having 90 per cent, of spirit con
tains: alcohol 90, water lo, — 100.
To reduce it to 30 per cent, there is required 200 volumes of water.
Hence 200+10 = 210, and ^ = ^-==3° ^ ^ or 20 per cent
210 70 70 water, ^
Proportion of A.lcoh.ol Per Cent.
In 100 Parts of Spirit^ by Weight or Volume, at 60°.
Alcohol.
Specific
Gravity.
Alcohol.
Specific
Gravity.
0
5
10
I
.984
20
30
40
•972
.958
•94
Alcohol.
Specific
Gravity.
Alcohol.
Specific
Gravity.
50
60
70
.918
.896
.872
80
90
lOO
.848
.823
•794
In 100 Parts 0/ Alcohol and Waier, by Weight, at 60°.
Specific
Gravity.
.987
•985
•984
Tides of A.tlantio and. Paci£Lo Oceans at Istliznus of
Panama. {Totten.)
Atlantic, Navy Bay.— Highest tide i.sfeet; lowest .6jfeet.
Pdcific, Panama Say.— Highest tide 17.72 to 21. 2 feet; lowest g-jfeet
Alcohol.
Specific
Gravity.
Alcohol.
Specific
Gravity.
Alcohol.
Specific
Gravity.
0
•53
1.02
I
1.99
3.02
4.02
.996
•994
•993
501
6.02
7.02
.991
.'p8
Alcohol.
7-99
905
10.07
Statx.
Illinois
Virginia
Pennsylvania* .
Kentucky ,
A^reas of XJ. S. Coal Fields.
Sq. Milea. State. Sq.Milei. Statb.
44000
21000
15437 1
i35<»
Ohio
Indiana . .
Missourit.
Michigant ,
II 900
7700
6000
5000
* BitamtaioQi »nd Anihracit*.
Tennessee . .
Alabama. . . .
Maryland...
Georgia
t Anthracite.
Sq. Milea.
4300
3400
550
150
XSxtremes of Heat in "Various Countries.
England.... 96*'
France..... 106.5°
Holland
Belgium
}•
I02''
Denmark )
Sweden S .. 99. 5^
Norway )
Russia io2<'
Greece 105°
Italy 104O
S{)ain 102**
Tunis iz2.s<
Egypt 116.1°
Africa. 133-4°
Asia 120°
Suez 126. 5°
Germany 103° | Manilla "3.5° I N. America — 102°
Extremes of temperature upon the Earth 240°.
Eactrexnes of Cold in Various
England...- 5°
Holland
Belgium
|— 12«
Denmark )
Sweden J —67°
Norway )
France — 24°
Russia —46°
Germany.. — 32°
t^ountriee.
Italy
.— to*-
Fort Reliance, N. A. .— 70°
Semipaiatinsk, " ..—76°
192
MISCELLANEOUS ELEMENTS.
Af eazi ^temperatures of Various Ljocalities.
London 51° | Rome 60° I Poles —13° I Polar Regiona . 360
Edinburgh 41^ | Equator 82° | Torrid Zone. 75° | Globe 50°
ILiiixe of nPerpetual Congelation, or Sno-w^ Ljine.
Latitude.
Height.
0
Feet.
10
14764
15
14760
20
13478
25
12557
Latitude.
O
30
35
40
45
Height.
Feet.
II 484
10287
9000
^670
Latitude.
O
50
55
60
65
Heifcfat.
Latitude.
Height.
Feet.
0
Feet.
6334
70
1278
5020
75
1016
3818
80
451
2230
8S
327
At the Equator it is 15260 feet; at the Alps 8120 feet; and in Iceland 3084 feeL
At Polar Regions ice is constant at surCace of the Earth.
X^imits of "Vegetation in Temperate Zone.
The Vine ceases to grow at about 2300 feet above level of the sea, Indian Corn at
2800, Oak at 3350, Walnut at 3600, Ash at 4800, Yellow Pine at 6200, and Fir at 6700.
Periods of Oestation and Number of Young.
WeelcB.
Elephant. 100
Horse .... M^
1 50
Camel. ... 45
Ass 43
No.
I
Cow. . . .
Buflhlo.
Stag. . . .
Bear . . .
Deer . . .
Weeks.
• 41
• 40
. 36
• 30
. 24
No.
I
I
I
2
2
WeeltB.
Sheep ... 21
Coat .... 22
Beaver.. 17
Pig. >7
Wolf to
No.
2
2
3
12
5
Weeks.
Hog 9
Fox 9
Cat 8
Rat 5
Squirrel . . 4
No.
6
S
6
8
6
Rabbit.. 4 6 Guinea Pig. 3
Periods of Incubation of Birds.
Swan, 42 days; Parrot, 40 days; Goose and Pheasant, 35 days; Duck, Turkey, and
Peafowl, 28 days; Hens of all gallinftceoui birds, 21 days; figoan and Canary, 14
day& Temperature of incubation is 104°.
.A^ges of A.nimals, eto
Raven,
Bear, 20; v^uw, 20 j uwv, zu^ rvmuwitJiuB, zt>, own
Dog, 15; Sheep, jo; Hare, Babbit, and Squiirel, 7.
Relative "^^eiglit-s of I3rain.
Man, 154-33; Mammifers, 29.88; Birds, 26.22; Reptiles. 4.2; Fiah, i.
Buoyancy of Casks.
Biutyancy of a submerged ciisk In fk*e8h water in lbs. =62. 425 times the volume
of it in cube feet, 7.48 times the volume in U. S. gallons, and 6.2355 tlmtn in
Imperial gallons, less the weight of the cask. >
HDransportation of Horses and Cattle.
Space required on beard of a Marine Transpert is: for Horeee, 30 ins. by 9 feet;
Beeves, 3^4 ins. by 9 feet. Provender required jw diem is: for Horses, Hay, 15 lbs.;
Oats, 6 quarts; Water, 4 gallons. Beeves, Hay, 18 lbs. ; Water, 6 gallons.
lioclc and JSartli ICxcavation and Smloanlzment.
Number of Cube iket 0/ various Etwika in a Ton.
Loose Earth 24 1 Clay 18.6 j Clay with Gravel 14.4
Coarse Sand 18.6 | Earth with Gravel. .. 17.8 | ComniooSoiL 15.6
The volume of Earth and Sand in embankment exceeds that in a primary ex<
cavation in following proportions:
Rock, large 1.5 I Rock, ballaet 1-2 J Clay m
" mediaro 1.25 | Sand i43)<xrav«l 09
Clay and Earth will subside about .12.
feet uput.
I
i-S
3
2-5
3
35
4
4-5
MISCELLANEOUS ELEMENTS.
Hills or Plants in. an A.rea or One A.ore.
From I to 40 feet apart from centres.
Vo. ~ "
193
43560
19360
10890
6969
4840
3556
2722
2 151
Feet apart.
No.
5
1742
5-5
1440
6
J2IO
6.5
5031
7
889
7 5
775
8
680
85
692
Feet apart.
No.
9
538
9-5
482
10
435
10.5
361
12
302
13
=58
»4
223
15
193
Feet apart.
No.
16
171
17
151
18
X35
20
J08
. 25
30
%
35
35
40
27
Naj3a"ber of several Seeds in a Bushel, and I^nml>er per
i5q.uare IToot per A.prem
No. Sq. Foot. No. Sq. Foot.
Timothy.
Clover...
41 823 360
16400960
960
376
Ryo . . .
Wheat.
888390
556290
20.4
12.8
Volumes.
PermaneDt gases, as air, eta, are diminished in their volume in a ratio direct
with that of pressure applied to them. With vapor, as steam, etc., this rule is
varied in consequence of presence of the temperature of vaporization.
Minerals.
Relative Hardness of* some IMinerals.
Talc I
Gypsum 2
Mica 2.5
Carbonate of lime. 3
Barytca 3.5
Fluor spar. ... 4
Feldspar 6
! Lapis {^azuli . 6
Opal 6
Quartz 7
Tourmalin .... 7
Garnet 7.5
Emerald. 8
Topaz 8
Ruby 9
Diamond 10
"^Veiglit of* X>iamonds.
Carats.
Bfattam 367
Grand Mogul* 279.9
Orloff. 194.25
Florentine, brilliant . 139.5
Crown of Portugal. . . 138.5
* Roaghgoo.
Carats.
Regent or Pitt 136.75
Star of the Souths . . 125
Koh-l-NoorJ 106,06
Piggott.. 82.25
Napac. 78.625
t Rough 254.5.
Carats.
Dresden 76.5
Sancy 53.5
Eugenie, brilliant . 51
Hope (blue) 48. 5
Polar Star 40.25
t Originally 793.
Heat of the Sxin.
Sir Isaac Newton 3138740° | Waterston 16000000°
Capt. John Ericsson 4 909 860° | Soret. ^0443 323°
Sundry others ranging from 2520° to 183600°.
Moon. — Distance of Moon from Earth 237 000 milea
K'rigorifio IVlixtnre.
lowest temperature yet procured. Faraday obtained 166° by evaporation of a
mixture orsolid carbonic acid and sulphuric ether.
Current of Rivers.
A fall of . I of an inch In a mile will produce a current in rivers.
Sandstones.
Structures of sandstone erected in England in 12th century ore yet in good
condition.
Canal rTransportation.
Erie Canal and Hudson River.— From Bnflfklo to New York, 495 miles, cost of
transportation 2.46 mills per ton (inclusive of tolls) per mile. Transportation of
wheat costs when it reaches New York 4.72 cents per bushel, and .6z cents per
bushel for elevating and trimming.
Towing.— Erie Canal— Four mules will tow 230 tons of freight down and 100
tons back, involving a period of 30 days, at a cost of 8 cents per mile for a course
of 690 miles.
194
MISCELLANEOUS ELEMENTS.
Matter.
Unit of the Physicist is a molecule, and a mass of matter is composed of them^
having same physical properties as parent mass.
It exists in three forms, known as solid, liquid, and gaseous. Solids have indi-
viduality of form, and they press downward alone. Liquids have not individuality
of form, except in spherical form of a drop, and they press downward and sideward.
Gases are wholly deficient in form, expanding in all directions, and consequently
they press upward, .downward, and sideward.
Liquids are compressible to a very moderate degree. Water has been forced
through pores of silver, and it may be compressed by a pressure of one pound per
square mch to the 3 300000th part of its volume.
Gases may be liquefied by pressure or by reduction of their temperature.
Combustible matter (as coal) may be burned, a structure (as a house) may be
destroyed as such, and the fluid (of an ink) may be evaporated, yet the matter of
which coal and house were composed, although dissipated, exists, and the water
and coloring matter of the ink are yet in existence.
Spaces between the particles of a body are termed pores. ■
All matter is porous. Polished marble will absorb moisture, as evidenced in its
discoloration by presence of a colored fluid, as ink, etc.
Silica is the base of the mineral world, and Carbon of the organized.
IM-inutexiess of* H^atter.
A piece of metal, stone, or earth, divided to a powder, a particle ot it, howevet
minute, is yet a piece of the original material from which it 'was separated, retain-
ing Its identity, and is termed a molecule.
It is estimated there are 120000000 corpuscles in a drop of blood of the musk-deer.
Thread of a spider's web is of a cable form, is but one sixth diameter of a fibre of
silk, and 4 miles of it is estimated to have a weight of but i grain.
One imperial gallon (277.24 cube ins.) of water will be colored by mixture therein
of a grain of carmine or indigo.
A grain of platinum can be drawn out the length of a mile.
Film of a soap-and- water bubble is estimated to be but the 300000th part of an
inch in thickness
It is computed that it would require 12000 of the insect known as the twilight
monad to fill up a line one inch in length.
A drop of water, or a minute volume of gas, however much expanded— even to
the volume of the Earth — would present distinct molecules.
Gold leaf is the 280000th part of an inch in thickness.
A thread of silk is 2500th of an inch in diameter.
A cube inch of chalk in some places in vicinity of Pftris contains 100 000 of shells
of the foraminifera. ^
There are animalcules so small that it requires 75 000 000 of them to weigh a grain.
•
Velocity, Weiglit, and Volunae of AColeotxles.
Fetocttj/.— Collisions among the particles oi Hydrogen are estimated to occur at
the rate of 17 million-million-million per second, and in Oxygen less than half this
number.
Weight.— K million-million-mlUioD-million molecules ot Hydrogen are estimated
to weigh but 60 grains.
Volume. — 19 million-milliOD-mill>o& molecules ot Hydrogen have a volume of .061
cube in& DxameUr.—Five millions in a line would meaaure but . i inch.
Cliarooal, ^looliol.
Charcoal as yet has not been liquefied, nor has Alcohol been solidified.
^MCetala*
Metals have five degrees of lustre^-^pZefuJen/, shining, glistening, glirnin^ring, »nd
duU.
All met^ can be vaporized, or exist as a gas, by application to them of their ap-
propriate temperature of conversion.
Repeated hammering of a metal renders it brittle ; reheating it restores its tenacity.
Repeated melting of iron renders it harder, and up to twelfth time it becomes
stronger.
Platinum is the most ductile of all metals.
MISGSLLANEO US SLSM JCNTS. 1 95
laaapenetrabilit^r.
Impenetrability expre8sea.the inability of two or more bodies to occupy same
space at same time.
A. mixture of two or more fluids may compose a less volume tban that due to sum
of their original volume, in consequence of a denser or closer occupation of their
molecules. This is evident in the mixture of alcohol and water in the proportion
of 16.5 volumes of former to 35 of latter, when there is a loss of one volume.
Slastioity. .
Elasticity is the term for the capacity of a body to recover its former volume,
after being subjected to compression by percussion or deflection.
Glass, ivory, and Steel are the most elastic of all bodies, and clay and putty are
illustrations of bodies almost devoid of elasticity. Caoutchouc (India rubber) is but
moderately elastic; it possesses contractility, however, in a great degree.
iMIoxneixtuxxx.
Momentum is quantity of motion, and is product of mass and its velocity. Thus,
the momentum of a cannon-ball is product of its velocity in feet per second and its
weight, and is denominated footpounds.
A foot-pound is the power that will raise one pound one foot
Souxid.
Telocity of sound is proportionate to its volume; thus, report of a blast with 2000
lbs. of powder passed 067 feet in one second, and one of 1200 lbs. 1210 feet. It passes
in water with a velocity of 4708 feet per second. Ck>nversation in a low tone has
been maintained through cast-irdn water pipes for a distance of 3120 feet, and its
velocity is from 4 to 16 times greater in metals and wood than air.
T-iiglit.
Sun's rays have a velocity of 185000 miles per second, equal to 7.5 times around
the Earth.
Color Slindness
Is absence of elementary sensation corresponding to red.
I^vixxiixiovis Point.
To produce a visual circle, a luminous point must have a velocity of 10 feet in a
second, the diameter not exceeding 15 ins.
All solid bodies become luminous at 800 degrees of heat.
ACirage.
When air near to snrfiice of Earth becomes so highly heated, as upon a sandy
plain, that its density within a defined distance ft*om it increases upwards, a line
of vision directed obliquely downwards will be rendered by refVaction, gradually
increasing, more and more nearly horizontal as it advances, until its direction is so
great as to produce a total reflection, and the reflected ray then, by sucdessive re-
fiactionSy is gradually elevated until it meets the eye of the observer.
looming is inverted mirage, firequently seen over calm water, and is. effect of
lower or surlkce stratum of air being colder than that above It
Siio-w Flakes.
96 forms of snow flakes have been observed.
Alelted. Sxio-w
Prodaces Arom .35 to . 125 of its bulk in water.
8treiis;t>i of* led.
Two inches thick wfll support men in single file on planks 6 feet apart; 4 inches
will support cavalry, light guns, and carts; and 6 inches wagons drawn by horses.
Temperature.
Sulphuric acid and water produce a much greater proportionate contraction than
alcohol and water. Both of these mixtures, however low their temperature, pro-
duce heat which it in a direct proportion to their diminution va volume.
At the depth of 45 feet, the temperature of the Earth is uniform throughout the
year.
Temperature of Earth'increases about z<' for every 50 to 60 feet of depth, and its
WQBt is eMfmated at 30 miles.
Abody at Equator weighs two hundred and eighty-nine parts less than at th« Polea
196
MISCELLANEOITS ELBMSNTS.
Agea of* A.iiixnats, Fislies, etc.
{Additional to page 192.)
Tiger, Leopard, Jaguar, and Hyena (in confinement), 25 years; Beaver, 50; Stag,
under 50; Ox and Ass, 30; Chamois, 25; Llama. Monkey, and Baboon, 15 to 18; Par-
rot, 200; Tortoise, 100 to 200; Crocodile, 100; Carp, 70 to 150; Goose, 80; Pelican,
45; Hawk, 30 to 40; Crane, 24; Peacock, Goldfinch, Cha£Qnch, f^om 10 to 25; Do-
mestic Fowls, Pigeons, Blackbird, Nightingale, and Linnet, 10 to 16; Thrush, Rubin,
and Starling, 8 to 12; Wren, 2 to 3; Salmon, 16; Eel, lo; Codfish, 4 to 17; Pike, 30
to 40; Queen Bee, 4; Bee, 6 months, and Drones, 4 months. {HoughtoMng.)
Birds and Iii^ects^ — (iV. De Lacjf.)
Elements of Flight— Reslslanve of air to a body in motion is in ratio of surface
of body and as square of its velocity.
Wing Surface.— EKient or area of winged surface is in an inverse ratio to weight
of bird or insect.
A Stag-beetle weighs 460 times more than a Gnat, and has but one fourteenth of
its wing surface; 150 times more than a I^dy Bird (bug), and has but one fifth.
An Australian Crane weighs 339 times mora than a sparrow, and has but one sev-
enth; 3ooocxx> times more than a Gnat, and has biu one hundred and fortieth. A
Stork weighs eight times more than a Pigeon, and has but one half. A Pigeon
weighs ten times more than a Sparrow, and has but one half; 97 000 times more than
a Gnat, and has but one fortieth.
A resisting surface of 3o.8q. yards will enable a man of ori^Inary weight to descend
safely ftom a great elevation.
Strength of Insects. — Insects are relatively strongest of air animala A Cricket
can leap 80 times its length, and a F'ea 200 tlmea
♦
A.pplication. fbr Stings and Siirns.
Sting of Insects. — Ammonia, or Soda moistened with water, and applied as a paste.
Bums.— Eoi alcohol or turpentine, and afterwards bathed with lime water and
sweet oil. Cold water not to be applied.
To Preserve Aleat.
Meat of any kind may be preserved in a temperature of from 80° to 100°, for a
period of ten days, after it has been soaked in a solution of i pint of salt dissolved
in 4 gallons of cold water and .5 gallon of a solution of bisulphate of calcium.
By repeating this process, preservation may be extended by addition of a solation
•f gelatin or white of an egg to the salt and water.
To Detect Starch, in Miillc.
Add a few drops of acetic acid to a small quantity of milk ; boil it, and
after it has cooled filter the whey. If starch is present, a drop of iodine
solution will produce a blue tint.
This process is so delicate that it will show the presence of a milligram of starch
in a cube centimeter of whey (i grain of starch in 2. 16 fluid-ounces).
Retaining "Walla of Iron I*iles.
Sheet PHe-s.—j feet fh)m centres, 18 ins. in width and 2 ins. in thickness, strength^
ened with 2 ribs 8 ins. in depth.
Plates.— 7 feet in length by 5 feet in width and i inch in thickness, with on*
diagonal feather i by 6 ins.
Tie-rods 2 ins. in diameter
Stone Sawing,
Diamond Stone Sawing.^(Emerson.) Alabama marble 6 fleet X a. 5 feet in 22 mill'
otes = 41 sq. feet per hour.
"Wood Salving.
7722 feet of poplar, board measure, firom 9 round logs in i hour. Engine 12 iaa.
diameter by 24 ins. stroke.
HISCELlANEOirS EUSMSKTS.
197
Coat of* IDvedigi-ng.
AehuU eottj if on an extended win% incVusive of Delivery^ if dredging into or on a
vessel alongside of dredger. — ( Trautwine, )
Labor al$i per day <md Repairs of Plant included.
Depth.
zo
15
Centa.
Depth.
Ceota.
Cube Yarda.
6
7
Feet.
20
22
Cube Yarda.
8
9
Depth.
Feet.
25
30
Cents.
Cube Yards.
10
13
Depth.
Feet.
35
40
Centa.
Cube Yarda.
18
25
Discharge of Scows or Came/*.— TOwing .25 mile 4 cents per cube yard, .5 mile 6
centSj .75 mile 8 cents, and z mile 10 cents.
Note. —A Scow is a flat bottomed vessel or boat A Camel is a shallow, flnt<
bottomed and decked vessel, designed for the transportation of heavy freight or the
tnisCaining of attached bodies, as a vessel, by its buoyancy.
X)redgins*
A steam dredge will raise 6 cube yards, or 8.5 tons, per hour per £P.
Aletal 3Boriiis and. 'Purxiing.
BoRiva.—Cast tron.-'Divide 25 by the diameter of the cylinder in inches for the
revolutions per minute.
tVrought iron. —The speed is one fourth to one fifth greater than for cast iron
Brass.— The speed is about twice that for cast iron.
TuBNiNO —Cast iron. —The speed is twice that of boring.
Wrought iron.— The*speed is one fourUi to one fifth greater than that for cast Iron
BraM.—The speed is twice that of boring.
Vertical boring. — ^The speed may be twice that of horizontal boring.
The feed depends upon the stability of the machine and depth of the cut
"Well Boring.
At Ck>ventry, Eng., 750000 galls, of water per day are obtained by two borings of
6 and 8 ins., at depths of 200 and 300 feet
At Liverpool, Eng., 3000000 galls, of water per day are obtained by a bore 6 ins.
in diameter and 161 feet In depth.
Tbis large yield is ascribed to the existence of & fault near to it, and extending to
a depth of 484 feet
At Kentish Town, Eng.. a well is bored to the depth of 1302 feet
At Passy, France, a well with a bore of i meter in d'ameter is sunk to a depth of
1804 feet, and for a diameter of 2 feet 4 ins. it is further sunk to a depth of 109 feet
10 ins., or 1903 feet 10 ins.^ tram which a y'eld of 5 582000 galls, of water are obtained
per day.
rrempering Boriixg Instruxnents.
Heat the tool to a blood-red heat; hammer it until it is nearly cold; reheat it to
a blood-red heat, and plunge it into a mixture of 2 oz. each of vitriol, soda, sal-am-
moniac, and spirits of nitre, i oz. of oil of vitriol, .5 oz. of saltpetre, and 3 galls, of
water, retaining it there until it is cooL
Circular Sa-ws.
Bevolutions per Minute. — 8 ins. 4500, 10 ina 3600, and 36 ins. looa
]\fa8onry.
Concrete or Beton should be thrown, or let fall from a height of at least 10 feet,
or well beaten down.
The average weight of brickwork in mortar is about 102 lbs. per cube foot
Plastering.
In measuring Plasterers' work all openings, as doors, windows, etc., are com-
puted at one half of their areas, and cornices are measured upon their extreme
edges; including that cut oflT by mitring.
O-lazinf?.
In Glaziers' work, oval and round windows are measured as squares.
R*
tgS HISCELLANBOUS ELEMENTS.
Two cube feet of corn in ear will make a bushel of corn when shelled.
Tenacity of* Iron Bolts in "'Woods.
Diameter 1.125 ins. and 12 ins. in length required for Hemlock 8 tons, and foi
Pine 6 tons to withdraw them.
X^eugtli of* G}-un Barrels. (C. T. Coaihupe.)
The length of the barrel of a gun, to shoot well, measured from vent-hole, should
not be less than 44 times diameter of its bore, nor more than 47.
Hay and. Stra"v*r.
Hay, loose. 5 lbs. per cube foot Ordinarily pressed, as in a stack or mow, 8 Ibt.
Close pressed, as in a bale, 12 to 14 lbs.
Ordinarily pressed, as in a wagon load, 450 to 500 cube feet will weigh a ton.
Straw in a bale 10 to 12 lbs. per cube foot.
r^atixral I*o"wrers.
Sun.~-7h.e power or work performed by the Sun's evaporation Is estimated at
90 000 000 000 H*.
Niagara. — Volume of water discharged over the falls is e^iroated at 33000000
tons per hour, and the entire fall from Lake Erie at BuO'alo to Lake Ontario is 323.35
feet.
Velocity of Stars.
According to computation of Mr. Trautwine a Star passes a range in 3' 55.91" less
time each day,
S*»rvi<?e Train of a Quartermaster.
Quartermaster's train of an army averages z wagon to every 24 men; and a well-
equipped army in the field, with artillery, cavalry, and trains, requires i horse of
mule, upon the average, to every 2 men.
Tides.
The difference in time between high water averages aboilt 49 minutes each day.
Atlantic and Pacific Oeeavu.— Rise and fall of tide in Atlantic at Aspinwall a feet,
in Pacific at Panama 17.72 to 31.3 feet
Diiiieiisioiis of r>rawiijg8 and l-*aper for XJ. S. I*atents.
Drawings, 8 X 12 inches, one inch margin. Paper, 8 X 12.5 inches.
I^atitvide.
One minute of latitude, mean level of Sea, nearly 6076 f^et = 1.1508 Statute milea
A^rtesian '>Vell.
White Plains, Nev., Depth 2500 feet.
F*oundation Files.
A pile, if driven to a fair refusal by a rnm of i ton, falling 30 feet, will bear z ton
weight for each sq. foot of its external or frictional surface, or a safe load of 750 lbs.
per sq. foot of surface.
G^artli.
Density of its mass 5.67.
TripolitH.
A new building material, compounded of Coke, Sulphate of liime, and Oxide of
Iron. It has increased tensile strength after expoenre to the air, being much in
excess of that of lime and cement.
G}-as and Electric I^ight.
Gas light of x6 candle power costs 5 cent per hour; Electric, 4.15 centa
IN'iagara.
Discovered, 1678. Falls have receded 76 feet in 175 yeans. Height, American
Falls, 164 feet; Horseshoe, 158 feet.
BRIDGES. — U. S. ENSIGNB, PENNANTS, AND FLAGS. 1 99
U. S. ENSIGN, PENNANTS, AND FLAGS,
{Fi'om April 20, 1896.)
ICxisis:!!. — Head {Depths or JTaist), ^-Ten nineteenths of its length.
Fidd, — Thirteen horizontal stripes of equal breadth, alteruately red and
ivbite, beginning with red.
Union, — A blue field in upper quarter, next the head, .4 of length of field,
and seven stripes in depth, with white stars ranged in equidistant, horizontal
lines and set staggered, equal in number to number of States of the Union.
PennantB (Narrow). — Head.— 6.2^ ins. to a fength of 70 ffeet; 5.04 ins. to a
length of 40 feet; 4.2 ins. to a length of 35 feet Night, 3.6 ins. to a length of 20
fcet^ and 3 ina to a length of 9 feet— Boat, 3. 52 ins. to a length of 6 feet.
Union, — A blae field at head, one fourth the length, with 13 white stars in a hori-
zontal lina Fidd. — A red and white stripe uniformly tapered to a point, red up
peroiost NigfU and Boat i^nanto.— Union to have but 7 stars.
Union Jack.— Alike to the Union of an Ensign in dimensions and stars.
JB^Iags.^^lr'resident. — Rectangle, with arms of the U. S. inj^entre of
a blue field, over which are 13 stars in an arc
Secretary of Navy. — Rectangle, with a vertical white foul anchor
in centre of a blue fidd, with four white stars in a rectangle, set quadrilateral
around a foul anchor.
ivdixiiral. — Rectangle, with 4 white stars in centre of a blue field, set as
a lozenge.
^Vioe>A.dmiral. — Same as Admiral's, with 3 white stars set as an
equilateral triangle.
Rear- A.dxniral. — Same as AdmiTaI*s, with 2 white stars set vertically.
If two or more Rear- Admirals m command afloat should meet, their seniority is
to be indicated respectively by a Blue flag, a Red with White stars, and a White
with Blue stars, and another or all others, a White flag with Blue stars.
Conaxnodore. {Broad Pennant.) — Blue, Red, or White, according to
rank, with one star m centre of field, being white in blue and red pennants,
and blue in white.
Swallow- tailed, angle at tail, bisected by a line drawn at a right angle ft*om centre
of depth or hoist, and at a distance H-om head of three fifths of length of pennant;
the lower side rectangular with head or hoist; upper side tapered, running the width
of pennant at the tails z the hoist Head. — 6 length. Fly 1.66 hoist.
Divisional Alarlcs. — Triangle, ist Blue, 2d Red, 3d White, Blue
vertical. Reset ve Division, — ^Yellow, Red vertical. Division mark is worn
by Commander of a division of a squadron at niizzen, when not authorized
to wear Broad Pennant of a Commodore or Flag of an Admiral. Fly .8 haist.
Biflrnal Nxamtoers. — Fltf 1.25 hoist. Signal J*enn(mts, Fly 4,6 hoist.
Repeaters 1.89 hoist,
Diatiiictive Pennants. — Of a Senior Officer Present, is the Dis-
tinctive Mark of the First Division of a fleet.
JS'isht fe^iguals. — Very*s System.
Intematumal^ Signal Nttmber, Square, and Signed Pennants, Fly., 3 Imiat.
Suspension Bridges. Length of Spam in Feet
Yon-Kau. China. 330
Schuylkill (Pbfla.) 34a
Hammersmith, Eng. 422
Peisth (Danube) 660
Niagara 822
Lewistown and Queenstown 1040
Cincinnati 1057
Niagara Falls 1280
New York and Brooklyn* 9301 1595. 5t and 930; clear height of Bridge above higti
irater, at 90**, 135 feet.
200
AmMAL FOOD.
AlimerLtary Principles,
Primary division of Food is into Organic and Inorganic.
Organic is subdivided into Nitrogenous and Non-Nitrogenous ; Inorganio
is composed of water and various saline principles. The former elements
are destined for growth and maintenance of the body, and are termed "" plas-
tic elements of nutrition." The latter are designed for undergoing oxidation,
and thus become source of heat, and are termed ^* elements of respiration," or
"Calorifident"
Although Fat is non-nitrogenous, it is so mixed with nitrogenous matter that it
becomes a nutrient as well us a caloriflcient.
Alimentary Principles. — i. Water; 2. Sugar; 3. Gum; 4. Starch; 5. Pectine;
6. Acetic Acid; 7. Alcohol; 8. Oil or Fat Vegetable and AnimaL—g. Albumen;
zo. Fibriue; 11. Gaseine; 12. Gluten; 13. Gelatine; 14. Chloride of Sodium.
These alimentary principles, by their mixture or union, form our ordinary foods,
which, by way of distinction, may be denominated compound aliments ; thus, meat
is composed of flbrine, albumen, gelatine, fat, etc. ; wheat consists of staritb, gluten,
sugar, gum, etc.
i^zialysis of IMeats, ITiali, Vegetal>leB, eto.
Food.
Arrowroot
Barley Meal
Beans, White
Beef, roast.
fat
lean
salt
Beer and Porter. . . .
Buckwheat
Butter and Fats....
Cabbage
Carrots
Che^e
Corn Meal
Cream
Egg
yolk
Fish, white flesh...
Eels.
Lobster, flesh.
Oysters
Liver. Calf 'a
Milk, Cow's
Mutton, tax
Oatmeal
Oata
Parsnips
Peas
Pork, fat
Bacon, dry. . .
Potatoes.
Poultry
Rice
Rye Meal
Sugar.
Tripe
Turnips.
Voal
Wheat Flour.
Bread*
Bran
Water.
Nitro-
(tenous
M«ttor.
* Fat.
Aaime
Matt«r.
18
«
•—
__
15
6.3
2.4
2
9.9
25-5
2.8
—
54
27.^
1545
3.95
51
14. &
29.8
4 4
72
19-3
3-6
5'i
491
29.6
.2
2Z.Z
9»
.1
—
.2
13
131
„3
•4
15
B3
2
91
2
•5
•7
hr.
1.3
.2
Z
36.8
33-5
243
5.4
6l
ii.i
8.Z
*-7
2.7
26.7
Z.8
74
^
10.5
1-5
52
x6
307
1-3
78
18. 1
2.9
X
75
9.9
13-8
13
76.6
19.17
X.Z7
z.8
80.39
14.01
1-52
2.7
72-33
20.55
5-58
I.S4
86
4.1
3.9
.8
53
12.4
31.1
3-5
15
Z2.6
5.6
3
21
14.4
5-5
—
82
I.Z
•5
z
15
23
2.x
2.5
39
rl
48.9
2.3
15
73-3
2.9
75
2.Z
.2
•7
74
2Z
3-8
Z.2
13
6.3
•7
.5
15
8
2
Z.8
5
68
132
Z6.4
2-4
91
X.2
—
.6
63
16.5
15-8
4-7
15
10.8
2
1-7
37
8.Z
Z.6
2-3
13
z8
6
—
Non-Nitn>-
nnoas
Matter.
82
69.4
55-7
64.5
.5I
7-4
57-6
Z.26
X.38
58.4
48.2
9.6
5a 2
t6.8
78. z
69-5
95
4-3
61. 1
45-4
60
Sugar.
Cello-
lo«e.
Ash, etc
4.9
2.9
3a
—
—
■""*_
—
3-5
25
6.Z
, ,^
X
—
~-
—
•4
2.8
5-9
X.3
—
—
^—
5-2
. —
—
5-4
^8
2
7^6
31
3-3
3.1
3-2
z
z
•4
3-7
.^^
z
2.Z
—
.8
4.2
3.6
3-5
»-7
a
—
-~
3
* Water absorbed by floor variea from 40 to 60 per cent, of weight of floor, the beat qoality
log most. 100 lbs. floor yield 130 lbs. bread.
ANIMAL F001>.
201
A.iial3rsi« of* Difierent irooda*
In their NoluvoL CondiUon.
Apples
Barley
Beans
Beef.
Backwheat . .
Cabbage
Chicken
Coni,North'n
" South'n
Cucumbers. . .
Lamb
w.
Caibon-
Pboft.
trat«s.
■fliOv*
phatM.
Wnter.
5
10
z
84
«7
69-5
3-5
10
24
57-7
35
14. 8
«S
30
5
50
8.6
75-4
Z.8
14.2
4
5
X
90
«9
3-5
4-5
73
12
73
X
«4
35
4«
3
14
IS
X
•5
97
II
35-5
3-5
50
Milk of cow..
Mutton
Oats
Parsnips
Pork
Potatoes
"> sweet
Rice
Turnips
Veal
Wheat
Ni-
Carbon-
Phoa.
trates.
atea.
phatea.
5
8
I
12.5
40
4-5
'7
66.4
3
9.2
7
I
zo
50
1-5
2.4
22.5
•9
1-5
28.4
2.6
6.5
79-5
.5
5
4
•5
i6
16.5
^•5
15
69.3
1.6
Watar.
86
43
13.6
82.8
3«-5
74.2
67-5
135
90.5
63
14.2
JVt/rafe«— Are 'that class which supplies waste of muscle.
Carb<mata—\Te that class which supplies lungs with fliel, and thus ftirnishes heat
to the system, and supplies fat or adipose substances. '
Pho^phaU$^Are that class which supplies bones, brains, and nerves, and gives
vital power, both muscular and mental.
From above it appears, that Southern com produces most muscle and least fat,
and contains enough of phosphates to give vital power to brain, and make bones
strong. Mutton is the meat which should be eaten with Southern corn.
"Hie nitrates in all the fine bread which a man can eat will not sustain life beyond
fifty days; but others, fed on unbolted flour bread, would continue to thrive for an
indefinite period. It is immaterial whether the general quantity of food he reduced
too low, or whether either of the muscle-making or heat-producing principles be
withdrawn while the other is fUlly supplied. In either case the effect wijl be the
same. A man will liecome weak, dwindle away and die, sooner or later, according to
the deficiency; and if food is eaten which is deficient in either principle, the appe-
tite will demand it in quantity till the deficient element is supplied. AH food, be-
yond the amount necessary to supply the principle that is not deficient, is not only
wasted, but burdens the system with efibrts to dispose of it.
Analysis of Fruits.
FaviT.
Apple, white
Apricot, average.
Blackberry
Cherry, red .. .^
sour
black
Currant, red
Gooseberry, red
yellow . . . .
Grape, white
Peach, Dutch.
Pear, red
Plum, yellow gnge....
large '' . . . .
black blue
" red
Italian, sweet . .
Raspberry, wild
Stiawberry, ''
Banana < .
Water.
85
835
86.4
75-4
80.5
79-7
85-4
85.6
85.4
80
85
83.5
8a8
SJ
83.3
81.3
839
87
73-9
Sugar.
7.6
1.8
4-44
>3 I
8.77
fo.7
5-6
8
7
13-78
1.58
7-5
2.96
3-4
2
2.25
6-73
3.6
4
Sugar,
Acid.
z
I.I
X.X9
•35
T.28
.56
'•7
'•35
1.2
z
.61
.07
.96
.87
X.27
«-33
■84
2
'•5
Pectin,
Albumi-
nous aub-
•tancM.
22
5«
51
36
44
46
83
46
25
48
4
4
43
83
55
6
Salt, Acid,
Insoluble
matter.
1.83
5- 26
583
5.91
6.04
3-74
2.92
3-17
.2.48
5-49
3-54
3.98
6.86
423
4.0Z
8.37
5-5
etc., a6.r.
Pectona
•ub-
•tances.
3-88
7-55
1.72
3-73
2.C7
1-33
2-4
1.26
2.4
1.44
6.4
4.8
10.48
"•3
•23
5.85
5-63
z.28
Aah.
47
84
48
64
67
8
43
37
47
46
34
34
42
54
6z
66
4
Suffctr ctnd TVater in Vario-us Products xxot Inoluded in
Sojjar.
Sugar, crude 95
Molasses 77
Buttermilk. 6.4
tlie Tat>le. (Per Cent.)
Water.
Molasses 23
I^an beef 72
Buttermilk 88
Water.
Cabbage 91
Ale and Beer 91
CofTeeandTea zor
302
ANIMAL POOD
Relative Values of* "Vegetable Floods to proetire an H^quai
' Volume of FlesK in Beeves or Slieep.
(Etoart.)
Abticlk.
Beeves.
Peaineal ...
I
Beaumeal. . .
I -03
Oatmeal ....
I 06
Cornmeal . .
1.09
Barley
Wheat bran .
x-4
Linseed cake
1.50
Sheep.
1.87
3.25
Abttclk.
Meadow hay.
Oat Btraw. . . ,
Turnips .. ..
Oats
Bean straw..
Potatoes
Ue'dow grass
Beeves
Sheep.
3- 18
398
6.24
3.12
12.48
—
2.18
^7
6.24
6.24
125
—
Artici.b.
Beeves.
Parsnips
18.72
BeansorPeas
_„
Buckwheat. .
—
Pea straw. . .
.^
Cabbage
—
Beets.
i&7a
Carrots
19.67
Sheep.
6.24
»-7
2.03
6.24
T.8
936
NOTR. — When these values express weight in
about 4 to 5 lbs. beef or mutton.
lbs., then such {ood will produce
H>elative N'utritive Value of lOO parts of Human.
ITood.
NuirUnt RnJtU* — Is determined by the ratio of atbumiaokls to the digestible
carbohydrates and oil, considered as starch. NtUrieM Value — Is the percentage
of starch, albuminoids, oil, and sugar converted into their equiTalenta of sturcli. —
{A. H. Church.)
Almond, Sweet
Apple
Banana
Barley
Beans
Buckwheat
Beetroot
Carrot
Celery
Cabbage
Cocoanut.. ..
Cheese, Glos'r
Date
Egg-
R«iio.
Value
5-3
158
27
II. 5
M
24
13
85
2-5
80
5
86
29
12
14
7.5
4.5
5
4
7-5
16
90
2.4
99
10
68
9
40
Pig, Dried
Grap«
Gooseberry
Ground nut. ..
Macaroni. It^an
Maise, Corn. . .
Oatmeal
Onion
Parsnip
Pea.
Pistachio -nut.
Potato
" Sweet..
Milk, Cow
Ratio
Value
10
65
20
16
20
9
5-2
»5»
6.2
88.3
8.5
87
5-8
102
3-5
65
12
16
2.5
79
5 7
143
«7
22
13
22
4
— '
Milk, Human..
" Skim...
Riee
Rye l<"^»ir.
Tomato
Turn rp
Marrow Veg'e.
Moss, leotaiid.
" Irsh...
Walnut
Wheat, Indiiin.
*' Flour .
♦• Bran..
Bread
Ratio
9
1.
10
7
5
6
5
8
5
6.
»5
7-
4
4-
75
Value.
9
84
85
8-5
4
3-5
70
64
94
84.6
86.5
67
53
The Nutrient ratio generally adopted for Standard diet is x to 4.75, and the
proportion of (kt or oil to starch is x to 3.5.
The FvU Daily Diet of a man is held to be 12 oz. bread, 8 oz. potatoes,
6 oz. meat, 4 oz. boiled rice with milk, .375 pint of broth or [)ea sonp, i pint
milk, and I pint of beer.
Nutritive Values and Constituents of ^lilte.— </\iy«».)
Animal.
(;oal. . . .
Cow
Woman.
Nitrofcenons
&lott«r nnd
Inaotuble
Sahs.
4-5
4- 55
3-35
Butter.
Uctic
and
soluble
SrMs.
4-»
3.7
3-34
5.8
5-35
3-77
Water.
85.6
86.4
8954
Animal.
Ass..
Mare
Ewe.
Nitrogeriou'*
Mititer aiid
inimiuble
Salts.
J-7
1.62
4.68
Batter.
Irftctk
and
•olUble
Satta.
Water.
1-4
.a
4a
«-4
8.75
5-5
fe-^
TVeighfc of some UifTei^nt yoocls required, to Aimi»l&
ISSO Orains of Nitroeeixoua ^fatter*
Cheese 4
Prase 7
Neat, lean 9
Fish, White . . . x
Lbs.
Bacon, fat,.... 1.8
Bread 2. 1
Rye Meal 2.3
Rice 2.8
Turnips, 15.9 lbs. ; Beer or Porter, 158.6 lbs.
Lbs.
Meat, fot 1.3
Oatmeal 1.5
Com Meal 1.6
Wheat Flow.. 1.7
Barley Meal.. 2.9
Milk 4.2
Potatoes 8.3
ParsHifi«. . . . 15.9
ANIMAL FOOD.
203
Proportion o€ Sugar
Fkuit.
axxd A-oid
{Fi-ejsenius.)
in Various ITrxiita.
Apple
ApricoL
Blackberry ,
Cumuitfl...,
Gooseberry.
Grape ,
Mulberry. . ,
Peach ,
Sugar.
Add.
PerCwt.
Per Cent.
.8
Z.I
t.i
Z.2
a
7.2
14.9
1.6
•7
1.9
•7
Fbcit.
Plum
Prune
Raspberry....
Red Pear
Sour Cherry. .
Strawberry. . .
Sweet Cherry.
Whortleberry.
Sngar.
Per Coat.
2.Z
6.3
4
I.B
5-7
10.8
5.8
Add.
Per Cant.
1-3
•9
1-5
.1
x-3
1-3
.6
1-3
Proportlcm of Oil in. Varions Air-dry Seeds. (Beijot)
Beechnut 24
Hemp 28
Watermelon ... 36
Mustard 30
Flax 34
Peanut 38
Almond 40
Colza {^°
(45
Orange.
Poppy.
4»
5«
A-nalysis of di^erent Articles of* F'ood, tvith. Rererence
only to their lE'roperties ibr giving Heat and Strengtli.
{Fayen.) In 100 ParU,
Nitro-I
SvaaTAHCi
Alcohol
Barley
Beaos
Beef, meat —
Beer, strong. .
Bread, stalo. . .
Baclcwbeat. . .
Butter
Carrots.
Caviare
Cheese.Chestt
Chocolate
Cod-fish, salt'd
CM^
Nitro-ll
U». gen. II
5*
—
40
»9
4a
4-5
II
1.07
sr
2.2
.64
55
•31
27.41
4-49
41.04 4.13
58 1.5a
16
502 11
SOBSTANCn.
Coffee
Com
Eels
Eggs.........
Figs, dried
Herring, salt-
ed
Liver, Calf's. .
Lobster
Mackerel
Milk, Cow'& . .
Nuts
Car-
bon.
9
I.I
44
'•7
30-05
2
13-5
1.9
34
.92
'3.«
3"
15.68
3-93
10.06
2-93
t'*
3-74
.66
10.65
1-4
44
1-95
gen.
SUBITANCn.
oil, Olive
Oysters
Pease
Potatoes
Rye Flour. . . .
Salmon
Sardines
Tea
Truffes
Wheat
" Flour. .
Wine
Car-
bon.
18
98
7-
44
II
41
41
16
29
2.1
9-45
4«
38.5
4
Nlti«.
2.13
3.66
.:?
1-75
2.09
6
1-35
3.
1.64
.015
Oatmeal. . . .
NoTB. — Multiply figures representing nitrogen by 6.5, and equivalent amount of
nitrogenous matter is obtained.
Human and A.nimal Sustenanoe.
Least Quantity of Food required to Sustain Life. {E. Smithy M.D.)
Carbon. Hydrogen.
Qn. Gre.
13»!{ W^man. '^\ «»». 4'~ X} X-"- •«-
An adult man, for his daily sustenance, requires about 1220 grs. nitrog-
enous matter or 200 of nitrogen, and bread contains 8. i per cent, of it.
I320
Hence, — - = 15 062 grains which -f- 7000 in a 26. r= 2 lbs. 2.43 oz. of bread.
.081
These quantities and proportions are also contained in about 16 lbs* of
turnips.
Thus, by table of nutritive values, page 302, turnips have 263 grains of carbon and
13 of nitrogen
Hence, ^-^ and — = 16.35 lbs, for the necessary carbon and 1^4 Ws.fwr tks
263 13
nitrogens
Relative Value of F'oods compared -witli lOO lbs. of*
Oood VL&ym
Lba.
Clover, green. . 400
Cora, green . . . 275
Wheat straw . . 374
Lbe.
Rye straw. .... 442
Oat straw 195
Cornstalks .... 400
Lbe.
Carrots 276
Barley 54
Oats.. 57
Lba.
Com 59
Linseed cake . . 69
Wbsat bran. ... 10^
204
ANIMAL FOOD.
VSTeigh.t of* Articles of yood. ire<i"aired to l^e consumed! in
tlie liuiniaxx system to d.evelop a po"wer eq.ual to rais-
ing 14rO lbs. to a heiglit of* lO OOO feet. (Frankland.)
Substances. iWeigbt. { Subbtancks. W«i{;bt. Subbtancks. Weight.
Cod-liver oil.
Beef, fat
Bacon ,
Butter
Cocoa
Fat of Pork.
Cheese
Oatmeal ....
Arrowroot. .
Wheat flour.
Lbs.
•553
•555
.67
•693
•797
1. 150
1.287
I 311
Rice
Isinglass
Sugar, lamp
Cream
Egg, boiled
Bread
Salt Pork
Ham, lean, boiled.
Mackerel
Ale, bottled
Lbs.
1341
'•379
1-505
2.062
2.209
2345
2.826
3.001
3.124
3.461
Salt Beef
Veal, lean
Porter
Potatoes
Fish
Apples
Milk
Egg, white of.
Carrots
Cabbage
Lbs.
3-65
4-3
4-615
5.068
6.316
7-815
8.02I
8.745
9.685
12.02
Relative "Value of Various Foods as I^roduotiv* of* Force
wlien Oxidized iii. the J)od5r.
Cabbage i
Carrots 1.2
Skimmed Milk. 1.2
White of Egg.. 1.4
Milk 1.5
Apples 1.5
Ale I 8
Fish 1.9
Potatoes 2.4
Porter 2.6
Vccil, lean 2.8
Salt Beef 3.3
Poultry 3.3
Lean Beef..... 3.4
Mackerel 3.8
Ham, lean 4
Salt Pork 4.3
Bread, crumb. . 5.1
Egg, hard boiPd
Cream
Egg, yolk
Sugar
Isinglass
Rice
Pea Meal
Wheat Flour . .
Arrowroot
5.4 , Oatmeal 9.3
5.9 : Cheese zo.4
7.9 ' Fat of Pork. 12.4
8 j Cocoa 16.3
8.7 i Pemmican.. 16.9
8.9 j Butter 17.3
9. Bacon 17-94
9.1 I Fat of Beef., 21.6
9.3 I Cod-liver Oil. 21.7
JN'utritious Properties of different Vegetables and Oil-
cake, compared Avitli eaoli other in Quantities.
Oilcake X
Pease and Beans 1.5
Wheat, flour. . . 2
" grain ..2.5
Oats 2. 5
Rye 2.5
Bran, wheat |^'75
Com ,
Barley
3
3
Clover hay 4
Hay 5
Potatoes 14
" old.... 20
Cabbage x8
Wheat straw.. 26
Barley '* 26
Oat *' 27.5
Carrots 17. 5 Turnips 30
Illustration.— I lb. of oil-cake is equal to 18 lbs. of cabbage.
Volume of Oxygen required to Oxidize 100 pai'ts 0/ following Foods as con^
sumed in the Body.
Grape Sugar . . 106 | Starch 120 | Albumen 150 | Fat 393
Hence, assuming capacity for oxidation as a measure, albumen has half value of
fkt as a food-producing element, and a greater value than either starch or sugar.
Proportion of Alcohol in lOO Parts of fbllowing; ILiiq.uors.
{Brande.)
Small Beer. . . i and 1.08
Porter 3. 5 and 5.26
Cider 5.2 and 9.8
Brown Stout. 5.5 and 6.8
Ale 6.87 and 10
Rhenish 7.58
Moselle 8.7
Johannisberger 8. 71
Elder Wine 8.79
Claret ordinaire 8.99
Tokay 9. 33
Rudesheimer 10.72
Marcobruuner 11.6
Gooseberry Wine ... iz.84
Hockheimer 12.03
Vin de Grave 12.08
Hermitage, red 12.32
Champagne 12.61
Amontillado 12.63
Frontignac 12.89
Barsac 13.86
Sauterne 14.22
Champagne Burg'dy, 14.57
White Port 15
Bordeaux 15. i
Malmsey 16.4
Sherry 17.17
Malaga 17.2
Alba Flora. 17.26
Hermitage, white . . . 17.43
Cape Maacat 18.25
Constantia, red 18.93
Lisbon 18.94
liachryma 19.7
Teneriff'e 19-79
Currant Wine 20.55
Madeira 22. 37
Port 23
Sherry, old 23.86
Marsala 25.09
Raisin Wine 25. xa
Madeira, Sercial .... 27.4
Cape Madeira 29-51
Gin 51.6
Brandy 53.30
Rum 53.68
Irish Whiskey 53,9
Scotch Whiskey 54.39
ANIMAL FOOD.
Proportion of* F'ood A.ppropriated and Expended
follo'Viring* .A.nixnal8.
<
Oxen. Sheep. Swioe.
Proportion appropriated 6.2 8 17.6
** in manure 36.5 31.9 16.9
** respired 57-3 60.1 65.5
100 ICX> xoo
205
by
Specific Q-rarvity of l^ilk and Feroentetge of* Creaxn, etc.
Specific
MlUE.
Milk, pure*
" 10 per cent water.
it — Q i( il CI
Volume
Volume
Speeific
of
of
Gravity.
Cream.
Curd.
1030
12
6.3
1027
ia5
5.6
1024
?-5
4-9
102 1
6
4-2
Gravity when
■kimmed.
1032
ZO29
XO26
1023
* For s method of teeting the parity of mills, see Pavy on Food (Philadelphia, 1874), page 196.
NoTB. — ^The average proportion of cream is 10, or 10 per cent
^Proportion JPer cent, of* Starcli in enndry Vegeta'bles.
Arrowroot. ... 82 I Wheat flour. . . 66.3 I Oatmoal 58.4 I Potatoes 1^8
Rice 79.1 I Com meal.... 64.7 | Pease 55.4 | Turnips. 5.2
Composition of Cfa-eese of Different Conn tries. — {Payen.)
Fat.
Nenfchatel.
Parmesan .
Brie
Holland . . .
Fat.
Nitrogen,
Salt.
425
7.09
563
6.21
Water.
18.74
21.68
24.83
25.06
2.28
5.48
2-39
4X
61.87
30-31
53-99
41.41
Chester
Gruydres . . .
MaroUes . . . .
Roquefort. . .
25.41
28.4
28.73
32.31
Nitrogen.
Salt.
Water.
5.56
5-4
3-73
507
4.78
4.29
5-93
4-45
3039
32.05
40.07
26.53
Nntritive Bquivalents. Computed from Amount of Ni-
trogen in Su'bstanoes -wlien X>ried. Kuman IMilk at 1.
Rice....
Potatoes.
Com ...
Rye
Wheat..
Barley . .
Oats
.81
.84
I
1.06
1. 19
1-25
X.38
Bread, White.
Milk, Cows' . .
Pease
Lentils.
Egg, Yolk. ...
Oysters
Beans.
1.42
2.37
2-39
2.76
3'05
3-05
3-2
Cheese
Eel
Mussel
Liver, Ox
Pigeon
Mutton
Salmon
3-31
4-34
5.28
5.7
7- 56
7-73
7.76
Lamb
Egg, White. . .
I/)bster
Veal
Beef
Pork
Ham
8-33
8.45
8. 59
8.73
8.8
8-93
9.x
Herring, 9.14.
Xhermoraetrio Po-wer and ^Mechanical Energy of lO
O-rains of Various SnlDStances in their Natural Con*
dition, -^^lien Oxidised in the A.nimal Body into Car-
l>onio Acid, Water, and XJ rea,—{Frankland.)
Be
AJfCS.
Ale, Bass's . .
Apples
Arrowroot. . .
Beef, lean . . .
Bread
Butter
CiU>bage
Carrots.
Water
Lifted
raised
X foot
i'
high.
Lbe.
Lbe.
;:?i
1-54
x.29
iao6
7-77
3.66
2.83
5-52
4.26
18.68
14.42
1.08
•83
X.33
z4oa|i
SOBRANCB.
v/nocso ..... •
Cocoa-nibs . .
Cod-liver oil.
Egg, hM boil.
" yolk
" white...
Flour, wheat.
Water
Lifted
railed
x foot
i».
high.
Lbe.
Lbs.
XI.2
&65
17-
Z-3
XI
X8.I2
5.86
4.53
8.5
6.56
x.4«
1.X4
9.87
7.62
4-3
3.32
SVBSTANCB.
Mackerel....
Milk
Oatmeal
Pea meal . . . .
Potatoes
Porter
Rice, ground.
Sugar, grape.
Water
Lifted
raised
I foot
i\
high.
Lbs.
Lbe.
4-14
32
X.64
'•2^
xax
7.8
9-57
7-49
2.56
X.99
2.77
2.19
9.52
7-45
8.42
6.--
8
2o6
ANIMAL FOOD.
IDieestioix.
Time required, for I>igestioii of* several A.rtioleB of F'ood.
(Beaumoni^ M.D.)
Food. Time. Food. Tim*.
Apple, sweet and mellow . . . .
sour and mellow
sour and hard
Barley, boiled
Bean, boiled
Hean and Green Corn, boUed .
Beef, roasted rare
roasted dry
Steak, broiled
boiled
boiled, with mustard, etc.
Tendon, boiled
fried
old salted, boiled ,.
Beet, boiled
Bread, Com, baked
Wheat, baked, fresh . . .
Butter, melted
Cabbage, crude
crude, vinegar
crude, vin'r, boiled ]
Carrot, boiled
Cartilage, boiled
Cheese, old and strong
Chicken, fricasseed
Custard, baked
Duck, roasted \
Dumpling, Apple, boiled
whipped
boiled hard
" soft
fried
Fish, Cod or Flounder, fried . .
Cod, cured, boiled
Salmon, salt'd and boiFd
Trout, boiled or fried. . .
Fowl, boiled or roasted
Goose, roasted
Gelatine, boiled
I 50
2
2
2
3
3
3
3
2
3
5
4
4
3
3
3
3
a
2
4
4
3
4
3
2
2
4
4
3
2
I
3
3
3
3
2
4
1 30
4
3
2 30
30
45
30
45
30
30
15
45
IS
30
30
30
30
IS
IS
30
45
45
30
30
3D
30
30
Heart, Animal, fried
LAmb, boiled
Liver, Beefs, boiled
Meat and Vegetables, hashed .
Milk, boiled or fresh [
Mutton, roasted
broiled or boiled ....
Oyster
roasted
stewed
Parsnip, boiled
Pig, sucking, roasted
Feet, soured, boiled
Pork, fat and lean, roasted . . .
recently salted, boiled . .
" " fried . . .
" " broUed .
" raw
Potato, boilei
baked
roasted
Rice, boiled
Sago, boiled
Sausage, Pork, broUed ......
Soup, Barley
Beef and Vegetables . . .
Chicken
Mutton or Ovster
Sponge-cake, baked.
Suet, Beef, boiled
Mutton, boiled ...-«....
Tapioca, boiled
Tripe, soured
Turkey, roasted {W^;^jV;;
boiled
Turnip, boiled
Veal, roasted
fried
Brain, boiled .........
Venison Steak, broiled ,
4
2 30
2
30
15
IS
55
IS
30
30
30
15
30
15
IS
30
20"
30
2
2
2
3
3
2
3
3
2
2
I
5
4
4
3
3
3
3
2
I
I 45
3 20
1 30
4
3
3 3P
2 30
5 3D
4 30
2
I
2
2
2
3
4
4
X
X
x8
30
25
30
50
45
35
Greneral Notes.
The per ccntage of loss in the cooking of meats is as follows: Boiling 23; Baking
31; Koa8tiug34.
I'otatoes possess anti-scorbutic power in a greater degree than any other of the
succulent vegetablea
The average yearly consumption of wheat and wheat flour in Great Britain is 5.5
bushels per capita of its population.
The daily ration of an Esquimaux Is 20 lbs. of flesh and blubber— (i9ir«/bAf» Ami./
ANIMAL FOOD.
207
An adult healthy man, acoonlisg to Dr. Kdward Smith, requires daily of
Phosphoric acid flrom . . 3a to 79 grains. Potash .... 27 to 107 graina
(ChlSrine ..5»"'75 ;' J^fda 80 171
{ororcommoii8alt....85" a9« " Lime 2.3*' 6.3"
and of Magnesia 2. 5 to 3 gram&
A common fowl's egg contains lao grains of Carbon and 17.75 of Nitrogen.
An ordinary working-man requires for his daily sustenance
Oxygen X'47 Starch 66
Albuminous matter 305 S^!;!',"' /^«
pm 22 Water 4-535
^ 7. 23 IbB. Hvoirdupoia
MiVe —If the milk of an animal is token at three immediately successive periods,
that which is first received will not be as rich in milk fafas the last.
In a Devon cow, milked in this manner^ the first milk gave but ..166 per cent of
fat, and the last, or that known as '^strippings," 581 per cent.
Relative Ricliiieas of M.ill£ of Several Animals.
Milk-fat. CaMin. Sngar.
A88 5 -B* -94
Sheep 2.52 2.1 .72
Milk-fat.
Cow. 1.66
Mare 1.19
Goat 2
CaMin.
1.38
•75
X.04
Susar.
.69
.69
Camel 1.4
.96
Tbe condensation of milk reduces it to about one third of its original volume.
A Farm of second-rate quality, properly cultivated, will sustain 100 bead of cattle
per 100 acres, besides laborihg stock (employed in cultivation of farm), and swine.
— (Ewart)
Thus, calves 25; do. i year 25; do. 2 years 25; cows 25.
Cane Sugar (Saccharose)— Is insoluble in absolute alcohol, and in diluted alcohol
it is soluble only in proportion to its weakness. Loaf sugar, as a rule, is chemically
pure
But Rttot 5uf^ar— Conteins 85 to 96 per cent, of cane sugar, 1.6 to 5 1 of organic
matter, and 2 to 4.3 of water.
iy>n<y— Contolns 32 per cent, of sugar (levulose), 25.5 of water, 27.9 of dextrine,
and 14.6 of other matter, as mannite, wax, pollen, and insoluble matter.
Molcuses—ContSLxns 47 per cent of cane sugar, 20.4 of fruit sugar, 2.6 of salts, 2.7
extractive and coloring matter, and 27. 3 of water.
Flour.— TeslB of flour, see A W. Blyth, T.ondon, 1882, page 152.
0r<*ad.— Wheat, water lost by drying after 1 day 7.71 per cent, 3 days 8.86, and
7 days 14.05 per cent
Sago. — 2.5 lbs. per day will support a healthy man.
^j^— Gontoins aeaily as much gluten as wheat bread (as 6 to 7), and in starch and
sugar it is 16 per cent richer.
Qooubtrry (dry) — Is as nutritious as wheat bread.
WaUrmeUm^ Vegetable ma/nrow^ and Cfucumber — Contain 94, 95, and 97 per cent
Of water re^Mctiv^.
Oman (dry)— Contains 25 to 30 per cent of gluten. Potato contain 1 g but 5.
Cabbage^ Cauliflower^ Broccoli^ and Leaves are generally rich in gluten, while the
polato Is poor.
Ratio of IPlesh-ibrniera of 1?ubers.
Pty Cent
TUBBBS.
FtMh-
fbrmtra.
Starcb,
«Cc.
Beet root
Turnip
Carrot
Potitto
•4
•5
.5
1-3
134
4
5
i9
Ratio to
HMt-glT'n.
1:30
1:8
1:10
1:16
TUBBBS.
Parsnip
Onion
Sweet Potato.
Yam
Fle»h-
SUrcb,
fomwra.
«t«.
1.2
8.7
1-5
4.8
1-5
2a a
3.8
.6.3
Ratio to
Heat-ftfv'r«.
■ ' ' t0
i: 10
1: 3-5
1:13
I- 7$
268 GBAVITY OP BODIES. — GBAVITY AHD WEIGHT.
GRAVITY OF BODIES.
Gravity acts equally on all bodies at equal distances from Earth^s
centre ; its force dimiuishes as distance increases, and increases as dis-
tance diminishes.
Gravitating forces of bodies are to each other,
I. Directly as their masses.
- 2. Inversely as squares of their distances.
Gravity of a body, or its weight above Earth's surface, decreases as
square of its distance from Earth's centre in semi-diameters of Earth.
Illustration i. — If a body weighs 900 lbs. at surface of the Earth, what will h
w«igh 2000 miles above surface ?— Earth's semi-diameter is 3963 miJes (say 4000).
Then 2000 -f- 4000 = 6ocx> = 1.5 semi-diam^s, and 000 -f- x. «;' = •^— - = 400 lbs.
2.25
Inversely, If a body weighs 400 lbs. at 2000 miles above Earth's surface, what will
it weigh at surface?
400 X i.s'^=9oo lbs.
2. — A body at Earth's surface weighs 360 lbs. ; how high must it be elevated to
weigh 40 lbs.?
— = 9 semi-diameters^ if gravity acted directly; but as it is inversely as square
40
of the distance, then y/^ = 3 semi-diameters = 3 X 4000 = 12 000 miies.
3.— To what height must a body be raised to lose half its weight?
As -y/i : y 2 : : 4000 : 5656 = as si^uare root of one semi-diameter is to square root
of two semi-diameters, so is,one semi-diameter to distance required.
Hence 5656 — 4000 = f656 = distance from EarVi's surface.
Diameters of two Globes being equcd^ and their densities different, weight
of a body on their surfaces will be a^ tJieir densities,
Th^r densities being equal and their diameters different, weight of them
will be as tJieir diameters.
Diameters and densities being different, weight will be as their product.
Illustration.— If a body weighs 10 lbs. at surface of Earth, what will it weigh at
surface of Sun, densities being 394 and 100, and diameters 8000 and 883000 miles?
883 000 X 100 -r- 8000 X 392 = 28. 157 = quotient of product of diameter of Sun and
its density, and product of diameter of Earth and its density.
Then 28. 1 57 X xo = 281. 57 lbs.
Note.— Gravity of a body is .003 46 less at Equator than at Polea
SPECIFIC GRAVITY AND WEIGHT.
Specific Gravity or Weight of a body is the proportion it bears to the
weight of another body of known density or of equal volume, and which is
adopted as a standard.
If a body float on a fluid, the part immersed is to whole body as specific
gravity of body fs to specific gravity of fluid.
When a body is immersed in a fluid, it loses such a portion of its own
weight as is equal to that of the fluid it displaces.
An immersed body, ascending or descending in a fluid, has a force equal
to diflTerence between its own weight and weight of its bulk of the fluid, less
resistance of the fluid to its pass^e.
Water is well adapted for standard of gravity ; and as a cube foot of it
at 62° F. weighs 997.68 ounces avoirdupois, its weight is taken as the uni^
or approximately 1000.
SPBCIFIC GRAVITY AND WEIGHT. 209
French standard temperature for comparison of density of solid bodies
and determination of their specific gravities, is that of maximum density of
water, at 4° C. or 39.1° F., and for gases and vapors under one atmosphere or
.76 centimeters of mercury is 32° F. or 0° C, and specific gravity of a body
is expressed by weight in kilogrammes of a cube decimeter of that body.
Densities of metals vary greatly.
Potassium, Sodium, Barium, and Lithium are lighter than water. Mercury
is heaviest liquid, and Iridium heaviest metal. Volcanic scoriae are lighter
than water.
Pomegranate and Lignum-vitsB are heaviest of woods. Pearl is heaviest
of animal substances, and Flax and Cotton are heaviest of vegetable sub-
stances, former weighing nearly twice as much as water.
Zircon is heaviest of precious stones, being 4.5 times heavier than water.
Garnet is 4 times heavier, Diamond 3.5 times, and Jet, lightest of all, is but
^ heavier than water.
To .A.0oertairi Speoifio GKravity of a Solid Body lieav.ier
tlian Water.
Rule. — Weigh it both in and out of water, and note difference ; then, as
weight lost in water is to whole weight, so is 1000 to specific graWty of body.
W X 1000
Or, -^y-^ = G, W and to representing weiyhts out and in water ^ and G
ipecific gravity.
Example. — What is specific gravity of a stone which weighs in air 15 Iba, in
water 10 Iba?
15 — 10 = 5; then 5 : 15 :: 1000 : 3000 Spec. Orav.
To .A.8certain Speoiflo Gravity of a Body iigliter tliaxL
AVater.
Rule. — Annex to lighter body one that is heavier than water, or fluid
used ; weigh piece added and compound mass separatelv, both in and out of
water, or fluid ; ascertain how much each loses, by subtracting its weight
from its weight in air, and subtract less of these diflerences from greater.
Then, as last remainder is to weight of light body in air, so is 1000 to
specific gravity of body.
ExAJiPLS.— What is specific gravity of a piece of wood that weighs 90 lbs. in air-
annexed to it is a piece of metal that weighs 24 lbs. in air and 21 Iba in water, and
the two pieces in water weigh 8 Iba?
2o-{-24 — 8 = 44 — 8 = ^6 = loss of compound mass in toater ;
24 — 21 = 3 = loss 0/ heavy body in water.
33 : 20 :: 1000 • 606.06 Spec Orav.
To A.8oertain. Speoiflo Gravity of a ITlviid.
Rule. — Take a body of known specific gravity, weigh it in and out of
the fluid ; then, as weight of body is to loss of weight, so is specific gravity
of body to that of fluid.
ExAMPLK. —What is specific gravity of a fluid in which a piece of copper {spec
grav. = 9000) weighs 70 lb& in, and 80 lb& out of it ?
80 : 80 — 70 = 10 : : 9000 : 1125 £ipec. Orav.
To Ascertaiix Speoiiio Gravity of a Solid Body -wliioh.
is soluble iti '^^ater.
Rule. — ^Weigh it in a liquid in which it is not soluble, divide its weight
out of the liquid by loss of its weight in the liquid, and multiply quotient
by specific gravity of liquid ; the product is specific gravity.
ExAMPLB. — What is specific gravity of a piece of clay, which weighs 15 lbs. in air
and 5 lbs. in a liquid of a specific gravity of 1500, in which it is insoluble ?
xs -f- 10 X 1500= 2250 Spec. Grav
S*
2IO
SPXCIFIC GBAYITY AND WSIGHT.
80LIIM3.
SamnMMCMM.
Aletals.
Aluminom, cast
♦* wrought. . . .
^* Bronxe
Antimony
Arsenic
Bariam
Bismuth.
Boron -
Brass.
Sheet, cop. 75, zinc 25.
Yellow •' 66, " 34.
MuDtz " 60, " 40.
Plate
Cast
Wire
Bromine
Bronze, gun metal
" ■ ordinary mean .
" cop. 84, tin 16 . .
" " 81, " 19..
" Tobin
" 35t tin 65
" 21, tin 74
Cadmium
Calcium
Chromium
Cinnabar
Cobalt
Coiumbium
Copper, cast
" plates.
" wire and bolts..
'* ordinary meun.
Gold, pure, cast
'' hammered
*^ 22 carats fine
»' 20 " '•
Iridium
" hammered
Iron, Cast, gun metal. . .
*' minimum
" maximum
" ordinary mean....
" mean, Eug
*' cast, hot blast
*' " cold '•
** Wrought, bars
♦» " wire
•♦ " rolled plates
" " average . . .
•» " Eng. rails .
" " Lowmoor. .
" " pure
*' ordinary mean. . .
Lead, cast
*' rolled
Lithium
Magnesium
Manganese
Mercury — 40°
'' +32^
BpMi«e
Weight
of » Cabe
OniTUj.
loch.
Lb.
3560
.0936
3O70
.0906
7700
3785
6712
.3438
5763
.3084
^70
9823
.017
•3553
aooo
•0733
8450
.3056
8300
.2997
8200
.2966
8380
.3026
8100
.2930
8214
.297a
3000
.1085
8750
.3165
8217
.2972
8832
.3194
8700
.2929
8379
.3031
8060
.291
7390
.2668
8650
3129
1580
057
§9<»
•2134
8098
.2929
8600
.3111
6000
.217
8608
•3»'3
8698
8880
.3146
.3213
8880
.3212
19258
.6965
19 361
.7003
17486
•6335
15709
.5683
18680
.6756
23000
8319
7308
.264
6900
.2491
7500
.2707
7207
.2607
7217
.2609
7065
•2555
7218
.2611
7788
.2817
7 774
281 1
7704
.2787
7698
.2779
7540
.2722
7808
,2810
.3938
8140
7 744
.280X
"353
.4106
XI 388
.4119
590
.0813
1750
.0633
8000
.2894
1563a
13598
.4918
SCBITANCra.
]Metala.
Mercury 60° ;
" aiao
Molybdenum.
Nickel
" cast
Osmium
Palladium
PllUinmn, hammered . .
*' native
" rolled
Potaasiam, 59^^
Red lead
Rhodium
Rabidiom ■
Ruthenium
Selenium
Silver, pure, cast
" " hammered.
Sodium
Steel, minimum
maximum
plates, mean
soft
tempered and hard-
ened
wire
blistered
crucible
cast
Bessemer
ordinary mean. . . .
Strontium
Tellurium
Thalium
Tin, Cornish, hammered.
** " pure
Titanium
Tungsten
Uranium
Wolfram
Zmc, cast
" rolled
Gnrity.
it
(t
(t
i(
t(
it
Ci
It
tt
It
"WoociB
Alder
Apple
Ash
Bamboo
Baytree
Beech ,
{Dry).
Birch
Blackwood, India .
Boxwood, Brazil. . .
" France..
'* Holland.
Bullet-wood
Butternut. ........
'3569
«337o
8600
8800
8279
to 000
"350
! 30337
x6ooo
22069
865
8940
10650
1530
8600
4500
10474
10511
970
7700
7000
7806
7833
7818
7847
7823
7842
7848
7853
7834
2540
6 no
11850
7390
7291
•5300
17000
1833c
7 119
6861
7 191
800
Wdfflil
oTaCabt
Inch.
l\
*45 i
690
400 i
822 I
852
690
567
790
898
1031
1328
913
998
376
Lb.
.4008
.4836
.3111
^3183
•2994
.3613
•4105
•7356
•5787
•7983
•0313
.334
.3853
.055
.3111
.1637
.3788
.3803
.0351
.3785
.3857
.2823
.3833
.2828
.3838
.383
.2836
.3899
.384
39x6
.0918
.231
.4286
3673
•3637
.19x7
.6639.
3575
.3483
.26
Cub*
FoH.
50
49-5^
53.8xa
43 "S
35
5x375
5335
43- "5
35-437
45
56.135
$4-437
83
57
58
33.5
SPHeiFIC GBAVITY AND WEIGHT.
211
flOMtAHCM.
{Dry).
^Voods
Campeacby
Cedar
*• Indian
Gharooal, pine
'* fresh burned..
•» oak
'* soft wood . . . .
" triturated....
Cherry
Chestnut, sweet
Citron "...
Cocoa
Cork
Cypress, Spanish
Dog- wood.
Ebony, American
** Indian
EMer
Elm 1
" rock
ErronI, India
Filbert
Fir, Norway Spruce. . . .
*' Dantzic
Fustic
GroMibeart or Sipiri. . . .
Cum, bine ..,
"'^ water
Hackmatack
Hawthorn
Hazel
Hemlock
Hickory, pig-nut
'* shell-bark. . » . .
Holly
Iron-wood.
Jasmine
Juniper.
Kbair, India
Lanoewood, mean
Larch
Lemon
Lignum-vitflB |
Lime
Linden
Ixxsust.
Logwood
Mahogany |
" Honduras. . . .
<« Spanish.
Maple
'* bird's-eye
MasUc
Mulberry |
Cak, African
»i Canadian
" Oantilo
Spaelfie
9»3
56t
i3«S
44"
380
1573
a6o
1380
7«5
610
■ 726
1040
240
644
756
1 331
1909
695
570
671
800
1014
600
5»a
58a
970
843
1000
59a
)ZO
368
792
690
760
770
566
1I7I
720
544
560
703
650
«333
804
604
728
9'3
720
1063
560
852
750
576
849
561
^
823
872
759
Weight
Foot.
57- 062
3S-o6»
82. 157
27.562
as- 75
98.31a
86.25
44-687
38.125
45-375
65
«5
40- as
47-85
83.187
75562
43-437
35625
41937
50
63375
37-5
3a
36.375
6a 695
65-95
52.687
62.5
37
56.875
53-75
a3
49-5
43- "5
47-5
61.875
48.125
35-375
73-X87
45
34
35
43 937
40.625
83.312
50-35
37-75
45-5
57062
66.437
35
53- as
46.875
53062
35-o6a
56.062
5«-437
54-5
47-437
fltntriiicsi.
"^VoodB
Oak, English.
{DryY
" greea
" heart, 60 years. . . .
" live, green
it a seasoned
" white
Olive
Orange
Pear
Persimmon
Plum
Pine, pitch.
" red
*^ white
" yellow
" Norway..
Pomegranate
Poott
Poplar
" white..
Quince
Rosewood
Sassaflras
Satinwood
Spruce
Sycamore
l^marack
Teak (Aft-ican oak).. . . |
Walnut
'< black
Willow
Yew, Dutch.
^' Spanish
{
{Well Seasoned.*)
Ash
Beech
Cherry
Cypress
Hickory, red
Mahogany, St. Domingo.
Pine, white
" yellow
Poplar
White Oak, upland
'* *^ James River
Stones, Sartlis,
eto«
Alabaster, white
*' yellow
Alum
Amber.
Ambergris
Asbestos, sUrry
Asphalte
Bary tes, sulphate . . . . |
Beton, N. Y. StCon'g Co.
SpMille
Gnvity.
858
93a
1146
1170
1260
1068
860
680
705
661
710
785
660
590
554
461
740
»354
580
383
529
705
728
48a
885
500
623
657
671
500
486
585
788
807
722
624
606
441
838
720
473
54«
587
6B7
759
2730
2699
1714
1078
866
3073
2250
4000
486s
2305
Wflifffat
oTaCab*
Foot.
Lb*.
53-625
58.35
71-625
73- "5
78.75
66.75
53-75
43.5
44.062
41.312
44-375
49.062
41-25
36.875
34-625
28.812
46.25
84.625
36 as
23.937
33.062
44.06a
45-5
30125
55-3"
31 35
38.937
33-937
41. 063
61.25
41937
31- 35
30-375
3^562
4935
50-437
4S-»a5
37875
a7. 562
Sa-375
45
29.562
33- 81 2
36.687
43.937
43.437
17a 625
168.687
107. 125
67.375
192.062
140.625
250
304.063
144.06
* U. ft. OrdnanM Maaosl, 1841.
212
SPECIFIC GBAVITY AND WEIGHT.
StTBSTAKCM.
Stones, Karths,
etc.
Basalt.
Bitumen, red . . .
" brown.
Borax
Brick.
** pressed
" fire
" work in cement . .
((
" " mortar
Carbon
Cement, Portland
Roman..
•{
(t
Chalk.
Clay
" with gravel.
Goal, Anthracite.
It
(4
t(
U
l(
((
i(
i(
it
Borneo
Cannel .
Caking
Cherry
Chili
Derbyshire . .
Lancaster. . . .
Maryland. . . .
Newcastle . . ,
Rive de Gier.
" Scotch.
ti
tt
Splint
Wales, mean
Coke '.
" Nat'l, Va.«
Concrete, in cement. . . .
*' mean
Earth,*^ common soil,dry
loose
moist sand
mold, fresh
rammed
rough sand
with gravel ....
Potters'
light vegetable. .
ti
tt
ti
it
it
tt
tt
it
Emery
Feldspar.
Flint, black
•' white. . . .
Fluorine
Fuel, Warlich's
•' Lignite. . .
Glass, bottle....
Crown...
It
It
flint.
Specific
Weight
ofaCabe
Gravity.
Foot.
I.be.
2740
171.25 !
2864
179
1 160
72.3
830
517
1714
107.125
1367
85437
1900
118.75
2400
150
2201
137562
1800
112.5
1600
100
2000
125
3500
218.75
1300
81.25
1560
97-25
1520
95
2784
«74^
1930
120.025
2480
155
1350
84-375
1436
8975
1640
102.5
1290
8a 625
1238
77-375
1318
82.375
1277
79.812
1276
79-75
X290
80.625
1292
80.75
"73
79.562
"355
84.687
1270
79-375
1300
81.35
"59
78.687
1300
81.25
1302
81.375
i3»5
82. 187
1000
62.5
746
46.64
2200
137-5
2000
125
X2l6
76
1500
93-75
2050
128.125
2050
128. 125
1600
100
1920
X20
2020
126.25
Z900
118.75
1400
87.5
4cx)o
250
2600
162.5
2582
161.375
2594
162.125
1320
82.5
1 150
71-875
1300
81.25
2732
170-75
2487
155-437
2933
183.312
3200
196
BUBSTAiraXB.
stones, KartliB,
etc.
Glass, green
*''' optical
" white
** window
" soluble
GniesB, common
Granite, Egyptian red..
*' Patapsco
" Quincy
" Scotch
'^ Susquehanna..
it 41 gray
Graphite
Gravel, common
Grindstone.
Gypsum, opaque
Hone, white, razor
Hornblende.
Iodine,
it
tt
tt
tt
tt
it
tt
it
tt
tt
Lava, Vesuvius |
Lias
Lime, quick
" hydraulic
Limestone, white
*♦ green
Magnesia, carbonate. . . .
Magnetic ore
Marble, Adelaide
Aflrican
Biscayan, black.
Carrara
common
Egyptian
French
Italian, white. . .
Parian
Vermont, white.
Silesian
Marl, mean
tough
Masonry, nibble
"■ Granite
*' Limestone
" Sandstone
" Brick
" ''rough work
Mica
Millstone
'' Quartz
Mortar |
Mud
'' wet and fluid
tt it it pressed...
Nitre
Oyster-shell
Paving-stone
Peat, Irish, light
" " dense
tt ^gyy ti
* Specific gr&Tity of earth b ettimated at from 1520 to aaoo.
Specific
Gravity.
2642
3450
2892
2642
1250
2700
2654
2640
2652
2625
2704
2800
2200
1749
2143
2168
2876
3540
4940
1710
2810
1350
804
2745
3156
3180
2400
S094
271S
2708
269s
2716
2686
2668
2640
2708
2838
2650
2730
1750
2340
2050
2640
26^0
2160
2240
1600
2800
2484
1260
1384
1750
1630
1782
1920
1900
2092
2416
278
562
675
Weislit
of a Cab*
Foot.
Lba.
165.125
215.625
i8a75
165.125
78. 125
167.4
165.87s
165
165-75
164.06a
169
175
»37-5
109.31a
«33-937
135-5
179-75
221.25
106.875
175.625
146.875
50.25
171.568
197-25
198.7s
150
3'7-6
169.687
169.25
168.437
169.75
167.87s
166.75
165.56ft
169.25
177-375
16557
170.625
109-375
146.25
128.125
16s
165
«35
140
100
175
155.25
78.75
86.5
109-375
101.875
112
lao
118.75
130.75
151
17.375
35-125
43.187
SPECIFIC GEAVITY AKD WEIGfiT.
213
SVBKAltCIS.
Stones, Karths,
etc.
Peat, black
Pbospborus
Plaster of Paris.
(t
t(
((
dry —
Plumbago
Porcelain, Cbina
Porpbyry , red.
Pumice-Btone
Qaartz.
Red lead
Resin. «.
Rock, crystal
Rotten-stone
Salt, common
" rock
Saltpetre
Sand, coarse
common
damp and loose. .
dried " "
dry
mortar, Ft. Rich m'd
*' Brooklyn..
silicious.
Sandstone, mean
♦* Sydney
Scborl
Scoria, volcanic
Sewer pipe, mean
Sbale
tt
((
((
((
II
II
Slate
(* purple
Smalt
Soapetone
Spar, calcareous
Feld, blue ,
" green ,
Fluor ,
Specular ore ,
Stalactite ,
Btone, Batli,EngI
Blue Bill
Bluestone (basalt)
Breakneck, N.T..
Bristol, Engl
Caen, Normandy.
common
Craigleith, Scotl. .
Kentish rag, '' . .
Kip's Bay, N. Y. .
Norfolk (Parlia-
ment House). . .
Portland, Engl. . .
StatenIsl'd,N.Y.
Sullivan Co., "
Sulphur, native
Terra Cotta
Tile
Trap. .*ttrf •>
It
II
II
II
«i
ti
It
<t
It
If
•I
II
<t
tt
II
ti
Wtiglit I
Specific
of a Cube
Gravity.
Foot.
Dm.
1058
66. X25
1329
83.062
1770
1x0.625
1 176
73-5
3400
212.5
1400
87.5
2IOO
131.25
2300
143-75
2765
172.812
9«5
57- 187
2660
166.25
8940
558.75
1089
,68.062
8735
170.937
123.812
1981
2130
133-125
2200
137-5
2090
130.625
1800
X12.5
1670
104-375
1392
87
X560
?Z-S
1420
88.75
1659
X03.66
1710
107.25
1 701
106.33
2200
137-5
2237
x39-8x
3170
X98.125
830
51-875
2250
140.625
2600
162.5
2672
167
2900
181.25
2784
174
2440
152.5
2730
170.625
2735
170-937
2693
168.312
2704
X69
3400
212.5
525«
328.187
2415
150.937
1961
122.562
2040
165
2625
164.062
' 2704
X69
2510
156.875
2C76
129.75
2520
157-5
2316
M4-75
2651
165.687
2759
172
2304
144
2368
148
2976
186
2688
168
2033
127.062
1953
1815
X22
"3-437
979Q
170
SuBSTAMcaa.
O-ranite.
iGenHGiUmore,U. S. A.)
Dulutb, Minn., dark. . . .
Fall River, Mas&, gray. .
Garrison's, N. Y " ..
Jersey City^ N. J., soap..
Keene, N. U., bluish gray
Maine
Millstone Pt, Conn
New Ix>ndon, "
Quincy, Mass., light ....
Richmond, Va.
" u gray
Staten Island, N Y. . . . .
Westchester Co., N. Y. .
Westerly, R. I., gray. . . .
Xjinaestone.
{OenH GiUm&re, U. S. A. )
Bardstown, Ky., dark . .
Caen, France
Canajoharie, N. Y
Cooper Co. , Mo. , d'k drab
Erie Co., N. Y , blue...
Garrison's, N. Y
Glens' Falls, "
Joliet, 111., white
Kingston, N. Y
Lake Champlain. N. Y. .
Lime Island, Mich., drab
Marblebcad, Ohio, white
Marquette, Mich., drab .
Sturgeon Bay, Wis., blu-
ish drab
Specific
Gravity.
AlarlDle.
(Gen'lOUlmore.U.S.A.)
Dorset, Vt....
East Chester, N. Y.
Italian, common
Mill Creek, 111., drab....
North Bay, Wis., " ....
Sandstone.
(GenH GiUmore, U. S. A.)
Albion, N.Y., brown. . . .
Belleville, N. J., gray . . .
Berea. Ohio, drab
I Cleveland, " olive green
Edinb'h,Sc'tl., Craigleith
Fond du lAC,Wis., purple
FoutenaCjMinnnrg'tbuff
Haverstraw, N. Y., red. .
Kasota, Minn., pink....
Little Falls, N. Y, brown
Marquette, Mich., purple
Masillon, O., yellow drab
Medina, N. Y, pink
'■ Middletown, Ct., brown.
Seneca, Ohio, red ''
; Vermillion, Ohio, drab. .
I Warrensbargh, Mo
3780
2635
3580
3030
2656
2635
2706
2660
2695
2727
2630
2861
2655
2670
2670
1900
2685
2320
2640
2635
2700
2540
2690
2750
2500
2400
2340
2780
2635
2875
2690
2570
2800
2420
2259
2110
2240
2260
2220
2325
2130
2630
2250
2285
2x10
2410
2360
2390
2160
2140
Weisht
of a Cab
Foot.
Lbt.
173-7
164.7
161. 2
189-3
166
164.7
169 x
166.25
168.5
170.5
164.4
178.8
165.9
X66.9
66.9
18.8
67.8
41-3
65
64.7
68.7
58.7
68.1
71.9
56.3
50
46.25
X73-7
164.7
; 179-7
> 168. z
171.9
'75
X41.3
»3i-9
X40
X41.25
138-7
145-3'
133- 1
X64.375
140.6
142-5
131.87
150.6
«47-5
149.4
135
133-75
2X4
spsciFio GBAvrry and wiught.
Spae. Gmr.
Agate 3590
Amethyst. 3920
CarnelittD 2613
Chrysolite 2782
Diamond, Oriental. . . 3521
*■*■ Brazilian.. 3444
" pure 3520
Emerald 3950
Precious Stones.
Spec. Gr«T.
Emerald, aqua ma-
rine 2730
Garnet 4189
" black 3750
Jasper. 2600
Jet 1300
ijipiB lazuli : . 2960
Mijachite 4030
SpocGfiiT.
Onyx 2700
Opal 2090
Pearl, Oriental 2650
Ruby 3980
Sapphire 3994
Topaz 3500
Tourmaline 3070
Turquoise 2750
SuBSTAHCBa.
l^iscellaneovis.
Amber
Atmospheric Air
Beeswax
Bone
Butter
Camphor
Caoutchouc
Cotton
Dynamite
Egg
Fat of Beef
Hogs
Mutton
Flax
Gamboge
Glycerine, 60°
Grain, Barley
" Wheat
" Oats
Gum Arabic.
Gunpowder, loose ,
'''■ shaken
It
it
it
solid..
Gutta-percha
Hay, old compact.
Horn
Human body
Ice. at 32^
Indigo
Isinglass
Ivory
Lard
Leather
Mastic
Myrrh
Nitro-Glycerine . . .
Opium
Potash
Resin
Snow
Soap, Castile
Spermaceti
Starch
Sugar
" .66
TaUow
Wax
SpMific
Weicbt
of a Cube
Gravity.
Foot.
Lbs.
1090
68.125
.001292
.080728
965
60.312
1900
118.75
942
58.875
988
61.75
930
58.125
950
59-375
1659
103.125
1090
—
923
57.687
936
58.5
923
57.687
1790
X11.875
1222
—
I26Z
78.752
590
36.875
750
46.875
500
3125
1452
90.75
900
56.25
1000
62.5
96.875
1550
1800
112.5
980
61.25
128.8
8.05
1689
105.563
1070
66.935
923
57-5^
1009
63.063
IXII
69-437
1825
114.062
947
59187
960
60
1074
67.125
1360
85
1600
xoo
1336
835
2100
131.25
io8q
.0833
68.062
5-2
1071
66.937
943
58.937
950
59-375
x6o6
"00-37S
972
60.25
1326
82.875
941
58.812
964
60.25
970
60.695
SlXHTAKCES.
ti
tt
tt
Ct
t(
{(
tt
tt
(t
tt
tt
tt
t(
tt
tt
tt
tt
tt
tt
tt
(t
tt
tt
tt
ft
ILiiquids.
Acid, Acetic
Benzoic
Citric
Sulphuric, Gou'd. .
Fluoric
Muriatic
Nitric
Nitrous
Phosphoric
" solid. .
Sulphuric
Alcohol, pure, (kP
95 per cent.
50
40
as
10
S
proof spirit, •so
per cent. , 60*
proof spirit, 50
per cent. , 80°
Ammonia, 27.9 percent.
Aquafortis, double
" single
Beer
Benzine
Bitumen, liquid
Blood (human)
Brandy, .83 or .5 of spirit
Bromine
Cider
Ether, Acetic. . . .
'' Muriatic.
" Nitric...
'' Sulphuric
Honey
Milk
Oil, Anise-seed . .
Codfish
Whale
Linseed
Naphtha
Olive
Palm
Petroleum...
Rape
Sunflower. . .
Turpentine .
Spociflc
GrftTity.
(I
((
tt
((
i(
((
it
i(
<t
1063
667
1034
1531
1500
1200
1217
1550
1558
2800
1849
794
816
863
934
951
970
986
992
I 934
[ 875
891
1300
1200
1034
850
848
1054
924
2966
1018
866
845
IIIO
715
1450
1032
9i6
933
933
040
850
915
Weisht
of a Cub*
Foot.
80
70
I
Urn.
66.375
41.687
64.635
95-063
93-75
75
76.063
96.87s
97 375
175
115.563
49.633
51
53-937
58.375
60.635
61.635
62
58.375
54687
55687
81.35
75
64.635
53. "5
53 .
65.875
57-75
185. 375
63.635
54- "5
52.81a
69-375
44-687
90.635
64.5
61.625
57.687
57.687
58.75
53125
57- 187
60.563
55
57.1 as
57875
54 37S
• Sp0oifl« f;tvi\ij of pfoof ipirif Mcoptlj^^ |e Uro^ T«bU for Byket'a HydroimUri 93%
SPECIFIC <3lBAVlTlr ANt> WGIOHT.
Hi
Xiiquids.
Bpirii, rectified —
Steam, al ai2° . . . .
I'ar
Vinegar
Water, at 330.
" 391°.
" 620t..
212
distilled, at 39O.
• 03818.
Sp«eifie
Wfllffkt
ofsCvbe
Grafity.
Foot.
Lbt.
824
51-5
.00061
.038*
1015
63-437
1080
67-5
998.7
62.418
998.8
62.425
997-7
62.35s
956.4
59-64
998
62.379
SOBBTAIfCW.
XjiquicLs.
Water, Dead Sea.
" Mediterranean.
** sea..
" Black Sea.*!.*!!
*' rain
Wine, Burgandj
'' Champagne
" MadeiRi
" Port
Specific
<;nivlty.
1240
1029
1029
lOiO
1000
992
997
1038
997
Weight
ofaOalM
Foot
Lbs.
77-5
64.312
64.312
63-5
62.5
62
62.312
64-375
62.312
1 1 cnbe inch at standard temperature => 252.5954 graiiu.
Compression of Tollowing fluids under a pressure of 15 lbs. per square inch:
AlcoboL. .00002x6 I Mercury.. .00000265 | Water.. .00004663 | Ether.. .00006x58
Slastio iriuids.
X Ctibe JFkxd of AlmasfAearie Air aJt yi^ weighs .080728 Ibt. .iootn^ujiow = 565.096
ffrainBy tmd at 62° 532.679 gramt.
Its cusumed Gravity <ifi is Unit /or Elastic Fluids.
Spec.
Acetic Ether 3
Ammonia
Atmos. air, at 32^. .
AKOte
Carbonic acid
'* oxide
CarbnretM H jdrog.
Chlorine 2
Cbloro-carbonic. . . 3
Chloroform 5
Cyanogen 1
Gas,*coal........ j
Hydrochloric acid . i
Hydrocyanic *' .
Hydrogea
Muriatic aoUL z
Onv. j Spec. Orar. 1
04 Nitric acid 1.217
589 ' ** oxide 1.094
Nitrogen 974
976 Nitrous acid 2.638
53 Nitrous oxide ... . 1.527
972- ' Oleflant gas 9672
559 I Oxygen no6
421 I Phoephurett'd Hy-
389 dregen 1.77
3 Sulphuretted Hy-
815 drogen x.17
438 Sulphurous acid.. 2.21
752 Steam,! at 212°. . . .47295
278 Smoke.
942 Bltum. Coal . . .
0692 Coke
247 Wood
% Weight of a cabe foot 267.26 graifu, and compared with water at
.102
.105
09
Spec. Orsr.
Vapor.
Alcohol 1.613
Bisulphuret of
Carbon 2.64
Bromine 5.4
Chloric Ether .... 3.44
Chloroform 4. 2
Ether 2. 586
Hydrochlor. Ether 2.255
Iodine 8.7x6
Nitric acid 3.75
Spirits of Turpen-
tine. 5-0x3
Sulpburicaoki ... 2. 7
" Ether.. 2.586
Sulphur 2.214
Water 623
62* epecific gravity = .000 6ia 3.
Weighl of a Cvbe Foot of Gtues at 32*^ P,^ and under Pressure of one Atntot'
pkere^ or 2116.4 UfB.per Square Foot.
Lbs.
Air,at3aO 080728
-' '* 63O 076097
Alcohol 130 2
Carbonic acid 12344
Carburet. Hydrog. .04462
Lbs.
Chlorine. 197
Chloroform 428
Cbal gas 035 36
Ether, Sulpharic. . .2093
Gaseous steam 050 22
Hydrogen . .
Nitrogen . . .
Olefiant gas.
Oxygen
Steam
Lbs.
•005 594
.078 596
.0795
.089256
.050 22
Sulphurous acid 1814 Ib&
To Oonxptxte TVeinlit of a Sody or Su'betaxxoe -virhezi
Speci^jo Qravxty is isiveii.
Rule. — Multiply- spccifio ^^nrvtty by umt or standard of body or sul>-
stance, and product is the weight.
Or, Divide specific gravity of body or subatauce by i6| and quotient will
give weight o€ a enbe loot eil it in lbs.
ExAxruL — Specific gravity is 2250; what is weight of a cube foot of it?
3250 X 62. 5 = X40.635 U>s.
2l6
WEIGHTS OP VABIOUS SUBSTANCES.
Weigbits and Volumes of* various Su-'batanoes in
Ordinary TJse.
SUBSTAHCBS.
Cabe Foot.
IMLetals.
Brass i^^P^erej)
Brass., j^jjjj, ^^>
«< gun metal.
** sheets
" wire
Copper, cast
^* plates
Iron, cast
" gun metal
" heavy forging..
" plat-es
" wrought bars. . .
Lead, cast
" rolled
Mercury, 60°
Steel, plates
" soft
Tin
Zinc, cast
" rolled
Ash
Bay
Blue Gum
Cork
Cedar
Chestnut
Hickory, pig nut
" shell-bark..
Lignum- vit«e
Logwood
Mahoga'y,Hondur'8 {
Oak, Canadian
English
live, seasoned...
" white, dry
" " upland. . .
Pine, pitch....*
" red
" white
" well seasoned..
Pine, yellow
Lbs.
488.7s
543 75
5»3-6
514.16
54725
543-625
450437
466.5
479-5
481.5
486.75
709.5
711.75
848.7487
48775
489. 562
455-687
428.812
449-437
52.812
51-375
643
15
35-062
38. "5
49-5
43-125
83-3"
57.062
35
66.437
54-5
58.25
66.75
53-75
42-937
41.25
36.875
34-625
29.562
33-812
Cabe loch.
Lb*.
.2829
•3147
.297
•3033
•3179
•3167
.2607
.27
-2775
.2787
.2816
.4x06
•4119
.491174
• 2823
.2833
.2637
.2482
.2601
Cab« Feet
in M Ton.
42.414
43.601
34.837
149-333
63.886
58.754
45252
51-942
26.886
39255
64
33-714
41.X01
38.455
33-558
41.674
52.169
543^3
60.745
64.693
75-773
66.248
SI7B8TA.IICBS.
"Woods.
Spruce
Walnut, black, dry. . .
Willow
" dry
A£ i seel 1 ail ecus.
Air.
Basalt, mean
Brick, fire
Cabe Foot.
ii
mean.
Coal, anthracite.... |
(t
bitumin., mean.
Cannel
Cumberland. . . .
" Welsh, mean...
Coke
Cotton, bale, mean . . .
" " pressed {
Earth, clay
*' common soil..
** gravel
dry, sand
loose
moist, sand...
mold
mud
with gravel...
Granite, Qui ucy
'^ Susquehanna
Gypsum
Hay, bale.
*' hard pressed. . . .
Ice, at 32°
India rubber
" " vulcanized
fiimcstone . .'
Marble, mean
Mortar, dry, mean. . .
Plaster of Paris
Water, rain
»' salt
" at 62°
it
K
a
ii
ii
((
Lb«.
31-25
31-25
36.562
30.375
.075291
175
137-562
102
89.7s
102.5
80
94875
84.687
81.25
62.5
14s
20
25
120.625
137-135
109.312
I20
93-75
128.125
128.125
101.87s
126.25
165.75
169
135-5
12
25
57-5
56.437
MetaU.—Toh'm Bronze.
Cabe fbot.
522.02 lbs.
197.25
167.875
97.98
73-5
62.5
64.312
62.355
Cube incn.
3021 lb&
Cube Feet
in • Ton.
71.68
7168
61.265
73.744
12. 8
16.284
21.961
24.958
21.854
28
23.609
26.451
27- 569
3584
154-48
114
89.6
18.569
16.335
20.49
18.667
23-893
17.483
17.482
21.987
17.742
»3-5i4
13-254
i6.'53x
186.66
80.6
38-95
39-69
"-355
13-343
22.869
30.476
35.84
3483
35-955
To Compvite Proportions of T-w-p Ingredieixts in a Com-
pound, or to DiHCOver Advilteration in ^iletals.
Rule.— Take differences of each specific gravity of ingredients and spe-
cific gravity of compound, then multiply gravity of one by difference of
other ; and, as sum of products is to respective products, so is specific
gravity of body to proportions of the ingredients.
Example. — A compound of gold [spec. grav. = 18.888) and silver («p«c. grao. :»
10-535) b&A A speciQc gravity of 14; what is proportion of each moUJ?
18.8S8— r4=:4- 888 X 10.535 = 51-495- 14—10.535=3-465X18.888=65.447.
65.447+51-495 = 65-447 "-14: 7835 P»W, 65. 447+51.495: 51. 495'. '.14: 6. 165 Wtoeil
WSIGHTS OP VARIOUS SUBSTAJ^CES IN BULK. 21/
'Weiglk.ts of* Various Su.'bstazioes per Cixlae foot in Sulk.
LiM.
Lead, in pigs 567
Iron, " 360
Marble, in blocics )
Limestone, " J • '^^
Trap 170
Granite, in blocks .... 164
Sandstone -. 141
LbB.
Potters' clay 130
Loam 126
Gravel 109
Sand 95
Bricks, common .... 93
Ice, at 32° 57.5
Oak, seasoned 52
Ash, dry, 100 feet BM 175 ton.
" white, *' '• 141 "
Cement, struck bushel and
packed* 100 lbs.
Cement, Portland, bushel. no lbs.
Cherry, dry, 100 BM 156 ton.
Chestnut, dry, 100 BM... .153 "
Coal, anthracite, i cub. yd.
broken and loose ... 1.75 yds.
" " '* I ton.. 41.5 cub. feet
Coke, ton = 80 to 97 cub. feet.
Earth, common soil 137-125 lbs.
* One packed basbel = z.43 looee.
Comparative AVeiglit of* G^reezi and Seasoned Xixn'ber.
Lb»
Coal, caking 50
Wheat 48
Barley 38
Fruit and vegetables.. 22
Cottonseeds. 12
Cotton 10
Hay, old '. 8
Earth, loose 93.75 lbs.
Elm, dry, icx) feet BM 13 ton.
Gypsum, ground, str. bush. 70 lbs.
" " well shaken 80 "
Hemlock, dry, 100 feet BM. .093 ton-
Hickory, " " '• . .197 "
Masonry, Granite, dressed.. 165 lb&
" '* rough... 126 *'
" Limestone, dresM 165 "
" Sandstone 135"
" Brick, pressed ... 140 **
" ♦♦ com'n, rough. 100 '*
TiMBBX.
AiacTican Pine.
Ash
Beech
Weie^t of • Cube Foot.
Green. Seasoned.
Lbe.
44-75
58.18
60
Lbs.
30-7
50
53-37
TlMBBB.
Cedar
English Oak
Riga Fir
Weight of a Cube Foot.
Green. Seasoned.
Lbs.
32
71.6
48-75
Lba.
28.25
43-5
35-5
^pplioatioxi of tlie 'Pa'bles.
When Weiffkt of a Solid or Liquid Subttance is required. Rule. — Ascer-
Ain volume of substance in cube feet ; multiply it by unit in second column
of tables (its specific gravity), and divide proauct by 16 ; quotient will give
weight in lbs.
When Volume is given 01* ascertained in Inches. RtiLE.—Multiply it by
nnit in third column of tables (weight of a cube inch), and product will give
weight in lbs.
EzAMFLB.— What is weight ol a cube of Italian marble, sides being 3 feet?
33 X 3708 = 731160*., which -r- 16 = 4569. 75 Uu.
Or of a sphere of cast iron 2 inches m diameter?
2^ X • 5336 X .2607 weight of a cube inch = 1.092 lbs.
When Weight of an EScutic Fluid is required. Rule. — Multiply specific
gravity of fluid by 532.679 (weight of a cube foot of air at 62° in grains),
divide product by ycxxn. (grains in a lb. Avoirdupois), and quotient will give
weight of a cube foot in lbs.
EzAMPLB.— What is weight of a cube foot of hydrogen?
Specific gravity of hydrogen .0692.
532.679 X .0692 -T- 7000 =r .005 265 9 lbs.
To Compute "Weiglit of Cast iMetal t>y "Weiglit of Pattern.
When Pattern is of White Pine, Rule.— Multiply weight of pattern in
lbs. by following multipliers, and product will give weight of casting :
Iron, 14 ; Brass, 15 ; Lead, 22 ; Tin, 14 ; Zinc, 13.5.
When the Cores w Prints are of White Pine. Multiply the product of their
area and length in inches by .0175 or .02, according to the dryness of the wood, and
proportionately for other woods, and result is weight of core or print to be deducted
firom weight of pattern.
2l8 BALLOONS, SdRINKAGB OF CASTINGS, ETC.
To OoTOpu.te Weiglits of Ingredients, tliat of CoxnpoTixid.
1361113 given.
Rule. — As specific ^avity of compound is to weight of compound, so are
each of the proportions to weight of its material.
ExAJiPLB.— Weight, as p. 2x6, being 28 lbs., what are weights of the ingredients f
lA- 28" f7-^35 : 1567 gold,
'4 • *** •• \6.i65 : 12.33 silver.
Note. — Specific gravity of alloys does not usually follow ratio of their compo-
nents, it being sometimes greater and sometimes less than their mean.
To Compute Capacity of* a Salloon.
Rule. — From specific gravity of air in grains per cube foot, subtract that
of the gas with which it is inflated ; multiply remainder by volume of bal-
loon in cube feet ; divide product by 7000, and from quotient subtract weight
of balloon and its attachments.
ExAMPLB.— Diameter of a balloon is 26.6 feet, Us weight is 100 lbs., and specific
gravity of the gas with which it is inflated ts .oy (air being assumed at i); what is
its capacity, specific gravity of air assumed at 527.04 grains.
527.04 — (527.04 X .07) X 26. 6 3 X. 5236 ^
7^^^ ioo=59ao4n*
To Compute Diameter of* a Salloon.
Weight to be raised being given. — By inversion of preceding rule.
/W -^ 7000 ^" 8 •" s'
^ ■— ^ - — *— =.d', 8 and s' representing loeight of mr and gas
in grains per cube foot ^ W weight to he raised in Ibs.j and d diameter of bal-
loon in feet.
Illustration.— Given elements in preceding case.
Then 3/ 59004 -f 100 X 7000 -^5^7^4-36J9^ 3 /S^^±^ = ^6.6 feet.
sf .5236 V -5236
Proof of Spirituous Liquors.
A cube inch, of Proof Spirits weighs 234 grains ; then, if an immersed
cube inch of any heavy body weighs 234 grains less in spirits than air, it
sliows that the spirit in which it was weighed is Pi oof
If it lose less of its weight, the spirit is above proof; and if it lose more,
it is below proof.
Illustration. —A cube inch of glass weighing 700 grains weighs 500 grains when
weighed in a certain spirit; what is the proof of it?
yc)o — 500 = 200 = grains = weight lost in spirit.
Then 200 : 234 :: i : 1.17= ratio of proof qf spirits compared to proof spirits^ or
X =3 . 17 above proof
Note.— For Hydrometers and Rules for ascertaining Proof of Spirits, see page
67; and for a very full troatise on Specific Gravities and on Floatation, see Jamie-
sou's Mechanics of Fluids. Load., 1837.
Slirixikage of Castings.
It is customary, in making of patterns for castings, to allow for shrinkage
per lineal foot of pattern as follows :
Iron, small cylinders . . . = ^ in. per ft. Ditto in length. ... =r 3^ in 16 ins.
" Pipes = >^ " Brass, thin = >^ in 9 ins.
" Girders, beams, etc. = >^ in 15 ins. " thick = >^ in 10 ins.
" Large cylinders, ") ' Zinc =^ ^ in a foot
tlie contraction > = ^ per foot. Lead = ^ "
of diam.at top. J
♦* Ditto at bottom..^ A "
Ck)pper =^
Bismuth ar^V **
GEOMETRY.
IDefiiiitioiis.
PtfifU has poeition, but not magnitude.
Line is length without breadth, and is either Rights Curvedf or Mixed.
RUfht lAne is shortest distance between two points.
Curved Line is one that continually changes its direction.
Mixed Line is composed of a right and a curved line.
Suwrficies has length and breadth only, and is plane or curved.
Solid Das length, breadth, and thickness, or depth.
Angle is opening of two lines having different directions, and is either
Rightj A cute^ or Obtuse.
Biffht Angle is made by a line perpendicular to another falling upon it.
Acute Angle is less than a ri^ht angle.
Obtuse Angle is greater than a right angle.
Triangle is a figure of three sides.
Equilateral Tiiangle has all its sides equal.
/.tveceles Triangle has two of its sides equal.
Scalene Ti^ngle has aU its sides unequal.
Right-angled Triangle has one right angle.
Obtuse-angled Triangle has one obtuse angle.
A cHte-angled Tin angle has all its angles acute.
Oblique-angled Triangle has no right angle.
Quadrangle or Quadrilateral is a figure of four sides, and has following
particular designations — viz.,
ParaUehgram^ having its opposite sides paralleL
Square, miving length and breadth equal.
Rt'ctangle, a parallelogram having a right angle.
Rhombus or Lozenge^ having equal sides, but its angles not right angles.
Rhomhmdy a parallelogram, its angles not being right angles.
Trapezium, having unequal sides.
Trapezoid, having only one pair of opposite sides paralliel.
Note. — Triangle is sometiines termed a Trigon, and a Square a Tetragon.
Gnomon is space included between the lines forming two similar parallelo-
grams, of which smaller is inscribed within larger, so as to have one angle
m each common to both.
Polggons are plane figures having more than four sides, and are either
Regular or Irregular, according as tiieir sides and angles are equal or un-
equal, and they are named from number of their sides or angles. Thus :
Pentagon has five sides.
Hexagon " six "
Heptagon " seven"
Octagon " eight "
Nonagon has nine sides.
Decagon " ten "
Undecagon " eleven "
Dodecagon " twelve"
Circle is a plane figure bounded by a curved line, termed Circum/erence
or Periphery.
Diameter is a right line passing through centre of a circle or sphere, and
terminated at each end by periphery or surface.
A re is any part of circumference of a circle.
Chord is a right line joining extremities of an arc.
Segment of a circle is any part bounded by an arc and its chord.
Radius of a circle is a line drawn from centre to circumference.
Sector is any part of a circle bounded by an arc and its two radii.
Semicircle is half a circle.
Quadrant is a quarter of a circle.
Zone is a part of a circle included between two parallel cords.
Lune is sjNice between the intersecting arcs of two eccentric circles.
2^0 GEOMETRY.
Secant, is line running from centre of circle to extremity of tangent of arc.
Cosecant is secant of complement of an arc, or line running from centre of
circle to extremity of cotangent of arc.
Sine of an arc is a line running from one extremity of an arc perpendicu-
lar to a diameter passing through other extremity, and sine of an angle is
sine of arc that measures that angle.
Versed Sine of an arc or angle is part of diameter intercepted between sine
and arc.
Cosine of an arc or angle is part of diameter intercepted between sine and
centre.
Coversed Sine of an arc or angle is part of secondary radius intercepted
between cosine and circumference.
Tanffent is a right line that touches a circle without cutting it.
CotanfferU is tangent of complement of arc.
Circvmference of every circle is supposed to be divided into 360 equal
parts, termed Degrees ; each degree into 60 Minutes^ and each minute into 60
Seconds^ and so on.
Complement of an angle is what remains after subtracting angle from 90
degrees.
Supplement of an angle is what remains after subtracting angle from 180
degrees.
To exemplify these definitions^ let Acb^ in/ollomng Figure, be an (usumed
arc of a circle described with radius B A :
A c 6, an Arc of circle AGED.
A 6, Chord of that arc.
BA, an Initial radius.
B C, a Secondary radius,
e D d, a Segment of the circle.
A B 6, a Sector.
A D£, a Semicircle.
€13 E. a Quadrant.
A « (J E, a Zone,
no A, a Liine.
B g, Secant of arc A c 6; written Sea
\ \ J bk. Sine of arc A c 6 ; written Sin.
\ Vc --/ A fc, Versed Sine of arc A c 6; written Versin.
N. ^ y B Ar or 711 6, Cosine of arc A c 6.
\CSs. >/ A g. Tangent of arc A c 6.
li""--'-.^ -^ C B 6, Complement, and 6 B E, Supplement of
Jj arc kcb.
C«, Cotangent of arc, written Cot B», Cosecant of arc; written Cosec.
m C, Coversed sine of arc, or, by convention, of angle A B 6 ; written Coversin.
Vertex of a figure is its top or ujjper point. In Conic Sections it is point
through which generating line of the conical surface always passes.
A Uitude^ or height of a figure, is a perpendicular let fall from its vertex
to opposite side, termed base.
Mecisure of an angle is an arc of a circle contained between the two lines
that form the angle, and is estimated by number of degrees in arc
Segment is a part cut off by a plane, parallel to base.
Frvstum is the part remaining after segment is cut off.
Perimeter of a figure is the sum of all its sides.
Problem is something proposed to be done.
Postulate is something required.
Theorem is something proposed to be demonstrated.
I^mmd is something premised, to render what follows more easy*
Coi\>ll(try is a truth consequent upon a preceding demonstration.
Scholium is a remark upon something going before it.
For other definitions «ee Mensuration of Surfaces and Solids, and Conic Sections
X^uBths of ibllowinc Sli
/ ^b" 'iny^mulll^eVorDSra .-■''' /
--^r~~---^Ar. (Fig.s.)
/ T From «ny two poinls, lui c d, at a proper
^ difiUnceapan,<leKnlw«rcsculllngallB, ,^
(Dd wuiiecl lb«m. (Ftg.
e. ^
'
/7
ra; ,
i
222
GEOMETRY.
T^
To Bisect a Riglxt X^ine or axx A.ro of a
Circle, aud to Dra-w a Ir'erpeiidioix^
lar to a Circular or fiiglxt I^ine, or a
]Eiadial A.ro.— I^^ig. 7.
From A B as centres describe arcs catting each other
at c and d, connect c d, and line and arc are bisected
at e and o.
Line c d is also perpendicular to a right line as A B,
and radial to a circular arc as A o B.
Xo IDra-w a X^iixe Parallel to a Oiven
Riglxt I^iiie, as c d, Fig. 8.'
From A B describe arcs Ac, Bd,and draw a line par-
allel thereto, touching arcs c and u.
.Aji.gles.
To Describe Angles of 3O0 and 60°, Kig. 9, and 460,
Fig. lO.
From A, with ar radius, A o, de-
scribe or, and ft'om o with a like ra-
dius cut it at r, let &U perpendicular
r«; then oAr = 6o^y and Ars.
(Fig. 9)
30
To
12.
Describe an
f
Set off* an^ distance, a^ A B, erect
perpendicular A0 — A B, and connect
o B. (Fig. 10./
To Bisect Inclination of T-^^o Xjines.
-when Point of Intersection is Inao^
oessible.^Ifig. 11.
Upon given lines, A B, C D, at any points draw |)erpen-
diculars eo^sr, of equal lengths, and fVom o and s draw
parallels to their respective lines, cutting at n; bisect
angle on$, connect nm^ and line will bisect lines as re-
quired.
IRectilineal IHigiares.
Octagon upon a X^ine, as A B.^Fis. 18-
From points A B erect indefinite perpendiculars A/, Be;
produce A B to m and n, and bisect angles m A 0 and nBp
Vfith A u and B r.
Make A u and B r equal to A B, and draw « s, r v parallel
to A/, and equal to A B.
From z and v, as centres, with a radius equal to A B, de-
scribe arcs cutting A/ Be, in / and e. Connect e/,/e,
and ev.
To Inscribe any Regular Polygon in a
Circle, or to Divide Circuniference into
a given TQ'umber o£ Sq.ual Parts.— Fig. 13.
If Cirdt U to contain a Heptagon. — Draw angle A o B at
centre o for 360® -r- 7 = sr** 42' 5i"-|-» or Si^' *^^° ^^ **^ «pon
circumference diatance A 6 or remaining angles A 0 6.
GBOMETBY.
223
To Ixxvovibe a Hexaeoix ixi
a Circle.— Kig. 14:.
Draw a diam-
eter, AoB. From
A and B as ceu
tre:i, with Aoand
B o, cot circle at
cm and
connect
eM, and
To Ineorilie a Pentagoxi
a Ctpole.— Kig. 16.
in
ij—
--4r.-
8
"<>!
•*i
H /
1
/
\
/,
^.
^
one side oi'a iM'iUugou.
Draw diameters
Ac i|Qd m n, at
right angles to
each other; bigevt
0 n in r, and with
9- A describe
from A with
describe « B.
Connect AB,and
distance is equal to
A s\
A s
To Describe a Hexagon
«ibou.t a Circle.**irig. 1£3.
Draw a diam-
eter as a ri b ; and
with ati cut uirole
ate; join ac^and
bisect it with ra-
) dius o r, through
r draw e r paral-
lel to c a, cutting
diameter at m;
then with radius
0 m describe circle, within which describe
a hexagon as above.
To Describe a Pentagoii
upon a Line, as A B— irig.
Draw B m per-
pendicular to A B,
and equal to one
half of it; extend
A m until m n is
equal to B m.
From A and B,
with radius Bn, de-
scribe urcs cutting
each other in »:
then from 0, with radius o B, describe
circle A 'J B,.and line A B is equal to one
side of a pentagon upon circle described.
To Describe a Regular Polygon of any reCLuired. Number
of fcsides.— I^ig. 18.
From point o, with distance o B, describe semicircle
B 6 A, which divide into as many equal parts, A a, o b, b c,
etc. , as the polygon is to have sides.
Thus, let a Hexagon be required :
From o to second point b of six divisions draw 0 6, and
through other points, c, <f, and e, draw o C, o D, etc.
Apply distance 0 B, from B to E, from E to D, from D to
G, eta Join these points, a» b C, C D, etc.
Constrxict a Hexagon
To Cotistrnct
a Keotangle
Line.— ITig. 10.
19. mx ?!cn
a Square " or
on a given
A
B n, and join 0 r.
2X, To XxxBcribo
On A B as cen-
tres, with A B as
radius, describe
arcs cutting at
a; one describe
arcs CQtting at
0 r; and on 0 r
descrbe otiiera,
cutting at mM;
draw A m and
To
-upon
20.
a given Line.— F'ig.
From ends of line,
A B, describe arcs
cutting each other
at o, and from o as
acentre, with radius
o A, describe a cir-
cle, and with same
radius set off A c,
c d, B/,/e, and con-
nect them.
an. Octagon in a Circle.— Fig. Sl«
Draw diameters, A C, B D, at right
angles, bisect ares, A B, B C, etc. , at », r,
0, e, and join A p, 0 B, eta (Fig. 21.)
To Describe an Octagon,
about a Circle.- Fig. S3.
Descriiie a squf^re about circle A B,
draw diagonals cf, e d, draw o i, eta,
perpendicular to diagoaal^ and ioucli-
ing circle. (Fig. 22.)
224
QEOMETBY.
To Izisoribe a Sq^taare in a Circle.— Fig. 83u
Draw line A B throagh centre of circle ;
take any radius, as A e, and describe the
arcs Aee, Bee; connect ee, continuing
line to C and D ; join AC, AD, etc. (Fig. 23.)
A -
/
1
'-7-
V
/\
' \
24.
B
To Describe a Sqixare about
a Circle.— Kig. 34.
Draw line A B through centre of circle.
Take any radius, as A e; describe arcs
Aee, Bee; connect ee, continuing line
to CD.
Describe B r and D r ; draw and extend B r a^d D r, and sides A and C parallel tc
them. (Fig. 24. )
Describe an Octagon in a Sq.uare.— Fig. SO.
D
To
Let A B C D be given square
Describe A o r r, B o r r, etc. ; join in-
tersections rrrr^ etc., and figure formed y^
is octagon required. (Fig. 25.) "^
pal I
D --
To Inscribe an £2q^uilateral
Triangle in a Circle
Fig. 26.
From point A, with A o equal to radius
x:
d
of circle, describe oo\ from 0 and o describe 0Ty0r\ join A r, r r, and r A. (Fig. 26.)
Note. — All figures of 10 or 20 sides are readily determined from side of a pentagon,
being halved or quartered; and in like manner, all figures of 6, 12, or 24 sides are
readily determined fVom radius of a Circle, being equal to the side of a hexagon.
Circles.
To Describe an A.rc of a Circle,
tlirougli Tavo given Ifoint^,
^witli a given Rcuiius.- Fig.
sr.
On A B as centres, with given radius, de- '^'
scribe arcs cutting at o, and from o with
same radius describe arc A B. (Fig. 27.)
To Ascertain Centre of a Circle
or of an Arc of a Circle.— Fig.
28.
Draw chord A B, bisect it with perpendicular c d, then bisect c d for centre 0.
(Fig. 28.)
To Describe a Circnlar Segment tliat
Avill botb. iill tbe angle bet-ween t-wo
diverging lines and. toncli tbem.^
Fig. S©.
Bisect inclined lines, A B, D E, by line e/ and connect
perpendicular thereto, B D, to define boundary of seg-
ment to be described. Bisect angles at B and D by lines
cutting at o, and from 0, with radius 0 r, describe arc
Dra-^^ a Series of Circles bet-ween T^wo Inclined
I-iines, touclxing tbexn and eacb otiier.— Fig. 30.
Bisect given lines AB, CD, by line oc.
From a point r in this line erect r .« peri)en-
dicnlar to A B, and on r describe circle «m,
cutting centre line at u ; ft'om u erect u n
perpendicular to centre line, cutting A B at
n, and fVom n describe an arc n ti v, cutting
A B at », erect x v parallel to r «, making a;
•B centra of next circle to be described, with
radius x u, and so on.
Wow laififi circle may b« dMcribed flrtt.
To
GXOHBtB-r.
225
7o Desoribe a Circle tliat shall pass tlirougli any tjbree
given Points, as A B C— ITigs. 31 and. 32.
Upon points A and B,
with any opening of a
dividers, describe arcs
cutting each other at ee.
On points B C describe
two more cutting each
other in points c c.
Draw lines e e and c c,
and intersection of these
lines, 0, is centre of circle
ABC. (Fig. 31.)
When Centre is not attainable. — From A B as centres, describe arcs A g,Bh;
through C draw A «. B c. Divide A e and B c into any number of equal parts, also
c g and B h into a like number. Draw A i, 2, ^, etc., and B i, 2, etc., and intersec-
tion of these lines as at 0 are points in the circle required. (Fig. 32. )
Or, let A B G be given points, connect
A B, A C, C B, and draw e c parallel to A B.
Divide C A into a number of equal parts,
as at 1, 2, and 3, and fh>m G describe arcs
through these points to meet right lines
firom C to points x, 2, and 3, on A e, and
these are points in a circle, to be drawn as
before directed. (Fig. 33.)
To Dra-w a Xangent to a
Circle 1 ronx a given X*oint
in Circuxnfbrence. ^ Fig.
84. e
84.
Through point A draw radial line Ao,
and erect perpendicular ef. (Fig. 34.)
To T>-p&vir Tangents to a
Circle from a foint %vit]:i*
oxxt it.— Fig. 36.
85.
From A draw A 0, and bisect it at s;
describe arc through o, cutting circle at
m n ; Join A m or A ra.
To Dra"^^ from or to Circumference of a Circle, Lines
leading to an Inaccessible Centre.^ITig. 36.
Divide whole or any given portion of
"■ '*. ^ U
I
/
circumference into desired number of
.parts; then, with any radius less than
distance of two divisions, describe arcs
cutting each other, as A r, & r, c r, d r,
etc. ; draw lines b r, c r^ etc., and they
will lead to centre.
To draw end lines^ as A r, F r. From b describe arc 0, and with radius b i, from
A or F as centres, cut arcs A r, etc., and lines A r, F r, will lead to centre.
To Oesori'be an .A.rc, or Segment of a Circle, of a large
Radius.— Fig. ST.
Draw chord A c B; also line hDi
parallel with chord, and at a distance
equal to height of segment ; bisect
chord in c, and erect perpendicular
cD; Join AD, DB; draw A A and Bt
perpendicular to A D, B D; erect also perpendiculars A.n, B n; divide A B and h %
into any number of equal parts; draw lines i i. 2 7, etc., and divide lines A n, B n,
each into half number of equal parts in A B; draw Mnes to D from each division io
lines A n, B n, and at points of intersection with former lines describe arc or segment
226
GEOMETRY
Ellipse.
To II>esori'be an Ellipse to any JLiexigtla. and Breadtli
given.— yig. 38.
Let longest diameter be C D, and shortest E F. T.akc
distance (J o or o D, and with it, from points £ and F,
describe arcs h and/ upon diameter C D.
Insert pins at h and at /, and loop a string around
them of such a length that when a penci2«iB introduced
within it it will just reach to £ or F. Bear upon
string, sweep it around centre o, and it will describe
ellipse.
NoTK.— It Is a property of Ellipse that sum of two Hues drawn from foci to meet in any point in
curve is equal to transverse diameter.
Bisect transverse axis A B at o, and on centre o
erect perpendicular C I), making o D and o C each
equal to half conjugate axis. From C or D, with
radius A o, cut transverse axis at < x for foci. Divide
A o into any n\unber of equal parts, as i, 2, 3, etc.
With radii A i, B i, qu < and s as centres, describe
arcs, and repeat this operation for all other divis-
ions I, 2, 3, etc., and these points of intersection will
give line of curve.
To Ascertain Centre and Tavo Diameters of an Ellipse.
Let A B c u be diameters of an Kllipse.
Draw at pleasure two lines, q q, o'm, parallel to
each other, and equidistant from A and B; bisect
them in points An, and draw line ur; bisect it
in s, and upon s, as a centre, describe a circle at
pleasure, as/ 1 1>, cutting figure in points/ ».
Draw right line fv; bisect it in t, and through
points i « draw greatest diameter A B, and through
centre, «, draw least diameter c u, parallel to/©.
To Describe an Ellipse approxinriately l^y Circxilar Arcs.
— Kig. 41.
Set off differences of axes from centre o to a.and
c 01) 0 A and f> C; draw a c and bisect it. and set ofl'
its hair to r ; draw r s iiarallel to a c, set off o n
equal to o r, connect n s, and draw parallels r m,
nm; from m, with radii m s and s m, describe arcs
through C and D, and from n and r describe arcs
through A and B. ,
Note. — This method is not satisfactory when con-
jugate axis is less than two thirds of transverse axis.
Sexni-Slllptio Aro -witli Three
Centres.— Fig, 43.
Draw A M, B Mj parallel naspectively to B C, A C,
meeting in M. Draw M Oi perpendicular to A B.
cutting B Bi in Qi, and A As in 03 Find a mean
proportional (B D) between C A and C B. (This
may be done by marking B c on M B produced, equal
to B C and describing a semicircle on M c cutting
B C in D). Make A K equal to B D. With centres
Oi, 03, and radii O' D. 03 K, describe arcs intersect*
ing in 0=. Then 0», O^, 0-^are points which can be
used as centres for successive arcs of the required
curve —A. L. Lucas^ Asi't Etig^r U S. Dtp^U
18.
6EOMBTBT.
227
To Construct an Sllipse fvorxx Tviro
Ciroles.^F'ig. <4r3.
Describe two semicircles, as A R, C D, diameters of
which are respectively lengths of msjor and minor
azea The intersection of the horizontal and vertical
lines drawn flrom any radial line will give a point in
D the carve C D.
To Construot an Ellipse, "w-lien Tvir©
Dianieters are Ghiven.^Fis. 44.
Make c o and A v equal to each other, but less
than half breadth. Draw vo, and from its centre t
draw and extend perpendicular at t to d, draw d v m,
make B u = A v, draw d ti r, fVom u and v describe
B r and A m, from d describe m cr, extend c 2 to «,
and it will be centre for other half of figure.
To OonstTOCt an Kllipse by Ordinates.— ITigj. 4S.
Divide semi -transverse axis, as A 6, into 8 or 10
divisions, as may be convenient, and erect ordi-
nates, the lengths of which are equal to semi-con-
jugate, multiplied by the units for each division as
follows:
Ili.llii
1 9 34«<Tb
,.\
I
2
3
4
Eightht.
484 12 5
.66144 6
.78063
.86603
— I
Divisions.
Tenths.
92703
I — 435385
5 — .86602
9— .99499
96824
a — .6
6 — .91651
10 — I
992 16
3 — .71414
7 — -95394
4-.8
8 — .97979
To Constrnot An. ICllipse -^^lien Diameters do not Inter-
sect at fiiglxt A.ngles.-^lF'iS. ^B. •
«6. ~~-~.
Let A B and C D be given diameters.
Draw boundary lines parallel to diameters,
divide longest diameter into any number of
equal parts, and divide shortest boundary lines
into same number of equal part&
From one end of shortest diameter, D, draw
L radial lines tftrough divisions of longest diame-
" ter, and fVoin opposite end, C, draw radial lines
to divisions on shortest boundary lines ; the
intersection of these lines will give points in the
curve.
To. Describe a O-othic Arc.— Kig. -^T.
Take line A B. At points A and B draw arcs Ba and Ac.
and it will describe arc required.
To Describe an
Elliptic A.ro^ Chord and Keigbt being
Ip.ven.^-Fig. 48.
Bisect A B at c ; erect perpendicular A 9, and
draw line q D equal and parallel to A c.
Bisect A c and A 9 in r and n ; make c I equal to
e D. and draw line Irq; draw also line nsD\ bisect
f D with a line at right angles, and cutting line
e D at 0; draw line 0 q; make cp equal to e k, and
draw line op i.
Then, flrom o as a centre, with radius o D, describe
arc f D i; and from k and p as centres, with radius
A k, describe arcs A s and B t.
228
GEOMKTBT*
To
49.
U,
y\
Describe ci Q-otliio A.ro.-*Fie8< ^& and SO.
Divide line A B into three equal parts, e c ; horn points
A and B let fall perpendiculars A o and B r, equal in lengtb
to two of divisions of line A B;
draw lines o h and r g ttom points
«, c ; with length of c B, describe arcs
A g and B A, and flrom points o and r
describe arcs g t and i h. (Fig. 49.)
B
Or, divide line A B into three
equal parts at a and 6, and on points
A, a, b, and B, with distance of two
divisions, make four arcs intersect-
ing at c and o.
Through points c, o, and divisions a, &, draw lines c/and o «, on points a and I
describe arcs A e and B/, and on points c 0 arcsfs and e «. (Fig. 50.)
o
51.
Cycloid and ICpicycloid.
To Describe a Cycloid.— Fig. Ol.
When a circle, as a w^heel, rolls over a
straight right line, beginning as at A and
ending at B, it completes one revolution,
and measures a straight line, A B, exactly
equal to circumference of circle cer, which
is termed the generating circUj and a point
or pencil fixed at point r in circumference
traces out a curvilinear path, A r B, termed a
cycloid. A B is its base aod c r its axis.
Place generating circle in middle of Cy-
cloid, OS in figure; draw a line, m n, paral-
lel to base, cutting circle at «; and tangent
The following are some of properties of Cycloid : ^
n t to curve at poipt n.
Horizontal line «n = arc of circl^ e r.
Half- base A cr=half-circumference cer.
Arc of Cycloid rn=: twice chord r e.
Half arc of cycloid Ar=twice diameter
of circle r c
Or, whole arc of Cycloid A r Brr: four
times axis cr.
Area of Cycloid A r B A = three times
arearof generating circle r c.
Tangent n % is parallel to chord e r.
To Describe Cu.rve of a Cycloid.— Fig.. 6S.
On an indefinite line, A B, set o(rc0=
circumference of generating circle, di-
vide this line into any number of equal
parts (8 in figure), and at points of divis-
ion erect perpendiculars thereto. Upon
. j> each of these lines describe a circle =
generating circle. On c i take ix =
To Describe an Interior Bpioycloid or Kypocycloid.«>
Fig. 63.
If generating circle is rolled on inside of Hmdnmentar
circle,* as fn Fig. 53, it forms an interior epicycloid^ or
hypocudoid, A c B. which becomes in this case nearly a
L straight line. Other points of reference in figure cor-
respond to those in Fig. 51. When diameter of generat-
ing circle is equal to half that of flindamental circle,
epieyeloid becomes a straight line, being diameter 01
tbe larger circle.
* 8m u:pUofttIoD, Fig. 54.
GEQMKTJIY.
229
To Describe an £]xterior SpioT-oloid.**
Fig. a^.
An Epicycloid differs from a Cycloid in this, that it is
generated by a point, o"\ in one circle, 0 r, rolling upon
circumference of another, A r «, instead of upon a right
line or horizontal surface, former being generating circU
and latter fundamental circle.
Generating circle is shown in four positions, in which
its gcueratiug point is indicated by o</o^'o"'. A&" t
is an Epicycloid.
Involute.
To Describe aix Involute.— IPig. OS.
Assume A as centre of a circle, bco\Q. cord laid partly
upon its circumference, as 6«; then the curve et'mn,
described by a tracer at end of cord, when unwound A'om
a circle, is an involute.
This curve can also be defined by a batten, x, rolling on
a circle, as « u.
I^araljola.
To Construct a Parabola by Ordinates or
j^bsoissa.^IT'ig^. 60 and. 67.
By Ordinates.
Divide ordinate a b into 10 equal parts, and erect perpendicu-
lars, length of which will be determined by multiplying abscissa
a cpy respective units for each perpendicular, as follows: gy^
Divisions.
I— .19
a— .36
3— .51
4— 64
5— -75
6 — .84
8 — . 96
9— .99
10 — z
Division*.
•79057
6~ .86602
7— •935 4«
z —
2'
3 — •
7 —
8 —
9 —
10 —
.7746
.83666
•89443
.94868
By Abscissa.
Divide abcissa a c into 8 or 10 equal parts, as may be convenient,
and draw ordinates thereto, the lengths of which will be deter-
mined by multiplying half ordinate a 6 by respective units for
each ordinate, as foUows:
lenuts.
31623
.44721
•54773
4 — .63245
5 — .707 IX
"With, a Sq.nare and Cord.— Fig. ©8.
Place a straight edge to directrix A B, and apply to it a
square, e o.
Attach to end o end of a cord equal to 0 A, and attach other
end to focus e; slide square along straight edge, maintaining
cord taut against edge of square, by a point or pencil, and curve
will be traced. (Fig. 58.)
"When Height and
Sase are given. «■
Fig. 6©.
Assume AB axis and c <2 a double ordinate or basa
Through A draw m n parallel to c d, and through c
and d draw cm,dn, parallel to axis A B. Divide c m,
d n into any number of equal parts, as at a c <; o, also
c B, B d, into a like number of parts. Through points c- "{"2~^"^'n"±'t'9^t'^^
1, 2, 3, and 4 draw lines parallel to axis, and through i<o4i54 3^i
aceo draw lines to vertex A, cutting these perpendiculars, and through these points
curve may be traced. (Fig. 59.)
'30
GBOMKTRY.
To DesorilDe Curve of* a Parabola, Sase and
Heielit loeing given. "-F'igr. 60.
Draw an isosceles triangle, as a 6 d, base of which shall be eqnal
to, and its height, c b, twice that of proposed parabola. Divide
each side, a5, d6, into any number of equal parts; then draw lines,
I 1, 2 2, 3 3, etc., and their intersection will define curve. (Fig. 6o.)
To IDesori'be a Parabola, any Ordinate to Ajcis
and itts A.'bscissa being given-^Fiflr. 61.
Bisect ordinate, as A o in r; Join
B r, and draw r s perpendicular to it,
meeting axis continued to «. Setoff
Be, Be, each equal to o «; draw m
c u perpendicular to B «, then m u is directrix and
B e focus; through e and any number of points, i, i,
I, etc., in axis, draw double ordinates v i v, and on
centre e, with radii e c, i c, etc., cut respective or-
dinates at V V, etc., and trace curve through these
point&
NoTi.— Une « « v panlnic tIiroug:h focaa ts parameter.
Spiral.
To Dra-^v a Spiral about a given Point.—
Fig. 6S.
Assume c the centre. Draw A h, divide it into twice number
of parts that there are to be revolutions of line. Upon c de-
scribe r e, o s, A A, and upon e describe r8,os, etc.
To
Hjrperbola.
Describe a Hyperbola, Transverse and Conjugate
Diameters being given.— Fig. 63.
Let A B represent transverse diameter, and C O
conjugate.
Draw C e parallel to A B, and e r parallel to C D;
draw o e, and with radius o e, with o as a centre,
describe circle F e r, cutting transverse axis pro-
duced in F and /; then will F and /be foci of fig-
ure.
In o B produced take any number of points, n, n,
etc., and from F and/as centres, with A n and B n
as radii, describe arcs cutting each other in g, «,
etc. Through <, <, etc. , draw cu rve tstsBsMMS.
NoTB. —If straight lines, aa oey and ory, are drawn fh>m centre o through ex-
tremities e r, they will be asymptotes of hyperbola, property of which is to ap-
proach continually to curve, and yet never to touch it. ,
Wh^n Foci and Conjugate Axu are given.— Let F and/ be foci, and C D ooi^ugate
axis, as in preceding figure.
Through C draw gC e parallel to F and /; then, with o as a centre and o F afi a
radius, describe an arc cutting ^ C e at ^r and e: from these points let fall perpen-
diculars upon line connecting F and/ and part intercepted between them, as A B,
will be transverse axi&
Catenary.
Delineate a Catenary, Span and Versed Sine being
given. — Fig. 64. ( W. Hildenbrand. )
Divide half span, as A B, into any required
number of equal parts, as i, 3, 3, and let fall B G
and A o. each equal to versed sine of curve; divide
A o into like member of parts, i', 2', 3', as A B.
Connect C i', C 2', and C 3', and points of intersec-
tion of perpendiculars let fall (t'om A B will give
points through which curve is to be drawn.
Or, suspend a finely linked chain against a ver-
tical plane, trace curve iVom it on the plane in accordance with conditions of given
length and height, or of given width or length of arc.
NoTB.— For other methods see D. R. Clark's Manual, pp. 18, 19.
AREAS OF CIBCLBS.
231
OtAW.
a;
H
H
%
%
X
^4
%
%
%
AjresLB of Circles, fi»om
DiAM.
Aria.
.000192
.000767
.003068
.012 272
.027612
.049087
.076699
.110447
•15033
•19635
.248505
.306796
.371 224
.441 787
.518487
.601 322
.690292
•7854
.8866
DiAM.
Pi
Aria.
7.0686
7.3662
7.6699
7.9798
82958
8.618
8.9462
92807
96211
9.96S
03206
0,679
1.0447
I.416
1-7933
2.177
2.5664
2962
33641
3772
4.1863
4606
5033
5-465
5-9043
6.349
6.8002
7-257
7.7206
8.19
8.6655
9.147
9-635
20.129
20.629
2i^i35
21.6476
22.166
22.6907
23.221
23-7583
24.301
248505
25406
259673
26.535
27-1086
27.688
28.27444
29.4648
30.6797
31.9191
33-1831
34-4717
35.7848
I 37-1224
}4
}^
%
H
%
%
%
8
K
%
%
%
%
}i
%
%
lO
II
%
%
%
%
%
%
12
H
%
•I
13
%
%
%
%
A to ISO.
Area. | | Diam.
38.4846
39-8713
41.2826
42.7184
44.1787
45.6636
47-1731
48.7071
50.2656
51.8487
534563
550884
56.7451
58.4264
60.1322
61.8625
63.6174
65.3968
67.2008
69.0293
70.8823
72-7599
74.6621
76.5888
78.54
80.5158
,82.5161
84.5409
86.5903
88.6643
90.7628
928858
950334
972055
99.4022
101.6234
103.8691
106.1394
108.4343
"0.7537
113.098
115.466
117.859
120.277
122.719
125.185
127.677
130.192
132.733
135-297
137.887
140.501
143-139
145.802
148.49
151.202
14
15
16
17
18
19.
20
Aria.
153-938
156.7
159-485
162.296
165.13
167.99
170.874
173.782
176.715
179.673
182.655
185661
188692
191.748
194.828
197933
201.062
204.216
207.395
210.598
213.825
217.077
220.354
223.655
226.981
230.331
233.706
237-105
240.5-29
243 977
24745
250.948
25447
258.016
261.587
265.183
268803
272.448
276.117
279.811
283.529
287.272
291.04
294.832
298.648
302 489
306.355
310245
314.16
318.099
322.063
326.051
330.064
334.102
338.164
342.23
AEEAH OF CIRCLES.
Diui.
Am.
Dl.H.
Am.
Dim.
AUL
Diu.
AIU.
M
346.361
38
615-754
963.1,5
4«
'385.4s
«
3S0.497
621.264
9^
^
'393-7
K
354-657
626,798
975.909
.401.99
%
358-843
633.357
982,843
363-051
637-94'
989-8
1418.63
367-285
643-549
996-783
If
.426.99
37' -543
649. 1E3
143537
375-836
654-84
%
'443-77
3S0.134
660-5^1
36"
1017-878
43
1452.2
384.466
666.228
%
.02496
.460.66
388.8J2
671.959
X
'6.13.065
.469.14
393 ™3
677,714
g
'039 '95
1477.64
397.609
683.4W
.046.349
.486.17
402.038
689.399
1053-528
»
1494-73
406.494
695.128
1060-733
410.973
700.982
1067.96
%
151 '-9'
33
415-477
30
706.S6
.075.213
44
1520.53
420.004
7.3,763
1083,49
bi
1529.19
424-558
718.69
1089.79=
%
'537-86
g
4^9-135
H
724643
1097. "8
.546.56
..04.469
1
438*364
1
736^619
..11.844
1564-04
443.01s
743.645
1119.244
.572-8.
447-69
748-695
1.26.669
.581.6.
3'
754-769
38"
1134.1.8
45
1590-43
^
;irsa
?^:^
!;£^
IffiS
1
466.63a
773-14
1.56613
.617.05
471.436
%
779-313
1164.159
1635.97
476.259
g
785-51
%
1
163492
481.107
791.733
I '79-337
.643.89
485-979
%
797-979
X
.186.948
.652.89
»s
490-875
33
804,25
1194593
46
1661,91
495-796
8.0-S4S
1203.263
167095
500.74a
816.865
1209.958
.580-O2
505-713
823-2.
.2.7.677
1689,..
510.706
>i
829.579
1225.42
.69823
i
515-7*6
835.973
^
1707-37
5*1-769
843-39'
1240981
.716-54
%
535-838
848-833
.248.798
'725-73
■A
530-93
33
855-30.
40
.256.64
'734.95
536^)48
>S
861.792
1364,506
S4..19
yi
868.309
1272.397
■753 45
546-356
%
87485
^
1280.313
.763.74
>4
881,4.5
.288.353
1
556^^63
%
RSS.dBS
^
.296.3.7
;?8i:f
56a«i3
%
894-62
1304.206
1790.76
S67-367
%
901.259
1312.219
1800.15
"7
573-557
34
907.92a
1330.357
4a"
'809.56
577 87
914-6.1
1338.33
^
.8.9
583-309
921.333
.336-407
1828.46
588.57'
s
9=8.06.
1344-5 '9
1837-95
593-959
1352.655
.847-46
K
5W-371
94.-609
1360.8.6
i
'856.99
604.S07
948.43
.369-001
18665s
%
Gio.36)i
%
95S-3S5
%
1377.2"
%
.876.14
ABBAS OF CIRCLES.
A»^
Dun.
*™-
SlU.
«»..
D1.X.
AUA.
■ S85-75
56
2463.01
31.7-25
70
3848.46
1893.38
H
3'29-6t
3862.32
1905,04
K
2485-05
3876
1914.72
2496.. I
3.54-47
3889.8
2507.19
3166.93
3903-63
1934.16
H
2518.3
i
39>7-49
i«3-9i
2529.43
3191.9.
393" -37
'9S.I-69
2540.58
3204.44
3945-27
'9635
S7
255.-76
3317
71
"973.33
2362.97
3229.58
3973-15
19S3.18
2574.2
3242.8
3987-13
1993.06
2585.45
325481
4001.13
ao<H.g7
3267.46
40.5-16
aoia.59
3280..4
i
3031.8S
36.9.36
3292.84
4043.39
303^.81
3630.71
3305-56
4057-39
=041.83
58
of 59
33.8.31
72
■4071-5'
205»-85
S
2( t9
333'-09
2
4085-66
4099.84
ss!s
i i
i^-^
;iK
ao93.3
i
2f »
3382-44
s
4142.51
2103.3s
»
3395-33
4156.78
3113.52
3408.26
4171.08
33-98
66
73
4185.4
2133.94
45-57
3434- '7
4199.74
2144.19
3447-17
2134.46
2768.84
3460.19
4228.51
2.64.76
2780.51
3473-24
4242.93
2175.08
2792.21
S
3486.3
S
4257-37
2.85-12
280393
3499-4
4271.84
2815.67
4286.33
2206. .9
ar 44
3525-66
4300.85
22.6.61
2f 23
3538-83
43'5.39
2227.05
2S 05
3SS2-02
4329.96
2237.52
2t 89
3565.24
4344-55
2248.01
3578.48
4359- '7
2258.53
3591.74
1
43738.
2269X>7
a* 57
3605.04
43S8.47
2279.64
2910.5.
36'8.35
4403-16
2290.23
61
a< 47
363.-69
75
4417-87
2J30.84
^
2.
46
^
3645-05
4432-61
33I1.4B
48
3658.44
4447-38
2313.15
52
3671.86
4462.16
3332-83
58
3685.29
4476-98
a354.29
i
*
67
78
S
3698.76
3712.24
s
449.-8.
4506.67
2365.05
4521.56
2375.83
62
3019.08
69
3739-29
76
453647
2386.65
^
3031.26
3752-85
4551-41
2397-48
3043-47
3T66-43
4i66-36
2408.34
3780.04
4581.35
2419.23
3067-97
3793-68
4S96..16
2430.14
3080,25
380J.34
$
4611.39
2441 'O?
3092-56
3821.02
4626.45
2432.03
H
3
104.89
K
3834-73
%
464.-53
TH...
A....
Jn.H.
Ah..
B..-.
A.^..
p..-.
Au..
77
46S6.64
5541-78
9'
98
7543-98
^
467' -77
5558-29
%
t
%
7563.34
468693
SS74-83
H
^
7581.52
4702.1 ■
5591-37
fi
7600.82
560795
t
76=0-15
H
473=54
gJ:S
i
6;
6611.55
Si,
4763.07
5657-84
6629,57
7678.28
78
4778-37
5674-5"
92
6647,63
7697.7'
i
47<13-7
5691-22
M65.7
77.7.16
4B09.05
66838
7736-63
4824.43
5724.69
6701.93
7756-13
4839.83
5741.47
7775.66
H
485S-'6
4870-71
5758-27
5775-1
i
6738.25
6756.45
s
7795-21
78.4-78
4886,18
6774.68
7834.38
4901.68
86'"
5808.83
6792.92
7854 .
^
5*" 7S
6811.3
^
7S9l133
4932.7s
5f &4
6829.49
7932.74
4948.33
5f 59
6847.82
4
■4963.9=
sf 56
6866.16
8o.i!87
i
4979-55
S
5* 55
6884.53
8051.58
%
55 58
8c|..5;
%
%
K 52
6921.35
8131.3
80
5<«6.s6
5944.69
94
6939-79
8171.3
5043.28
5961-79
6958.26
X
5058.03
5978.91
6976,76
^
8251:6!
% ; S073 79
5996.05
6995-28
%
K S089-59
6013,32
7013,83
J 03
8332.31
8372.81
X 51054'
6030.41
i
7032,39
5121-25
6047.63
7050.98
84134
S"3;-12
606487
7069.59
H
8454-09
81
88"
6083.14
7088.23
8494.89
^
5168:93
609943
7.06.9
K
8535.78
5184.87
6116.74
K
8576.76
5200.83
6134.0a
7144.31
%
8617.85
6151.45
7163.04
8659,03
M
5232.84
5248.8S
^
6168.84
61S6.25
i
7.81.8.
'1
8700.32
8741.7
%
5264.94
6203.69
,1
.06^
8783,18
to
5*8. oj
623.. IS
96
7338.25
88=4-75
^
^
6238,64
7257- 1'
}i
8866.43
5313-38
6356,15
7275-99
'^
8908.2
6373.69
%
8950.07
5345-63
6391.25
7313-84
107
8993.04
i
5361-84
i
630884
^
7333.8
a
5378.08
1
63264s
7351-79
a
9076:38
5394-34
6344.08
%
7370.79
%
9118.54
83
5410,62
90
6361.74
97
7389-83
9160.91
S4«5.93
1
637943
H
7J08.89
H
9203.37
5443- =6
6397-13
H
7427.97
H
ss.a
5459.63
641486
7447-oS
%
^
S4Ao.
6433,62
7466.3.
109
9331-34
li
6450.4
s
748537
9374.19
^
5508^84
6468.21
5525.3
f<
6486.04
K
7523.75
H
946ai9
AUKAS OF CIBCLBS.
235
DiAM.
Arba.
no
%
III
H
>i
112
}i
%,
H
%
114
H
yi
"5
116
H
H
%
117
'A
%
118
3^
■X
%
119
%
950334
9546.59
958993
9633-37
9676.91
9720-55
9764.29
9808.12
9852.06
9896.09 1
9940.22 1
9984-45
10028.77
10073.2 I
10117.72
10162.34
10207.06
10251.88
10296.79
10 341.8
10386.91
10432.12
I0477-43 ]
10522.841
10568.34!
10613.94 j
10659.65
10705^41
10751.34
10 797-34 1
10843.43,
10889.62 >
io935-9i_:
10982.3
I
X
I
I
I
I
DiAM.
120
028.78
075.37 I
122.05
168.83 i
215-71 I
262.69,
121
122
123
124
125
126
Akba.
127
X
M
a^
128
%
129
yi
11309.76
"356.93
11404.2
"451-57
11499.04
11546.61
11 594.27
11(542.03
11689.89
"73785
11785.91
II 834 06
1 1 882.32
11930.67
11979.12
12027.66
12076.31
12 125.05
12173.9
12 222.84
12271.87
12321.01
1237025
12419.58
12469.01
12518.54
12568.17
12618.09
12667.72
12717.64
12 767.66
12817.78
12867.99
X2918.31
12968.72
13019.23
13069.84
13 120.55
13 171.35
13222.26
DlAM.
130
131
%
yi
132
yi
yi
%
133
yi
yi
134
AmBA.
135
H
%
136
yi
%
137
138
3i
139.
3^
13273.26
13324-36
13375-56
1342685
13478.25
1352974
13581,33
1363302
13684.81
1373669
13788.68
13840.76
1389294
13945.22
13997.6
14050.07
14 102.64
14 155-31
14208.08
1425309
14313-91
14366.98
14420.14
144734
14526.76
14580.21
1463377
14687.42
14741.17
1479502
14848.97
14903.01
14957.16
15011.4
15065.74
15 120.18
15174-71
1522935
1528408
1533891
DiAM.
140
141
yi
yi
%
yi
yi
%
Akba.
142
143
3^
yi
144
yi
145
yi
yi
146
147
148
yi
yi
%
yi
yi
149
yi
yi
150
15393-84
15448.87
1550399
1555922
15614.54
15669.96
15725-48
15781.09
15836.81
15892.62
15948.53
16004.54
16060.64
16116.85
16173.15
16229.55
16286.05
16342.65
1639935
16456.14
16513.03
16 570.02
16627.11
16684.3
16741.59
16798.97
16856.45
16914.03
16971.71
17029.48
17087.36
17 145-33
17203.4
17261.57
17319.84
17378.2
17436.67
17495-23
17553.89
17671.5
To Compute Ajirea or a. Circle greater tliaii any in Talsle.
Rule. — Divide dimension by two, three, fonr, etc., if practicable to do so,
until it is reduced to a diameter to be found in table.
Take tabular area for this diameter, multiply it by square of divisor, and
product will give area required.
EzAMPLC.— -What is area for a diameter of 1050?
1050-5-7 = 150; (o^. ar«a, 150 = 17671.5, which X 7' = 865 903. 5, cwea.
7o Compute .A.rea of* a Circle in. I^eet and Indies, et6.,
\yy preceding 1?al>le.
Rule. — Reduce dimension to inches or eighths, as the case may be, and
take area in that term from table for that number.
236
AREAS OF CIRCLES.
Divide this number by 64 (square of 8) if it is in eighths, and quotient will
p^ve area in inches, and divide again by 144 (square of 12) if it is in inches,
and quotient will give area in feet
ExAMPLB.— What is area of 1 foot 6.375 ins.?
I foot 6. 375 ins. = 18. 375 ins. = 147 eightfis. Area of 147 = 16 971.71, which -?- 64
= 265. 181 25 in$.; and by 144 = 1.84 125 feet
To CoTxipute A.rea of a Circle Composed of an Integer
and a Fraction.
Rule. — Double, treble, or quadruple dimension given, until fraction is in-
creased to a whole number, or to one of those ui the table, as ^, 3^, etc..
provided it is practicable to do so.
Take area for this diameter ; and if it is double of that foi which area is
required, take one fourth of it ; if treble, take one sixteenth of it, etc.
ExAMPLB.— Required area for a circle of 2.1875 ins.
2. 1875 X 2 = 4. 375, area for which = 15.0331, which -f- 4 = 3.758 ins.
When Diameter is composed oflviegers and Fractions contained in Table,
Rule. — Point off a decimal to a diameter from table, and add twice as
many figures or ciphers to the right of the area as there are figures cut off
from the diameter.
Example i.— What is area of 9675 feet diameter?
Area of96.75 = 7351.79; hence, area =73 517 900/ccft
2. —What is area of 24 375 feet diameter ?
Area of 2. 4375 = 4. 6664 ; hence, area = 466 640 000 feet
To A.8oertaiix ^rea of a Circle as 300, 3000, etc., not
contained in, Tal)le.
Rule.— Take area of 3 or 30, and add twice the excess of ciphers to the
result. *^
Example.— What is area of a circle 3000 feet in diameter?
Area of 30 = 706. 86, hence area of 3000 = 7 068 6oofeee.
To Compute ^rea of a Circle by Logarithm^.
Rule.— To bvice log. of diameter add r.895091 (log. of .7854), and sum
IS log. of area, for which take number. ^^^ ^ ^ 1 y^J^ »""*
Example.— What is area of a circle 1200 feet in diameter?
whi^b =Ti3^97t^^°^' ^ 6.158362 + 1:895091 = 6.053453, and number for
Diam.
No.
I
2
3
4
5
6
7
8
.A.reas of
Area. | Dlam.
SirxningliaTxx "Wire GKaiige*
Sq. Inch.
.070686
•063347
.053685
.044 488
.038013
.032365
.025 447
.021382
.01 7 20^
No.
10
II
12
13
14
15
16
17
18
Area.
Dlam.
Sq. Inch.
No.
.014 103
19
.011309
ao
•009331
.007088
21
22
.005411
23
.004071
.003318
.002 642
.OOJ8S0
24
25
26
27
Area.
Dlam.
Sq. Inch.
No.
.001 385
28
.000962
29
.000804
.^
.000616
31
.000491
32
.00038
33
.000314
34
.000254
35
.000201
36
I Ana.
Sq. Inch.
.000154
.000133
.000 1 13
.000078
.000064
.00005
.000038
.00002
.000013
CIBCUMFBBBMCES OF CIB0L&3.
Ciroumfe
rence
s of CiTOlee, fVom ^ to ISO.
""-• 1 '^■"'"■
A
.04909
3
9,424a
6
25-13^8
47.124
%
.09818
9.6211
98175
^
">g
47-5167
47-9094
)i
.19635
1
10.014
26.3109
48.3021
H
26,7036
48.6948
S.
■589
1
t^
s
37,0963
27,489
^
49.0875
49.4802
}i
■78s 4
10.799
^
49.8729
>i
-9817s
10,9956
9
38,3744
16
SO.26^
1
28,667,
50-6583
%
1.1781
":^3
29,0598
51.051
'•37445
1.5708
1.767 15
i
1..5&t
11.781
^
29.4525
29A»S2
H
51-8364
g
11-977
1
ssgs
^
52.6218
%
1.963 s
%
"''■S
3i-<»33
53.0145
4
12.5664
31.416
%
2.15985
s
12.762
^
31,8087
g
53-7999
%
2.3563
12.9591
322014
541926
X
1
13.155
32.5941
54-5853
»-552 55
13.3518
32,9868
54-978
%
2.7489
13-547
33-3795
^
%
2.9*525
55.7634
1394
34.1649
31416
14.1372
34-5576
56^5488
'k
3-337 9
1+333
349503
56.9415
3-534 3
14.5299
35-343
57-3342
3-7306
35-7357
57.7269
14.9226
36,1=84
58.. 196
i
4.1233
4-3197
g
15.119
15.3153
i
36,5211
36,9138
%
58.5123
58.905
4.516
?i;
15.511
37.306s
4.7124
15.70S
37-6992
59.6904
490S7
^
i6.icx)7
38,0919
60.0831
5-ios I
16.4934
38.4846
60.4758
5.3014
i
i6,S86i
38.8773
60.8685
17.2788
39-27
6t.26l3
1
5.&M1
17.6715
i
39.6627
61.6539
S-890S
18.0642
63^1466
%
6.0868
%
18.456Q
62.4393
6.283 if
6
.8,8496
'3
62.832
6-f795
19.2423
41-2335
63.2247
6.6759
19-635
4.,^
63.6174
6JI722
43,0189
64.0101
7.0686
20.4204
42,4.16
64^*028
7.'6^9
20,8131
i
42,8043
64.7955
7-4613
21.2058
4.1-197
65.1882
7-6576
2..598S
43-5897
65,5809
7Jt54
31,9912
43.9824
8*503
^
".38.W
%
8.a,6 7
22.7766
%
M:767a
66.759
8~t43
23.1693
%
45-1605
67,1517
8.6394
33.562
^
67-5444
883S7
^
'3-9547
45 9459
67-937'
90331
24.3474
46.3386
68.3298
%
9^m84
, Ji
24.7401
46.7313
%
68,7325
C1RCUMFBBEMC£S OF CIBCLBS.
69.5079
70.3933
70,686
71.0787
7i-47'4
71.8641
7I.S56S
72.6495
73 W
73-4349
738276
74-a203
74-613
75-0057
75-3984
91.1064
91,4991
91,8918
>a,2845
)3.&!73
93.0699
93-4626
93-8553
94.348
94.6407
950334
93.4361
95.8188
96.=' 15
56.604a
96.9969
.7-3896.
97 7833 '<
98.175 <
9S5677 I
98.9604 I
993S3I I
997458 ■
«>-'3as I
105312
136.267
136.66
137-053
137-445
137-838
138.23
138.623
143-55
■43.943
143335
143-728
5
8i,6Si6
a
82.0743
K
82.467
82.8597
83.2524
83-645'
84.0378
84-4,105
84.8232
85-2159
^
ass
H
aD.0013
86-394
86,7867
87-1794
87-5721
87,9648
109,171
109.563
109.956
124,093
124.486
124.879
129.198
129.591
129.984
130,376
'3' -554
'3' -947
'32,34
145-692
146.084
146.477
146.87
147-263
147-655
148.048
148^41
153-938
154-331
154.724
156-585
CIBCnHFKBSNCBS OF CIBCLBS.
i..85 ,
1-S78 I
161.97 [|
163-363 I
163.756 I
i64-'49 :
164.541
164.934
'6S-3^7 I
i6s.7«9
179-857 1
180.349 :
180.64J i
183.784 '
184,176 I
184.569 I
184.96a :
'S5.354 II
185.747 ■
'89,674 ]
190.067 I
'90-459 I
176.331
176.715
177.893
178.286 :
178.678
r>i.«
1 ClBCIFH.
Dlllt.
Cnam.
~64
201.063
7'
^33-054
>i
201.4SS
jl
«J^46
i
201.848
223-839
202.6J3
224.624
203J)26
^
225.017
20J.419
303.8M
225802
65
J04.204
7a
226..95
X
204.597
226.5B8
%
k
204989
1
226.9S1
^S^^S
^Sn^
H
206.167
228,. 59
y
206.56
I
228.551
%
206.953
66
207.346
229.337
207.73a
229.729
208.131
230.121
208.5S4
230.515
23a908
H
209.309
231-3
%
209.702
231.693
K
232.086
67
210.487
P
232.478
>i
232.87.
%
233.264
%
2.1:665
233.656
'-
2.2.058
334-049
I
2.2.451
234.442
2.2.843
234.835
2.3.236
68
2.3.629
235.62
X
214.021
236.0.3
H
214.414
236,405
2.4.807
2.5.2
§
236.798
337.191
P
2.5.593
i
237.583
213.985
237-976
%
2.6.378
■k
238.369
2.6.77
76
238.762
2.7-163
239.154
a.7-556
339.547
^;7.948
239.94
2i8i734
s
340.725
34..1.8
2.9.519
141.51
M
1 219912
VL
241.9^
343.689
»t3.474
243-867
ClHCtlWFliKENCKa (
Dl.ll.
Ciicinc.
CllK.
Caa~-
Dl.H.
CIUUIL
85
167,036
93
289^7
99
3" -018
S
267.429
>i
28942
%
267.82.
X
289.B.3
268-314
290,305
i
s68Jfc7
290.59a
i
=68.999
269.392
$
290.991
29' .383
i
312-983
313.375
%
269.785
391.776
313.767
S6
270. 1J8
393,169
270.57
293,562
314-945
270.963
393.954
315-731
=71 -336
=93-347
316.5.6
=71-748
=93-74
317.303
294-132
)i
318.087
2 7= '534
294-525
H
318.873
272.926
394^,18
%
319.658
t
273-319
=9S3'
,330.443
273.712
¥.
331.229
374.105
i<
396.48S
%
3=2-799
27<^
.03
333.585
275.283
=97-274
H
334-37
275^5
297,667
<i
3=5-156
276-068
298,059
%
as"
95
298-452
3=6-7*6
^
2?t'^
=98-843
299,237
^
337-5"
3=8.397
277:629
n
399-63
329^3
278.033
300/)=3
'*^,
329.868
^
J78-434
300.415
H
330-653
278-817
S
300^18
"A
331-439
279.21
301.201
%
332-224
89 ] 379.602
96
301 -594
106
>« ! a79.99S
H
301.986
333-795
080.388
a
334-58
380.78
302-772
335.956
281.173
303-164
107
336-151
1
281-566
i
303,557
K
336-937
281.959
30,1-95
H
,137.722
282.351
3^-342
%
338.507
90
282.744
97
loS
339-293
% 1 =83.137
305.128
H
340.07a
X 1 =83.529
^
305-S2I
H
340.864
%
283-912
H
341.649
%
284-3IS
109
342-434
384.707
H
343-33
285.1
307,091
%
285.493
3o;-484
%
344-79'
98
307,877
345-576
% ■ 586,278
308,27
346.36.
308.662
347147
% \&iX.
309055
347-93=
H 287.456
309,448
34871a
8 SSI
^
309-84
H
349503
H
350-388
%
288.634
K
310^626
%
351-074
CIBCUMFERENCES OF CIRCLBS.
241
DiAM.
Cncmi.
DlAM.
CtKCCM.
DiAM.
Cntcmi.
DiAM.
ClBCUlC
112
351-859
121
380.134
130
408.408
139
436.682
H
352.645
3i
380.919
}i
409.192
3^
437-467
X
353-43
K
381.704
K
409.979
K
438.253
%
354.215
%
382.49
%
410.763
Va,
439037
"3
.355-OOI
122
383.275
131
411.55
140
439.824
}i
355.786
}i ! 384.061
K
412.334
3^
440.608
¥.
356.572
X , 384.846
y^
413-12
3i
441-395
%
357-357
H 385.631
%
413.905
%
442.179
114
358.142
123 386.417
132
414.691
141
442.966
H
358.928
X , 387.202
X 1 415-476 1
3^
443-75
K i 359-713 1
K i 387.988
K
416.262
^6
444.536
%
360.499
% 388.773
%
417.046
%
445.321
"5
361.284
124
38^.558
133
417833
142
446.107
X
362.069
H
390.344
X
418.617
}i
446.891
K
362.855
X
391.129
X
419.404
}4
447.678
5^
363.64
%
391.915
K
420.188
%
448.462
116
364.426
'25,,
392.7
134
420.974
^^3_
449.249
H
365.211
H
393.484
3^
421.759
yi
450.033
K
365.996
H
394.271
K
422.545
y^
450.82
%
366.783
Vi,
395.055
%
423.33
%
451.604
117
367.567
126
395.842
^35,,
424.116
144
452.39
X
368.353
X
396.626
3i
424.9
yi
453175
K
369.138
X
397.412
K
425687
K
453-961
%
369-923
%
398.197
%
426.471
%
454.745
118
370.709
127
398.983
^36.
427258
145
455.532
3^
371-494
}i
399.768
3^
428.042
yi
456.316
>i
372.28
X
400.554
K
428.828
%
457.103
%
373.065
%
401.338
!^
429.613
146
458.674
119
373-85
128
402.125
1 137
430.399
yi
460.244
3^
374-636
yi
402,909
3^
431.183
H7
461.815
375.421
yi
403.696
^
43197
X
463.386
%
376.207
%
404.48
%
432.754
148
464957
120
376.992
129
405.266
'3^.
433.541
y^
466.528
li
377.777
3i
406.051
Ya,
434325
149
468.098
H
378.563
K
406.837
X
435112
'A
469.669
H
379-348
%
407.622
%
435-896
150
471.24
fTo Compute Ciroxiznferexioe of* a IDiazneter greater th.au
an^ iu precediuff Table.
Rule. — Divide dimension by two, three, four, etc., if practicable to do so,
until it is reduced to a diameter in table.
Take tabular circumference for this dimension, multiply it by divisor,
according as it was divided, and product will give circumference required.
ExAMPLS.— What is circumference for a diameter of 1050?
1050-i- 7 = 150; tab. circum., 150 = 471.24, which X 7 = 3298.68, cireumfei'ence.
To Compute Ciroumfereuce o£ a Diameter iu Feet aud
IiiolieB, etc., "by preceding Table.
RuLR. — Reduce dimension to inches or eighths, as the case may be, and
take circumference in that term from table for tliat number.
Divide this number by 8 if it is in eighths, and by 12 if in inches, and
quotient will give circumference in feet
242
CIECUMFEEENCES OF CIROLES.
ErucPLB.— Required circumference of a circle of i foot 6.375 ina
I foot 6.375 ins- = 18.375 ins. = 147 eighths. Circum. of 147 = 461.815, which~8
= 57727 .tn& / and by 1 2 = 4. 8 106 feet.
To Compute Ciroiamfereiioe for a Diameter ooznposed of
an Integer and. a ITraotion.
Rule.— Double, treble, or quadruple dimension given, until fraction is in-
creased to a whole number or to one of those in the table, as i^, V, etc. pro-
vided it is practicable to do so. ' *'
Take circumference for this diameter ; and if it is double of that for which
circumference is required, take one half of it; if treble, take one third of it •
Mid if quadruple, one fourth of it. *
iCxAMPLE.— Required circumference of 2.21S7"; ^^'*
2.?i875X 2 = 4.4375, which X 2 = 8.875; circum. for which = 27. 8817, which -7- a
=6.9704 ins. -^
When Diameter cotisists of Integers and Fractions contained in Talhe,
Rule.— Point a decunal to a diameter in table, take circumference from
table, and add as many figures to the right as there are figures cut off.
Example.— What is circumfo?ence of a circle 9675 feet in diameter?
Circumference of 96. 75 = 303.95 ; hence, circumference of 9675 = 30 395/erf.
To Ascertain Oironmrerence fbr a Diameter, as 600,
SOOO, et<»., not contained in Table.
Rule.— Take circumference of 5 or 50 from table, and add the excess of
ciphers to the result.
Example.— What is circumference of a circle 8000 feet in diameter?
Circumference of 80 = 251. 38 ; hence, circumference of 8000 = 25 138 ^efc
To Compute Circnrnference of a Circle "by I^ogarithms.
Rule. — To log. of diameter add .497 15 (log. of 3.1416), and sum is log.
of circumference, from which take number.
Example. —What is circumference of a circle laoo feet in diameter?
Log. 1200 = 3.079 18 4- 497 15 = 3 576 33, and number for which = 3769.92/e«t
t>inin.
No.
X
2
3
4
5
6
7
8
Circnmfferenoes of Birmingliaxn "^Vire Grange.
Circatn.
Circam.
Diam.
Ins.
No.
.94248
10
.89221
II
.81367
12
.7477
13
.69115
14
.63774
15
•56549
16
.51836
17
.46495
18
Ins.
.420 97
•37699
.342 43
.29845
.26075
.226 19
.2042
.18221
•15394
Diam.
Cirrnm.
No.
Ins.
19
•13195
20
.10995
21
•10053
22
.08796
23
.07854
24
.06911
25
.06283
26
.05655
27
.050 26
)inm.
Circum.
No.
Ina.
28
.04398
29
.04084
30
.0377
31
.031 41
32
.02827
33
•02513
.34
.02199
35
.01571
3<> 1
.01357
ABBAS AND CIBCUHFBBBNCBS OF CIBCLBS.
243
-A.reas and. Ciroumferences,
DiAU.
.1
.2
•3
.4
S
.6
•7
.8
.1
.2
•3
•4
•5
.6
•7
.8
.1
.2
.3
.4
.5
.6
•7
.8
.1
.2
•3
.4
•5
.6
•7
.8
.1
.2
•3
•4
•5
.6
•7
.8
.1
.2
•3
•4
•5
Area.
ClBCtTM.
.007854
.31416
.03T 416
.62832
.070686
.94248
.125664
1.2566
•19635
1.5708
.282 744
1.885
.384846
2.1991
.502656
2.5133
.636174
2.8274
.7854
3.1416
•9503
34558
1. 131
37699
13273
4.0841
1-5394
43982
1.767 I
4.7124
2.0106
5 0266
2.2698
53407
2.5447
56549
28353
5969
3. 141 6
6.2832
34636
6-5974
3-8013
6.9115
4.1548
7.2257
45239
7-5398
4.9087
7854
53093
8.1682
57256
8.4823
6.1575
8.7965 i
6.6052
9.1106 1
7.0686
9.4248
7 547 7
9739
8.0425
10.0531
8.553
10.3673
9.0792
10.681 4
9.621 1
10.9956
10.1788
11.3098
10.752 I
11.6239
11.3412
11.9381
11-9459
12.2522
12.5664
125664
13.2026
12.8806
13.8545
13-1947
14522
135089
152053
13-823
159043
14-1372
16 619 1
14.4514
17-3495
147655
18.0956
15.0797
18.8575
15-3938
19-635
15.708
20.4283
16.022 2
21.2372
16.3363
2».o6i 9
16.6505
22.9023
16.9646
33-7583
17.2788
DiAM.
8
10
I
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
(Adwrneing by Tenths.)
Aksa.
CfBCOH.
24.6301
17593
25-5176
17.9071
26.4209
18.2213
273398
18.5354
28.2744
18.8496
29.2247
19.1638
30.1908
19.4779
311725
19.7921
32-17
20.1062
331831
20.4204
34.212
20.7346
35-2566
21.0487
36.3169
21.3629
37-3929
21.677
38.4846
21.9912
39-592
22.3054
40.7151
22.6195
41-854
22.9337
43.0085
23.2478
44-1787
23.562
45-3647
23.8762
46.5664
24.1903
477837
24.5045
49.0168
24.8186
50.2656
25 1328
51-5301
25447
52.8103
25 7611
54.1062
260753
554178
26.3894
56.7451
267036
58.0882
270178
59.4469
27.3319
60.8214
276461
62.2115
279602
636174
28 2744
65039
28.5886
664763
28.9027
67.9292
292169
693979
29531
70.8823
29.8452
723825
30.1594
73-8983
30.4735
75.4298
30.7877
76.9771
31.1018
78.54
31.416
80.1187
31.7302
81.713
320443
833231
32.3585
84.9489
32.6726
86.5903
32.9868
88.2475
33301 -
89.9204
336151
91.6091
339293
93-3134
34.2434
244 ABEAS AND CIBCUHFEBENGBS OF CIBCLBS.
DUM.
11
X2
'3
14
15
i6
I
2
3
4
5
6
7
8
I
2
3
4
S
6
7
8
I
2
3
4
5
6
7
8
I
2
3
4
5
6
7
8
I
2
3
4
5
6
7
8
I
2
3
•4
Abba.
95-0334
96.7691
98.5206
100.2877
102.0706
103.8691
105.6834
107.5134
109.3591
II 1. 2205
113.0976
114.9904
116.8989
118.8232
120.7631
122.7187
124.6901
126.6772
128.6799
130.6984
132.7326
134-7825
136 8481
1389294
141.0264
1431391
145.2676
147.4117
149.5716
151-7471
153.9384
156.1454
158 3681
160.6064
162.8605
165.1303
167.4159
169.7171
172.034
174.3667
176.715
179.0791
181.4588
1838543
186.2655
188.6924
191.1349
1935932
196.0673
198557
201.0624
203.5835
206.1204
208.6729
2x1.2412
CtBcm.
34-5576
34.8718
35.1859
355001
358142
36.1284
36.4426
36.7567
37.0709
37385 •
37.6992
38.0134
383275
38.6417
38 9558
39.27
39584?
39-8983
40.2125
40.5266
40.8408
41.155
41.4691
41.7833
420974
42.4116
42.7258
430399
43-3541
436682
43.9824
44.2966
44.6107
44.9249
45239
45.5532
45.8674
461815
46.4957
46.8098
47.124
47.4382
47.7523
48.0665
48.3806
48.6948
49.009
49.3231
496373
49-9514
50.2656
50.5797
50.8939
51.2081
51.5222
DlAM.
Abba.
CiBcim.
•5
213.8251
51.8.364
.6
,216.4248
52.1505
•7
219.0402
52.4647
.8
221.6713
52.7789
^ -9
224.3181
53.093 ^
17
226.9806
53.4072*
.1
'229.6588
537214
.2
232.3527
540355
•3
235.0624
54-3497
•4
237.7877
54-6638
•5
240.5287
54-978
.6
243-2855
55-2922
.7
246058
556063
.8
248.8461
55-9205
•9
251.65
56.2346
18
254.4696
56.5488
.1
257.3049
56.863
.2
260.1559
571771
.3
263.0226
57-4913
••4
265.905
57.8054
.5
268.8031
58.1196
.6
271.717
58.4338
•7
2746465
58.7479
.8
2775918
59.0621
•9
280.5527
59.3762
19
283.5294
59.6904
.1
286.5218
6^.0046
.2
289.5299
60.3187
•3
292.5536
606329
.4
295 5931
60.947
•5
298.6483
61.2612
.6
301.7193
61.5754
■ .7
304.806
61.8895
.8
307.9082
62.2037
•9
311.0263
62.5178
20
314-16
62.832
.1
3173094
63.1462
.2
320 4746
634603
•3
323-6555
637745
•4
326.8521
640886
.5
330.0643
64.4028
.6
333.2923
64.717
•7
336.536
65.0311
.8
339.7955
65-3453
•9
343.0706
65.6594
21
3463614
65.9736
.1
3496679
66.2878
.2
352.9902
66.6019
•3
356.3281
66.9161
•4
359.6818
67.2302
•5
363 05 1 1
67.5444
.6
366.436*
67.8586
•7
369-837
68,1727
.8
373-2535
68.4869
•9
376.6857
^/k>i
ABBAS AND CIBCUMFERSNOBS OF CIBCLBS. 245
DiAM.
Arba.
ClBCUM.
22
380.1336
69.1152
.1
383.5972
69.4294
.a
387.0765
69.7435
.3
390.5716
70.0577
•4
394.0823
70.3718
.5
397.6087
70.686
.6
401.1509
71.0002
.7
404.7088
71.3143
.8
408.2823
71.6285
.9
4IT.8716
71.9426
23
415.4766
72.2568
.1
419.0973
72.571
.2
422.7337
72.8851
.3
426.3858
73.1993
•.4
4300536
73.5134
.5
433-7371
73.8276
.6
4374364
74.1418
•7
44i'i5i3
74-4559
.8
444.882
74.7701
.9
448.6283
75.0842
24
452.3904
753984
.1
456.1682
75.7126
.2
4599617
76.0267
.3
463.7708
76.3409
•4
467.5957
76.655
•5
471-4363
76.9692
.6
475.2927
77.2834
.7
479.1647
77-5975
.8
483.0524
77.9117
•9
486.9559
78.2258
25
490.875
78.54
.1
494.8099
78.8542
.3
498.7604
79-1683
.3
502.7267
79-4825
•4
506.7087
797966
•5
510.7063
80.1108
Jb
514.7196
80.425
•7
518.7488
80.7391
.8
522.7937
81.0533
•9
526.8542
81.3674
a6
530.9304
81.6816
.1
535-0223
81.9958
.a
S39»3
82.3099
.3
543-2533
82.6241
4
547.3924
82.9382
.5
551-5471
83.2524
.6
555.7176
83.5666
•7
559-9038
83.8807
.8
564.1057
84.1949
•9
568.3233
84.509
27
572.5566
84.8232
.1
576.8056
85.1374
.2
581.0703
85.4515
•3
585.3508
85.7657
•4
589.6469
86.0798
DlAM.
-5
.6
-7
.8
28
.1
.2
-3
•4
.5
.6
•7
.8
•9
29
.1
.2
•3
-4
-5
.6
•7
.8
-9
30
31
32
.1
.2
3
.4
.5
.6
-7
.8
•9
.1
.2
•3
-4
.5
.6
.7
.8
•9
.1
.2
-3
-4
•5
.6
.7
.8
Absa.
593.9587
598.2863
602.6296
606.9885
611.3632
615.7536
620.1597
624.5815
629.019
633.4722
637.94"
642.4258
646.9261
651.4422
6559739
660.5214
665.0846
669.6635
674.258
678.8683
683.4943
688.1361
692.7935
697.4666
702.1555
706.86
711.5803
716.3162
721.0679
7258353
730.6183
7354171
740.2316
745.0619
7499078
754.7694
759.6467
764.5398
769.4485
774-373
779-3131
784.269
789.2406
794.2279
799.2309
804.2496
809.284
814-3341
819.4
824.4815
829.5787
834-6917
839.8204
8449647
850.1248
ClBCCM.
86.394
86.7082
87.0223
87-3365
87.6506
87.9648
88.279
88.5931
88.9073
89.2214
89-5356
89.8498
90.1639
90.4781
90.7922
91.1064
91.4206
91-7347
^.0489
92.363
92.6772
92.9914
93.3055
93.6197
939338
94.248
94.5622
94.8763
951905
95.5046
95.8188
96.133
964471
96.7613
970754
97.3896
97.7038
98.0179
98.3321
98.6462
98.9604
99.2746
99-5887
99.9029
100.217
100.5312
100.8454
101.1595
101.4737
101.7878
102.102
102.4162
102.7303
103044s
103.3586
X*
246 AREAS A^D OIBGUMPEBENOSS OF CIBCLBB.
DiAM. I
Akba.
33
I
2
3
•4
5
6
7
8
34
I
2
3
-4
5
6
7
8
35
36
37
38
I
2
3
4
5
6
7
8
I
2
3
4
5
6
7
8
I
2
3
4
5
6
7
8
I
2
3
•4
855.3006
860.4921
865.6993
870.9222
876.1608
881.4151
886.6S52
891.9709
897.2724
902.5895
907.9224
913.271
918.6353
924.0152
929^109
934 8223
940.2495
9456923
951.1508
956.6251
962.115
967.6207
973.142
978.6791
984.2319
989.8003
995-3845
1000.9844
1006.6001
1012 2314
loi 7.8784
1023.5411
1029.2 196
1034.9137
1040.6236
1046.3491
1052.0904
1057.8474
1063.6201
1069.4085
1075.2126
108 1. 0324
1086.8679
1092.7192
1098.586J
1 104.4687
1 1 10.367 1
1 1 16.2812
1 122.2109
1 128.1564
1134.1176
1 140.0945
1 146.0871
1152.0954
1 158. 1 194
ClBCUM.
03.6728
03987
04.3011
04.6153
04.9294
05.2436
05-5578
05.8719
06.1861
06.5002
06.8144
07.1286
07.4427
07.7569
08.071
08.3852
08.6994
09.0135
09.3277
09.6418
09.956
0.2702
0.5843
0.8985
I.2I26
1.5268
I.84I
2.I55I
2.4693
2.7834
3.0976
3.41 18
37259
4.0401
4-3542
4.6684
4.9826
5-2967
5.6109
5-925
6.2392
6.5534
6.8675
7.1817
7.4958
7.81
8.1242
8.4383
8.7525
9.0666
9-3808
9-695
20.0091
20.3233
?o.^74
DliM.
Arxa.
CnuHTif.
.5
1 164.1591
120.9516
.6
1170.2^46
121.2658
.7
II 76.2857
121.5799
...8
1 182.3726
121.8941
•9
1188,4751
122.2082
39
1 194-5934
122.5224
-.1
1200.7274
122.8366
.2
1206.8771
123.1507
•3
1213.0424
1234649
•4
1219.2235
123.779
.5
1225.4203
124.0932
.6
1231.6329
124.4074
.7
1237.8611
124.7215
.8
1244.105
125-0357
•9
1250.3647
125.3498
40
1256.64
125.664
.1
1262.93x1
125.9782
.2
1269.2378
126.2923
.3
1275.5603
126.6065
A
1281.8985
126.9206
.5
1288.2523
127.2348
.6
1294 62x9
127.549
.7
1301.0072
127.8631
.8
1307 4083
128.1773
•9
13x3 825
128.4914
41
1320,2574
128.8056
.1
1326.7055
129.1198
.2
1333-1694
129.4339
•3
1339-6489
129.7481
•4
1346. 1442
130.0622
•5
1352-6551
130.3764
jS
1359.1818
130.6906
•7
1365*7242
131.0047
.8
1372.2823
131-3189
•9
1378.8561
131-633
42
1385.4456
131.9472
.1
1392.0508
132.2614
.2
1398.6717
132.5755
.3
1405.3084
132.8897
A
14 II. 9607
i33-»038
•S
1418.6287
133-518
.6
1425.3125
133-8322
.7
1432.012
134- 1463
.8
1438.7271
134-4605
•9
1445458
1347746
43
1452.2046
135.0888
.1
1458.9669
135-403
.2
1465.7449
135.71 71
.3
1472.5386
136.0313
•4
1479.348
136.3454
•5
1486.1731
136.6596
.6
1493.014
136.9738
•7
1499*8705
137.2879
.8
1506.7428
137.6021
•9
1513.6307
137-9163
AREAS AND CIBCUMFBBENGES OF CIRCLES. 247
DiAM.
AmBA.
Ctscom.
44
1520.5344
138.2304
.1
1527-4538
138.5446
.2
1534-3889
138.8587
3
1541-3396
139.1729
•4
1548.30C1
139.487
•5
1555.2883
139.8012
.6
1562.2863
140.1154
•7
1569.2999
140.4295
.8
1576.3292
140.7437
•9
1583.3743
141.0578
45
1590-435
141.372
.1
i597-S"S
141.6862
.a
1604.6036
142.0003
3
1611.7115
I423145
•4
1618.8351
142.6286
•5
1625.9743
142.9428
.6
163.3.1293
143 257
•7
1640.3
14357"
.8
1647.4865
1438853
•9
1654.6886
144.1994
46
1661.9064
144.5136
.1
1669.1399
144.8278
.2
1676.3892
145.1419
•3
1683.6541
145.4561
•4
1690.9348
145.7702
•5
1698.231 1
146.0844
.6
17055432
146.3986
•7
1712.871
146.7127
^
1720.2145
147.0269
•9
1727-5737
147-341
47
1734.9486
147.6552
.1
1742.3392
147.9694
.2
1749.7455
148.2835
.3
1757.1676
148.5977
.4
1764.6053
148.9118
•5
1772.0587
149.226
.6
1779-5279
149.5402
•7
1 787.0128
149.8543
.8
1794-5133
150.1685
•9
1802.0296
150.4826
48
1809.5616
150.7968
.1
1817.1093
151.111
.2
1824.6727
151.4251
•3
1832.2518
151.7393
•4
1839.8466
152.0534
.5
1847.4571
152.3676
.6
1855.0834
152.6818
•7
1862.7253
152.9959
.8
1870.383
153-3101
•9
1878.0563
153.6242
49
1885.7454
1539384
.1
1893.4502
154.2526
.2
1901.1707
1545667
'3
1908.9068
154.8809
•4
1916.6587
155.195
DlAlt.
Abba.
ClBCUM.
.5
1924.4263
155.5092
.6
1932.2097
155.8234
.7
1940.0087
156.1375
.8
1947.8234
156.4517
.9
1955 6539
156.7658
50
19635
15708
.1
1971.3619
1573942
.2
1979.2394
157.7083
.3
1987.1327
158.0225
•4
1995.0417
158.3366
.5
2002.9663
158.6509
,6
2010 9067
158.965
.7
2018.8628
159279*
.8
2026.8347
159.5933
•9
2034.8222
1599074
51
2042.8254
160.2216
.1
2050.8443
160.5358 .
.2
2058.879
160.8499
.3
2066.9293
161.1641
•4
20749954
161.4782
.5
2083.0771
161.7924
.6
2091.1746
162.1066
.7
2099.2878
162.4207
.8
2107.4167
162.7349
'9
21 15.5613
163049
52
2123.7216
163.3632
.1
213I.8976
163.6774
.2
2140.0893
1639915
'3
2148.2968
164.3057
•4
2156.5199
164.6198
•5
2164.7587
164.934
.6
21 73.0133
165.2482
•7
2181.2836
165.5623
.8
2189.5695
165.8765
.9
2197.8712
166.1906
53
2206.1886
166.5048
.1
2214.5217
166.819
.2
2222.8705
167.1331
•3
2231.235
167.4473
•4
2239.6152
167.7614
•5
2248.0111
168.0756
.6
2256.4228
168.3898
•7
2264.8501
168.7039
.8
2273.2932
169.0181
•9
2281.7519
169.3322
54
2290.2264
169.6464
.1
2298.7166
169.9606
.2
2307.2225
170.2747
.3
2315-744
1705889
•4
2324.2813
170.903
.5
2332.8343
171.2172
.6
2341.4031
171-5314
•7
23499875
171-8455
.8
2358.5876
172.1597
•9
2367.2035
372.4738
248 ABKAS AND CIBCUMFERENGSS OF CIBCL£S.
DlAM.
Abba.
ClBCUM.
55
2375-835
172.788
.1
2384.4823
173.1022
.2
2393-1453
173-4163
•3
2401.8239
173-7305
•4
2410.5 183
174.0446
.5
2419.2283
174.3588
.6
2427.9541
174.673
.7
2436.6957
174.9871
.8
2445.4529
175.3013
.9
2454.2258
175.6154
56
2463.0144
175.9296
.1
2471.8187
176.2438
.2
2480.6388
1A5579
.3
24^.4745
176.8721
^
2498.326
177.1862
.5
2507. 1931
177.5004
.6
2516.076 /
177.8146
.7
25249736
178.1287
.8
2533.8889
178.4429
•9
2542.8189
178.757
57
2551.7646
179.0712
.1
2560.726
179.3854
.2
2569-7031
179.6995
•3
2578.696
180.0137
•4
2587.7045
180.3278
•5
2596.7287
180.642
.6
2605.7687
180.9562
.7
2614.8244
181.2703
.8
2623.8957
181.5845
•9
2632.9828
181.8986
58
2642.0856
182.2128
.1
265 1. 2041
182.527 '
.2
2660.3383
182.841 1
.3
2669.4882
183.1553
•4
2678.6538
183.4694
•5
2687.8351
183.7836
.6
2697.0322
184.0978
•7
2706.2449
184.4119
.8
2715.4734
184.7261
•9
2724.7175
185.0402
59
2733-9774
185.3544
.1
2743253
185.6686
.2
2752.5443
185.9827
•3
2761.8512
186.2969
•4
2771-1739
186.61 1
.5
2780.5123
186.9252
.6
2789.8665
187.2394
.7
2799.2363
187.5535
.8 •
2808.6218
187.8677
•9
281 8.0231
I88.I818
60
2827.44
188.496
.1
2836.8727
188.8102
.2
2846.321
189.1243
•3
2855.7851
189.4385
•4
2865.2649
189.7526
DlAM.
Ar«a.
.5
2874.7603
.6
2884.2715
•7
2893-7984
.8
2903.3411
•9
2912.8994
61
2922.4734
.1
2932.0631
.2
2941.6686
-3
2951.2897
.4
2960.9266
•5
2970.5791
.6
2980.2474
•7
2989.9314
.8
2999.631 1
•9
3009.3465
62
3019.0776
.1
3028.8244
.2
3038.5869
-3
3048.3652
•4
3058.1591
•5
3067.9687
.6
3077.7941
•7
3087.6341
.8
3097-4919
•9
3107.3644
63
3117.2526
.1
3127.1565
.2
3137.0761
.3
3147.01 14
•4
3156.9624
•5
3166.9291
.6
3176.9116
•7
3186.9097
.8
3196.9236
•9
3206.9531
64
3216.9984
.1
3227.0594
.2
3237. 1361
-3
3247.2284
.4
3257-3365
.5
3267.4603
.6
3277-5999
•7
3287.7551
.8
3297.9261
•9
3308.1127
65
3318.31S
.1
3328.5331
•2
3338.7668
-3
33490163
4
3359.2815
.5
3369.5623
.6
3379-8589
•7
3390.1712^
.8
3400.4993
.9
3410.843
Ciacnc.
190.0668
190.381
190.6951
191.0093
191-3234
191.6376
191.9518
192.2659
192.5801
192.8942
193.2084
193.5226
193.8367
194.1509
194.465
194.7792
195.0934
195.4075
195.7217
196.0358
196.3s
196.6642
196.9783
197.2925
197.6066
197.9208
198.235
198.5491
198.8633
199-1774
199.4916
199.8058
200.1199
200.4341
200.7482
201.0624
201.3766
201.6907
202.0049
202.319
202.6332
202.9474
203.2615
203.5757
203.8898
204.204
204.5182
204.8323
205.1465
205.4606
205.7748
206.089
206.4031
206.7173
207.0314
AREAS AND CIBCUMFBBSNOES OF CIBGLB8. 249
DiAM.
66
.1
.2
•3
•4
•S
.6
•7
.8
67
.1
.2
•3
•4
•5
.6
.7
.8
68
.1
.2
•3
•4
.5
.6
.7
.8
69
.1
.2
.3
•5
.6
•7
.8
70
.1
.2
.3
•4
•5
.6
•7
.8
71
.1
.9
•3
•4
J421.2024
3431-5775
3441.9684
3452.3749
3462.7972
3473a35i
34836888
3494.1582
3504.6433
3515.1441
3525.6606
3536.1928
3546.7407
3557-3044
3567.8837
3578^1787
3589.0895
3599.716
3610.3581
3621.016
3631.6896
36423789
3653-0839
3663.805
3674.541
3685.2931
3696.061
3706.8445
3717-6438
3728.4587
3739.2894
3750.1358
3760.9979
3771.8756
3782.7691
3793.6783
3804.6033
38155439
3826.5002
38374722
3848.46
3859-4635
3870 4826
3881.517s
3892.5681
39036343
3914.7163
3925-814
3936.9275
3948.9566
3959.2014
3970.3619
3981.5382
3992.7301
4003.9378
ClBCUM.
207.3456
207.6598
207.9739
208.2881
208.6022
208.9164
209.2306
209.5447
209.8589
210.173
210.4872
210.8014
2II.II55
211.4297
211.7438
212.058
212.3722
212.6863
213.0005
213.3146
213.6288
213.943
214.2571
214.5713
214.8854
215.1996
215.5138
215.8279
216. 142 1
216.4562
216.7704
217.0846
217.3987
217.7129
218.027
218.3412
218.6554
218.9695
219.2837
219.5978
219.912
220.2262
220.5403
220.8545
221.1686
221.4828
221.797
222.1 III
2^2.4253
222.7394
223.0536
223.3678
223.6819
223.9961
224.3102
DiAM.
Abba.
ClBOClC.
.5
4015.161 1
224.6244
.6
4026.4002
224.9386
.7
4037.655
225.2527
.8
4048.9255
225.5669
'9
4060.21 1 7
225.881
72
407I.5136
226.1952
.1
4082.8312
226.5094
.2
4094.1645
226.8235
.3
4105.5136
227.1377
.4
4116.8783
227.4518
•5
4128.2587
227.766
.6
4139-655
228.0802
•7
415 1. 0668
228.3943
.8
4162.4943
228.7085
•9
4173.9376
229.0226
73
4185.3966
229.3368
.1
4196.8713
229.651
.2
4208.3617
2299651
.3
4219.8678
230.2793
.4
4231.3896
230.5934
.5
4242.9271
230.9076
.6
4254.4804
231.2218
.7
4266.0493
231.5359
.8
4277.634
231.8501
•9
4289.2343
232.1642
74
4300.8504
232.4784
.1
4312.4822
232.7926
.2 *
4324.1297
233.1067
.3
4335-7928
233.4209
-4
43474717
233.735
.5
4359.1663
2340492
.6
4370.8767
234.3634
•7
4382.6027
2346775
.8
4394.3444
234.9917
.9
4406. 1019
2353058
75
4417.875
235.62
.1
4429.6639
235.9342
.2
4441.4684
236.2483
•3
4453.2887
2365625
.4
4465.1247
236.8766
.5
4476.9763
237.1908
.6
4488.8437
237505
.7
4500.7268
237.8191
.8
4512.6257
238.1333
•9
4524.5402
238 4474
76
4536.4704
238.7616
.1
4548.4163
2390758
.2
4560.378
239.3899
.3
4572.3553
239.7041
.4
4584.3484
240.0182
•S
4596.3571
240.3324
.6
4608.3816
240.6466
•7
4620.4218
240.9607
.8
4632.4777
241.2749
.9
4644.5493
241.589
2SO
ABEAB JLSAD CIBCUMFBBENCSS OF CIBCLBS.
DiAU.
Akba.
ClBCDM.
DiAM.
77
4656.6366
241.9032
•5
.1
4668.7396
242.2174
.6 ,
.2
4680.8583
242.5315
•7
•3
4692.9928
242.8457
.8
•4
4705.1429
243.1598
•9
5
4717.3087
243474
83
.6
4729.4903
243.7882
.1
•7
4741.6876
244 1023
.2
.8
4753-9005
244.4165
.3
•9
4766.1292
2447306
.4
78
4778.3736
245.0448
•5
.1
4790.6337
245359
.6
.2
4802.9095
2456731
•7
.3
4815.201
2459873
.8
•4
4827.5082
246.3014
•9
.5
4839.8311
246.6156
84
.6
4852.1698
246.9298
.1
•7
4864.5241
247 2439
.2
.8
48768942
2475581
.3
•9
48892799
247.8722
•4
79
4901 .6S14
248.1864
•5 1
.1
4914.0986
2485006
.6 ;
.2
4926.5315
248 8147
.7
•3
4938.98
249.1289
.8
•4
4951.4443
249443
•9
•5
4963.9243
2497572
85
.6
4976.4201
250.0714
.1
.7
4988.9315
250 3855
.2
.8
5001.4586
250.6997
•3
.9
5014.0015
251.0138
.4
80
5026.56
251.328 1
•5
.1
5039.1343
251.6422 '
.6
.2
5051.7242
251.9563
.7
•3
5064.3299
252 2705
.8
•4
5076.9513
2525846
•9
.5
5089.5883
252.8988
86
.6
5102.241 1
253213
.1
•7
51 14.9096
2535271
.2
.8
5'27.5939
253-8413
.3
•9
5140.2938
2541554
.4
81
5153.0094
254.4696
.5
.1
5165.7407
2547838
.6
.2
5178.4878
255-0979
•7
•3
5191.2505
255.4121
.8
•4
5204.0289
255.7262
•9
•S
5216.8231
256.0404
87
.6
5229633
256.3546
.1
•7
5242.4586
256.6687
.2
.8
52552999
256.9829
.3
•9
5268.1569
257.297
•4
82
5281.0296
257.6112
•5
.1
5293918
257.9254
.6
.2
5306.8221
258.239s
•7
•3
5319742
258.5537
.8
•4
$3326775
2588678 .
•9
Aria.
5345.6287
5358.5957
53715784
5384.5767
53975908
54106206
5423.6661
54367273
54498042
54628968
54760051
5489.1292
55022689
5515.4244
5528.5955
5541.7824
5554.985
5568.2033
5581.4372
55946869
5607.9523
5621.2335
5634.5303
5647.8428
5661. I711
5674515
5687.8747
5701.25
5714.6411
5728.0479
5741.4703
57549085
5768 3624
5781.8321
5795.3174
5808.8184
5822.3351
5835.8676
58494157
5862.9796
5876.5591
5890.1544
5903.7654
5917.3921
59310345
5944.6926
5958.3644
59720559
5985.7612
5999.4821
6013.2187
6026.971 1
6040.7392
6054.5229
6068.3224
ClKCCM.
259.182
259.4962
259.8103
260.1245
260.4386
260.7528
261.067
261.3811
261.6953
262.0094
262.3236
262.6378
262.9519
263.2661
263.5802
263.8944
264.2086
264.5227
2648369
265.151
265.4652
265.7794
266.0935
266.4077
266.7218
267.036
267.3502
267.6643
267.9785
268.2926
2686068
268.921
269.2351
269.5493
269.8634
270.1776
270.4918
270.8059
271.1201
271.4342
271.7484
272.0626
272.3767
272.6909
273005
273.3192
2736334
273 9475
274.2617
2745758
274.89
275.2042
275.5183
275 8325
276.1466
ABSAS AND CIBOtTMF£R]&KC£S OB* CIBCLES. 2$ I
DiAM.
Akia.
ClBCVM.
DlAM.
Abba.
CiBcim.
88
6082.1376
276.4608
•5
6866.1631
293.7396
.1
6095.9685
276.775
.6
6880.858
294.0538
.2
61098151
2770891
•7
6895.5685
2943679
•3
6123.6774
2774033
.8
6910.2948
294.6821
•4
6137-5554
277.7174
•9
69250367
294.9962
•5
6151.4491
278.0316
94
69397944
295.3104
.6
6165.3586
278.3458
.1
6954.5678
295.6246
•7
6179.2837
278.6599
.2
6969.3569
295.9387
•8
6193.2246
278.9741
.3
698/I.1616
296.2529
•9
6207.181 1
279.2882
•4
6998.9821
296.567
89
6221. 1534
279.6024
.5
7013 8183
296 8812
.1
623^1 1414
279.9166
.6
7028.6703
297.1954
.2
6249 1451
280.2307
•7
70435379
297-5095
•3
6263.1644
280.5449
.8
7058 4212
297 8237
•4
6277.1995
280.859
•9
7073.3203
298.1378
•5
6291 2503
281.1732
95
7088.235
298.452
.6
63053169
281.4874
.1
7103. 1655
298.7662
•7
6319 3991
281.8015
.2
7118.II16
299.0803
8
6333 497
282.1157
.3
71330735
299.3945
9
63476107
282.4298
.4
7148 0511
299.7086
90
6361.74
282.744
^•5
7163 0443
300.0228
.1
63758851
283 0582
.6
71780533
300.337
.2
63900458
2833723
•7
7193.078
300.6511
3
6404.2223
283.6865
.8
7208.1185
300.9653
•4
6418 4144
284.0006
.9
7223.1746
301.2794
.5
6432.6223
284.3148
96
7238.2464
301.5936
.6
6446.8459
284.629
.1
72533339
301.9078
•7
6461.0852
284.9431
.2
7268.4372
302.2219
.8
^75.3403
285.2573
.3
7283.5561
302.5361
•9
6489.61 1
285.5714
•4
7298.6908
302.8502
91
6503.8974
285.8856
•5
73138411
303.1644
.1
6518.1995
286.1998
.6
7329 0072
3034786
.2
65325^74
286.5139
.7
7344.189
303.7927
•3
6546.8509
286.8281
.8
7359.3865
304 1069
4
6561.2002
287.1422
•9
7374 5997
304.421
•5
6575 5651
287.4564
97
73898286
304-7352
. .6
6589.9458
287.7706
.1
74050732
305.0494
•7
660^.3422
288.0847
.2
7420.3335
305.3635
.8
66187543
288.3989
.3
7435.6096
305.6777
9
66331821
288.713
•4
74509013
305.9918
92
66476256
289.0272
•5
7466.2087
306.306
.1
66620848
289.3414
.6
7481 .5319
306.6202
.2
. 6676 5598
289.6555
•7
7496.8708
3069343
•3
66910504
289.9697
.8
7512.2253
307,2485
•4
6705 5567
290.2838
•9
75275956
307.5626
•S
6720.0787
290.598
98
7542.9816
307.8768
^
6734 6165
290.9121
.1
75583833
308.191
•7
674917
291.2263
.2
7573.8007
308,5051
.8
6763.7391
2915405
•3
7589 2338
308.8193
9
6778 324
291.8546
•4
7604.6826
3091334
93
6792.9246
292.1688
.5
7620. 147 1
309.4476
.1
6807.5409
292.483
.6
7635 6274
309,7618
.a
6822.1729
292.7971
.7
7651.1233
310.0759
.3
68368206
293-"i3
.8
7666.635
310 3901
•4
6851.484
293-4a54
•9
7682.1623
310.7042
252 ABBAS AND CIBCUKFBBENOBS OV CIBOLBS.
DiAM.
Abba.
CiBcnt.'
DlAM.
Arxa.
CimcnM.
99
7697.7054
311.0184
•5
7775.6563
312.589a
.1
7713.2643
311.3326
.6
7791.2937
312.9034
.2
7728.8337
311.6467
•7
7806.9467
313-2175
•3
7744.4288
311.9609
.8
7822.6154
313 5317
•4
7760,0347
312.275
•9
7838.2999
313.8458
Q?o Coxupute A.rearOr Cirouxxiferenoe era IDiaxneter greater
than, any in. preoecLing Xable.
See ^ules, pages 235-6 and 241-2.
Or, If Diameter exceeds 100 and is less than looi.
Pat a decimal point, and take out area or circumference as for a Whold
Number by removing decimal point, if for an area, two places to right , and
if for a circumference, one place.
Example. — What is area and what circnmference of a circle 967 feet in diame-
ter?
Area of 96.7 is 7344.180; hence, for 967 it is 734 418.9; and circumference of 96.7
is 303.7927, and for 967 it is 3037.927.
To Compute A^rea an.d Circumrerenoe of a Circle by Xjog*
aritliins.
See Rules, pages 236, 242.
JLreas and Ciroutixfbrenoes of* Circles.
From x to 50 Feet (advancing by an Inch).
Or, From i to 50 Inches {advancing by a Tiveyth).
DiAM.
I
2
3
4
5
6
7
8
9
10
II
a. A
I
2
3
4
5
6
7
8
9
10
II
Akba.
FMt.
•7854
.9217
1.069
1.2272
1-3963
1-5763
1. 7671
1.969
2.I8I7
24053
2.6398
2.8853
3.I4I6
3.4088
3.687
3.9761
4.2761
4.5869
4.9087
5.2415
5.5852
5.9396
6.305
6.6814
ClBCVM.
Feet.
3-I416
3-4034
3.6652
3927
4.1888
4-4506
4.7124
4-9742
5236
5.4978
57596
6.0214
6.2832
6.545
6.8068
7.0686
7.3304
7.5922
7-854
8.II58
8.3776
8.6394
8.9012
9.163
DlAM.
3 A
I
2
3
4
5
6
7
8
9
10
II
4A
I
2
3
4
S
^
7
8
9
10
II
Aria.
Feet.
7.0686
7.4668
7.8758
8.2958
8.7267
9.1685
9.621 1
10.0848
10.5593
11.0447
II.54I
12.0483
12.5664
130955
13.6354
14.1863
14.7481
15.3208
15.9043
16.4989
17.1043
17.7206
18.3478
18.9359
ClROTM.
Feet.
9.4248
9.6866
9.9484
10.2102
10.472
10.7338
10.9956
11.2574
XI. 5192
11.781
12.0428
12.3046
12.5664
12.8282
13.09
13.3518
13.6136
138754
14-1372
14.499
14.660S
14.9226
15.1844
15.4462
AREAS AND CIBCUMFERENCES OF CIBCtKft. 253
T>.AU
AXSA.
C1BCUIC.
Feet.
Feflt.
5/^-
19-635
15-708
I
20.2949
15.9698
2
20.9658
16.2316
3
21.6476
16.4934
4
22.3403
16.7552
5
230439
17.017
, 6
237583
17.2788
7
24.4837
17.5406
8
25.22
17.8024
9
25.9673
18.0642
lO
26.7254
18.326
It
27.4944
18.5878
6ft.
28.2744
18.8496
I
29.0653
I9.III4
2
29.867
19.3732
3
30.6797
19.635
4
31-5033
19.8968
5
32-3378
20.1586
6
33-1831
20.4204
7
340394
20.6822
8
34.9067
20.944
9
35.7848
21.2058
lO
36.6738
21.4676
II
37-5738
21.7294
7^.
38.4846
21.9912
I
39.4064
22.253
2
40.339
22.5148
3
41.2826
22.7766
4
42.2371
23.0384
5
43.2025
23.3002
6
44.1787 •
23.562
7
451659
23.8238
8
46.1641
24.0856
9
47-1731
24.3474
lO
48.193
24.6092
II
49.2238
24.871
syi!.
50.2656
25.1328
I
51-3183
25.3946
2
52.3818
25.6564
3
53-4563
25.9182
4
54.5417
26.18
5
55638
26.4418
6
56.7451
26.7036
7
57.8632
26.9654
8
58.9933
27.2272
9
60.1322
27-489
lO
61.283
27.7508
II
62.4448
28.0126
9 A.
63.6174
28.2744
I
64.801
28.5362
2
659954
28.798
3
67.2008
29.0598
4
68.417
29.3216
Mr
696442
29-5834
DiAM.
Aria.
ClBCUM.
Vf 3t.
Feet.
6
70.8823
29.8452
7
72-1314
30.107
8
73.3913
30.3688
9
74.6621
30.6306
lO
75-9439
30.8924
II
772365
31-1542
JO ft.
78.54
31-416
I
798545
31.6778
2
81.1798
31.9396
3
82.5161
32.2014
4
83.8633
32.4632
5
85.2214
32.725
6
86.5903
32.9868
7
87.9703
33.2486
8
89.3611
33.5104
9
90.7628
33-7722
10
92.1754
34-034
II
93-599
342958
lift.
. 950334
34.5576
1
96,4787
34.8194
2
97-935
35.0812
3
99.4022
35-343
4
100.8803
35.6048
5
102.3693
35.8666
6
103 8691
36. 1284
7
105.38
36.3902
8
106.9017
36.652
9
108.4343
36.9138
10
109.9778
371756
II
I II. 5323
37.4374
12 ft
113.0976
37.6992
1
114.6739
37-961
2
116,261
38.2228
3
1 1 7.8591
38.4846
4
119.468
38.7464
5
121.088
39.0082
6
122.7187
39.27
7
124.3605
39.5318
8
126.0131
39.7936
9
127.6766
40.0554
10
129.351
40.3172
II
131.0366
40.579
^3A
132.7326
40.8408
1
134-4398
41.1026
2
136.1578
41-3644
3
137.8868
41.6262
4
139 6267
41.888
5
141-3774
42.1498
6
143-1391
/I2.4116
7
144.91 1 7
42.6734
8
146.6953
42.9352
9
148.4897
43-197
10
150.295
43.4588
II
152. 1 113
43.7206
254 ABBAS AND CIBCUMFEBENCES OF CIBCLSS.
DlAH«
Akca.
CUCUM.
Feet.
Feet.
14 /f-
1539384
43.9824
I
155.7764
44.2442
2
157.6254
44.506
3
159-4853
44.7678
4
161.3561
45.0296
S
163.2378
45.2914
6
165.1303
455532
7
167.0338
45-815
8
168.9483
46.0768
9
170.8736
46.3386
lO
172.8098
46.6004
II
174-7569
46.8622
ISA
176.715
47.124
I
178.684
47.3858
2
180.6638
47.6476
3
182.6546
479094
4
184.6563
48.1712
5
186.6689
48.433
6
188.6924
48.6948
7
190.7267
.48.9566
8
192.7721
49.2184
9
194.8283
49.4802
lo
196.8954
49-742
IT
198.9734
50.0038
it ft.
201.0624
50.2656
I
203.1622
50.5274
2
205.273
50.7892
3
207.3947
51-051
4
2095273
51.3128
5
211.6707
51-5746
6
213.8252
51.8364
7
215.9904
52.0982
8
218.1667
52.36
9
220.3538
52.6218
lO
222.5518
52.8836
II
224.7607
531454 •
17 A
226.9806
534072
I
229.2113
53669
2
231-453
539308
3
233.7056
54.1926
4
2359691
54-4544
S
238,2434
54-7162
6
240.5287
54-978
7
242.8249
55-2398
8
245.1321
55.5016
9
247.4501
557634
i«
-249.779
56.0252
II
252.1188
56.287
i8.A
254.4696
56.5488
I
256.8312
56.8106
2
259.2038
57.0724
3
261.5873
57.3342
4
263.9817
57.596
5
266.3869
' 57-8578
1 DlAM.
AjtSA.
Feet.
6
268.8031
7
271.2302
8
273.6683
1
9
276.1172
10
278.577
II
281.0477
19 A
283.5294
I
286.0219
2
288.5255
3
291.0398
4
293.5651
5
296.1012
6
298.6483
7
301.2064
8
303.7753
9
306.3551
10
308.9458
II
311.5475
20/15.
314.16
I
316.7834
2
319.4178
3
322.0631
4
324.7193
5
327.3864
6
330.0643
7
332.7532
8
335.4531
9
338.1638
10
340.8854
II
343.618
21 A
346.3614
I
349-1157
a
351.881
3
354.6572
4
3574442
5
360.2422
6
363.0511
7
365.8709
8
368.7017
9
371.5433
10
374.3958
II
377.2592
a2/<.
380.1336
I
383.0188
2
385915
3
388.8221
4
391.74
5
394.6689
6
397.6087
7
400.5594
8
403.5211
9
406.4936
10
409.477
II
412.4713
CntovM.
Feet.
58.1196
58.3814
58.6432
58.905
59-1668
59.4286-
59.6904
59-9522
60.214
60.4758
60.7376
60.9994
61.2612
61.523
61.7848
62.0466
62.3084
62.5702
62.832
63.0938
63.3556
63.6174
63.8792
64.141
64.4028
64.6646
64.9264
65.1882
65.45
65.7118
65.9736
66.2354
66.4972
66.759
67.0208
67.2826
675444
67.8062
68.068
68.3298
685916
68.8534
69.1152
69.377
69.6388
69.9006
70.1624
70.4242
70.686
70.9478
71.2096
7-4714
71.7332
71-995
AREAS ATSTD CIBCUHFSBENCBS OF CIBCLES.
255
DiAM.
23 A
I
2
3
4
5
6
7
8
9
10
II
24ft,
I
2
3
4
5
6
7
8
9
10
II
I
2
3
4
5
6
7
8
9
10
II
26A
I
2
3
4
5
6
7
8
9
10
II
I
a
3
4
%
A SB A.
Cntomi.
DiAM.
Aria.
ClBCUM.
Feet.
Feet.
Feet.
Feet.
415.4766
72.2568
6
593.9587
86.394
418.4927
72.5186
7
597-5639
86.6558
421.5198
72.7804
8
601.18
86.9176
424.5578
73.0422
9
604.8071
87.1794
427.6067
73.304
10
608.445
87.4412
430.6664
73.5658
II
612.0938
87-703
4337371
738276
0
28//.
6157536
87.9648
436.8187
74.0894
I
619.4242
88.2266
43991
74-3512
2
623.1058
88.4884
443.0147
74613
3
626.7983
88.7502
446.129
74.8748
4
630.5016
89.012
449.2542
751366
5
634.2159
89.2738
452.3904
753984
6
637.9411
89.5356
455-5374
75.6602
7
641.6772
89.7974
4586954
75922
8
645-4243
90.0592
461.8643
76.1838
9
649.1822
90.321
465.044
76.4456
:o
652.951
90.5828
4682347
76.7074
11
6567307
90.8446
471-4363
474.6488
477.8723
481.1066
484.3518
" 487.6076
76.9692
20 ft.
660.5214
91.1064
77.231
77.4928
77.7546
78.0164
78.2782
I
2
3
4
5
664.3229
668.1354
671.9588
675-7931:
679.6382
91.3682
91.63
91.8918
92.1536
92.4154
490.875
78.54
6
683.4943
92.6772
494.1529
78.8018
7
687.3613
92,939
497.4418
79.0636
8
691.2393
93.2008
500.7416
793254
9
695.1281
93.4626
50*0523
79.5872
10
699.0278
937244
507.3738
79.849
II
702.9384
93.9862
510.7063
514.0485
517.404
520.7693
524.1454
527-5324
80.1108
80.3726
80.6344
80.8962
81.158
81.4198
30/?.
I
2
3
4
5
706.86
710.7924
714 7358
718.6901
722.6553
726.6313
94.248
945098
94.7716
950334
95.2952
95-557
530.9304
816816
6
730.6183
958188
534.5397
81.9434
7
734.6162
96.0806
537-759
82.2052
8
738.6251
96.3424
541.1897
82467
9
742.6448
96.6042
544.6313
82.7288
10
746.6754
96.866
5480837
82.9906
11
7507164
97.1278
551.5471 .
555-0214
5585066
562.0028
5655098
569.0277
83.2524
83.5142
83.776
84.0378
84.2996
84.5614
31 yv.
I
2
3
» 4
5
754.7694
758.8327
762.907
766.9922
771.0883
775.1952
97.3896
97.6514
97.9132
98.175
984368
98.6986
572.5566
84,8232
6
779-3131
98.9604
576.0963
85.085
7
783.4419
99.2222
579.6467
85.3468
8
787.5817
99.484
583.2086
85.6086
9
791-7323
997458
586.781
85.8704
10
795.8938
100.0076
590.3644
86.1322
II
.800.0662
100.2694
256 ABEAS AKD CIBGUHF£BSXCES OF CIBCLBS.
DiAM.
Absa.
CtKctm.
Feet.
Feet.
32 A
804.2496
100.5312
I
808.4439
100.793
2
812.649
101.0548
3
816.8651
101.3166
4
821.092
101.5784
5
825.3299
101.8402
6
829.5787
102.102
. 7
8338384
102.3638
8
838.1091
102.6256
9
842.3906
102.8874
10
846.683
103.1492
11
850.9863
103.41 1
33 A
855.3006
103.6728
I
859.6257
103.9346
2
863.9618
104.1964
3
868.3088
104.4582
4
872.6667
104.72
S
877-0354
104.9818
6
881.4151
105.2436
7
885.8057
105.5054
8
890.2073
105.7672
9
894.6197
106.029
10
899.043
106.2908
II
9034772
106.5526
34 A
907.9224
106.8144
I
912.3784
107.0762
2
916.8454
107.338
3
921.3233
107.5998
4
925.812
107.8616
5
93O.3117
108.1234
6
934.8223
108.3852
7
939-3439
108.647
8
943-8763
108.9088
9
948.4196
109.1706
10
952.9738
109.4324
II
957.5392
109.6942
35 A
962.115
109.956
I
966.7019
110.2178
2
971.2998
1 10.4796
3
975.9086
1 10.7414
4
9805287
111.0032
5
985.1588
111.265
6
989.8005
111.5268
7
9944527
111.7886
8
999.116
112.0504
9
1003.7903
112.3122
xo
1008.4754
"^•574„
II
1013.1714
112.8358
36 A
loi 7.8784
113.0976
X
1022.5962
"3-3594
9
1027.325
113.6212
3
1032.0647
113-883
4
1036.8153
114.1448
5
1041.5767
X 14.4066
DiAM.
Abba.
CiBcim.
Feet.
Feet.
6
1046.3491
114.6684
7
1051.1324
114.9302
8
1055.9266
115.192
9
1060.7318
115.4538
10
1065.5478
115.7156
II
1070.3747
115.9774
37 A
1075.2126
116.2392
I
1080.0613
116.501
2
1084.921
116.7628
3
1089.7916
117.0246
4
1094.6731
117.2864
5
1099-5654
117.5482
6
1104.4687
117.81
7
1109.3829
118.0718
8
1114,308
118.3336
9
11 19.2441
1185954
10
1124.191
118.8572
11
1 129.1489
119.119
38A
II34.II76
1193808
1
1139.0972
119.6426
2
1144.0878
119.9044
3
1149.0893
120.1662
4
1154.1017,
120.428
5
1159.1249
1206898
6
1164.1591
120.9516
\ 7
1 169.2042
I2I.2134
8
II74.2O03
121.4758
9
11793272
121.737
10
1184.405
121.9988
11
1189.4937
122.2606
39A
"94.5934
122.5224
1
1199.7039
122.7848
2
1204.8254
123.046
3
1209.9578
123.3078
4
1215.101
1235696
5
1220.2552
123.8314
6
1225.4203
124.0932
7
1230.5963
124.355
8
1235-7833
124.6168
9
1240.9811
124,8786
10
1246.1898
125.1404
11
1251.4094
125.402a
40 A
1256.64
125.664
I
1 261 .88 14
125.9258
2
1 267. 1338
126.1876
3
1272.3971
126.4494
4
1277.6712
126.7113
5
1282.9563
ii6.973
6
1288.2523
127.2348
7
1293-5592
127.4966
8
1298.877
127-7584
9
1304.2058
1280203
10
1309-5454
128.383
II
1314-8959
128.5438
ABEAS AKD ClBOtJMFSSSNCBS OF CIRCLES. 2^7
DUM.
41 A
I
2
3
4
5
6
7
8
9
10
II
42 A
I
2
3
4
5
6
7
8
9
10
II
I
2
3
4
5
6
7
8
9
10
II
44 A
I
2
3
4
5
6
7
8
9
10
II
45 A
I
2
3
4
5
Abia.
320.2574
325.6297
331 013
336.4072
341.8123
347.2282
352-6551
358.0929
363.5416
369.0013
374.4718
3799532
385.4456
390.9488
396.463
401.9881
407.5241
4130709
418.6287
424.1974
429.777
4353676
440969
446.5813
452.2046
4578387
4634838
469.1398
474.8066
480.4844
486.1731
491.8717
4975833
5033047
509037
514.7802
520.5344
526.2994
532.0754
537.8623
543-66
549.4687
5552883
561.1188
566.9603
572.8126
578.6756
584.5499
590.435
596.3309
602.2378
608.1556
614.0843
620.0238
CmcvM.
Feet.
28.8056
29.0674
29.3292
29.591
29.8528
30.1146
30.3764
30.6382
309
31.1618
31.4236
31-6854
31-9472
32.209
32.4708
32.7326
329944
332562
33518
33-7798
34.0416
34-3034
34-5652
34.827
350888
35-3506
35.6124
35.8742
36.136
36.3978
366596
36.9214
37.1832
37-445
37.7068
37.9686
38.2304
38.4922
38.754
390158
39.2776
39 5394
39.8012
40.063
40.3248
40.5866
40.8484
41.1102
41-372
41.6338
41.8956
42.1574
42.4192
42.681
Y*
Duif.
Ab«a.
CisaDM.
Feet.
Feet.
6
1625.9743
142.9428
7
163I.9357
143.2046
8
1637.9081
143.4664
9
1643.8913
143-7282
10
1649.8854
143.99
II
1655.8904
144.2518
46A
1661.9064
144.5136
I
1667.9332
144-7754
2
1673.971
1450372
3
1680.0197
145.299
4
1686.0792
145.5608
5
1692. 1 497
145.8226
6
1698.231 1
146.0844
7
1 704.3195
146.3462
8
1 710.4267
146.608
9
1716.5408
146.8698
10
1722.6658
147.1316
11
1728.8017
147-3934
47 .A
1734.9486
147-6552
I
1 741. 1063
147917
2
1747275
148.1788
3
1753-4546
148.4406
4
1759-6451
148.7024
5
1765.8464
148.9642
6
1772.0587
149.226
7
1778.2819
149.4878
8
1784.516
149-7496
9
1 790.761 1
150.0114
10
1797.017
150.2732
II
1803.2838
150.535
48 A
1809.5616
150.7968
I
1815.8502
151.0586
2
1822.1498
151-3204
3
1828.4603
151.5822
4
1834.7817
151.844
5
184I.II39
152.1058
6
1847.4571
152.3676
7
1853.81 12
152.6294
8
1860.1763
152.8912
9
1866.5522
153153
10
1872.939
153-4148
11
1879-3367
153 6766
49/'-
1885.7454
1539384
I
1892.1649
154.2002
2
1898.5954
154 462
3
19050368
154-7238
4
191 1. 4897
154-9856
5
I917.9522
1552474
6
1924.4263
1555092
7
1930.91 13
155-771
8
1937-4073
156.0328
9
1943.9142
156.2946
10
1950.4318
156.5564
II
1956.9604
156.8182
SoA
1963.5
157-08
ijS 8IDBB OF BQUAABS BQUAl, TO ABEA8.
Sides of SQiiares— eQtial in Area to a C:
if I
SU.DrSq.
Diua.
Sl*..rfSq.
.8863
"4
12.4072
..T078
a
X
12.8503
1.5509
K
i3-07'8
'3,,
I3.»934
H
'3-S'5
2.^,56
S
13.7365
13-9581
^.6587
16
14-1796
i.ma
)i
14.4012
3.1018
H
.4.6237
%
14,8443
3-5449
'7
15.0659
3.766s
15.3874
4.2096
■5.7305
iS
'5-9531
4-65a7
16.. 736
4.87+3
s
.6.39SI
5.0958
16.6168
5.3' 74
19
1&8383
t^
I
17.0599
17.2814
5^
6.2036
x>
1 7- 7*45
64151
X
■ 7-946.
6.6467
K
18..677
6.8683
H
.8.3893
7.0898
H
18JI333
7S3»9
^
19^539
7.7545
H
.9.3754
7.976
■9497
8.1976
■9.7185
8^6407
i
30.1617
8.8623
=3
=0.3833
9.0838
H
ao.te48
9.3054
^
20.8263
9.5369
3I.04J9
97485
31.3694
9-97
H
21.491
10,4132
I
21.7126
31.9341
10.6347
»5
10-8563
H-
32.3772
11.0778
H
33.5988
11.3994
%
333303
11.5309
36
23.0419
33.3634
i.W
i
=3.485
ia.1856
33.7066
814..(S,-
PUoi.
33-9381
40
24.1497
K
'.<
34:59^8
%
34.8144
41
35-0359
H
35,3575
H
35-479
K
25.7006
35,9321
a
=6.1437
a
36.,i653
36.5868
43
26.8084
¥
27.0299
37473
37-6M6.
27-9161
28.1377
$
38-3593
38.580S
28,8024
i
29.0339
29467
39.6886
30.1317
47
30-3533
}i
30-5748
30.7964
g
3..0.79
48
31-3395
31.4611
31.6836
i
31.9043
49
33.1357
33^5688
8
33.790*
33-0.. 3
33-4551
8
33.6766
51
33-8983
34.1197
M
34-3413
34-5638
53
34-7884
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35-006
a
35.3375
35-4491
35-6706
358933
36-1137
36-3353
36-5569
36.7784
40.3333
40.5449
40.7664
43.3036
434351
43.6467
43-8683
44.976
45- ■976
45 4^ 9'
456407
45.8633
46.0838
46-3054
46.5369
46.74SS
SIDES OF SQUABES EQUAI. TO ABBAS.
259
Dlam. I Side of Sq.
53
46.97
}i
47.1916
%
47.4131
%
47-6347
54
47.8562
K
48.0778
M
48.2994
%
48.5209
55
48.7425
yi
48.964
^
49.1856
%
49 4071
5^.
49.6287
^
49-8503
n
50.0718
H
50.2934
57,
50.5149
H
50.7365
^
50958
H
51-1796
58 .
51.4012
X
51.6227
K
51.8443
9i
52.0658
59,
52.2874
H
52.5089
^
52.7.305
5i
52.9521
60
53.1736
)^
533952
K
536167
5i
53 8383
61
540598
3i
54-2814
K
54503
H
54-7245
62
54.9461
K
55.1676
K
553892
%
55 6107
63
55.8323
H
56.0538
K
56.2754
?i
56.497
64
56.7185
^
56.9401
K
57.1616
%
573832
[1 Dlam.
Sid«ofSq.
1 65
576047
H
57.8263
H
58.0479
%
58.2694
66
58.491
H
58.7125
}4
58.9341
%
59.1556
67
59.3772
59.5988
}4
59.8203
%
60.0419
68
60.2634
yi
60.485
}4
60.7065
H
60.9281
69
61.1497
H
61.3712
K
61.5928
%
61.8143
70
62.0359
3^
62.2574
K
62.479
%
62.7006
71
62.9221
X
63.1437
K
63.3652
%
635868
72
63.8083
H
64.0299
X
64.2514
H
64.4730
73
646946
H
64.9161
: H
65.1377
%
65.3592
74
65.5808
H
65.8023
I i^
66.0239
1 %
66.2455
1 75
66.467
1 H
66.6886
, K
66.9104
^
67.1317
7^,.
67.3532
3^
67.5748
K
67.7964
' %
68.0179
Diam.
77
^
M
78
79.
80
81
82
%
83
84
8s
3^
86
87
88
3^
SIdAofSq.
68.2395
68.461
68.6826
68.9041
69.1257
69-3473
69.5688
69.7904
70.01 19
70.2335
70.455
70.6766
70.8981
71.1197
71.3413
71.5628
71.7844
72.0059
72.2275
72.4491
726706
72.8921
73.1137
73.3353
73.5568
73.7784
73.9999
74.2215
74.4431
74.6647
74.8862
75.1077
75.3293
75.5508
75.7724
75-9934
76.2155
76.4371
76.6586
76.8802
77.1017
773233
77.5449
77.7664
77.988
78.2095
78.4316
78.6526
Dlam.
8ld«orSq.
89
78.8742
K
79.0957
K
793173
%
79.5389
90
79.7604
X
79.982
K
80.2035
%
80.4251
91
80.6467
H
80.8682
K
81.0898
H
81.31 13
^..
81.5329
U
81.7544
H
81.976
%
82.1975
93_
82419I
K
82.6407
K
82.8622
%
83.0838
94
83.3053
83.5269
)?
83.7484
^
83.97
95 .
84.1916
3^
84.4131
K
846347
%
848562
96
85.0778
3^
85.2993
3^
85-5209
%
85.7425
97 ,
85.9646
3^
86.185
>^
86.4071
^i
86.6289
98,.
86.8502
K
87.0718
M
87.2933
%
87.5449
^w
87.7364
3^
87.958
%
88.1796
%
88.4011
100 ! 88.6227
^Application of Tal>le.
Q?o A.0oertain. a Square tliat lias same A.rea as a d-iven
Cirole.
Illus.— If side of a square that has same area as a circle of 73. 25 ins. is required.
By Table of Areas, page 233, opposite to 73.25 is 42x4.11; and io this Uble is
64.9161, which is side of a square haying same area as a circle of that diameter.
266
LENGTHS OF OIBCULAB ABC&
Lengtlis of Circu-lar -A.rcs, lap to a Seiiiioircle.
Diameter of a Circle = i, and divided into looo equai Parts,
H'ght.
.1
.lOI
,102
.103
.104
.105
.106
.IQ7
.loS
.109
.11
.III
.112
"3
.1x4
.1x6
.117
,118
.119
.12
.121
,122
.123
.124
.125
.126
.127
.128
.129
•13
•131
.132
•133
■134
•13s
.136
•137
.138
•139
.14
.141
.142
•143
.144
•1451
,146
.147
.148
.149
Length.
.02645
.02698
.02752
.02806
.0286
.029 14
.0297
.030 26
.03082
•03-39
.03196
.03254
.03312
■03371
.0343
•0349
•03551
.036 1 1
.036 72
•03734
•03797
.0386
•03923
.03987
.04051
.041 16
.04181
.04247
•043 13
.0438
.04447
•04515
.04584
•04652
.04722
.04792
.04862
.04932
.05003
•05075
.05147
.0522
.05293
.05367
.05441
.055 16
•05591
.05667
.05743
•Q5319
H'ght.
5
51
52
53
54
55
56
57
58
59
6
61
62
63
64
65
66
67
68
69
7
71
72
73
74
75
76
77
78
79
8
81
82
83
84
85
86
87
88
89
9
91
92
93
94
95
96
97
98
?99
Length.
H'ght. 1
1.05896
.2
1.05973
.201
1
1.06051
.202 '
I.0613
.203
1.06209
.204
1.06288
.205
1.06368
.206
1.06449
.207
1.0653
.208
1.066 1 1
.209
1.06693
.21
1.06775
.211
1.06858
.212
1. 069 41
.213 1
1.07025
•214 1
I.O7109
.215
I.07194
.216
1.07279
.217
I •073 65
.218
1.074 5 1
.219
1.07537
.22
1.07624
.221
1.077 11
.222
1.07799
.223
1.07888
.224'
1.07977
.225
1.08066
.226
1.08156
.227
I 08246
.228
108337
.229
1.08428
.23
1.085 19
.231
1.086 11
.232
1.08704
•233
1.08797
•234
1.0889
•235
1.08984
.236
1.09079
.237
1.091 74
.238
1.09269
.239
1.09365
.24
1.09461
.241
109557
.242
1.09654
.243
1.09752
.244
10985
•245
1.09949
.246
1. 100 48
•247
1. 101 47
.248
f. 109 47
.949
0348
0447
0548
065
0752
0855
0958
1062
1165
1269
1374
1479
1584
1692
1796
1904
20II
21 18
2225
2334
2445
2556
2663
2774
2885
2997
3108
3219
3331
3444
3557
3671
3786
3903
402
4136
4247
4363
448
4597
4714
4831
4949
5067
5186
5308
5429
5549
567
5791
H'ght.
Length.
25
251
252
253
254
255
256
257
258
259
26
261
262
263
264
265 I
2661
267 I
268,
269
27
271
272
273
274
275
276
277
278
279
28
281
282
283
284
^85
286
287
288
289
29
291
292
293
294
29s
296
297
298
299
.15912
.16033
.161 57
.16279
.16402
.16526
.16649
.16774
.16899
.17024
•1715
.17275
.17401
.17527
•17655
•17784
.17912
.1804
.18162
.18294
.18428
•18557
.r8688
188 19
.18969
.19082
.19214
•19345
19477
.1961
•19743
.19887
.20011
.201 46
.20282
.20419
.20558
.20696
.20828
.20967
.21202
.21239
.21381
.2152
.21658
.21794
.21926
.22061
.22203
.823471
H'ght. I Length.
3
301
302
303
304
305
306
307
308
309
31
311
312
313
314
315
316
317
318
319
32
321
322
323
324
325
326
327
328
329
33
331
332
333
334
335
336
337
338
339
34
341
34a
343
344
345
346
347
348
349
2249s
22635
22776
22918
23061
23205
23349
23494
23636
2378
23925
2407
24216
2436
24506
24654
24801
24946
25095
25243
25391
25539
25686
25836
25987
26137
26286
26437
26588
2674
26892
27044
27196
27349
27502
27656
2781
27964
28118
28273
28428
28583
28739
2889s
29053
29209
29366
29523
29681
29839
LENGTHS OF OlBCULAB ABCS.
261
H'gbt
.35
.351
.352
.353
•354
.355
.356
.357
.358
359
36
.361
.362
•364
•365
.366
•367
368
•369
37
371
372
•373
•374
•375
^76
377
•378
•379
Langth.
29997
301 56
30315
30474
30634
30794
30954
3" 15
31276
31437
31599
31761
31923
32086
32249
32413
32577
32741
32905
33069
33234
33399
33564
3373
33896
34063
34229
34396
34563
34731
H'Rht.
Length.
38
381
382
383
384
385
386
387
388
389
39
391
392
393
394
395
396
397
398
399
4
401
402
403
404
405
406
407,
408
•409 1
34899
35068
35237
35406
355 75
35744
35914
36084
36254
36425
36596
36767
36939
371 II
37283
37455
37628
37801
37974
38148
38322
38496
38671
38846
39021
39196
39372
39548
39724
399
H'glit.
41
411
412
413
414
415
416
417
418
419
42
421
422
423
424
425
426
427
428
429
43
431
432
433
434
435
436
437
438
439
Leogth.
40077
40254
40432
4061
40788
40966
41145
41324
41503
41682
41861
42041
42222
42402
42583
42764
42945
43127
43309
43491
43673
43856
44039
44222
44405
44589
44773
44957
45142
45327
H'^ht.! Lengtb.
44
441
442
443
444
445
446
447
448
449
45
451
452
453
454
455
456
457
458
459
46
461
462
463
464
465
466
467
468
469
46512
45697
45883
46069
46255
46441
46628
46815
47002
47189
47377
47565
47753
47942
48131
4832
48509
48699
48889
•49079
.49269
.4946
•49651
•49842
•50033
.50224
.504 16
.50608
.508
.50992
H'ght.
47
471
472
473
474
475
476
477
478
479
48
481
482
483
484
485
486
487
488
489
49
491
492
493
494
495
496
497
498
499
5
Lengtii.
.51185
.513 78
.51571
.51764
.51958
.521 52
.52346
.52541
.52736
•52931
.531 26
.53322
•535 18
•537 14
•5391
.54106
•54302
.54499
.54696
.54893
.5509
.55288
•55486
•55685
•55854
.56083
.56282
.56481
.5668
.56879
.57079
Xo -A-scertain. Ijength. of an Arc of a Circle "by pre-
ceding Talkie.
Rule. — Divide height by base, find quotient in colamn of heights, take
len^h for that height opposite to it in next column on the right hand.
Multiply length thus obtained by base of arc, and product will give length.
Example —What is length of an aro of a circle, base or span of it being 100 feet,
and height 25?
25-r-ioos=.a^; and .25, per table, = 1.15912, length ofbase^ which^ multiplied by
lao — iis.gi2 Jeet.
When, in division of a height by baae^ the ^otierU has a remainder after
third place of decimals^ and great accura:cy w required.
Rule.— Take len^ for first three figures, subtract it from next following
length; multiply remainder bv this Pactional remainder, add product to
first length, and sum will give length for whole quotient
Example.— What is length of an arc of a circle, base of which is 35 feet, and
height or versed sine 8 feet?
8-5-35-^.2285714; tabular length for .228 = x. 133 31, and for -229 = 1.13444,
Vie difference beboeen wfticA is . 001 13. Then . 571 4 x .001 13 = . 000 645 682.
Hence .228 = 1. 133 31,
and .0005714= .000645682
X- «33 955682, the sunn by which b€Ue 0/
ore is to be multiplied ; and 1.133955683 X 35 =^39. 688 45 ^eet
262
LENGTHS OF CIRCULAR ARCS.
XjengtHs of Ciroular Arcs fl-om 1° to lSO«.
' {Radius^ %.)
.legrtiM.
1
3
3
4
5
6
7
8
9
lO
II
I?
13
14
IS
i6
17
i8
19
20
21
22
23
24
35
26
27
28
29
30
31
33
33
34
35
36
37
38
39
40
41
42
43
44
45
L«qgth.
.0174
.0349
.0524
.Q698
•0873
.1047
.T222
.1^96
•157*
•1745
.192
.2094
.2269
•2443
.2618
.2792
•3967
•3141
.3316
.3491
.3665
.384
.4014
^4189
4363
•4538
.4712
.4887
.5061
•5236
.541
•5585
•5759
•5934
.6109
.6283
.6458
,6632
.6807
.6981
•7156
•733
•7505
.7679
.7854
DefprMt.
46
47
48
49
50
S«
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
LeDgth.
.8028
.8203
.8377
.8552
.8727
.8901
.9076
.925
.9424
•9599
.9774
,9948
.0123
.0297
•0472
.0646
,0821
:0995
.117
•1345
•1519
.1694
.1868
.2043
.2217
.2392
.2566
.2741
.2915
•309
.3264
.3439
•3613
•3788
•3963
•4137
•4312
.4486
.4661
4835
.501
.5184
'5359
•5533
•5708
Degre«a.
Length.
91
1.5882
92
1.6057
93
1 6231
94
1.6406
95
1. 6581
96
1-6755
97
1.693
98
1.7104
99
1.7279
100
1-7453
101
1.7628
102
1.7802
103
1-7977
104
1.8151
los
1.8326
106
1.8s
107
1.8675
108
1.8849
109
1,9024
110
1.9199
III
1-9373
112
1.9548
"3
1.9722
114
1.9897
115
2.0071
116
2.0246
117
2.042
118
2.0595
119
2.0769
190
2.0944
121
2.1118
122
2.1293
123
2.1467
124
2.1642
125
2.1817
126
2.1991
127
2.2 166
128
2.2304
129
22515
130
^.2689
131
132
2.286d
2.303S
^33
2.3313
134
2.3387
135
2.356a
PegroM.
Length.
136
2.3736
137
2.39"
138
2.4085
139
2.426
140
2^435
141
2.4609
142
2.4784
143
24958
144
25133
145
25307
146
2.5483
147
25656
148
2.5831
149
2.6005
150
2.618
151
2.6354
152
2.6539
153
2.6703
154
2.6878
155
2-7053
156
3. 722 7
157
2.7403
158
2.7576
159
2-7751
160
3.7935
161
3.81
162
3.8374
3.8449
3.8633
3.879«
3.8972
2.9147
2.9331
3.9496
170
171
2.967
2.9845
173
3003
173
174
30194
3.0369
175
176
177
178
30543
3-0718
3-0893
3.1067
179
180
3-1241
3.1416
To iVaoertaln Lenstli of a Cirovilar Aro by Table.
Rule. — Prom column opposite to degrees of arc, take length, and multli
ply it by radius of circle.
EJ(AMrLK.>-Nainber of degrees In ^n arc are 4s<', and diameter of circle 5 feet
Then .7854 Ub. length x 5-^ a s= t'^35,^*^
LENGTHS OF ELLIPTIC ARCS.
263
Len^tlis of EJlliptio A.ros.
Up to a Semi-eUipse*
Transffene Diameter z^i, and divided into 1000 equal Parts,
^'ght.
Length. IjH'ght
.1 1.04^62
.101 1.04262
.102 * 1.04362
.103 ' 1.04462
.104 1.04562
.105 1.04662
.106 1.04762
.107 I.Q4862
.108 1.04962
.109 1.05063
.II 1.05164
.III 1.05265
.112 1.05366
.113 1-05467
.114 I 1.05568
.115 , 1.05669
.116 I 1.0577
.117 I 1.05872
.118 1.03974
.119 1.06076
.12 1.06178
.121 ' 1.0628
.122 1.06382
.123 1.06484
.124 1.06586
.125 1.06689
.126 1.06792
.127 1.06895
.128 I.0699S
.129 1. 07001
.13 1.07204
.131 1.07308
.132 1.074 12
.133 1.07516
.134 1.07621
.135 1.07726
.136 1.07831
.137 1.07937
.138 1.08043
.139 1. 081 49
.14 1.08255
.141 1.08362
.142 1.08469
.143 108576
.144 1.08684
.145 1.08792
.146 1. 08901
.147 1.0901
.148 1. 091 19
•149 1.09238
IS
151
152
153
154
155
156
157
158
159
16
161
162
163
164
165
166
167
168
169
17
171
172
173
174
175
176
177
178
179
18
181
182
183
184
18s
186
187
188
1851
19
191
192
193
194
195
196
197
198
^99
L«|f«>.
0933
09448
09558
09669
0978
09891
10002
101 13
10224
10335
10447
1056
10672
10784
10896
11008
1II2
11232
"344
11456
11569
11682
"795
11908
1302I
12134
12247
1236
12473
12586
12699
12813
12927
I3O4I
131 55
13269
13383
13497
136 II
13726
13841
13956
14071
14186
14301
144 16
145 31
14646
14762
14888
H'jfM.
2
201
202
203
204
205
206
207
208
209
21
211
212
213
214
215
216
217
218
219
22
221
222
223
224
225
.226
227
228
229
23
231
232
233
234
235
236
237
238
239
24
241
242
243
244
24s
246
247
248
249
Leairth.
SO 14
51 31
5248
5366
5484
5602
572
5838
5957
6076
6196
6316
6436
6557
6678
6799
692
7041
7163
7285
7407
7529
7651
7774
7897
802
8143
8266
839
8514
8638
8762
8886
901
9134
9258
9382
9506
963
9755
988
20005
2013
20255
2038
20506
20632
20758
20884
2101
H'ght.
25
251
252
253
254
255
256
257
258
259
26
261
262
263
264
265
266
267
a68
269
27
271
272
273
274
275
276
277
278
279
28
281
282
283
284
285
286
287
288
289
29
291
292
293
294
295
296
297
298
«99
Lmfctb.
21136
21263
2139
215 17
21644
21772
219
22628
22156
22284
22412
22541
2267
22799
22928
23057
23186
23315
23445
23575
23705
23835
23966
24097
24228
24359
2448
24612
24744
24876
.2501
.25142
.252 74
.25406
•25538
.2567
.25803
•25936
.26069
.26202
•26335
.26468
.26601
•26734
.26867
.27
•27133
.27267
.27401
•2753s
H'ghL
3
301
302
303
304
305
306
307
308
309
31
3"
312
313
3H
315
316
317
318
319
32
321
322
323
324
32s
326
327
328
329
33
331
332
333
334
335
336
337
338
339
34
341
342
343
344
345
346
347
348
349
Lenglb.
[.27669
f. 278 03
•27937
[.28071
.28205
•28339
[.28474
1.28609
:.28744
.28879
.29014
.29149
t. 292 85
.29421
.29557
[.29603
[.29829
.29965
[.30102
C.30239
[.30376
•305 13
[.3065
[.30787
•30924
[.31061
[.31198
•31335
•31472
[•3161
[.31748
[.31886
.32024
[.32162
•323
f.32438
t.32576
•32715
^3^854
•32993
•33132
•33272
•33412
•33552
.33692
^338 33
•33974
•34115
34256
•34397
LENGTHS OF ELLIPTIC ABCB.
I H'||hl.l Lnip>. ||H-.hl. Lnga. II
1.34681 1
1-348=3; ■
'■34965 .
1.351 oS|
'■3S394 .
'-35537 .
'■38439' ./
'■38s 85, .<
I^3S73'| -1
■.38879' -1
1 ■52074
■5=384!
'■52539
1.52691
'■53937
1-54093
■-54=49
1.54403
I-S4S6l;
1.54718
1-54875'
'-5503=
i.56iS9
1^5^47
1.56605
'■56763
.403 1.42092 ' ,
H'gH.
u«u,. 1
-515
1,59408 1
■5'(>
'■59564
-517
'■597= '
.518
'.59876;
■519
1.60032 '
I.6018SI
■ 52.
'■60344
■522
'■60s 1
1.60656 1
■5=4
1.60812 :
1.60968 '
■5=6
1.6TI94
■527
-528
I.61436 !
■5=9
1.61592
53
1.61748
1.61904
532
533
'■632161
'■6=3 7= 1
535
i.6as=a
536
1.62684 '
537
1.62S4 <
538
1.62996,
539
r63iS2
54
i^63309
541
"■6346s
163623
543
■ ■6378
544
163937
545
1.64094
546
■.64251
1,64408
548
i.&tS65
1.647==
1.6,879
551
1-65036
1.65193
353
1-6535
554
1.65507 I
555
..65665
556
1.658=3!
5S7
1.6598.1
SS8
'.66.39
559
1.66297!
56
'.664SS
561
',666.3,
562
1.66771 ,
5^3
..66929 !
564
1.67087,:
565
1.67245 1 -
5«
1.67403
567
1.67561 .
568
1.67719
569
1.67877,1.
1 ■69467
1.69626
1.69785
'-69945
1.701 05
1.70264
1.70424
1.70584
1.70745
1,70905
■ ■71065
1.7.225
.595 1.72029
1.74283
1.74444
1. 7460s
1.74767
1.74929
1.75091
1-75252
LENGTHS OP ELLIPTIC ABCS.
265
H'ghi.
.625
•626
.628
.629
.63
.631
.632
.633
.634
.636
.637
.638
.639
.64
.641
.642
.643
.644
•645
.646
.647
.648
.649
.65
.651
.652
.653
.654
.655
.656
.657
.658
.659
.66
.661
J662
.663
.664
.665
.666
.667
.668
.669
.67
.671
.672
•673
.674
.675
.676
.677
J678
^9 1
Length.
76872
77034
77197
77359
77521
77684
77847
78009
781 72
78335
78498
7866
78823
78986
79149
79312
794 75
70038
79801
79964
80127
8029
80454
80617
8078
80943
811 07
812 71
81435
81599
81763
81928
82091
82255
82419
82583
82747
829 II
83075
8324
83404
83568
83733
83897
84061
84226
84391
84556
8472
84885
8505
85215
85379
85544
^5709
H'ght.
68
681
682
683
684
685
686
687
688
689
69
691
692
693
694
695
696
697
698
699
7
701
702
703
704
705
706
707
708
709
71
711
712
713
714
715
716
717
718
719
72
721
722
723
724
725
726
727
728
729
73
731
732
733
734
Leni^h.
85874
86039
86205
8637
86535
867
86866
87031
87196
87362
87527
87693
87859
88024
8819
88356
88522
88688
88854
8902
89186
89352
89519
.89685
89851
90017
90184
9035
90517
90684
90852
910 19
,91187
91355
91523
916 91
91859
92027
92195
92363
92531
927
92868
93036
■93204
93373
93541
9371
93878
94046
94215
94383
94552
94721
9489
H'ght.
735
736
737
738
739
74
741
742
743
744
745
746
747
748
749
75
751
752
753
754
755
756
757
758
759
76
761
762
763
764
765
766
767
768
769
77
771
772
773
774
775
776
777
778
779
78
781
782
783
784
785
786
787
788
789
Length. H'ght.
95059
95228
95397
95566
95735
95994
96074
96244
96414
96583
96753
96923
97093
972 62
97432
97602
97772
97943
981 13
98283
98453
98623
98794
98964
99134
9930s
99476
99647
99818
99989
0016
00331
00502
00673
00844
010 16
01 1 87
01359
015 31
01702
01874
02045
02217
02389
02561
02733
02907
0308
03252
03425
03598,:
03771 1 [
03944'
041 17!
0429 1 1
Length.
79 2.04462
791 2,04635
792 2.04809
793 1 2.04983
794 2.05157
795 2.05331
796 2.05505
797 2.05679
798 2.05853
799 2.06027
,8 2.06202
8oi 2.06377
,802 2.06552
,803 2.06727
,804 2.06901
,805 2.07076
,806 2.07251
807 2.07427
,808 2.07602
,809 2.07777
,81 2.07953
811 2.08128
812 2.08304
813 2.0848
814 1 2.08656
,815 '2.08832
,816 2.09008
,817 ; 2.091 98
818 2.0936
819 2.09536
82 2.097 12
821 2.09888
,822 2.10065
823 2.10242
,824 2.104 19
,825 2.10596
826 2.10773
,827 2.1095
,828 2.1 II 27
,829 2.1 13 04
83 2.1 14 81
,831 2.1 16 59
,832 2. 1 18 37
833 2.12015
,834 2.12193
.835 2.123 71
.836 2-12549
,837 2.12727
,838 2.12905
839 2.13083
84 2.132 61
841 2.13439
842 2.136 18
843 2.13797
,84412.13976
H'ght. Lnigth.
845
846
847
848
849
85
851
852
853
854
855
856
857
858
859
86
861
862
863
864
865
866
867
868
869
87
871
872
873
874
875
876
877
878
879
88
881
882
883
884
885
886
887
888
889
89
891
892
893
894
895
896
897
898
899
4155
4334
4513
4692
4871
505
5229
5409
5589
57 7
595
613
6309
6489
6668
6848
7028
7209
7389
75 7
7751
7932
81 13
8294
8475
8656
8837
9018
92
9382
9564
9746
9928
201 1
202 92
20474
20656
20839
21022
21205
21388
21571
21754
21937
221 2
22303
22486
2267
22854
23038
23222
23406
2359
23774
23958
e66
LPKGTHS OF EI.UPTIC A^CS.
ft'gbt.
Lenprth.
H'ght
L«|igth.
H'gbt
•94
Length.
H'ght.
I/engtb.
H'gbt.
•9
2.241 42
.92
2.27803
2.31479
2.31666
.96
235241
.98
.901
2.24325
.921
2.27987
.941
.961
2.35431
.981
.902
2.24508
.922
2.281 7
•942
2.31852
.962
2.35621
.982
•903
2.24691
•923
2.28354
•943
2.32038
.963
2.3581
.983
.904 , 2.248 74
.924
2.28537
•944
2.322 24
.964
2.36
.984
.905 2.25057
•925
2.287 2
•945
2.32411
.965
2.361 91
.985
.906 , 2.2524
.926
2.28903
946
2.32598
.966
2.36381
.986
.907 '2.25423
•927
2.29086
•947
2.32785
•967
2.36571
.987
.908 . 2.25606
.928
2.2927
.948
2.32972
.968
2.36762
.988
.909 2.25789
.929
2.29453
•949
2.3316
•969
2.36952
.989
•99
•991
.91 2.25972
.93
2.29636
•95
2.33348
•97
2.37143
.911 2.26155
•931
2.2982
•951
2.33537
.971
237334
.992
.912 2.26338
.932
2.30004
•952
2.33726
•972
2.37525
•993
.913 12.26521
•933
2.30188
•953
2.33915
.973
2.377 161 .994
.914 2.26704
•934
2.30373
■954
2.34104
•974
2.37908 .99s
.915 2.26888
•935
2.30557
•955
2.34293
•975
2.381
.996
.916 2.27071
•936
2.30741
.956
2.34483
•976
2.382 9J
•997
.917 12.27254
•937
2.30926
.957
234673
•977
238482
•998
.918 2.27437
•938
2.31 1 II
.958
2.34862
•978
2.38673
•999
.919
2.2762 ■
•939
2.31295
•959
2.35051
•979
2.38864
I.
2.3905s
2.39247
2.39439
2.39631
2.39^23
2.^00 16
2.40208
2.404
2.40593
2.407 84
2.409 76
2.4II09
2.41362
2.41556
2.41749
2.41943
2.42136
2.42329
2.425 23
2.427 15
2.42908
To A.8oerta.in. i^ength of a,xi B^lliptic A.ro (right Bemi-
S^llipee) "by preceding Table.
KuLK. — Divide heif^ht by base, find quotient in column of heists, and
take len«?th for tliat height from next right-hand column. Multiply length
thus obtained by base of arc, and product vil) give length.
Example.— What is length of arc of a semi-ellipse, base being 70 feet, and height
30.10 feet?
30. ID -4- 70 = . 43 ; and 43, per <ab2^ = X. 463 68.
.Then 1.46268 x 70 = 102.3876/56^
When Curve is not thai of a right Semi-EUipse^ Height being half of Trans-
verse Diameter.
Rui.K. — Divide half base by twice height, then proceed as in prexseding
example ; multiply tabular length by twice hei^t, and product will give
length.
ExAHPLis.— What is length of arc of a seroi-eUipse, height being 35 feet, and base
60 feet ?
Lenjftli.
60 -j- 2 = 30, and 30 -4-35X2 = . 428, tcUnUar Ungth qfwkick = i. 459 66.
Then 1.45966 X 35 X 2 = 102. 1762/584.
When^ in Division of a Height by Base, Quotient bat a Remainder after
third Place of Decimals, and great A ccuracy is required,
Rule.— Take length for first three figures, subtract it from next following
length ; multii^ly remainder bv this fractional remainder, add product to
first length, and sum will give length for whole quotient
Example. —What is length of an arc of a semi-ellipse, base being 171. 9 feet aai
height J 25 feet?
171.3-7-2 = 8565. an* i2SX2 = a5a 85.65 -7-250 = . 3426 : tabuUxr length Jvr
342 = J. 334 12, and for .343 = 1.335 52, the difference between which is .0014.
Then .6 x -0014 = .0084.
Hence, .342 =1.33412
.0006= .0084
•.* I. ,*. f .J J t3A^59jhe sum, bffwkUh bate qfwre
utohe muUtplted ; and 1.343 5a X 171.. 3 = 239.973 676/wt
AKKAS OF SEGMENTS OF A CIRCLE.
267
A.reas of* Sesznents of a Circle.
The Diameter of a Circle ss i, and divided into 1000 equxsi Parts.
V«nMl
SiiM.
.001
•002
003
.004
005
006
007
.008
.009
01
.Oil
oia
013
.014
.015
.016
.017
.018
.019
.02
.021
.022
.023
.024
.025
.026
.027
.028
.029
•03
•031
•032
•033
034^
•035
.036
•037
038
•039
•<H
.041
.042
.043
.044
045
.046
.047
.048
•049
•05
^51
V«Md
S«g. ArM.
Slno.
8«f. ArM.
.cx>oa4
.052
.01556
.00012
•053
.01601
.00022
.054
.01646
.0U034
.055
.01691
.00047
.056
.01737
.00062
.057
.01783
.00078
.058
.0183
.00095
•059
•OJ877
.00113
.06
.01924
.001.13
.061
.019 72
.001 53
.062
.0202
•0017s
.063
.02068
.00197
.064
.021 17
.0022
.065
.02165
.00244 ,
.066
.02215
.00268
.067
.02265 ,
.00294
.068
.023 IS 1
•0032
.069 .02366 i
00347
.07
02417
.003 75 1
.071 .02468
.004031
.072
.025 19
.00432
.073
.02571
.00462
.074
.02624
.00492
•075
.02676
•00523,
.076
.02729
.00555
.077
.02782
-00587
.078
.02835
.00619
.079
.02889
.00653
.c3
.02943
.00686
.081
.02997
.00721
.082
.03052
.00756
.083
.031 07
.00791
.084
.03162
.00827
.085
.03218
.00864
.086
.03274
.00901
xA^
.0333
.00938
x>88
.03387
.00976
.089
.03444
.01015
.09
.03501
.01054
.091
•03558
.01093
.092
.036 16
.01133
.093
.03674
.01173
.094
.03732
.012 14
.095
•0379
.o"55
.096
.03849
.01297
.097
.03908
01339
.098
.03968
.01382
.099
.04027
.01425
.1
.04087
.01468
.101
.04148
.015 12
.102
.04208
VctMd
Sin*.
S«fc. Area.
V«rMd
Sine.
03 .04269
04 .0433
05 .04391
06 .04452
07 .045 14
08 I .045 75 !
09 .04638 I
1 .047
11 .04763
12 .04826 I
13 .04889
14 .04953
15 .05016
16 .0508 I
17 .05M5
18 .05209
19 .05274
2 .05338
21 .05404
22 .05469
23 .05534
24 .056
25 .05666
26 .05733
27 .05799
28 .05866
29 .05933
3 .06
31 .06067
32 .061 35
33 .06203
34 .06271
35 .06339
36 .06407
37 .06476
38 .06545
39 .06614
4 .06683
41 .06753
42 .06822
43 .06892
44 .06962
45 07033
46 .07103
47 .07174
48 .07245
49 07316
5 .07387
51 .07459
52 .07531
53 -07603
54
55
56
57
58
59
6
61
62
63
64
65
66
67
68
69
7
7J
72
73
74
75
76
77
78
79
8
81
82
83
84
85
86
87
88
89
9
91
92
93
94
95
96
97
98
99
2
201
202
203
204
Seg. Area.
07675
07747
0782
07892
07965
08038
oSi II
08185
08258
08332
08406
0848
08554
08609
,08704
08779
08853
08929
09004
0908
09155
09231
09307
09384
0946
09537
09613
0969
09767
09845
09922
0077
0155
0233
0312
039
0468
0547
0626
0705
0784
0864
0943
1023
1102
II 82
1262
1343
1423
1503
VeiMd
Siue.
Seg. Area.
.205
.11584
.206
.11665
.207
.11746
.208
.11827
.209
.11908
.21
.1199
.211
.12071
.212
.121 53
.213
.12235
.214
.12317
.215
.12399
.216
.12481
.217
.12563
.218
.12646
.219
.12728
.22
.12811
.221
^12894
.222
.12977
.223
.1306
.224
.13144
.225
.13227
.226
•133"
.227
•13394
.228
•13478
.229
.13562
.23
.13646
.231
•137 31
.232
.13815
•233
.139
.234
.13984
.235
.14069
.236
.14154
.237
.14239
.238
.14324
.239
.14409
.24
.14494
.241
•1458
.242
.14665
.243
.14751
.244
.14837
.245
.14923
.246
.15009
.247
.15095
.248
.15182
.249
.15268
.25
.15355
.251
.15441
.252
.15528
.253
.15615
.254
.15702
.255
.15789
268
AREAS OF SEGMENTS OF A CIRCLE.
Ven«d
Sine.
.256
•257
.258
•259
.26
.261
.262
.263
.264
.265
.266
.267
.268
.269
.27
.271
.272
•273
.274
.275
.276
•277
.278
.279
.28
.281
.282
.283
.284
.285
.286
.287
.288
.289
.29
.291
.292
•293
.294
•29s
.296
.297
.298
.299
.3
.301
.302
.303
.304
Seg. Area.
~~58"76
5964
6051
6139
6226
6314
6402
649
6578
6666
6755
6844
6931
702
7109
7197
7287
7376
7465
7554
7643
773.3
7822
7912
8002
8092
8182
8272
8361
8452
8542
8633
8723
8814
8905
8995
9086
9177
9268
936
9451
9542
9634
9725
9817
9908
2
20092
20184
Versed
Sine.
305
306
307
308
309
31
3"
312
313
314
315
316
317
318
319
32
321
322
323
324
32s
326
327
328
329
33
331
332
333
334
335
336
337
338
339
34
341
342
343
344
345
346
347
348
349
35
351
353
353
Seg. Area.
20276
^0368
2046
20553
2064s
20738
2083
20923
210 15
21108
2I20I
21294
21387
2148
21573
21667
2176
21853
21947
2204
22134
22228
22321
22415
22509
22603
22697
22791
22886
2298
23074
23169
23263
23358
23453
23547
23642
23737
23832
23927
24022
241 17
24212
24307
24403
24498
24593
24689
24784
Veraed
Sine.
354
355
356
357
358
359
36
361
362
363
364
365
366
367
368
369
37
371
372
373
374
375
376
377
378
379
38
381
382
383
384
385
386
387
388
389
39
391
392
393
394
395
396
397
398
399
4
401
402
Seff . Area.
2488
24976
25071
25167
25263
25359
25455
25551
25647
25743
25839
25936
26032
26128
26225
26321
26418
26514
26611
26708
26804
26901
26998
27095
27192
27289
27386
27483
27580
27677
27775
27872
27969
28067
28164
28262
28359
28457
28554
28652
2875
28848
28945
29043
291 41
29239
29337
29435
29533
Verted
Sine.
•403
.404
•405
.406
•407
.408
.409
.41
.411
.412
•413,
.414
•415
.416
.417
.418
.419
•42
.421
.422
•423
.424
•425
.426
.427
.428
.429
•43
•431
•432
•433
•434
435
•436
•437
.438
•439
•44
.441
•442
•443
•444
•445
•446
•447
•448
•449
•45
t! -451
Seg. Area.
29631
29729
29827
29925
30024
30122
3022
30319
30417
30515
30614
30712
30811
30909
31008
311 07
31205
31304
31403
31502
316
31699
31798
31897
31996
32095
32194
.32293
•32391^
•3249
•3259
.32689
.32788
.32887
.32987
.33086
.331 85
.33284
.3.3384
.33483
82
\2
•33781
.3388
.3398
•34079
•34179
•34278
•34378
•335
.33681
Versed
Sine.
•452
•453
.454
-455
.456
•457
.458
•459
.46
.461
.462
.463
•464
•465
.466
.467
.468
.469
•47
.471
.472
•473
•474
•475
•476
•477
•478
•479
.48
.481
.482
.483
•484
.485
.486
•487
.488
.489
•49
u^gi
.492
.493
•494
•495
.496
•497
•498
•499
Seg. Area.
344 77
345 77
34676
34776
34875
34975
35075
351 74
35274
35374
35474
35573
35673
357 73
35872
35972
36072
36172
36272
36371
36471
36571
36671
36771
36871
36971
37071
3717
3727
3737
3747
3757
3767
377 7
3787
3797
3807
3817
3827
3837
3847
3857
3867
3877
3887
3897
3907
3917
3927
To Coxxipute ^rea of a Segment of a Circle by preoediutr
Table.
Rule.— Divide height or versed sine by diameter of circle ; find quotient in
column of versed sines. Take area for versed sine opposite to it in next col-
umn on right hand, multiply it by square of diameter, and it will give area.
AREAS OP ZONES OP A CIRCLE.
269
E^XAHPLB. — Required area of a segment of a circle, its beight being 10 feet and
diameter of circle 50.
io-^5o=.2, and .2,p«rto6fe, =.11182; then .11182 X 50' = 279. 55 /«jct
WkeUj in Division of a Height by Base, Quotient has a Remainder after
Third Place oj" Decimals, and great Accuracy is required.
Rule. — Take area for first three figures, subtract it frona next following
area, multiply remainder by said fraction, add product to first area, and
sum will give area for whole quotient
Example.— What is area of a segment of a circle, diameter of which is 10 feet, and
height of it 1-575?
I- 575 -^ 10 = • 1575 ; tabular area for . 157 = .078 92, and for . 158 = .C79 65, the dif-
ference between which is . 000 73.
Then . 5 x .000 73 = .000 365.
Hence, .157 =.07892
.0005 = .000 365
.079 285, sum, by which square of diameter
of circle is to be mvUiplied ; and .079285 X io* = 7.9285/«g?.
^reas of Zones of a Circle,
7%e Diameter of a Circle = i, vnid divided into 1000 equid Parts,
H'ght.
Area.
.001
.001
.002
.002
.003
.003
.004
.004
.005
.006
.005
.006
.007
.008
.007
.008
.009
.009
.01
.01
.Oil
.01 r
.012
.012
.013
.013
.014
.014
.015
.016
.015
.016
.017
.018
.017
.018
.019
.019
.02
.02
.021
.021
.022
.022
.023
.023
.024
.024
.025
.026
.027
.028
.029
.025
.03599
.02699
.02799
.02898
•03
.031
.02998
.03098
.032
.033
.03198
.03298
^34
.03397
H'ght.
Area.
.035
.036
•037
.038
•039
.04
,041
.042
•043
.044
•045
.046
.047
.048
.049
.05
.051
.052
•053
•054
.055
.056
.057
.058
.059
.06
.061
.062
.063
.064
.065
.066
.067
.068
.03497
•03597
.03697
.03796
.03896
.03996
.04095
.04195
.04295
.04394
.04494
.04593
.04693
.04793
.04892
.04992
.05091
.0519
.0529
.05389
.05489
.05588
.05688
.05787
.05886
.05986
.06085
.06184
.06283
.06382
.06482
.0658
.0668
.0678
H'ght.
.069
Area.
.06878
.07
.06977
.071
.070 76
.072
.071 75
•073
.07274
.074
•07373
.075
.07472
.076
•0755
.077
.07669
.078
.077 68
.079
.07867
.08
.07966
.081
.08064
.082
.08163
.083
.08262
.084
.0836
.085
.08459
.086
•08557
.087
.08656
.088 .08754
.089
.08853
.09
.08951
.091
.0905
.092 1 .09148
•093
.09246
.094
.09344
.095 i .09443
.096 .0954
•097 -09639
.098 .09737
•099
.09835
.1
•09933
.101
.10031
•loa-
.101^29 !
H'ght.
Area.
.103
.10227
.104
.10325
.105
.10422
.106
.1052
.107
.10618
.108
.10715
.109
.10813
.11
.10911
.III
.11008
.112
.11106
•"3
.11203
.114
•113
•115
.11398
.116
."495
.117
.11592
.118
.1169
.119
.11787
.12
.11884
.121
.11981
.122
.12078
.123
.121 75
.124
.12272
.125
.12369
.126
.12469
.127
.12562
.128
.12659
.129
.12755
•13
.12852
•131
.12949
.132
.13045
•133
•13141
•134
.13238
•135
.13334
' .136
•1343 '
H'ght.
37
38
39
4
41
42
43
44
45
46
47
48
49
5
51
52
53
54
55
56
57
58
59
6
61
62
63
64
65
66
67
68
69
7
Area.
13527
13623
13719
13815
13911
14007
14103
141 98
14294
1439
14485
14581
14677
14772
14867
14962
15058
15153
15248
15343
15438
15533
15628
15723
15817
15912
16006
161 01
16195
1629
16384
16478
16572
16667
z*
270
ABEAB OF ZONES OF A CIBCLB.
H*gfat.
.171
.172
•173
.174
•175
176
.177
.178
.179
.18
.181
.182
.183
.184
.185
.186
.187
.188
.189
.19
.191
.193
•193
.194
.195
.196
.197
.198
.199
.2
.201
■202
•203
.204
•205
.206
.207
.208
.209
.21
.211
.212
.213
.214
.215
.216
.217
.2X8
.2x9
.22
.221
.222
.223
.224
•ass
Aiw.
6761
6855
6948
7042
7136
723
7323
7417
751
7603
7697
779
7883
7976
8069
8162
8254
8347
844
8532
8625
8717
8809
8902
8994
9086
9178
927
9361
9453
9545
9636
9728
98x9
991
20001
20092
20x83
20274
20365
20456
20546
20637
20727
208x8
20908
20998
2io83
21 X 78
21268
21358
21447
21537
21626
2x716
H'KhLI Afh. llH'Rlit.
.226
.227
.228
.229
•23
.231
.232
233
•234
•235
.236
237
238
239
24
.241
.242
243
•244 I
245
246 !
•247 I
248
249
.25
251
252
253
254
255
256
257
258
259
26
261
262
263
■264
.265
266
267
.268
269
.27
.271
.272
•273
.274
•275
.276
.277
.278
.279
.28
21805
21894
21983
22072
221 61
2225
22335
22427
22515
22604
22692
2278
22868
22956
23044
23131
23219
23306
23394
234 8x
23568
23655
23742
23829
23915
24002
24089
24175
24261
24347
24433
24519
24604
2469
24775
24861
24946
25021
251 16
25201
25285
2537
25455
25539
25623
25707
25791
25875
25959
26043
26126
26209
26293
26376
.26459
i|
Aka.
281
282
283
284
285
286
287
288
289
29
29X
292
293
294
295
296
297
298
299
3
301
302
303
304
305
306
307
308
309
31
311
312
3^3
314
315
316
317
318
319
33
321
322
323
324
325
326
327
328
329
33
331
332
333
334
<33S
26541
26624
26706
26789
26871
26953
27035
27X 17
27199
2728
27362
27443
27524
27605
27686
27766
27847
27927
28007
28088
28x67
28247
28327
28406
28486
28565
28644
28723
28801
2888
28958
29036
29115
29192
2927
29348
2942s
29502
2958
29656
29733
2981
29S86
29962
•30039
.30114
.30x9
.30266
•30341
.304x6
.30491
.30566
.3064X
•30715
0079
H*gfat.
•336
•337
•338
.339
•34
•341
•343
•343
•344
345
346
347
348
349
35
351
352
353
354
355
356
357
358
359
36
361
362
363
364
365
366
367
368
369
37
371
373
373
374
375
376
377
378
379
38
381
382
383
384
385
386
387
388
389
39
ArML
H'gfct.
.30864
•391
•30938
•393
.310x2
.393
.31085
•394
.31159
•395
•3" 32
•396
•31305
•397
•31378
•398
•3145
•39S
•31523
•4
•31595
.401
.31667
.402
•31739
•403
•31811
.404
.31882
•405
•31954
.406
.32025
•407
.32096
.408
.321 67
.409
•32237
•41
•32307
.411
•32377
.412
•32447
•413
32517
.4x4
•32587
•415
.32656
.4x6
■32725
•417
•32794
.4x8
.32862
•419
•32931
•42
•32999
.42 X
•33067
.422
•33135
•423
.33203
.424
•3327
•425
•33337
.426
•33404
•427
•33471
.428
•33537
•429
.33604
•43
•3367
•431
•33735
•433
•3.3801
•433
.3386b
•434
.33931
' 435
•,33996
436
.34061
437
.34125
•438
•3419
.439
.34253
.44
.34317
•441
.3438
•442
.34444
•443
.34507
i -444
.345691
1445
.34632.
•34694
•34756
.34818
.34879
.3494
.35001
.35062
•351 22
.351 82
•35242
•35302
•35361
•3542
•354 79
.35538
•35596
•35654
.35711
•35769
.35826
•35883
•35939
•35995
•36051
.361 07
.36162
.36217
.36272
.36326
•3638
.36434
.36488
•36541
•36594
.36646
.36698
•3675
.36802
.36853
•36904
.36954
.37005
.37054
•37104
•37153
.37202
•3725
•37298
•37346
.37393
.3744
.37487
37533
•37579
AKBAS OF ZONES OF A Cl&CLE.
271
fTgbt.
446
•447
.448
449
.45
•45J
^52
•453
•454
•455
.456
ArML
IJHVht.
.37624
.37669
•377 14
-37758
.37802
•37845
.37888
•37931
•37973
.38014
.38056
I -457
L458
i -459
I .46
1^61
.462
•463
I 464
•465
.466
! .467
Ar6A«
.38096
•38137
•381 77
.382 16
.382 55
.38294
.38332
.38369
.38406
.38443
•38479
H'ght.
468
469
47
471
472
473
474
475
476
I 477
•478
Area.
H'gfat.
•479
Area.
•38514
.38867
•38549
.48
•38895 '
.38583
.481
•38923
.38617
.482
•3895 i
.3865
•483
38976'
.38683
.484
.39001
.387151
.485
.39026
•38747 !
.486
•3905
•387 78
.487
•39073
.38808
.488
•39095
•38838 :
.489
•39117'
iH'Rfat.
•49
•491 ;
.492 1
•493
•494
•495
■496,
•497 ,
•498;
•499
•5
Akb.
•39137
•391 56
•39175
•39192
.39208
•39223
.392 36
•392 48
.39258
.39266
•3927
mt Table is compiUed only for Zones^ low/est Chord oj* which is Diamr
tier.
To Compute .A^rea of* o. Zone "b^-* preceding Talkie.
When Zone is Iau than a Semicircle,
Rule. — Divide height by diameter, find quotient in column of heights.
Take area for height opposite to it in next column on ci^riit hand, uiuhiplv
it by square of diameter, and pruduct will give area of zone.
KxAMPLB. — Required area of a 2one, diameter of which is 50, and its height 15.
1 5 -r- 50 = . 3 ; and 3, as per table, = . 280 88.
Hence .28088 X 50^ = 702.2 area.
Whm Zone is Greater than a Semicircle,
kuLE. — Take height on each side of diameter of circle, and ascertain, by
preceding Rule, their respective areas ; add areas of these two portions to-
gether, and sum will give area.
EXAMPLB. — Required area of a zone, diameter of circle being 50, and heights of
cone on each side of diameter of circle 20 and 15.
90-5-50 = .4; .4, o«p«r^aftte, =.35182; and .351 82 X 50= = 879. 55.
15-5-50 = .3; 3. tupcr fti*te, =.28088; and .28088X50^ = 702.2.
Hence 879. 55 -f 702.2 = 1581.75 area.
When^ in Division of a Height by Chords Quotient has a Remainder after
Third Place of Decinuds, and great Accuracy is reqvired.
Rule. — Take area for first three figures, subtract it from the next follow-
ing area, multiply remainder by said fraction, and add product to first area ;
snm will give area for whole quotient.
ExAMPLR. — What is area of a zone of a circle, greater chord being 100 feet, and
breadth of it 14 feet 3 ins.?
14 feet 3 in& = 14.25, and 14. 25-7-100=. 1425; tahular length for .142 = .14007,
anil for .143 = .141 03, difference between which it .00096.
Then . 5 X .000 96 := .000 48. Hence . 142 = . 140 07
.0005 = .00048
.14055, sum by which square of greater
chord is to be muU^ftHed ; and . 140 $$ X xoo* -= 1405. 5 feet.
272
SQUABES, CUBES, AND BOOTS.
Sqviareis, Cu'bes, and. Square and. Cube I^oots,
From I to 1600.
NUMKK.
S^UARB.
Cube.
SquARB Root.
CuBB Root.
I
2
I
4
I
8
I
I.4142136
I
1.259 921
3
9
27
1-7320508
1.442 2496
4
16
64
2
1.587 401 I
5
25
125
2.236068
1.7099759
6
36
216
2.4494897
I.817 1206
7
49
343
2.645 751 3
I.9129312
8
64
512
2.828 427 I
2
9
81
729
3
2,0800837
10
100
IOCX>
3.16227/7
2.1544347
II
121
1331
3.3166248
2.2239801
12
144
1728
3.464 loi 6
2.2894286
13
169
2197
36055513
2.3513347
14
196
2744
3.7416574
2.410 142 2
15
225
3375
38729833
2.466 212 I
16
236
4096
4
2.519 842 I
17
289
4913
4.123 105 6
2.571 281 6
18
324
5832
4.242 640 7
2.620 741 4
19
361
6859
4.3585989
2.6684016
20
400
8000
4.472 136
2.7I44177
21
441
9261
4-5825757
2.7589243
22
484
10648
4.6904158
2.8020393
23
529
12 167
4.7958315
2.843867
24
576
13824
4.8989795
2.8844991
25
62s
15625
5
2.9240177
26
676
17576
5.0990195
2.962496
27
729
19683
5.196 1524
3
28
784
21952
5.2915026
30365889
29
841
24389
5.3851648
3.0723168
30
900
27000
5.4772256
3.1072325
31
961
29791
5.5677644
3. 141 3806
32
1024
32768
5.6568542
3.174 802 1
33
1089
35937
57445626
32075343
34
1156
39304
5.8309519
3.239 61 1 S
35
12 25
42875
5.9160798
3.271066^
36
1296
46656
6
3.301 927 2
37
J369
50653
6.082 762 5
3.3.32 221 8
38
1444
54872
6.164 414
3-3619754
39
15 21
593'9
6.244998
3.3912114
40
1600
64000
6.3245553
3.419 951 9
41
168I
68921
6.4031242
3.4482172
42
176^
74088
6.480 740 7
3.4760266
43
1849
79507
6.5574385
3.5033981
44
1936
85184
6.6332496
35303483
45
20-25
91125
6.70S2039
3.5568933
46
21 lb
973j6
6.78233
3-5830479
47
2209
103823
6.8556546
3.60S8261
48
23 <H
110592
6.938 303 2
3.6J42411
49
2401
ii7«M9
7
3-6593057
SO
2500
125000
7.0710678
3.6840314
51
aooi
13-2651
7.1414284
3.7084298
52
27 <H
140 60S
7.311 1026
3.7325111
S3
2809
148877
7.2801099
3.7562858
54
2916
157464
7^84692 1
37797631
SQUABES, CUBES, AND ROOTS.
273
Vvummu.
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
93
93
94
95
96
97
98
99
100
lOI
102
103
104
105
106
107
108
109
zzo
8«I7ABB.
3025
3136
3249
3364
3481
3600
3721
3844
3969
4096
4225
4356
4489
4624
4761
4900
5041
5184
5329
5476
5625
5776
5929
6084
6241
64cx>
6561
6724
6889
7056
7225
7396
7569
77 44
7921
8icx>
8281
8464
8649
8836
9025
9216
9409
9604
9801
IOOCX>
1 02 01
10404
10609
1 08 16
1 1025
11236
11449
I 1664
1 1881
I 2100
Cubs.
166375
175 616
185 193
195 "2
205379
216000
226981
238328
250047
262 144
274 625
287496
300 763
314432
328509
343000
3579"
373248
389017
405 224
421 875
438976
456533
474552
493039
512000
531 441
551368
571 787
592704
614 125
636056
658503
681472
704969
729000
753571
778688
804357
830584
857375
884736
912673
941192
970299
1000 000
1 030 301
1 061 208
1092727
1 124864
1157625
1 191016
1 225 043
1259712
1295029
I 331000
Sqcabb Root.
7.416 198 5
7-4833148
7-5498344
7-615 773 I
7.681 145 7
7.7459667
7.810 249 7
7.8740079
7.9372539
8
8.062 257 7
8.1240384
8.1853528
8.2462113
8.306623-9
8.3666003
8.426 149 8
8.485 281 4
8.5440037
8.602 325 3
8.660 254
8.7177979
8.7749644
8.831 7609
8.8881944
8.9442719
9
9-0553861
9.1104336
9.165 151 4
9.2195445
9.2736185
9-3273791
9.3808315
9.4339811
9.486833
9539392
9.591 663
9.6436508
96953597
9.7467943
9-797959
9.8488578
9.8994949
99498744
10
10.049 875 6
10,0995049
10.1488916
10. 198 039
10.2469508
10.295 630 1
103440804
10.392 304 8
10.4403065
104880885
CVBB Root.
3.8029525
3.8258624
3.848 501 1
3.8708766
3.8929965
3.914 867 6
39364972
39578915
3979057 I
4
4.020 725 6
4.041 240 1
4.061 548
4.081 655 1
4.101 566 1
4.1212853
4.1408178
4. 160 167 6
4179339
4.1983364
4.2171633
4.2358236
4.254321
4.272 658 6
4.2908404
4.3088695
4.3267487
4.3444815
4.3620707
4-3795191
4.3968296
4.4140049
4.4310476
4.4479602
4.464 745 I
4.481 404 7
4.4979414
45143574
45306549
45468359
4.562 902 6
4.578857
45947009
4.6104363
4.626065
4.6415888
4.6570095
4.6723287
4.6875482
4.7026694
4.717694
4.7326235
4.7474594
4.7622032
4.7768562
4.791 4199
274
SQUARES, CUBES, AJTD ttOOtEJ.
NUMBIS.
SOUABS.
Ill
12321
1X2
I2S44
"3
12769
114
12996
115
13225
116
13456
117
13689
118
13924
119
1 41 61
120
14400
121
I 4641
122
14884
123
1 51 29
124
15376
125
15625
T26
15876
127
161 29
128
16384
129
16641
130
16900
131
I 71 61
132
17424
133
17689
134
17956
135
18225
136
18496
137
18769
138
19044
139
1 9321
140
19600
141
19881
142
20164
H3
20449
144
20736
MS
2 1025
146
2 13 16
147
2 1609
148
21904
149
22201
ISO
22500
'51
22801
^52
23104
153
23409
154
23716
iSS
24025
156
24336
»57
24649
158
24964
'59
25281
160
25600
161
25921
162
36244
163
26569
164
26896
i6s
27225
166
27556
Cub*.
1 367 631
I 404 928
1442897
1 481 544
I 520 875
1560896
1 601 613
1643032
1 685 159
I 728000
I 771 561
I 815 848
1860867
1906624
1 953 125
2000376 '
2048383
2097152
2 146689
2197000
2 248 091
2299968
2352637
2406104
2460375
2515456
2 571 353
2 628 072
2 685 619
2744000
2803221
2 863 288
2 924 207
2985984
3048625
3112136
3176523
3241792
3307949
3375000
3442951
35"8o8
3581577
3652264
3723875
3796416
3860893
3944312
4019679
4096000
4173281
4251528
4330747
4410944
4492125
4574296
S^UAKB Root.
10.5356538
0.5830052
0.630 145 8
0:677 078 3
0.7238053
0.7703296
0.8166538
0.862 780 5
0.908 712 I
0^9544512
.045 361
.0905365
.135 528 7
.1803399
.224 972 2
.269 427 7
313 708 5
•3578167
401 754 3
•445 523 I
•4891253
•532 562 6
•5758369
.61895
.661 903 8
.7046999
•7473401
.7898261
.8321596
.8743421
•9163753
.958 260 7
2.041 594 6
2.083 046
2.1243557
2.1655251
2.2065556
2.247 448 7
2288 205 7
2.328828
2.3693169
2.4096736
2.4498996
2.489996
2.5^9964 I
2.5698051
2.6095202
2.6491106
2.688 577 5
2.727922 I
2.7671453
2.806 248 5
2.845 232 6
3.8840987
CuBxRbdf.
4.8058955
4.820 ^84 5
4.834 588 1
4.8488076
4.8629442
4.876999
4.8909732
4.9048681
4.9186847
4.932 424 2
4.9460874
4.9596757
4.9731898
4.986631
5
S.0132979
5.0265257
5.0396842
50527743
5.065 797
5.0787531
5.0916434
5.1044687
5.1172299
5.1299278
5.1425632
5.1551367
5. 167 649 3
5.180 101 5
5.1924941
5.204 827 9
5.2171034
5.2293215
5.241 482 8
5.2535879
5.2656374
5.2776321
5.2895725
5.3014592
5 313 292 8
5325074
53368033
5.34^4812
5.3601084
5.3716854
5.3832126
53946907
5.4061202
5-4175015
5.4288352
5.440 121 8
5451 361 8
54625556
5-473 703 7
5.4848066
54958^7
SQtTABEB, CUBBS, AKD BOOTS.
275
NCMBBB.
SqCABB.
167
87889
168
28224
169
88561
170
28900
lyi
89241
17a
29584
173
29929
174
30276
17s
30625
176
30976
177
31329
178
31684
179
32041
180
32400
181
32761
1S2
33^24
183
33489
184
33856
185
34225
186
34596
187
34969
188
35344
189
35721
190
36100
191
36481
193
36864
193
37249
194
37636
195
38025
196
38416
197
38809
198
39204
199
39601
200
40000
30X
40401
ao3
40804
ao3
41209
304
4 16 16
205
42025
206
42436
207
42849
208
43264
209
43681
210
44100
211
4v45 2i
212
44944
213
45369
214
45796
315
46225
316
46656
317
47089
218
47524
219
47961
220
48400
221
48841
223
49284
CVBC.
4657463
4 741 632
4826809
4913000
5000211
5088448
5 177 717
5268024
5359375
5451776
5 545 233
5639752
5 735 339
5832000
5929741
6038568
6138487
6 229 504
6331625
6434856
6539203
6644672
6751269
6859000
6967871
7077888
7189057
7301384
7414875
7529536
7645373
7762392
7880599
8000000
8130601
8342408
8365427
8489664
8615125
8 741 816
8869743
8998912
9139329
9261000
9393931
9528138
9663597
9800344
9938375
10077696
10318313
10360232
10503459
10648000
lo 793 861
10 941 048
8ttUASB Root.
2.922 848
2.961 481 4
3
3.0384048
3.0766968
3.II4877
3.1529464
3.190906
3.2287566
3.2664992
3.304 134 7
3.341 664 1
33790882
3.4164079
3.453624
3-4907376
3 527 7493
356466
3.6014705
3.638 181 7
3.6747943
3.71 1 3092
3.747 727 I
3.7840488
3.820 275
38564065
3.89244
39283883
396424
4
4.0356688
4.0712473
4.106736
4.1421356
4,1774469
4.2126704
4.2478068
4.2828569
4.317821 I
4.352 700 I
43874946
4.422 205 I
4.4568323
4 491 376 7
4525839
4.5602198
45945195
4.628 738 8
4.6628783
4.6969385
4.7309199
4.764 823 I
4.79S6486
4832397
48660687
4.8996644
Cdb'k Root.
5.5068784
5.5178484
5.5287748
5-5396583
5-5504991
5.561 297 8
5.5720546
5.582 770 3
5-593 444 7
5.6040787
5.6146724
5.6252263
56357408
5 6462162
5.6566528
5.6670511
5.6774114
5.687 734
5.6980192
5.708 267 5
5.718 479 I
5.7286543
5-7387936
5-7488971
5.7589652
5.768998a
5.7789966
5.7889604
5.79889
5.8087857
5.8186479
5.8284767
5.8382725
5.8480355
5.857 766
5.8674643
5.8771307
5.8867653
5.8963685
5.9059406
5.9154817
5.9249921
5.9344721
5.943922
5-9533418
5.962 732
5.9720926
5.981 424
59907264
6
6009245
6.018 461 7
6 027 650 2
6.036 810 7
6045943s
6.055 0489
276
6QUABES, CUBES, AND BOOTS.
Number.
Squakb.
CUSB.
Sqoarb Root.
CvBB Root.
823
49729
II 089 567
14.9331845
6.064 127
224
50176
II 239424
14966629 s
6.0731779
225
50625
11390625
15
6.082202
226
51076
11543176
150332964
6.091 1994
227
51529
II 697 083
15.0665192
6.1001702
228
51984
11852352
15.0996689
6.1091147
229
52441
12008989
15.132746
6.1180332
230
52900
12 167 000
15-1657509
6.1269257
231
53361
12326391
15.1986842
6.1357924
232
' 53824
12 487 168
15-2315462
6.1446337
233
54289
12649337
15-2643375
6.1534455
2.34
54756
I28I2904
15.2970585
6.1622401
235
55225
12977875
15.3297097
6.1710058
236
55696
13144256
15.3622915
6.1797466
237
56169
13 312 053
15.3948043
6.1884628
238
56644
13 481 272
15.4272486
6.197 1544
239
5 71 21
13 651 919
15.4596248
6.205 821 8
240
57600
13824000
15-4919334 -
6.214 465
241
58081
13997 521
15.5241747
6.223p8^3
242
58564
14 172488
15.5563492
6231 679 7
243
59049
14348907
15-5884573
6.2402515
244
59536
14526784
15.6204994
6.2487998
245
60025
14706125
15.6524758
6.2573248
246
60516
14886936
15.6843871
6.2658266
247
61009
15069223
15-7162336
6.2743054
248
61504
15 252 992
15.7480157
6.282 761 3
249
62001
15438249
15-7797338
6.291 194 6
250
62500
15625000
15.8113883
62996053
231
63001
15 813 251
15.8429795
6.3079935
252
63504
16003008
15-8745079
6.3163596
253
64009
16194277
15-9059737
6.3247035
254
64516
16387064
159373775
6.3330256
255
65025
16581375
15.9687194
6.341 325 7
256
65536
16777216
16
6.3496042
257
66049
16974593
16.03121^5
6.357 861 1
258
66564
17I735I2
16.062 378 4
6.3660968
259
67081
17373979
16.0934769
6.3743111
260
67600
17576000
16.1245155
6.3825043
261
681 21
17779581
16.1554944
6.3906765
262
68644
17984728
16.186 4141
6.3988279
263
69169
18 191 447
16.2172747
64069585
264
69696
18399744
16.2480768
6.4150687
265
70225
18609625
16.2788206
6.4231583
266
70756
I882I096
16.3095064 '
6.431 2276
267
71289
19034163
16.3401346
6.4392767
268
7 1824
19248832
16.3707055
64473057
269
72361
19465109
16.401 2195
64553148
270
72900
19683000
16.431 676 7
6.4633041
271
73441
19902 511
16.462 077 6
6.4712736
272
73984
20123648
16.492 422 5
64792236
273
74529
20346417
16.5227116
6.487 154 1
274
75076
20570824
16.5529454
6.4950653
275
75625
20796875
16.583 124
6-502 957 2
876
761 76
21 024 576
16 613 247 7
6.51083
277
76729
21253933
16643317
6.5186839
278
77284
21484952
16.678332
6.5265189
SQUABE3, CUBES, AND HOOTS.
277
NvmMM,
279
280
281
28a
283
284
28s
286
287
288
28$
290
291
292
293
394
29s
296
297
298
299
300
301
J02
303
304
305
306
307
308
309
310
3"
312
313
314
315
316
317
318
319
320
321
^ 322
323
324
325
326
327
328
329
330
331
332
333
3^
StUAXB.
OtTBB.
77841
78400
78961
79524
80089
80656
81225
81796
82369
82944
83s 21
84100
84681
85264
85849
86436
87025L
87616
88209
88804
89401
90000
90601
91204
91809
924 16
93025
93636
94249
94864
95481
961 00
96721
97344
97969
98596
99225
99856
100489
10 II 24
101761
X02400
10 30 41
103684
104329
10 49 76
105625
106276
106929
107584
10 82 41
108900
10 95 61
II 02 24
110889
JI1556
21 717639
21952000
22 188 041
22 425 768
22665187
22906304
23 149 125
23393656
23639903
23887872
24 137 569
24389000
24642 171
24897088
25153757
25412 184
25672375
25934336
26198073
26463592
26730899
27000000
27270901
27543608
27818127
28094464
28372625
28652616
28934443
29218 112
29503629
29 791 000
30080231
30371328
30664297
30959144
31255875
31554496
31 855 013
32157432
32461759
33768000
33076161
33386248
33698267
34012224
34328125
34645976
34965783
35287552
35 61 1 289
35937000
36264691
36594368
36926037
37^59704
Aa
Square Root.
Cdbb Root.
16 703 293 I
6.5343351
16.7332005
6.542 132 6
16.763 054 6
6.5499116
16.7928556
6 557 672 2
16.8226038
6.5654144
168522995
6.5731385
16 881 943
6.5808443
16 911 5345
65885323
16.9410743
65962023
16.970 562 7
6.6038545
17
6.611489
17.0293864
6.619 106
17.0587221
6.626 705 4
17.0880075
6.634 287 4
I7.II72428
6.641 852 2
17.1464283
6.6493998
17175564
66569302
17.2046505
66644437
172336879
66719403
17.2626765
6.679 42
17.2916165
6.6868831
17.3205081
6.6943295
17-3493516
6.7017593
17-3781472
6.709 1729
174068952
6.71657
17.4355958
67239508
17.4642492
6.7313155
17.4928557
6-7386641
17-5214155
6.7459967
17.5499288
6.7533134
175783958
6.7606143
17.6068169
6,7678995
17.635 192 I
6.775 169
17.6635217
6.7824229
17.691806
6.7896613
17.7200451
67968844
17.7482393
6.8040931
17.7763888
6.8113847
17.8044938
6.818463
17-8325545
6.825 624 3
17.860571 I
6.832 771 4
17.8885438
6.8399037
17.9164729
6.847 021 3
17-9443584
6.854 124
17.9722008
6.861 212
18
6.8682855
18.0277564
6.8753443
18.0554701
6.8823888
18.083 141 3
68894188
18.1107703
6.8964345
18.138357 I
6.9034359
18.1659021
6.9104232
18.1934054
6.9173964
18.220 867 2
6.9243556
18.248 287 6
6.9313088
18.2756669
6 938 232 1
278
SQUARES, CUBES, AND BOOTS.
NUMBBll.
Square. |
Cdbb.
Squakb Root.
CuBB Root.
335
1 1 22 25
37 595 375
18.3030052
6.945 1496
336
II 2896
37933056
18.3303028
6.9520533
337
"3569
38 272 753
18.3575598
6.9589434
338
114244
38614472
18.3847763
6.9658198
339
II492I
38958219
18.4119526
6.972 682 6
340
II 56 00
39304000
18.4390889
6.9795321
341
I16281
39651821
18.4661853
6.9863681
342
II6964
40001688
18493242
6.9931906
343
II 7649
40353607
18.520 259 3
7
344
118336
40707584
18.547 237
7.006 796 2
345
II9025
41063625
18.5741756
70135791
346
II 97 16
41 421 736
18 601 075 2
7.020349
347
120409
41 781 923
18.627936
7.027 105 8
348
121104
42 144 192
18.654 758 1
7.0338497
349
12 18 01
42508549
18.681 541 7
7.0405806
350
122500
42 875 000
18.7082869
70472987
351
12 32 01
43243551
18.734994
7.0540041
352
123904
43614208
18.761 663
7.0606967
353
124609
43986977
18.788 294 2
7.0673767
354
12 53 16
44361864
18.814 887 7
7.074044
3SS
126025
44738875
18.841 443 7
7.0806988
356
126736
45118016
18.8679623
7.087341 1
357
127449
45499293
18.8944436
7.0939709
358
12 81 64
45 882 712
18.9208879
7.1005885
359
12 88 81
46 268 279
18.9472953
7.1071937
360
129600
46656000
18.973666
7.1137866
361
130321
47045831
19
7.1203674
362
131044
47437928
19.0262976
7.126936
363
131769
47832147
190525589
71334925
364
132496
48 228 544
19.078 784
7.140037
365
133225
48627125
19.1049732
7.1465695
366
133956
49027896
19.131 1265
71530901
367
134689
49430863
19.157 244 I
71595988
368
135424
49836032
19 183 326 I
7.1660957
369
13 61 61
50243409
19.2093727
7.1725809
370
136900
50653000
19235 384 1
7.1790544
371
137641
51 064 811
19.261 3603
7.1855162
37a
138384
51478848
19.2873015
7.1919663
373
139129
51895117
19.3132079
7.198405
374
139876
52313624
19-3390796
7.2048322
375
140625
52734375
19.3649167
7.2112479
376
141376
53157376
I9'39P7I94
7.2176522
377
14 21 29
53582633
. 19.4164878
7.22404s
378
142884
54010152
19.442 222 1
7.2304268 0
379
143641
54439939
19.4679223
l'^2f>19rj^
380
144400
54 872 000
»9-493 588 7
72431565
381
14 51 61
55306341
19.519 221 3
7.2495045
382
145924
55742968
19.5448203
7.2558415
383
146689
56 181 887
»9-570 3858
7.262 167 5
384
147456
56623 104
19-5959179
7.2684834
385
148225
57066625
19.621 4169
7.2747864
386
148996
57512456
19.6468827
7.281 0794
3!7
149769
57960603
i9'672 315 6
7.287 361 7
388
150544
58411072
19.6977156
7293633
389
15 13 21
58863869
19.7230829
7.2998936
390
152100
593»9«»
19.7484177
73061436
SQITABBS, CrBBS, Am) BOOTS.
m
NUMBSB.
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
40S
409
410
411
4J2
4^3
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
SquASB.
CUB«.
Sqvabb Root.
Cubb Root.
[52881
59776471
19-7737199
7.312 382 8
153664
60236288
19.7989899
7.318 61 1 4
^5 4449
6q 698 457
19.824 227 6
7.3248295
155236
61 162 984
19.8494332
73310369
15602s
61 629 875
19.8746069
73372339
[56816
62 099 136
19.8997487
7.3434205
[57609
62 570 773
19,924 858 8
7.3495966
[58404
63044792
19.9499373
7-355 762 4
[59201
6^521199
19.9749844
7.3(^19178
[60000
64000000
20
7.308063
[60801
64481 201
20.024 984 4
7-3741979
[6 1604
64964808
20.0499377
7.3803227
[62409
65450827
20.0748599
73864373
[632 16
65939264
200997512
20 124011 8
7.3925418
[64025 *
66430125
73986363
[64836
66923416
201494417
7.4047206
[65649
67 419 143
20 174241
7410795
[6 64 64
67 917 312
20.1990099
7.4168595
[67281
68417929
20.2237484
7.4229142
[68100
68921000
20.248 456 7
7.4289589
[6 89 21
69426531
20.2731349
74349938
[69744
69934528
20 297 783 1
7.4410189
[70569
70444997
20.322 401 4
7-4470342
[71396
70957944
20.3469899
7-4530399
[7 22 25
71473375
20.3715488
74590359
173056
71 991 296
20.396 078 I
74650223
[73889
72 511 713
20.4205779
7.4709991
[74724
73034632
20.445 048 3
7.4769664
175561
73560059
20.469 489 5
7 482 924 2
[76400
74088000
20.4939015
7.488 872 4
[7724T
74618 461
20.5182845
7.4948113
[78084
75 151 448
20.542 638 6
7.5007406
[78929
75686^^7
20.5669638
7.5066607
[79776
76 225 024
20.591 260 3
7-51257x5
[80625
76 765 625
20.6155281
7-518473
[8 14 76
77308776
20.639 767 4
7.5243652
[8 2^ 29
77854483
20.663 978 3
. 7.5302482
[8 31 84
78402752
20.688 160 9
7.536 122 I
18 40 41
78953589
20.7123152
7.541 986 7
[84900
79 507 000
20.7364414
7.5478423
[85761
80062991
20.7605395
7.5536888
[86624
80621568
20.7846097
7-5595263
[87489
81 182 737
20.808 652
75653548
[88356
81746504
20.832 666 7
7-571 1743
[89225
82312875
20.8566536
7.5769849
[90096
82 881 856
20.880613
7.582 786 5
[99969
83453453
84027072
20.904545
7-5885793
[91844
20.9284495
7-5943633
[92721
84604^19
20.9523268
7.600 138 5
[93600
85184000
20.976177
7.6059049
[94481
85 766 121
21
7.6116626
195364
86350^
21.023796
7.6174116
[96249
.86938307
21.0475652
7.623 151 9
9 71 36
87528384
21.0713075
7.6288837
[9 So 25
88121 125
21.0950231
7.634 606 7
[98916 J
88716536
21.1187121
7.6403213
28o
SQUARES, CUBES, AND BOOTS.
Number.
Sqvasb.
447
199809
448
200704
449
20 16 01
450
202500
451
203401
452
204304
453
205209
454
2061 16
455
207025
456
207936
n57
208849
458
209764
459
21 0681
460
21 1600
461
21 2521
462
213444
463
214369
464
21 5296
465
216225
466
21 71 56
467
218089
468
219024
469
21 9961
470
220900
471
22 18 41
472
222784
473
223729
474
22 46 76
475
22 56 25
476
22 65 76
477
22 75 29
478
228484
479
229441
480
230400
481
23 13 61
482
23 23 24
483
233289
484
234256
485
23 52 25
486
236196
487
237169
488
238144
489
239121
490
240100
491
24 10 81
492
242064
493
243049
494
244036
495
245025 ..
496
246016
497
247009
498
248004
499
249001
Soo
250000
501
25 1001
502
252004
CCBS.
S<it7ABB Root.
89314623
89915392
90518849
91 125000
91 733851
92345408
92959677
93576664
94196375
94818816
95 443993
96071912
96 702 579
97336000
97972 181
98611 128
99252847
99897344
100544625
101 194696
101847563
102 503 232
103 161 709
103 823 000
104 487 III
105154048
105823817
106 496 424
107 171 875
107850176
108531333
109215352
109 902 239
no 592 000
III 284641
111980 168
112678587
1 13 379 904
114084 125
114 791 256
115 501 303
116214272
116930 169
117649000
118370771
119095488
1 19 823 157
120553784
121287375
122023936
122763473
123505992
124251499
125000000
125 751 501
126506008
21.1423745
21.1660105
21.1896201
21.2132034
21.2367606
21.2602916
21.2837967
21.3072758
21.330729
21.3541565
21.3775583
21.4009346
21.4242853
21.4476106
21.4709106
21.4941853
21.5174348
21.5406592
21.5638587
21.5870331
21.6101828
21.6333077
21.6564078
21.6794834
21.7025344
21.725561
21.7485632
21.771 541 I
21.7944947
21.8174242
21.8403297
21.863211 1
21.8860686
21.9089023
21.931 7122
21.9544984
21.977261
22
22.022 715 5
22.0454077
22.0680765
22.090 722
22.1133444
22.1359436
22.1585198
22.181 073
22.2036033
22.2261108
22.248 595 5
22.271 057 5
22.293 496 8
22.3159136
22.3383079
22.360 679 8
22.3830293
22.405 356 5
CvBB Root.
7.646 027 2
7.6517247
7.6574138
7.6630943
7.6687665
7.6744303
7.6800857
7.6857328
7.691 371 7
7.6970023
7.7026246
7.7082388
7.7138448
7.7194426
7.7250325
7.7306141
7.736 187 7
7-7417533
7.7473109
7.7528606
7.7584023
7-7639361
7.769463
7.7749801
7.7804904
7.7859928
7.791487 s
7.7969745
7.8024538
7.8079254
7.813389 a
7.8188456
7.824 294 a
7-8297353
7.835 1688
7.8405949
7.8460134
7.8514244
7.8568281
7 862224 a
7.867613
7.8729944
7.8783684
7-8837353
7.8890946
7.894 446 8
7.8997917
7.9051294
7.9104599
7-9157833
7.9210994
7.926 408 5
7.931 7104
7-9370053
7.942 293 1
7-947 5739
SQUABES, CUBES, AND BOOTS.
281
503
504
50s
506
507
508
509
510
512
513
514
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
S^VASK.
253009
254016
255025
256036
257049
258064
259081
260100
261I 21
2621 44
263169
264196
265225
266256
267289
268324
269361
270400
27 14 41
27 24 84
273529
274576
275625
276676
277729
27 87 84
279841
280900
28 19 61
283024
284089
285156
28 62 25
287296
288369
289444
290521
291600
292681
293764
294849
295936
297025
2981 16
299209
300304
30 14 01
302500
303601
304704
305809
306916
308025
309136
310249
31 1364
Cdbb.
127 263 527
128 024 064
128 787 625
129 554 216
130323843
131 096 512
131 872 229
132 651 000
133432831
134 21 7 728
135005697
135796744
136590875
137388096
138 188 413
138991832
139798359
140608000
141 420 761
142 236 648
143055667-
143877824
144 703 125
145531576
146363 183
147 197 952
148035889
148 877 000
149 721 291
150568768
151419437
152 273 304
153 130375
153990656
154 854 153
155720872
156590819
157464000
158 340 421
159220088
160 103007
160989 1S4
161 878625
162 771 336
163667323
164566592
165 469 149
166375000
167 284 151
168 196608
169 112 377
1 70 031 464
170953875
171 879616
172808693
173 74J 113
SqDAEB Root.
CuBB Root.
22.427 661 5
22.4499443
22.472 205 I
22.4944438
22.5166605
22.5388553
22.561 028 3
22.5831796
22.605 309 I
22.627 41 7
226495033
22.671 5681
22.6936114
22.7156334
22.737634
22.7596134
22.781 571 5
22.8035085
• 22.8254244
22.8473193
22.8691933
22.8910463
22.9128785
22.9346899
22.9564806
22.9782506
23
23.021 7289
23043 437 2
23.0651252
23.086 792 8
23.10844
23.130067
23.1516738
23.1732605
23.194827
23.2163735
23.237 900 1
23 259 406 7
23.280 893 5
233023604
233238076
23345 23s I
23.366 642 9
23,388 031 1
234093998
23-430 749
23452 078 8
234733892
23.494 680 2
23515952
23-5372046
23558438
235796522
23.600 847 4
23.622 023 6
7.9528477
7.9581144
79633743
7.968 627 I
7-9738731
7.979 112 2
7.9843444
7.9895697
79947883
8
8.0052049
8.010 403 2
8.0155946
8.0207794
8.0259574
8.031 1287
8.0362935
8.041 451 5
8.046 603
8.0517479
8.0568862
8.062018
8.067 143 2
8.072 262
8.0773743
8.08248
8.0875794
8.092 672 3
8.0977589
8.102839
8.1079128
8.1129803
8.1 18 041 4
8 1230962
8.1281447
8.133187
8.138223
8.1432529
8.1482765
8.1532939
8.1583051
8.1633102
8.1683092
8.173302
8.1782888
8.1832695
8.188244 I
8.1932127
8.1981753
8.203 131 9
8.2080825
8.213027 I
8.2179657
8.222 898 5
8.227 825 4
8.2327463
282
SQUABESy CUBES, AKD BOOTS.
NOMBXS
SOUAXB.
559
31 24 81
560
313600
S6i
31 47 21
562
315844
563
316969
564
318096
565
319225
566
320356
567
321489
S68
32 26 24
369
32 37 61
570
324900
571
326041
572
327184
573
328329
574
329476
575
330625
576
331776
577
332929
578
334084
579
335241
580
336400
581
337561
582
338724
583
339889
584
341056
585
34 22 25
586
343396
587
344569
588
34 57 44
589
346921
590
348100
591
349281
592
350464
593
35 1649
594
352836
595
354025
596
35 52 16
597
356409
598
357604
599
358801
600
360000
601
36 12 01
602
362404
603
363609
604
364816
605
366025
606
367236
607
368449
60S
369664
609
370881
610
372100
611
373321
612
37 45 44
613
375769
0«4
376996
Cube.
Squarb Root.
Cvbb Rooiv
174676879
23.6431808
8.237 661 4
175616000
23664 319 1
8.2425706
176558481
236854386
8.247474
177504328
23.7065392
8.2523715
178453547
23.727 621
8.2572633
179406 144
23.7486842
8.2621492
180362 125
23.7697286
8.2670294
181 321 496
23.7907545
8.2719039
182 284 263
23.8117618
8.2767726
183250432
238327506
8.2816255
184 220 009
23.8537209
8.2864928
185193000
23.8746728
8.2913444
186169411
23.8956063
8.2961903
187 149 248
23.916 521 5
8.3010304
188 132 517
23.9374184
8.3058651
189 119224
23.958 297 1
8.3106941
190109375
239791576
8.3155175
191 102 976
24
8.3203353
192100033
24.020 824 3
8.325 147 5
193 100 552
24.041 630 6
8.3299542
194 104 539
24.0624188
8.3347553
195 1 12 000
24.0831891
8.3395509
196122941
24.1039416
8.344341
197 137 368
24.1246762
8.3491256
198155287
24.1453929
8.3539047
199176704
24.1660919
8.3586784
200201625
24.1867732
8.3634466
201230056
24.2074369
8.3682095
202262003
24.228 082 9
8.3729668
203297472
24.2487113
8.3777188
204336469
24.2693222
8.3824653
205379000
24.2899156
8.3872065
206425071
24.310 491 6
8.3919423
207 474 688
24 331 050 1
8.3966729
208527857
24351 591 3
8.401 398 1
209584584
24.3721152
8.406 1 18
210644875
24.392 621 8
8.4108326
211 708736
24.413 III 2
8.415 54^9
212 776 173
244335834
8.420246
213847192
244540385
8.424 944 8
214921799
244744765
8.4296383
216000000
24.4948974
8.4343267
217081801
24-5153013
8.4390098
218 167 208
24-5356883
8.4436877
219256227
24-5560583
8.4483605
220348864
24.5764115
8.4530281
221 445 125
245967478
8.4576906
222 545 016
24.6170673
8.4623479
223648543
24-63737
8467
224 755 712
24.657 656
8u|7i 647 I
225866529
24.6779254
8^762892
226981000
24.698 178 1
8.4809261
228099131
24.7184142
8.4855579
229 220 928
247386338
8.4901848
230346397
24-7588368
8.4948065
231475544
84.7790234
8.4994233
SQUABBS, CUBES, AND BOOTS.
283
JfWVMM.
Squabb.
Cube.
Squabb Root.
CcBB Root.
61s
378225
232 608 375
24.7991935
8.504035
616
379456
233744896
24.8193473
8.5086417
617
380689
234885 113
24.8394847
8.5132435
618
381924
236029032
24.8596058
8.5178403
619
3831^1
237176659
24.8797106
8.522 432 1
620
384400
238 328 000
24.8997992
8.5270189
621
385641
239483061
24.9198716
8.531 6009
62s
386884
240641848
24.9399278
8.536178
623
388129
241804367
24-9599679
8.540 750 1
624
389376
242 970 624
24.979992
8.5453173
625
390625
244140625
25
8.5498797
626
391876
245134376
25.019992
8.5544372
627
393129
246491 883
25.0399681
8.5589899
628
394384
247673152
250599282
8.5635377
629
395641
248 858 189
25.0798724
8.5680807
630
396900
250047000
25.0998008
8.5726189
631
39 81 61
251239591
25.1197134
8.5771523
632
399424
252435968
25.1396102
8.5816809
633
400689
253636137
35-1594913
8.5862047
634
401956
254 840 104
25.1793566
8.5907238
635
403225
256047875
25.1992063
8.595238
636
404496
257259456
25.2190404
8.5997476
637
405769
^258474853
25.2388589
8.604 252 5
638
407044
259694072
25.258 661 9
8.6087526
639
408321
260917119
352784493
8.613 248
640
409600
262144000
25.2982213
8.6177388
641
41 08 81
263374721
25.3179778
8.622 224 8
642
41 21 64
264609288
25-3377189
8.6267063
643
413449
265847707
25-357444 7
8.631 183
644
414736
267089984
35.377 155 1
8.6356551
645
416025
268336125
353968502
8.6401226
646
41 73 16
269585136
35.4165301
8.6445855
647
418609
270840023
25.4361947
8.6490437
648
419904
272097792
35.4558441
8.6534974
949
42 12 01
273359549
25-4754784
8.6579465
650
422500
274625000
35.4950976
8.662391 1
651
42 38 DI
275894451
35 514 701 6
8.666831
652
425104
420409
277 167 808
35.5342907
8.6712665
653
278445077
355538647
86756974
654
42 77 16
279726264
35.5734237
8.680 123 7
65s
429025
281 Oil 375
35.5929678
8.6845456
656
430336
282300416
25.6124969
8.688963
657
431649
283593393
25.6320112
8.6933759
658
432964
284890312
25,6515107
8.6977843
659
454281
286191 179
25.6709953
8.7021882
660
4356OQ
43692^
287496000
25.6904652
8.7065877
661
288804781
25.7099203
8.7109827
662
438244
290117528
35-7293607
8.7153734
663
439569
291434247
25.7487864
8.7197596
664
440896
293754944
25.768197 s
8.724 141 4
66s
44 32 2 J
294079625
25.7875939
8.7285187
666
443556
29s 408 296
258069758
8.7328918
667
444889
296740963
25.8263431
8.7372604
668
446224
298077632
95.845696
8.741 ^^4 6
669
447561
299418309
35.8650343
8.7459846
670
448900
300763000
35.8843583
8. 7503491
2S4
SQUABES, OtTBES, AKD BOOTS.
NtTBIBKB.
S<IUABB.
CUBR.
671
450241
302 III 711
672
451584
303464448
673
452929
304821 217
674
454276
306 182 024
675
455625
307546875
676
456976
308915776
677
458329
310288733
678
459684
311 665 752
679
46 10 41
313046839
680
462400
314432000
681
463761
315 821 241
682
465124
317 214 568
683
466489
3186II987
684
467856
320013504
685
469225
321 419 125
686
470596
322828856
687
471969
324 242 703
688
473344
325660672
689
474721
327 082 769
690
476100
328509000
691
477481
329939371
692
478864
331373888
693
48 02 49
332812557
694
481636
334255384
695
483025
335702375
696
484416
337153536
697
485809
338608873
698 •
48 72 04
340068392
699
488601
341532099
700
490000
343000000
701
49 14 01
344472 lOI
702
49 28 04
345948408
703
494209
347428927
704
49 56 16
348913664
705
497025
350402625
706
498436
351 895 816
707
499849
353393243
708
501264
354894912
709
502681
356400829
710
504100
357911000
711
505521
359425431
712
506944
360944128
713
508369
362467097
714
509796
363994344
71S
51 1225
36552587s
716
512656
367 061 696
717
514089
368601813
718
51 55 24
370146232
719
516961
371694959
720
518400
373248000
721
5198 41
374805361
722
52 1284
376367048
723
52 27 29
377933067
724
52 41 76
379503424
72s
52 56 25
381 078 125
726
52 70 76
382 657 176
S<it7ARB Root.
Cubs Root.
25.9036677
8.7546913
25.922 962 8
8.7590383
25.942 243 5
8.7633809
25.961 51
8.767 7^9 2
25.980 762 1
8.7720532
26
8.776383
26.0192237
8.7807084
26.0384331
8.7850296
26.0576284
8.7893466
26.0768096
8.7936593
26.095 976 7
8.7979679
26.115 129 7
8.802 272 I
26.1342687
8.8065722
26.1533937
8.8108681
26.1725047
8.815 1598
26.191601 7
8.8194474
26.2106848
8.8237307
26.229 754 1
8.8280099
26.248 809 5
8,832285
26.267 851 1
8,8365559
26.2868789
8.8408227
26-3058929
8.8450854
26.3248932
8.849344
26.3438797
8.8535985
26.362 852 7
8.8578489
26.3818119
8.862 095 2
26.400 757 6
8.8663375
26.4196896
8.8705757
26.4386081
8.8748099
26.4575131
8.87904
26.4764046
8.8832661
26.495 282 6
8.8874882
26.5141472
8.891 7063
26.5329983
8.8959204
26.551 836 1
8.9001304
26,5706605
89043366
26.5894716
8.908 538 7
26.608 269 4
8.912 7369
26.6270539
8.916931 1
26.645 825 2
8.921 121 4
26.6645833
8.9253078
26.6833281
8.9294902
26.702 059 8
8.9336687
26.7207784
8.9378433
26.7394839
8,942014
26.7581763
8,9461809
26.7768557
8.9503438
26.795522
8.9545029
26.8141754
8.9586581
26.8328157
8,962809 s
26.8514433
8.966957
26.8700577
8.971 1007
26,8886593
8.9752406
26.907 248 1
8.9793766
26.925 824
8.9835089
26.9443872
8.9876373
SQUABES, CUB£8, AKD KOOTS.
285
fTcmn.
Squabs.
CUVM.
Squabi Root.
CiTBK Root.
727
528529
384 240 583
26.9629375
8.991 762
728
539984
385828352
26.981 475 I
8.9958829
729
53 14 41
38742048^
27
9
730
532900
389017000
27.0185122
9.004 113 4
731
534361
390617 891
27.037 01 1 7
9.008 333 9
732
535824
393 333 168
27-0554985
9.0133388
733
537289
393832837
27.0739727
9.0164309
734
538756
395446904
27.0924344
9.0305293
735
540225
397065375
27.1108834
'^^ 9.024 623 9
736
541696
398688356
37.1393199
9.0287149
737
543169
40031^553
27-1477439
9.032 803 I
738
5^:644
401 947 373
27.1661554
9.036 885 7
739
546131
403583419
37.1845544
9.0409655
740
547600
405334000
37.303941
9.0450417
741
549081
406869031
27.3313153
9.0491143
742
550564
408518488
27.3396769
9053 183 1
743
552049
410 173 407
27.3580363
9.057 348 3
744
553536
41 1 830 784
27.2763634
9.0613098
745
555025
413493635
37.3946881
9.0653677
746
556516
415160936
37.3130006
9.069 422
747
558009
416833733
27-331300^
90734726
748
559504
418508993
273495887
9.0775197
749
56 10 01
430189749
27.3678644
9.081 563 1
750
562500
431875000
37.3861279
9.085 603
751
564001
423564751
27-4043792
9.0896392
752
565504
435359008
37.4336184
90936719
753
567009
426957 777
87.4408455
9097701
754
568516
438 661 064
37.4590604
9.1017365
755
570035
430368875
27.4773633
9.1057485
756
571536
433081 316
274954542
-9.1097669
757
573049
433798093
27-513633
9.1137818
758
574564
435 519 512
27-531 7998
9.1177931
759
576081
437245479
275499546
9.121 801
760
577600
438976000
27.568 097 5
9.1258053
761
57 91 31
440 71 1 081
27.586 228 4
9.129 806 1
762
580644
443450738
27.6043475
9-1338034
763
582169
444194947
37.623 454 6
9.137 797 1
764
583696
445943744
27.6405499
9.1417874
765
585235
447697135
37.6586334
9.1457742
766
586756
449455096
27.676 705
9-1497576
767
588289
451 217663
27.6947648
9-153 7375
768
589824
453984833
27.7128129
9157 7139
769
59 13 61
454756609
27.7308492
9.161 6869
770
592900
456533000
27.7488739
9.1656565
771
594441
458 314 on
27.7668868
9.1696335
773
595984
460099648
27.784888
9-1735852
773
597529
461 889917
27.802 877 5
91775445
774
599076
463 684 834
27.8208555
9. 181 5003
775
600625
465484375
27.8388218
9.1854527
776
60 31 76
467388576
27.8567766
9.1894018
777
603739
469097433
27.874 719 7
9-1933474
778
605284
470910953
27.8926514
9.1972897
779
606841
473739139
27.9105715
9.201 2286
780
608400
474552000
27.928 480 z
9.205 164 1
781
609961
476379541
279463772
9.2090963
783
61 1524 .
478311768 i
27.9643629
9.213025
286
SQTTABBS, CUBES, AND BOOTS.
NOMBER.
SaUAKK.
Cube.
8<ti7ARi Root.
783 .
613089
480048687
27.982 137 2
784
614656
481890304
38
785
61 62 25
483736625 '
38.0178515
786
61 7796
485587656
28.035 691 5
787
619369
487443403
28.0535203
788
620944
489303872
28.0713377
789
622521
491 169069
28.089 1 43 8
790
624100
493039000
28.1069386
791
62^681
494 913 671
28.1247222
792
627264
496793088
28.1424946
793
628849
498677257
28.1602557
794
630436
500566184
28.1780056
795
63 20 25
502 459 875
28.1957444
796
633616
504358336
28.213 472
797
635209
506261573
28.231 1884
798
636804
508169592
28.2488938
799
63 84 01
510082399
28.2665881
800
640000
512000000
38.2842712
801
64 16 01 .
513922401
38.3019434
802
643204
515849608
28.319604 s
803
644809^
517781627
28.3372546
804
6464 16
519718464
28.3548938
805
648025
521 660 125
28.372 521 9
806
649636
523606616
28.390 139 1
807
651249
525557943
28.407 745 4
808
652864
527 514 112
28.4253408
809
654481
529475129
28.4429253
8to
656100
531 441 000
28.4604989
811
65 77 21
5334" 731
28.478061 7
812
659344
535387328
28.4956137
813
660969
537367797
28.5131549
814
662596
539353144
28.5306852
815
664225
541343375
28.548 204 8
816
665856
543338496
28.5657137
817
667489
545 338 513
28.5832119
818
669124
547343433
28.6006993
819
67 07 61
549353259
28.618 176
820
672400
551368000
28.635 642 I
821
674041
553387661
28.6530976
822
675684
555412248
28.6705424
823
677329
557441767
28.6879766
824
67 89 76
559476224
28.7054002
825
680625
561515625
28.722 813 2
826
682276
563559976
28.7402157
827
683929
565609283
28.757 607 7
828
685584
567663552
28.7749891
829
687241
569722789
28.7923601
830
688900
571787000
28.8097206
831
690561
573856191
28.827 070 6
83a
692224
575930368
28.844 410 2
833
693889
578009537
28.8617394
834
695556
580093704
288790582
835
697335
582182875
28.8963666
836
698896
584277056
289136646
837
700569
586376253
289309523
838
702244
588480472
38.948 229 7
CuBB Roon
9.216950 s
9.2208726
9.2247914
9.2287068
9.2326189
9.2365277
9.2404333
9-244335 5
9.2482344
9.252 13
9.256 022 4
9.259 91 1 4
9.2637973
9.267 679 8
9-2715592
9-2754352
9.2793081
9.2831777
9.287044
9.2909072
9.294 767 1
9.298 623 9
9.3024775
9.3063278
9-310175
9.314 019
93178599
9.321697 s
9325532
93293634
9-333 191 6
9.3370167
9.3408386
9-3446575
93484731
9.3522857
9-3560952
93599016
93637049
9-3675051
9.3713023
9-3750963
9.3788873
9.3826753
9.38646
9.3902419
9.3940206
9-3977964
9.401 569 1
9-4053387
94091054
9.412869
9.4166297
9.4203873
9.424 143
9.4278936
SQUAB£:S, CUBJSfe, Al^D BOOTS.
287
(fmBn.
Sqv
Cvss.
839
703921
840
705600
841
70 72 81
842
708964
843
710649
844
71 23 36
845
714025
846
71 57 16
847
717409
848
719104
849
720801
850
722500
85^
72 42 01
852
725904
853
727609
854
729316
855
731025
856
732736
857
7344 49
858
736164
859
737881
860
739600
861
74 13 21
862
743044
863
744769
864
746496
865
748225
866
749956
867
751689
868
753424
869
755161
870
756900
871
758641
872
760384
873
762129
874
763876
87s
765625
876
767376
877
7691 29
878
770884
879
772641
880
774400
881
77 61 6i
882
777924
883
779689
884
781456
885
783225
886
784996
887
786769
888
788544
889
790321
890
792100
891
793881
892
795664
893
797449
799236
894
590589719
592704000
594823321
596947688
599077107
601 211 584
603351 125
605495736
607645423
609800192
611960049
614125000
616295051
618470208
620650477
622 835 864
625026375
627222016
629422793
631 628 712
633839779
636056000
638 277 381
640503928
642735647
644972544
647214625
649 461 896
651 714363
653972032
656234909
658503000
660776311
663054848
665338617
667 627 624
669921875
672 221 376
674526133
676836152
679 151 439
681 472 000
683797841
686128968
688465387
690807 104
693 154 125
695506456
697 864 103
700 227 072
702595369
704969000
707347971
709 732 288
712 121 957
7X4516984
S^CARB Root.
28.9654967
28.982 753 5
29
29.0172363
29.0344623
290516781
29.0688837
29.0860791
29.1032644
29.1204396
29.1376046
291547595
29.1719043
29.189039
29.206 163 7
29.223 278 4
29.240383
292574777
29.2745623
29 291 637
29.308 701 8
293257566
29.342 801 5
293598365
29.3768616
29-3938769
29.4108823
29.4278779
294448637
29.461 839 7
29.4788059
29.4957624
29.512 709 1
29.5296461
295465734
29563491
295803989
29 597 297 2
29 614 185 8
29.631 0648^
29.6479342"
296647939
29.681 644 2
296984848
297153159
29-7321375
29.7489496
29 765 752 I
29.782 545 2
297993289
29.816 103
29.8328678
29.849623 1
29.866369
29.883 105 6
29.8998328
CiJBB Root.
9.4316423
9-43538
94391307
9.4428704
9.446 607 2
9.450341
9.4540719
9 457 7999
9.461 524 9
9.465 247
9.468 966 1
9 472 682 4
94763957
9.480 106 1
9.4838136
9.4875182
9.491 22
9.4949188
94986147
9.5023078
9505998
9.5096854
95133699
9-5170515
9-5207303
9.5244063
9.5280794
95317497
95354172
9 539081 8
95427437
9.5464027
95500589
95537123
9557363
9 561 010 8
95646559
9.568 298 2
9-5719377
9-575 5745
95792085
9.5828397
9.586 468 2
95900937
95937169
9-597 3373
9.600 954 8
9.604 569 6
9608181 7
9.61 1 791 1
9-6153977
9.619001 7
9 622 603
9.626 201 6
9.629 797 5
0.6333907
288
BQUABBS, CUBES, AMD BOOTS.
NulfBKB.
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
9SO
SQOAftS.
801025
802816
804609
806404
80 $2 01
810000
81 18 01
813604
815409
81 72 16
819025
820836
82 26 49
824464
826281
828100
829921
831744
833569
835396
83 72 25
839056
840889
84 27 24
844561
846400
84 82 41
850084
851929
853776
855625
857476
85 93 29
861184
863041
864900
866761
868624
870489
872356
874225
876096
877969
879844
881721
883600
885481
887364
889249
891136
89. 325
894916
896809
898704
900601
902500
CUBK.
716917375
719 323 136
721734273
724 150 792
726 572 699
729000000
731 432 701
733870808
736314327
738763264
741 217625
743677416
746 142 643
748 613 312
751089429
753571000
756058031
758550528
761 048 497
763551944
766060875
768 575 296
771 095 213
773620632
776 151 559
778688000
781 229961
783777448
786330467
788889024
791453125
794 022 776
796597983
799178752
801 765089
804357000
806954491
809557568
812 166237
814780504
817400375
820025856
822 656 953
825 293 672
827936019
830584000
833237621
815896888
838561807
841 232 384
843908625
846590536
849278 123
851 971 392
854670349
857375000
Sqdabr Root.
29.9165506
299332591
29.9499583
29.966648 I
299833287
30
30.016662
300333148
30.0499584
30.066 592 8
30.0832179
30.0998339
30.1164407
30.1330393
30.1496269
30.1662063
30.1827765
30.1993377
30.2158899
30.232 432 9
30.248 966 9
30.265 491 9
30.282 007 9
30.2985148
303150128
30.331 501 8
30.347 981 8
30.3644529
30.3809151
30.3973683
304138127
30.4302481
30.4466747
30.4630924
30.4795013
30.4959014
30.5122926
30.528675
30.5450487
30.5614136
30.5777697
30.5941171
30.6104557
30.626 785 7
30.6431069
30.6594194
30.6757233
30.692 018 5
30.708305 I
30.724583
30.7408523
30.757113
30.7733651
30.7896086
30.8058436
30.823 07
CuBB Roof.
9.636 981 2
9.640 569
9.6441542
9.647 736 7
9.6513166
9.6548938
9.658 468 4
9.662 04Q 3
9.6656096
9.6691762
9.672 740 3
9.676 391 7
9.6798604
9.6834166
9.686 970 1
9.690521 1
9.6940694
.9.6976151
9.7011583
9.7046989
9.7082369
9.7117723
9-7153051
9.7188354
9.722 363 I
9.725 888 3
9.7294109
9.7329309
9.7364484
97399634
9-7434758
9.7469857
9750493
9-7539979
9-7575002
9.761 000 1
9-7644974
9.767 992 2
9.771 484 5
9-7749743
9.778 461 6
9.7819466
9.7854288
9.7889087
9.792 386 1
9.795 861 1
9-7993336
9.802 803 6
9.806271 1
9.8097362
9.8131989
9.816659 I
9.8201169
9.8235723
9.827 025 2
9.8304757
BQITABBS, CtTBBS, AND BOOTS.
289
SQOilBI.
9SI
904401
860085351
95a
906304
862801408
953
908209
865523177
954
91 01 16
868250664
955
912025
870983875
956
913936
873 722 8i6
957
915849
876467493
958
917764
879 217 912
959
91 96 81
881974079
960
921600
884736000
961
923521
887503681
963
925444
890277128
963
927369
893056347
964
929296
895841344
96s
931225
898632125
966
933156
901428696
967
935089
904231063
968
937024
907039232
969
938961
909853209
970
940900
912673000
971
942841
915 498 61 1
972
944784
918330048
973
^.!l3
921167317
974
948676
924010424
975
950625
926859375
976
95 25 76
929714176
977
954529
932574833
978
956484
935441352
979
958441
938313739
980
960400
941 192000
981
962361
944076141
982
964324
946966168
983
966289
949862087
984
968256
952763904
98s
970225
955671625
986
972196
958585256
987
974169
961504803
988
976144
964430272
989
97 81 21
967361669
990
980100
970299000
991
982081
973242271
992
984064
976 191 488
993
986049
979146657
994
988036
982 107 784
995
990025
985074875
996
992016
988047936
997
994009
991026973
9Q8
996004
994011992
999
998001
997002909
1000
lOOQOOO
1000000000
zooz
looaooi
z 003 003 001
I003
ZOO 40 04
z 006012008
XOO3
zoo 60 09
z 009027027
1004
Z0080Z6
Z012048064
1005
XOZ0025
1015075125
1006
1019036
1018108216
CVBK.
Squakb Root.
30^382879
30.8544972
30.8706981
30.8868904
30.9030743
30.9192477
30.9354166
30.951 575 1
30.967 725 I
30.9838668
31
31.016 124 8
31.0322413
31.0483494
31.0644491
31.0805405
31.0966236
31.1126984
31.1287648
31.144823
31.1608729
31.1769145
31.1929479
31.2089731
31.22499
31.2409987
3Z.2569992
3Z.27299Z5
31.2889757
31.304951 7
31,3209195
31*3368792
31*3528308
31.3687743
31.3847097
31.4006369
31.4165561
31.4324673
31.4483704
31.4642654
31.4801525
31.4960315
31.5119025
31-5277655
31.5436206
31-5594677
31-5753068
31.591 138
31.6069613
31.6227766
31.638584
31.6543836
31.6701752
31.685959
31.7017349
3i*7i7503
CvBB Root.
9-8339238
9.8373695
9.8408127
9.8442536
9.847692
9.851 128
9-8545617
9-8579929
9.861 421 8
9.8648483
9.868 272 4
9.871 694 1
9-8751135
9-8785305
9.881 945 1
9-8853574
9.8887673
9.8921749
9-8955801
9.898983
9-9023835
9.9057817
99091776
9.912 571 2
9.9159624
9.9193513
9.9227379
9.926 122 2
9.9295042
99328839
9.9362613
9.9396363
99430092
99463797
9-9497479
9-9531138
9956477 s
99598389
9.963 198 1
9-9665549
9-9699095
9.9732619
9.976612
9-9799599
9-9833055
9.9866488
9.98999
9-9933289
9.9966656
10
10.003 322 2
10.0066622
10.0099899
10.0133155
10.016^89
zox>i996ox
290
SQtTABBS, OUBBS) AND BOOTS.
NUMBBB.
SqUARB.
Ct'BB.
1007
1 01 40 49
1021 147343
1008
1 01 6064
1024 192 512
1009
1 01 8081
1027243729
lOIO
1 02 01 00
I 030 301 000
lOlI
1 02 21 21
XO3336433I
10x2
1024144
1036433728
IOI3
1 02 61 69
I 039 509 197
IOI4
1 02 81 96
1042590744
IOI5
1030225
104567837s
IOI6
1 03 22 56
1048772096
1017
1034289
I 051 871 913
IOI8
1036324
1054977832
IOt0
1038361
1058089859
1020
10404UO
1061208000
102 1
104244X
1064332261
I023
1044484
1067462648
1023
1046529
1070599167
1024
1048576
1073741824
1025
1050625
1076890625
1026
1 05 26 76
1080045576
1027
1054729
1083206683
1028
1056784
108637395a
XO29
1058841
1089547389
1030
1060900
1092727000
IO3I
1 06 2961
1095 912 791
1032
1065024
1099104768
«033
1067089
1102302937
1034
1 0691 56
1105507304
X035
107x225
1108717875
X036
1073296
1111934656
1037
1075369
I 115 157653
X038
1077444
1 1 18 386 872
1039
1079521
1121 622319
X040
io8i6xx>
I 124864000
1041
1083681
1 128111921
i04d
1085764
1 X31 t66o88
X 134626507
1043
1087849
J044
1089936
1137893184
1045
1092025
1 141 166x25
1046
1 09 41 16
114444533^
1047
1096209
1147730833
1048
1098304
1151022593
1049
1 10040X
1154320649
1 157625000
X050
1 102500
1051
1 104601
1 160935651
1053
1 106704
1 164252608
1053
1108809
1167575877
IOS4
1 11 09 16
1170905464
«o55
I II 3035
1174241375
1056
111 51 36
1177583616
I0S7
1117249
1180932T93
1058
1119364
z 184287x12
1059
1121481
1187648379
1060
1 123600
1 191 016000
1061
1125721
1194389981
tote
1137844
1197770388
SquABB Root. | Cvbb BooIL
31-7332633
10.023 379 1
31.7490157
10.0265958
31.7647603
10.0299x04
31.780497 a
10.033 223 8
31.7962263
10.036533
31.81 1 9474
10.039 641
31.8276609
10.043 1469
31.843 3O6 6
10.0464506
31.8590646
10.0497531
31.8747549
10.0530514
31.8904374
10.0563485
3x9061123
10.0596435
31.9217794
10.0629364
31-9374388
10.066 337 1
31.9530906
10.0695156
31.9687347
10.072 803
31.9843712
10.0760863
32
10.0793684
32.0x56212
10.0826484
32.0312348
10.0859262
32.0468407
10.0892019
32.063 439 X
10.0924755
32.0780298
10.0957469
32.0936131
10.0990163
32.1091887
10.1022835
32.1247568
10.1055487
321403173
10.1088117
32.1558704
10.1120736
32.1714159
10.1155314
32.1869539
10.1185882
32.2024844
10.1218438
33.3x80074
10.126095.3
32.3335239
10.1283457
32.24^31
10.1315941
32.2645316
10.1348403
32.3800248
10.1380845
33.3955105
10.1413266
333109888
10.1445667
33.3264598
10.1478047
33.3419233
10.15x0406
32.3573794
XO.I549744
32.373 828 1
10.1575062
33.38^2695
10.1607359
32.4037035
10.1639636
32.419 130 1
10.167 1893
32.4345495
10.1704139
32.4499615
10.1736344
32.465366 a
10.1766539
33.4807635
10.1800714
33.496 1536
10.1832868
32*5115364
10.1865002
33.5369119
10.1897116
33.543 280 a
10.1939209
32.5576413
XO.I961283
32.5729949
10.1993336
38-5883415
10.202 5569
SQUABES, CUBSSy AND BOOTS.
291
NUMBSB.
Sqvabb.
1 129969
Ctm.
Squakx Root.
Cv» Rook.
1063
X20X 157047
32.6036807
10.205 738 S
XO64
1x32096
1204550x44
32.6190129
10.2089375
1065
1 134225
1207949625
32.6343377
10.212 134 7
1066
1136356
I 2X1 355496
32-6496554
10.21533
1067
1 138489
X 214 767 763
32.6649659
10.2185233
IO6S
1 140624
X 218 186432
32.6802693
10.221 7146
1069
1 14 27 61
X 221 6X1 509
32.6955654
10.2249039
1070
1 144900
1225043000
32.7108544
10.228091 3
XO7I
X 147041
X 228 480 911
32,726x363
10.23x2766
1072
X 149x84
X 231 925 248
32.74141x1
10.2344599
XO73
1151329
1235376017
32.7566787
10.2376413
1074
II53476
1238833224
32.7719392
10.240 820 7
1075
1 155625
1242296875
32.7871926
10.2439981
1076
1157776
1245/66976
32.8024389
10.2471735
1077
1159929
1249243533
32.8176782
XO.250347
1078
1 162084
X 252 726 552
32.8329103
10.2535186
1079
I X6424I
1 256216039
32.848x354
XO.2566881
1080
1 166400
I 259712000
32.8633535
10.2598557
IO8I
1168561
1263 214 441
32.8785644
102630213
1082
1 170724
1266723368
32.8937684
10.266 185
1083
1 172889
1 270 238 787
33.9089653
10.2693467
1084
1 175056
1273760704
32.9241553
10.2725065
1085
1177225
1 277 289 125
32.9393382
10.2756644
1086
1 179396
1280824056
32.9545141 •
10.2788203
1087
1 181569
1284365503
32.969683
10.281 974 3
1088
1x83744
1287913472
32.984845
X0.285 1264
1089
X x8592X
1 291 467 969
33
X0.288 276 5
1090
X188100
1295029000
33.015 148
10.291 424 7
XO9I
X X90281
1 298 596 571
33.030 289 1
10.2945709
1092
X 192464
1302170688
33.0454233
10.2977153
1093
1x94649
1 305 751 357
330605505
10.3008577
1094
XX96836
1309338584
33.0756708
10.3039983
1095
X 199025
.1312932375
330907843
10.3071368
XO96
I 20 12 16
1 316 532 736
33.1058907
10.3102735
1097
1203409
I 320 139673
33.1209903
10.3x34083
1098
1205604
I 323 753 192
33.136083
X0.316 541 X
1099
X 20 78 01
1327373299
33.151 1689
10.3196721
1 100
X 2x0000
X 331 000000
33.1662479
10.322 801 2
IIOI
I 21 2201
1 334 633 301
3318132
10.3259284
XI02
I 21 4404
1338273208
33.1963853
10.3290537
1X03
12x6609
1 341 919 727
33.2114438
10.332177
1X04
1 21 88 x6
1345572864
33.2266955
10.3352985
ixos
1221025
1349232625
33.2415403
10.3384181
1x06
1223236
X 352 899016
33.2565783
10.3415358
1x07
1225449
1356572043
33.2716095
10.3446517
1 108
I 227664
13602517x2
33.2866339
10.3477657
1x09
X 229881
1363938029
33.301 651 6
10.3508778
IXIO
I 23 21 00
1367631000
33.3166625
10.353988
IKII
I 234321
1 371 330631
33.3316666
10.3570964
XXI2
1236544
1375036928
33.346664
10.3602039
i"3
X 238769
1378749897
33-3616546
10.363.3076
IXI4
1240996
1382469544
33.3766385
10.3664103
"I5
1243225
I 386 195 875
33391 615 7
10.3695113
1X16
1245456
1389928896
33.4065862
10.3726103
III7
X 24 76 89
I 393668613
33.4215499
10.3757076
XI18
1349924
1397415032
33.436507
10.378803
292
BQUABBS, CUBBS, AND BOOTS.
NUMBBK. '
[1 19
:i20
tI2I
[122
CI23
[124
:i25
[I26
[127
[I28
;i29
130
131
132
133
134
135
:i36
137
138
1 139
[140
[141
[142
fi43
[144
ti45
[146
[147
[148
[I49
:i5o
151
:iS2
C153
C154
^155
[156
ti57
:iS8
C159
[160
[161
[162
:i63
;i64
165
166
[167
:i6g
169
170
171
:i72
X73
:x74
Squarb.
J
Cube.'
I 25 21 61
1254400
I 256641
1258884
I 261129
1263376
1265625
I 26 78 76
1 2701 29
1272384
I 27 46 41
I 276900
I 27 91 61
I 28 14 24
1283689
I 28 59 56
1288225
1290496
1292769
1295044
I 29 73 21
1299600
1 30 i8-8i
1304164
1306449
1308736
1 31 10 25
1 31 33 16
1315609
1317904
132020Z
1322500
1 32 48 01 .
I 32 71 04
1329409
1331716
133402s
1336336
1338649
1340964
1343281
1345600
1347921
1350244
1352569
1354896
135722s
1359556
136 1889
1364224
1 3665 61
1368900
1371241
1373584
1375929
1378276
401 168 159
404928000
408694561
412 467 848
416 247 867
420034624
423828125
427628376
431435383
435249152
439069689
442897000
446731091
450571968
454419637
458274104
462135375
466003456
469878353
473760072
477 648 619
481544000
485446221
489355288
493 271 207
497193984
SOI 123625
505 060 136
509603523
512953792
5 16 910 949
520875000
524845951
528823808
532808577
536800264
540798875
544804416
548816893
552836312
556862679
560896000
564936281
568983528
573037747
577098944
581 167 125
585 242 296
589324463
593413632
597509809
601 613000
605723211
609840448
613964717
618096024
S<iDABB Root.
334514573
33.466401 1
33.481 338 I
33.4962684
33.51U921
335261092
33.5410196
33.5559234
33.5708206
33.585 711 2
33.6005953
33.6154726
33.6303434
33.6452077
33.6600653
33.6749165
33.689 761
33.7045991
33.7194306
33.7342556
33.7490741
33.7638860
33.7786915
337934905
33.808 283
33.8230691
33.8378486
33.8526218
33.8673884
33.8821487
33.8969025
33.9116499
33.9263909
33.9411255
33-9558537
33.9705755
33.985291
34
34.014 702 7
34.029399
34.044089
34.0587727
34.0734501
34.088 121 I
34.102 785 8
34.1174442
34.1320963
34.1467422
.34.1613817
34.176015
34.190642
34.205 262 7
34.2198773
34.2344855
34.2490875
34.2636834
Cum Root.
[0.381 896 5
[O.3849882
[O.3880781
[O.391 166 1
10.3942523
10.3973366
[O.4004192
[&.4034999
[O.4065787
10.4096557
[O.412 731
[O.4158044
[O.418 876
[O.421 945 8
[O.425 013 8
[O.42808
[O.431 1443
[0.4342069
[O.437 267 7
[O.440 326 7
10.4433839
10.4464393
10.4494929
10.4525448
10.4555948
[0.4586431
[ 0.461 6896
10.4647343
[04677773
[O.4708185
104738579
[0.4768955
10.4799314
[O.482 965 6
[O.485998
[0.4890286
[0492057S
[O.4950847
[0.4981101
10.5011337
[0.5041556
[O.5071757
[0.510 194 2
[0.5132109
[0.5162259
[O.5192391
[0.522 2506
[0.5252604
[O.5282685
10.5312749
10.5342795
[0.5372825
[0.540 283 7
[0.543283 a
[0.546281
[0.5492771
6<)tTABBS, CUBES, AND BOOTS.
293
"75
1x76
1177
1 178
1179
1 180
1 181
1182
I183
I184
1 185
1186
1 187
I188
I189
I190
1191
1192
"93
"94
"95
1196
"97
1198
"99
1200
I20I
X202
1203
1204
I20S
1206
1207
1208
1209
I2IO
I2XI
I2I2
1213
I2I4
1215
12X6
I217
12X8
I2I9
1220
I22I
1222
1223
1224
X225
1226
1227
1228
Z229
K2J0
8«VAK>.
380625
382976
385329
387684
390041
393400
394761
397124
399489
401856
404225
406596
408969
41 1344
41 37 21
41 61 00
41 84 81
420864
423249
425636
428025
430416
432809
435204
437601
440000
442401
444804
447209
449616
452025
454436
456849
459264
46 16 81
464100
466521
468944
471369
473796
476225
478656
481089
483524
485961
488400
490841
493284
495729
498176
500625
503076
505529
507984
5*0441
512900
CUBB.
622 234 375
626379776
630532233
634691752
638858339
643032<xx>
647 212 741
651400568
655595487
659797504
664006625
668 222 856
672 446 203
676676672
680914269
685159000
689 410 871
693669888
697936057
702209384
706489875
710777536
715072373
719374392
723683599
728000000
732323601
736654408
740992427
745337664
749690x25
754049816
758416743
762790912
767172329
771 561 000
775 956 9"^!
780360128
784770597
789188344
7936x3375
798045696
802 485 313
806932232
811 386459
815848000
8203x6861
824793048
829 276 567
833 767 424
838265625
842771 X76
847 284 083
85x804352
856331 989
860867000
BquAKm Root.
34.278273
34.2928564
34-3074336
34.3220046
34-3365694
34.351 128 I
34.3656805
34.380 226 8
34-394767
34-409301 X
34.4238289
344383507
34.4528663
34-4673759
34.4818793
34.4963766
34.5108678
34-525353
34-5398321
345543051
34.568772
34.5832329
34.5976879
34.6x21366
34.6265794
34.64X 0x6 2
34.6554469
34.66987x6
34.6842904
34.698 703 X
34-7131099
34.7275x07
34.74x9055
34.7562944
34.7706773
34-7850543
34.7994253
34.8137904
34.828x495
34.842 502 8
34.8568501
34.87X 19X 5
34.885 527 X
34.8998567
34.9141805
34.9284984
34.9428x04
34.957x166
34.9714169
34.985 7" 4
35
35.0x4 282 8
35.0285598
35.0428309
35.0570963
35.071.3558
Chbb Root.
10.552 27 X 5
10.555 264 2
10.558 255 2
XO.5612445
10.564 232 2
10.567 2x8 I
10.570 202 4
10.5731849
XO.576 165 8
10.5791449
XO.582X225
XO.5850983
XO.5880725
10.591 045
XO.594OX58
10.596985
10.5999525
10.6029184
XO.605 882 6
10.608 845 1
10.61 1 806
X0.6X4 765 2
10.6177228
10.6206788
10.6236331
10.626 585 7
XO.6295367
10.632 486
10.6354338
10.6383799
10.641 324 4
XO.644 267 2
10.647 208 5
10.650 X48
10.653086
XO.6560223
X0.658957
XO.661 890 2
XO.664 821 7
XO.667 751 6
10.6706799
10.673 606 6
10.6765317
10.6794552
10.682 377 1
10.6852973
10.6882x6
10.691 133 1
10.6940486
10.696 962 5
XO.699 874 8
10.702 785 5
10.7056947
10.7086023
10.7x15083
10.714 412 7
294
SQtJABBS, CUBES, AND BOOTS.
[231
[232
t234
^235
[236
t237
[238
1239
[240
[241
[242
C243
[244
C245
[246
[247
[248
[249
1250
[251
[252
t253
1254
t255
1256
t257
[258
t259
[260
[26t
[262
[263
[264
[265
[266
[267
[26S
[269
1270
[271
[272
t273
[274
127s
[276
[277
C278
t279
t28o
[281
[282
[283
[284
t285
286
SqUARB.
151 5361
I 51 7824
I 520289
1 52 27 56
1525225
1527696
I 5301 69
1532644
1535121
1537600
1540081
1542564
1545049
1547536
1550025
1 55 25 16
1555009
1557504
1 560001
1 56 25 00
1565001
1567504
1570009
1572516
1575025
1577536
1580049
1 58 25 64
1585081
1587600
1590121
1592644
1595169
1597696
1600225
1602756
1605289
1 60 78 24
1 61 03 61
161 2900
1615441
161 7984
1 62 05 29
1 62 30 76
1625625
1628176
1630729
1633284
1635841
1638400
1640961
1643524
1646089
1648656
1651225
1653796
CVBB.
I SqvAKC Root. | Cubs Root.
1865409391
1869959168
1874516337
1879080904
1883652875
1 888 232 256
1 892 819053
1897413272
1 902 014 919
1 906 624 000
191 1 240521
1915864488
1920495907
1925134784
1929781 125
1934434936
1939096223
1943764992
1948441249
1953125000
1957816251
1962515008
1 967 221 277
1971935064
1976656375
1 981 385 216
1 986 121 593
1990865512
1995616979
2000376000
2005 142581
2009916728
301469S447
2019487744
2024284625
2029089096
2033901 163
2038720832
2043548109
2048383000
2053225511
2058075648
2062933417
2067798824
2072671875
2077552576
2082440933
2087336952
2 092 240 639
2 097 152 000
2 102 071 041
2 106 997 768
2 III 932 187
2 1 16 874 304
2 121 824 125
2126781656
35.0856096
35.0998575
35.1140997
35128 3361
35.1425568
35-1567917
35.171 0108
35.1852242
351994318
352136337
35.2278299
35.2420204
35.2562051
35.2703842
352845575
35.298 725 2
35.3128872
353270435
35 341 1941
35-3553391
353694784
35.383612
35 397 74
35 411 8624
354259792
35.4400903
35-4541958
35.4682957
35.48239
35.4964787
35-5105618
355246393
355387113
355527777
35.5668385
355808937
35-5949434
35.6089876
35.6230262
356370593
35."65i 0869
35.665 109
35.6791255
35.6931366
35.707 142 I
35.721 1422
35.7351367
35-7491258
35.7631095
35.7770876
35.7910603
35.8050276
35.8189894
35.8329457
35.8468966
35.8608421
0.7173155
0.7202168
0.7231165
0.7260146
0.7289112
0.7318062
0.7346997
07375916
0.7404819
0.7433707
0.7462579
0.7491436
0.7520277
0.7549103
0.757 791 3
0.7606708
0.7635488
0.7664252
0.7693001
0.7721735
0.7750453
0.7779156
0.7807843
0.7836516
0.7865173
0.7893815
0.792 244 T
0.7951053
0.7979649
0.800823
0.8036797
0.8065348
0.8093884
0.8122404
0.8150909
0.81794
0.820 787 6
0.8236336
0.8264782
0.8293213
0.8321629
0.835003
0.837 841 6
0.8406788
08435144
08463485
0-849 181 2
0.8520125
0.854 842 2
08576704
0.860 497 2
0.8633225
08661464
0.8689687
0871 7897
0-8746091
SQUABBS, CUBES, AKD ROOTS.
««'"■
Con.
S4u.ll R»I.
Cd«R»i. '
1656369
B 131 746 903
35.8747822
10.8774271
16S89M
2136719872
35.8887.69
.O.8S03436
i66isai
3141700569
35.902646.
16641 «.
3.46689010
35.9165699
10.8858723
2151685171
35.9304834
10-8886845
16693 6^
2156689088
35.94440.5
10.891 495 2
1671B49
3161700757
359583093
.0.8913044
167443S
2166720.84
.0.8971123
1677025
35^9«6>o8 4
.0-8999186
.679616
21767833^5
2 iS. 825 073
36
l6Baa09
36.0.3 886 3
.09055369
1684S04
2.86875593
36.037767'
.0,^08339
.68 7401
2191933899
36.0416436
10,911 .296
.6900™
3.97000000
360555138
10.9.39287
.69=60.
3 202073901
36.0693776
109.67365
.695204
3 307 .55 60a
36.083 337 1
10.9.95238
.697809
2 212 345 137
36.09709.3
10,9223177
1700+16
2217343464
36.1.09403
10925.11.
.703025
2222447635
36.1347837
10.9279031
.705636
2227560616
36.. 33 623
10.9306937
.708249
2332681443
36.. 52455
10.9334839
17.0864
23378101(2
36.1662836
10.9363706
I 71 3481
2342946629
36.180 .05
10.9390569
1716.00
2 248 09. QOO
36.1939331
10.941 S41 8
171873.
36.307734
.0.9,46253
2258403328
3622.5406
.0.9475074
1733969
3363571297
36.2353419
10.950.88
17=6596
36.349 137 9
10.9529673
1729235
3273930875
36.3639387
10.9557451
1731S56
2379 '23 496
363767.43
36.3904946
1734489
2284323013
loile.^s
1737.24
3289539433
36.3043697
.0.96,070.
.739761
3394744759
36.3>8o396
10.966 B43 3
1742400
3299 96S 000
36.33' 80, 3
10.9696131
174504.
3 305 199 >6l
36.3455637
10-9733825
1747684
if'stiX
36.3593179
.0,975.505
1750329
36.37,1 '*7
3320940234
36.i!«iHio3
10.980 6S2 3
1755635
3336303.25
36.400 s+9 4
10-9834462
.758^76
3 33" 473 976
-' -.4 38--9
10.9863086
1760939
3336753783
10.9889696
1763584
2343039553
10-99. 7293
.766341
23473342S9
554533
10-9944876
1768900
3352637000
69^65
10.9973445
177156.
2357947691
1774334
336326636S
965753
i..oD3 754i
1776889
3368593037
1.-0055069
1779556
2373937704
36^5339647
.7833JS
337937037s
36.537651a
U.01IOO8 3
.784896
23B463T056
36.5513338
11.013 7569
1787569
3389979753
365650.06
11.0.6 504 1
I 79" 44
36.5786833
340072.3.9
36.5933489
.1-02. 9MS
.795600
3 4C6,04000
36.6060.04
11.0247377
I 798381
24.. 494821
36.6.96668
11.0374795
1800964
3416893688
36.633318 I
11.0302199
296
SQEJABBS, CUBSS, AMD BOOTS.
Bo-....
8tiii».
Cun.
S«C.Ulb»T.
Cm Root.
1343
1803649
3433300607
36.6469644
■ 1.033959
■344
■ 8063.16
36.6606056
...0356967
134s
I 80 90 IS
2433138625
36.67434.6
".038433
■346
1 81 17 16
3438569736
36.6878726
ii^.'U
"347
18.4409
3444008923
36.70. 4986
..x)439o. 7
.348
.817104
3449456193
36.715 ■19s
...0461339
'349
1 81 9801
= 4S49'>S49
36.7287353
...0493649
l^asoo
2460375000
36.7433461
...0520945
'35'
2 465 84655-
~* -15 95. 9
...0548227
13SJ
■ 827904
3471326308
■95536
"*«7 549 7
1353
18.10609
24768.3977
(31483
'3S4
■ 8333^6
3482309864
16739
1IJ3639994
I3SS
■ 836025
= 487813875
103346
"J3657233
1356
■83B736-
24933360.6
'39053
...068^437
1357
,84:449
2498846393
174809
.1J37. 1639
"3S8
1844164
= S04 374 7'3
;■ 05. 5
11.0738838
I3S9
1846881
350991.279
■46.72
1I.OJ66003
1360
■ 849600
35.5456000
---J8.778
11.0793.65
i36r
■ 853321
252.00888.
36.891733 s
1.. 083 0314
1363
■855044
252656992S
36.9053843
...0847449
-363
1857769
3533139.47
.16,9.88399
1.0B74571
13&I
1860496
2537716544
36.933 37"^
11.0901679
1365
■ 863225
3543303125
36.9459064
11.0938775
13M
■865956
3548895896
36.9594373
1..095 585 7
1367
.868689
'554497863
36,972963 I
..,0982936
"368
■ 87 14 34
2 560 108 033
36.986484
ii.iSo^Ssa
1369
I 87 41 61
35657364^9
11.1037035
1370
1876900
a 571333000
37.0.3 s..
11.106^05 J
'37'
187964.
35769878.1
37.0370.73
I. .109 107
137a
.883384
3582630848
37.0405.84
■■,■..8073
■373
.885139
2 588 282. .7
37.0540.46
.....45064
■374
.887876
25939,, 624
37.067 506
"...7204.
1375
I 89 06 25
359960937s
37.0S99934
'376
.893376
2605285376
37.094474
1...325955
1377
.896139
3 6i0969«3J
37.1079506
....353893
'378
.898884
36.6663.53
37-'31433 4
•379
..901641
3623363939
37.1348893
.1..306729
13S0
2638073000
37.^48 35.a
1..1333638
>3S'
1907.6.
= 633789341
37.^6.8o84
II, .36051 4
.383
1909924
3*395.4968
37.1753606
.1.387386
■383
.91.3689
3645248887
37-.887079
11,1414346
1384
■9'S4S6
3650991.04
37.202.505
11..44K193
138s
.9.&J25
3656741635
37-3.55881
11,1467^6
1386
.930996
3663500456
37.3299309
11,1494747
.387
1933769
2668267603
37.3434489
11.1531555
138S
1936544
2674043072
37.355873
11, .54835
1389
.939331
3679826869
37.3692903
"■■575133
1390
1933100
3685619000
37.3837037
lilies 8^1
139'
193488.
3691419471
37.396 "3 4
139a
1937664
2697228388
37.3095.63
..,.655403
"3W
1940449
3703045457
37 .333 9.5 3
....682134
'394
.943336
3708870984
37.3363094
..,.708852
■395
37.3496988
".■735558
"396
19488.6
3720547136
37.3630834
",.76225
1397
195 '6 09
3726397773
37.376463 3
11..78893
■398
1954404
3733356793
37.389838 a
".181 5^8
SQUAKES, CUBES, AND BOOTS.
297
NVU»9WL.
1399
1400
140X
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1413
1413
1414
141S
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
143s
1436
1437
1438
1439
1440
1441
144a
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
Z454
8«VABB.
1 95 72 OX
1960000
1 96 28 01
1965604
1968409
1 97 12 16
1974025
1976836
1979649
1982464
1985281
X988100
199 0921
1993744
1996569
1999396
2 00 22 25
2005056
2007889
2010724
2013561
20x6400
201924X
2022084
2024929
2 02 77 76
2030625
2033476
2036329
2039184
204204X
2044900
2 04 77 6x
2050624.
2053489
2056356
2059225
2062096
2064969
2067844
207072X
2073000
2076481
2079364
2 08 22 49
2085x36
2088025
20909x6
2093809
2096704
20996 ox
2102500
2 10 54 ox
2x08304
2x1 1209
21x41 16
Cubs.
2 738 X24 X99
2744000000
2 749 884 20X
2755776808
2 761 677 827
2 767 587 264
2773505125
2 779431 416
2785366143
2791309312
2797260929
2 803 22X 000
280918953X
2815x66528
282X X5X997
2 827 X45 944
2833148375
2839159296
2845x78713
2 85X 206 632
2857243059
2863288000
286934146X
2875403448
2 88x 473 967
2887553024
2893640625
2899736776
290584x483
2911954752
2918076589
2 924 207 000
2930345991
2936493568
2942649737
2948814504
2954987875
2 96X X69 856
2967360453
2973559672
2979767519
2985984000
299220912X
2998442888
30046853*7
30x0936384
30x7x96125
3023464536
3029741623
3036027392
3042321849
3048625000
30549368SX
3061257408
3067586677
3073924664
SquABB Root.
37.4032084
374165738
37-4299345
37.4432904
37.45664x6
37.469988
37.4833296
37.4966665
375099987
37523 326 X
37-5366487
37.5499667
37-5632799
37.5765885
37.5898922
37.603 X9X 3
37.6x64857
37.6297754
37.6430604
37.6563407
37.6696164
37.6828874
37.6961536
37.7094x53
37.7226722
37-7359245
37.7491722
37.7624152
377756535
37.7888873
37.8021163
37-8153408
37.8285606
37.8417759
37.8549864
37.868 192 4
37.8813938
37.8945906
37.9077828
37.9209704
379341535
37-9473319
37.9605058
37-9736751
37.9868398
38.0x31556
38.0263067
38.0394532
38.0525952
38.065 732 6
38.0788655
38.0919939
38.105x178
38.118237 X
38.1313519
CcBB Root.
X84 225 2
X868894
1895523
X922X39
1948743
1975334
200x9x3
2028479
205 503 2
208x573
2x08x01
2x346x7
2X6X12
2x8 761 1
22X 408 9
2240054
226 700 7
2293448
23X0876
2346292
2372696
2399087
2425465
245 X83 X
2478x85
2504527
2530856
2557173
2583478
260977
26360s
26623x8
2688573
27 X 48X 6
274 X04 7
276 726 6
2793472
28x9666
2845849
287 20X 9
2898177
2924323
2950457
2976579
3002688
3028786
3054871
3080945
3x07006
3133056
3159094
3185119
3211132
3237134
3263x24
3289x02
298
SQUARES, CUBES, AND BOOTS.
NoitfeBtt.
S40AXB.
Cuts.
SauARB Root.
CUBlRoOT.
1455
211 7025
308027137$
38.1444622
11.3315067
1456
2 II 9936
3086.626816
38.1575681
IJ.334 102 2
1457
1458
2 12 28 49
21257^
3092990993
38.1706693
11.3366964
3099363912
38.1837662
11.3392894
1459
1460
2128681
3105745579
38.1968585
11.3418813
2 13 1600
3X12136000
38.209^63
11.3444719
1461
a 1345 21
3118535181
38.2230297
11.3470614
1462
2*3 7444
3124943128
38.2361085
11.3496497
1463
2140369
3131359847
38.2491829
11.3522368
1464
2143296
3137785344
3144219625
3150662696
38.262 252 9
11.3548227
1465
2146225
38.2753184
11-3574075
1466
2149156
2152089
38.2883794
11-3599911
1467
1468
3157114563
38.301 436
11-3625735
2 15 so 24
3163575232
38.3144881
11-3651547
1469
2 15 7961
3170044709
38.3275358
11-3677347
1470
2160900
3176523000
38.340579
"•3703136
1471
2 16 38 41
3 183010 111
38.3536178
11.3728914
1472
2166784
3189506048
38.3666522
11-3754679
1473
2169729
3 196 010 81 7
38.3796821
11.3780433
1474
2172676
3202524424
38.3927076
11.3806175
147s
2175625
3209046875
38.405 728 7
11.3831906
1476
2178576
3215578176
38.4187454
11.3857625
1477
2181529
3222118333
38.431 757 7
11-3883332
1478
21844S4
3228667352
38.4447656
11.3909028
1479
2187441
3235225239
38.457 769 1
11-3934712
1480
2190400
3 241 702 000
3248367641
38.4707681
11-3960384
1481
2 19 3361
38.483 762 7
11.3986045
1482
2196324
3254952168
38.496 753
11.4011695
1483
2199289
3261545587
38.509739
11-4037332
1484
2 20 22 56
3268147904
38.522 7206
38.5350977
11.4062959
1485
2205225
3274759125
11.4088574
i486
2208196
3281379256
38.5486705
11.4x14177
1487
1488
221 1109
3288008303
38.5616389
11.4139769
2214144
3294646272
38.574603
11.4165349
1489
221 7121
3301293169
38.587 562 7
11.4190918
1490
2 22 01 00
3307949000
38.6005181
1X.4206476
1491
2223081
3314613771
38.6134691
11.4242022
1492
2226064
3321287488
38.6264158
11.4267556
1493
2229049
3327970157
38.6393582
11.4293079
1494
2232036
3^34661784
38.652 296 2
11.431 859 X
1495
2235025
334136237s
38.6652299
11.4344092
1496
2 23 80 16
3348071936
38.678x593
11.4369581
1497
1498
2 24 to 09
3354790473
38.691 084 3
11.4395059
2 24 40 04
3361517992
38.704005
1x4420525
1499
2 24 70 01
3368254499
38.7169214
11.444598
1500
2250000
3375000000
38.7298335
IX.4471424
1501
2 25 30 01
3381754501
38.7427412
X1.4496857
1502
2256004
3388518008
38.7556447
XX.4522278
1503
2259009
3395290527
38.7685439
IX.4547688
1504
2 26 20 16
3 402 072 064
38.7814389
11.4573087
150S
2 26 50 25
3408862625
38.7943294
IX.4598474
1506
2 26 80 36
3415662216
38.8072158
11.462385
1507
2 27 10 49
3422470843
38.8200978
11.4649215
1508
2 27 40 64
3429-288512
38.8329757
11.4674568
1509
2 27 70 81
3436115229
38.845 849 1
11.469991 1
15x0
2280100
3442951000
38.8587184
11.4735343
SQUARES, CUBES, AND BOOTS.
299
SfOIIBSB.
SQVAmi.
15"
22831 21
I5I2
2286144
I5I3
2289169
1514
2292196
1515
2 29 52 25
1516
2298256
I5I7
2301289
1518
2304324
I5I9
2307361
1520
2310400
I52I
231 3441
1522
2316484
1523
2319529
1524
2322576
1525
2325625
1526
2328676
1527
2331729
1528
2334784
1529
2,137841
1530
2340900
I53I
2343961
1532
2347024
1533
2350089
1534
2353156
1535
23^6225
1536
2359296
1537
2362369
1538
2365444
1539
2368521
1540
2371600
1541
2374681
154a
2377764
1543
2380849
1544
2383936
1545
2387025
1546
23901 16
1547
2393209
1548
2396304
1549
2399401
1550
2 40 25 00
1551
2405601
1553
2408704
1553
241 1809
1554
341 49 16
1555
2 41 80 25
1556
2421136
1557
3424249
1558
2427364
1559
2430481
1560
2433600
1561
2436721
1562
2439844
1563
2442969
X564
2446096
1565
2449225
1566
2452356
Cobs.
3449795531
3456649728
3463512697
3470384744
3477265875
3484156096
3 491 055 413
3497963832
3504881359
35118080OO
3 518 743 761
3525688648
3532642667
3539605824
3546578125
3553559576
3560558183
3567549952
3574558889
3581577000
3588604291
3595640768
3602686437
3609741304
3616805375
3623878656
3630961 153
3638052872
3645 153 819
3 652 264 000
3659383421
3666512088
3673650007
3680797184
3687953625
3695 119 336
3 702 294 333
3709478592
3716672 149
3 723 875 000
3 731 087 151
3738308608
3 745 539377
3752779464
3760028875
3 767 387 616
3774555693
3 781 833 113
3789119879
3 796 416 000
3803721481
3 81 1 036328
3818360547
3 825 641 144
3833037125
3840389496
Squarb Root.
38.8715834
38.884 444 a
38.8973006
38.9101529
38.9230009
38.9358447
38.948 684 1
38.961 5194
38.9743505
38.9871774
39
39.0128184
39.0256326
39.0384426
39.0512483
39.0640499
39.0768473
39.0896406
39.1024296
39.115 2144
39.1279951
39.1407716
39-1535439
39.166313
39.179076
391918359
39.804591S
39-2173431
39.3300905
39.2428337
39-2555728
39.2683078
39.281 038 7
392937654
39.306488
39.3192065
39-3319208
393446311
39-3573373
39.3700394
39-3827373
39-395 431 8
39.408 121
39.420 806 7
39.4334883
39.4461658
39-4588393
39.4715087
39.484174
39-4968353
39.5094925
39.522 145 7
395347948
39-547 4399
39.5600809
39.5737179
CuBB Root.
".4750563
"•4775871
11.480 I169
11.4826455
".4851731
11.4876995
11.4902249
11.4927491
11.4952722
".4977942
11.500315 I
11.5028348
".5053535
".507871 I
11.5103876
11.512903
".5154173
11.5179305
11.5204435
".5229535
".5254634
11.5279723
"•5304799
11.5329865
".535492
"5379965
"5404998
11.543002 I
".5455033
11.5480034
".5505025
11.5530004
"5554973
"•5579931
11.5604878
11.5629815
11.565474
115679655
".5704559
11.5729453
"•5754336
11.5779208
11.5804069
11.5828919
"•5853759
11.5878588
"-S903407
11.5928215
"•5953013
"•597 7799
11.6002576
H.6027342
11.6052097
1 1.607 684 1
11.610157 s
11.61363^3
300
SQUARES, CUBES, AND ROOTS.
NVMBSB.
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
»S90
1591
1592
1593
1594
IS95
1596
1597
1598
XS99
1600
Sqvabs.
<?m.
8«UABB Root.
2455489
3847751263
395853508
2 45 86 24
3855122432
39597 979 7
2 46 17 61
3862503009
39.610 604 6
2 46 49 00
3869893000
39.6232255
. 2 46 80 41
3 877 292 411
39635 842 4
247 II 84
3 884 701 248
39.6484552
2474329
3892 119 517
39.661 064
2477476
3899547224
39.6736688
2 48 06 25
3906984375
39.686 269 6
2483776
3914430976
39.6988665
2486929
3921887033
39.7114593
2 49 00 84
3929352552
39.7240481
2493241
3936827539
397366329
2496400
3944312000
39.7492138
2499561
3951805941
39-76r790 7
2 50 27 24
3959309368
397743636
2505889
3 966 822 287
397869325
2 50 90 56
3974344704
39 799497 5
2 51 22 25
3981876625
39.8120585
2515396
3989418056
39.824615 s
2 51 85 69
3996969003
39.8371686
2521744
4004529472
39.8497177
2524921
4012099469
39 862 262 8
2 52 81 00
4 019 679 000
39874804
2 53 12 81
4027268071
39.8873413
2534464
4 034 866 688
39.8998747
2537649
4042474857
39,9124041
2540836
4050092584
399249295
2544025
4057719875
39937451 I
2 54 72 16
4065356736
39.9499687
2550409
4073003173
39 962 482 4
2553604
4 080 659 192
39.9749923
2556801
4088324799
39.987498
2560000
4096000000
40
Cubs Boot.
11.615 101 a
11.6175715
11.6200407
11.6225088
11.6249759
11.627442
11.629907
11.632371
"•6348339
11.6372957
"6397566
11.6422164
11.6446751
11.6471329
11.6495895
11.6520452
11.6544998
11.6569534
11.6594059
11.6618574
11.6643079
11.6667574
II 6692058
11.6716532
11.6740996
11.6765449
11.6789892
11.6814325
11.6838748
11.6863161
11.6887563
11.6911955
"6936337
11.6960709
Uses of preceding table may be extended by aid of followiujif Rules, tc
Compute Square or Cube of a bigher Number than is contained in it.
Q?o Compute Square.
When Number is cm Odd Number.
RiTLB. — Take tbe two nambers nearest to each other, which, added together,
make ihat sum ; then flrom sum of squares of these two numbers, multiplied by a,
lubtract i, and remainder will give result
To Compute Square or Cu'be.
When Number is divisible by a Number without leaving a Remainder,
RpLK.— If number exceed by a, 3, or any other number of times, any number
contained In table, multiply square or cube of that number in table by square of a
), eto., and product will give result.
EZAJIPLI.— Required square of 170a
1700 is 10 timet X70, and square of 170 is 3890a
Then, 28900 X io' = 389oooa
•...-What is cube of 2400?
3400 IB twice Z20O, and cube of 1999 i| f 728000000^
IbOD I 738 000000 X 9^ =^ 13 834000009,
SQUABBS, CUBES, AND BOOTS. 3OI
Example. —What Is sqoara of 1745?
Two nearest nambers ^^ {gis } ^ '745-
Then, per table, {«73:= 76 g.g9
15225x3X2 = 3045026 — x=:3045oa5.
To Compute Square or Culse Root of* st liigh.er Nrxzxiloev
tliaix is ooiitained in Xable.
When Number is divisible 2y 4 or 8 without leaving a Remainder,
RuLK.— Divide namber by 4 or 8 respectively, as square or cube root is required ;
take root of quotient in table, multiply H by 2, and product will give root required.
ExAMPLK— What are square and cube roots of 3200?
320o-r-4 = 8oo, and3aoo-r-8=:400w
Then, square root for 800, per table, is 28. 28 42 71 2, which, being x 2 = 56. 56 85 42 4
rooL
Cube root for 400, per table, Is 7.368 063, which, being X 2 = 14-736 126 root
When the Root (which is taken as Number) does not exceed 1600. V
The Numbers in table are roots of squares or cubes, which are to be taken
as numbers.
Illubtratiov.— Square root of 6400 Is 80, and cube root of 5x2000 is So.
When a Number has Three or more Ciphers at its right hand,
RcTLX.— Point off number into periods of two or three figures each, according as
aquare or cube root is required, until remaining figures come within limits of table;
then take root for these figures, and remove decimal point one figure for every pe-
riod pointed ofil
EzAJCPLK.— What are square or cube roots of 1 500000?
1 500000= X50, remaining figure, square root of which=x2.247 45; hence 1224.745,
iquare root
X 500000 = 1500, remaining- figures, cube root of which s= zx.447 X4 ; hence
iZ4.47i4, cu6eroo&
T*o ^eoertaiu Cul>e Root of* axiy 19'uzn'ber over 1300.
RcLB.— Find by table nearest cube to number given, and term it assumed cube*
multiply it and given number respectively by 2 ; to product of assumed cube ada
given number, and to product of given number add assumed cube.
Then, as sum of assumed cube Is to sum of given nomber, so Is root of assumed
cube to root of given number.
ExAMPLB.— What is cube root of 224 809 T
By table, nearest cube is ai6ooo, and Its root Is 60.
2x6 000 X 3 + 224 809 = 656800,
And 224 809 X a 4- 216 000 = 665 6x8.
Then 656 809 : 665 6x8 :: 60 : 60.804+, root
7o A^Boertaiu Square or Oulae Root of a Number oon*
sistiufi; of* lutegers and. IDeciznals.
RuLK.— Multiply difference between root of integer part and root of next higher
flot^er by decimal, and add product to root of integer given ; the sum will give root
of number required.
This is eorrect/or Square root to three places o/decimals, and for Cube root to seven.
302 SQUABEB, CUBES, AND BOOTS.
ExAMPLs. —What l8 square root of 53. 75, aad enlie root of 843. 75 ?
'844 =9.45<
'843 =9.4466
V.54 =7-3484 1^844 =9.4503
V*
V53 =7-2801
.0683
•75
.051 225
^53 =7.2801
V53-75 = 7- 33*325
.0037
•75
•a»775
V843 =94466
^843.75 = 9.449375
Wken the Square or Cube Root is required for Numbers not exceeding Roots
given in Table.
Numbers in table are squares and cubes of root&
RuLB. — Find, by table, in colnmn of numbers that number representing figures
of integer and decimals for which root is required, and point it off' decimally by
places of 2 or 3 figures as square or cube root is required; and opposite to it, in
column of roots, take root and point off i or 2 additional places of decimals to those
In root, as square or cube root is required, and result is root required.
ExAMPLB I.— What are square roots of .15, x.50, and 15.00?
In table, 15 has for its root 3.87 298; hence .387298 = sqiuire rootjur ,1^
150 has for its root 12.24745; benoe 1.224745 = square root for 1.5a
1500 has for its root 38.7298; hence 3.87 298 = square root fir 15.
3.— What are cube roots of .15, z.50, and 15.00?
Add a cipher to each, to give the numbers three places of figures, as .150, 1.500^
and 15.00Q1
In table 150 has for its root 5.3x33; hence. 531 33 = cube root of .1^
1500 has for its root 11.447; hence 1.1447 = cube root of i.^
x5 has for its root 3.466a; and 15.000, by addition of 3 places of figures, has
04.662 ; hence 3. 466a = CMde root of 1^.00.
"Po A-soertaixx Square or CuIdo H.oot8 or Deoiznals alone.
RuLB.— Point off number from decimal point into periods of two or three figures
each, as square or culie root is required. Ascertain fVom table or by calculation
root of number corresponding to decimal given, the same being read off by remov-
ing the decimal point one place to left for every period of 2 figures if square root is
required, and one place for every period of 3 figures if cube root is required.
EzAMPLB. — What are square and cube roots of .810, .081, and .0081 V
.810, when pointed off = .8x, and V.Sz =.9.
,081, " " " =.oSi, ♦• v^oSi =.8846.
.0081, " " " =.«)8i, " Voo8« = .o9.
.810^ wbeo pointed off =.8zo» and ^.8x0 = 93217.
.081, " " " =.o8i, " V.o8i =.4336^.
.oo8x, " " " =.oodx, " ^.0081 =.30083.
To Compute 4th. Root of* a r^uxxilser*
RuLs.— Take square root of its square root
ExAMFLK.— What is the -^ of x6oo?
•^1600 = 40, and v'40 = 6. 32 45 55 3.
To Coxnpute 6tli H.oot of a Nuxn'beib
Bulk. —Take cube root of its square root.
ExAMPLB-^What is the ^ of 44X t
V441 = ai, and ^ai = a. 7 589 34^
FOUBTH AND FIFTH POWBBS OF NVHBSBS.
303
<4rth. and 5th. Po-wers of IN'uixi'bers*
fVom I to 15a
Namtier,
4th Power.
I
9
1
x6
3
8x
4
356
5
635
6
1396
i
3401
J^
9
10
zoooo
sx
14641
12
30736
'3
28561
X4
38416,
X5
50625
z6
65536
*7
83521
z8
X04976
»9
130321
90
160000
21
194 48X
39
234256
23
279841
84
331 776
25
39062s
456976
26
S
614 036
907 98Z
810000
89
30
31
923 52X
32
X 048 576
33
X 185 92X
34
1336336
35
X 500625
36
X 679616
37
z 874 i6x
38
2085136
39
3313441
40
0560400
41
3 825 761
42
3ZII696
43
34I880Z
44
3748096
45
4 X00625
46
4477456
47
4879681
48
5308416
49
5764801
50
6250000
51
6 765 201
52
7 3XX 6x6
53
7890481
8503056
54
55
9150625
56
9834496
11
xo 556 001
1x3x6496
59
X2 117 361
60
13060000
13845841
61
63
X4 776 356
63
X5 753 961
Sth Power.
32
243
X034
312s
7776
X6807
33768
59049
100 000
z6x 051
348832
371 293
537 824*
759375
X 048 576
X 41981
i889 5(
2476099
3000000
4084 lOI
5x53639
6436343
7 962 624
9765625
zi 881 376
14348907
17 910368
30511 X49
24300000
38629x51
33554432
39 135 393
45435424
53 521 875
60466x76
69343957
79235168
90 224 X99
102400000
X1585620X
X30691233
147008443
X64 916 334
X84 528 125
205 962 976
229345007
254803968
382 475 249
312 500000
345025251
380904033
418x95493
459165024
503384375
550731776
601 693 057
656 356 768
7x4934299
777600000
84459630X
916 X39 833
992436543
Namber.
64
65
66
f7
68
69
70
7«
73
73
74
75
76
77
78
80
8x
83
83
84
85
86
87
88
89
90
9>
92
93
94
96
98
99
zoo
xox
Z03
XO3
XO4
XOO
»07
X08
109
xxo
XIX
XX3
XI3
"4
xxs
X16
"7
118
XX9
120
X2Z
X22
133
124
125
Z36
4tii Power.
16777316
17850635
18974736
90x51 X3Z
21 381 376
32 667 X3Z
94010000
35411681
86.873 856
28 398 241
39986576
31 640 625
33 362 176
35153041
370x5056
389qoo8x
409000Q0
4304672X
45 212 176
47458321
49787136
52200635
547080x0
57 289 76X
59969536
62 742 24X
656x0000
6857496?
71639996
7480390X
78074896
81 450635
84034656
88580381
98 330 8x6
9605960Z
XOO 000 000
X04 060 40Z
X08 243 2x6
X1255088X
116985856
X3X 550625
X26 247 690
131 079601
X36048896
141 158 161
146410000
X5X807Q4X
157 3Si 93^
163 047 36X
X68896016
174900625
i8z 063 936
187 388 721
X93877776
200 533 92X
207360000
9x4358881
221533456
338886641
936 421 376
844140635
252047376
5tli Power.
1073741834
1 160990635
X 353 333 576
1 350 125 107
1453933568
1564031349
1680700000
X 804 329 251
5^934917633
2073071593
9319006694
2373046875
2535525376
8 706 784 157
8887x74368
3077056399
3276800000
3 486 784 40X
3707398433
3939040643
4182 119 424
4437053x25
4704*70x76
4 984 209 207
52773x9168
5584059449
5904900000
6 940 33X 4<;x
65908x5339
6956883693
7339040234
7737809375
8x53720976
8387340*57
9039207968
9509900499
XOOQOOOOOOO
X05IOI0050X
X]K>4o8o8o32
XI 592740743
13 166 599094
Z2 762 815 625
13382255776
14035517307
14693280768
15386239549
16x05100000
1685058x551
176234x6833
18 424 351 793
19 254 145 824
801x3581875
2X 003 416 576 .
21024480357
22 877 577 568
23 863 536 599
3488320OOOQ
2593742460X
27027081632
28153096843
39316350624
305X7578X85
31757969376
304
POWEBS OF NCHBBBS. — RKC1PBOCAL8.
Nnmber.
4th Power.
Sth Power.
Number.
4th Power.
127
260 144 641
33038369407
139
373 30 '641
138
368435456
976933881
385610000
34359738368
140
384 160000
139
35723051649
141
395254161
130
37 129300000
142
406586896
131
394499921
38579489651
>43
418 161 601
133
303595776
40074642432
144
429981696
133
313900721
41 615 795 893
145
442050625
134
322417936
43204003424
146
455371856
^35
332150625
4484033437s
X47
466948881
136
342102016
46525874176
148
479785216
'3Z
352375361
48261724457
149
492 884 401
138
362673936
50049003168
ISO
506250000
5th Power.
51888844699
53782400000
55730896701
5773533923a
59797108943
61917364224
64097340625
66 338 290976
68 641 485 507
71008211968
73 439775749
75937500000
To Compute 4tli Fewer of a N"vim"ber greater th.axi is
contained in Table.
Rule. —Ascertain square of number by preceding table or by calculation, and
square it; product is power required.
EzAMPLB— What IS 4tb power of 1500?
1500^ = 2 250000, and 2 250 006^ = 5 063 500 000 00a
To Compute Sth. Po^xrer of a I^uzn'ber greater tlian is
contained in Table.
R0LB. — Ascertain cube of number by preceding table or by calculation, and mul-
tiply it by its square; product is power required.
To Compute 4th and 6tlx Powers \>y another Afethod.
RuLi. — ^Reduce number by 2 until it is one contained within table. Take power
which is required of that numl>er, and multiply it by 16, x6', or i63 respectively
for each division, by 3 for 4th power, and by 32, 33', or 323 respectively for each
division by 2 for 5th power.
Example.— What are the 4th and 5th powers of 600?
600 -T- 3 = 300, and 300-7-2 = 15a
The 4th power of 150, per table, = 506 250000, which x z6^, multiplier for a teoond
division 256 = 129600000000, 4th power.
Again, the 5th power of 150=75937 500000, which X 33", multiplier for a second
division 1034 = 77 760000000000 =j}oioer.
To Compute Oth. Po"wer of a dumber.
Rule —Square its cube.
Example.— What is the 6th power of 3?
3
33 = 64.
To Compute '^th or Bth. Root of a K'umber per Table.
Rule— Find in column of 4th and 5th powers number given, and number fh>m
which that power is derived will give root required.
Example.— Whkt is the 5th root of 3 200000?
3 200 000 in table is 5th power of 20; hence 20 is root required
RECIPROCALS.
Reciprocal of a number is quotient arising firom dividing i by number; thua, re-
tiprocalof 2 is 1 -{-2=1.5
Product of a number and its reciprocal is always equal to i ; thus, 3 x 5 = z.
Reciprocal of a vulgar (htction Is denominator divided by numerator ; thus, - z= . c
liOGABITHMa 305
LOGABITHMS.
XjOgaritlixns of* I4'iiin.'bei*s«
Logarithms are a series of numbers adapted to facilitate the operation of
nimierical computation,
Addition being substituted for Multiplication, Subtraction for Division,
Multiplication for Involution, and Division for Evolution
The ILiOfiraritlixn of a number is the exponent of a power to which 10
must be raised to give that number.
It is not necessary, however, that the bcue should be xo, it may be any other num>
ber; but Tables of Logarithms, in common use, are computed with 10 as the base.
* Thus, Number xoo Log. = 2, as lo^ base and exponent = loa
" 10000 " =4, »» lo* " " " =10000.
The Vmt or Integral part of a Logarithm is termed the Index, and the Decimal
part the Mantissa ; tJbe sum of the Index and mantissa is the Logarithm.
The Index of the Logarithm of any immbery Integral or Mixed, when the base is 10,
Is equal to the number of digits to the left of the decimal point less i. From o to
9, it is o; firom 10 to 99, it is i, and flrom 100 to 999, it is 3, eta
Thus, logarithm of 3304 = 3.51904, 3 being the index and .5x904 the mantissa.
The Index of the Logarithm of a Decimal FraiMon is a negative number, and is
•qoal to the number of places which the first significant figure of the decimal is re-
moved from Uie place of unita
Thus, index of logarithm .005 is 3 or —3, the first significant figure, 5, being re-
moved three places from that of unita The bar or minus sign is placed over an
index to indicate that this alone is negative, while the decimal part is positive.
The Difference is the tabular difilBrence between the two nearest logarithms
The Proportional Part is the difllerence between the given and the nearest less
tabular logarithm.
The Arithmetical Complement of a number is the remainder after subtracting it
from a number consisting of i, with as many ciphers annexed as the number has
Integers. When the index of a logarithm is less than 10, its complement is ascer-
tained by subtracting it from zo.
Illvistratioiia.
Number. Lc^pirithm.
4743 3676053
474-3 2.676053
47-43 1.676053
4-743 676053
Nnmber. Lofvithm.
.4743 1.676053
.047 43 -. 3. 676 053
•004743 3-676353
CompTitatioii of M'eg;ati^e Indices. _ _ _
To add two Negative Indices. Add them and put the sum negative. As 5 -f 3 = 8.
To add a Positive and Negative Index. Subtract the less from the greater, and
to remainder give the positive or negative sign, according as the positive or nega-
tive index is the greater. As 6 + 3 = 4, and 6 -f s = 4.
Illcstration. —Add 6. 387 57 and 2. 924 59. 6. 387 57
g- 934 59
5.313x6
Here the excess of x fkt)m 13 in the first decimal place, being positive, is carried
to the positive 6, which makes 7, and 7 -— 2 = 5.
To Subtract a Negative Index. Change its sign to plus or positive, and then add
it as in addition. As 3 tram 2, = 3 -f 2 =: 5. And 5 fh>m 2] = 5 -)- a = 3 ; also
Jftoms, = 3 + s = 2. _ _
iLLusTRATioir.— Sabtract 5. 765 59 from 3. 346 74. 2. 346 74
5-765 Sa
3.58132
Here, excess of x in the first decimal place used with the .3 in subtracting the .8
from the 1.3 Is to be subtracted from the upper number 2, which maices it 3 ; then
3o6
LOaABITHKS.
To Subtract a Potitive Index. Cbaoge ita sign to negative, and then add as in
addition. As 2 — 2 = 2-|-3 = 4<
To Multiply a Negative Index. Multiply the fractional parts by the ordinaij rule,
then multiply the negative index,wh\ai will give a negative product, and when an
excess over 10 is to be carried, subtract the less index from the greater, and the re-
mainder gives the positive or negative index, according as the positive or negalive
index is the greater. As 2 x 5 =3 10, and i to be oarrled =£9.
Illustration.— Multiply 2.3681 by 2, and 3.7856 by 6.
2.3681 3-7856
2 6
4.7362 Z4-7Z36 •
Here 2X2 = 4, ftlso 3X6 = 18, with a positive excess of 4 = 14.
To Divide a Negative Index. IT index is divisible by divisor, without a remain*
d«r, put quotient with a negative sign. If negative exponent is not divisible by
divisor, add such a negative numl)er to it as will make it divisible, and prefix an
equal positive integer to fVactional part of logarithm; then divid« increased Nega-
tive exponent and the other part of logarithm separately by ordinary rules, and for-
mer quotient, taken negatively, will be index to firaotional part of quotient. As
6-4-3 = 2. 10 -}- 3 requires 2 to be added or 2 to be subtraoted, to make it divisible
without a remainder, then io'-4-T= 12, 12-^-3 = 4, and 2 (the sum subtracted)^
3 = .66, the quotient therefore Is 4,66.
Illustration l— Divide 6.324282 by 3.
6. 324 282 -j- 3 = 2. 108 094.
2. — Divide 14.326745 by 9.
14. 326 745 -4- 9 = is + 4.326 745 ^ 9 = 2. 480 7494-.
Here 4 is added 10*14, ^^^ ^^^ ^'^^ ^ "^^7 ^ divided by 9, and as 4 is added, 4
must be prefixed to the fractional part of the logarithm, and thus the value of the
logarithm is unchanged, for there is added 4, and 4 = o, or 4 is subtracted and 4
added.
To ^soertain JjogaritHixi of a l^Tum.'ber "by Ta"ble.
When the Number is less than loi.
Look into first page of table, and opposite to number is its logarithm with its
index prefixed.
_ Illustration. ^Opposite 7 is .845098, its logarithm; Jience 70=1.845098, .7 =
1.845098, and .07=3.845098.
When the Number is hetioeen 100 and 1000.
Rule. — Find the given number in left-band column of table headed No., and un-
der o in next column is decimal part of its logarithm, to which is to be prefixed a
whole number for an index, of i or 2, according us the number consists of 2 or 3
flgurea
Example.— What is logarithm of 450, and what of .45 f
Log. 450 = 2.653 213, and of .45 = 1.653 2x3.
When the Number is between looo and 10 000.
RuLB.— Find the three left-hand figures of the number in the left-hand column
of the table headed No. , and under the 4th figure at top of table is the four last
figures of the decimal part of logarithm, to which is to be prefixed the proper
index.
Example.— What is logarithm of 4505, and what of .04505?
Log- 4505 = 3-653 695> ^°<* of -045 05 = 2- 653 695-
LOGARITHMS. 307
When the Number eofuists of Five Figures.
RuLB.— Find the logarithm or the number composed of the first four figures as
preceding, then take the tabular difference from the right-hand column under D
and multiply it by the fifth figure; reject the right-hand figure of the product and
add the other figures, which are, and are termed, a proportional part to the logarithm
found as above, observing that the right-hand figure of the proportional part iB to
be added to that of the logarithm, and the rest in order.
ExAMPLS.— -Required logarithm of 83 407 ?
Note. — When the number consists of less than 4 figures conceive a cipher an-
nexed to make it four.
Log. of 8340 (83 407) = 4. 921 166
Tabular difliBrence 52, which x 7 (5th figure) = 364 = 364
4.921 2024 logarithm.
The difference of the numbers is nearly proportionate to the difference of their
logarithma
Thus, difference between the numbers 8340 and 8341, the next in order, is x, and
the difllbrence lietween their logarithms or tabular difference is 52.
The log. of this i in the 4th place is therefore 52. The correction then, for the 7
of the 5th place, which is .7 of x in the 4th place, is ascertained by the proportion
X : 52:: .7 : 36.4.
The correction is obtained by multiplying the tabular difference by 7. rejecting
the right hand figure of the product, if the log. is to be confined to six decimal
place&
When the Number connsts of any Number over Four Figures.
RuLB. — Proceed as for four flgnres for the first four, multiplying the tabular dif-
ference by the excess of figures over 4 and rejecting one right-hand figure of the
product for a number of five figures, and two for one of six, and so on.
ExAMPLB L— Required logarithm of 834079?
Log. of 8340 (a34079)= 5.921 166
Tabular difference 5a, which X 79 = 4108
5.921 20708 logariUim.
2.— Required logarithm of 8340794?
\jog. of 8340 (8 340 794) = 6. 921 x66
Tab. diff. 52, which x 794 {5th, 6th, and 7th figures) = 4x288
6. 921 207 388 logariOim.
Or, Mantissa of 8340 = .921166
'• *' 7 (5th figure) X'52 tab. dif =s 364
" " 9 (6th " )X52 " " = 468
" " 4 (7th " )X52 " •' = 208
Log. with index for 7 figures 6.921 207 288
To A.8certaixi ILiOgaritlixn of a Alixed N'u.xn'bor.
RuLB. — ^Take out logarithm of the number as if it were an integer or whole nam-
ber, to which prefix the index of the Integral part of the number.
Example.— What is logarithm of 834.0794?
Matttfaea of log. of 834 . 0794 =9319 073 ; hence log. of 834^0794 = 2. 921 207 3.
To ^soertain Xjosaritlini, of* a I>eoicaal ITvaotioja.
Rule.— Take logarithm fh)m table as if the figures were all integers, and prefix
index as by previous rules.
Example.— Logarithm of . X234 =1.091 305.
To A.8oertain. Xjogaritlxni ot a Vulgar Fraction.
Rdlb. — Reduce the fhiction to a decimal, and proceed as by preceding rule. Or,
subtract logarithm of denominator flrom that of numerator, and the difference will
give logariUun required.
Example.— Logarithm of ^?
^ = . X875. Log. .1875 =7. 273 001 logarithm.
Or, Log. 3 = .477 I2X
" X6 = X.204I2
X.37300X logarithm.
3o8
LOGARITHMS.
To J^soertain th.e 19'uiaci'ber Correepoxxding; to a O-iven
Uogaritlxzn.
When the given or exact Logarithm U in the Table.
Operation.— Opposite to first two figures of logarithm, neglecting the index^ in
column 0, look for the remaining figures of the log. in that column or in any of the
nine at the right thereof; the first three figures of the number will be found at the
left in column under No., and the fourth at top directly over the log.
The number is to be made to correspond to index of logarithm, by pointing off
decimals or prefixing ciphers.
Illustration. — What is number corresponding to 1(^. 3.963 977 ?
Opposite to 963977, in page 339, is 920, and at top of column is 4; hence, num-
ber =: 9204.
When the given or exact Logarithm it not in the Table,
Operation.— Take the number for the next less logarithm from table, which will
give first four figures of required number.
To ascertain the other figures, subtract the l(^;arithm m table fh>m the given
logarithm, add ciphers, and divide by the difference in column D opposite the
logarithm. Annex quotient to the four figures already ascertained, and place deci-
mal point.
Illustration i.— What is number corresponding to log. 5.921 zoj ?
Given log. = 5-92i 207
Next less in table 5.921 166 8340
D= 53)4100(78+ 78
J64 834078
460
.4'6
Hence, number =: 834 078. 44
s.— What is number corresponding to-Iog- 3. 922 853 T
Given log. = 3-923853
Next less in table 3.922829 837 2
D = 53) 2400 (46 + 46
!2L 837 346
320
3"
Hence, number = 8373.46. u
IMultiplioatioxL.
Rule.— Add together the logarithms of the numbers and the sum will give the
logarithm of the product.
Examplb I. — Multiply 345.7 by 3.581.
Log- 345-7 =3.538690
" 3.581= .411788
3.950 487 log. qf product Number =£ 893.351.
s.— Multiply .03903, 59.71, and .003 147.
Log. .039 03 = 2. 591 387
** 59- 7» =1^.776047
" .003 147 = 3- 4^7897
3. 865 231 log. of product. Number =: .007 33a i^
X>ivisionL.
Rule.— From logarithm of dividend subtract that of divisor, and remainder will
give logarithm of the quotient
EzAMPLK.— Divide 371.4 by 53.37.
Log. 371.4 =3.569843
** 53.37 = 1-7 '9 083
. 850 759 log. qf quotient Number = 7. 091 85.
LOGABITUMS. 3O9
Rrile of* Tliree, or Proportion.
RuLS.— Add together the logarithms of the second and third terms, from their
sum subtract logarithm or the first, and the remainder will give logarithm of the
fourth term.
Or, instead of subtracting logarithm of first term, add its Ari^metical Comple-
ment, and subtract 10 flrom its index.
Example i.— What is fourth proportional to 723.4, .025 19, and 3574?
As 723.4 log. =s _ 2859379
Is to .025 19 '* := 2.401 228
So is 3574 " =3553155 .
1.954 383
First term *' 2.859379
1 . 095 cx)4 log. of 4th term. Number = . 124 453.
Bjf Arithmetical ComplemenL
Illubtratioh. — ^As 723.4 log. = 2.859 379, Ar. com. =2* 140621
Is to .025 19 ** = 2.401 228
So is 3574 " = 3-553155
I 095 004 log. o/j^Ot term.
Number =: . 124 453.
2. — If an engine of 67 W can raise 57 600 cube feet of water in a given time, what
H^ is required to raise 8 575000 cube feet in like time?
Log. 8 575 000 = 6.933 234
" 67 = 1.826075
, 8-759309
" 57600 = 4.760422
3.998 877 log. of^ik term. N umber = 9974. 4 HP
3. — If 14 men in 47 days excavate 5631 cube yards, what time will it require to
excavate 47 280 at same rate of excavation ? 394. 626 days.
I XX volution..
RuLB. — Multiply logarithm of given number by exponent of the power to which
It is to be raised, and the product will give the logarithm of the required power.
ExAMPUB.— What is cube of 3a 71 ?
Log. 3a 71 = 1.487 28
3
4.461 84 log. of power. Number = 28 962.73.
B volution.
Rdul — Divide logarithm of given number by exponent of the root which Is to be
oKtracted, and quotient will give logarithm of required root
ExAMPLB L— What is cube root of 1234 ?
Log. 1234 = 3.091315
Divide by 3 = i. 030 438 log. qf root Number = xa 726 01.
a.*— What is 4th root of .007 654 ?
Log. .007654 = 3.883888
Divide by 4 (here 3 -f i -|- 1) = 1.470 972 log. of root Number = .295 78.
To A^soertain Reciprocal of a M'uznber.
RuLS.— Subtract decimal of logarithm of the number trom .000000; add i to iQ<
dex of logarithm and change its sign. The result is logarithm of the reciprocal.
EZAMFUL— Required reciprocal of 230?
.000000
IX)g. 230 = 2. 361 728
3.638 273 =s log. of .004 348 reetproooL
X
3IO
I.OGAKITHMS.
Sizziple Interest.
RuLS. — Add together logarithm of principal, rate per cent., and time in years, firom
the sum subtract 2, and the remainder will give logarithm of the interest.
ExAMFLB.— What is interest on $500, @ 6 per cent., for 3 years?
Log. 500 = 2.698 97
6= .778151
3= .477121
3954242
2
1 . 954 242 log. of interest. Number = 90 dollars.
Compound. Interest.
RuLB.— Ck)mpQte amount 6f $ i or X i, etc., at the given rate of interest for one
year for the first term, which is termed the ratio.
Multiply logarithm of ratio by the time, add to product logarithm of the principal,
and sum is logarithm of the amount.
I^ogaritlxxiis of* Katios at given
Rate.
I
«-25
1-5
1-75
2
2.25
2.5
2.75
3
Log. of Ratio.
Rate.
.004 321 4
325
.005 395
3-5
.006466
3-75
•0075344
4
.0086002
425
.0096633
4-5
.0107239
4-75
.0117818
5
.0128372
525
Log. of Ratio.
.013 890 I
0149403
.0159881
.0170333
.0180761
.0191163
.020154
.02X 1893
.022 222 I
Rate.
5-5
5-75
6
6.25
6-5
6.75
7
7.25
7-5
1 liates
Per C
Log. of Ratio.
Rate.
.0232525
.0242804
l''
.0253059
.0263289
.0273496
.0287639
•0293838
8.25
8.5
8.75
9
9-25
•0303973
.0314085
9-5
9-75
Cent.
Log. of Ratio.
.0324373
.0334238
.0344279
•0354297
•0364293
.0374265
.0384214
.0394141
.0404045
Example— Whut will $364, at 6 per cent, per annum, compounded yearly, amount
to in 23 years?
Log. of ratio from above table .025 305 9
23
(t ti
364
.5820357
2.561 lOI
3. 143 1 36 7 log. of amoMfi/. Number =s 139a 39 doU
Afisoellaneons Illustrations.
I. What is area and circumference of a circle of 21.72 feet in diameter?
Log. of 21.72 1,336860
Log. of 21.72" =2.673720
«* »» .7854=1.895091
(t
2. 568 81Z =: 370. 54 ftiti area.
Log. of 21.72 =1.33686
" " 3.1416= .49715
t(
((
X.834 OS = 68.236 feet ctrctMii,
3. Sides of a triangle are 564, 373, and 747 feet; what is its ana?
Log. of sides
u
5644-373+747 ^,,^,g 3,,
*• . 5 side — o = 842 — 564 = 2. 444 045
" .5 side — 6 = 842 — 373 = 2.671173
*' . 5 side — c = 842 — 747 = 1.977724
2)10.018254
Area = Number of 5.009127 = 102120.4 /«et
3.— What is logarithm of 8^'^?
Log. ^ = — X log. 8 = 3.6 X. 903 09 = 3. 251 124. Number =1783.8^
IiOOABtTBMS OF NUIIBXBS.
3ii
XjOfsaritliixis of* ^uxxi'bexTS.
From 1 to loooo.
No. I Logarithm.
1
2
3
4
5
6
7
8
9
lo
11
13
14
15
i6
17
i8
19
ao
21
22
23
24
25
No.
100
lOI
I02
I02
103
104
104
106
106
107
107
108
109
109
110
III
1x2
112
"3
114
"4
Ma
.0
.30103
.477 121
.60206
.69897
.778 151
.845098
.90309
'954 243
1
1-041 393
1.079 ^8i
1-113943
1. 146 128
1.176 091
1.204 12
1.230449
1255273
1.278754
1.301 03
1.322219
1-342423
1. 361 728
1.380211
1-39794
No. I Logarithm.
26
27
28
29
30
81
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
1.414973
1. 431 364
1.447 158
1.462398
1.477 121
1.491 362
1505 15
1.518514
1531 479
1.544068
1.556303
1.568202
1579784
1.591 065
1.60206
1. 61 2 784
1.623 249
1.633468
1.643453
1.653 213
1.662 758
1.672098
1.681 241
1.690 196
1.69897
No.
61
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72.
73
74
75
Logarithm.
•70757
.716003
.724 276
.732394
•740363
.74S188
.755 875
.763 428
.770852
.778 151
•785 33
.792 392
•799341
.80618
.812 913
.819544
.826 075
.832 509
.838849
.845098
.851 258
.857332
•863 323
.869232
.875061
No.
00- 0000 0434 0868 1301 1734
00- 4321 4751 5181 5609 6038
00- 86 9026 9451 9876 —
01- — — — -—03
01- 2837 3259 368 41 4521
01- 7033 7451 7868 8284 87
02- — — — — —
02- I 189
02- 5306
03- 9384
03- —
03- 3434
03- 7426
04- —
1603 20l6
5715 6125
9789 —
— 0195
3826 4227
7825 8223
2428 2841
6533 6942
06 1004
4628 5029
862 9017
04- 1393
04- 5323
04- 92x8
05- —
05- 3078
05- 6905
06- —
1787 2183
5714 6105
9606 9993
3463 3846
7286 7666
2576 2969
6495 6885
038 0766
423 4613
8046 8426
76
7*^
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
8
Logarithm.
3166 2598 3029
6466 6894 7321
0724 1147 157
494 536 5779
9116 9532 9947
3252 3664 4075
735 7757 8164
3461 3891
7748 8174
1993 2415
6197 6616
0361 0775
4486 4896
8571 8978
1408 1812 2216
543 583 623
9414 9811 —
— — 0207
3362 3755 4148
727s 7664 8053
2619 3021
6629 7028
o6o2 0998
454 4932
8442 883
1153 1538 1924
4996 5378 576
8805 9185 9563
2309 2694
6142 6524
9942 —
— 032
.880814
.886491
.892095
.897 627
.90309
.908485
.913 814
.919 078
.924279
•929419
.934498
.939519
.944483
•94939
.954243
.959041
.963788
.968483
•973 128
.977 724
.982 271
.986772
.991 226
•995635
D
432
438
425
424
420
417
416
412
408
40s
404
400
398
397
393
389
388
386
383
383
379
312
LOOABITHMS OF NT^KBBBS.
No.
115
0
1 a 3 4
I 5 6
789
D
06-
0698
1075 1452 1829 2206 , 2582 2958
3333 3709 4083
376
ii6 1 o6-
117 06-
4458
8186
4832 5206 558 5953 6326 6699
firr** flrkoR rvvoS /W>M >
7071 7443 7815
373
380
0557 0920 929" yuuo , — —
117 07-
—
■ 0038 0407
0776 1 145 1514
370
118
07-
1882
225 2617 2985 3352 , 3718 4085
4451 4816 5182
366
119
120
07-
5547
9181
5912 6276 664 7004
7368 7731
8094 8457 8819
3^3
362
07-
9543 9904 — —
X20
08-
—
— — 0266 0626
0987 1347
1707 2067 2426
360
121
08-
2785
3144 3503 3861 4219
4576 4934
5291 5647 6004
357
122
08-
08-
636
6716 7071 7426 7781
8136 849
8845 9198 9552
355
123
9905
^■^ — — ^—
355
123
09-
—
0258 061 1 0963 13 1 5
1667 2018
237 2721 3071
353
124
09-
3422
3772 4122 4471 482
5169 5518
5866 6215 6562
349
126
09-
691
7257 7604 7951 8298
8644 899
9335 9681 —
348
125
10-
— _— — —
— —
— — 0026
346
126
10-
0371
0715 1059 1403 1747
2091 2434
2777 3"9 3462
343
127
10-
3804 4146 4487 4828 5169
551 5851
6191 6531 6871
341
128
10-
721
7549 7888 8227 8565
8903 9241
9579 9916 —
338
128
II-
—
— — — __
— —
— — 0253
337
129
II-
059
0926 1263 1599 1934
227 2()OS
294 3275 3609
335
180
II-
3943
4277 4611 4944 5278
56H 5943
6276 6608 694
,133
131
11-
7271
7603 7934 8265 859s
8926 9256 9586 9915 —
331
»3i
12-
—
— — — —
— — _
— — 0245
330
132
12-
0574
0903 1231 156 1888
2216 2544
2871 3198 3525
328
133
12-
3852
4178 4504 483 5156
5481 5806 6131 6456 6781
325
134
12-
710S
7429 7753 8076 8399
8722 9045
9368 969 —
323
134
13-
— ^
— * ^— — ^—
— -^
— — C»I2
323
185
13-
0334
065s 0977 1298 1619
1939 226
258 29 3219
321
136
13-
3539
3858 4177 4496 4814
5133 5451
5769 6086 6403
318
137
138
138
13-
13-
14-
6721
9879
7037 7354 7671 7987
8303 8618
8934 9249 9564
316
0 r ^
0194 0508 0822 1136
145 1763 2076 2389 2702
315
314
139
14-
3015
3327 3639 3951 4263
4574 4885
5196 5507 5818
3"
140
141
14-
14-
6128
9219
6438 6748 7058 7367
7676 7985 8294 8603 891 1
309
308
9527 9^35
~~~ """■
«^^ ^"^ ^"^^
141
15-
— —
— — 0142 0449
0756 1063
137 1676 1982
307
142
15-
2288
2594 29 3205 351
3815 412
4424 4728 5032
30s
143
15-
5336 564 5943 6246 6549
6852 7154
7457 7759 8061
303
144
15-
8362 8664 8965 9266 9567
9868 —
302
144
l6-
—
— - — — —
— 0168
0469 0769 1068
301
145
16-
1368
1667 1967 2266 2564
2863 3161
346 3758 4055
299
146
16-
4353
46s 4947 5244 5541
5838 6134 643 6726 7022
297
M7
16-
7317
7613 7908 8203 8497
8792 9086 938 9674 9968
295
148
17-
0262
0555 0848 1 141 1434
1726 2019
231 1 2603 2895
293
149
17-
3186 3478 3769 406 4351
4641 4932
5222 5512 5802
291
160
17-
6091
6381 667 6959 7248
7536 7825
81 13 8401 8689
289
151
17-
8977 9264 9552 9839 —
— —
— -» —
287
151
18-
—
— — — 0126
0413 0699 0986 1272 1558
287
152
18-
1844
2129 2415 27 2985
327 3555
3839 4123 4407
285
153
18-
4691
4975 5259 5542 5825
6108 6391
6674 6956 7239
283
154
18-
7521
7803 8084 8366 8647
8928 9209
949 9771 —
281
154
19-
^—
— — — —
— —
— — 0051
281
Na
0
1 a 3 4
5 6
789
I>
LOOABTTHHS OF NIJMBEBS.
313
0333
3125
59
8657
0612
3403
6176
8932
0893 1 1 71 1451
3681 3959 4237
6453 6729 7005
9206 9481 9755
1397
412
6826
9515
167
4391
7096
9783
1943 2216 2488
4663 4934 5204
7365 7634 7904
0051 0319 0586
272 2986 3252
5373 5638 5902
801 8273 8536
0631 0892 1 153
3236 3496 3755
5826 6084 6342
84 8657 8913
0449 0704 096 1 215 147
2996 325 3504 3757 4011
5528 5781 6033 6285 6537
8046 8297 8548 8799 9049
0799 1048 1297 1546
3286 3534 3782 403
5759 6cx>6 6252 6499
8219 8464 8709 8954
CX42
2853
5273
7679
0071
2451
4818
7172
9513
[89 . 27-
100 27-
2074
4389
6692
8982
0908 1151 1395
3338 358 3822
5755 5996 6237
8158 8398 8637
0548 0787 1025
2925 3162 3399
529 5525 5761
7641 787s 811
998 - -
— 0213 0446
2306 2538 277
462 485 5081
6921 7151 738
9211 9439 9667
1033 1261 1488 1 715 1942
3301 3527 3753 3979 4205
5557 5782 6007 6232 6456
7802 8026 8249 8473 8696
0035 0257 048 0702 0925
2256 2478 2699 292 3141
4466 4687 4907 5127 5347
6665 6884 7104 7323 7543
8853 9071 9289 9507 9725
4
8
201
173
4514 4792
7281 7556
2289 2567 2846
5069 5346 5623
7832 8107 8382
0029 0303
2761 3033
5475 5746
8173 8441
0577 085 1 124
3305 3577 3848
6016 5286 6556
871 8979 9247
0853 1121
3518 3783
6166 643
8798 906
1414 167s
4015 4274
66 6858
917 94a6
1388 1654
4049 4314
6694 6957
9323 9585
1936 2196
4533 4792
7"5 7372
9682 9938
1724 1979
4264 4517
6789 7041
9299 955
1795 2044
4277 4525
6745 6991
9198 9443
2234 2488
477 5023
7292 7544
98 -
— 005
2293 2541
4773 5019
7237 7482
9687 9933
163S 1881
4064 4366
6477 6718
8877 91 16
1263 1501
3636 3873
5996 6232
8344 8578
2125 2368
4548 479
6958 7198
9355 9594
1739 1976
4109 4346
6467 6702
88x2 9046
192 1
4579
7221
9846
2456
5051
763
0193
2742
5276
7795
03
279
5266
7728
0176
261
5031
7439
9833
2214
4582
6937
9279
0679 0912
3001 3233
53" 5542
7609 7838
9895 -
— 0123
2169 2396
443t 4656
6681 6905
892 9143
1 147 1369
3363 3584
5567 5787
7761 7979
9943 —
— 0161
"44 1377
3464 3696
5772 6002
8067 8296
0351 0578
2622 2849
4882 5107
713 7354
9366 9589
1591 1813
3804 4025
6007 6226
8198 8416
1609
3927
6232
8525
0806
3075
5332
7578
9812
2034
4246
6446
8635
0378 059s 0813
279
278
276
27s
274
272
371
269
268
267
266
264
263
361
259
358
257
356
25s
253
253
251
350
249
248
246
246
245
243
242
241
239
238
237
235
234
234
233
232
230
229
228
228
227
226
225
223
222
221
220
219
218
218
314
L06A£ITHM& OF NIJKBBB8.
No.
200
20I
202
203
204
204
806
206
207
208
209
«10
211
212
213
214
215
2x6
2x7
218
218
219
820
221
222
223
223
224
225
226
227
228
229
229
230
231
232
233
234
234
2a5
236
237
238
30- 103 1247 1464
30- 3196 3412 3628
30- 5351 5566 5781
30- 7496 771 7924
30- 963 9843 —
31- — — 0056
31- 1754 1966 2177
31- 3867 4078 4289
31- 597 618 639
31- 8063 8272 8481
32- 0146 0354 0562
16811 1898
3844 4059
5996 621 1
8137 8351
2219 2426 2633
4282 4488 4694
6336 6541 674s
838 8583 8787
32
32
32
32
33- —' ~ — —
33- 0414 0617 0819 1022
0268
2389
4499
6599
8689
0769
2839
4899
695
8991
0481
26
471
6809
8898
0977
3046
5105
7155
9194
33-
33-
33-
33-
34-
34-
34-
34-
34-
34-
35-
35-
35-
35-
35-
35-
35-
36-
36-
36-
36-
36-
36-
37-
37-
37-
37-
37-
2438 264 2842
4454 4655 4856
646 666 686
8456 8656 8855
1225
3044 3246
5057 5257
706 726
9054 9253
0444 0642 0841
2423 262 2817
4392 4589 4785
6353 6549 6744
8305 85 8694
1039 1237
3014 3212
4981 5178
6939 7135
8889 9083
8
2 1 14 2331 2547 2764
4275 449» 4706 4921
6425 6639 6854 7068
8564 8778 8991 9204
0693
2812
492
7018
9106
1 184
3252
531
7359
9398
1427
3447
5458
7459
9451
0248 0442 0636
2183 2375 2568
4108 4301 4493
6026 6217 6408
7935 8125 8316
9835 - -
— 0025 0215
1728 191 7 2105
3612 38 3988
5488 5675 5862
7356 7542 7729
9216 9401 9587
1435
3409
5374
733
9278
0906 1118 133 1542
3023 3234 3445 3656
513 534 5551 576
7227 7436 7646 7854
9314 9522 973 9938
1391 1598 1805 2012
3458 3665 3871 4077
5516 5721 5926 6131
7563 7767 7972 8176
9601 9805 — —
— — 0008 021 1
163 1832 2034 2236
3649 385 4051
5658 5859 6059
7659 7858 8058
965 9849 —
— — 0047
1632 183 2028
3606 3802 3999
557 5766 5962
7525 772 7915
9472 9666 986
298 I 217
5136 216
7282 215
9417 313
213
212
211
210
209
208
207
206
20s
204
204
203
202
0829 1023
2761 2954 3147
4685 4876 ' 5068
6599 679 I 6981
8506 8696 ' 8886
1 216 141 1603 1796
3339 3532 3724
526 5452 5643
7172 7363 7554
9076 9266 9456
0404 0593 0783
2294 2482 , 2671
4176 4363 4551
6049 ^3^ '. 6423
7915 8101 8287
9772 9958
239 37-
239 I 38-
240 38-
241 38-
242 38-
243 38-
244 38-
1068 1253 1437
2912 3096 328
4748 4932 51 15
6577 6759 6942
8398 858 8761
0972 1 161 135
2859 3048 3236
4739 4926 5113
661 .6796 6983
8473 8659 8845
0143
1991
3831
1622 1806
3464 3647
5298 5481 ; 5664
7124 7306 7488
8943 9124 9306
0328 0513
2175 236
40X5 4198
5846 6029
767 7852
9487 9668
02 1 1 0392 0573
2017 2197 2377
3815 3995 4174
5606 5785 5964
739 7568 7746
0754 0934 1 115
2557 2737 2917
4353 4533 4712
6142 6321 6499
7923 8xoi 8279
1296 1476
3097 3277
4891 507
6677 6856
8456 8634
4253 202
626 ' 201
8257 200
— 200
0246 ' 199
2225 198
4196 , 197
6157 I 190
811 195
— I 194
0054 194
1989 193
3916 I 493
5834 192
7744 I9»
9646 190
189
189
188
188
187
186
186
0698 0883 X85
2544 2728 184
4382 4565 X84
6212 6394 183
8034 8216 182
9849 —
— 003 I
1656 1837
3456 3636
5249 5428
7034 7212
8811 8989 '
1539
3424
5301
7169
903
I
8
182
x8i
181
180
179
178
178
LOGABITHMS OF NUMBSBS.
315
Ko.
846 I 38- 9166 9343 952 9698 987s
245
246
247
248
249
350
251
251
25a
353
254
855
256
257
257
258
259
260
261
26a
263
2<^
264
265
266
267
a6S
269
269
270
271
272
273
274
875
27s
276
277
278
279
280
281
281
282
283
39-
39-
39-
39-
39-
39-
39-
40-
40-
40-
40-
40-
40-
40-
41-
41-
41-
41-
41-
41-
41-
42-
42-
42-
4a-
42-
42-
42-
43-
43-
43-
43-
43-
43-
43-
44-
44-
44-
44-
44-
44-
44-
45-
45-
45-
0935
2697
4452
6199
794
9674
140X
3121
4834
654
824
9933
162
33
4973
6641
8301
9956
1604
3246
4882
6511
8135
9752
1364
2969
4569
6163
7751
9333
1 1 12 1288
2873 3048
4627 4802
6374 6548
81 14 8287
9847 -
— 002
1573 1745
3292 3464
5005 5176
671 6881
841 8579
1464 1641
3224 34
4977 5152
6722 6896
8461 8634
8
0192 0365
1917 2089
3635 3807
5346 5517
7051 7221
8749 8918
0102 0271
1788 1956
3467 3635
S14 5307
6807 6973
8467 8633
044 0609
2124 2293
3803 397
5474 5641
7139 7306
8798 8964
0121 0286
1768 1933
341 3574
5045 5208
6674 6836
8297 8459
9914 —
— 0075
1525 1685
313 329
4729 4888
6322 6481
7909 8067
9491 9648
0451 0616
2097 2261
3737 3901
5371 5534
6999 7161
86ai 8783
0236 0398
1846 2007
345 361
5048 5207
664 6799
8226 8384
9806 9964
0051 0228
1817 1993
3575 3751
5326 5SOI
7071 7245
8808 8981
0405
2169
3926
5676
7419
9154
0582
2345
4101
585-
7592
9328
07S9
2521
4277
6025
7766
9501
0538 07 n 0883 1056 1228
2261 2433 2605 2777 2949
3978 4149 432 4492 4663
5688 5858 6029 6199 637
7391 7561 7731 7901 807
9087 9257 9426 9595 9764
0777 0946 1 1 14 1283 1451
2461 2629 2796 2964 3133
4137 4305 4472 4639 4806
5808 5974 6141 6308 6474
7472 7638 7804 797 8135
9129 9295 946 9625 9791
0781 0945 III 1275 1439
2426 259 2754 2918 308a
4065 4228 439a 4555 4718
5697 586 6023 6186 6349
7324 7486 7648 7811 7973
8944 9106 9268 9429 9591
! 0559 072 0881 1042 1203
' 2167 2328 2488 2649 2809
i 377 393 409 4249 4409
5367 5526 5685 5844 6004
6957 71 16 7275 7433 7593
, 854a 8701 8859 9017 9175
0909 1066 1334
248 2637 2793
4045 4201 4357
5604 576 5915
7158 73>3 7468
8706 8861 9di5
1381 1538
29s 3106
4513 4669
6071 6226
7623 7778
917 9324
0249
1786
3318
4845
6366
7883
9392
0403 0557
194 2093
3471 3624
071 1 0865
2247 24
3777 393
284 45-
885 , 45-
286 I 45-
287 ' 45-
288 45-
288 46-
289 t 46- 0898 X048 X198 1348 1499
4997 515
6518 667
8033 8184
9543 9694
5302 5454
6821 6973
8336 8487
9845 9995
OI23 0279 0437 0594
1695 1852 2o«9 2166
3263 3419 3576 3732
4825 4981 5137 5293
6382 6537 6692 6848
7933 8088 8242 8397
9478 9633 9787 9941
1018 1 1 72 1326 1479
2553 2706 2859 3012
4082 4235 4387 454
5606 5758 591 6062
7125 7276 7428 7579
8638 8789 894 9091
075a
2323
3889
5449
7003
8553
0095
1633
3165
4692
6214
7731
9242
N&
0146 0296 0447 0597 0748
1649 1799 1948 2098 2248
D
177
177
176
176
175
174
173
173
173
172
171
171
170
169
169
X69
168
167
167
166
165
165
165
164
164
163
162
162
162
161
161
160
159
159
158
158
158
J57
X57
156
»55
155
154
154
154
153
153
152
152
151
151
151
150
8
3i6
LOGABITHM^ OF KUKBBBS.
No.
290
291
292
393
294
296
295
296
297
298
299
800
301
302
303
304
306
307
308
309
309
810
3"
312
313
314
8I0
316
316
317
318
319
880
321
323
323
323
324
826
326
327
328
329
880
331
331
332
333
334
No.
46- 2398 2548 2697 2847
46- 3893 4042 4191 434
46- 5383 5532 568 5829
46- 6868 7016 7164 7312
46- 8347 8495 8643 879
46- 9822
47- —
47-- 1292
47- 2756
47- 4216
47- 5671
2997
449
5977
746
8938
9969 — — —
— 0116 0263 041
1438 1585 1732 1878
2903 3049 319s 3341
4362 4508 4653 4799
5816 5962 6107 6252
7266 741 1 7555 77
871 1 885s 8999 9143
01 5 1 0294 0438 0582
1586 1729 1872 2016
3016 3159 3302 3445
47- 7"i
47- 8566
48- ooo^
48- 1443
48- 2874
48- 43 4442 4585 4727 4869
48- 5721 5863 6005 6147 6289
48- 7138 728 7421 7563 7704
48- 8551 8692 8833 8974 9114
48- 9958 -----
49- — 0099 0239 038 052
56789
3146 3296 3445 3594 3744
4639 4788 4936 5085 5234
6126 6274 6423 6571 6719
7608 7756 7904 8052 82
9085 9233 938 9527 967s
49- 1362
49- 276
49- 41SS
49- 5544
49- 693
49- 831 I
49- 9687
so- —
50- 1059
SO- 2427
50- 3791
SO- 515
SO- 6505
SO- 7856
50- 9203
51- —
51- 0545
1S02 1642 1782 1922
29 304 3179 3319
4294 4433 4572 4711
5683 5822 596 6099
7068 7206 7344 7483
8448 8s86 8724 8862
9824 9962 —
— — 0099
1 196 1333 147
2564 27 2837
3927 4063 4199
5286 5421 S557
664 6776 691 1
7991 8126 826
9337 9471 9606
0236
1607
2973
4335
5693
7046
8395
974
0557 0704 o8si 0998 114s
202s 2171 2318 2464 261
3487 3633 3779 3925 4071
4944 509 5235 5381 5526
6397 6542 6687 6832 6976
7844 7989 8133 8278 8422
9287 9431 9575 9719 9863
072s 0869 1012 iis6 1299
2159 2302 2445 2588 2731
3587 373 3872 401S 4157
5011 5153 529s 5437 5579
643 6572 6714 685s 6997
784s 7986 8127 8269 841
9255 9396 9537 9677 9818
0661 0801 0941 X081 1223
2062
3458
485
6238
7621
2201
2341
3597 3737
4989 S128
6376 651s
7759 7897
2481 2621
3876 4015
S267 5406
66S3 6791
8035 8173
8999 9137 9275 9412 955
0374 0511 0648
1744 188 2017
3109 3246 3382
4471 4607 4743
0785 0923
2IS4 2291
3518 3655
4878 5014
0679 0813 0947 1081
SI-
51-
51-
51-
SI-
SI-
52-
52-
52-
52-
1883
3218
4548
5874
7196
8514
9828
1 138
2444
3746
2017 21SI 2284
3351 3484 3617
4681 4813 4946
6006 6139 6271
7328 746 7592
8646 8777 8909
9959 — —
— 009 0221
1269 14 153
2575 2705 283s
3876 4006 4136
5828 5964 6099 6234 637
7181 7316 7451 7586 772X
853 8664 8799 8934 9068
9874 — - — —
— 0009 0143 0277 04H
1 215 1349 1482 1616 175
2418 2551 2684
375 I 3883 4016
5079 ' 5211 5344
6403 6535 6668
7724 7855 7987
904
0353
1661
2966
4266
2818 2951 3084
4149 4282 4415
5476 5609 5741
68 6932 7064
81 19 8251 8382
9171 9303 9434 9566 9697
0484 061S 0745 0876 1007
1792 1922 2053 2183 2314
3096 3226 3356 3486 3616
4396 4526 4656 4785 4915
56780
[5^
[49
[49
[48
148
t47
147
[46
[46
t46
145
t45
[44
[44
^3
t43
143
14a
141
[41
[40
[40
[40
139
139
^39
t38
138
137
137
t37
136
t36
136
^35
^35
134
134
^34
^33
t33
^33
t33
133
^31
131
131
131
130
[JO
LOOABITHHS OF IfTTMBBBS.
317
Na
S86
336
337
338
338
339
S40
341
342
343
344
146
346
346
347
348
349
850
351
352
353
354
354
865
356
357
358
359
860
361
362
363
363
364
865
366
367
368
369
870
371
371
372
373
374
876
376
377
378
379
No.
52- 5045
52- 6339
52- 763
52- 8917
53- —
53-02
53- 1479
53- 2754
S3- 4026
53- 5294
53- 6558
53- 7819
53-9076
54- —
54- 0329
54- 1579
54- 282s
54- 4068
54- 5307
54- 6543
54- 7775
54-9003
55- —
55- 0228
55- 145
55-2668
55- 3883
55- 5094
55- 6303
55- 7507
55- 8709
55- 9907
56- —
56- IIOI
56- 2293
56- 3481
56-4666
56- 5848
56- 7026
56- 8ao2
56- 9374
5174 5304 5434 5563
6469 6598 6727 6856
7759 7888 8016 8145
9045 9174 9302 943
0328 0456 0584 0712
i6c7 1734 1863 199
2882 3009 3136 3264
4153 438 4407 4534
5421 5547 5674 58
6685 681 1 6937 7063
7945 8071 8197 8322
9202 9327 9452 9578
0455 058 0705 083
1704 1829 1953 2078
295 3074 3199 3323
4192 4316 444 4564
5431 5555 5678 5802
6666 6789 6913 7036
7898 8021 8144 8267
9126 9249 9371 9494
0351 0473 059s 0717
1572 1694 1816 1938
279 2911 3033 3155
4004 4126 4247 4368
5215 5336 5457 5578
6423 6544 6664 6785
7627 7748 7868 7988
8829 8948 9068 9188
0026 0146 0265 0385
1221 134 1459 1578
2412 2531 265 2769
36 3718 3837 3955
4784 4903 S021 5139
5966 6084 6202 632
7144 7262 7379 7497
8319 8436 8554 8671
9491 9608 9725 9842
57- —
57- 0543
57- 1709
57- 2872
57- 4031
57- 5188
57- 6341
57- 7492
57- 8639
066 0776 0893
1825 1942 2058
3988 3104 322
4147 4263 4379
5303 5419 5534
6457 6572 6687
7607 7722 7836
8754 8868 8983
zoi
2174
3336
4494
56s
6802
8
5693 5823 5951
6985 71 14 7243
8274 8402 8531
9559 9687 9815
084 0968 1096
2117 2245 2372
3391 3518 3645
4661 4787 4914
5927 6053 618
7189 7315 744X
8448 8574 8699
9703 9839 9954
095s 108 1305
3303 3337 3453
3447 3571 3696
4688 48x3 4936
5935 6049 6172
7159 7383 7405
8389 8513 863s
9616 9739 9861
6081 631
7372 7501
866 8788
9943 —
— 0073
1333 1331
35 2637
3772 3899
5041 5167
6306 6433
7567 7693
8835 8951
0079 0204
133 1454
2576 2701
382 3944
506
6296
7529
8758
9984
084 0963 1084
206 3181 3303
3276 3398 3519
4489 461 4731
5699 583 594
6905 7036 7146
8108 8338 8349
9308 9438 9548
1206
2425
3^
4852
6061
5183
6419
7653
8881
0106
1328
2547
3762
4973
6182
7267 7387
8469 8589
9667 9787
0504 0624 0743
1698 181 7 1936
2887
4074
5257
6437
7614
8788
9959
1 126
2391
3452
461
5765
6917
7951 8066
9097 9313
3006 3125
4192 431 1
5376 5494
6555 6673
7732 7849
8905 9023
0076 0193
1243 1359
2407 3523
3568 3684
4726 4841
588 5996
7032 7147
8181 8295
9326 9441
0863 0982
2055 2174
3244 3362
4429 4548
5612 573
6791 6909
7967 8084
914 9357
0309
1476
2639
38
4957
6111
7363
841
9555
0436
1592
2755
3915
5072
6336
7377
8525
9669
4 I 5
8
139
139
129
128
128
138
138
137
137
136
136
136
126
135
125
125
124
124
1 124
! 123
: 123
I 123
i 123
123
122
121
121
121
I30
I30
120
120
119
119
H9
119
118
118
118
117
"7
117
117
116
116
116
"5
"5
"5
"4
D
318
LOGABITHMS OF NUKBSB8.
No. I o
88o|'s7- 9784
380! 58
381 ' 58- 0925
382 58- 2063
383 I 58- 3199
384 58- 4331
386
386
387
388
389
389
890
391
392
393
394
S8
58
58
58
58
59
59-
59-
59-
59-
59-
9898
1039
2177
3312
5574
67
7823
8944
0012
"53
2291
3426
4557
5686
6812
7935
9056
8
0126 0241 0355 0469 0583 0697 081 1
1267 1381 I 1495 1608 1722 1836 19s
2404 2518 I 2631 274s 2858 2972 3085
3539 3652 3765 3879 3992 410S 4218
467 4783
5461
6587
7711
8832
995 — — — —^
I- — 0061 0173 0284 0396
4896 5009 5122 5235 5348
5799 5912 6024 6137 625 6362 6475
6925 7037 , 7149 7262 7374 7486 7599
8047 816
9167 9279
1065
2177
3286
4393
5496
895 59- 6597
396 I 59- 769s
397 I 59- 8791
398 . 59- 9883
398 60- —
399 60- 0973
60-
60-
400
401
402 I 60-
403 i 60
404 I 6o-
40o
406
407
407
408
409
410
4"
412
413
4x4
416
416
416
417
418
419
420
421
422
423
424
60-
60
60-
61-
61'
61-
61-
61-
6i-
61-
61-
61-
61-
62-
62-
62-
62-
2o6
3144
4226
5305
6381
7455
8526
9594
1 176 1287
2288 2399
3397 3508
4503 4614
5606 5717
6707 6817
7805 7914
89 9009
9992 —
— OIOI
1082 1 191
2169 2277
3253 3361
4334 4442
5413 5521
6489 6596
7562 7669
8633 874
9701 9808
1399 151
251 2621
3618 3729
4724 4834
5827 5937
6927 7037
8024 8134
91 19 9228
8272 8384 8496 8608 872
9391 9503 9615 9726 9838
0507 0619 073
1621 1732 1843
2732 2843 2954
384 395 4061
4945 5055 5165
6047 6^57 ^^7
0842 0953
1955 2066
3064 3175
41 71 4282
5276 5386
6377 6487
066 0767 0873
1723 1829 19;^
2784 289 2996
3842 3947 4053
4897 5003 5108
595 605s 616
7 7105 721
8048 8153 8257
9093 9198 9302
021 0319
1299 1408
2386 2494
3469 3577
455 4658
5628 5736
6704 681 1
7777 7884
8847 8954
9914 —
— 0021
0979 1086
2042 2148
3ica 3207
4159 4264
5213 5319
6265 637
7315 742
8362 8466
9406 9SII
0136
1 176
22x4
62- 3249
62- 4282
62- 5312
62- 634
62- 73^
024 0344
128 1384
2318 2421
3353 3456
4385 4488
5415 5518
6443 6546
7468 7571
0448 0552
1488 1592
2525 2628
3559 3663
4591 4695
5621 5724
6648 6751
7673 7775
7146 7256 7366 7476 7586
8243 8353 8462 8572 8681
9337 9446 9556 9665 9774
0428 0537 0646 0755 0864
1517 1625 1734 1843 1951
2603 271 1 2819 2928 3036
3686 3794 3902 401 4 118
4766 4874 4982 5089 5197
5844 5951 6059 6166 6274
6919 7036 7133 7241 7348
7991 8098 8205 8312 8419
9061 9167 9274 9381 9488
0128
119a
2254
3313
437
5424
6476
7525
8571
9615
0234. 0341 0447 0554
1298 1405 1511 16x7
236 2466 2572 2678
3419 3525 363 373^
4475 4581 4686 479a
5529 5634 574 584s
6581 6686 679 6895
7629 7734 7839 7943
8676 878
9719 9824
0656
1695
2732
3766
4798
5827
6853
7878
076 0864
1799 1903
2835 2939
3869 3973
4901 5004
5929 6032
6956 7058
798 8082
8884 8989
9928 —
— 0032
0968 1073
2007 211
3042 3146
4076 4x79
5107 52 X
6135 6238
7 161 7263
8x85 8387
~0 9~
14
^4
14
14
13
'3
C3
[2
[2
L2
[2
[2
I
[I
;i
[O
[O
[O
[O
[09
[09
[09
[09
[08
[08
[08
[08
[07
107
107
[07
107
[06
106
[06
[06
105
105
105
loS
105
104
[04
104
103
103
103
103
t02
LOGARITHMS OF NTTMBBBS.
319
426
426
426
427
438
429
4S0
431
433
433
434
486
436
436
437
438
439
44«
441
443
443
446
446
446
447
448
449
460
451
453
453
454
166
456
457
457
458
459
460
461
462
463
464
166
466
467
467
468
469
Now I
62-
62-
63-
63-
63-
63-
63-
63-
63-
^-
63-
63-
63-
64-
64-
64-
64-
64-
64-
64-
64-
64-
64-
64-
65-
65-
65-
65-
65-
65-
65-
65-
65-
8389 8491 8593 869s 8797
941 9512 9613 9715 9817
0428 053 0631 0733 0835
1444 154s 1647 1748 1849
3457 2559 266 2761 2862
3468 3569 367 3771 3873
4477 4578 4679 4779 488
5484 5584 5685 5785 5886
6488 6588 6688 6789 6889
749 759 769 779 789
8489 8589. 8689
9486 9586 9686
8789 8888
9785 98S5
0481 0581 068
1474 1573 167a
2465 2563 2662
3453 3551 365
4439 4537 4636
5422 5^21 5619
6404 6502 66
7383* 7481 7579
836 8458 8555
9335 9432 953
0779 0879
1771 1871
2761 286
3749 3847
4734 4832
5717 5815
6698 6796
7676 7774
8653 875
9627 9724
0308 0405 0502
1278 1375 1472
2246 2343 244
32x3 3309 3405
4177 4273 4369
5138 5235 5331
6098 6194 629
7056 7152 7247
65- 8011 8107 8202
65- 8965 906 9155
65- 99x6 — —
66- — 0011 0106
66- 0865 096 105s
66- 1813 1907 80O2
66- 2758 2832 2947
66- 3701 3795 3889
66- 4642 4736 483
66- 5581 5675 5769
66- 6518 66ia 6705
66- 7453 7546 764
66- 8386 8479 8572
66-9317 941 9503
67- — — —
67- 0246 0339 0431
67- 1173 1265 1358
0599 0696
1569 1666
2536 2633
3502 3598
446^ 4562
5427 5523
6386 6482
7343 7438
8298 8393
925 9346
0201 0296
"5 1245
2096 2191
3041 3135
3983 4078
4924 5018
5862 5956
6799 ^892
7733 7826
8665 8759
9596 9689
0524 0617
»45« 1543
8
89 9002
9919 —
— 0021
0936 1038
1951 205a
2963 3064
3973 4074
4981 S081
5986 6087
6989 7089
799 809
898S 9088
9984 —
— 0084
0978 1077
197 2009
2959 3058
3946 4044
4931 5029
5913 601 1
6894 6992
7872 7969
8848 8945
9821 99x9
0703 089
1762 x8s9
273 2826
3695 3791
4658 4754
5619 5715
6577 6673
7534 7629
8488 8584
9441 9536
9104 9206 9308
0x23 0224 0326
1x39 1241 1342
2x53 22SS 2356
3x65 3266 3367
4175 4276 4376
5182 5283 5383
6187 6287 6388
7189 729 739
8x9 829 8389
9x88 9287 9387
0x83 0283 0382
1177 1276 X37S
2x68 2267 2366
3156 325s 3354
4143 4242 434
5x37 5226 5324
6x1 6208 6306
7089 7187 7285
8067 8x65 8262
9043 914 9237
c»i6 0XX3 021
0987 1084 1x81
1956 2053 2x5
2923 3019 31 16
3888 3984 408
485 4946 5042
581 5906 6cx>2
6769 6864 696
7725 782 7916
8679 8774 887
9631 9726 982X
0391 0486
1339 1434
2286 238
323 3324
4x72 4266
51 12 5206
605 6143
6986 7079
792 80x3
8852 8945
978a 987s
07t 0803
1636 1738
0581 0676 0771
1529 1623 1 7 18
2475 2569 2663
3418 3513 3607
436 4454 4548
5299 5393 5487
6237 6331 6424
7x73 7266 736
8x06 8x99 8293
9038 9x31 9224
9967 — —
— 006 0x53
0895 0988 X08
1831 1913 2C05
780
D
X03
X02
X02
X03
XOI
XOI
lOI
XOI
XOO
XOO
100
XOO
XOO
99
99
99
99
99
98
^
98
98
97
97
97
97
97
97
^
96
96
95
95
95
95
95
95
94
94
94
94
94
93
93
93
93
93
93
D
320
LOGABITHMS OF KUHBBBd.
No.
0
1
2
3
4
5
6
789
470
67-
2098
219
2283
2375
2467
256
2652
2744 2836 2929
471
67-
3021
3"3
3205
3297
339
3482
3574
3666 3758 385
472
67-
3942
4034
4126 4218
431
4402
4494
4586 4677 4769
473
67-
4861
4953
5045
5137
5228
532
5412
5503 5595 5687
474
67-
5778 587
5962 6053 6145
6236 6328 6419 65 1 1 6602
475
67-
6694 6785 6876 6968
7059
7^51
7242
7333 7424 7516
476
67-
7607
7698
7789 7881
7972
8063 8154 824s 8336 8427
477
67-
8518 8609 87
8791
8882
8973 9064
915s 9246 9337
478
67-
9428
9519
961
97
9791
9882
9973
— — - -
478
68-
—
—
—
—
—
—
—
0063 0154 0245
479
68-
0336
0426
0517
0607 0698
0789 0879
097 106 1 151
480
68-
1 241
1332
1422
1513
1603
1693
1784
1874 1964 2055
481
68-
2145
2235
2326
24x6
2506
2596
2686
3777 3867 2957
482
68-
3047
3137
3227
3317
3407
3497
3587 3677 3767 3857 1
483
68-
3947
4037
4127
4217
4307
4396 4486 4576 4666 4756 1
484
68-
484s
4935
5025
5"4
5204
5294
5383
5473 5563 5652
486
68-
5742
5831
5921
601
61
6189 6279 6368 6458 6547
486
68-
6636 6726 6815 6904 6994
7083
7172
7261 7351 744
487
68-
7529
7618
7707
7796 7886
7975
8064
8153 8242 8331
488
68-
842
8509 8598 8687 8776
8865 8953
9042 9131 922
489
68-
9309
9398 9486
9575
9664
9753
9841
993 — —
489
69-
——
—
-^
— ^
— -
~^
-^
— 0019 0107
490
69-
0196
0285
0373
0462
055
0639 0728
0816 0905 0993
491
69-
1081
117
1258
1347
1435
1524
1612
17 1789 1877
492
69-
1965
2053
2142
223
2318
2406
2494
2583 2671 2759
493
69- 2847
2935
3023
3"i
3199
3287
3375
3463 3551 3639
494
69-
3727
3815
3903
3991
4078
4166
4254
4342 443 4517
495
69- 4605 4693 4781
4868 4956
5044
5131
5219 5307 5394
496
69- 5482
5569 5657
5744
5832
5919
6007 6094 6182 6269 1
497
69- 6356 6444 6531
6618
6706
6793
688
6968 7055 7142
498
69-
7229
7317
7404
7491
7578
7665
7752
7839 7926 8014
499
69-
8101
8188
8275 8362 8449
8535
8622
8709 8796 8883
600
69- 897
9057
9144
9231
9317
9404
9491
9578 9664 9751
501
69-9838
9924
—
—
—
—
—
— ___ —
501
70-
—
—
001 1
0098
0184
0271
0358
0444 0531 0617
502
70-
0704
079
0877 0963
los
1 136
1222
1309 1395 1482
503
70-
1568
1654
1 741
1827
1913
1999
2086
2172 2258 2344
504
70- 2431
2517
2603
2689
2775
2861
2947
3033 3119 3205
606
70- 3291
3377
3463
3549
3635
3721
3807 3893 3979 4065
S06
70- 4151
4236
4322
4408
4494
4579
4665
4751 4837 4922
S07
70-
5008
5094
5179
5265
535
5436
5522
5607 5693 5778
508
70-
5864
5949
6035
612
6206
6291
6376 6462 6547 6632 1
509
70-
6718 6803
6888
6974
7059
7144
7229
7315 74 7485
510
70-
757
7655
774
7826
79"
7996
8081
8166 8251 8336
511
70-
8421
8506 8591 8676 8761
8846 8931
9015 91 918s
512
70- 927
9355
944
9524
9609
9694
9779
9863 9948 —
512
71-
—
—
—
—
—
—
—
— — 00.1^
5x3
71-
OH7
0202
0287
0371
0456
054
0625
071 0794 0879
514
71-
0963
1048
1 132
1217
1301
138s
147
1554 1639 1733
Na
0
1
a
3
4
5
6
789
93
93
92
92
93
91
91
91
91
91
91
90
90
90
90
90
89
89
89
89
89
89
89
88
88
88
88
88
87
87
87
87
87
87
87
86
86
86
86
86
86
8S
85
8S
85
85
8S
85
84
L06ABITHMS OF KT7MBBBB.
321
No.
515
516
517
518
519
620
522
523
524
524
525
526
527
528
529
580
53«
532
533
534
535
536
537
537
538
539
640
541
542
543
544
545
546
547
548
549
549
650
551
552
553
554
655
556
557
558
559
1807 1892 1976 206 2144
26(5 2734 2818 2902 2986
3491 3575 3659 3742 3826
433 4414 4497 458i 4665
8
71
71
71
71
71- 5167 5251 5335 5418 5502 5586 5669 5753 5836 592 , 84
2229 2313 2397 2481 2566 1 84
307 3154 3238 3323 3407 84
391 3994 4078 4162 4246 84
4749 4833 4916 5 5084 84
71-
71-
71-
71-
71-
72-
72-
72-
72-
72-
72-
72-
72-
72-
72-
72-
72-
72-
72-
73-
73-
73-
73-
73-
73-
73-
73-
73-
73-
73-
73-
73-
74-
74-
74-
74-
74-
74-
74-
74-
74-
74-
74-
6003 6087 617 6254 6337
6838 6921 7004 7088 7171
7671 7754 7837 792 8003
8502 8585 8668 8751 8834
9331 9414 9497 958 9663
0159 0242 0325 0407 049
0986 1068 1151 1233 1316
181 1 1893 1975 2058 214
2634 2716 2798 2881 2963
3456 3538 362 3702 3784
4276 4358 444 4522 4604
5095 5176 5258 534 5422
5912 5993 6075 6156 6238
6727 6809 689 6972 7053
7541 7623 7704 7785 7866
8354 8435 8516 8597 8678
9165 9246 9327 9408 9489
9974 — — — —
— CXD55 0136 0217 0298
0782 0863 0944 1024 1 105
1589 1669 175 183 191 1
2394 2474 2555 2635 271S
3197 3278 3358 3438 3518
3999 4079 416 424 432
48 488 496 504 512
5599 5679 5759 5838 59i8
6397 6476 6556 6635 6715
7193 7272 7352 7431 751 1
7987 8067 8146 8225 8305
8781 886 8939 9018 9097
9572 9651 9731 981 9889
0363 0442 0521 06 0678
1 152 123 1309 1388 1467
1939 2018 2096 2175 2254
2725 2804 2882 2961 3039
351 3588 3667 3745 3823
4293 4371 4449 45^8 4606
5075 5153 5231 5309 5387
6421 6504 6588 6671 6754
7254 7338 7421 7504 7587
8086 8169 8253 8336 8419
8917 9 9083 9165 9248
9745 9828 991 1 9994 —
— — — — OQ77
0573 0655 0738 0821 0903
1398 1481 1563 1646 1728
2222 2305 2387 2469 2552
3045 3127 3209 3291 3374
3866 3948 403 41 12 4194
4685 4767 4849 4931 S013
5503 5585 5667 5748 583
632 6401 6483 6564 6646
7134 7216 7297 7379 746
7948 8029 811 8191 8273
8759 8841 8922 9003 9084
957 9651 9732 9813 9893
0378 0459 054 0621 0702
1186 1266 1347 1428 1508
1991 2072 2152 2233 2313
2796 2876 2956 3037 3117
3598 3679 3759 3839 3919
44 448 ^ 456 464 472
52 5279 5359 5439 55^9
5998 6078 6157 6237 6317
6795 6874 6954 7034 7113
759 767 7749 7829 7908
8384 8463 8543 8622 8701
9177 9256 9335 9414 9493
9968 ~ - - -
— 0047 0126 0205 0284
0757 0836 0915 0994 1073
1546 1624 1703 1782 186
2332 2411 2489 2568 2647
31 18 3196 3275 3353 3431
3902 398 4058 4136 4215
4684 4762 484 4919 4997
5465 5543 5621 5699 5777
5855 5933 601 1 6089 6167 6245 6323 6401 6479 6556
6634 6712 679 6868 6945 7023 7101 7179 7256 7334
7412 7489 7567 7645 7722 j 78 7878 7955 8p33 811
V1234I56799
83
83
83
83
83
83
83
82
82
82
82
82
82
82
81
81
81
81
81
81
81
81
80
80
80
80
80
80
79
79
79
79
79
79
79
79
78
78
78
78
78
78
78
322
LUGABITHMS OF NUHBBBS.
No.
660
0 1 a 3 4 ^
56789
D
74- 8188 8366 8343 8431 8498
8576 8653 8731 8808 888s
77
S6i 74- 8963 904 9118 9195 9273
935 9427 95<H 9582 9659
77
562 74- 9736 9814 9891 9968 —
77
562 75- — — — — 0045
0133 03 0377 0354 0431
77
563 75- 0508 0586 0663 074 0817
0894 .0971 IG48 1 135 I303
77
564 75- 1279 1356 1433 151 1587
1664 1741 1818 1895 1973
77
665 75- 2048 2125 2203 2379 2356 2433 2509 2586 2663 «74
77
566 75- 2816 2893 297 3047 3123
32 3277 3353 343 35o6 . 77
567 75- 3583 366 3736 3813 3889
3966 4042 4"9 4^95 4272 ; 77
568
75- 4348 442s 4501 4578 4^54
473 4807 4883 496 5036 , 76
569
75- 5112 5189 5265 5341 5417
5494 557 5646 5722 5799
76
570
75- 5875 5951 6027 6103 618
^56 6333 6408 6484 656
76
571
75- 6636 6713 6788 6864 694
7016 7093 7168 7344 733
76
572
75- 7396 7472 7548 7624 77
7775 7851 7927 8003 8079 1 76
573
75- 8155 823 8306 8382 8458
8533 8609 8685 8761 8836 1 76
574
75- 8913 8988 9063 9139 9214
929 9366 9441 9517 9592
76
576
75- 9668 9743 9819 9894 997
76
575
76- - - - - -
0045 OI2I 0196 0272 0347
75
576
76- 0422 0498 0573 (^9 0724
0799 0875 095 1025 IIOI
75
577
76- 1J76 1251 1326 1403 1477
1552 1627 1702 1778 1853
75
578
76- 1928 2003 2078 3153 3228
2303 2378 2453 2529 2604
75
579
76- 2679 2754 2829 2904 2978
3053 3128 3203 3278 3353
75
580
76- 3428 3503 3578 3653 3737
3802 3877 3952 4027 4101
75
581
76- 4176 4251 4326 44 4475
455 4624 4699 4774 4848 75
582
76- 4923 4998 5072 5147 5221
5296 537 5445 552 5594 75
583
76- 5669 5743 5818 5893 5966
6041 61 15 619 6264 6338 . 74
584
76- 64.13 6487 6563 6636 671
6785 6859 6933 7007 7082 1 74
685
76- 7156 723 7304 7379 7453
7527 7601 7675 7749 7823 74
586
76- 7898 7973 8046 8i3 8x94
8268 8343 8416 849 8564 74
587
76- 8638 8713 8786 886 8934
9008 9083 9156 933 9303 74
588
588
76- 9377 9451 9525 9599 9^73
^^— ■ ^^. ^^ ^^_ ^^_
9746 983 9894 9968 — , 74
■^^w ■v^v* ^^^K - ^^^\A^% mm M
77 — — — — —
— — — — 0043 , 74
589
77- 01 15 0189 0363 0336 041
0484 0557 0631 0705 0778 74
690
77- 0853 0926 0999 »«>73 1^46
133 1293 1367 144 1514 74
591
77- 1587 1661 1734 1808 1881
1955 2038 3 102 3175 3348 , 73
592
77- 2322 2395 2468 3543 2615
3688 3763 3835 3908 3981 . 73
593
77- 3055 3128 3201 3274 3348
3421 3494 3567 364 37x3 73
594
77- 3786 386 3933 4006 4079
4153 4325 4398 4371 4444 73
L
506
77- 4517 459 4663 4736 4809
4883 4955 S038 51 5173 73
596
77- 5246 5319 5392 5465 5538
561 5683 5756 5839 5903 73
597
77- 5974 6047 613 6193 6365
6338 6411 6483 6556 6629 73
598
7064 7137 7209 7383 7354 73
599
77- 7427 7499 7572 7644 7717
7789 7863 7934 8006 8079 7a
600
77- 8151 8334 8396 8368 8441
8513 8585 8658 873 8803 73
601
77- 8874 8947 9019 9091 9163
9236 9iy>8 938 9452 9534 , 7a
603
77- 9596 96^ 9741 9813 9885
9957 — — — — ' 7a
603
78 — — — —
— 0039 o'o* 0173 0245 7a
603
78- 0317 0389 0461 0533 0605
0677 07^9 0831 0893 0965 73
604
78- IQ37 1109 1 181 1353 1334
1396 1408 154 1613 1684
7a
D
No.
• • « I 4
S « 7 8 0
LOGABITHMS OF NUMBBBS.
323
No.
«05
606
607
608
609
610
611
612
613
614
616
616
616
617
618
619
3S0
621
622
623
624
686
626
627
628
629
680
631
632
633
634
685
636
637
638
639
640
641
642
643
644
646
645
646
647
648
649
660
651
652
654
Na
1755
2473
3189
3904
4617
533
6041
6751
746
8168
78-
78-
78-
78-
78-
78-
78-
78-
78-
78-
78- 8875
78- 9581
79- —
79- 0285
79- 0988
79- 1691
79- 239a
79- 3093
79- 379
79- 4488
79- 5185
79- 588
79- 6574
79- 7268
79- 796
79- 8651
79- 9341
80- 0029
80- 0717
80- 1404
8cH 2089
80- 2774
80- 3457
80- 4139
80- 4821
80- 5501
80- 618
80- 6858
80- 7535
80- 821 I
80- 8886
80- 956
81- —
I- 0233
I- 0904
I- 1575
I- 2245
I- 2913
1- 3581
i> 4348
I- 4913
I- 5578
1827 1899
2544 2616
326 3332
3975 4046
4689 476
5401 5472
6112 6183
6822 6893
7531 7602
8239 831
8946 9016
9651 9722
1 97 1 2042
2688 2759
3403 3475
4118 4189
4831 4902
5543 561S
6254 632s
6964 7035
7673 7744
838X. 8451
9087 9157
9792 9863
0356 0426 0496 0567
1059 1 129 1 199 1269
1 761 1831 1901 197X
2462 2532 2602 2672
3162 3231 330I 3371
386 393 4 407
4558 4627 4697 4767
5254 5324 5393 5463
5949 60x9 6088 6x58
6644 67x3 6782 6852
7337 74^ 7475 7545
8029 8098 8167 8236
872 8789 8858 8927
9409 9478 9547 9616
0098 0167 0236 0305
0786 0854 0923 0992
1472 X541 X609 X678
2x58 2226 2295 2363
2842 291 2979 3047
3525 3594 3662 373
4208 4276 4344 44x2
4889 4957 5025 5093
5569 5637 5705 5773
6248 6316 6384 645X
6926 6994 7061 7129
7^3 767 7738 7806
8279 8346 84x4 848X
8953 9021 9088 9x56
9627 9694 9762 9829
03 0367
097X X039
1642 X709
23x2 2379
298 3047
3648 37H
4314 4381
498 5046
5644 571 1
0434 0501
XX06 XX73
X776 X843
2445 2512
3XX4 3x8x
3781 3848
4447 4514
5113 5179
5777 5843
8
21x4 2x86 2258
2831 2902 2974
3546 3618 3689
4261 4332 4403
4974 504s 5"6
5686 5757 5828
6396 6467 6538
7x06 7x77 7248
781S 7885 7956
8522 8593 8663
9228 9299 9369
9933 — —
— 0004 0074
0637 0707 0778
134 X4X 148
2041 2XXI 21S1
2743 28x2 2882
3441 35H 3581
4139 4209 4279
4836 4906 4976
5532 5602 5672
6^27 6297 6366
6921 699 706
7614 7683 7752
8305 8374 8443
8996 9065 9134
9685 9754 9823
0373 0442 05 1 1
X061 X129 XX98
X747 1815 X884
2432 25 2568
3xx6 3184 3252
3798 3867 3935
448 4548 4616
5x61 5229 5297
5841 5908 5976
6519 6587 6655
7x97 7264 7332
7873 7941 8008
8549 8616 8684
9223 929 9358
9896 9964 —
— — 003X
0569 0636 0703
X24 X307 1374
X9X X977 2044
2579 2646 27x3
3247 3314 3381
39M 3981 4048
458X 4647 4714
5246 5312 5378
591 5976 6043
2329 240X 73.
3046 3x17 72
3761 3832 7«
4475 4546 71
5187 .5259 71
5899 597 7»
6609 668 71
7319 739 71
8027 8098 71
8734 8804 71
944 95« 71
— — 70
0x44 02x5 70
0848 0918 70
X55 x63 70
2252 232a 70
2952 3022 70
3651 3731 70
4349 '4418 70
5045 5"5 70
574X 581 X 70
6436 6505 69
7129 7198 69
782 X 789 69
8513 8582 69
9203 9272 69
9892 9961 69
058 0648 69
1266 X335 69
1952 2021 69
2637 2705 69
3321 3389 68
4003 407 X 68
4685 4753 68
5365 5433 68
6044 61 12 68
6723 679 68
74 7467 68
8076 8x43 68
8751 8818 67
9425 9492 67
^ ~ 67
0098 0165 67
077 0837 67
X441 X508 67
2XXX 2178 67
278 2847 67
3448 3514 67
4II4 4181 67
478 4847 67
5445 55" 66
6109 6x75 66
~9 0 sT
324
LOOABITHMS OF KUMBEBfi.
No.
9 I D
666
81-
6241 6308 6374 644 6506
6573 6639 6705 6771 6838 '
66
656
81-
6904 697 7036 7102 7169
7235 7301 7367 7433 7499
66
657
81-
7565 7631 7698 7764 783
7896 7962 8028 8094 816 i
66
658
8i-
8226 8292 8358 8424 849
8556 8622 8688 8754 882
66
659
81-
8885 8951 9017 9083 9149
9215 9281 9346 9412 9478
66
660
81-
9544 961 9676 9741 9807
9873 9939 — -- —
66
660
82-
— — ^ — -•-
— — 0004 007 0136
66
661
82-
0201 0267 0333 0399 0464
053 059s <j66i 0727 0792
66
662
82-
0858 0924 0989 1055 I"
1 186 1251 1317 1382 1448
66
663
82-
1514 1579 1645 171 1775
184 1 1906 1972 2037 2103
65
66i
82-
2168 2233 2299 2364 243
2495 256 2626 2691 2756
65
665
82-
2822 2887 2952 3018 3083
3148 3213 3279 3344 3409
65
666
82-
3474 3539 3605 367 3735
38 3865 393 3996 4061
6S
667
82-
4126 41 91 4256 4321 4386
4451 4516 4581 4646 471 1
65
668
82-
4776 4841 4906 4971 5036
5101 5166 5231 5296 5361
65
669
82-
5426 5491 5556 5621 5686
5751 5815 588 5945 601
65
670
82-
6075 614 6204 6269 6334
6399 6464 6528 6593 6658
65
671
82-
6723 6787 6852 6917 6981
7046 7111 7175 724 7305
65
672
82-
"7369 7434 7499 7563 7628
7692 7757 7821 7886 7951
65
673
82-
8015 868 8144 8209 8273
8338 8402 8467 8531 8595
64
674
82-
866 8724 8789 8853 8918
8982 9046 91 1 1 9175 9239
64
636
82-
9304 9368 9432 9497 9561
9625 969 9754 9818 9882
64
676
82-
rf'W<4 T , ^^_ «^^ ^^i-
64
9947 — — — —
676
83-
— 0011 007s 0139 0204
0268 0332 0396 046 0525
64
677
83-
0589 0653 0717 0781 0845
0909 0973 1037 1 102 1 166
64
678
83-
123 1294 1358 1422 i486
155 1614 1678 1742 1806
64
679
83-
187 1934 1998 2062 2126
2189 2253 2317 2381 244s
64
680
83-
2509 2573 2637 27 2764
2828 2892 2956 302 3083
64
681
83-
3147 3211 327s 3338 3402
3466 353 3593 3657 372i
64
682
83-
3784 3848 39" 3975 4039
4103 4x66 423 4294 4357
64
683
83-
4421 4484 4548 461 1 4675
4739 4802 4866 4929 4993
64
684
83-
5056 512 5183 5247 531
5373 6437 55 5564 5627
63
685
83-
5691 5754 5817 5881 5944
6007 6071 6134 6197 6261
63
686
183-
6324 6387 6451 6514 6577
6641 6704 6767 683 6894
63
687
83-
6957 702 7083 7146 721
7273 7336 7399 7462 7525
63
688
83-
7588 7652 7715 7778 7841
7904 7967 803 8093 8156
63
689
83-
8219 8282 8345 8408 8471
8534 8597 866 8723 8786
63
690
83-
8849 8912 8975 9038 910X
9164 9227 9289 9352 9415
63
691
83-
84-
9478 9541 9604 9667 9729
9792 9855 9918 9981 —
63
— — — — 0043
692
84
0106 0169 0232 0294 0357
042 0482 0545 0608 0671
63
693
84-
0733 0796 0859 0921 0984
1046 1109 1172 1234 1297
63
694
84-
1359 1422 1485 1547 161
1672 1735 1797 186 1922
;63
696
84-
1985 2047 '211 2172 2235
2297 236 2422 2484 2547
62
696
84-
2609 2672 i734 2796 2859
2921 2983 3046 3108 317
62
697
84-
3233 3295 3357 342 3482
; 3544 3606 3669 3731 3793
62
1
698
84-
3855 3918 398 4042 4104
4166 4229 4291 4353 4415
! 62
699
84-
4477 4539 4601 4664 4726
; 4788 485 4912 4974 5036
i 62
700
84-
5098 516 5222 5284 5346
5408 547 5532 5594 5656
63
701
84-
5718 578 5842 5904 5966
6028 609 6151 6213 6275
6a
702
84-
6337 6399 6461 6323 6585
6646 6708 677 6832 6894
i 62
703
84-
• 6955 7017 7079 7141 7202
7264 7326 7388 7449 75 1 1
62
704
84-
■ 7573 7634 7696 7758 7819
7881 7943 8004 8066 8127
6a
No.
• t 9 9 A
S 6 7 8 9
D
LOGARITHMS OF lOJMBSBS.
32s
Ko.
706
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
724
726
726
727
728
729
7S0
731
732
733
734
785
736
737
738
739
740
741
741
742
743
744
745
746
747
748
749
750
751
752
753
754
Na
4*
8
84- 8189 8251 831a 8374 8435
84- 8805 8866 8928 8989 9051
84- 9419 9481 9542 9604 9665
85- 0033 0095 0156 0217 0279
85- 0646 0707 0769 083 0891
85- 1258 132 1381 1442 1503
8s- 187 1931 1992 2053 21 14
85- 248 2541 2602 2663 2724
85- 309 31S 321 1 3272 3333
85- 3698 3759 382 3881 3941 ,
85- 4306 4367 4428 4488 4549
85- 4913 4974 5034 5095 5156
85- 5519 558 564 5701 5761
85- 6124 6185 6245 6306 6366
85- 6729 6789 685 691 697
85- 7332 7393 7453 75»3 7574
85- 7935 7995 805^ 81 16 8176
85- 8537 8597 8657 8718 8778
85- 9138 9198 9258 9318 9379
85- 9739 9799 9859 99i8 9978
86-
86- 0338
86- 0937
86- 1534
86- 2131
86- 2728
86- 3323
86- 3917
86- 4511
86- 5104
86- 5696
86- 6287
86- 6878
86- 7467
86- 8056
86- 8644
86- 9232
86- 9818
87
87- 0404
87- 0989
87- 1573
87- 2156
87- 2739.
87- 3321
87- 3902
87- 4482
87- 5061
87- 564
87- 6218
87- 6795
87- 7371
0398 0458 0518
0996 1056 11x6
1594 1654 I7»4
2191 2251 231
2787 2847 2906
3382 3442 3SOI
3977 4036 4096
457 463 4689
5163 5222 5282
5755 5814 5874
6346 6405 6465
6937 6996 7055
7526 7585 7644
8115 8174 8233
8703 8762 8821
929 9349 9408
9877 9935 9994
0462 0521 0579
1047 1106 1164
1631 169 1748
2215 2273 2331
2797 285s 2913
3379 3437 3495
396 4018 4076
454 4598 4656
5"9 5177 5235
5698 5756 5813
6276 6333 6391
6853 691 6968
7429 7487 7544
0578
1176
1773
237
2966
3561
4155
4748
5341
5933
6524
7114
7703
8292
8879
9466
0053
0638
1223
1806
2389
2972
3553
4134
4714
5293
5871
6449
7026
7602
4
£s
8497 8559
9112 9174
9726 9788
034 0401
0952 1014
1564 1625
2175 2236
2785 2846
3394 3455
4002 4063
461 467
5216 5277
5822 588a
6427 6487
7031 7091
7634 7694
8236 8297
8838 8898
9439 9499
OQ38 0098
0637 0697
1236 129s
1833 1893
243 2489
3025 3085
36a 368
4214 4274
4808 4867
54 5459
5992 6051
6583 6642
7173 7232
7762 V^2I
835 8409
8938 8997
9525 9584
862
9235
9849
0462
1075
1686
2297
2907
3516
4124
8682
9297
991 1
0524
1 136
1747
2358
2968
3577
4185
4731 479a
5337 5398
5943 6003
6548 6608
7152 7212
7755 7815
8357 8417
8958 9018
9559 9619
Q158 03l8
0757 0817
1355 1415
1952 2012
2549 2608
3144 3ao4
3739 3799
4333 4392
4926 4985
5519 5578
611 6169
6701 676
7291 735
788 7939
8468 8527
9056 91 14
9642 9701
8743
9358
9972
0585
1 197
1809
2419
3029
3637
4245
4852
5459
6064
6668
7272
7875
8477
9078
9679
0278
0877
1475
2072
2668
3263
3858
4452
5045
5637
6228
6819
7409
7998
8586
9173
976
oiii 017
0696 0755
1281 1339
1865 1923
2448 2506
303 3088
361 1 3669
4192 425
4772 483
5351 5409
5929 5987
6507 6564
7083 7141
7659 7717
02Cc 0287 0345
0813 0872 093
1398 1456 1515
I981 204 2098
2564 2622 2681
3146 3204 3262
3727 3785 3844
4308 4366 4424
4888 4945 5003
5466 5524 5582
6045 ^T^02 616
6622 668 6737
7199 7256 7314
7774 7832 7889
780
62
6x
61
61
61
61
61
61
61
61
61
61
6x
60
60
60
60
60
60
60
60
60
60
60
60
60
59
59
59
59
59
59
59
59
59
59
59
59
59
58
58
58
58
58
58
58
58
58
S8
58
S8
S8
326
LOGARITHMS OF NUMBEB8*
No.
0123
4
5
6 7
8 9 1
755
87-
7947 8004 8062 81 19
8177
8234 8292 8349 8407 8464
756
87-
8522 8579 8637 8694 8752
8809
8866 8924
8981 9039
757
87-
9096 9153 92 1 1 9268
9325
9383
944 9497
9555 9612
758
87-
9669 9726 9784 9841
9898
9956
758
88-
— — — —
—
—
0013 007
0137 0185
759
88-
0243 0299 0356 0413
0471
0538
0585 0642
0699 0756
760
88-
0814 0871 0928 0985
1042
1099
1156 1213
1371 1328
761
88-
1385 1442 1499 1556
1613
167
1727 1784
1841 1898
762
88-
1955 2012 2069 2126
2183
224
2297 2354
241 1 2468
763
88-
2525 2581 2638 2695
2752
2809
2866 2923
298 3037
764
88-
3093 315 p207 3264
3321
3377
3434 3491
3548 3605
765
88-
3661 3718 377S 3832
3888
3945
4003 4059
41 15 4172
766
88-
4229 4285 4342 4399
4455
4512
4569 4635 4682 4739}
767
88-
4795 4852 4909 4965
5022
5078
5135 5193
5248 5305
768
88-
5361 5418 5474 5531
5587
5644
57 5757
5813 587
769
88-
5926 5983 6039 6096 6152
6309 6265 6321
6378 6434
770
88-
6491 6547 6604 666
6716
6773 6829 6885 6942 6998
771
88-
7054 71 1 1 7167 7223
728
7336
7392 7449
7505 7561
772
88-
7617 7674 773 7786 7842
7898
7955 801 1
8067 8123
773
88-
8179 8236 8292 8348 8404
846
8516 8573 8629 8685 1
774
88-
8741 8797 8853 8909 8965
9021
9077 9134
919 9246
775
88-
9302 9358 9414 947
9526
9582
9638 9694
975 9806
776
88-
9863 9918 9974 —
—
—
776
89-
— — — 003
0086
0141
0197 CWS3
0309 0365
777
89-
0421 0477 0533 0589 0645
07
0756 0813
0868 0924
778 89- 098 I03S 1091 U47
1203
1259
1314 137
1436 1482
779 89-
1537 1593 1649 1705
176
1816
1873 1938 1983 2039
780 , 89-
2095 215 2206 2262
2317
2373
3429 2484
254 2595
781 89-
2651 3707 2762 2818
2873
2929
2985 3<?4
3096 3T51
782 89-
3207 3263 3318 3373
3429
3484
354 3595
3651 3706
783
89-
3763 3817 3873 3928 3984
4039
4094 415
4305 4261
784
89-
4316 4371 4427 4482
4538
4593
4648 4704
4759 4814
786
89-
487 4925 498 5036
5091
5146
Ssoi 5357
5312 .«67
786
89-
5423 5478 5533 5588 5644
5699
5754 5809 5864 593 1
787
39-
5975 603 6085 614
6195
6251
6306 6361
6416 6471
788
89-
6526 6581 6636 6692
6747
6802
6857 6913
6967 7033
789
89-
7077 7132 7187 7242
7297
7352
7407 7463
7517 7572
7f>0
89-
7627 7682 7737 7792
7847
7903
7957 8013
8067 8133
791
89-
8176 8231 8286 8341
8396
8451
8506 8561
8615 867
792
89-
8725 878 8835 889
8944
8999
9054 9109
9164 9218
793
89-
9273 9328 9383 9437
9492
9547
9603 9656
971 I 9766
794
89-
9821 9875 993 9985
—
—
— —
794
90-
— ^— ^^ _-
0039
0094
0149 0303
0258 0313
795
90-
0367 0422 0476 0531
0586
064
0695 0749
0804 0859
796
90-
0913 0968 1022 1077
1131
1186
134 1295
1349 1404
797
90-
1458 1513 1567 1622
1676
1 731
1785 184
1894 1948
798
90-
2003 2057 21 12 2166
2221
2275
3329 3384
2438 2493
799
90-
2547 2601 2655 271
2764
2818
3873 2937
2981 3036
800
90-
309 3144 3199 3253
3307
3361
3416 347
3524 3578
801
90-
3633 3^7 3741 3795
3849
3904
3958 4013
4u66 413
802
90-
4174 4229 4283 4337
4391
4445
4499 4553
4607 4661
803
90-
4716 477 4824 4878
4932
4986
504 5094
5148 5202
804
90-
5256 531 5364 5418
5472
5526 558 5634 5688 5742 1
No.
0 1 a ^
4
S
6 7
8 9 \
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
56
56
56
56
56
56
56
56
56
56
S6
56
56
56
56
55
55
55
55
55
55
55
55
55
55
55
55
55
55
55
54
54
54
54
54
54
54
54
LOGASITHMS OF NUMBESS.
327
806
806
807
808
809
SIO
81 X
812
812
813
814
815
816
817
818
819
820
821
822
823
824
82S
826
827
828
829
880
831
831
83a
83.3
834
885
836
837
838
839
840
841
842
843
844
845 '
846!
847;
848 I
849 I
850
851
85t
852
853
854
Kp.
90- S796
90- 633s
90- 6874
90- 7411
90- 7949
90- 8485
90- 9021
90- 9556
91- —
I- 0091
I- 0624
I- 1158
I- 169
I' 2222
I- 2753
I- 3284
I- 3814
I- 4343
I- 4872
I- 54
1- 5927
I- 6454
I- 698
I- 7506
t- 803
1- 8553
I- 9078
1- 9601
92- —
92- 0123
92- 064s
92- I 166
92- 1686
92- 2206
92- 2725
92- 3244
92- 3762
92- 4279
92- 4796
92- 53^2
9a- 5828
92- 6342
92- 6857
92- 737
92- 7883
92- 8396
92' 8908
92- 9419
92- 993
93- —
93- 044
93- 0949
93- 1458
585 5904 5958 6012
6389 6443 6497 6551
6927 6981 703s 7089
7465 7519 7573 7626
800a 8056 811 8163
8539 8592 8646 8699
9074 9128 9181 9235
9609 9663 9716 977
8
9
9
9
9
9
9
91
91
9
9
91
91
9
9
9
91
91
9
9
0144 0197 0251 0304
0678 0731 0784 0838
1211 1264 1317 1371
1743 1797 185 1903
2275 2328 2381 243s
2806 2859 2913.2966
3337 339 3443 349^
3867 392 3973 4026
4396 4449 4502 455S
4925 4977 503 5083
5453 5505 5558 5611
598 6033 6085 6138
6507 6559 6612 6664
7033 7083 7138 719
7558 -7611 76^ 77*6
8083 8135 8188 824
8607 8659 8712 8764
913 9183 9235 9287
9653 9706 9758 981
0176
0697
1218
1738
2258
2777
3296
3814
4331
4848
5364
5879
6394
6908
7422
7935
8447
8959
947
9981
0491
I
1509
0228 028 0332
0749 0801 0853
127 1322 1374
179 1842 1894
231 2362 2414
2829 2881 2933
3348 3399 3451
3865 3917 3969
4383 4434 4486
4899 4951 5003
5415 5467 5518
5931 5982 6034
644s 6497 6548
6959 701 1 7062
7473 7524 7576
7986 8037 8088
8498 8549 86ot
901 9061 91 12
9521 9572 9623
0032 0083 0134
0542 059a 0643
1051 iioa 1 153
156 i6f i66t
6066 6119
6604 6658
7143 7196
768 7734
8217 S27
8753 8807
9289 9342
9823 9877
6173 6227
671a 6766
725 7304
7787 7841
8324 8378
886 8914
9396 9449
993 9984
0358 04 1 1
0891 0944
1424 1477
1956 2009
2488 2541
3019 3072
3549 3602
4079 413a
4608 466
5136 5189
5664 5716
6191 6243
6717 677
7243 7295
7768 782
8293 8345
8816 8869
934 9392
9862 9914
0384 0436
0906 0958
1426 1478
1946 1998
2466 2518
2985 3037
3503 3555
4021 4072
4538 4589
5054 5106
557 5621
6085 6137
66 6651
7114 716s
7627 7678
814 8191
8652 8703
9163 9215
9674 972s
0464 0518
0998 1051
153 1584
2063 21 16
2594 2647
3125 3178
3655 3708
4184 4237
4713 4766
5241 5294
5769 5822
6296 6349
6822 6875
7348 74
7873 7925
8397 845
8921 8973
9444 9496
9967 —
— 0019
0489 0541
loi 1062
153 1582
205 2102
257 2622
3089 314
3607 3^58
4124 4176
4641 4693
5157 5209
5673 5725
61 88 624
6702 6754
7216 7268
773 778t
8242 8293
8754 880s
9266 9317
9776 9827
6281
683
7358
789s
8431
8967
9503
0037
0571
1 104
1637
2169
27
3231
3761
429
4819
5347
5875
6401
6937
7453
7978
8502
9026
9549
c»7i
0593
1 1 14
1634
2154
2674
3192
371
4228
4744
5261
5776
6291
6805
7319
7832
8345
8857
9368
9879
0185 0236 0287 0338 0389
0694 0745 0796 0847 0898
1203 1254 1305 1356 1407
1712 1763 1814 1865 1915
& $ 7 9 9
D
54
54
54
54
54
54
54
54
53
53
53
53
53
53
53
53
53
S3
53
S3
53
53
53
52
52
52
52
5^
52
52
52
52
52
52
52
52
52
52
52
52
55
51
51
5^
51
51
51
5^
51
51
5]
51
51
328
LOeABTTHMS OF NUHBEBS.
No.
01234
5 « 7 8 9
866
93- 1966 2017 2068 2118 2169
222 2271 2322 2372 2433
856
93- 2474 2524 2575 2626 2677
2727 2778 2829 2879 293
857
93- 2981 3031 3082 3133 3183
3234 3285 3335 3386 3437
858
93- 3487 3538 3589 3639 369
374 3791 3841 3892 3943
859
93- 3993 4044 4094 4145 4195
4246 4296 4347 4397 4448
860
93- 4498 4549 4599 465 47
4751 4801 4852 4902 4953
861
93- 5003 5054 5104 5154 520s
5255 5306 5356 5406 5457
862
93- 5507 5558 5608 5658 5709
5759 5809 586 591 596
863
93- 6oii 6061 61 1 1 6162 6212
6262 6313 6363 6413 64^
864
93- 6514 6564 6614 6665 6715
6765 6815 6865 6916 6966
866
93- 7016 7066 71 17 7167 7217
7267 7317 7367 7418 7468
866
93- 7518 7568 7618 7668 7718
7769 7819 7869 7919 7969
867
93- 8019 8069 81 19 8169 8219
8269 8319 837 842 847
868
93- 852 857 862 867 872
877 882 887 892 897
869
93- 902 907 912 917 922
927 932 9369 9419 9469
870
93- 9519 9569 9619 9669 97*9
9769 9819 9869 9918 9968
871
94- 0018 0068 01 18 0168 0218
0267 0317 0367 0417 0467
872
94- 0516 0566 0616 0666 0716
0765 0815 0865 0915 0964
873
94- 1014 1064 X114 1 163 1213
1263 1313 1362 1412 1462
874
94- 151 1 1561 161 1 166 171
176 1809 1859 1909 1958
876
94- 2008 2058 2107 2157 2207
2256 2306 2355 2405 2455
876
94- 2504 2554 2603 2653 2702
2752 2801 2851 2901 295
877
94- 3 3049 3099 3148 3198
3247 3297 3346 3396 3445
878
94- 3495 3544 3593 3^43 3692
3742 3791 3841 389 3939
879
94- 3989 4038 4088 4137 4186
4236 4285 4335 4384 4433
880
94- 4483 4532 4581 4631 468
4729 4779 4828 4877 4927
881
94- 4976 5025 5074 5124 5173
5222 5272 5321 537 5419
882
94- 5469 5518 5567 5616 5665
5715 5764 5813 5862 5912
883
94- 5961 601 6059 6108 6157
6207 6256 6305 6354 6403
884
94- 6452 6501 6551 66 6649
6698 6747 6796 6845 6894
886
94- 6943 6992 7041 709 714
7189 7238 7287 7336 7385
886
94- 7434 7483 7532 7581 763
7679 7728 7777 7826 7875
887
94- 7924 7973 8022 807 81 19
8168 8217 8266 8315 8364
888
94- 8413 8462 85 1 1 856 8609
8657 8706 8755 8804 8853
889
94- 8902 8951 8999 9048 9097
9146 9195 9244 9292 9341
890
891
94- 939 9439 9488 9536 9585
9634 9683 9731 978 9829
94- 9070 99-^u 9975
891
95- — — — 0024 0073
0121 017 0219 0267 0316
892
9t5- 0365 0414 0462 0511 056
0608 0657 0706 0754 0803
893
95- 0851 09 0949 0997 1046
1095 1 143 1192 124 1289
894
95- 1338 1386 1435 1483 1532
158 1629 1677 1726 1775
896
95- 1823 1872 192 1969 2017
2066 2114 2163 221 1 226
896
95- 2308 2356 240s 2453 2502
255 2599 2647 2696 2744
897
95- 2792 2841 2889 2938 2986
3034 3083 313^ 318 3228
898
95- 3276 3325 3373 3421 347
3518 3566 3615 3663 371 1
899
95- 376 3808 3856 3905 3953
4001 4049 4098 4146 4194
900
95- 4243 4291 4339 4387 4435
4484 4532 458 4628 4677
901
95- 4725 4773 4821 4869 4918
4966 5014 5062 511 5158
902
95- 5207 525s 5303 5351 5399
5447 5495 5543 5592 564
903
95- 5688 5736 5784 583a 588
5928 5976 6024 6072 6l2
904
95- 6168 6216 6265 6313 6361
6409 6457 6505 6553 6601
Na,
0 12 3 4
56789
51
51
51
51
51
50
50
50
50
50
so
50
50
SO
50
SO
50
50
SO
SO
SO
SO
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
49
48
48
48
48
48
48
48
48
48
48
jbOOAKITHMS OF NUMBUSS.
•329
No.
0
1 s 3 4
56789
•05
95- 6649 6697 6745 6793 684
6888 6936 6984 7032 708
906
95- 7128 7176 7224 7272 732
7368 7416 7464 7512 7559
907
95- 7607 7655 7703 7751 7799
7847 7894 7942 799 8038
908
95- 8086
8134 8181 8229 8277
8325 8373 8421 8468 8516
909
95- 8564
8612 8659 8707 8755
8803 885 8898 8946 8994
910
95- 9041
9089 9137 9185 9232
928 9328 9375 9423 9471
911
r\T»5i
95- 95<8 9566 9614 9661 9709
rtf • rw^c ^.^ •^— ^— —
9757 9804 9852 99 9947
913
912
95 9995
96- —
0042 009 0138 0185
0233 028 0328 0376 0423
913
96- 0471
0518 0566 0613 0661
0709 0756 0804 0851 0899
914
96- 0946
0994 X041 1089 1 136
1184 1231 1279 1326 1374
016
96- 1421
1469 1516 1563 161 1
1658 1706 1753 1801 1848
916
96- 1895
1943 199 2038 2085
2132 2i8 2227 2275 2322
917
96- 2369
24x7 2464 251 1 2559
2606 2653 2701 2748 2795
918
96- 2843
289 2937 2985 3032
3079 3126 3174 3221 3268
919
96- 33»6 3363 341 3457 3504
3552 3599 3646 3693 3741
020
96- 3788 3835 3882 3929 3977
4024 4071 4118 4165 4212
921
96- 426
43C7 4354 440i 4448
4495 4542 459 4^37 4684
922
9^ 4731
4778 4825 4872 4919
4966 5013 5061 5108 5155
923
96- 5202
5249 5296 5343 539
5437 5484 5531 5578 5625
924
96- 5672
5719 5766 5813 586
5907 5954 6001 6048 6095
925
96- 6142
6189 6236 6283 6329
6376 6423 647 6517 6564
926
96- 661 1
6658 6705 6752 6799
6845 6892 6939 6986 7033
927
96- 708
7127 7173 722 7267
7314 7361 7408 7454 7501
928
9^ 7548
7595 7642 7688 7735
7782 7829 7875 7922 7969
929
96- 8016
8062 8109 8156 8203
8249 8296 8343 839 8436
980
9^ 8483 853 8576 8623 867
8716 8763 881 8856 8903
931
96-895 '
8996 9043 909 9136
9183 9229 9276 9323 9369
932
933
933
96- 9416 9463 9509 9556 9602
06- t^Vi^ /w^ft tfv^«9r .^^ «i_
9649 9695 9742 9789 9835
97- —
— — 0021 0068
01 14 oi6x 0207 0254 03
934
97- 0347
0393 044 0486 0533
0579 0626 0672 0719 0765
08&
97- 0812
0858 0904 0951 0997
1044 109 1137 1183 1229
936
97- 1276
1322 1369 1415 1461
1508 1554 1601 1647 1693
937
97- 174
1786 1832 1879 1925
1971 2018 2064 2x1 2157
938
97-2203
2249 2295 2342 2388
2434 2481 2527 2573 2619
939
97- 2666
2712 2758 2804 2851
2897 2943 2989 3035 3082
940
97- 3128
3174 322 3266 3313
3359 3405 3451 3497 3543
941
97- 359
3636 3682 3728 3774
382 3866 39x3 3959 4005
942
97- 4051
4097 4143 4189 4235
428X 4327 4374 442 4466
943
97- 4512
4558 4604 465 4696
4742 4788 4834 488 4926
944
97- 4972
5018 5064 511 5156
5202 5248 5294 534 5386
945
97- 5432
5478 5524 557 5616
5662 5707 5753 5799 5845
946
97- 5891
5937 5983 6029 607s
6i2x 6167 6212 6258 6304
947
^"5^o
6396 6442 6488 6533
6579 6625 667X 67x7 6763
948
97- 6808
6854 69 6946 6992
7037 7083 7129 7x75 722
949
97- 7266
7312 7358 7403 7449
7495 7541 7586 7632 7678
950
97- 7724
7769 7815 7861 7906
7952 7998 8043 8089 8135
951
97- 8181
8226 8272 8317 8363
8409 8454 8s 8546 8591
952
97- 8637 8683 8728 8774 8819
8865 891 X 8956 9002 9047
953
97- 9093
9138 9184 923 9275
9321 93O6 9412 9457 9503
954
97- 9548
9594 9639 9685 973
9776 982X 9867 9912 9958
Ka
0
1234
56789
48
48
48
48
48
48
48
48
48
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
47
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
46
Ek»
330
LOGABITHKS OP NUMBBBS.
Ko.
956
957
958
959
•60
961
962
964
065
966
967
968
969
970
971
972
973
974
975
976
977
977
978
979
980
981
982
983
984
085
986
987
988
989
090
991
992
993
994
995
996
997
998
999
Na
8
98- 0003
98- 0458
98- 0912
98- 1366
98- 1819
98- 2271
98- 2723
98- 3175
98- 3626
98- 4077
98- 4527
98- 4977
98- 5426
98- 5875
98- 6324
98- 6772
98- 7219
98- 7666
98- 81 13
98- 8559
98- 9005
98- 945
98- 9895
99- —
99- 0339
99- 0783
99- 1226
99- 1669
99- 2111
99- 2554
99- 3995
99- 3436
99- 3877
99- 43>7
99- 4757
99- 5196
99- 5635
99- ^74
99- 6512
99- 6949
99- 7386
99- 7823
99- 8259
99- 8695
99- 9131
99-9565^
0049 0094
0503 0549
0957 1003
141 I 1456
1864 1909
2316 2362
2769 2814
322 3265
3671 3716
4122 4167
4572 4617
5022 5067
5471 5516
592 5965
6369 6413
6S17 6861
7264 7309
771 I 7756
8157 8202
8604 8648
9049 9094
9494 9539
9939 9983
0383 0428
0827 0871
127 1315
1713 1758
2156 22
2598 2642
3039 3083
348 3524
3921 3965
4361 4405
4801 4845
524 5384
5^79 5723
6117 ^i^i
6555 6599
6993 7037
743 7474
7867 791
8303 8347
8739 8782
9174 9218
9609 9632
014 0185
0594 064
1048 1093
1501 1547
1954 2
2407 2452
2859 2904
331 3356
3762 3807
4212 4257
4662 4707
5"2 5157
5561 5606
6oi 6055
6458 6503
6906 6951
7353 7398
78 7845
8247 8291
8693 8737
9138 9183
9583 9628
0028 0072
0472 0516
0916 096
1359 1403
1802 1846
2244 2288
2686 373
3127 3173
3568 3613
4009 4P53
4449 4493
4889 4933
5328 5372
S767 5811
6205 6249
6643 6687
708 7124
7517 7561
7954 7998
839 8434
8826 8869
9261 9305
9696 9739
0231 0276 0322
0685 073 0776
1x39 1 184 1229
1592 1637 1683
304s 309 3135
2497 2S43 2588
2949 2994 304
3401 3446 3491
3852 3897 3942
4302 4347 4392
4752 4797 4842
5202 5247 5292
5651 5696 5741
61 6144 6189
6548 6593 6637
6996 704 7085
7443 7488 7532
789 7934 7979
8336 8381 8425
8782 8826 8871
9227 9272 9316
9672 9717 9761
0367 0412
0821 0867
1275 132
1738 1773
2 18 1 2326
2633 3678
3085 313
3536 3581
3987 4032
4437 4482
4887 4932^
5337 5382
5786 583
6234 6279
6682 6727
713
7577
8024
847
89x6
9361
9806
7175
7622
8068
8514
896
9405
985
01 17 0161 0206 025
0561 0605 065 0694
1004 1049 ^093 1 137
144B 1492 1536 158
189 193s 1979 2023
2333 2377 2431 2465
2774 2819 2863 2907
3316 326 3304 3348
3657 3701 3745 3789
4097 4141 4185 4229
4537 4581 4625 4669
4977 5Q2I 5065 5108
5416 546 5504 5547
5854 5898 5942 5986
6293 6337 638 6424
6731 6774 68i8 6862
7168 7212 7255 7299
7605 7648 7692 7736
8041 8085 8129 8172
8477 8521 8564 8608
8913 8956 9 9043
9348 9392 9435 9479
9783 9826 987 9913
S 6 7 8
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
44
44
44
44
44
1625 ! 44
3067 , 44
3509; 44
2951 i 44
3392) 44
3833 44
4273 44
4713 I 44
5»S2 44
0294
0738
1 182
5591
44
^3 44
6468 44
6906 , 44
7343 - 44
7779 ' 44
8216 44
8652 ; 44
9087
9522
9957
1
44
44
43
HTPEBBOLIC LOOABITHUB OF NDMBEBS.
331
UyperT3olio Ijogjarith.iiis of !N'uxxil>ers.
From 1. 01 to 30.
In following table, the numbers- range from 1.01 to 30, advancing by .01,
op to the whole number 10 ; and thence by larger intervals up to 3a The
hvperbolic logarithms of numbers, or Neperian logarithms, as they are 8oine>
times termed, are computed by multiplying the common logarithms of num>
bers by the constant multiplier, 2.302 585. •
The hyperbolic logarithms of numbers intermediate between those which
are given in the table may be readily obtained by interpolating proportional
differences.
No.
1. 01
1.02
1.03
ix>4
1.05
ijdS
1.07
1.08
1.09
I.I
1. 11
1. 12
1. 14
1. 15
1.16
1. 17
i.iS
t.19
1.2
1. 21
1.22
123
1.24
1.25
1.26
1.27
1.28
1.29
1-3
I-3I
1.32
i»33
»«34
JOS
1.36
1-37
1.38
1-39
Log.
0099
0198
0296
0392
0488
0583
0677
077
0862
0953
1044
"33
1222
131
1398
1484
157
165s
174
1823
1906
1988
207
2151
2231
23H
239
2469
2546
2624
27
2776
2852
2927
3001
3075
3148
3221
3293
3365
No.
1. 41
1.42
1-43
1.44
1-45
1.46
147
1.48
M9
15
1.5^
1.52
153
1.54
1-55
1.56
1-57
1.58
1-59
1.6
1. 61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.71
X.72
1-73
1.74
1-75
1.76
1.77
1.78
1.79
1.8
Log,
•3436
•3507
.3577
.3646
.3716
.3784
•3853
•393
.3988
.4055
.4121
.4187
.4253
.4318
.4383
.4447
45"
•4574
•4637
•47
.4762
.4824
.4886
•4947
.5008
.5068
.5128
.5x88
.5247
•5306
•53(^5
•5423
.5481
•5539
•5596
•5653
•571
.5766
.5822
.5878
No.
.81
.82
.83
.84
■85
.86
.87
.88
89
•9
.91
.92
•93
■94
•95
.96
•97
.98
•99
2.01
2.02
2.03
2.04
2.05
2.06
2.07
2.08
2.09
2.x
2.II
2.12
2.13
2.14
2.X5
2.16
2.17
2.18
2 19
3.3
Log.
•5933
•5988
.6043
.6098
.6152
.6206
.6259
•6313
.6366
.6419
.6471
.6523
.6575
.6627
.6678
.6729
.678
.6831
.6881
.6931
.6981
.7031
.708
.7129
.7178
.7227
.7275
•7324
.7372
.7419
.7467
•7514
.-75^1
.7608
.7655
.7701
•7747
•7793
.7839
.7885
No.
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.3
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.4
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
3.49
2.5
2.51
2.53
2.53
2.54
2.S5
2.56
2.57
2.58
2.59
2.6
Log.
793
7975
802
806s
8109
8154
8198
8242
8286
8329
8372
8416
8458
8502
8544
8587
8629
8671
8713
8755
8796
8838
8879
892
8961
9C»2
9042
9083
9123
9163
9203
9243
9282
9322
9361
94
9439
9478
95*7
9555
No.
2.61
2.62
2.63
2.64
2.65
2.66
2.67
268
2.69
2.7
2.7X
2.72
2.73
I 2.74
' 2.75
2.76
i 2.77
2.78
2.79
2.8
2.81
2.82
2.83
2.84
2.8s
2.86
2.87
2.88
2.89
2.9
2.91
2.92
2.93
2.94
2.95
2.96
2.97
2.98
2.99
3
Log.
•9594
.9632
.967
.9708
.9746
•9783
.9821
.9858
.9895
•9933
.9969
1.0006
1.0043
1.008
1.0116
1.0152
1. 0188
1.0225
1.026
1.0296
1.0332
1.0367
1.0403
1.0438
1.0473
1.0508
1.0543
1.0578
1.0613
1.0647
1.0683
1.0716
1.075
1.0784
1.0818
1.0853
1.0886
1. 0919
10953
1.0986
332
HTPXBBOLIO L06ABITBMB OF jmUBEBS.
No.
1^. f
301
1.1019
3.02
1.1053
3.03
1. 1086
304
1.1119
305
1.1151
3'<^
1.1184
307
1.1217
308
1.1249
309
1.1282
3.1
1.1314
3."
1.1346
3-12
1.1378
3.13
1. 141
314
1.1442
3J5
1.1474
3.16
1. 1506
3-17
1.1537
3.18
1.1569
3.19
1. 16
3-2
1.1632
321
1.1663
3-22
1.1694
323
1.172s
3.24
1.1756
325
1.1787
3.26
1. 1817
327
1.1848
328
1.1878
329
1.1909
33
I-I939
3-3^
1.1969
332
1.1999
3-33
1.203
3-34
1.206
3.35
1.209
336
1.2119
3-37
1. 2149
3.38
1.2179
3.39
1.2208
3.4
1.2238
341
1.2267
3^
1.2296
3*43
1.2326
3^
1.235s
3-45
1.2384
3.46
1.2413
3-47
1.2442
3.48
1.247
3-49
1.2499
3.5
1.2528 !
No.
Log.
351
J.2556
352
1.2585
3-53
1.2613
3-54
1.2641
3-55
1.2669
356
1.2698
357
1.2726
3.58
1.2754
3-59
1.2782
3.6
1.2809
3.61
1.2837
3.62
1.2865
3-^3
1.2892
3.64
1.292
365
1.2947
3.66
1-2975
367
1.3002
3.68
1.3029
369
1.3056
3-7
1.3083
3.71
1.3"
372
1. 3137
3-73
1. 3164
3-74
1.3191
3-75
1.3218
376
1.3244
3-77
1.3271
3.78
1.3297
3-79
1.3324
3.8
1-335
3-8i
1.3376
382
1.3403
3.83
1.3429
384
1-3455
3-85
1. 3481
3.86
1.3507
3.87
1-3533
3.88
1.3558
3.89
1.3584
3-9
1.361
3.9X
1.3635
3.92
1.3661
393
1.3686
3-94
1.3712
3.95
1.3737
3.96
1.3762
3-97
1.3788
398
1.3813
3.99
1.3838
4
1.3863
No.
Log.
No.
Log.
4.01
1.3888
4.51
1.5063
4.02
1.3913
4.52
1-5085
403
1.3938
4-53
1-5107
4.04
1.3962
4.54
1.5129
4.05
1.3987
4.55
1.5151
4.06
1.4012
456
1.5173
4.07
1.4036
4-57
1.5195
4.08
1.4061
4.58
1.5217
4.09
1.4085
4-59
1.5239
4.1
1. 411
4.6
1.5261
4.11
1-4134
4.61
1.5282
4.12
1.4159
4.62
1.5304
4.13
1.4183
4.63
1.5326
4.14
1.4207
4.64
1-5347
4.15
1.4231
4.65
1-5369
4.16
1.4255
4.66
1.539
4.17
1.4279
4.67
1-5412
4.18
1-4303
4.68
1-5433
4.19
1.4327
4.69
1.5454
4.2
1.4351
4.7
1-5476
4.21
1.4375
4.71
1-5497
4.22
1.4398
4.72
15518
4.23
1.4422
4.73
1.5539
4.24
1.4446
4-74
1556
4.25
1.4409
4-75
1.5581
4.26
1.4493
4.76
1.5602
4.27
1.4516
4.77
15623
4.28
1-454
4.78
15644
4.29
1.4563
4.79
1.566s
4-3
1.4586
4.8
1.5686
4.31
1.4609
4.81
1.5707
4.32
1.4633
4.82
1.5728
4.33
1.4656
'4.83
1.5748
4-34
1.4679
,4.84
1.5769
4.35
1.4702
4.85
1-579
4.36
1-4725
4.86
1.581
4.37
1.4748
4.87
1.5831
4-38
1.477
4.88
1.5851
4.39
1-4793
4.89
1.5872
4.4
1.4816
4.9
1.5892
4-41
1.4839
4.91
1.5913
4.42
1./I861
4.92
1-5933
4.43
1-48H4
4.93
1-5953
4.44
1.4907
4.94
1-5974
4.45
1.4929
4.95
1-5994
4.46
14951
4.96
1.6014
4-47
1.4974
4.97
1.6034
4-48
1.4996
4.98
1.6054
14-49
1.5019
4-99
1.6074
I4.5
1.5041
5
1.6094
No.
5-01
502
5.03
5.04
5.05
5.06
507
5.08
509
5-1
5.11
5.12
5-13
5.14
5.15
5.16
5.17
5.18
519
5-2
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5-28
s-29
5-3
5-31
5-32
5-33
5-34
5.35
5.36
5.37
S.38
5-39
5.4
5.41
5-42
543
5-44
5-45
5.46
5.47
548
5.49
5.5
l^.
[.6114
1.6134
:.6iS4
r.6174
[.6194
[.6214
1-6233
^.6253
1.6273
[.6292
t.6312
.6332
c-635*
.6371
.639
[.6409
;.6429
.6448
1.6467
t.6487
[.6506
1.6525
[.6514
[.6563
[.6582
[.6601
[.663
t.6639
[.6658
[.6677
.6696
•6715
.6734
1.6752
i.6771
•679
[.6808
[.6827
.6845
[.6864
[.6889
[.6901
[.6919
[.6938
t.6956
f.6974
t.6993
.7011
.7029
■7047
HYt-dBBOLIC LOOABITHUS OF MtTUBBBS.
333
No.
5-51
5.5a
5-53
5-54
5-55
5.56
5-57
5.58
5*59
5.6
5.61
5.62
563
5.64
5.65
566
567
5.68
5.69
5-7
5.71
572
5-73
5-74
5-75
576
5-77
5.78
5-79
5^
S.81
583
583
5.84
5.85
5.86
5.87
5.88
S89
5.9
5.91
5.9B
5.93
5-94
5-95
5.96
5-97
598
5-99
6
Loj.
[.7066
[.7084
,7102
.712
[.7138
[.7156
.7174
•7193
.72X
[.7228
.7246
7263
[.7281
.7299
•7317
.7334
•7352
•737
.7387
.7405
.7422
.744
•7457
.7475
.7492
.7509
.7527
.7544
t.7561
•7579
f.7596
1.7613
^•763
1.7647
N7664
[.7681
17699
[.7716
•7733
•775
[.7766
f.7783
[.78
[.7817
^•7834
[.7851
1.7867
1.7884
.7901
[.7918
No.
6.01
6.02
6.03
6.04
6.05
6.06
6.07
6.08
6.09
6.1
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.2
6.21
6.22
6.23
6.24
6.25
6.26
'6.27
J6.28
i 6.29
16.3
'6.31
6.32
6.33
6.34
6.35
6.36
6.37
6.38
6.39
6.4
6.4X
6.42
6.43
6.44
, 6.45
6^46
6.47
6.48
6.49
6.5
P<«.
•7934
•7951
.7967
.7984
.8001
.8017
.8034
.805
.8066
.8083
.8099
.8116
.8132
.8148
.8165
.8181
•8197
.8213
.8229
.8245
.8262
.8278
8294
831
8326
8342
8358
8374
839
8405
8421
8437
8453
8469
8485
85
8516
8532
8547
8563
8579
8594
861
8625
8641
8656
8672
8687
8703
8718
No.
6.51
i^.
1.8733
6.52
1.8749
16.53
1.8764
!6.54
1.8779
,6.55
1.8795
1 6.56
1.881
i6.57
1.8825
6.58
1.884
6.59
1.8856
6.6
1.8871
6.61
1.8886
6.62
1.8901
6.63
1.8916
6.64
1. 8931
6.65
1.8946
6.66
1.8961
6.67
1.8976
6.68
1.8991
6.69
1.9006
6.7
1.9021
6.71
1.9036
6.72
1.9051
6.73
X.9066
6.74
1.9081
6.75
19095
6.76
1.91 1
6.77
i.9"5
6,78
1.914
6.79
1-9155
6.8
1.9169
6.8x
I. 9184
6.82
1.9199
6.83
1.9213
6.84
1.9228
6.85
I.9C42
6.86
1-9357
6.87
1.9272
6.88
1.9286
6.89
1.9301
6.9
1-9315
6.91
1-933
6.92
1-9344
6.93
1.9359
6.94
1-9373
6.95
19387
6.96
1.9402
6.97
1.9416
6.98
1-943
6.99
1.9445
7
1*9459
No.
7.01
7.02
7.03
7.04
7-05
7.06
7.07
7.08
7.09
7-1
7-11
7.12
7.13
7.14
7-15
7.16
7.17
7.18
7.19
7-3
7.21
7.22
733
7.24
7-35
7.26
7.37
7.28
7-39
7-3
7-31
7.33
7.33
7-34
7-35
7.36
7-37
7-38
7-39
7.4
7.41
7-43
7-43
7-44
7-45
7.46
7-47
7.48
7-49
Log.
•9473
.9488
.9502
.9516
•953
•9544
•9559
•9573
•9587
.9601
.9615
.9629
-9643
-9657
.9671
.9685
.9699
•9713
.9727
-9741
-9755
-9769
.9782
-9796
.981
.9824
.9838
.9851
•9865
.9879
.9892
.9906
.992
•9933
-9947
.9961
.9974
.9988
2.0001
2.0015
2.0028
2.0042
2.0055
2.0069
2.0082
2.0096
2.0109
2.0122
2.0136
2.0149
No.
7^51
7-52
753
7^54
7-55
7-56
7-57
7-58
7-59
7.6
7.61
7.62
7-63
7.64
7^65
7.66
7.67
7.68
7.69
7-7
7.71
7.72
773
774
7^75
Log.
2.0162
2.0176
2.0189
2.0202
2.0215
2.0229
2.0242
2.025s
2.0268
2.0281
2.0295
2.0308
2.0321
3.0334
2.0347
2.036
3.0373
2.0386
3.0399
2.0412
2.0425
2.0438
2.0451
2.0464
2.0477
7.76 i 2,049
7-77 1 3.0503
7.78 I 2.0516
7.79 I 2.0528
7.8
2.0541
7.81 , 2.0554
7.82 I 2.0567
7.83 I 2.058
7.84 I 2.0592
7.85 • 2.060s
7.86
7.87
7.88
7-89
7.9
7.91
7.92
7-93
7-94
7-95
7-96
7.97
7.98
799
8
2.0618
2.0631
2.0643
2.0656
2.0669
d.o68i
2^0694
2.0707
2.0719
2.0732
2.0744
3.0757
2.0769
2.0782
2.079^
334
UYPBBBOLIC LOGABITUMB OF NUMBKBS.
No.
8.0I
8.02
8.03
8.04
8.05
8.06
8.07
8.08
8.09
8.1
8.11
8.13
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.3
Lof.
a.0807
3.0819
3.0830
3.0844
3.0857
3.0869
3.0882
3.0894
3.0906
3.0919
3.0931
20943,
3.0956 I
3.0968
3.098
3.0992
3.1005
3.IOI7
3.1099
3.1041
N*.
I^
8.31 13 1054
8.33 I 3.1066
8.33 3 1078
8.34 I 3.109
8.35 3 1102
8.36
8.37
8.38
8.39
83
8.31
8.33
8.33
834
83s
8.36
8.37
8.38
8.39
8.4
10.35
10.5
10.75
IX
11.35
1 1.5
".75
3.III4
a 1136
3.1138
3.1 15
3.1 163
3.1 175
3,1187
3.1199
3.I3II
3.1333
3.1335
3.1347
a. 1358
3.137
3.1383
3.3379
^•3Si3
3-3749
2.3979
3.4201
3»443
3.4636
34849
8.41
8.43
8.43
8-H
845
8.46
8.47
8.48
8.49
8.5
8.51
8.52
8.53
8.54
8.5s
8.56
8.57
8.58
8.59
8.6
8.61
863
8.63
8.64
8.65
8,66
8,67
8.68
8.69
8.7
8.7X
8,73
8.73
8.74
8.75
8.76
8.77
8.78
8.79
8.8
13.35
ia.5
13-75
13
13-2S
13.S
13-75
14
No,
3.1394
3-1306
3.1318
3.133
3.1343
3.1353
3.1365
3.1377
S.I389
3.1401
3.1413
3.1494
2.1436
2,1448
2.1459
3.1471 1
2.1483',
3.1494
3.1506
3.1518
3.1539
3.1541
3.1552
3.i56d
3.1570,
3.1587 !
3.1599
3.I6I
3.1622
3.1633
3.1645
3,1656
9.1668
3.1679
3.1691
3.1703
3.I7I3
3.1735
3.1736
3.1748
a.5053
3.5363
3.5455
3.5649
2.584
3.6027
3.6311
3.6391
8.81
8.83
8.83
8.84
8,85
8.86
8.87
8.88
8.89
8.9
8.91
8.93
8.93
8.94
8.95
8.96
8.97
8.98
8.99
9
9«oi
9.03
9-03
9.04
9.05
9.06
9.07
9.08
9.09
9.1
9.1 X
9,13
9.13
9.14
9.15
9.16
9.17
9.18
9.19
9.3
14.35
14.5
14.75
15
15-5
x6
16.5
ii7
3.1759
3.177
3.1783
3.1793
3.1804
3.1815
3.1837
3,1838
3,1849
3.1861
3.1873
3.1883
3.1894
3,1905
2.1917
3.1938
3.1939
2.195
3.1961
3.1973
3.1983
3.1994
3.3006
3.3017
3.9038
3.ao39
3.305
3.9061
3.3073
3.3083
a.3094
3.3105
3.31X6
3.3137
3.3138
3.3148
3.3159
3.317
3.3181
3.3X93
3.6567
3.674
3.6913
3.7081
3.7408
3.7736
2.8034
3,8333
N*.
9.31
9.33
9-33
9.34
9-35
9.36
9.37
9.38
9-39
9-3
9-31
932
9-33
9-34
9-35
936
9-37.
9.38
9.39
9.4
9.41
9.43
9-43
9.44
9-45
9.46
9-47
948
949
9.5
951
9-53
953
9 54
9-55
9-S6
9-57
9-58
9-59
9.6
17-5
x8
18.5
19
19-5
90
31
33
UK-
3.3303
3.33X4
3.3335
3.3335
3.3346
2.3357
3.3368
3.3379
2.3389
2.33
3.3311
3.3333
3.3333
2.3343
2.3354
3.3364
2.3375
23386
a.3396
2.3407
2.3418
3.3428
33439
2345
3346
3.3471
3.3481
33493
3.3503
2.2513
3.3523
3.3534
3.3544
3.3555
3,3565
3.3576
3.3586
3.3597
3,3607
3.3618
3.8621
3^8904
3.9173
2.9444
3.9703
9.9957
30445
3.0911
No.
9.61
9.63
963
9-64
9-65
9.66
9.67
9.68
9.69
9.7
9.71
9.73
9 73
974
9 75
L-t.
3.3638
2.3638
2.3649
3.3659
3.367
3,368
3.369
3.3701
3.3711
3.3731
3.3733
2.3742
3.3752
2 3762
23773
9.76 3.3783
9.77 33793
978 33803
9 79 3.3814
9 8 3.3824
9.81
9.83
983
984
98s
9.86
9.87
9.88
9.89
9.9
9.91
9-99
993
994
995
9.96
9-97
9-98
9.99
10
33
34
35
26
27
38
39
30
3.3834
3.3844
33854
3.3865
3.3875
3.2885
3.2895
3.2903
3.2915
3.2935
3-3935
3.394c
3.395^
3.396<
3.397<
fl.398C
9.399^
9.3006
9.3016
3.3036
3.1355
3.1781
3.3189
3.3581
3-3958
3.3333
3.3673
3.401a
10BN8UBATION OF ABSAS, LINXS, AND SURFACES. 33$
MENSURATION OF AREAS. LINES, AND SURFACED
iParalleloerams*
DiF(inTf05.^QuadrtlatemIs, having (hdir opposite sides parallel.
To Coznpvite A^rea of a. Sq.uare, Xteotangle, R.h.om'bus, or
H.h.oiu'boid.'F'igs. 1, 8, 3, and •^.
RuLB. — Multiply length by breadth or height
Or, < X b = aretif I reprtKnting lengthy and b breadth.
Fig. I.
Fig. 3-
£f
»
! 1
L_J
Fig. 2.
Fig. 4.
117
EzAMPLt.— Sides a &, Cf c, Fig. i, are 5 feet 6 ins. ; what is area?
5. 5 X 5- 5 = 30- 25 square feet.
NoTB I. — Opposite angles of a Rhombus and a Rhomboid are equal,
a. — In any parallelogram the (bar angles equal 360*^.
3.~3kle of B square multiplied by 1.52 Is equal to side of an equilateral triangle
of equal area.
Grixoxnoxi.
DsFiinTiov. «• Space included between the lines forming two similar parallel-
ograms, of which smaller is inscribed within larger, so that one angle in each is
common to both, as shown by dotted Hues, Fig. z.
1*0 Compute .A.rea o^* a GI-noitton.**P^ig. 1.
RuT.K.'^ABCertain areas of the two paraUelograms, and subtract less from
greater.
Or, a—a' = area, a and o' representing areax
ExAMPLB.— Sides of a gnomon are io by 10 and 6 by 6 ins. ; what is its area?
10 X 10 = ic», and 6 x 6 = 36. Then 100 — 36 = 64 square ins.
1?riaiigles.
DsFUfinoK. — Plain superficies having three sides and angles.
To Conxpute Area of a 7riax^gle.•— Fiss. 6^ G, and 7«
Rule. — Multiply base by height, and divide product by a.
Or, ?^^1^. Or, 5i = area, b represenHng base, and h height.
2 2
Vfifrm I. — Hypotenuse of a right angle is side opposite to right angla
a.'^Perpendicular height of a triangle ^ twice ito area divided by its basoi
3.— Perpendicular height of an equilateral triangle = a side x -866.
4. — Side of an equilateral triangle x .658255 = side of a square of equal area,
Or -;- 1.3468 = diameter of a circle of equal area.
Fig. 5- Fig. 6. Fig. 7.
CO c
CxAMrLB. — Base a b, Fig.
5. is 4 feet, and height c 6, 6;
what is area ?
4 X 6 =: 24, and 24-^9 =»
square feet
33^ MENSUBATION OF ABEAS, LIKES, AND gTTBFACBS.
To Compute Area of a Triangle by Tuength. of* its Sidee.**
ITies. 6 and 7.
Rule. — From half sum of the three sides subtract each side separately;
then multiply half sum and the three remainders continually togc^er, and
take square root of product.
Or, y/{t — a) X (s—b) X (»— c) S = area, a, 6, c representing sidety and S half sum
of the three sides.
Example.— Sides of a triangle, Figs. 6 and 7, are 30, 40, and 50 feet; what is area?
■30 -♦- 40 -I- so 120 60— 30 = 30 J
^ ~ — — =60, or half sum of sides. 60 — 40 = ao J remainien.
^ ^ 60 — 50=10)
Whence, 30 x 20 X xo x 60 = 360000, and y/ 360 000= 600 sqtuirefeeL
When all Sides are Equal. Rule. — Square length of a side, and multi-
ply product by .433.
Or, S^ X .433 = areOy S representing length qfa side.
To Compute X^eugtli of One Side of* a R.igb.t-A.neled
THangle.
When Length of the other Two Sides are given.
To Ascertain Hjrpotenuse. ^ Fis. G.
Rule. — Add together squares of the two legs, and take square root of
sum.
Or, Va 6« -|- 6 c* = hypotenuse. Or, vW-fh^.
Example.— Base, a b, Fig. 5, is 30 in&, and height, & c, 40; what is length of hy-
potenuse?
30' -f 40' = 3500, and -^2500 = 50 ins.
To ^Lsoertain -otlier ILiefi:.
When Htfpotenuse and One of the Juega are piw».— Fig. 5. Rule.— Sub-
tract square of given leg from square of hypotenuse, and take square root
of remainder.
or.yi^Hl^sS; or.7:;3{«fri
= 6c
b.
Example.— Base of a triangle, a &, Fig. 5, is 30 feet, and hypotenuse, a c, 50;
what is height of it?
50' — 30* = 1600, and •v/1600 = ^ofeet
To Compute IL<ength. of a Side.
When Hypotenuse of a Right-angled Triangle of Equal Sides alone is
given.— ¥\g. 8. Rule.— -Divide hypotenuse by 1,414 313-
Or, ^'^^' = length of a side.
1.414213
Fig. 8. o ^ ^ ^
ExAVPLK. — Hypotenaae a e of a right-angled triangle, Fig. 8, Is
300 feet ; what is length of its sides ?
300 -T- 1. 414 213 = 312. 1321 fiet,
b
To Compute Perpendioixlar or Height of* a Triangle.
When Base and Area alone are given. — Fig. 9. Rule. — Divide twice
area by its base. Or, 20^ 6 = fc.
Example.— Area of a triangle. Fig. 9, is 10 feet, and length of its base, a 6, .5;
what is its perpendicular, c di
10 X a := 20, and ao-S- 5 = 4 feet.
MENSUBATION OF AREAS, ONES, AND SURFACES. 33^
To Compute Ferpendioular or £Lelgh.t of* s Triangle.
When Bcue and Two Sides are given. Rule. — As base is to sum of the
sides, so is difference of sides to difference of divisions of base. Half this
difference being added to or subtracted from half base will give the two di-
visions thereof. Hence, as the sides and their opposite division of base con-
stitute a right-angled triangle, the perpendicular thereof is readily ascertained
by preceding rules.
Or, — - — r^ = bd^da.
' ba
ac^A-ab^ — bd' . /
Or, r sad; whence vac^— ad^sKde.
aab
Fig. 9. ExAMPLB.— Three sides of a triangle, a 6 e, Fig. 9, are 9.928,
c 8, and 5 feet; what is length of perpendicular on longest side ?
As 9.928 : 8 + 5 :: 8 fv 5 : 3.928 = difference of divuunu of
tKtbOM.
Then 3.928 -7- 3 = x.964, which, added to ^^' = 4.964 ■\-
2
1.964 = 6 928 = length of longest division ofbaie.
ad b
Hence, there is a right-angled triangle with its base 6.928, and its hypotenuse 8;
consequently, Its remaining side or perpendicular is -^(8^ — 6.928') = 4 feet.
When any Two of the Dimensions of a Triangle and One of the corresponding
Dimensions of a simiUu' Figure are given^ and it is required to ascertain
the other carreiponding Dimensions of the last Figure,
Fig. xa Fig. 11.
Let a & c, a' b' c\ he two similar triangles, Figs, zo
and II.
Then ab'.bcv. a'b' : 6'c', or a'6' : 6'c' ::ab:be.
KoTB. —Same proportion holds with respect to the
similar lineal parts of any other similar Qgures, whether
plana or solid.
ExAMPUL—Shadow of a vertical stake 4 feet in length was 5 feet; at same time^
shadow of a tree, both on level ground, was 83 feet; what was height of tree?
5 a' 6* : 4 6' c' :: 83 o 6 : ^.^feet
To Compiate i^oreace*
Divide area into convenient triangles, and multiply base of each triangle
in links by half perpendicular in links ; cut off^5 figiires at the riglU^ remam-
ing figures will give acres ; multiply the 5 figures so cut off" by 4, and again
cut off 5, and remainder will give roods ; multiply the 5 by 40, and again
cut off 5 for perches.
Trapezium.
Dnminioir.— A Quadrilateral havIng^ unequal sides of which no two are paraUeL
To Compute Ajveek of a Trapezium. i— Fig. IS.
Rule. — Multiply diagonal by sum of the two perpendiculars falling upon
it from the opposite angles, and divide product by 2.
_ dbxa-\-e
Or, =.area.
Pig. 19, a *
y^ ! ^^^^»v^, ExAMPLB.— Diagonal d 6, Fig. 12, Is 125 feet, and perpen-
il^»__j .^ — .^j dlculars a and c 50 and 37 ; what is area?
^v^l/^ «a5 X 50 -|- 37 = 10875, and 10 875 -r 2 = 5437. 5 square feet.
e
Ff
Jjg MBNSUBATION OF ABEAS, LINKS, AND SURFACES.
When the Turn omotiU AngUs are SupplementM to etich other^ thai t«, tchen
a TvaptZMon can he inaci-ibed in a Circle^ the Sum o/* its oppotite Anylea
being equal to Two Right Anglei^ or i8o°. Bule. — From hau* sum of the
four sides, subtract each side severally ; then multiply the four reuiaiudcrs
continually together, and take square root of product
ExAXPiji.-^In a trapeiium the sides are 15, 13, 14, and 13 feet; its oppueito an-
gles being sapplements to each otber, required its area.
15 + X3 + 14 + " = 54i M»d 51 =s 87.
37 37 37 37 * ^
15 13 M ££
IS X 14 X 13 X 15 = 3a 760, and -/sa 760= 180.997 iquare/ket
Trapezoid.
DKFiinTiON. — A Quadrilateral with only one pair of opposite sides parallel.
To Compute Area of* a Trapezoid. «»l4^igr. 13.
RuLK. — Multiply sum of the parallel sides by per|)endicular distance be-
tween them, and divide product by 3.
Or, . Or, = area, s and «* representing sides.
***?• '3- a e b ExAMPLB. —Parallel sides a b, c d. Fig. 13, are xoo and 13a
feet, and distance between them 62.5 feet; whjit is area?
100 -f 132 X 62. 5 = 14 500, and 14 5CX3 -»- 2 = 7250 sqwitt
c-% d f"^
^Polygons.
DsviNiTioif.— Plane figures having three or more sides, and are either regular or
irregular, according as their sides or angles are equal or unequal, and they are named
trom the number of their sides and angles.
Regular Polygons.
Xo Comptate A.rea of a Regular Polygon. ^Fig. 1-^.
Rule.— Multiply length of a side by perpendicular distance to centre;
multiply product by number of sides, and divide it by a.
0 6 X c ^ X w
= area^ n representing nwnher of sides.
2
' '^ >^ ExAiiPi.K.^Wtaat is area of a pentagon, side a 6, Fig. 14, being
5 feet, and distance c e 4. 25 feet t
5 X 4-25 X 5 (n) = 106.25 = product of length of a side^ dis-
tance to centre, and number of sides.
Then, 106.25 -J- 2 = 53.125 square feet.
To Oompxite rtadi-us of a Circle that contains a GUveix
1*01 ygon.
When Ijength of a Perpendicular yrom Centre aioiie ia given, Rulb.—
Multiply distance from centre to a side of the poly^^on, by unit in column A
of following Table.
ExAMpLK— What is rattius of a circle that eontattis a hexagon, diatance to centre
being 4.33 inches?
4-33 X 1.156 = 5 tn«.
To Compute XjengtU ot a Side of a I^olygon th.at is oon-
tained in a d-iven Circle.
When Radius of Circle is given. Rule. — Multiply radius of circle, by
imit in column B of following Table.
Example.— What is length of side of a pentagon contained in a circle 8.5 fiset in
diameter?
8.5 -r- 2 = 4.25 radiqs, and 4.25 x 1. 1756 = 5 /«?*•
MENSUEATION OF ABEAS, LINES, AND SURFACES. 339
To Ooxnpute Radl-ttv of a CiTOVLram^vitiiJis Oirole.
When length qf a Side is given. Rule.— Multiply length of a side of the
polygon, by nnit in column C of following T»ble.
ExAMPLB-^What is radius of a circle that will contain a hexagon, a aide being 5
inches?
To Compvite Radius -oT a Circle that can. be Inacribed
in a GUven. Folygon.
When Length of a Si^ is given. Rule.— Multiply length of a side of
polygon, by unit in column D of following Table.
Example.— What is radius of the circle that is bounded by a hexagon, it^ Sides
being 5 Inches?
|X.866=4-33"'*'
To Compute A.rea of a Regular Polygon^
Wlten Letigth of a Side only is given. Rulk.— Multiply square of side,
by multiplier opposite to term of p )lygoii in following Table:
B.
No. of
Sid«.
POIVOON.
3
Trigon
4
Tetrageo
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
to
Decagon
II
Undecagon
12
Dodecagon
Arba.
•43301
I
1.72048
2.59808
3-6339"
4828^3
6. 1 81 82
7.69421
9-36564
II. 196 15
A.
RHdiw of
Circaaiscri()e4
Circle.
2
1.414
1.338
1. 156
I.XI
1.083
X.064
1.051
1.042
1037
Length of a
I 732
1. 4142
1.1756
I
8677
7653
684
618
5634
5176
C.
RiMHmof
Circumacrib-
ing Circle.
5773
.7071
.8506
X
r.1524
1.3066
1. 4619
1.618
1-7747
1.9319
Radlw of
(OBGribed
Circle.
.2887
.5
.6889
.866
1.0383
x.ao7x
1-5^8
I 7028
1.866
Example. — What is area of a square (tetragon) when length of its sides is
70710678 inches?
7.071 067 82 = 50, and 50 X 1 = 50 square, ins.
To Compute Uength. of* a Side and Radii of a Regular
I^olygon.
When Area ahne is given. Rule. — Multiply square root of area of poly-
gon by multiplier in column E of the following table for length of side ; by
multiplier in column G for radius of circumscribing circle, and by muHiplier
in column H for radius of inscribed circle or perpendicular.
TBagent.
•5774
X
1-3764
i.7aai
?.Q76s
2.4142
2-7475
30777
3-4057
3-7321
Example L-«Area of a square (tetragon) is 16 inches; what is length of its side?
V16 ^ 4, and 4X1—4 ins,
2.— Area of an octagon is 70.698 yards; what is diameter of its circumscribing
circle?
•v/7a698 X • 5946 = 5, and 5 X 2 = 10 yards.
E.
0.
H.
No. of
SMm.
POLYOON.
Lengtli of
Radios of
Circunuorlb-
Radius of
Inscribed
Angl«.
Angle of
Polygon.
tng Circle.
Circle.
3
Trigon
1.5197
.8774
.4387
120^
60O
4
Tetragon
1
.7071
•5
90
90
5
Pentagon
.7624
.6485
.5247
72
108
6
Hexagon
#61204
.5246
•6^04
•5373
'5440
60
*^
7
Heptagon
•604s
5* 95-7^'
198 34*99'
8
Octagon
•4551
•5946
•5493
45
»35
9
Nonagon
.4092
.588
.5525
•5548
^5
140
10
Decagon
J605
•5833
36
^^ . .
II
Undecagon
.3268
■5799
•5564
32 43-64'
147 16.36'
12
Dodecagon
.2989
•5774
-5577
30
ISO
340 MJEKSUBATION OP ABSAS^ LIlfES^ AND SUBFAGE8.
AddeUanal Utu iffvregmn§ TViUe.— 6th and vth 'colamns of Uble facHitaM con-
Btruction of these figures with aid of a sector. Thus, if it is required to describe an
octagon, opposite to it in column 6th, is 45; then, with chord of 60 on sector as
radius, describe a circle, taking length 45 on same line of sector; mark this dis-
tance off on the circumference, which, being repeated around the circle, will give
points of the sides.
7th column gives angle which any two adjoining sides of the respective figures
^ake with each other; and 8th gives tangent of .5 angle in column 7th.
To Compute H>adius of Iiisoriloed. or Ciroumsoritoed.
Circles.
When Radius of (Srcunucribing Circle is given. Rule.— Multiply radius
given by unit in column E, in following Table, opposite to term of polygon
for which radius is required.
When Radius of Inscribed CircU is given.^ Rulb.— Multiply radius given
by unit in column F, in following Table, opposite to term of pqlygon for
which radius is required.
To Coxupute A.r&&>»
When Radii of Inscribed or Circumscribir^ Circles are given. Rule.—
Square radius given, and multiply it by unit in columns G or H, in following
Table, and opposite to term of polygon for which area is required.
When Length of a Side is given. Rule. — Square length o£ side and
multiply it by unit in column I, in following Table, opposite to term of
polygon for which area is required.
To Compute Uengtfa. of a Side.
When Radius of Inscribed Circle is given. Rule.— Multiply radius given
by nmt in colunm K, in following Table, and opposite to term of polygon for
which length is required.
No. of
SidM.
3
4
5
6
5
9
zo
II
12
POLYOOIf.
Trigon
Tetragon
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Undecngon
Dodecagon
E.
lUdiatof
Inscribed
by Cireain-
■ori^ing
Circle.
F.
Radios of
ClrcuniKrlb-
log by
InKiiblng
Circle.
G.
Area.
ByRadiiu
of Inscribed
Circle.
•5
2
.707 11
.80902
.8660a
1.41421
1.23607
'•1547
•90097
.92388
.93969
.95106
r.zo992
X. 082 39
1.064 10
1.051 46
•95949
•96593
X. 042 22
1.035 3^
5- "96 15
3.63272
3- 464'
3.37102
3-3«37«
3-275 73
3.2492
3-88989
3.21539
H.
L
Area.
Bt Radius
ofCircum-
Area.
By Tjenetb
scribhig
of Side.
Circle.
1.29904
.43301
2
1
2.37764
2.59808
1.72048
2.59808
2.73641
3- 6339"
0.82842
4.81845
2.89254
6.18282
2-93893
7.69421
2-973 53
9.36564
3
1X.19615
K.
Length of
Side.
By Radioa
of Inscribed
Circle.
3- 464*
2
1-45308
^-1547
?63i5
2843
.72704
.64984
•58725
•535 9
Regular Bodies.
To Compute Surfaoe or Uinear XQdge of Regular Sodjr.
Rule. — Multiply square of linear edge, or radius of circumscribed or in-
scribed sphere, by units in following table, under head of dimension used :
Radios of
Circa mscribed
Sphere.
No. of
Sides.
t
8
12
20
Boot.
Tetrahedron
Hexahedron
Octahedron
Dodecahedron
Icosahedron
Sarfiwe by
Linear Edg*.
i.732«S 1.63299 4.89898 .75984
6 Z-I54 7 2 .40825
3.4641 1.41421 2.44949 .53720
20.64578 .71364 .89806 .22008
8.66025 1.05146 1.32317 -33981
EzAMrLi.— What is surface of a hexahedron or cube, having sides of $ inchest
5' X 6 = 25 X 6 = 150 square ins.
Radial of
Inscribed
Sphere.
Linear Edf^e
by Sarf^oa.
HBNfiUHATIO^ OF ABBAS^ LINES, AKD StJBFACES. 3^1
rTo Ooznptite I^ixieaar I3dge.
When Surface ahne ii given. Rule. — Multiply square root of surface^
by multiplier opposite to term of body under head of Linear Edge by Sur-
face in preceding Table.
ExiMFLB.— What n linear edge of a hexahedron, surfkce being 6 inches?
y/6 X 40825 = X iruik.
When Radius of an Inscribed or Circumscribed Sphere is given. Rule. —
Multiply radios given, by multiplier opposite to term of body in preceding
Table, under head of the Radius given.
Example.— Radius of circumscribing sphere of a hexahedron is zo inches; what
is its linear edge?
10 X ^•i547 = "'547 **»*•
To Compute Surfbtoe.
When Linear Edge is given. Rule. — Multiply square of edge, by multi-r
plier opposite to term of body in prec^ng Table, under head of Surface.
Example. —Linear edge of a hexahedron is x inchj what is its surface?
x' X 6 = 6 square ins.
Irregttlctr Polygona,
Definition <— Figures with unequal sides. •
To Compute Afreet of* axi Irregular Polygon.— Fig>s. Ifi
axid le.
Rule. — Draw diagonals and per-
pendiculars, as df^ dg, a, and'c, Fig.
J i5,and/<f,^d,^<ft,^tt,andt,o,r,ftBd
5, Fig. 16^ to divide the figures into
triangles and quadrilater^s : ascer«
Q tain areas of these separately, and
take their sum.
NoTS. — ^To ascertain area of mixed or compound figures, or
such as are composed of rectilineal and cuivllloeal figures to-
gether, compute areas of the several figures of which the whole is composed, then
add them together, and the sum will give area of compound figure. In this manner
any irregular sur&ce or field of iand may be measured by dividing it into trapeziums
and triangles, and computing area of each separately.
When any Part qfa Figure is hounded hu a.Cui've the Area may he ascer-
tained aafoUows:
■ ■ ' • ■ ...
Erect any number of perpendiculars upon base, at equal distances, and
ascertain thieir lengths.
Add lengths of the perpendiculaFa thus ascertained together, and their
sum, divided by their number, will give mean breadth ; then multiply mean
breadth by length of ba^e*
To Compute A:rea of* ct Ijo3]ig» Ikvegular ITigure.^^E^ig. 17.
Fig. x7 Rule. — Take mean breadths at several places, at equal
distances apart, as i, 2, 3, b d, etc. ; add them together,
b divide their sum bv number of breadths for total mean
bretidth, and multiply quotient by lengtli of figure.
Or.
j-|-6'4.b'',etc.
X I = are€L
F k-
342 MSNSUBATION OF ABSU^S, LINES, AND SUBFACBS^
To Cozupute an A.re^ 'boundad "by a Curve. — Fig. 18,
{8impson^8 Rule.)
-X'^i '^ Opkration.— Divide line a b into any number of equai parU,
>^'ii}*S^ l>y perpendiculars from base, as i, 2, j, etc., whicn will give
X' ! ! ! i\ an ocW number of points of division. Measure lengths of
u~i 8 8 A s 6 these perpendicuiars or ordinates, and proceed as follows:
To sum of lengths of first and last ordinates, add four times sum of lengths of all
even numbered ordinates and twice sum of odd; multiply their sum by one ttiird
of distance between ordinates^ and product will give area required.
Illustration.— Water-line of a vessel has a length of 80 feet, and ordinates o, i.
1.2, 1.5, 2, t.9, 1.5, I.I, and o, each 10 feet apart; what is its area?
Ordinates.
Cveti. Odd. ButM.
I 1.2 first o
Z.5 a last o
1.9 1.5 even 22
I.I odd 9.4
^X4 = a2. 4.7X2 = 9.4 31. 4 X 10 =314, which 4-3 = 104. 66 «5uare/e«t
Circle.
Diameter Is a right line drawn through its centre, bounded by its periphery.
Radius is a right line drawn from its centre to Its clrenmference.
Circum/erence is assumed to be divided into 360 equal parts, termed d^rees;
each degree is divided into 60 parts, termed mintUes; each minute into 60 parts,
termed seconds ; and each second into 60 piuts, termed thirds^ and so on.
To Compute Circuxiafbrenoe o€ a Circle.
Rule. — Multiply diameter by 3.1416.
Or, as 7 is to 22, so Is diarodter to clrcumfertnce. »
Or, as 113 is to 355, so Is diameter to circumference.
EzAMTLB. — Diameter of a circle is 1.25 inches; what is its circumference?
1.25 X 3.1416 = 3.927 ins.
To Compute Diaixieter of a Circle.
RuLK. — Divide circumference by 3.1416.
Or, as 22 Is to 7, so is circumference to diameter.
NoTB. —Divide area by . 7854, and square r6ot of quotient will give diameter of circlo,
To CoTnpute A.rea of a Circle.
Rule. — Multiply square of diameter by .7854.
Or, multiply square of clrcumfbrenoe by .07958.
Or, multiply half ciroaroferenoe by half diameter.
Or, multiply square of radius by 3. 1416.
Or, pr^=. area^ r refnsenUng rodttM.
Example.— The diameter of a circle is 8 inches; what Is the area of it?
8*= 64, and 64 X . 7854 = 50. 2656 ins.
Proportions of* a Circle, its Kq.ual, Inscribed., and. Oir*
ouxnaoril>ed S^L'u.ares.
CIRCLB.
1. Diameter X 8f6« I = side of an fiqual Square.
2. Circumference x .2821 j ^ dh"»"»-
3. Diameter X .7071}
4. Circumference X .2251 [ = Side of Inscribed Square.
5. Area x .9003 -r- diam. )
6. Diameter X 1.3468 as Side of as Equilateral Triaoglek
SQUARE.
7. A Side X !• 41 42 3= Diameter of its Circumscribinf Circle.
8. " X 4.443 = Circumference of its CircumscribiQgClrcte.
9. •* X1.128 = Diameter }
10. " X 3-545 = Circumference} of an EquitlCiitle.
11. Square inches X 1.273 :& Circle inohss )
Note.— Square described wHl)iR a pifcle is one half area of one described without ii.
MBNSUBATION OF ABKAS, LINBS, AND SCBFACBS. 343
To Coznpnte Side of Q-reateat Square tba^t oan. be In-
scribed in a Circle,
Rule. — ^Multiply diameter by .7071, or take twice square of radius.
TTsefu.! JHaotors.
In wliioli p or IT represent* Oircuxnf^rence of a Circle.
Diameter := z.
pz=i 3- MX 59« 653 589+
ap= 6.283185307179+
4 p = la. 566 370 6f 4 359-f
>ip= 1.570796326794+
XP= .785398163397+
Jp»4.t8879+
^p= .5*3598+
HP=- .3^699+
.^p=' .461 799+
ThP= 008726+
Diameter = 10.
y/P^
2
VP
*• 77a 453
.797884
Log.,J>= .497 '4987
)^y/P= .886226+
36^=113.097335+
X.
3.
3-
4-
5-
6.
7-
&
9-
10.
II.
12.
X3-
Chord of arc of semicircle = xo
Cbord of half arc of semicircle =: 7.071067
Versed sine of arc of semicircle. = 5
Versedsineof half arc of semicircle = 1.46446^
Chord of half arc, of half of arc of semicircle = 3. 826 83
Half chord, of chord of half arc = 3, 535 533
Length of arc of semicircle = 1 5. 707 963
Length of half arc of semicircle s=s. 7. 853 981
Square of chord, of half arc of semicircle (2) = 50
Square root of versed sine of half arc (4) = 1.210151
Square of versed sine of half arc (4) = 2. 144 664
Square of chord of half arc, of half arc of semicircle (5) = 14.64467
Square of half chord, of chord of half arc (6) = 12. 5
NoTK—In all eompntationsp is taken at; 3.14x6, )^ ptit .7854, ^p at .5336; and
whenever the decimal figure next to the one last taken exceeds 5, one is added.
Thus, 3. 141 59 for four places of decimals is taken as 3.1416.
7o Oonxpute Xjengtb of an A.ro.of a Circle. ^^S^ijy. 19.
\^en Ntanber of Degrees and Radius are mven. Rvlb 1. — Multiply
number of degrees in the arc by 3.1416 times tne radius, and divide by 180.
3. — Multiply radius of circle by .01745329, and product by degrees in
the arc.
If length is required for minuted, multiply radius by .000290889; if for
seconds, by xxx> 004 848.
EzAMPLR I. — Number of degrees in an arc, 006, Fig. 19, are
90, and radius, o 6, 5 inches; what is length of arc?
90 X (3- 1416 X 5) = 1413.72, which -f- 180 = 7.854 iru.
3.^Radius of an arc is xo, and measure of its angle 44^ 3<y
30"; what is length of arc?
JO X .0x7 453 ^ == • »74 53* Of which X 44 = 7-679 447 6, length
for 440.
10 X -000390 889 = .002 908 80, which X 30 =: .087 866 7, Ungik/pr y>'.
xoX 000 004 848 = .000 048 48, which X 3o = .oox4544^fonflr<A/or 30".
61
• 7^ =7.768x687 ins.
4)
Or, reduce minutes and seooods to decimal of a degree, and multiply by it
See Rule, page 93. 30^ 30" = .5083, and .1745329 from above x 44-5083
7.768x63 int.
Then 7.6794476]
.087266;
.001454,
344 MENSUBATIO];^ OF ABEAS, LINES, AND SUBFAGBS.
When Choird of Half Arc and Chord of A re are given. Rule. — From eight
times chord of half arc subtract chord of arc, and one third of remainder will
give length nearly.
g g» f>
Or, , cf rqnresenHng chord o/ha^arc^ and c chord of arc
3
ExAHpLB.— Chord of hajf arc, a c, Fig. 19, is 30 inches, and chord of arc, a 5, 48;
what is length of arc?
30 X 8 = 240=8 times chord ofhaifare; 340—48 = 192, and 192-5-3=64 ifu.
When Chord of Arc and Versed Sine of Arc are given. Rule. — Muk
tiply square root of sum of square of chord, and four times square of the
versed sine (equal to twice chord of half arc), by ten times square of yersed
sine ; divide this product by sum of fifteen times square of chord and thirty-
three times square of versed sine ; then add this quotient to twice chord of
half arc,* and sum will give length of arc very nearly.
^ y/c^ + 4 t). sin.' X 10 v. sin.^ , ^ • ^. j. .
Or, '- ^-1 r-^ \-2&jV. nn. representing versed tine.
EzAMPLB. —Chord of an arc is 80, and its versed sine, c r, 30; what is length of arc?
80^ = 6400 = square ofdutrd ; yjfzi: 900 = square of versed sine.
<\/(64oo-|-9ooX4) = 100 = square root ofsqttare of chord and fawr times square
of versed sine = tunce dufrd ofhaifarc
Then 100 X 3cy»x 10 = 900 000 =^pTodM(A of to Hmes square of versed sine and root
above obtained.
And 80^ x 15 =96000 = 15 times squcwe of chord.
30^ X 33 = 29700 = 33 times square €^ versed sine.
125700
Hence ^^^^ = 7.1599, and 7.1599-1- loo^ or twice chord of ha{fare = loj.tsoa
135700
length.
When Diameter and Versed Sine are given. Rule. — Multiply twice chord
of half the arc by 10 times versed sine ; divide product by 37 times versed
sine subtracted from 60 times diameter, add quotient to twice chord of half
.arc, and the sum will give length of arc very nearly.
^ sc* X 10 V. sin. . .
' 6ott — 27 V. sin.
EzAMPLB.— Diameter of a circle is 100 feet, and versed sine, c r, of arc 25 ; what
is length of arc?
V25 X 100 = 50 = chord ofha^arc. See Rule, page 345.
50 X 2 X 25 X »o = 25000 = twice chord of half arc by 10 times versed sine
100X60 — 25X27 = 5325 = 27 Hmes versed sine from 60 times diameter.
Then ■ °°^ = 4-^4^) (^i^d 4.6948 -f- 50 x 2 — 104.6948 feet
rFo Coxnpute Chord of an. A,to»
When Chord of Half the Arc and Versed Sine are given. Rule. — From
square of chord of half arc subtract square of versed sine, and take twice
square root of rem&inder.
Or, y/ (c'« — r. »fn.«) X 2 = c.
ExAVPLB.— cau>rd of half arc, a c, is 60, and versed sine, c r, 36; what is length
of chord of arc?
60'— 36>sr3304, and ^3304 X 2 = 96.
* Sqa«r« root of •am of aqoar* of chord aftd foor Umet aqoaiv of Ik* renti rint li Mod to feiftaf
cihord of half arc.
MSNSUBATIOK OF ABBAS, LINBS, ANB SUBFACES. 34J
When Diameier and Versed Sine are given. Multiply versed sine by 3,
and subtract product from diameter ; subtract square of remainder from
square of diameter, and take square root of that remainder.
Or, V^^^^^nid^^^^vTiinrxlp = c.
Example.— Diameter of a circle is 100, and- versed sine of the arc is 36; what is
length of chord of arc ?
(100 — 36 X 2)* — 100' = 9216, and '\/92i6 = 96.
To Compu-te Ch.ord. of ££alf an ^ro.
When Chord of the Arc and Versed Sine are given. Rule i. — Divide
square root of sum of square of chord of the arc and four times square of
versed sine by two.
2. — Take square root of sum of squares of half chord of arc and versed
sine.
Or, *-^ = 0*. Or, ^/ ( — ) -f V. sm.^ = &.
When Diameter and Versed Sine are given. Rule. — ^Multiply diameter
by versed sine, and take square root of their product.
Or, Vd X V. «n. = c*.
To Compute I>iaxxieter.
Rule i. — Divide square of chord of half arc by versed sine.
Or, c'^ _!. t,, jju, ^ diameter.
2. — Add square of half chord of arc to the, square of versed sine, and divide
this sum by versed sine.
Or,"'-"°+''-"-' = d
V. sin.
To Compute Versed, Sine.
Rule. — Divide square of chord of half arc by diameter.
Or, -7 = V. sin.
When Chord of the Arc and Diameter are given. Rule. — From square
of diameter subtract square of chord, and extract square root of remainder ;
subtract this root from diameter, and divide remainder by 2.
Or, = u rfn.
2
When it is greater than a Semidiameter, Rule. — Proceed as before, but
add square root of remainder (of squares of diameter and chord) to diam-
eter, and halve the sum.
Or, — ^t — V. sin.
2
ExAXPLB.— Diameter of a circle is 100, and chord of arc 97-9796; what is Its versed
sine?
100 -f- V 100* — 97. 9796 ' 100 -|- 20
= 60.
To Compute Ordiziate of a Circular Curve.— Fig. SO.
^**^*^ y^^^\ "^^ Vr* _ x2 — (r — 1>) = ordinate.
Illustration. — Radius of circle 5 ins., versed sine
2, and distance x 2 ; what is length of ordinate 0 ?
Vs"— 2« — (5 — 2) = 4.58-3 = i.58t»w.
346 MEKSUBATION OF ABBAS^ LOBS, AND STJBFACBS.
Sector of a Circle.
Definition.— A part of a circle bounded by an arc and two radii.
To Coxxipute A^rea. of a Sector of a Circle.
When Degrees in the Arc are given. — Fig. 21. Rule. — As 360 is to num-
ber of degrees in a sector, so is area of circle of which sector is a part to area «
of sector.
tt /I
*"'& 21-^^-^ ^^^ Or, = areOj d representing degrees in arc^ and a area
**^" "~^^ ofcircie.
\^ / Example. — Radius of a circle, 0 a, Fig. 21, is 5 ins., and
\y. number of degrees of sector, o b o, is 22° 30' ; what is area f
o Area of a circle of 5 ins. radius = 78. 54 ins.
Then, as 360° : 22^ 30' :: 78.54 : 4-90875 *'»»•
When Length of the Arc^ etc, are given. Rule.— Multiply length of arc
by half length of radius, and product is area.
Or, i> X r -j- a =x areOy b representing arc, and r radius.
Segment of a Circle.
Definition. — A part of a circle bounded by an arc and a chord.
To Compnte iVrea of a Segment of a Circle.
When Chord and Versed Sine qfArCj and Radius or Diameter of Circle are
given.
When Seament is less than a Semicircle, as abc, Fig. 21. Rule. — Ascer-
tain area of sector having same arc as segment ; then ascertain area of tri- .
angle formed by chord of segment and radii of sector, and take difference of
these areas.
Note. _ Subtract versed sine from radius; multiply remainder by one half of
chord of arc, and product will give area of triangle.
Or, a — a' = area, a and a' representing areas of sector and triangle.
When Segment is greater than a Semicircle. Rule. — Ascertain, by pre-
ceding rule, area of lesser portion of circle; Subtract it from area of whole
circle, and remainder will give area.
Or, a — a'' = area, a and a' representing areas ofcircie and lesser portion.
See Table of Areas of Segments, page 267.
Fig. 22. ;^ Example. — Chord, a c. Fig. 22, is 14. 142; diameter, b e, is 20
.^^ ins. ; and versed sine, b r, is 2.929; what is area of segment?
-^•9 14. 142 -r- 2 = 7.071 = halfcfwrd of arc.
\ '\/7.o7i^-{- 3.929" = 7.654 — square root of sum of squares of
s half chord of arc and versed sine, which is chord ab of hjdf are
/ abc.
y By Rule, page 344,
7. 654 X 2 X 2. 929 X 10 = 448. 37 1 = <toic« chord of ha^ arc by 10
times versed sine.
20 X 60 2.929 X 27 = 1120.917 = 60 times diarneter subtracted from 27 times
versed sine.
Then 448. 371 -f- 1120.917 = .4, and .4 added to 7.654 X 2 (twice chord of half arc)
= 15.708 inches, length of arc.
By Rule above, 15.708 X — = 78.54 = tfc« are mtdtipHed by half length of radius.
z= area of sector.
10 — 3.929 = 7.071 =v«r«ed sine subtracted from a radius, which is height of tri
angle aoc, and 7.071 X '^ '^^ = 50 = area qf triangle.
Consequently, 78. 54 — 50= 28.54.
MENSURATION OF ABSAS^ LINES, ANP SXJBITACSS. 347
When the Chords of Arc, and ofhgifo/Arc, and Verted Sine are given,
RuiJs.— To chord of whole arc add chord of half arc and one third of it
more ; multiply this sum by versed sine, and thi^ product, multiplied by
404 261, will give area nearly.
c'
Or, <r+ c' H ». nn. x .404 26 = area nearly.
3
Exjkxpix.— Chord of a segment, a c, Fig. 32, is 38 feet; cbord of balf arc, a 6, is
1 5 ; and versed sine, b r, 6 ; what is area of segment ?
28 + IS + — = chord of arc added to chord of "haXf arc and one. third of it more.
3
48 X 6 = 288 = product qf above turn, and versed sine. Hence 288 x .404 26 = 116.427
sqiuire feet.
When tke Chord of Arc and Versed Sine only are given. Rule. — Ascer-
tain chord of half arc, and proceed as before.
To Compute ClxOFcl and Hoislxt of* a Segment of a Circle.
When A rea is given. Rule. — Divide area by square of diameter of circle,
take tab. height for area from table of Areas of Segments of a Circle, p. 267,
multiply it by diameter, and product will give required height,
FrtMU diameter subtract height, multiply remainder by height, take square
root of product and multiply it by 2 for required chord.
Or, — = [tab. area for height) xd = h, and Vd — AX A x 2 =sc.
Circular IVIeasure. (See Rule, page 113.)
Spliere.
DEFimmoN.— A figure, surface of which is at a uniform distance fh)m centre.
Xo Compute Coixvex Surraoe of a Spliere.— Tfig. Q3.
Fig. 33. Rule. — Multiply diameter by circumference, and prod*
/^""'^^^ uct will give surface.
/ ^^k ^''' 4 P ''^ = surface. * Or, pd^ = surface.
a[— iSM^ Example.— What is convex surface of a sphere, Fig. 23, hav-
Y ^«a^F ^^^ ^ diameter, a 6, of 10 ins?
\f^B^^^ 10 X 31- 416 = 314. 16 square ins.
Segment of a Sphere.
DspiMTiow. —A section of a sphere.
To Compute Surface of a Segment of a SpKere.— Fig. 24.
Rule. — Multiply height by the circumference of sphere, and add product
to the area of base.
Or, 2prh=: cor .2X surface aXone.
Fig. 34. Example H:.ight, & o, of a segment, a he. Fig. 24, is 36 ina.
and diameter, b e, of sphere 100 ; what is convex surface, and
what whole surlkce?
36 X 100 X 3. 1416 = 11 309. 76 = height of segment multiplied by
eircumftrence of sphere.
To ascertain area of base ; diameter and versed sine being
given, diameter of base of segment, being equal to chord of arc,
is, by Rule, page 344^
100 — 36X2 = 28; Vioo= — 28' = 96.
96* X . 7854 = 7238. 2464 = convex surface, and 7238. 2464 -|- 1 1 309. 76 = 18 548.0064
=. convex surface added to area of bases:, square ists.
Nora. —When convex surface of a figure alone is required, area or areas of base
or ends mast be omitted.
* par w nprwento in this, sad In all cmm w1i«r* It b VMd, ratio of elrcnmforMiM of a cficlo to ik
" r»or3.s4i&
348 MENSUBATION OF ABEAS, LINES^ AJfB SURFACES.
When the Diameter of Bcue bf Segment and Height of it are aXona given.
Rule. — Add square of half diameter of base to the square of height ; divide
this sum by height, and result will give diameter of sphere.
3
Or, d-r- 2 + h^-T-h=.diameter.
Spherical ZaTi.ei (or EVustum of* a Sphere).
Dbfinition.— The part of a sphere included between two parallel chorda
To Compute Surface of a Spherical Zone.— ITig. SiC
^ \ Rule.— Multiply height by the circumference of sphere,
yT >v and add product to area of the two ends.
/ T — T^^m OXyhc-{-a-\-a* z=gurf(ux.
tX .;..-, ^Htj Or, 2p r A = conwx surface cUone.
V £ y ExAMPLM. — Diameter of a sphere, a 6, Fig. 25, from which a
\^ y zone, c g, is cat) is 35 inches, and height, c ijr, is 8 ; what is convex
^•^-^ -^ surface?
25 X 3.1416 X 8 = 628.32 = A«tpW X circumference ofq)here=:zsqttare ins.
When the Diameter of Sphere is not given. Rule. — ^Multiply mean length
of the two chords by half their difference ; divide this product by breadth
of zone, and to quotient add breadth. To square of this snm add square of
lesser chordf ana square root of their sum will give diameter of sphere.
Spheroids or B^llipsoids.
Definitiok.— Figures generated by the revolution of a semi-ellipse about one of
Its ci)ameters.
When revolution is about Transverse diameter they are Prolate, and when it is
about Conjugate they are Oblate.
To Compute Surface of a Spheroid.— ITlg. SQ.
When Spheroid is Isolate. Rule. — Square diameters, and multiply
square root of half their sum by 3.1416, and this product by conjugate
diameter.
Fig. 26 (, Or, / — — — X 3. 1 4 16 X d= «Mr/acc, d and d* represent-
ing corrugate and transverse diameters.
ExAMPLK. — A prolate spheroid, Fig. 26, has diameters, ed
and a by of 10 and 14 inches; what is its surface?
10' -|- 142 = 296 = sum of squares of diameters.
i2i^-^^ = 148. and v^i48 = 12. 1655 = «9uare root of half
sum of squares of diameters.
12. 1655 X 3. 1416 X 10 = 382. 191 ins. = product of root al>ove obtained X 3. 1416,
and by coi^vi{fate diameter.
When Spheroid is Oblate. Rule. — Square diameters, and multiply square
root of half their sum by 3.1416, and this product by transverse diameter.
Or, / — ^ — X 3- H»6 X d' = surface.
ExAMPLa— An oblate spheroid has diameters of 14 and xo inches; what is its
Burfkce?
12^ -f- 10' = ^ = <v^ of squares of diameters.
296 -T- 2 = 148, and •\/i48 = 12. 1655 = square root of haJlf sum of sqwurt* of di^
ampler.
13.1655 X 3-1416 X 14 = 5^0679 ins.z=produ^ of root above obtained X 3.14x61
and by transverse diameter.
MENSURATION OF ASEAS, LINES^ AND SURFACES. 349
Xo Coxnpixte Convex Sxirfaoe of a Segxnent of a Splie*
roid.^Kig^s. 27 and 88.
Rule. — Square diameters, and take square root of half their sum ; then^
as diameter fr<Mn which the segment is cut is to this root, so is the height
of segment to proportionate height required. Multiply product of other dU
ameter and 3. 14 10 by proi^ortionate height of segment, and this last product
will give su^ce.
Or,
Vd='+d'^-H2
Xhxd^ or dx 3.1^16 = surf ace.
Pig. s&
--i -d*
. --X....
dord'
EXAMPLK. — Height, a o, of a seg-
ment, «/, of a prolate spheroid, Fig.
27, is 4 inches, diameters being 10 and
14; what is convex surface of it?
Square root of half sum of squares a
of diameters, 12. 1655.
Then 14 : 12. 1655 1:4: 3.4758 = height
of segmerUy proportionate to mean of
diametert, and 10 X 3-1416 X 3-4758 = 109. 1957 ins.
9.— Height, CO, of a segment of an oblate spheroid, Fig. 28, is 4 inches, the diam
•ters being 14 and 10; what is convex surface of it? 214.0272 square ins.
To Coxnpute Convex Surface of a Fruatvim or Zone
of a Splieroid.— FigTB. Q& and 30.
Rule. — Proceed as by previous rule for surface of a segment, and obtain
propOTtionate height of frustum ; then multiply product of diameter par-
allel to base of frustum and 3.1416 by proportionate height of frustum, and
it will give surface.
Fig. 29.
Fig. 3a
Example.— Middle fVustum, 0 e, of
a prolate spheroid, Fig. 29, is 6 inch-
es, diameters of spheroid being 10
and 14; what is its convex surface?
Mean diameter, as per preceding
example, is 12. 1655.
Diameter parallel to base of Orus-
turn is la
Then 14 : 12.1655 •'• <^ • 5«'38, and 10 X 3.1416 X 5.2138 = 163.7967 square ins.
2.— Middle frustum of an oblate spheroid, as o «, Fig. 30, is 2 inches in height,
diameters of spheroid, as in preceding examples, being 10 and 14; what is its con-
vex sorfiioe? 107.0136 square ins.
Circular Zone.
DiFiiiinoN.~A part of a circle included between two parallel chord&
Xo Compute Area, of a Cironlar Zone.
RuiiB. — From area of circle subtract areas of segments.
Or, see Table of Areas of Zones, page 269.
When Diameter of Circle is not given. — Multiply mean length of the two
chorda by half their difference ; divide this product by breadd of zone, and
to quotient add the breadth.
To square of this sum add square of lesser chord, and square root of their
sum will give diameter of circle.
ExAXPLB.— Greater chord, %^, is 90 inches; lesser, a c, is 80; and breadth of zonei
a Of is 7x526; what is its diameter?
Then V78. 385'+ 8o»=V« 544- » = "»
Go
: diamdo''
3JO MEKHl'KATION OF AREAS, LINES, ASD SUKFACEfl.
riipn 30' X .?Ss4 -7cVj.S6 = 01-/0 of one end; jatt.ib X a = *4
urea of both tndi^uti 4712-4 + J413. 72 ^ 612^,19 SfUdm'rit.
Lrfaii<> or a IliKlit I>i
„ „.a tliein logtlher.
lDcbes.uid leIiElb,(i«, 30;
tfbtlhndi; i-i}(.ya = iia = artaofo!>eti
,o^a
m.V/^'- "■■'". ""1=88+ M40
flHi
r(\iiip of ail Oliliqiie 01-
FiB. 3*.
RlT
ic.-MuUi|>ly perimGUi of
,..j r -- — -'nd, by perpendic-
4" ular lii'igliL, 11 n. Or, multiply perimeter as >t c, at a right
7 Hiiglii tu sides by actual lengtli of li^'ure, and add area of endi.
■'•iHt'l.K.— 3ii]«,ac,DriU) obliqna baiagoDSI iirism, Fig. 34. art
iliat, and perpeudicular belgtit, a d, IB 5 f»t^ what ia lu aut-
■^o J»,10
5.9-6.6
,ii».6.6 a^aan I
"Wedfiie.
laiTiDX — A wedge la a pnlile triaogular priem. and Ita nrftce )B compnled
Lf n.r ttut of a riglit prtem.
To Cotiipnl^ SurAofl oC a 'Wad ee.— Fig. 3S.
KiiufLB— Back oravvdgp, a»ed. P>g 35. Ii nbyilDcbea,
= «.w.of,q»ar„ofl,olfba
M ^fiHb. nance So< -{- ^o-f tesUi a
MENSITJKATIOIir OF ABSAB, LINES, AND SURFACES. 3$!
Fig. 38.
Frlsmoids.
DsFiNinoy.— Figures alike to » prism, having only one pair of sides parallel
To Compute Surface of a P*ris33aoid.— Fig. 30.
RuLB. — Ascertain area of sides and ends as by rules for
squares, triangles, etc., and add them togetlier.
ExAHPLK-^-EDds ofaprisrnoid, efgk and abed. Fig. 36, are 10 and
8 inches square, and its slant height, d A, 25; what is its surface?
10 X 10 =ziooz= area of baie; 8 X 8=64 = areao/'top.
— 5— X 25 = 225, and 225 X 4 =9»=area qfnda.
2
Then loo + 64 + 900 = 1064 = sqiuire ins.
To CoiTipute Surface of an Oblique or Irregular Frisznoid,
Proceed as directed for an Oblique or Irregular Prism, page 35a
TJngnlas.
Definition.— Cylindrical uugulas are the parts (including all or part of the base)
led by a plane cutting a cylinder through any portion ^nd at any angle.
To Compute Curved Surface of an XJiiffvila.^F'iss* 37,
38, 39, aud 40,
When Section is paraUd to Axis of the Cylinder^ Fig. 37. Rule i,— Mul-
tiply length of arc of one end by height
ExAMPLB. — Diameter of a cylinder, a c, from which an
ungula, Fig. 37, is cut, is 10 inches, its length, b d, 50, and
versed sine or depth of ungnla is 5 inches; what Is curved
sarfiace?
lo-r- 2 = s = radius of cylinder.
Hence radius and versed sine are equal ; the arc, there-
fore, of ungula is one half circumference of the cylinder,
which is 31.416 -r- 2 = 15.708, and 15.-708 x 50 = 785-4
square ins.
When Section passes obliqueli/ through opposite Sides of Q/l-
inlerj Fig. 38. Rule 2. — Multiply circumference 01 base of cylinder by
half sum of greatest and least heights of ungula.
Example.— Diameter, cd, of a cylindrical ungula, Fig. 38, is 10 inches, and great-
er and less heights, b d and a c, are 25 and 15 inches; what is its curved surface?
10 diameter = 31. 416 circumference; 25 + 15 = 40, and 40 -f- 2 = 20. Henco 31.416
X 20 = 628.32 square ins.
When Section passes through Base of Cylinder and one of its Sides, and
Versed Sine does not exceed Sine^ or Base is equal to or less than a Semi-
circkf Fig. 39, Rule 3. — Multiply sine, a d, of half arc, d g, of base, d gf
by diameter, e g^ of cylinder, and from this product subtract product * of arc
and cosine, a o. Multiply difference thus found by quotient of height, g c,
divided by versed sifae, a g.
NoTE.~Tbe sine of base is half of the longest chord that can be drawn in base.
Y'lft ,0 ExAMFLB.— Sine, a d, of half arc of base of an nngula. Fig. 30, is 5,
..- : diameter of cylinder, eg^ is xo, and height, c^, of ungula 10 inches;
whal is carved surf«ce?
5 X 10 ss 50 = »n« q^Aoy arc fry dmmcier.
length of arc, versed sine and radius being equal, under Rule, page
346 = 15.708, and as versed sine and radius are equal, cosine is a
Hence, when cosine is o, product is a Therefore 50 — o = 5o=dt/-
ference of product b^ore obtained and product of arc and cosine, and
50 X io-»-s = 50 X azszioosquare ins.
• WliiD the eodM ia o, this products- o>
352 MENSURATION OF ABBAS, LINES, AND SUEFACEB.
When^ Section pastes through Base o/Q^Under^ and Versed Sine, ao^ea^'
ceeds Sine^ or when Base exceeds a Semicircle^ Fig. 40. Ruuc 4. — Multiply
Fig. 4a
sine of half the arc of base by diameter of cylinder, and t(» tnis
product add product of arc and the excess of versed sine over
the sine of base. Multiply sum thus found by quotient of
height divided by versed sine.
ExAUPLK. — Sine, a d, of half arc of an ungnla, Fig. 40, is 12 inches;
versed sine, ag, is 16; height, c 9, 16; and diameter of cylinder, h g,
35 inches; what is carved surface?
la X 25=3oo=<tn« of half arc by diameter of cylinder, and length
of arc of base. Rule, page 344 = arc qfd hf— circumference of bast =
46-39g-
Then 46. 392 X 16 — 12. 5 = 162. 372, and 300 -f* 162. 372 = 462. 372 ; z6 -r- z6 =r x, and
462.372 X X =462.372 square ins.
NoTB.— When sine of an arc is o, the versed sine is equal to diameter.
When Section passes obliqueig through both Ends of Cylinder^
Fig. 41. Rule 5. — Conceive section to be continued to wi, till it
meets side of cylinder produced ; then, as difference of versed
sines, a e and d 0, of arcs of two ends of ungula is to versed sine,
a e, of arc of the less end, so is height of cylinder, a (2, to the
part of side produced.
Ascertain surface of each of ungulas thus found by Rules 3
and 4, and their difference will give curved surface.
Definition.— Space between mtorsecting arcs of two eccentric circles.
To Compnt© A,vea. of a Lviiie.— Fig. 48,
Rule. — Ascertain areas of the two segments from which lune is formed,
and their difference will give area.
Fig. 42.
ExAMPLB-^Length of chord ac. Fig. 42, is ao inches, height
e d is 3, and e & 2 ; what is area of lune ?
By Rule 2. page 345, diameters of circles of which lune is
formed are tnus ascertained:
Forade,
io* + (3 + 2)'
== 35. For a e tf.
xo»+a«_
= Sa.
Then, by Rule for Areas of Segments of a Circle, page 267,
Area of a d c is 70.5577 sq. ins.
ate '■'■ 27.1638
t(
i(
Tkdr difference 43'3939.<9. ins.
Cycloia.
Dkpinition.— A curve generated by revolution of a circle on a plane.
To Compute Area of a Cycloid.— B^ifc. 43.
Fig. 43. J ^^ Rule. — Multiply area of generating circle by ^
^ ^ ExAMPLK.— Generating circle of a cycloid, a 6 c, Fig. 43,
has an area of 1 1 5. 45 sq. inches ; what is area of cycloid ?
"5-45 X 3 = 346- 35 *qwire ins.
Compute I^engtb. of a Cyoloidal Cxxx^re*
Rule. — Multiply diameter of generating circle by 4.
ExA]fPLR.~Diameter of generating circle of a cycloid, Fig. 43, is 8 inches; what
is length of carve dsc^
8X4 = 32 =prodtte( of diameter and 4 = ins.
Note.— The curve of a cycloid is line of swiftest descent; that is, a body will fall
through arc of this curve, from one point to another, in less time than through^any
other path.
To
BCSNSUBATION OF AREAS, LINES, AND 6UBFACSS. 353
Circular Xlings.
Definition.— Space between two concentric circles.
To Conupiite Sectional A.rea of a Circular 'Rii\s,^Fig,'4At
Rule. — From area of greater circle subtract that of less.
Cylindrical Rings.
DKn^TiON.— A ring formed by curvature of a cylinder.
To Compnte SuriUoe of a Cylindrical Ring.— F'ig. 44.
Rule. — To diameter of body of the ring add inner diameter of the ring ;
multiply this sum by diameter of the body, and product by 9.8696.
Fig. 44. Or, c X i = surface.
ExAMPLK.— Diameter of body of a cylindrical ring, a 6, Fig. 44,
ia 3 inches, and inner diameter, b c, is 18 ; what is surface of it?
3 4- 18 = 2o = Ihickness qf ring qdded to inner diameter.
2o X 2 X Q 8696 = mm, above obtained X thickneu of ring^ and
thai product by 9. 8696 = 394. 784 int.
Xjinls.
, Definition.— An elongated ring.
To Compnte Surface of a I^ink.— ITigs. 4f5 and 4G.
Rule. — Multiply length of axis of link hy circumference of a section of
body, a b.
Or, i X c = surface.
To Coxnptite T^ength. of A^xis and Circumference.
When Rinff is Elongated, Rule.— To less diameter add the diameter of
the body of the link, and multiply sum by 3.1416; subtract less diameter
from greater, multiply remainder by 2, and sum of these products is length
of axis.
Example.— Link of a chain, Fig. 45, is x Inch in diameter
of body, a b, and its inner diameters, b c and ef are 13.5
and 3.5 inches; what ia its circumference?
3. 5 -|- I X 3- 1416 = 10.9956 = length of axis of ends.
13.5— 3.5 X :t^ 20 = length of sides of body.
Then 10.9956 -f- 20 = 30.9956 = length of axis of link, and
30-9956 X 3.1416 (cir. of I inch) =97.3758 square ins.
When Rinff is FMij)tical^ Fig. 46. Rule. — Square diameters of axes of
ring, multiply square root of half their sum by 3.1416, and product is length
of axis.
Cones,
DanxiTiov. —A figare described by revolution of a right-angled triangle about
one of its leg&
For Sections of a Cone, see Conic Sections, page 379.
To Compute Surface of •» Cone.—ITig. 47',
Rule. — Multiply perimeter or circumference of base by slant height, or
aide of cone ; divide product by 2, and add the quotient to area of the base.
Fig: 47. o Or, c X * -r- 2 + «' = sutfaoe, c representing perimeter.
ExAMPLB. — Diameter, a b. Fig. 47, of base of a cone is 3 feet,
ttud slant height, a c, 15; what is surface of cone?
Ciroam. of 3 feet =9. 4248, and ^^^ ^:=z 70.686 =s sur-
face of side; area of base 3=7.068, and 70.686-1-7.068 = 77.754
tquarefeet.
4 i u«
354 MENSURATION OF ABEAS^ LINES, AND SUBFAGE8.
To Compnte Sixrfaoe of tUo EVixBtum of a Cone.—
Fig. 48.
Rule. — Multiply sum of perimeters of two ends by slant height of frus-
tum ; (fivide product by 2, and add it to areas of two ends.
Or, -T-^ l-a + a =«Mr/acfi
Example.— Frustuin, abed. Fig. 48, has a slant height, c d, of 26 inches, and
circumferences of its ends are 15.71 and 22 inches respectively;
what is its surface?
j/rr3:l^ d + (rrid^ ^ *^®^^ ^ ^^' ' '^ "^ *'^"" ''•^ ^''^' ^^'^ 490-23 +
58. 119 = 548. 349 square ins.
Pyramids.
Definition— A figure, base of which has three or more sides, and sides of which
are plane triangles.
To Compute Surface of a Pyramid.— Figs. 40 and SO.
Rule.— Multiply perimeter of base by slant height; divide product by 2,
and add it to area of base.
Fig. 40. o o. c ^ I ^ ^'8- so.
A ^^' H <» = surface.
// V Example.— Side of a quadrangular pyramid, a 6,
// vk Fig. 49, is 12 inches, and its slant height, o c, 40;
// 1^ what IS its surface?
/l.ll!~"So 12 X 4 = 48 =perimeter of base. ^ — = 960 =
^ J ft area of sides, and 12 X 12 + 960 = 1104 square ins.
To Coxnpute Surface of Frustum of a Pyramid.—
Fig, 01.
Rule. — Multiply sum of perimeters of two ends by slant height ; divide
product by 2, and add it to areas of ends.
Fig. 5,. Or, -^^~- + a + a' = «*rface,
fi ^ Example. —Sides a &, c d, Fig. 51, of fhistum of a quadrangular
pyramid are 10 and 9 inches, and rtsidaot height is so ; what
is itssQrfkce?
10 X 4 = 40, and 9 X 4 = 36; 40-I- 36 = 76 = ««m ofperimetert.
h. t ■ yg ^ 2Q _ J jjjQ^ j^qji 520 __ y^ _ ^j.g^ of sides ; 10 X xo = loo,
*■ to 2
and 9X9 = 81. Then zoo -|- 81 +760=941 rrxguafvifM.
When I\framid is Irregular sided or Oblique. Rule. — The surfaces o£
each of the sides and ends must be computed and added together.
Helix (Sore-w).
DEFnnnoN.— A line generated by progressive rotation of a point around an axis
and equidistant fVom its centre.
To Compute Xjengtli of a Helix.- Fig. 6S.
Rule. — To square of circumference described by generating point, add
square of. distance advanced in one revolution, extract square root of theii
suiUi and multiply it by number of revolutions of genejatmg point.
MENSUBATIOK OF AREAS, LINES, AND SURFACES. 355
Fig. 52. Or, y/{p^ -|- 1*) n = lengthy n repretenting nvimher of revoltUion*.
ExAMPLi.-^What is length of a helical line, Fig. 52, running 3.5
times mound a cylinder of 23 inches in circumference, and advancing
16 inches in each revolution ?
22^ -|- 16 2 = ^^o = sum of squares of circumference and of distance
advanced. * Then ^74© X 3. 5 = 95. 21 ins.
To Compute I-ieiigrtlx of a Revolution of Tliread of a
Sore-wr.
Rule.— Proceed as above for length and omit number of revolutions.
Spirals.
Definition.— Lines generated by the progressive rotation of a point around a
fixed axia
A Plane SpircU is when the point rotates around a central point.
A Conical Spiral is when the point rotates around an axis at a progressing dis-
tance from its centre, as around a cone.
To Compxite Lengtli of a Plane Spiral I-.iue.— Kig. ©3.
Rule. — Add together greater and less diameters ; divide their sum by 2 ;
multiply quotient bv 3.1416, and again by nmnber of re\ olutions.
Or, when circumferences are given, take their mean length, and multiply
it by number of revolutions.
_. 0T,d-\-d'-i-2K 3. 1416 n = length of line; P x n = radius, and
* '8- 53^, ^^ pr'-i-l =pitch. P representing the pitch.
Exam PLE.— Less and greater diameters of a plane spiral spring,
as a b, c d, Fig. 53, are 2 and 20 inches, and number of revolutions
d 10* what is length of it?
<r+-~2o -^ 2 = II = wm of diameters -j- a ; 11 X 3. 1416 =
. 34-5576.
Then 34.5576 X 10= 345. 576 inches.
NoT«. — Above rale Is applicable to winding engines, see page 86«, where it is re-
quired to ascertain length of a rope, its thickness, number of revolutions, diameter
of drum, etc
To Coixipiite I^ength of a Conical Spiral Line.— Fig. 54:.
Rule. — Add together greater and less diameters; divide their sum by
2, and multiply quotient by 3 14 16.
To sqoare of product of this circumference and number of revolutions of
spiral, add square of hci;^ht of its axis, and take square root of the sum.
Or. \/{d -\- d*^ 2 X 3. 1416 n 4- A«) = length of line.
Example. — Greater and less diameters of a conical spiral. Fig. 54, are
20 and 2 inches; its height, cd, 10, and number of revolutions 10; what
is length of it?
2o + a-i-a = ii X 3.1416 = 34- 5576 = <wm of diameters -r- a, and x
3. 1416; 34.5576 X 10 = 345- 576-
Then V 345. 576*-!- 10* = 345. 72 inchet.
Spindles.
Dwnmrtos. — Fignires generated by revolution of a plane area, when the curve is
revolved about a chord perpendicular to its axis, or about its double ordinate, and
they are designated by the name of the arc or curve ft*om which they are generated,
as Circular, Elliptic, Parabolic, etc.
# Whtn tb« tpiral !• otlMr tlMUi • Up«f nwMlire diuatton of It from middl* of body compoalng II
356 MENSUBATION OF AREAS, LINES, AND SURFACES.
Cironlar Spindle.
To Compute Ooiftvesc Surfaoe of a Circular Spindle, Zoxie»
or Segment of it.—Ii^igs. GCS, 66, and. £37.
Rule. — Multiply length by radius of revolvinj^ arc ; multiply this arc by
central distance, or distance between centre of spindle and centre of revolv-
ing arc ; subtract this product from former, double remain-
der, and multiply it by 3.1416.
Or, / r — (awr*— f -J ) 2 p — surf cue, a representing length
ofarc^ and e the spindle chord.
ExAMPLB.— What is surface of a circular spindle, Fig. 55, leugth
y of it,/c, being 14.142 inches, radius of its arc, oc^ 10, and central
*^*-^-— -*' distance, o e, 7.071 ?
14. 142 X 10 = 141.42 = lengtJi x radius. Length of arc.,/ a c, by Rules, page 344
= 15.708.
i5-7o8x 7.071 = 111. 0713 = /«n^ of arc X central distance; 14J. 42 — 111.0713 =
30. 3487 = difference of products. Then 30. 3487 X 2 X 3. 1416 = 190.687 square vns.
Fig. 56. Zone.
d b Example. — What is convex surface of zone of a circular
y''lfr e /St***- spindle, Fig. 56, length of it, i c, being 7.653 inches, radius of
^..».l....-^fl-^^ its arc, our, 10, central distance, o«, 7.071, and leugth of its
-v>V9^^^^^^;^ side or arc, d 6, 7.854 inchei^?
\ I / 7.653Xio=76.53=i€n^W«X»adtt«; 7 854 X 7- 07* = 55- 5356
\\y = tmgtk of arc X central distance ; 76. 53 — 55. 5356 = 20. 9944
0 =: difference of products.
Then 2a9944 X a X 3- 1416 = 131.9x2 square ins. dL — — ,^' 57-
Segment. *4^"'T '^y^
Example.— What is convex surface of a segment of a cir- \ "— !• — '''/
cular spindle. Fig. 57, length of it, tc, being 3.2495 inches, \ : ,/
radius of its arc, 0 jjr, 10, central distance, o «, 7.071, and length <]/
of its side, t d, 3. 927 inches ? o
3.2495 X 10 = 32.495 = length X radius; 3.927 X 707» = 37.7678 = Unglh of arc
X central distance ; 32. 495 — 27. 7678 = 4. 7272 = difference of products.
Then 4.7272 x 2 x 3. 1416 = 29.702 square ins.
'General Formcla.— S = 2 Ji r — o c)p = surfoux^ I repi'esenting length ofspindU^
segment, or tone, a length of its revolving arc, r radius of generating circle, and c
central distance.
Illustration.- TiCngth of a circular spindle is 14.142 inches, length of its revolv-
ing arc is 15.708, radius of its generating circle is 10, and distance of its centre ttom
centre of the circle fVom which it is generated is 7.071 ; what is its surface?
2 X (14.142 X 10 — 15.708 X 7071) X 3.1416= 190.687 square indies.
Note.— Surfhce of a fVustum of a spindle may \)e obtained by division of the
surface of a zone.
Cyoloidal Spindle.
1?o Compute Convex Surfietce of a Cyoloidal Spindle.-^
ITig. 68.
Rule. — Multiply area of generating circle by 64, and divide it by 3.
f 'g- 58. ... /x a X 64 -
** ^ — - » Or, ^ = surface.
3
Example.— Area of generating circle, a 6 c, of a cycloidal
spindle, d«, is 32 inches; what is surface of spindle?
32 X 64 3= 2048 =: area of circle x 64 , and 2048 ^ 3 =
682.667 square ins.
NoTL—Area of greatest or peQti^ I^^QP pf A c^roloidal spindle ig twloe (trea of
(he cjroloi4.
MJIsINSUBATIOX OF AREAS, LINES, AND SUBFACES. 357
£:ilipsoicU Para'boloicU or iHyperlsoloid of Rev-
olution..
Obfinitiox. — Figaree alike to a cone, generated by roTolution of a conic secUon
cround its axis.
NoTB.— These figares are asually known as Conoids.
When they are generated by revolution of an ellipse, they are termed Ellipsoids,
and when by a parabola, Paraboloids, eta
Revolution of an arc of a conic section around the axis of the curve will give a
segment of a conoid.
!E211ipsoid..
To Coxupixte Couvex Su.rfEbce or an ICllipsoid.^ITig. &0.
RcLK. — Add together square of base and four times square of height;
multiply square root of half their sum by 3.1416, and this product by radius
of the base.
Fig. 59. ^ ^'* \/~^~ ^' '*'^ '' = '^•^^^
Example.— Base, a b, of an ellipsoid, Fig. 59, is zo inches, and
vertical height, c il, 7 ; what is its surface?
«o*+ 7* X 4 = 296 = sum of square o/base and 4 times square
of height; 296 -i- 2 = 148, and v '4^ = !>• i655=<9uai'e root of half
above fum. Then 12.1655 X 3-i4i6 X — = 191.0957 square ins.
To Compute Convex Snrflaoe of* a Segizxent, Frustuxn,
or Zone of* an Kllipsoici.—irig. 69.
See Rules for Convex Surface of a Segment, Frustum, or Zone of a
Spheroid or Ellipsoid, pages 348-9.
<i or d' X 3- 1416 X A = surfact,
ynean. diam. Xh . ^, , , . j,
-=5 A ; then d X 3.M«6 X A = surface.
and
dord'
I*ara"boloid.
To Compute Convex Surface of a Faraboloid.-^iFig. GO.
Rule. — From cube of square root of sum of four times square of height,
and square of radius of base, subtract cube of radius of base ; multiply re-
mainder by quotient of 3.14^6 times radius of base divided by six times
square of height
Fig. 60. b
Or, (V4A«+r=')3-r3 x ^^ = surface.
Example.— Axis, 6d, of a paraboloid, Fig. 60, is 40 inches; ra-
dius, a cf, of its base is 18 inches; what is its convex surface?
40' X 4 = 6400 = 4 times square of height ; 6400 -f- 18' = 6724 —
sum ofv^w product and square of radius of base; (■v/6724)3 — 183
545 536 = remainder of cube of radius of base subtracted from cube
of square root of pr^eding sum ; 3.14x6 X i8-f-(6 X 40*)^.oo58905
—quotient 0^3.1416 Hmes radius ofbase-i-e times square of height
Then 545 536 X .005 890 5 =:; 3213. 48 square ins.
Cylinder Sectioxxs*
To Compute Surface of* a Cylinder Section.
— Kie. ei.
Ruijc. — From entire surface of cylinder a o subtract
surface of the two ungulas, r 0, o c, as per rule, page 351^
and multiply result by 4.
3S8 MEl^SUBATION OP ABEAB, LINES, AND SUBFAoES.
Any WUsoTG of Revolution.
To A.0oertaiii Convex Surface of any I^igure of Revolu*
tiou.— Kigs. a^, &3, and 6*^.
RuLB.— Multiply length of geiieratiug line by circumference described
by its centre of gravity.
Or, * 2 r p = sur/acey r repreKuting radius of centre of gravity.
ExAMPLK I. —If generating line, a c, of cylinder, acdf,jo inches
Fig. 6a. ^ ^ In diameter, Fig. 62, is xo, then centre of gravity of it will be in 6,
^' jj- -'^ radius of which is 6 r = 5.
r,
Cv-'.ir ' Hence 10 X 5 X 2 X 3i4>6 = 3»4- 1<5 itu.
\ Again, if generating line \b eacg, and it is (<• a r= 5, a e=:: 10.
I and cfli=: 5) = 20, then centre of gravity, o, will be in micUile or
V line Joining centres of gravity of triangles eac and ac p = 3.75
fVom r.
/ * •
blot-
Hence 20 x 3-75 X a X 3. 1416 = 471.24 square ifu.= entire surface.
^ I Convex surface as above 314. 16
VERIFICATION. J ^^.^ ^f ^^j^ ^^^ ^^a ^ ^g^^ ^ ^ z= .157.08
471.24 mcftM.
Fig. 63. 2.— If generating elements of a cone. Fig. 63, are ad=io.
^^ dc= 10, and a c. generating line, = 14. 142, centre of gravity of
y] \ which is iu o, and o r = 5,
o/....\r \ .pijgjj 14.14a X5X2X 3.1416=444.285, con-
/ I \, 2
^- "i * w*** surface^ and 10 X 2 X .7854 = 314.16, area
of base.
Hence 444.285 -f- 31 4' 16 = 758.445, cn<ir« surface.
3.— If generating elements of a sphere, Fig. 64, are a c = vo, a 6 0
will be 1 5. 708, centre of gravity of which is in 0, and by Rule, page
606, o r = 3. 183.
Hence 15.708 X 3.183X2 X 3.1416 = 314.16 square ins.
Capillary Tube.
To Compute X)iaxneter of a Capillar^r T-a"be.
liULE. — Weigh tube when empty, and again when filled with mercury;
subtract one weight from the other ; reduce difference to grains, and divide
it by length of tube in inches. Extract square root of this quotient, multi*
ply it by .019 224 5, and product will give diameter of tube in inches.
— X .019224 5 = diameter y w representing difference in weights in grains
and I length of tube.
ExAMPLK — Difference in weights of a capillary tube when empty and when filled
with mercury is 90 grains, and length of tube is 10 inches; what is diameter of it?
90 -s- 10 — 9 — weight of mercury -i- length of tube ; y/a — 3, and 3 X .019 224 5 =
■057 673 5 — square root of above quotient x .019 224 5 incnes = diameter ofhibe.
Proof. —Weight of a cube inch of mercury is 3442.75 grains, and diameter of a
circular inch of equal area to a square inch is 1.128 (page 342).
If. then, 3442.75 grains occupy i cube inch, 90 grains will require .026 141 9 cube
inch, which, -^ 10 for height of tube =:= .002614 '9 ii^^h for area of section of tube.
Then v/.no2 614 19 = .051 129 = side of square of a column of mercury of this area
Hence .051 129 X i.iaS (which is ratio between side of a square and diameter of a
circle of equal area) = .057 673 5 ins.
1*0 A^soertain A.rea of an Irregular ITig-ure.
Rui.R. — Take a uniform piece of board or pasteboard, weigh it, cut out
figure of which area is required, and weigh it ; then, as weight of board or
pasteboard is to entire surface, so is weight of figure as cut out to its sur&ce.
Or, see rule page 341, or Simpson's rule, page 34^.
MENSURATION OF ABSAS, LINES, SURFACES, ETC. 359
To A.scertaixx A.rea of any Plane Figure.
Rule. -" Di\ide surfaces into squaresj triangles, prisms, etc. ; ascertain
their areas and add them together.
Reduction, of an A-soending; or Descending Line to Hor«
izontal IVleasurement.
In Link and Foot.
Foot.
i>BffreM.
Uok.
Foot.
D^p^es.
Link.
Foot.
DOgl'068.
Link.
X
.000099
.00015
7
.004917
•00745
13
.016915
a
.000403
.00061
8
.006421
.00973
14
.019602
3
.000904
.00137
9
.008125
.01231
15
.022486
4
.001 61
00244
zo
.010025
.015 19
16
.025569
5
.002515
.00381
II
.012124
.01837
>7
.028925
6
.003617
00548
12
.014421
.02285
18
.0323
02563
•0297
.0340^
•03874
•0437
.04894
Illustbation l — 1q an ascending grade of 14O, what is reduction in 500 feel?
14° = 500 X .0297 = i4.85^i?c< = 14 feet laa ins.
2.— What IB reduction in 500 links?
14O = 500 X .019 602 = 9.801 feet = gfe«t 9.6 ins.
Reduction ofGI-rade of* an .Ascending or IDescendiug Ljine
to Degrees.
Per 100 Links, Feet, etc.
Grado. Dflffrees. Grade. T>egreM. Grade. Degree*.
Grade.
De
»
.25
' 8
•5
17
'75
25
I
34
I-25
42
15
51
352
10.3
47.6
22.7
57-9
35-2
1-75
2
2-5
3
3-5
4
1
Oegi
'ees.
/
»*
0
10.3
3
845-5
25 57-6
43 8.3
0 20.7
2
17
33-1
45
5
6
\
2
2
3
4
4
5
34
51
26
o
35
9
45-
57-
22.
49.
18.
49.
10
II
12
13
14
15
5
6
6
7
8
44 20.7
18 55.8
53 31
38 10.3
2 51-7
8 37 37-2
To Plot Angles -witliout a Protractor.
On a given line prick off 100 with any convenient scale, and from the
point so pricked off lay off at right angle with the same scale the natural
tan^nt due to the angle (see table of Natural Tangents and Sines) ; or
strike out a portion of a circle with radius 100 and lay off a chord = 2 sin.
of half the angle required.
To Compute Ch.ord. of an ^ngle.
Double sine of half angle.
Illustration. -> What is the chord of 21^ 30'?
Sine of _L_32. = jqO 45', and sine of \cP 45' = .18652, which, X 2 = .37304 cftorA
To -A^soertain. Value of a FoT?ver of a Quantity,
• •
Rtii.E.-^Maltiply logarithm of quantity by fractional exponent, and prod-
net is logarithm of required number.
Example.— What ig the valno of 16^ '
^ X log. 16 = 3j^ X 1.304 13 = -90309. J!«Iumber for whichsft
MENBUBATIOH OF VOLUME&
KuLE.— Multi|ily a siile of cube by itoelf, md that product
sgain by a aide.
Or, *3 = V. a r^TESenting Ifng/h of a side, and V votwne,
[AMPLE.— Side, a A, Fig. I, la la Inches; wbat laiolums otllf
iPrisras, Prismoide, and "hedges.
Prisma.
jal, Bimllar, aod parallel plaaea, aad
a irlanglea, il la lermed a Iriangular
Lnllelogratna.
of a Pri
Flga. 3 and 4.
RULK.-Mulliply SKH oPbaae by height.
A
EiAKPLK. -A Iplangiilar prlani, a be. Fig. 4, h«a Bld«
By Rule, page 339, a.5' x.433 = » T^'S = o™> V
J Ufa, Bddi.;a(iis X 10= 17.1169; cube y^f.
LI
Wim a /Vtjin ii Oblique or tmgular.
Rule. — Hulti|>]y nr«a of an end by heii;lit, aa
niuUiply area taken at a rigbt angk to aidts, as
uclual Icnj^tii.
Rule.— Multiply area of base h_ . ,
distances between it and centre of gravity of uppw
or other end.
gula''"r''cy"hndrl(!al prBm. Fig 6, la .s tn«l
Geigbt 10 ccnlra of gMsity, e, 13 u ; what IB
MENSURATION OF VOLUMES.
361
Prifionoids* •
X£> Compnte "Volvixne of a Prisxnoid..— •F'ig. 8.
Rule. — To sum of areas of the two ends add four times area of middle
section, parallel to them, and multiply this sum by one sixth of perpendicu-
lar height.
NoTB.— This is the general rule, and known as the Fasmoidal Formula^ and ii
applies equally taall figures of proportionate or dissimilar ends.
Or, o + a' -|- 4 »« X A -i- 6 = V, a and a* repretenting areat ojendt^
and m area of middle section.
Example. — What is volame of a rectangular prismoid, Fig. 8,
lengths and breadths, e g and gh^ ab and 6 d, of two ends being
7X6 and 3X2 inches, and height 15 feet?
7X6 + 3X 2 = 42 + 6 = 48 = «*i»o/'orea«o/'<uwend«; 7 + 3-^-
2 =: 5 = length of middle section; 64-2-7-2 = 4 = breadth of middle
tectum; 5 X 4 X 4 = 80 =four times area of middle section.
Then 48 4- 80 X '^^ " = 128 X 30 = 3840 cube ins.
NoTB I.— Length and breadth of middle section are respectively equal to half
sum of lengths and breadths of the two enda
2.— Frisraoids, alike to prisms, derive their designation from figure of their ends,
as triangular, square, rectangular, pentagonal, etc
When ii is Irregular or Oblique and their ends are united by plane or
curved surfaces, through which and every point of them, a right line may be
drawn from one of the ends or parallel faces to the other, — Figs. 9, 10, and iz.
Figi la Fig. IX.
/ • \ n
Pig. 9.
ExAMPLC— Areas of ends, a c and ors. Fig. 10, a 6 c d, and t m n u. Fig. n, and
abce and vxws, Fig. 9, are each 10 and 30 inches, that of their middle section
30, and their perpendicular heights j8; what is their volume f
xo-f-3o-t-2oX4 = 120 = sum of areas of ends 4- 4 times middle Kction. And
120 X -7- = 360 cube ins.
"Wedge.
To Compute Volnme of a, l^edge.— Fig. IS.
Rule. — ^To length of edge add twice length of back ; multiply this sum
by perpendicular height, and then by breadth of back, and take obe sixth
of product.
Or,(l4-rx2XAb)-^6 = V.
ExuiPLB. —Length of edge of a wedge, e p, is 20 inches, back,
abed, is aoby 2, and its height, ef, 20; what is its volume f
ao4-2oX2=s6o = length of edge added to twice length of
back; 60 X 20 X 2 = 2400 =above sum muUij^ied by height, and
that product by breadth ofttack.
Then 2400 -!- 6 = 400 cube ins.
KoTK. — When a wedge is a true prism, as represented by
Fig. 12, volume of it Is equal to area of an end multiplied by its length.
* An •zoiTatkMi or cmtMoksMnt of • road, when terminated by parallel croM
gttlar priamoid.
H H
Mctiou,ia • reeUv-
362 MENSURATION OP VOLUMES.
To Compnte ITrxiatrxxii of a "Wedge.— Fig. 13.
Rule. — To sum of areas of both ends, add 4 times area
<rf section parallel to and equally distant from both ends,
and multiply sum by one sixth of length.
^ Or,A + a-|-4a'Xj = V.
Example.— liengths of edge and back of a frustum of a wedge
a b and c d are 20 x i and 20 x 2 ins. , and height o r is ao in& ;
what is its volume?
20X 2-l-j
/ 2 4- >\ 20
X2 + 4X(20X-^JX-^
20
60 -f lao X ^ = 600 cube im.
6
2 \ 2
Note. —When frustum is a true prism, as represented Fig. 13, volume of it is equal
to mean area of ends multiplied by its length.
Regular Bodies (Polyhedrons).
Dkfixition. — \ regular body is a solid contained under a certain number of simi-
lar and equal plane feces,* all of which are equal regular polygons.
NoTB I. — Whole number of regular bodies which. can possibly be formed is five.
2. — ^A sphere may always be inscribed within, and may always be circumscribed
about a regular body or polyhedron, which will have a common centra
Fig.,x4.
Fig. IS.
Fig. 16.
Fig. 17.
1. Tetrahedron, or Pyramid, Fig. 14, which has four triangular fkces.
2. Hexahedron, or Cube, Fig. z, which has six square faces.
3. Octahedron, Fig. 15, which has eight triangular faces.
4. Dodecahedron, Fig. 16, which has twelve pentagonal facea
5. Icosahedron, Fig. 17, which has twenty triangular faeea
To Compute Klexnents o£ axxy XI,egulAr Sody.i^SHgs. 14,
16, 16, and 17.
To Compute Baditis of a Sphere that witl Circumscribe a given Regular
Body^ or that may be Ifiscribed within it.
When Linear Edge is given* Rule. — Mtiltiply it by multiplier opposite
to body in columns A and B La following Table, under head of dement re-
quired.
Example.— Linear edge of a hexahedron or cube. Fig. i, is 2 inches; what are
radii of circumscribing and inscribed spheres?
2 X .86602 = 1.73204 inches := radius of circumscribing tphcre; 3 X .5 = 1 inch=:
radius &f inscribed sphere.
When Surface is given. Rule. — Multiply square root of it by multiplier
opposite to body in columns 0 and D in loUowing Table, under head of
element required.
When Volume is given. Rule. — Midtiply cube root of it by multiplier
opposite to body in columns K and F in fcllowiDg Table, under head of ele-
ment required.
- — ■
* AngU of wyacanl facM of • polyiioD it termed diedral angle.
MENSURATION OP VOLUMES 363
When one of the Radii of Circumscribing or Inscribed Sphere alone is re-
quired, the other being given. Rule. — Mul^ly given radius by multiplier
opposite to body in columns G and .H in Table, page 364, under head of
other radius.
To Coi-npnte I^inear lBld.ge,
When Radius of Clrcttmscribiiw or Inscribed Sphere is given. Rule. —
Multiply radius given by multiplier opposite to body in coluums I aud K in
Table, page 364.
When Swface is given. Rule. — Multiply square root cf it by multiplier
opposite to body in column L in Table, page 364.
When Volume is given. Rule. — Multiply cube root of it by multiplier
opposite to body in column M in Table, p^e 364.
To Compute Surface.
When Radius of Circumscribing Sphere is given. Rule.— Multiply square
of radius by midtiplier opposite to body in column N in Table, page 364.
When Radius of Inscribed Sphere is given. Rule. — Multiply square of
radius by multipuer opposite to body in column O in Table, page 364.
When Linear Edge is given. Rule. — ^Multiply square of edge by multi-
plier opposite to body in column P in Table, page 364.
When Volume is given. Rule. — Extract cube root of volume, and multi*
ply square of root by multiplier opposite to body in column Q in Table,
page 364.
To Coxnpute Volarpe.
When Linear Edge is given. Rule. — Cube linear edge, and multiply it
by multiplier opposite to body in column R in Table, page 364.
When Radius of Circumscribing Sphere is given. Rule. — Multiply cube
of radius given by multiplier opposite to body in coliimn S in Table,
page 364.
When Radius of Inscribed Sphere is given. Rule. — Multiply cube of
radius given by multiplier oppasite to body in column T in Table, page 364. ^
When Surface is given. Rule. — Cube surface given, extract square root,
and multiply the root by multiplier opposite to bmly in column U in Table, r
page 364.
Fig. 18. Cylinder.
To Compute Volume of a Solid Cylinder.—
Fig. 18.
Rule. — Multiply are^ of base by height.
ExAMPLB.— Diameter of a cylinder, 6 c, is 3 feet, and its length, a b
7 feet; what is its volume?
Area of 3 feet = 7.068. Then 7.068 X 7 = 49.476 cube feet
To Coxupute "Volume of a HoUotv Cylinder.
Rule. — Subtract volume of internal cylinder from that of cylinder.
Fig.i9k c Cone.
To Compute Volume of a Oone.^Ifig:, 19.
Rule. — Multiply area of base by perpendicular height,
and take one third of product.
Ex AMPLK.— Diameter, aft, of base era cone is 15 inches, and
\b height, c«, 32.5 inches; what is its volume?
Area of 15 inches = 176.7146. Then '7 7'5X32.5 _ ,^,^,^„g ^ube i»w,
364
MENSURATION OF VOLUMES.
ajaqdg paqijos
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■8.
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duiquosiuna
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aSpa jvaaiq
N ^ ^ rO •-•
'djaqds
• poquosai Xg
W -ajdqds 'ajquas
-uinajio ju snipvH
m
9
0
n
e8
»-«
4)
l<
■♦»
0
«
a
<8
■
■♦J
d
*8iaqds
8niqij3suinaiio Aq
'ajaqds
paquasaxjosnipcH
1010 H M
o o -«♦• ^
C« C4 00 00
rO ro m »0
• • • p
f) M M M M
fO >o lO »o 10
fO fO fOvO vO
ro r* t-* ^ «*
CO r* t^ Ov Q»
ro «o 10 t-* r>.
'amniOA Aq
^ -ajaqdg
pequosai jo snip«H
\0 M
1000 t^
^ NnO 00
^ ■/) 10 >o 10
-omnioA Aq
^ 'ojaqdg Saiqijos
-mnaiio jo suipsg
0> O O t"^ N
Ov t^ t>.
'adttjjng is
aiaqdg
paqiiOsniJosnipvH
d 10 t^ M
^M M ro O 00
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-mnaiio jo sntpvn
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MBK6UBATION OF VOLUUKS.
365
To Compixte "Volume of Frixatum of a Cone.— P'ig. SO.
Rule.— Add together squares of the diameters or circumferences of greater
and lesser ends and product of the two diameters or circumferences ; mul-
tiply their sum respectively by .78^4 or .07958, and this product by height;
then divide this last product by 3.
Fig. 20
Or,d2 + d'a+£xd'X.7854*-5-3 = V.
Or, c» +c'» + c X c' X .079 58 A -=- 3 = V.
Example. — What is volume of frustum of a cone, drameters
of greater and lesser ends, 6 d, a c, being 5 and 3 feet, and heigb^,
«o,9?
5' + 3^+Tx3 = 49; and 49 X .7854 = 384846 = efbove sum
*, ,854; and 3iiMiii = ..5.4538 «*./«.
I'yramid.
Note. —Volume of a pyramid is equal to one tbird of that of a prism having equal
bases and altitude.
To Compxite Volume of a Pyramid.-" Fig. 81.
Rule. — Multiply area of base by perpendicular height, and
take one third of product.
Example.— What is the volume of a hexagonal pyramid, Fig. 21,
a side, a 6, being 40 feet, and its beigbt, e c, 60?
40' X 2.5981 (tabular mnllipller, page 339) = 4x56.96=: area o/baae.
^}^.^^2i^=.B3 139-^ cia>e feet
3
To Compute Volume of Frustum of a Pyramid.— Fig. 88.
Rule. — Add together squares of sides of greater and lesser ends, and
product of these two sides ; multiply sum by tabular multiplier for areas in
Table, page 339) and this product by height ; then divide last product by 3.
Or, «2 4- «'2 -{-TxP X tab. rnuU. x * -^ 3 = V.
Wheti A teas of Ends are knotcn^ or can bt obtained without reference to
a tabular muiUptkr^ usefoUotvinff.
Or, a-f a'+ \/ax a'X*-T-3 = V.
Example. —What is the volume of the IVustum or a hexagonal
pyramid, Fig. 22, the lengths of the sides of the greater and lesser
ends, ab,cd, being respectively 3.75 and 2.5 feet, and its perpen-
dicular height, 0 o, 7. 5 ?
3.75' + 2.5' = 20.3125 = mm of gqttares of sides of greater and
lesser ends: 2o.3i25'-f-3-75X2.5=29.6875=::afroiM sum (xdded to
product of the two sides ; 29.6875 x 2.5981 X 7.5= 578.48 X tab.
muiLy and o^atn by t!ie height^ which, -^ 3= 192.83 cube feet.
When Ends of a Pyramid are not those of a Rpf/ular Pclygon^ 07' when
Areas of Ends are given
Rule. — Add together areas of the two ends and square root of their prod-
act ; multiply snm by height, and take one third of product.
Or,a + a'4- Vaa^XA^3 = V.
ExAMPLK.—What fs the volume of an irregular-sided fVustum of a pyramid, the
areas of the two ends being 22 and 88 inches, and the length 20?
22 4-88 = iio = «tf}ii qf areas of ends; 22 X 88 = 1936, and >/i936.= 44 =«9uar0
root of product of areas. Then "°"r 44 — 20 _. ,^26. 66 cube ins.
368
MENSURATION OF TOLUMES.
Splierioal Zone (or BVustiain of a Spliere).
Dbfixition. — Part of a sphere included between two parallel chords.
*Fo Compute 'Volvixne of* a Splierioal Zone.— ir*igf. 30.
Defisition.— Part of a sphere included between two parallel planea
Rule. — To sum of squares of the radii of the two ends add one third of
square of height of zone ; multiply this sum by height, and again by 1.5708.
*'»8- 30- Or, r* + r*' -f- A»^ h x 1.5708 = V.
EzAMPLK.— What is the volume of a spherical zone, Fig. 30,
greater and less diameters, /A and d e, being 20 and 15 inches,
and distance between them, or height of zone, cg^ being 10 ins.?
io»-f- 7-5' = 156.25 = sum of squares of radii of the two endsf
156.25 + 10* -^ 3 = 189.58 = above sum added to one third oj
tquare of the height.
Then 189. 58 X 10 X 1.5708 = 2977.9226 cube ins.
Cylindrical IRing.
Dkfinition.— A ring fbrmed by the curvature of a cylinder.
To Coxnpute Volume of* a Csrliudrioal RixiK.^BHs. 31.
Rule. — To diameter of body of ring add inner diameter of ring ; multi-*
ply sum by square of diameter of body, and product by 2.4674.
Fig. 31. Or, TTfW d» 2. 4674 = V.
Or, a 2 = V, a representing area of section ofbody^ and I length
of axis of body..
ExAMPUE.— What is volume of an anchor ring, Fig. 31, diameter
of metal, a &, being 3 inches, and inner diameter of ring, 6 c, 8 ?
3 + 8 X 3' = 99 = product of sum of diameters and square of di-
ameter of body of ring.
Then 99 X a>4674 = 244.2726 cube inn.
Splieroids (X^llipsoids).
DKFnonoM.— Solids generated by the revolution of a semi-ellipse a'oout one of its
diameters. When the revolution is about the transverse diameter they are termed
Prolate, and when about the coi^ugate they are Oblate.
To Compute Volume of* a Sph,eroid.<->F*iK. 3S.
Rule. — ^Multiply square of revolving axis by fixed axis, and this product
by .5236.
Or, a'a'X- 5336 = V, a and a' representing revolving and
faedaxes.
Or, 4-T-3 X 3- 14x6 r* r'sr V, r and r' representing semi-axes.
ExAHPLS.— In a prolate spheroid. Fig. 32, fixed axis, a 5, is
14 inches, and revolving axis, c<l, 10; what is its volume?
xo' X 14 = i4oo=product of square of revolving axis and
fixed (xxis. Then 1400 x • 5936 = 733-04 cube ins.
NoTB.— Volume of a spheroid is equal to 5^ of a cylinder that will circumscribe it
Seipnents of Splieroids.
To Compute Volume orSefirmexit of* a Splieroid.^F^g. 33.
When Base, ef, is Circular^ or parallel to revdrit^ Axis, as cd. Fig. 33,
or as efto Axis a 6, Fig. 34. Rule. — Multiply fixed axis by 3, height of
segment by a, and subtract one product from the other ; multiply remainder
by square of height of segment, and product by .5236. Then, as square of
fixed axis is to square of revolving axis, so is last product to vouime of
segment.
Fig. 32.
MENSURATION OF VOLtJMES.
369
3 g — a ^ fc« X -Saa^ X o"» _ ^
ur, -5 _ V.
EzAifPLX. — In a prolate spheroid, Fig. 33, fixed or trans-
verse axis, a b, is 100 inches, revolving or cui^ugate, c d, 60,
and height of segment, a a, 10; what is its volume?
100 X 3 — 10 X 2 = 280= hm'cc the height of tegment wb-
traded fi-om three times fixed axis; 280 X 10' X .5236 =
X466a8 inches = product of <ibove remainder, square of he^U, and .5236. Then
100* : 60* :: 14669.8 : 5277.888 cube ins.
When Base^ ef, is Elliptical, or petpendicular to rerolciiuj Axis^ a 6, Fig.
33, or as ef to Axis c d^ Fig. 34. Rule. — Multiply fixed axis by 3,
and height of segment by 2, and subtract one from the "other ; multiply re-
mainder by square of height of segment, and product by .5236. Tnen, as
fixed axis is to revolving axis, so is last product to volume of segment
*■'& 34- _ 3 a' — 27* A' X .5236 X a „
JL^ J Or, ^, = V.
Example.— Diameters of an oblate spheroid. Fig. 34, are
100 and 60 inches, and height of a segment thereof is 12;
what is its volume?
100 X^ — 12 X 2 = 276 = twice the height of the segment sub-
^ tractedjrom three times the revolving axis ; 276 X 12^ x 5236
= 20809.9584= product of above remainder, the square of height, and .5236.
Then 100 : 60 :: 20809.9584 : 12485.975 cube ins.
BVasta of Spheroids.
To Coinpute Vol-ame of Alidclle Frustuxn of a Spheroid..—
ITijg. 35.
When Ends^ efand g h, are Circular, or parallel to revolving A 3ns, as c d.
Fig. 35, or a 6, Fig. 36. Rule.— 'To twice s<|uare of revolving axis add
square of diameter of either end ; multiply this sum by length of frustum,
and product by .2618.
Or, 2a'» + d«X/.26i8 = V.
Example. — Middle fVustum of a prolate spheroid, i o,
Fig. 35, is 36 inches in length, diameter of it being, in
middle, cd, 50, and at its ends, e/and g h, 40J what is its
volume f
5o» X 2 + 40' = 6600 = sum of tvfice square of middle di-
ameter added to square of diameter of ends. Then 6600 X
36 X 26x8 = 62 203.68 cube ins.
When EndSj e/and g h, are Elliptical, or perpendicular to revolving Axis,
a b. Fig. 3S^cr ef and g h to Axis, c d. Fig. 36. Rulb. — To twice product
of transverse and conjugate diameters of middle section, add product of
transverse and conj1^^te of either end; multiply this sum by length of
frustum, and product by .2618.
Fig. 36^
Or, d d' X 2 + d c/' rx .2618 = V.
Example.— In middle frustum of a prolate spheroid, Fig.
36, diameters of its middle section are 50 and 30 inches, its
ends 40 and 24, and its length, oi, 18; what is its volume?
50 X 30 X 2 = 3000 = twice product of transverse and con-
jugate diameters ; 3000 + 40 X 24 = 3960 = sum of above
pnduet and product of transverse and cof^jugate diameters
of ends.
Thea 3960 X 18 x .26x8 = x8 661.104 cubcins.
370
MENSURATION OF VOLUMES.
Fig. 38.
Definition. — Elongated or Elliptical rings.
Ifilongated. 01* S^lliptioal Jjizilcs.
To Compute Volume of aix Kloiigated or Klliptioal luink
— ITlgs. 37 axicl 38-
RuLB. — Multiply area of a section of the body of link by its length, 01
circumference of its axis.
Or, a J or c = V.
NoTB.— By Rule, page 353, Ciroumference or length of axis of an Elongated link
= ihe sum of 3.1416 times sum of less diameter added to thickness of ring, and
product of twice remainder of less diameter subtracted from greater.
Also, Circumference or length of axis of an Elliptical ring — square root of half
sum of diameters added to thickness of ring or axes squared x 31416.
Fifr 37* Example.— Elongated link of a chain, Fig. 37, is i inch in diameter
a of body, a 6, and its inner diameters, 6 c and e/ are 10 and 2. 5 inches;
what is its volume?
Area of i inch = .7854 ; 2-5 -h i X 3- 1416 = 10.9956 = 3. 14x6 tima sum
of less diameter and thickness of ring = length of axis of ends; 10 — 2. 5
X 2 = 15 = ttoice reTnainder of the less diameter subtracted from greater
= length of sides of body.
Then ia9956 + 15 = 25.9956 = length of axis of length.
Hence .7854 X 25.9956 = 2a 41 7 ctU)e ins.
2.— EllipMcal link of a chain, Fig. 38, is of the same dimensions as
preceding; what is its volume?
2 3 ll'Vk 2'?
2. 5 -|- 1 -}- 10 4- 1 = 133. 25 = diameter of axes squared ; / 3. 1416
= 25.643 — square root of half sum of diameters squared X 3- 1416 = cir-
cumference of axis of ring. Area of i inch = . 7854.
Then 25.643 x .'7854 = 2a 14 cube ins.
Spherical Sector.
Dbfinition.— A figure generated by the revolution of a sector of a circle about a
straight line through the vertex of the sector as an axis.
Note. — Arc of sector generates surface of a zone, termed base of sector of a
sphere, and the radii generate surfaces of two cones, having a vertex in common
with the sector at the centre of the sphere.
To Compute "Volume of a Splierioal Sector.— ITig. 30.
Rule. — Multiply external surface of zone, which is base of sector, by one
third of the radius of sphere.
Or, o r -f- 3 = V, a representing area of hose.
Note. —Surface of a spherical sector = sum of surface of zone and surfaces of the
two cones
Example.— What is volume of a spherical sector. Fig.
39, generated by sector, e a A, height of zone, a 6 c <l, be
ing ao, 12 inches, and radius, gh^ of sphere 15?
t2 X 94-248 = 1130.976 = height of zone X circumference
of sphere = external surface of zone {see page 350).
1130 976 X 15-T-3 = surface X one third of radiuB =
5654 88 cube ins.
Spindles.
Definition.— Figures generated by revolution of a plane area bounded by a curve,
when the curve is revolved about a chord perpendicular to its axis or about its
double ordinate, and they are designated by the name of arc from which they are
<<enerated, as Circular, Elliptic, Parabolft, etc
Fig 39-
MBNSUEATION OP VOLUMES. 37 1
Circu.lar Spindle.
To Compxite Volunae of a Circular Spindle.— Fig. 40.
Rule. — Multiply central distance by half area of revolving sepnent*,
subtract product from one third of cube of half length, and multiply re-
mainder by 12.5664.
( c X - j X 12. 5664 = V, a representing area of revolving segment
ExAMFLK.— What is volume of a circular spindle, Fig. 40, whec
central distance, o«, is 7.071067 inches, length,/c, 14.142 13, and
radius, oc, lo?
NoTK.— Area of revolving segment; /«, be ng=:sido of square
\ that can be inscribed in a circle of 20, is 20^ x 7854 — 14.142 13"
I -^ 4 = 28. 54 area.
T.orjx 067 X 28. 54-i-2=ioa904i = central distance X haJ/ared of
7.071 67^
revolving segment ; 10a 904 1 = 16. 947 = remainder of
above product and one third of.atbe of ka^ length.
Then 16.497 x 12-5664 = 212.9628 cttbe ins.
Frustum or Zone of a Circular Spindle.*
To Coxxiptite Volmue of a Frustviiii or Zone of a Ciroxilar
Spindle.— Kig. 41.
Rule. — From square of half length of whole spindle take one third of
square c€ half length of frustum, and nmltiply remainder by said half length
01 frustum ; multiply central distance by revolving area which generates
the frustum ; subtract this product from former, and multiply remainder by
6.2832.
2
2 J' _i- 2 I'
Or, 1^9 '■ — X (c X a) X 6. 2832 = V, 2 and t' repretenting lengths of
3 2
Spindle and of frustum^ and a area of revolving section of frustum.
Note. —Revolving area of n*iistum can be obtained by dividing its plane into a
segment of a circle and a parallelogram.
Example. — length of middle fyustum of a circular spindle,
«e. Fig. 41, is 6 inches; length of spindle./j/, is 8; central dis-
tance, o <;, is 3; and area of. revolving or generating segment
is 10; what is volume of frustum f
(8 -r- 2)2 — - ' = 13, and 13 x 3 = 39 = product of —
3 2
length of frustum, and remainder of one third square of half
ler^h of frustum subtracted from square of half length of
spindle ; 39 — 3 x 10 = 9 = product of central distance and area of segment subtracted
from preceding product
Then 9X6, 2832 = 56. 5488 cube ins.
Segment of a Cix*oular Spindle.
To Compnte "VoKimft of a Segment of a Circular
Spindle.— Fig. 4rS.
RuLR. — Subtract length of segment from half length of spindle ; double
remainder, and ascertain volume of a middle frustum of this length. Sub-
tract result from volume of whole spindle, and halve remainder.t
Or, C — c-4-2 = V, C and c representing volume of spindle and middle frustum.
* MIddl* fnMtam of » CircaUr Spindle la.one of tbo vnrioiu formt of cukt.
t This niU U ■m^ieabl* to Mfmont of any Splndlo or anj Conoid, Tolomo of tbo figaro and fnuisp
b«iM <nt obUfaMd.
372 MENSURATION OF VOLUMES.
Fig. 42. Example. — I/ength of a circular spindle, i a, Fig. 42, !»
^ff -..^^ 14. 142 13 inches; central distance, o e, is 7.C7107; radius of
j/^L\ 4*. y.-^a arc, ott, is 10; and length of segment, t c, is 3.53553; what is
»sgjj^ ] / its volume?
*\ T'""/' 14.14213 jr. .J .
\ » ,' 3. 535 53 X 2 = 7.071 07 = double remainder of
\ J / 2
*^ length of segment subtrcbcted from half length of spindle =
length of muldle frustum.
Note. — Area of revolving or generating segment of whole spindle is 28.54 inches,
and that of middle frustum is 19.25.
The volume of whole spindle is 212.0628 cube ins.
" " middle flrustum is 162.8982 " "
Hence 50.0646 -r- 2 = 25.0323 cube ins.
Cycloidal Spindle.*
To Compute "Volume of a Cycloidal Spindle.— Fig. 43.
KuLE. — Multiply product of square of twice diameter of generating circle
and 3.927 by its circuraferenee, and divide this product by 8.
Fiff A.-i —2
\/""-* ^^ 2dX3-927XdX3i4»6 ... s.- ^- , ■
>iC \ Or, Q ^— ^ — = ^ » f^ representing diameter
d(- T-p-.-j-V--' of circle^ or half width of spindle.
Example Diameter of generating circle, a & c, of a cy-
cloid, Fig. 43, is 10 inches; what is volume of spindle, d«?
_2
10 X 2 X 3-927 = ino.%z=i product of twice diameter squared and 3.927.
Then 1570.8 X 10 x 3.1416-7-8=6168.5316 cube ins.
Elliptic Spindle.
To Compute Volume of aii Klliptio Spin die. ^Fig. '^4.
Rule. — To square of its diameter add square of twice diameter at one
fourth of its length ; multiply sum by length, and product by .1309.!
Or, d^-\-2d' 1. 1309 = V, d and d' representing diameters a* above.
Fig. 44. Example. — liCngth of an elliptic spindle, a 6, Fig. 44, is
^ <- 75 inches, its diameter, c d, 35, and diameter, ef at . 25 of its
^x-T ! """v. length, 25; what is its volume?
{^^^^^^^^^^\ 35' -|- 25 X 2 = 3725 = sum of squares of diameter of
r ^^^^^^^ "J ^indle and of twice its diameter at one fourth of its length;
\. J \d J 2725 X 75 = 279 375 = a^ove sum x l/estigth of spindle.
^---..j__.'-' Then 279375 X .1309 = 36570- 1875 cube ins.
NoTK.— For nil such solid bodies this rule is exact when body is formed by a
conic section, or a part of it, revolving about axis of section, and will always be
very near when Qgure revolves about another line.
To Coxnpute "Volume of* Aliddle ITrustxim or Zone of*
an. Slliptio Spind.le.*«B*ig. 4S.
RiTi.K.T— Add together squares of greatest and least diameters, and square
of double diameter in middle between the two ; multiply the sum by length,
and product by .1309. |
3
Or, d^ -\-d'^-{-2 d" i. 1309 = V, d, d\ and d" reprewnting different diameten.
* Volume of x Cycloidal Spindla ia eqaal to .625 of lU circumtcribinK evlinder.
1 8«e pr«c«dinK Note. % See Note ftbove.
MENSURATION OP VOLUMES.
373
«l^45.
ExAMPLR.— Greatest and least diameters, ab and cd, of
the frustum of an elliptic spindle, Fig. ^5, ai'e 68 and 59
inches, its middle diameter, p/t, 60, and its length, e/, 75;
what is its volume?
682 ^_ 50^ -|- 60 X 2 = 21 524 = sum of squares of gi-ecUea
and least diameters and of double middle diameter.
Then 21 524 X 75 X 1309 = 211 311.87 cube ins.
To Compute "Volume of* a Segment of an fClliptio Spin-
dle.—ITig. 40.
Rule. — Add together s^juare of diameter of base of segment and square
of doable diameter in middle between base and vertex ; multiply sum by
length of segment, and product by .1309.*
Or, d?-\-2d" Ix . 1309 = V, (i cmd d" representing diameters.
Fig 46. 1«:xAMPLR. — Diameters, cd and gh, of the segment of an
c..—- »— ...,^ elliptic spindle, Fig. 46, are 20 and 12 inches, and length,
j *\ o«, is 16; what is its volume?
/ 20^ -j- 12 X 2 = 976 = sum of squares of diameter at bafe
" and in middle.
-..J.*-*
Then 976 X 16 X -1309 = 2044. 134 cube int.
I*ara"bolic Spindle.
To Compute Volume of a i*ara"bolio Spindle.— TTig. 47'.
RuLK I. — Multiply square of diameter by length, and the product by
.4i888.t
Or, (Z»2x.4i888 = V.
Rule 2. — To square of its diameter add square of twice diameter at one
fourth of its len.i>th; multiply sum by length, and product by .1309. J
Fig. 47-
Or,d»4-aU'iX.i309 = V.
Example.— Diameter of a parabolic spindle, a b. Fig.
47, is 40 ins., and its length, cd, 10; what is its volume?
40' X 10 = 16 000 = square of diameter X length.
Then 1 6 000 X • 41 8 88 = 6702. 08 cube ins.
Again, If middle diam. at .25 of its length is 30, Then,
ft
by Rule 2, 40' -|- 30 X 2 x 40 X . 1309 = 6806. 8 cube ins.
To Coianpute Volume of* ]VIiddle Frustum of a Parabolic
Spindle.— Fig. 48.
Rule i. — Add together 8 times square of greatest diamet-er, 3 times
square of least diameter, and 4 times product of these two diameters ; mul-
tiply sum by length, and product by .052 36,
Or,d»8 + d^-fdd'X4iX.o52 36=V.
Rule 2. — Add together squares of greatest and least diameters and
square of double diameter in middle between the two; multiply the sum
by length, and product by .1309.
Or, d' -f cT' + 2 d"* i X . 1309 = V, d" represenHng^iameter between the two.
ExAMPLB — Middle n*u8tum of a parabolic spindle. Fig.
48, has diameters, a b and ef, of 40 and 30 inches, and its
length, cd, is 10; what is its volame?
b 40' X 8 + 3o« X 3 + 40 X 30 X 4 = 20 3<» = sum of 8
tim^s square of greatest diameter, 3 times square of least
diameter, and 4 times product of these.
Then ao 300 x 10 X 052 36 = 10629.08 cube int.
• l«fKo(t,)>af«37a.
1 8-M of .7854,
t8««Not«,p«gf97t,
■*'
374
MENSURATION OF VOLUMES.
To Compute "Volume of a Segment of* a ParaTsolio
Spiixdle.— Fig. 49.
RuLK. — Add together square of diameter of base of segment and square
of double diameter in middle between base and vertex ; multiply sum by
height of segment, and product by .1309.
0r,d2 + d"2fx.i3O9 = V.
Flff. 4Q.
** ^ Example.— Segment of a parabolic spindle, Fig. 49, has
^7^.,_-«^x diameters, c/and g h, of 15 and 8.75 inches, and height,
^^'^^l—'V^^^f c d, is 2.5; what is its volume?
V i. 15' -f 8.75 X 2 = 531.25 = sum of square of base and of
double diameter in middle of segment. Then 531. 25 X 2.5
J ---' X .1309= 173.852 cube ins.
Hyperbolic Spindle.
To Compute "Volume of a Hyperl>olio Spindle. ~Fig. SO.
Rule.— To square of diameter add square of double diameter at one
fourth of its length ; multiply sum by length, and product by .1309.*
Or, d= + 2d'ix.i309 = V.
Example.— Length, a 6, Fig. 50, of a hyperbolic spindle
is 100 inches, and its diameters, c d and ef are 150 and
1x0: what is its volume?
150^ -j- 1 10 X 2 X 109 = 7 090000 = product of sum of
squares of greateM diameter and of twice diameter at one
fourth of length of spindJ^ and length. Then 7090000 x
. 1 309 := 928 081 cti^ inches.
To Coxrxpute Volume of A^iddle ITrustum of a Hyper-
l>olio Spindle.— IT'ig. Gl.
Rule. — Add together squares of greatest and least diameters and square
of double diameter in middle between the two ; multiply this sum by length,
and product bv .i309.t
Pigg,. ' Or,d« + d'2-|-(2d'r«X.i309=V.
Example. —Diameters, a b and c d, of middle flrustum of a
hyperbolic spindle, Fig. 51, are 150 and no inches; diam-
eter, g h, 140; and length, ef, 50; what is its volume?
X--'
1502 -f-iio» 4-140 X2=ii3 000 = sum of squares of great-
est and least diameters and qf double middle diameter. Iben
113000X 50 X -1309 = 739585 "mbeins.
To Compute "Volume of a Segment of a Hyperl3olio Spin-
dle.—Fig. 6S.
Rule. — Add together square of diameter of base of segment and square
of double diameter in middle between base and vertex j multiply sum by
length of segment, and product by .1309.
Or, d»+d"»i X. 1309 = V.
Example. —Segment of a hyperbolic spindle. Fig. 53, has
diameters, «/and ^ A, of no and 65 inches, and its length, a b,
25; what is its volume?
110*4-65 X 2 = 29ooo = mm of squares of diameter of base
and ofaov^le middle diameter.
Then 29 000 x 25 x • 1309 = 94 902.5 cube int.
Pig. 52
f &W Note, pag« 37?,
t Ibid.
MBK8UBATI0N OV VOLUMBS.
375
*'ig- 54.
Hillipsoid, ^Paraboloid, and Hyperboloid of Revo-
lution* (Conoids).
Dbfikition. — Figures like to a oooe, described by revolution of a conic section
around and at a right angle to plane of their fixed axes.
Sjllipsoid of Revolution (Sph.ei*oid).
DEFQanov.— An elliptoid of revolution is a semt-sphcroid. (See page 36&)
Paraboloid of Revolu.tion.t
^o Compvite Voluxue of* a> Para'boloid of Revolution."-
Fig. 63.
Rule. — Multiply area of base by half height
Pig. 53. ^ 0r,aA-r-2 = V.
Note. — This rule will hold for any segment of paraboloid,
whether base be ])erpcndicular or oblique to axis of solid.
Example. —Diameter, a b, of base of a paraboloid of revolution,
Fig. 53, is 20 Inches, and its height, d c, 20; what is its volume ?
^ Area of 20 inches diameter of base = 314. 16. Then 314. 16 X
2o-=-2 = 3i4i.6ctt^ ins.
KVustum of a Paraboloid of Revolution.
To Compute Volume of a frustum of a Paraboloid of
Revolution .^Pig. 64.
Rule. — Multiply sum of squares of diameters by
height of firustum, and this product by .3927.
Or,(d«H-(Z'2)AX.3927 = V.
Example. — Diameters, a b and d c, of the base and vertex
of firustura of a paraboloid of revolution, Fig. 54, are 20 and
X1.5 inches, and its height, ef, X3.6; what is its volume?
20^ -|- 1 1 . 5' = 532. 25 = «um of squares of diameters. Then
532.25 X X2.6 X .3927 = a633.5837 cube ins.
Segment of a Petraboloid of Revolution.
To Compute Volume of Segment of a Paral>oloid of Revo-
lution. .••Fig. SO.
Rule. — Multiply area of base by half height.
Or, axfc^Hl=:V.
Note.— This rule will hold for any segment of paraboloid,
whether base be perpendicular or oblique to axis of solid.
Example. — Diameter, a b, of the base of a segment of a para-
boloid of revolution. Fig. 55, is 11 5 inches, and its height, e/ is
7.4 ( what is its volume?
Area of 11. 5 inches diameter of base = 103.869. Then 103.869
X 7-4 -^ 3 = 384-315 cw*« »«*•
Hyperboloid of Revolution.
To Compute Volume of a Hypertooloid of Revolution.
—Pig. oe.
JiuhK. — To square of radius of base add square of middle diameter ; mul-
tiply tUs sam by height, and product by .5256.
• Tb«M fignrai !>•▼• been known m Ckmoidi. For the definition of % Conoid, Me Haaw^t Men
nmOiam, page 233.
lofePa
Fig 55
t Volnme 1
ranboloid of Revolution li = .5 of ite circumference.
376
M£liSU]£ATION OF VOLUMES.
Fig. 56- /
Or, r'+d» *x.S236=V, d rq>resenting middU diametef
ExAHPLB. — Base, a &, of a hyperboloid of revolution.
Fig. 56, is 80 inches; middle diameter, cdj66\ and height,
ef, 60; what is its volume?
80 -T- 2 + 66 * = 5956 = sum of square of radius ofbau and
middle diam. Then 5956 X 60 X • 5236 = 87 113.7 cube int.
Sejocment of a Hyperfeoloid. of Revolution.
To Coiupute Volvime of Segment of a. Hyperboloid of
Revolution, as Fig. G6.
Kui.B. — To square of radius of base add square of middle diameter; mul-
tiply this smn by height, and product by .5236.
Or, r* -f- d"' h X . 5236 = V, r represmling radiut of base.
RxjiiiPi.K.— Radius, a e, of base of a segment of a hyperboloid of revolution, as
Fig 56. is 21 inches; its middle diameter, c cl, is 30; and its height, ef 15; what is
its volume?
21' -|- 30' X 15 = 20 IIS =product of sum of squares of radius of base and middle
diameter mtUliplied by height. Then 20 1 x 5 X • 5236 =110532.214 cuJbe int.
■BVusitnin of a HjrperlDoloid of Revolntion..
To Compute Voluine of Frustum of a Hyperboloid of
K-evolution..— ITigp, OT'.
Rule. — Add (ogether sauares of greatest and least semi-diameters and
square of diameter iu middle of the two ; multiply this sum by height, and
product by .5236.
Or, ( - J + ( - j + d"» /* X . 5«36 = V, d, d', and d" representing several diametert.
Example.— Frustum of a hyperboloid of revolution. Fig.
57, is in height, «i, 50 inches; diameters of greater and
lesser ends, a b and c d, are no and 42 ; and that of middle
diameter, ^ A, is 80; what is volume?
iio-^2 = 55, and 42-=-9 =r 21. Hence 55»+2i'-|-8o'
. =9866=:«um of squares of semi-diameijrs of ends and of
" middle diam. Then 9866 X 50 X • 5236 = 258 291. 88 cube int.
A.ny r^gnire of Revoliation.
To Compute Voluxue of eaxy Figure of Itevolutioxx.^
Fig. OS.
Rule. — Multiply area of generating surface by circumference described
by its centre of gravity.
Or, a 2rp = V, r representing radius of centre of gravity.
Fig- 57- J^
Fig. 58.
'/" • 1
--V3|
iLLrsTRATioN I. — If generating surface, a ft c d, of cylinder,
b e dfy Fig. 58, is 5 inches in width and 10 in height, then will
a b = 5 and 6 d = 10, and centre of gravity will be in o, the ra-
dius of which is r o = 5 -=- 2 = 2. 5. Hence 10 X 5 = 50= area
of generating surfaoe.
a f"'*- 59-
Then 50 X 2.5 X 2 X 3- M^^ = 785-4 = «»*««
'.Tr.-.rJ f of generating surface X circumference of its
',"''" J centre ofgramty = volume of cylinder.
Proof. r- Volume of a cylinder 10 inches in diameter and 10
Inches in height. 10* x .7854 = 78.54, and 78.54 x 10 = 785.4.
2. —If generating surface of a cone, Fig. 59, is a e = 10, d e ^
5, then will ad = 11. 18, and area of triangle = 10 x 5 -j- 2 = 25,
centre of gravity of which is in o, and o r, by Rule, page 607, d
=: 1.666.
Hence, 25 x 1666 X 2 X 31416 = 261.8 = area of generating surface X cireun^
rence of its centre of gravity = volume of cone.
MBNSUBATION OF VOLUMES. 377
3. —If generating snrfl&ce of a sphere, Fig. 60, Is a be, and ae
= 10, a 6 c will be (— ] = 39.27, centre of gravity of
\ which is in 0, and by Rule, page 607, 0 r = 2. 122.
/ Hence, 39. 27 X 2. X22 X 2 X ^. 1416 = 523. 6 = area of generat-
J ing surface X circumference of its centre of gravity = volume oj
y gj^ere.
Irregulai? Sodies.
To Compute "Vol-unae of an Irregular Body.
Rule. — Weigh it both in and out of fresh water, and note difference in
lbs. ; then, as 62.5* is to this difference, so is i728t to number of cube inches
in body.
Or, divide difference in lbs. by 62.5, and quotient will give volume in
cube feet
Note.— If salt water is to be used, ascertained weight of a cube foot of it, or 64, is
to be used for 62. 5.
ExAMKLK.— An irregular-shaped body weighs 15 lb& in water, and 30 out; what
is its volume in cube inches?
30 — 15 = 15 = difference ofvoeights in and out of water.
62.5 : 15 :: 1728 : 414.72 = vo2um« in cube ins.
Or, 15 -i- 62. 5 = .24, and .24 x 1728 = 414. 72 ^ volume in cube ins.
CASK GAUGING.
"Varieties of Casks.
To Coxnpvite Volume of a Cask.
i8t Variety, Ordinary form of middle frustum of a Prolate Spheroid.
This class comprises all casks having a spherical outline of staves, as Rum
puncheons, Whiskey barrels, etc.
Rule. — To twice square of bung diameter add square of head diameter ;
multiply this sum by length of the cask, and product by .2618, and it will
give volume in cube inches, which, being divided by 231, will give result in
gallons.
2d Variety, Middle frustum of a Parabolic Spindle.
This class comprises all casks in which curve of staves quickens at the chime,
as Brandy casks and Provision barrels.
Rule. — ^To square of a head diameter add double square of bung diam-
eter, and from sum subtract .4 of square of difference of diameters ; multiply
remainder by length, and product by .2618, which, being divided by 231,
will give volume in gallons.
3d Vaanety, Middle frustum of a Paraboloid.
This class comprises all casks in which curve of staves quickens slightly at
bilge, as Wine casks.
Rule. — ^To square of bung diameter add square of head diameter ; mul-
tiply sum bv length, and product by .3927, which, being divided by 231,
will give volume in gallons.
4^ Variety, Two equal frustums of Cones.
This class comprises all casks in which curve of staves quickens sharply at
bilge, as Gin pipes.
Rule. — Add square of difference of diameters to three times square of
^eir sum ; multiply sum bv length, and product by .06566, and it will give
volume in cube inches, which, oeing divided by 231, will give result in
gallons.
* Weight of ft enbe foot of firwh mXtx, f Nomber of Inches In » cobe foot.
T tft
378 MKW8U RATION OP VOLUMES.
Examplk.— Bung and bead diameters of a cask are 24 and 16 inches, and length
36; what is its volume in gallons?
24 — 16 + (24 4-16)^X3 = 4864, which X 36 = 175 K04, and 175104 x.065 66 =
II 497.339« which -i- 231 = 49- 77 gallon*.
Generally.
Dd~pM^ .001 692 L — U. S. gaiUms, and .001 416 2 = Imperial gallons.
D, d, and M representing interior, head and bung diatneters, arui L length of cask
in inches.
Xo Ascertain M.ean Diameter of a Caalz.
RuLR. — Subtract head diameter from bun^ diameter in inches, and mul-
tiply difference by followinjij units for the four varieties; add product to
bea(l diameter, and sum will give mean diameter of varieties required.
ist Variety 7 I 3d Variety 56
2d Variety 68 | 4th Variety 52
ExAMPLK.— Bung and head diameters of a cask of ist variety are 24 and 20 inch-
es; what is its mean diameter?
24 — 20 = 4, and 4 X • 7 = 2- 8, which, added to 20, = 22.8 ins.
ULLAG£ CASKS.
Xo Compute Volume of XJllage Casks.
When a cask is only partly filled,' it is termed an ullage ccuk, and is con^
sidered in two positions, viz., as lying on its side, when it is termed a Seg-
ment Ufing^ or as standing on its end, when it is termed a Segment Standing.
Xo Ullage a I-iyilig Caelt.
Rule. — Divide wet inches (depth of liquid) by bung diameter ; find quo-
tient in column of versed sines in table of circular segments, page 267, and
take its .corresponding segment; multiply this segment by capacity of cask
in gallons, and product by 1.25 for ullage required.
Exam PLK. — Capacity of a cask is 90 gallons, bung diameter being 32 inches; what
is its volume at 8 inches depth? ^
%-r- 12 = .iS'.taJb. seg. of which {8.153 55, which X 90 = 13.8195, and again X 1.25 =
17.2744 gallons.
Xo Ullage a Standing Cask.
Rule. — Add together square of diameter at surface of liquor, square of
head diameter, and square of double diameter taken in middle between the
two; multiply sum by wet inches, and product by .1309, and divide by 231
for result in gallous.
Xo Compute Volume of a Cask \>y F'our Dimensions.
Rule. — Add together squares of bung and head diameters, and square of
double diameter taken in middle between bung and head; multiply the sum
by length of cask, and product by •1309, and divide this product by 231 for
result in gallons.
Xo Compute Volume of ansr Cask fVom Xliree Dinaen-
.sions onlsr.
Rule. — Add into one sum 39 times square of bung diameter, 25 timea
square of head diameter, and 26 times product of the two diameters ; mul-
tiply sum by length, and product by .008 726 ; and divide quotient by 231
for result in gallons.
For Rules in Gauging in all its conditions and for description and use of
instruments, see HofweU's Mensuration^ pages 307-23.
CONIC 6ECTI0NS.
379
CONIC SECTIONS.
A Con^ is a figure described by revolution of a right-angled triangle
about one of its legs, or it is a solid having a circle for its base, and
terminated in a vertex.
Omic Sections are figures made by a plane cutting a cone.
If a coiw Is cat by a plane through vertex and base, section will be a triangle,
and if cut by a piano parallel U> its base, section will be a circle.
Axi* is line about which triangle revolves. Base is circle which is described by
revolving base of triangle.
Fig. I. y\ 'An ^aiipde is a figure generated by an oblique plane cut-
ting a cone above its base.
Trturuvarse axia or diameter is longest right line that can be
drawn in it, as a b^ Fig. x.
Car^fugate axis or diameter is a line drawn
through centre of ellipse perpendicular to trans*
verse axis, aiacd.
A Parabola is a fij^ure generated by a
plane catting a cone ^utrallel to its side, as a 6 c, Fig. 2.
Axit is a right line drawn fVora vertex to middle of base, as 60.
NuTK. — A parabola has not a coqjugate diameter.
A Hyperhda is a figure generated by a plane
cuttin;; a cone at any angle with base greater than that of
side of ctme, as a b c, Fig. j.
TVansverse axis or diameter, o 6, is that part of axis, e 6, which,
if continued, as at o, would join an opposite cone, ofr.
GoiyngaU axit or diameter is a right line drawn through centre,
g^ or transverse axis, and perjwndicular to it.
Straight line through foci is indefinite transverse axis; that part
of it between vertices of curves, as o 6, is detlnite transverse axis.
Its middle point, g^ is centre of curve.
Eccenti-icity of a hyperbola is ratio obtained by dividing distance from centre to
either /octM by semi-transverse axis.
Parameter is cord of curve drawn through ^britf at right angles to axia.
Asymptotes of a hyperbola are two right lines to which the curve continually ap-
proaches, touches at an infinite distance but does not pass; they are prolongations
of diagonals of rectangle constructed on extremes of the axea
Two hyperbolas are conjugate when transverse axis of one is coAjugatQ of the
other, and contrariwise.
Oeneral X>efinitious.
An Ordinate is a right line fVom any point of a curve to either of diameters, as
a« and do. Fig. 4, and ab and d/, are double ordinates; cb. Fig. 5, is an ordinate,
and a 6 an abscissa.
An Abscittsa is that part of diameter which is contained between
vertex and an ordinate, as ce, ^o, Fig. 4, and a b,
Fig. 5-
. . Parameter of any diameter is equal to four times
l^ distance from focus to vertex of curve; parameter
'^ of axis is least possible, and is termed parameter
of curve.
Parameter of curve of a eon'c section is equal
to chord of curve drawn through focus perpendic-
alar to axis.
Pamn,eter of transverse axis is least, and is termed parameter of t^urve.
Paramder of a conic section and fod are sufficient elements for construction
of carve
38o
CONIC SECTIONS.
A Focut Is a point on principal axis where double ordinate to axis, through point,
is equal to parameter, as e/, Fig. 5.
It may be determined arithmetically thus: Divide square of ordinate by four
times abscissa, and quotient will give focal distances, as and », in preceding figures.
Fig. 6. Directrix of a conic section is a right line at right angles to
p. I ^ migor axis, and it is in such a position that
/: g::u : o.
Here a d, Fig. 6, is directrix, and o is offset to directrix.
L<iUis Rectum, or principal parameter, passes through a focus;
it is a double ordinate, which is a third proportion to the axis.
Or, A: a::a:1j.
A and a representing major and minor asxs. (See UasweWs
Mensuration^ I)age 232.)
A Conoid is a warped surface generated by a right
line being moved in such a manner that it will touch
a straight line and curve, and continue parallel to a
given plane. Straight line and cur\'e are called di-
rectiices^ plane a plane directrix^ and moving line the
genei'oirix.
Thus, let a h a\ Fig. 7, be a circle in a horizontal plane,
and d d* projection of right lines perpendicular to a ver-
tical plane, r' 6 e ; if right lines, da,rs^r*b, r" «, and d' a,
be moved so as to touch circle and right line d d' and be
constantly parallel to plane r' 6 e, it will generate conoid
daha' d ,
Radii vecUyres are lines drawn from, the foci to any point in the curve; hence a
raditu vector is one of these lines
Traced angle is angle formed by the radii vectores and the transverse diameter.
EUipaoidf Paraboloid^ and Hyperboloid of i^evo/u^ton— Figures generated
by the revolution of an ellipse, parabola, etc., aroimd their axes. (See i/en-
surcUion 0/ Surfaces and Solids, pages 357-75.)
Note i. — All figures which can possibly be formed by cutting of a cone are men-
tioned in these definitions, and are five following— viz., a lYiungle^ a Circlej&n El-
lipse^ a ParaboUtj and a Hyperbola ; but last three only are termed Conic Sections.
2. — In Parabola parameter of any diameter is a third proportional to abscissa
and ordinate of any point of curve, abscissa and ordinate being referred to that
diameter and tangent at its vertex.
3.->-Ib ElMpse and Hyperbola parameter of any diameter is a third proportional
to diameter and its coi^ugate.
To IDeterxniiie Parameter of an. Ellipse or Hyperbola.
RuLK. — Divide product of cotgugate
diameter, multiplied by itself, by trans-
verse, and quotient is equal to para-
meter.
** In annexed Figs. 8 and 9, of nn Ellipse
and Hyperboles, tmnsverse and conjugate *^
diameters, ab^cd^ are each 30 and 20.
Then 30 : 20 :: 20 : 13.333 ^parowicter.
Parameter of curve = e/, a double ordinate passing through
fbcuB, s,
iBllipse.
To Describe Kllipses. (See Geometry, page 226.)
To Compute Terms of* an Kllipse.
When any three of four Terms of an Ellipse are given, viz.. Transverse
and Coujvyate Diameters, an OrdinaU^ and its Abscissa, to ascerfain remattt-
•n^ Terms.
r
Fig. 9.
CONIC SECTIONS. 38 1
To CoTnp-ute Ordinate.
Traruwrse and Cot^ugate Diametera and Abscissa being given. Rulk. — As trans-
verse diameter is to coiijugate, so is square root of product of absciasHB to ordinate
which divides them.
Example. —Transverse diameter, a b, of an ellipse, Fig.
xo, is 25; coi^ugate, c d, 16; and abscissa, at, 7; what is
length of ordinate, t « ?
25 — 7 = 18 less abscissa ; Vt~X 18 = 1 1.225.
Hence 25 : 16 :: 11.225 : 7.184 ordinate
Or, \/c'— (-7-) =any ordinate^ c and t representing
semi-cofyugate and transverse diameUrSy and x distance of ordinate from centre of
figure.
rTo Compute A.'bscissaB.
Transverse and ConjugaJie Diameters and Ordinait being given, Rulr. — As conju-
gate diameter is to transverse, so is square root of difference of squares of ordinate
and semi-conjugate to distance between ordinate and centre; and this distance be-
ing added to, or subtracted from, semi-transverse, will give abscissas required.
ExAJii'LK.— Transverse diameter, a b, of an ellipse, Fig. 10, is 25; conjugate, cd,
16; and ordinate, t«, 7.184; what is abscissa, ibf
y/^' — 7. 184^ = 3. 519 943. Hence, as 16 : 25 : : 3. 52 : 5. 5.
Then 25-4-2= 12.5, and 12.5+5-5 = 18 = 6 i, ) ^^cissat.
35-:r2=:ia.5, and 12.5 — 5-5= 7 = «*)i
To Coinpute Transverse Diameter.
Coi^jugate, Ordinate, and Abscissa being given. Rulb. — ^To or f^om serai-coi\Ja>
gate, according as great or less abscissa is used, add or subtract square root of dif-
ference of squares of ordinate and semi -conjugate. Then, as this sum or diflference
is to abscissa, so is conjugate to transverse.
Example. — Conjugate diameter, cd, of an ellipse. Fig. 10, is 16; ordinate, i «,
7.184; and abscissffi, b i, t a, 18 and 7; what is fength of transverse diameter?
V(i6-^2)»— 7.184=* = 3. 5«.
i6 -H 2 -|- 3. 52 ; 18 :: 16 : 25; 16-5-2 — 3.52 : 7 :: 16 : 25 transverse diameter.
To Compute Conjugate IDiameter.
Transverse, Ordinate, and Abscissa being given. Rulk. — As square root of prod-
uct of abscissae is to ordinate, so is transverse diameter to conjugate.
Example. —Transverse diameter, a b, of an ellipse, Fig. 10, is 25; ordinate, t«,
7. 184 ; and abscissae, 6 1 and i a, 18 and 7 ; what is length of conjugate d anieter ?
Vx8 X 7 = II 225- Hence 11.225 • 7 ^84 :: 25 : 16 conjugate diameter.
To Compute Cirouxnfereiioe of aii £^llipse.
Rule. — MuUiply square root of half sum of the squares of two diameters by
3. 1 4 16.
Example. ^Transverse and conjugate diameters, a b and cd, of an ellipse. Fig. xo,
are 24 and 20; what is its circumference?
24' "+- 20'
= 488, and ^488 = 22.09. Hence 22.09 X 3. 1416 = 69. 398 circumference.
To Compute A.rea of an. Slllipse.
Rule.- Multiply the diameters together, and the product by .7854. Or, multiply
one diameter by .7854, and the product hy the other.
Example.— The transverse diameter of an ellipse, a ft, Fig. 10, is 12, and its con-
jugate, cd, 9; what is its area?
12 X 9 X -7854 = 84. 8232 area^
Hem. — Area of an ellipse is a mean proportional between areas of two circles,
diameter of one being major axis and of the other minor axis.
Illustration. — Area of circle of 40 = 1256. 64 ; area of ellipse ^o x 20 = 628. 32 ;
area of circle of 90 = 314.16, mean of the two circles 1256.64-}- 314. 16 = 785.4.
Therefore the conjugate diameter of an ellipse of an area of 785.4 sq. Ins., Us XXW»
Y«ne being 40, is 35 /«e<, as 40 x 35 x .7854 = 785.4 sq. iiw.
382
COKIC ^XCXIONS.
Fig II
Sesxxient or an Slllipse.
1?o Compute ^rea of a Segmei^t of* an. BUipse.
When its Base is paraUel to either Axis, as e if. Rulk. — Divide height of seg-
ment, b », by diameter or axis, a b, of which it is a part, and find in Table of Areas
of Segments of a Circle, page 267, a segment having same versed sine as this qoo-
tient; then multiply area of segment thus found and the
axes of ellipse together.
Example.— Height, frt, Fig. 11, is 5, and axes of ellipse are
30 and 20; what is area of segment?
5 -r- 30 = . 1666 tabular versed tiney the area 0/ which
(page 267) «. 085 54.
Hence .085 54 x 30 x ao= 51.394 area.
rVo A.8oertain L^ength. of an TClliptio Cuirve -vcrliioh is less
111 ail lialf of entire Figure.
Let curve of which length is required be A b C,
Fig. 12.
Extend versed sine 6 d to meet centre of curve in e.
Draw line e C, and from e, with distance « b, describe
b h\ bisect A C in t, and from «, with radius « », de-
scribe k t, and it is equal to half arc A 6 C.
Xo A.soertaixi X^eiistU '^vlien Curve is greater tlxaii lialf
entire Figure.
Ascertain by above problem curve of less portion of figure; subtract it flrom cir.
cumference of ellipse, and remainder will be length of curve required.
FsLralyolsu
To I>esoril>e a Faral>ola. (See Geometiy, page 229.)
fFo Compute either Ordinate or A-bsoissa of a Parabola.
When the other Ordinate and Abscissas, or other Abscissa and Ordinates are
given. Rulk. —As either abacissa is to square of its ordinate, so is other abscissa to
square of its ordinate.
Or, as square of any ordinate is to its abscissa, so is square of other ordinate to
ExAMFLB I.— Abscissa, a 6, of parabola, Fig. 13. is 9; its ordi-
nate, 6 c, 6; what is ordinate, d e, abscissa of which, a d, is 16 ?
Hence 9 : 6^ : : 16 * 64, and >/64 = 8 length.
2.— Abscissae of a parabola are 9 and 16, and their correspond-
ing ordinates 6 and 8; any three of these being taken, it is re-
quired to compute the fourth.
I. ^'^'^ = 8ord«nate.
9
«6X6a , . ._ 9X8=
3. —^^—-gUssabsciSia. 4. ^-^r-"~
,. ^ — _z = 6 ordinaU.
10
= itahscisgCL
8«
I>ara"bolio Curve.
To Compute ILien^^tlx of Curve of a Parabola out off "by
a X>ouble Ordinate.^^F'ig'. 13.
RuLS.— To square of ordinate add — of square of abscissa, and square root of
this sum, multiplied by two, will give length of carve nearly.
EzAMPUt.— Ordinate, d e, Fig. 13, is 8, and its abscissa, ad, 16; what is length of
curve, /a e?
iX 16'
5' + ' = 405- 333. «»»<^ V405 333 X 2 = 40. 267 Im^h.
CONIC SECTIOKS. 383
Fie. 14. A ^^ Compute A.rea of a £'aral>ola.
RuLB.— Maltiply base by height, and take two thirds of prodact
Corollary.— h parabola is two thirds of its circumscribing par-
allelogram.
Example.— What is area of parabola, a 6 c, Fig. 14, height, de,
being 16^ and base, or double ordinate, a c, 16 r
2
16 X x6 = 356, and — of2$t = X7a667 carea.
To Compute Aj*ea of* a Segment of a Paral>ola.
RuLK.— Multiply difference of cubes of two ends of segment, a c, d/, by twice its
he^ht, e o, and divide product by three times difference of sciaares of ends.
ExAMPLK.— Ends of a segment of a parabola, a c and df. Fig. 14, are 10 and 6, and
beigbt, e o, is to; what is its area?
10' 'V 6^ X 10X2 = 15 680, and -i- id=*'v6*X 3 = 81.667 area.
NoTK. — Any parabolic segment is equal to a parabola of the same height, the hose
of which is equal to base of segment, increased by a third proirartional to snm of
the two ends and lesser end.
Il3rper"bola.
To I>e8oribe a Hyperbola. (See Geometry, page 33a)
To Compute Ordinate of* a Hyperbola,
Traruverse and Covyugate Diameters and AbscUscR being given. Rulb.— As trans-
verse diameter is to conjugate, so is square root of product of abscissae to ordinate
required.
Fig. 15. ^ EXAXPLB. —Hyperbola, abc^ Fig. 15, has a transverse
diameter, a t, of 120; a conjugate, d/, of 72 ; and abscissa,
a e, 40; what is the length of ordinate, e c?
40 -|- ISO = 160 greater abscissa^ and
120 : 72 : : y/Uo X (60) : 48 ordinate.
Nora I.— In hyperbolas lesser abscissa, added to axis
(the transverse diameter), gives greater.
3. — Difference of two lines drawn nrom^bctof any hyperbola to any point in curve
Is equal to its tnuDSverse diameter.
To Compute .Absolssaey
Trantwne and ComguifaU Diameters and Ordinate being given. Ruls.— As con-
Jugate diameter is to transverse, so is square root of sum of squares of ordinate and
semi-coi^jugate to distance between ordinate and centre, or half snm of abscissae.
Then the sum of this distance and semi-transverse will give greater abscissa, and
their difference the lesser abscissa.
EzjuiPLK.— Transverse diameter, a t, of a hyperbola, Fig. 15, is 120; coi^ugate, cf/
73 ; and ordinate, < c, 48 ; what are lengths of abscissae, t e and aei
73 : 180 : : ViS' + (72 -i- 2)' = 60 : xoo ha^sum o/abtcissce, and 100 -f- (zso-j- 3) =
160 greater abtciua^ and 100 — (i30-f- 3) = 40 lesser cU>scissa.
To Conapute Conjugate X>iameter,
JYanstserse Diameter^ Abscissa^ and Ordinate being given. Ritlb.— As square root
of product of abscissae is to ordinate, so is transverse diameter to ceiyugate.
Example.— Transverse diameter, at, of a hyperbola, Fig. 15, is 120; ordinate, e«»
48; and atacissflB, te and a«, 160 and 40; what is length of conjugate, dfJ
V40X 160=80 : 48 :: I30 : 73 ofnyugale.
384 CONIC SECTIONS.
To Coxnp-ate Transverse Diameter,
Contjugate^ OrdinaU^ aatd an Abscissa being given. Rclb. — Add square of ordinate
to square of seroi-coi^Jugate, and extract square root of their sum.
Take sum or diflerence of semi-cotOngate and this root, according as greater or
lesser abscissa is used. Then, as square of ordinate is to product of abscissa and
conjugate, so is sum or difference above ascertained to transverse diameter required.
NoTK. — When the greater abecissa is used, the difference is taken, and con-
trariwise.
ExAMPLK.— Coi^ngate diameter, d/, of a hyperbola. Fig. 15, is 72; ordinate, e c,
48; and lesser abscissa, a e, 40; wnat is length of transverse diameter, a <?
V'48* + (73 -7- 2)2 = 60, and 60 -{- 7a -ir 2 = q6 lesser abscissa^ and 40X73=3880.
Hence, 48^ : 3880 :: 96 : 120 transverse diameter.
To Compute Xjengtli of any A.ro of a Hyperbola, com-
menoin^; at "Vertex.
RnLB.— To 19 times transverse diameter add 21 times parameter of axis.
To 9 times transverse diameter add 21 times pamrauicr, and multiply each of
these sums respectively by quotient of lesser abscissa divided by transverse di-
ameter.
To each of products thus ascertained add 15 times parameter, and divide former
by latter; then this quotient, multiplied by ordinate, will give length of arc, nearly.
Note.— ro ComptUe Parameter^ divide square of coiijugate by transverse diam-
eter.
Fig. 16.^^ ExAXPLB.— In hyperbola, abc. Fig. x6, transverse diameter is 120,
conjugate. 72, ordinate, e c, 48, and lesser abscissa, a e, 40; what is
length of arc, a 6 ?
^ = 43.2 parameter. x3oX 19 + 432X21 X -^ = 1063.4.
40
120x9 + 43.3X31 X -- =663.4. Then 1062.4 + 43.3 X IS -r- 662. 4
120
^ + 43.3 X 15 = 1.305. which X 48 = 62.64 length.
Note — As transverse diameter is to conjugate, so is conjugate to parameter.
(See Rule, page 380. )
To Compute .A.rea of a Hyperbola,
Transverse, Conjugate, and Lesser Abscissa being given. Rdle. — ^To product of
transverse diameter and lesser abscissa add five sevenths of square of this abscissa,
and multiply square root of sum by 21.
Add 4 times square root of product of transverse diameter and lesser abscissa to
product last ascertained, and divide sum by 75.
Divide 4 times product of coiuugate diameter and lesser abscissa by transverse
diameter, and this last quotient, multiplied by formor, will give area, nearly.
Example. — Transverse diameter of a hyperbola, Fig. 16, is 60, conjugate ^6, and
lesser abscissa or height, a«, so; what is area of tlgure ?
60 X 30+ — of 30* = 1485.7143, and y/i4Ss.7H3 X si = 809.43, and ^60X20 X
7
4 + 809. 43 = 901.02, which -r- 75 = 12.0136 and ~ — ^- X 13.0136 = 576.653 arfOL
Nbn.— For ordiaatM of • pvaboU in dlTiiioni of eigfaUu and tentba, Me pag« 229.
X>elta Aletal.
Delta Metal is an improved composition of Aluminium and its alloyR ; it is
non-corrosive, capable of being cast, forged, and hot roiled.
Tensile Strength per 8q, Inch,
Cast in green sand 48 380 lbs.
Rolled, hard 75260 **
I Rolled, annealed 60920 ]|>a
Wire, No. 33 WG 140000 "
PLANS TEIGONOMETBT. 385
PLANE TRIGONOMETRY.
By Plane Trigonometry is ascertained how to compute or determine
four of the seven elemeuts of a plane or rectilinear triangle from the
other three, for when any three of them are given, one of which being
a side or the area, the remaining elements may be determined ; and
this operation is termed Solving the 7'riangle.
The determination of the mutual relation of the Sines, Tangents, Secants,
etc, of the sums, ditferences, multiples, etc., of arcs or angles is also classed
luider this head.
For Diagram and Ejqplanation of Terms^ see Oeometry^pp. 219-21.
liiglit-angled. HPriangles.
For Solution hy Lines and Areas^ see Mensuration of Areas, IdneSj
and Surfaces^ pp. 335-39.
rPo Compute a Side.
When a Side and its OpjKmle Angle is given. Rule. — As sine of angle
opposite given side is to sine of angle opposite required side, so is given side
to required aide.
To Cotnprt'te an A.xigle.
Rule. — As side opposite to given angle is to side opposite to required
angle, so is sine of given angle to sine of required angle.
To Compute Base or Perpendicular in a Riglit-angled
Xria,ixj$le.
When Angles and One Side next Riykt Awjile are given. Rule. — As ra-
dius is to tangent of angle adjacent to given side, so is this side to other side.
To Compute tlie otlxer Side.
When Two Sides and Included An^le are given. Rule. — As sum of two
given sides is to their difference, so is tangent of half sum of their opposite
angles to tangent of half their difference ; add this half difference to half
sum, to ascertain greater angle ; and subtract half difference from half sum,
to ascertain less angle. The other side may then be ascertained by Rule
above.
To Compute A.ngles.
When Sides are given. Rule. — As one side is to other side, so is radius
to tangent of angle adjacent to first side.
To Compute an Angle*
When Three Sides are piven. Rule i. — Subtract sum of logarithms of
sides which contain required angle, from 20 ; to remainder add logarithm
of half sum of three sides, and tlmt of difference between this half sum and
Mide opposite to required angle. Half the sum of these three logarithms is
logarithmic cosine of half required angle. The other angles may be ascer-
tained by Rule above.
2. — Subtract sum of logarithms of two sides which contain required
angle, from ao, and to remainder add logarithms of differences between
these two sides and half sum of the three sides. Half result is logarithmic
sine of tialf required angle.
NoTK.^ — In all ordinary cases either of these rules will give suflBciently accurate
resulta Rule x should be used when required angle exceeds 90°; and Rule 2 when
It 18 less than 90^
Kic
386
PLANE TRIGONOMETRY.
ExAMPLK — The Bides of a trUngfle are 3, 4, amd 5; viiat are the fthgles of th*
bypothenufie?
20 — (Log. 4 = .60206 + Log. 5 = .69897) = 18.69897; Log. 3-f44-5-r-2 — 4 =
.30103; ftnd Log. 3-f-4-H5-H2 — 5 = 0.
Then 18. 698 97 + . 301 03 = 19, which -r- 2 = 9. 5 = log. sin. of half angle = iS^ 26',
which X 2 = 36° 52' angle.
Hence 90° — 36° 52' = 53** 8' remaSnUig angU.
In following fignres, z and a :
A = 90P, 8 = 450,0=450, Radius = i, Secant = i. 4142, GoBine =. 707*1 Sin. 45°
= .7071, Taiigent = i, Area=.25.
By Sin., Tan., Sec, etc., A B, etc., is expresaed Blue, Tangent, Secant, etc, of
angles, A, B, etc
To Cotnpvite Sides A C and B C— Figs. 1 and S.
When Hyp.^ Side B A, and Angles B and C are given.
Sin. B )«( B A
Sin.C"
B A X Cot. C = A C.
Hyp. xCos. C = AC.
Hyp X Sin. B = A C.
BA
Fig. I.
= AC.
iff
Goeine. A Vera.
Sin. C
AC
Sia.B
= BC.
= BC.
To Compute Side A C ajtid Angles.
When Hyp. and Side B A are ^>eit.— Fig. i and a.
AC
Hyp.
= Sin. B.
BA
Hyp.
= SiB.C.
B Ax Sin B
Sin. C
= AC.
B C X Sin. B = A G
AC
BA
To Compute Side B C and Hyp. or Angles.
When both Sides are ^ren.— Fi|;. a.
= Tan. B. J?r^; = BC. Va C^ 4. b~a^ = B C. ^ = Tan.a
Sin.C
BA
BC
AC
= Sin.C.
- ? = Sin. a
B C ° "• "■
«g3.
To Compnte Sides.— Figs. 3 and 4.
^ When a Side and an Angle are vjg. 4.
given.
B C X Cos. B = B A
B C X Sin. B = A C.
A B X Sec. B = B C.
^ ACxTanC „, ACxSin.C _. . .
Bad. Sin. B
i
C EadJuB. A ACxSec. C _- A C x Bad. __ O
— Rad.—^^^ "~Sin B~ = ®^-
Tan^rent. A
In B A C, Fig. 5, a ripfht-aiiffled trianpfle, C A, is assumed to be radius^
B A tangent of C, and B C secant to that radius ; Or, dividlDg each of these
V base, there is obtaiued the taujient and secant of C respectively to radius z«
FLANK TBIGONOMBTBY.
38;
Radias C A = I
Secant €6 = 1.4x43
Taogeot A B = I
Co-secant C B = 1.4143
Co-tangent 06 = 1
VA'ja-|-BA2 = hyp. B C.
AC-;- Cos. C = hyp. B C. :
/2 Area _ . Cos. C - . „
v/n ^=Rad. — — - = CoiC
V Tan. C Sm. C
B =
Sin. C
BAXSeo.
B A X Cot. C = Kad.
B C X Sin. C = B A.
1 -r- Sin. C = Cosec. 0.
Cos. C -r- Sin. C = Cot C.
B C X Cob. C = Rai
B A X Tan. B = Rad.
BC-7-BA = Sec. B.
BCxCo&B=BA.
Trigonometrical I<iq.\iivaleiits,
Sine dg=s_.yoji
Cosine Cg or od= .7071
Versed sine gA=: .2929
Co- versed sine o « = •29i9
Angle CAB=9o''
BA-^Sin. C = hyp. BC.
i-^Tan. C = Cot.C.
B C» X Sin. a C ^
4
BC.
BCxSin. B=Rad.
A C X Tan. C = B A.
I — Sin. C = Co-ver. sia
CBxSin. B=rAG.
Perp. -t-hyp. =Sln. C.
Base -T- hyp. = Coa C.
Base -i- hyp. = Sin. B.
Base ~- perp. = Cotan. C.
^ V (I — sin. 2) = Cos.
^ Sin. -T- tan. = Cos.
Sin. X cot. = Cos.
Sin. -i" COS. = Tan.
Cos. -H cot = Sin.
Coa -r- sin. :±: Cot
. Hyp. -f- base = Sec. C.
Base -r- perp. = Tan. B.
Perp. -f- hyp. = Coa B.
Hyp. — Base == Versln.
Tan. -r- sin. = Sec.
Tan. -r- sea = Sin.
Tan. X cot = Rad.
V(i--coa2) = Sin.
I -r- cot = Tan.
I -r- sin. = Cosec.
Perp. -r- base = Tan. C.
Hyp. -r- perp. = Sec. R
Hyp. -i- perp. =s Cosea 0.
Hyp. — Perp. = Cover, sin. C.
-T- coa = Sec
-r* cosec. = Sin.
-T-sec. s=Coa
— coa = Versin.
— sin. = Co-ver.sin.
-T- tan. = Cotan.
Illustrations. —Assume side A B of a right-angled triangle is 100, and angle C
53° 8'; what are its elements?
Fig. 6
Ol3liqi2e-ansled. rFriansles.
a?o Compute Sides B A and B C.
When Side A C and Anyles are given. — Fig. &
Sin. C X A 0
Sin. B
= BA.
Sin. A X A C
Sin B
Sin. C X B C
Sin. A
= B A.
= BC.
rFo Compute iVngled and Side A C.
When Sides A B, B C, and one of the Angles are given. — Fig. 6,
BCxSin. B
AG
t-'ig 7-
= Sia. A.
Sin. G X A C
BA
Sin. BxBC
Sin. A
= Sin. B.
A B X Sin. B
AC
= Sin. 0.
= Aa
To Compute Sides B A and B C.
Wfien Side A C and Angles are given, — Fig, 7.
Sin. C X B C
= BA.
Sin. A X A G
=fBG.
Sin. A ' Sin. B
When Side B C and Angles are given. — Fig, 7,
Sin. C X A C
B C X Sin. C
Sin. A
= BA.
SiaB
BA.
Nom. — Sine and Cosine t\f an arc are each equal to sine and cosine of their sup-
plementi.
Spherical Triangles^ Right -angled and Oblipie, For full formulas Se«
Moittvortlt Lend,. 1878. pp. 435-6.
388 PLANS TBIGONOMBTBT.
To Compute Angles and Side AOL
When Sides A B, B C, and Angle B <xre given, — Fig. 7.
Sip. B X B C
SiD. A
ACxSin. A
BC
= AC.
= Sin. B.
B C X Sip. B
AC
B A X Sin. A
Sin. A
= Sin. C.
B A X Sin. B
AC
B C X Sin. C
-Sin. a
= SiiL A.
BC AB
To Compute all tlie A^ugles.
When all the Sides are given. Figs. 6 and 7. Rule. — Let fa\\ a perpeiH
dicular, B r/, opposite to required angle. Then, as A C : sum of A B, B C ::
their difference : twice d g^ the distance of perpendicular, B (i, from middle
of the base.
Hence Xd^C g are known, and triangle, A B C, is divided into two right-
angled triangles, B C e2, B A d ; then, by rules for right-angled triangles,
ascertahi angle A or C.
Ofkration.— AC, Fig. 6, .5014 : A B+BC, 1.1174 +1.4142 = 2. 5316:: A Boo BC,
1.4142 — 1. 1174 = .2968 '. ^'X,dg=i 4986.
Hence A<l=;dsr — AC-t-2 =
J. 4986 .5014
= .4986, and Cd — kd'{-kGr=:x.
2 2
Consequently, triangle BdC, Fig. 6, is divided into two triangles, B ACand Bd A
To Compute Side A B and Angles.
When Ttoo Sides and One AngUy or One Side and Two Angles^ are given,—
Fig. 6.
A C X Sin. C
Sin. B
ACxSin.C
= AB.
B C X Sin. B
AC '
A B X Sin. B
= Sin. A.
= Sin. C.
ACxSia A
AB— (ACxCos. A)
ACxSin.C
= Tan. B.
rrr TaU, B.
2 Area
AC BC— (ACxCosC)
To Compute A.rea of a Triangle. —T«Hk. 8.
BAxBCxSin. B ACxBCxSin. C BAxAC X Sin. A
Sin.2C,BCa AC'Tan.O ^ BA'.CotC ^
\ ! and : = Area.
42 2
NoTR. —For other rules, see Mensuration of Areas, Lines, and
Surfaces, page 335.
To Compute Sides.
When Areas and Angles are given. — Figs. 6 and 7.
2 Area
=:AC.
= BA
v^
BC,Sin.C AC, Sin. A
To A.soertain. Distance of* Inaooes-
sil>le O'btjeots on. a Xjevel Plane.—
Figs. Q and lO.
2 Area, Sin. A
Sin. C, Sin. (A 4- C)
= B0.
Fig. la
Fig. 9
OraRATiov.— Lay oflT perpendic-
ulars to line A B, Fig. 9, as B c, d e,
on line A d, terminating on lino
e A.
. Tfaened— cB: cB ::B({: B A.
Whm there are T100 Tnacces-
tihle Objects, cu Fig, 10.
Operation. — Measure a base
line, A B. Fig. 10, and angles c A B,
dBA, dAB, cBA,eto. Then pro-
ceed by formulas, page 387, to deduce cd.
Note.— If course of cd is required, take difference of angles
<I c A and c 4 B ()r9m course A B.
PLAKB XBI60KOUETBT.
389
Fi0 iz.
When tkS Objects can he aiigned, —
Fig. II.
Operation.— Align c B, Fig. u, at A,
measure a base line at any angle there-
to, as A o, and angles o A c, c o A, and
B o A. Then proceed as per formula,
page 586, to deduce c B.
To Compute IDistaiice from
a Ghiveix X'oiut to aii In-
8M3oeaBit>le Ol^Jeot. <^ £^ig.
IS.
i
Fig.xft
i\
\
Operation.— Measure a level line, A e, Fig. 12, aud ascertain angles. B A c, B c A
Hence, having side, A c, and two angles, proceed as per formula, page 386, to de-
-termine A B.
To Compute Ueiglit of* an. Slevated. I*oiiit.-»Fig. 13.
Fig. 13.
Opkration. — Measure
distance on a horizontal
line, A c. Fig. 13 ; ascertain
Angle B A c. Then pro-
ceed as per formulas, pp.
386-8, to ascertain B c.
When a fforizorUcU
Base is not AUainable,
—Fig. 14.
■ Operation.— Measure or
compute distance Ac, Fig.
14 ; ascertain angle of depression c A o and of elevation ^
B A c Then proceed as per form u hi, page 386, to ascertain B c
Fig. 14.
Fig. IS
When a Full Base Line is not Attain'
able, — Fig. 15.
Operation. — Measure a base
line, A c, Fig. 15, and ascertain
angles A c B, c A li.
Then proceed as per for-
mula, page 386, to ascer-
tain d Bj, /"
y
Fig. z6.
Without Use of an Instrument.
— Fig. 16.
Opsbation. — Lay off any suitable and level distance, d d, set up a staff at each ex-
tremity at like elevation from base line d (f, and note distances y and x. at which
the lines of sight of object range with tops of the staffs; deduct height of eye from
length of staffs, and ascertain heights h.
and D Un(^ of line dd.
390
29
NATUKAL SIN£S AND COSIKES.
Statural Sines «ad Cosines.
X
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
xo
XI
XI
12
X2
"3
»3
X4
14
15
15
15
16
16
*7
>7
x8
x8
«9
*9
20
20
21
21
22
22
23
83
24
'4
25
«5
26
26
27
^
28
29
29
3
4
5
6
7
8
9
xo
XI
12
13
M
IS
16
17
x8
»9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
%
49
50
51
52
53
54
5
57
58
60
00
N. line.
00000
00020
00058
00087
00x16
00145
00175
00204
00233
0026%
00291
0032
00349
00378
00407
00436
00465
00495
00524
00553
00582
00611
0064
00669
00698
00727
00756
00785
00814
00844
00873
00902
00931
0096
00989
oioio
01047
01076
01 105
01134
01 164
01 193
01222
01251
0128
01309
01338
01367
01396
01425
01454
01483
01513
01542
01571
016
01620
01658
01687
01716
01745
N. CM.
99999
99999
99999
99999
99999
99999
99999
99999
99998
99998
99998
99998
99998
99998
99997
99997
99997
99997
99996
99996
99996
99996
99995
99995
99995
99995
99994
99994
99994
99993
99993
99993
99992
99992
99991
9999»
99991
9999
.9
99989
9998
99988
99987
99987
99986
99986
99985
99985
N. cot. N. sine.
8Q0
lo 2P
N. due.
0x745
01774
01803
01832
01862
0189X
0x92
01940
01978
02007
02036
02065
02094
02123
02152
02x81
oAii
0224
02269
02298
02327
02356
02385
02414
02443
02472
0250X
0253
0256
02589
02618
02647
02676
02705
02734
02763
02792
02821
0285
02879
02908
02938
02967
02996
03025
03054
03083
031 12
03141
0317
03199
03228
03257
03286
03316
03345
03374
03403
03432
03461
0349
N. eo0. N. sine. ' N. cos.
99985
99984
99984
99983
99983
99982
99982
99981
9998
9998
99979
99979
99978
99977
99977
99976
99976
99975
99974
99974
99973
99972
99972
99971
9997
99969
999^
99967
99966
99966
99965
99964
99963
99963
99962
99961
9996
99959
99959
99958
99957
99956
99955
99954
99953
99952
99952
99951
9995
99949
99948
99947
99946
99945
99944
99943
99942
99941
9994
99939
N. CM. ! N. line.
0349
03519
03548
03577
03606
03635
03664
03693
03723
03752
03781
0381
03839
03868
03897
03926
03955
03984
04013
04042
04071
041
04x29
04159
04188
04217
04246
04275
04304
04333
04362
04391
0442
04449
04478
04507
04536
04565
04594
04623
04653
0468a
047x1
0474
04769
04798
04827
04856
04885
049x4
04943
•04972
.0500X
.0503
05050
.05088
.05117
05146
05175
.05205
•05234
99939
99938
99937
99936
99935
99934
99933
99932
99931
9993
99929
99927
99926
99925
99924
99923
99922
99921
99919
99918
999»7
99916
99915
99913
99912
99911
9991
99909
99907
99906
99905
99904
99902
99901
99898
99897
99896
99894
99893
99892
9989
9988
99881
99886
99885
99883
99882
99881
99879
99878
99876
99875
99873
99872
9987
99869
99867
99866
99864
99863
N. cot. N. tine.
87°
30
N. line. N. cot,
05234
05263
05292
05321
0535
05379
05408
05437
05466
05495
05524
05553
05582
05611
0564
05669
05698
05727
05756
05785
05814
05844
05873
05902
05931
0596
05989
06018
06047
00070
06105
06134
06163
06192
06221
0625
06279
06308
06337
06366
06395
No6424
06453
.06482
.06511
.0654
06569
06598
06627
.06656
06685
.06714
•06743
.06773
.06802
.06831
.0686
.06889
.06918
.06976
lit
99863
99861
9986
99858
99857
99855
99854
99852
99851
99849
99847
99846
99844
99842
99841
99839
99838
99836
99834
99833
99831
99829
99827
99826
99824
99822
99821
99819
99817
99815
99813
99812
9981
99808
99806
99804 I
99803,
99801 I
99799 1
99797
99795 ,
99793
99792
99788
99786
99784
99782
9978
99778
99776
99774
99772
9977
99768
99766
99764
99762
9976
99758
99756
N. cot. N. tint.
86O
60
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
H
37
36
35
34
33
32
3»
30
27
26
25
24
23
22
21
20
\t
17
16
15
14
13
12
XX
10
t
7
6
5
4
3
2
I
o
2
2
s
2
2
2
2
2
2
2
2
2
a
2
2
2
O
o
o
o
o
o
o
o
o
o
o
o
o
o
o
HAXVUAh nSXB AND COSINSS.
391
»9
o
I
X
2
3
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
[I
13
'3
'4
14
'5
'5
'5
[6
16
17
17
[8
[8
'9
'9
ao
ao
31
3Z
33
33
83
23
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as
as
36
36
a7
27
38
38
S9
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I
a
3
4
5
6
7
8
9
10
II
13
«3
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16
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30
3l
33
23
84
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36
38
89
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3a
33
34
35
36
3
39
40
4x
4a
43
44
49
50
5"
Sa
53
54
55
56
57
58
N.
06976
070P5
07034
07063
07093
07131
071S
07170
07208
07237
07266
07295
07324
07353
07382
07411
0744
07460
07498
075a7
07556
07585
076x4
07643
07672
07701
0773
07759
07788
078x7
07846
07875
07904
07933
07962
07991
0802
08040
08078
08x07
08x36
08165
08194
08333
08353
08381
0831
^^
08397
08426
08455
08484
08513
0854a
08571
086
08639
08658
08687
08716
N. CO*. I N. siiMk
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99756
99754
9975a
9975^
99748
99746
99744
9974a
9974^
99738
99736
99734
99731
99729
99727
99735
99723
99721
99719
99716
99714
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99708
99705
99703
99701
99690
99696
99694
99687
99685
99683
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99678
99676
99673
99671
99668
99666
99664
99661
99659
99657
99654
9965a
99649
99647
99644
99642
99639
99637
99635
9963a
9963
99637
99635
99622
9^6x9
N. 00*. M. sin*.
N. cot.
o87i6
0874s
<»774
08803
08831
0886
08889
089x8
08947
08976
09005
09034
09063
09092
09121
0915
09170
09208
09237
09266
09295
09324
09353
09383 ;
094x1 1
0944 I
09469
09498,
09537 !
09556!
09585
09614
09642
09671
097
09729
09758
09787
098x6
09845
09874
09903
09932
09901
0999
00x9
0048
0077
0106
0135
0164
0192
022I
025
0270
0308
0366
0395
0424
0453
99619
99617
99614
996x3
99609
99607
99604
99603
99599
99596
99594
99591
99588
99586
99583
9958
99578
99575
99572
9957
99567
99564
99562
99559
99556
99553
99551
99548
99545
99542
9954
99537
99534
99531
99528
99526
99533
995a
99517
99514
99511
99508
99506
99503
995
99497
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99488
99485
99482
99479
99476
99473
9947
99467
99464
99461
99458
99455
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840
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N.iio*.
0453
0482
05 IX
0569
0597
0626
0655
0684
0713
0742
0771
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0839
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0973
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1080
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1147
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1205
1234
1363
I29X
132
1349
1378
1407
1436
1465
1494
1523
1552
158
1609
1638
1667
1696
1725
1754
1783
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1927
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2043
207 X
21
2120
2158
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99452
99449
99446
99443
9944
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99434
99431
99428
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99421
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99412
99409
99406
99402
99399
99396
99393
9939
99386
99383
9938
99377
99374
9937
99367
99364
9936
99357
99354
99351
99347
99344
99341
99337
99334
99331
99327
99324
9932
99317
99314
9931
99307
99303
993
99297
99293
9929
99286
99283
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99276
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99269
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70
N. aiam. N. co*.
2187
22x6
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2274
3302
3331
236
2380
2418
3447
2476
3504
3533
3562
2591
263
2640
2678
2706
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2764
2793
2822
2851
288
2908
2937
2966
2995
3024
3053
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3x1
3139
3168
3197
3226
3254
3283
331a
3341
337
3399
3427
3456
3485
3514
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3572
3687
3716
3744
3773
3802
3831
386
3889
3917
99255
99351
9924^
99244
9934
99237
99333
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99226
99222
99219
99315
99211
99308
99304
993
99197
99193
99«89
99186
99x82
99178
99'75
99171
99167
99163
9916
99156
9915a
99148
99«44
99141
99137
99133
99129
99x25
99x22
991x8
991x4
9911
99x06
99x02
99098
99094
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99083
99079
99075
99071
99067
99063
99059
99055
99051
99047
99043
99039
99035
99031
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60
5
57
56
55
54
53
53
51
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47
46
45
44
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35
34
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34
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21
20
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18
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'
:^
_:
0
N.'i.
NATUBAL SIKBS AND eOSIKBS.
399
III
33'
« 3
» 4
a 5
9 6
V I
3 I <>
3; 9
4 lo
4 1 "
5
5
5
6
6
i
7
7
12
»3
»4
15
i6
O 20
8 21
8; 22
9 . as
9 84
lo 25
10 I 26
10 I 27
II ! 28
II 39
13 30
12 31
12 32
»3 33
»3 34
«3 35
14 36
»4 37
15 38
»5 39
15 40
x6 . 41
x6 42
»6 43
»7 44
»7 45
x8 46
18 47
18 48
»9 49
«9 50
20 51
20 52
ao 53
«» 54
21 55
21 56
aa 5
360
N. line. I N.
I
«2 5
•3 59
»3 60
58779
58802
58826
58849
58873
58896
5893
58943
58967
5899
590*4
59037
59061
59084
59108
591 31
59*54
59178
5920X
59225
59248
59272
59295
593»8
59342
S9365
59389
594"
59436
59459
59482
59506
59529
59552
59576
59599
59622
59646
59669
59693
597*6
59739
59763
59786
59809
59832
59856
59879
59902
59926
59949
59972
59995,
60019 .
60042
60065
60089
601 12
60135
60158
60182
80902
80885
80867
8085
80833
80816
I
N. CM. K. sine.
630 _
370
N. alii«. N. fXM,
60182
60905
60228
60351
60274
60298
60321
60344
60367
6039
60414
60437
6046
60483
60506
60529
60553
60576
60599
60622
6o6j5
60668
60691
60714
60738
60761
60784
60807
6083
60853
60876
60899
60922
60945
60968
60991
61015
61038
61061
61084
61x07
6113
61 176
61 199
61222
61245
61268
61291
61314
61337
6136
61383
61406
61429
61451
61474
61497
6152
6i^M
79864
79846
79329
7981 1
79793
79776
79758
79741
79783
79706
79688
79671
79653
79635
79618
796
79583
79565
79547
7953
79513
79494
79477
79459
7944«
794241
79406
79388
79371
79353
79335
79318
793
79282
79264
79247
79229
79211
79*93
79176
79*58
79*4
79122
79105
79087
79069
79051
79033
79016
78962
78944
78926
78891
78873
78855
78837
78819
''8801
N. COS. N . tlnfl.
^
380
N.iine.
61566
61589
61613
61635
61658
6i68z
61704
61726
61749
61772
61795
61818
61841
61864
61887
61909
61932
61955
6x978
6300X
63024
63046
63069
63093
63115
63138
6316
63183
63306
63329
63351
63374
63397
6333
63348
62365
62388
6241 1
62433
62456
62479
62502
62524
62547
6257
62592
63615
62638
6266
62683
62706
62728
62751
62774
62796
62819
62842
62864
62887
63909
62932
N.
78801
78783
78765
78747
78729
78711
78694
78676
78658
7864
78633
78604
78586
78568
7855
7853a
78514
7^96
78478
7846
7844a
78424
78405
78387
78369
78351
78333
783*5
78297
78279
78261
78243
78225
78206
78188
7817
78152
78134
78116
78098
78079
78061
78043
78025
78007
77988
7797
7795a
77934
77016
77897
77879
77861
77843
77824
77806
77788
77769
7775*
77733
777*5
N. CO*. X. liiui.
61®
390
N.aine.
rl. COS.
•.6293a
•777*5
•62955
■77696
.62977
.77678
.63
.7766
.63022
.77641
■6304s
.77623
.63068
•77605
.6309
.77586
.631x3
.77568
.63135
•7755
.63158
•7753*
.6318
•775*3
■63203
•77494
.63225
•77476
.63248
•77458
.63271
•77439
.63393
.77421
.63316
.7740?
•63338
.77384
.63361
.77366
.63383
•77347
.63406
•77329
.63438
■773*
•63451
.77292
•63473
•77273
63496
•77255
.63518
.77236
.6354
.77218
•63563
•77*99
•6358s
.77181
.63608
.77163
•6363
•77*44
•63653
.77135
•63675
.63698
.77088
.6373
•7707
.63742
•7705*
•63765
•77033
63787
.77014
6381
.76996
.63832
•76977
•63854
•76959
.63877
•7694
.63899
.76931
.63933
.76903
.63944
.76884
.63966
.76866
.63989
.76847
.76828
.64011
•64033
.7681
64056
76791
.64078
.76772
641
•76754
.64123
•76735
64*45
.76717
.64x67
.76698
.6419
.76679
64212
.76661
64a34
.76642
.64256
.76623
.64279
.'_^-^>6o4
N. sin*.
N. c««.
60
0
60
II
57
56
55
54
53
5a
5*
50
%
47
46
45
44
43
4a
4*
40
3
37
36
35
34
33
32
3*
30
29
28
27
26
25
24
23
22
21
20
li
*7
16
*5
*4
*3
12
11
10
I
7
6
5
4
3
2
X
o
18
18
x8
*7
*7
*7
*7
x6
16
16
*5
*5
*5
*4
*4
*4
*4
'3
*3
>3
12
12
12
II
II
IX
II
10
10
10
9
9
8
8
8
7
7
7
6
6
6
5
5
5
5
4
4
4
3
3
3
2
a
2
3
E
X
X
o
o
400
NATDBAL SINES AND COSINES.
23
I
I
3
a
3
3
3
4
4
4
5
5
6
6
6
7
7
i
8
8
9
9
lO
lO
xo
XI
IX
XI
xa
12
xa
13
40©
N. tine.
3
4
5
6
7
8
9
[O
[I
[2
13
t4
15
[6
'7
[8
'9
30
ax
23
23
24
25
26
27
28
29
30
31
32
33
34
35
13 ' 36
M I 37
14: 38
M ' 39
15 I 40
15 41
15 i 42
>6 I 43
16 44
'7
17
'7
45
46
47
x8 I 48
18 149
x8 , 50
19 51
>9 52
»9 53
20 54
20 55
21 56
21 I 57
21 58
32 59
22 60
.64279
.64301
•64323
■64346
.64368
.6439
.64412
•64435
•64457
.64479
.64501
.64524
.64546
.64568
•6459
.64612
.64635
.64657
.64679
. 64701
•64723
.64746
.64768
•6479
.64812
.64834
.64856
.64878
.64901
•64923
.64945
.64967
.64989
.650IX
•65033
•65055
•65077
.651
.65122
.65144
.65166
.65188
.6521
.65232
•65254
. 65276
.65298
•6532
•65342
•65364
.65386
.65408
•6543
•65452
•65474
.65496
.65518
•6554
.65563
65584
.65606
N. CM.
6604
6586
6567
6548
653
65 1 1
6492
6473
6455
6436
6417
6398
638
6361
6342
6323
6304
6286
6267
6248
6229
621
6192
6x73
6154
6135
61 16
6097
6078
6059
6041
6022
6003
5984
5965
5946
5927
5908
5889
587
585'
5832
5813
5794
5775
5756
5738
57 «9
57
568
5661
5642
5623
5604
5585
5566
5547
5528
5509
549
547 »
41°
N. tine.
N. cot.
N. CM. N . sine.
490
65606
65628
6565
65672
65694
65716
65738
65759
65781
65803
65825
65847
65869
65891
65913
65935
65956
65978
66
66022
66044
66066
66088
66x09
66131
66153
66175
66197
66218
6624
66262
66284
66306
66327
66349
66371
66393
^6414
66436
.66458
.6648
.66501
.66523
•66545
.66566
.66588
.6661
.66632
.66653
.66675
.66697
.66718
.6674
.66762
.66783
.66805
.66827
.66848
.6687
.66891
66913
N. CM. ' N. tine.
480
75471
75452
75433
75414
75395
7^375
75356
75337
75318
75209
7528
75261
75241
75222
75203
75184
75165
75146
75126
75107
75088
75069
7505
7503
7501 X
74992
74973
74953
74934
74915
74896
74876
74857
74838
748x8
74799
7478
7476
74741
74722
74703
74683
74664
74644
74625
74606
74586
74567
74548
74528
74509
74489
7447
7445»
74431
744x2
74392
74373
74353
74334
74314
42P
N. tine. I N. coa.
669x3
66935
66956
66978
66999
6702 X
67043
67064
67086
67x07
67x29
6715X
67172
67194
672x5
67237
67258
6728
67301
67323
67344
67366
67387
67409
6743
67452
67473
67495
675x6
67538
67559
6758
67602
67623
67645
67666
67688
67709
6773
67752
67773
67795
678x6
67837
67859
6788
6790X
67923
67944
67965
67987
68008
68029
68051
68072
68093
68x15
68x36
68157
68179
682
N. CM.
74314
74295
74276
74256
74237
742x7
74x98
74x78
74159
74139
7412
741
7408
74061
74041
74022
74002
73983
73963
73944
73924
73904
73885
73865
73846
73826
73806
73787
73767
73747
73728
73708
73688
73669
73649
73629
7361
7359
7357
73551
73531
735"
73491
73472
73452
73432
734' 3
73393
73373
73353
73333
73314
73294
73274
73254
7323
73211
73195
73175
73155
73»35
N. sine.
470
430
N. sine.
N. CM.
60
.682
•73135
.68221
.731x6
5I
.68242
.73096
.68264
•73076
57
.68285
•73056
56
.68306
•73036
55
.68327
.730x6
54
.68349
•72996
53
.6837
.72976
52
.68391
■72957
51
.68412
•72937
50
.68434
.729x7
.72897
49
48
.68455
.68476
.72877
47
.68497
.72857
46
.685x8
•72837
45
.68539
.728x7
44
.68561
.72797
43
.68582
.72777
42
.68603
.72757
41
.68624
.72737
40
.68645
.72717
It
.68666
.73697
.68688
72677
37
.68709
.72657
36
.6873
73637
35
.68751
.726x7
34
.68772
•72597
33
.68793
.72577
32
.68814
•72557
3«
.68835
•72537
30
.68857
• 7251 7
2
.68878
.72497
.68899
.72477
27
.689?
•72457
26
.68941
72437
25
.68962
.724x7
24
.68983
72397
23
.69004
•72377
22
.69025
•72357
21
.69046
•72337
20
•^z
•72317
:i
.69088
.72297
.69x09
.72277
"7
•6913
•72257
x6
.69x51
.72236
15
.69x72
.72216
»4
.69193
.72196
13
.69214
.72x76
12
.69235
72x56
IX
.69256
.72x36
XO
•69277
.72x16
t
.69298
72095
.69319
72075
7
.6934
•72055
6
•69361
•72035
5
.69382
•720x5
4
69403
•71995
3
•69424
•71974
3
1 69466
•71954
•7»934
I
0
/
' N. CM.
N. sine.
1 u
50
Oil
19
i
8
8
7
7
7
6
6
6
6
o
o
o
9
9
1
8
8
7
7
7
6
6
6
5
5
5
4
4
4
3
3
3
3
2
3
3
X
X
I
o
o
NA.TUBAX. SINES AND COSINES.
401
440
Prop,
parte.
Prop,
parte.
440
n
IZ
0
N.dna.
N.eet.
60
>9
19
22
II
31
N.aine.
N.cos.
29
9
0
.69466
.71934
.701x2
.71305
9
0
I
.69487
.71Q14
59
19
12
32
.70x32
.71284
28
9
I
a
.69508
.71894
58
x8
X3
33
.70153
.71264
27
I
I
3
.69529
.71873
H
x8
X2
34
.70174
•71243
26
I
4
.69549
.7»853
56
x8
13
35
.70195
.71223
25
8
2
5
.6957
•71833
55
17
13
36
.70215
.71203
24
8
2
6
•69591
.71813
54
17
14
37
.70236
.71182
23
7
3
7
.69612
.71792
53
*Z
14
38
.70257
.71162
33
7
3
8
.69633
.7x773
52
16
14
39
.70277
.7114X
31
7
3
9
.69654
.7x752
5«
x6
15
40
.70298
.7x131
30
6
4
xo
.69675
•71732
50
16
15
41
.703»9
•7"„
;i
6
4
XX
.69696
.7171X
^2
x6
15
42
•70339
.7108
6
4
X2
.69717
.7169X
48
15
16
43
.7036
•71059
^l
5
5
13
.69737
.71671
47
15
16
44
.70381
•71039
x6'
5
5
«4
.69758
.7*65
46
15
17
45
.7040X
.71019
.70998
»5
5
6
15
.69779
.7163
45
14
'7
46
.70422
«4
4
6
16
-598
.7x6x
4*
14
17
47
.70443
.70978
13
4
6
17
.6982X
•7159
43
14
18
48
•70463
•70957
13
4
7
18
•^*
.71569
42
13
18
49
.70484
•70937
XI
3
7
'9
.69862
•7»549
41
13
18
50
•70505
.70916
.70896
XO
3
7
20
.69883
■71529
40
13
19
5>
•7052s
I
3
8
91
.69904
.71508
39
X3
>9
52
.70546
.70875
3
8
23
.60925
.7x488
38
X2
»9
53
.70567
•70855
7
3
8
83
.69966
.7x468
37
12
20
54
.70587
•70834
6
3
9
24
.7x447
36
XI
20
55
.70608
.70813
5
3
9
25
.69987
.71427
35
XI
21
56
.70628
.70793
4
I
JO
s6
.70008
.71407
34
XI
31
57
.70649
.70772
3
X
10
27
.70039
.7x386
33
XO
21
58
.7067
.70752
3
I
xo
28
.70049
.71366
32
XO
32
59
.7069
•70731
I
0
<I
29
.7007
.71345
31
XO
33
60
•70711
.7071X
0
0
<I
30
.70091
•71325
30
10
. .
*
N. COS.
N. tine.
N.cos.
N. sine.
4
50
4
50
Preceding Table contains Natural Sine and Cosine for every minute
of the Quadrant to Radius i.
If Degrees are taken at head of columns, Minutes, Sine, and Cosine must
be taken from head also ; and if they are taken at foot of column, Minutes,
etc., must be taken from foot also.
ILLUSTBATIOK — .3173 18 siue of x8o 30', and cosine of 7x0 30'.
To CoimpTite Sine or Cosine tor Seconds.
When Angle is less than 45°. Rule. — Ascertain sine or cosine of angle
for degrees and minutes from Table; take difference between it and sine
or cosine of angle next below it. Look for this difference or remainder,*
if Sine is i*equired, at head of column of Proportional Parts^ on left side ;
and if Cosine is required, at head of column on right side; and in these
respective columns, opposite to number of seocMids of angle in column, is
number or correction m seconds to be added to Sine, or subtracted from
Cosine of angle.
Illust&atiok I.— What is sine of 80 9' xo'^f
Sine of 8° 9', per Table = 141 77 ; ) ,,^ „« ahf^^^
Sine of 8° 10'; • " =.1^205;} •«^^^*•^*'^"^•
In led side column of proportional parts, under 28, and opposite to 10', is 5, cor-
rectioo for xo', whicb, being added to . 141 77 = . 141 83 Sine.
* Ths Ubls in •oiD* iattancss will givs a nait too much, but thi«. la geii«ral, U of Uttb imporUBcc
L L*
402 NATURAL SINES AND COBINBS.
3.— What is cosine of 8° 9' 10"?
CosineofSo 9', per Table = .989 00;) ^oo oa difFerence.
Cosine of 8° 10', " = .999 86 ; ) '^^^^ aijerence.
In right-side column of proportional parte, under 4, and opposite to to\ is z, thd
correction for 10', which, being subtracted ft'om .989 90 = .989 89 cosine.
When Angle exceeds 45°. Rule.— Ascertain sine or cosine for angle h*
degrees and minutes from Table, taking degrees at the foot of it ; then take
difference between it and sine or cosine of angle next above it. Look for re-
mainder, if Sine is required, at head of column of Proportionat Parts^ on right
side ; and if Cosine is required, at head of coluum oa left side ; and in these
respective columns, oi)posite to seconds of angle, is number or correction in
seconds to be added to Sine, or subtracted from Cosine of angle.
Illustration. — What is the Sine and Cosine of 81° 50' 50"?
In right-side coluinn ot proportional parts^ and opposite to 50', is 3, w^ich, added
to .989 86 = .989 89 Sine.
r'li^^ nJ K ^'''' P^"" 7^^^^ = • '^' °5 ' } .000 25 difference.
Cosine of 81° 51 , '* = . 141 77 ; j ^ •«'
In left-side column of proportional pai-ts, and opposite to 5p', is 24, Which, sab-
tracted ftom . 14205 = . 141 81 Cosine.
To Ascertain or Compute Num'ber of* Degrees, Alijxutes,
and Seconds of a given Sine or Cosine.
When Sine is given. Rui.E. — If given sine is in Table, the degrees of it
will be at top or bottom of page, and minutes hi marginal column, at left or
right side, according as sine corresponds to an angle less or greater than 45°.
If given sme is not in Table, take sine in Table which is next less than the
one for which degrees, etc., are required, and note d^rees, etc., for it. Sub-
tract this sine from next greater tabular sine, and also from given sine.
Then, as tabular difference is to difference between given sine and tabu-
lar sine, so is 60 seconds to seconds for sine given.
Example. — What are the degrees, minutes, and seconds for sine of .75?
Next less sine is .74092, are for which is 48° 35'. Next greater sine is .75011,
difference between tohiih and next less i« .75011 — .74992 = .00019. Difference be-
tween less tabular sine and one given is . 75 — .749 92 :±: ^
Then 19 : 8 :: 60 : 25-f , which, added to 480 35' = 48° 35' 25";
When Cosine is given. Rui.k. — If given cosine is found in Table, degrees
of it will be found as in manner specified when sine is given.
If given cosine is not in Table, take cosine in Table which is xnsxt greater
than one for which degrees, etc., are required, and note degrees, etc., for it.
Subtract this cosine from next less tabular cosine, and also from given cosine.
Then, as tabular difference is to difference between given cosine and tabu-
lar cosine, so is 60 seconds to seconds for cosine given.
Example.— What are the degrees, minutes, and seconds (br cosine of .75?
Next greater cosine is .750 1 1. arcfhr which is 41° 24'. Next less cosine is .74993,
difference between which and next greater t< . 750 1 i — .749 92 = .000 19. Difference
between greats tabular cosine and one given is .750 11 — .75000 =11.
Then 19 : n : : 60 : 35 —, which, added to 41© 24' = 4i<> 24' 35".
To Compxite "Versed Sine of an A-ngle.
Subtract cosine of angle from i.
Illustration.— What is the versed sine of 21® 30'?
Cosine of 3t° 30' is .930 42, which, — i = .069 58 versed tine.
To Compute Co-versed Sine of an Ajckst\9»
Subtract sine of angle from i.
Illustration. — ^What is the co-versed sine of si^ 30' ?
The sine of 21® 30 Is . 3665, which, — i = .6335 co-versed tim.
NATURAL SECANTS AND CO-SECANTS.
T«3"atiiral Secants and Co -secants.
403
o
I
a
3
4
5
6
9
10
II
12
13
«4
«5
16
'7
18
'9
20
21
22
«3
24
as
26
27
28
39
30
3«
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
%
49
50
5»
52
53
54
55
56
5
h
00
0001
.0001
X.OOOI
.0001
.ooox
.OOQI
.0001
I.OOOI
.0001
.aooi
.0001
.ooox
X.OOOI
ooox
ooox
.ooox
.ooox
X.OOOI
.ooox
ooox
.ooox
.ooox
I. ooox
iDflnite.
3437-7
1718.9
J45-9
859-44
687.55
57296
491. 11
29.72
381 97
343-77
12.52
286.48
64.44
45^55
229.18
14.86
02.23
X00.99
80.73
X71.89
637
56.26
49-47
43-a4
«37-5i
33.22
97.32
32.78
t8.54
«i4-59
xa9
07-43
04. X7
01. IX
98.223
5-495
a.914
8-469
88.149
85.046
3^849
1-853
79 95
76.396
4-736
3-146
X.622
i.x6
68.757
7409
6.113
4.866
3.664
62.507
1.391
i3«4
59-274
8.27
57- 299
Co-MC*T. SbgANT.
890
1 1
' SCCART.
0
C<KaBc'T.
1,0001
57299
.0001
6.359
.0002
5-45
.0002
4-57
.0002
3718
X.0002
52.891
.0002
2.09
.0002
i.3»3
.0002
0.558
.0002
49.826
t.0002
40.114
8.422
.0003
.0003
775
.0002
7.096
0003
6.46
1.0002
45^84
.0002
5237
.0002
4.65
.0002
4.077
.0003
352
1.0003
42.976
• 0003
2-445
.0003
1.938
.0003
>-423
.0003
4093
X.OOO3
40.'448
.0003
39978
.0003
9.518
.0003
9069
i.631
.0003
1.0003
38.301
.0003
7.782
.0003
7 37'
.0004
6.969
.0004
6.576
X.OOO4
36.i9»
.0004
5814
.0004
5-445
.0004
5084
4-729
X.OOO4
34382
.0004
4.042
.0004
3.708
U3O04
3-381
.0004
3.06
X.0005
32-745
.0005
2-437
.0005
a. 134
.0005
1.836
.0005
'•544
x.0005
3i'257
.0005
30-976
.0005
a699
.0005
a 428
0005
ax6i
x.0005
29.899
.0006
9.641
0006
9388
.0006
.0006
2-J39
8.894
X.0006
28.654
Co-BBC*T.
Sbcant. •'
8C
p i
20 i^
1.0006
.0006
.0006
.0006
.0006
1.0007
•0007
.0007
.0007
.0007
1.0007
.0007
.0007
.0007
0008
1.0008
0008
.0008
.0008
.0008
1.0008
0008
.0008
.0009
'.0009
1.0009
.0009
.0009
.0009
.0009
1.0009
.001
.001
.oox
.001
1. 001
.001
.001
.001
.ootx
X.OOII
.0011
.0011
.0011
.0011
X.OOII
.0012
.0012
001 3
.0012
X.OOI2
.0012
.0012
.0013
.0013
X.OO13
0013
• 0013
.0013
0013
1. 0014
28.654
8.417
8.184
7-955
7-73
27.508
7.29
7075
6.864
6.655
26.45
6.249
6.05
5-854
5.661
25.471
5.284
5-1
4.918
4 739
24.562
4-358
4.216
4.047
3.88
23.716
.3 553
3-393
3235
3079
23.925
2.774
2.624
2.476
233
22. 186
2044
1.904
» 765
1.629
21.494
1.36
1.338
1. 098
2a 97
20-843
0.717
0-593
0.471
0.35
20.33
O.IX2
19-995
' 9.88
9.766
19653
9-54«
9-431
9.322
9.214
19.107
Co-sic't.' Skcakt
870
3
Sbgant.
0
Co-bbc't.
1.00x4
19.107
.0014
9.002
8.897
.0014
.0014
8.794
.0014
8.693
I.OOI4
18.591
.0015
8.491
.0015
8.393
.0015
8.29s
.0015
8.198
1. 0015
18.103
.0015
8.008
.0016
7-9M
7-821
.0016
.0016
7-73
1. 0016
>7-639
.0016
7-549
.0016
7.46
.0017
7-372
0017
7285
x.0017
17-198
.0017
7-"3
.0017
7.028
.0017
6! 861
ooi8
1. 0018
16.779
.0018
6.698
.0018
6.617
.0018
6.538
.0018
16. 3&
1. 0019
.0019
6303
0019
6.326
.0019
6.15
.0019
6.075
I 0019
16
.002
X
.002
.002
578
.002
5-708
1.002
'5637
.0021
5566
.009I
5496
.003I
5-427
ooai
5.358
I.0O3I
»S-29
-0032
5.222
.0023
5-«55
.0032
5.089
.ooaa
5.093
I.0032
14-958
4.893
.0033
.0033
4-829
.0023
4765
.0033
4.70a
X.0033
14.64
.0034
4-578
.0024
4-5>7
0024
4-456
0024
4 395
1.0034
M-335
Co-«bc't.| Sac a NT.
. 86O
60
5'
57
56
55
54
53
52
51
50
4
47
46
45
44
43
42
41
40
3'
i
35
34
33
32
3«
30
2
27
26
25
24
23
22
21
20
:i
»7
16
IS
14
»3
la
II
10
7
6
5
4
3
9
I
0
404
NATUBAL SECANTS AND CO-SBCAKTS.
40 I
t
Skcant.
1.0024
Co-BIC'T.
o
14-335
I
.0025
4.276 j
2
.0025
4.217 '
3
.0025
4^«59
4
.0025
4.101
5
X.0025
"4- 043
6
.0026
3986
7
.0026,
3-93
3-874
8
.0020
9
.0026
3.818
xo
X.0026
13-763
XI
.0027
3.708
xa
.0027
3-654
«3
.0027
3-6
«4
.0027
3-547
15
Z.0027
13-494
i6
.0028
3-441
«7
.0028
3389
i8
.0028
3-337
'9
.0028
3.286
ao
Z.0029
13-235
21
.0029
3.184
22
.0029
3-134
23
.0029
3-084
24
•0029
3-034
'1
1.003
12.985
26
.003
2.037
2.888
27
•003
28
.003
2.84
29
.0031
2-793
30
1.O031
12.745
3'
.0031
2.698
32
.0031
2.652
33
.0032
2.606
34
.0033
2.56
35
1.0032
"5X4
36
.0032
2.469
37
•0039
2.424
38
•0033
2-379
39
•0033
2-335
40
X.0033
X2.291
4«
•0033
2.248
42
•0034
3.204
43
.0034
2. i6z
44
•0034
2.x 18
^§
1.0034
13.076
46
•0035
2-034
47
•0035
1.992
«8
•0035
x-95
49
50
•0035
1.0036 .
ix.^
51
.0036
1.838
52
.0036
X.787 .
53
.0036
1.747 '
54
•0037
X.707
55
1.0037
IX. 668
56
•0037
X.628
57
.0037
X.589
58
.0038
1-55
59
.0038
1.5x2
60
1.0038
11.474 1
#
Co-SBC 't.
Bl
Sbcamt.
50
6° 1
60 1
Skcawt.
Co-«ec't.
Skcant.
Co^sc't.
X.0038
"•474
10055
9.5668
.0038
1-436
-0055
•5404
.0039
X.398
.0056
•5i4«
.0039
X.36
.0056
.488
.0039
'-323
.0056
.463
1.0039
XI. 286
1.0057
9.4363
.004
1.249
-0057
•4105
.004
X.213
.0057
•385
.004
X.176
•0057
•3596
.004
1. 14
.0058
•3343
X.004I
1 1. 104
X.0058
9.3092
.0041
1.069
.0058
.2842
.0041
»-033
.0059
•2593
.0041
0.988
•0059
•2346
.0042
0.963
.0059
.21
X.0042
10.929
o.§94
X.006
9-1855
.0042
.006
.1612
•0043
0.86
.006
•137
•0043
0.826
.0061
.1x29
.0043
a 792
.0061
.089
1.0043
X0.758
i.oo6x
9-0651
.0044
0.725
" .0062
.04x4
.0044
0.692
.0063
•0x79
.0044
0.659
.0062
8-9944
.0044
a 626
.0063
•97"
1-0045
10.593
X.0063
8.9479
.9348
•0045
0.561
.0063
•0045
0.529
.0064
.9018
.0046
0.497
.0064
.679
.0046
0.465
.0064
•8563
1.0046
10.433
X.0065
8.8337
.0046
0.402
.0065
.8X13
•0047
0^371
.0065
.7888
•0047
0.34
.0066
.7665
.0047
0.309
.0066
•7444
1.0048
xa278
1.0066
8.7333
.0048
a 348
.0067
.7004
.0048
a 317
.0067
.6786
.0048
a 187
.0067
.6569
.0049
• 0.157
.0068
•6353
1. 0049
10.127
X.0068
8.6x38
.0049
aooS
.0068
•S924
.005
0.068
.0069
•57"
.005
0.039
.0069
•5499
.5385
.005
0.0X
.0069
1.005
9.9812
X.007
8.5079
.0051
-9525
.007
.4871
•0051
•9239
.8955
.007
.4663
.0051
.0071
•4457
.0053
.8673
.0071
•425*
X.0053
9-8391
1.007Z
8.4046
.005a
.81x3
.0073
•3843
•0053
•7834
.0073
.3640
.0053
-7558
•0073
•3439
•3238
-0053
•7283
•0073
10053
9.70X
X.0073
8.3039
.0054
.6739
-0074
.2840
•0054
.6469
.0074
.2642
•0054
.62
•0074
.2446
•0055
•5933
-0075
.335
10055
9.5668
1.0075
8.3055
Co-aic'T.
Sbcaht.
C0-«IC*T.
Sbcamt.
8
40
8:
P
70 1
Sbcant.
1 Co-8bc't.
1.0075
8.2055
•0075
.x86i
.0076
.1668
.0076
.1476
.0076
.1285
1.0077
8.1094
.0077
•0905
.0078
.07x7
.0078
•0529
.0078
o°342
X.0079
8.0x56
.0079
7-9971
•0079
.9787
.008
.9604
.008
•9421
1.008
7.924
■ 0081
.0081
.8879
.0082
.87
0082
.852a
X.0082
7-8344
.0083
.8x68
.0083
•7992
.0084
.7817
.0084
1.0084
77469
.0085
.0085
.7x24
.0085
.6953
.0086
•6783
X.0086
7.66x3
.0087
•6444
.0087
.6276
.0087
.6x08
.0088
.5942
1.0088
7.5776
.0089
.56x1
.0089
•5446
.0089
.5282
.009
.5"9
Z.009
7.4957
.009
•4795
.0091
•4634
.0091
•4474
.0092
•43"5
1.0092
7-4156
.0092
-3998
•0093
•0093
•3683
•0094
-3527
X.0094
7-3372
•0094
•3257
•0095
•3063
.0095
.2909
.0096
•2757
X.0096
7.2604
•0097
•2453
.0097
.2302
•0097
.2x52
.0098
.2002
.0098
7.1853
ComBC'T.
SiCAirr.
82
|0
60
II
57
56
55
54
53
5a
5«
50
ti
47
46
45
43
4a
4«
40
il
37
36
35
34
33
3«
3«
37
36
25
»4
23
33
3X
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*7
16
>5
14
"3
13
IZ
10
i
7
6
5
4
3
a
I
o
NA.TUBAL SECANTS AND CO-SECANTS.
405
80 1
90 II 100
110 1
»
Sboamt.
1
Co-«m't.
SaOAHT.
C<««c»i.'
6.3924
•3807
I Sbcakt.
CO-SBO**. ■
: SacAar.
1. 0187
CO-M0*T.
0
1.0098
71853
X.OI35
I.OI54
5. 7588
5.3408
I
.0099
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•7493
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a
.0099
•>5S7
.0135
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.0155
.7398
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3
.0099
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.0156
•7304
.0189
•2X74
4
.ox
.1363
.0x36
.3458
.0x56
.72X
.0x89
•2097
5
I. ox
7.III7.
X.OI37
6.3343
X.OI57
5-7"7
X.0X9
5.3019
6
.oxox
.0073
.0837
.0137
.0x28
.3228
.0157
.0x58
•^3
.0x91
:IU?
7
.oxox
•3"3
!6l38
.0191
8
.0x03
.0683
.0x38
:3I?
.0x58
.0193
.1788
9
.0X03
•0539
.0139
.0159
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.0x93
.171a
10
X.0X03
7.0396 .
X.OI29
6.2773
1. 01 59
56653
X.OX93
5.1636
II
•0x03
.0354 '
.013
.2659
.016
.6561
.0x93
.156
13
.0x03
.OII3 1
.013
•8546
.016
.647
.0194
.1484
'3
.0x04
6.997X 1
.0x31
.2434
.oi6x
:^SI
•0x95
.1409
14
.0x04
•983 !
.OI3X
.3322
.0163
.0195
•»333
15
X.OI04
6.969
Z.OI33
6.221X
1.0x63
5.6197
X.0196
5.1258
16
.0x05
•955
.0132
.31
.0x63
.6107
.0196
.X183
\l
•0x05
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.0163
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.0197
.1109
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.0x64
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.5838
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.0106
•9>3S
•0134
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.0x64
.0198
5!S?86
30
X.OI07
6.8993
I.OI34
6.I66X
X.0165
55749
1.0199
31
.0x07
.8861
•o«35
•>55a
.0165
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.0199
.0812
33
.0x07
.8725
•013s
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.0739
33
.0x08
.8589
.0136
•1335
.0166
•5484
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.0666
34
.0x08
.8454
.0136
.X227
.0167
•5396
.030X
•0593
as
X.OX09
6.833
1.0136
6. 1 13
X.OX67
S5308.
X.0302
505a
36
.0x09
.8185
•o"37
• X013
.0168
.5221
.0202
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'Z
.oxx
.8053
.0137
.0138
.0906
.0169
•5134
.0303
•0375
38
.oxx
.7919
.08
.0169
.5047
.0304
.0303
39
30
.oxxx
x.oxxz
6.7655
.0x38
1*0x39
6.^5^8
.017
X.017
54874
.0204
X.O205
.033
5.0x58
3»
.oxxx
•7533
.0139
.0483
.0X7X
.4788
.0305
.0087
33
.OXX3
•739a
.0x4
.0379
.0x71
•4702
.O306
.0015
33
.OXZ3
.7263
.014
.0374
.0173
.4617
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4-9944
-9873
34
.oxx 3
.7'3a
.0x41
.0x7
.0x73
•4532
.0307
35
X.0XX3
6.7003
X.0X4X
6.0066
1.0x73
54447
X.O308
4.9803
36
.0XX4
.6874
.0x43
59963
.0x74
.4362
.0208
.9732
37
.0x14
.6745
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.4278
.0209
.9661
38
.0x15
.6617
•0143
.9758
•0175
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•959'
39
.0x15
.649
•o«43
•9655
.0175
.411
.031
•9521
40
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Co^bc't. Sbcabt.
640
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56
55-
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53
53
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f
402 NATUBAX SINES AND COBINBS.
a.— What is cosine of 8° 9' 10"?
Cosine of 8° 9', per Table = . 08c 00;) a-««.— -
Cosine of 80 10', - =.595?6;1 ^^^^ *#;mice.
In right-side column ot proportional parts, under 4, and opposite to 10', is z, tbd
correction for 10', which, being subtracted fVom .989 90 = .989 89 cosine.
When Angle exceeds 45*^. Rule. — Ascertain sine or cosine for angle ip
degrees and minutes from Table, taking degrees at the foot of it ; then take
difference between it and sine or cosine <>f angle next above it. Look for re-
mainder, a Sine is required, at head of Cdlumn of Proportionat Paris, on right
side; and if Cosine is required, at head of column on left side; and in these
respective columns, opposite to seconds of aiigle, is number or correction in
seconds to be added to 8ine, or subtracted from Cosine of angle.
Illustration. — What is the Sine and Cosine of 81° 50' 50"?
Sine of 81° 50', per Table = .989 86 ; I ^^^^^ ^,wr*^*«A-
Sine of 81° 51', " =..98^9; J^^****-^^*^
In right-side column ot proportional parts, and opposite to 50', is 3, which, added
to .989 86 = .989 89 Sine.
Cosine of 81° 50', per Table = . 142 05 ; i ,^^^^ mif^^^
Cosine of 810 |i', " =.141 77;) '°^^^ ^^ff^^^^e.
In left-side column of proportional parts, and opposite to 50', is 24, Which, sub-
tracted f^om . 142 05 = . 141 81 Cosine.
1?o ^Boertaiu or Compute dumber oriDegrees, AlinuteSy
and Seconds of a given Sine or Cosine.
When Sine is given. Rule. — If given sine is in Table, the degrees of it
will be at top or bottom of page, and minutes in marginal culunm, at left or
right side, according as sine corresponds to an angle less or greater than 45 '^.
if given sine is not in Table, take sine in Table which is next less than the
one for which degrees, etc., are required, and note d^rees, etc., for it. Sub-
tract this sine from next greater tabular sine, and also from given sine.
Then, as tabular difference is to difference between given sine and tabu-
lar sine, so is 60 seconds to seconds for sine given.
Example. —What are the degrees, minutes, and seconds for sine of .75?
Next less sine is -74092, arc for which is 48° 35'. Next greater sine is 75011,
difference bettoeen whiik and next less is .75011 — .74992 = .00019. Difference be-
tween lest tabular sine and one given w . 75 — . 749 92 ^ ^
Then 19 : 8 : : 60 : 25+, which, added to 48© 35' =r 48° 35' as".
Cosine is given. Rule. — If given cosine is forind in Table, degrees
of it wiirtJfftsf^und as in manner specified when sine is given.
If given cosii^e is not in Table, take cosine in Table which is next^rfo^er
than one for whi^h degrees, etc., are required, and note degrees, etc., for it.
Subtract this cosin^rom next less tabular cosine, and also from given cosine.
Then, as tabular dflfference is to difference between given cosine and tabu-
lar cosine, so is 60 secOTni^^a to seconds for cosine given.
E.xample.— What are the degrees, minutes, and seconds for cosine of .75?
Next greater cosine is .750 iV^ arcfhr which is 41° 24'. Next less cosine is .74993,
difference between which and rirxt greater t* . 750 1 1 — .749 92 = .000 19, IHfference
between greater tabular cosine ^And one given is .j so it — . 75000 = 1 1.
Then 19 : 11 : : 60 : 35 — , wAich. added to 41O 24' = 41© 24' 35".
To CoTxipxite Verged Sine of an A.zisle.
Subtract cosine of angle from i.l
Illustration.— What is the versed dine of 2i<* 30' f
Cosine of 21^ 30' is .930 42, which, — 1 = .069 58 versed sine.
To Compute Go-vev,8ed Sixxe of an i^Lzisltt.
Subtract sine of angle from i.
JJ.U8TIUT10N.— What is the co-versed ^ine of 21® 30'?
The sine of 21© 30 is . 3665, wbfeh, — 1 = .6335 co-versed tkne.
NATniUX BBCANTS AKO OO-SBCANTB.
413
40O 1
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(CANT.
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NATUKAL SBCANTS AND CO-SKCAMTB.
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50
450
Preceding Table contains Natural Secants and Ck>-8ecant8 for every
minute of the Quadrant to R;idiu8 i.
If Degrees are taken at head of column, Minutes, Secant, and Co-secant
must be taken from head also; and if they are taken at foot of column,
Minutes, etc., mu.st be taken from foot also,
iLLrsTRATioN — 1.05 is secaot of 17O 45' and co-secant of 72° xs'.
To Coxwpute Secaxit or Co-secaxxt of any Angle.
RuLB.—Divide i by Cosine of angle for Secant, and by Sine for Co-secant.
ExAVPLB i.^Wbat is secant of 25^ 25' ?
Cosine of angle = .903 21. Then x -r- .903 3x = x. X073, Secant
9. —What is CO secant of 64O 35'?
Sine of angle = .903 21. Then i -f- .903 21 = X.X079, Co-secant
To Oomp-ute Dffgrees, :^f inxxtes, and Seconds of a Seoant
or Co-seoant.
When Secant is given,
Proceed as by Rule, page 402, for Sines, substituting Secants for Sines.
ExAMPLR. — What is secant for x.1607?
The next less secant is i. x6o6, arc far which =3 30° 30'.
Kext greater secant is 1.1608, difference between which and next less is z.x6o8—
1. 1 606 = ,0002.
JHfference between less tab. secant and one given is 1. 1607 — x. 1606 = .0001.
Then .000a : .0001 :: 60 : 30, which, added to 3o<> 3o'=3o<' 30' y/\
When Cosecant is given^
^"ooeed at by Rule^ page 400) rubstitutiug Co-secanta for CotlMi.
KATtJEAL TANGBNTS AND CO-TANCfBKTS.
415
TTatural Tangents
00 II 10
Tang. | Co-tano. |, Tako. Co^ano,
0
.00000
z
.00039
.00058
.00087
.OQX z6
a
3
4
5
6
.«>i45
.00175
i
9
.00004
.00233
.00262
10
.00291
IX
.0032
X3
13
»4
15
16
17
j8
19
30
31
33
33
24
«5
36
39
30
3«
32
33
34
35
36
37
38
39
40
4«
42
43
44
45
46
47
48
49
50
5«
5«
53
S4
55
56
57
58
£^
.00349
.00378
.00407
.00436
.00465
.00495
.00524
•00553
.00552
.006 II
.0064
00669
.00698
.00727
.00756
.00785
.008 14
.00844
.00873
.00902
.00931
.0096
.00980
.010 to
.0x047
.0x076
.01105
•o»x 35
.01x64
.oix 93
.oxa 32
.0x251
.oxa 8
.01309
.01338
.01367
.0x396
.0x435
0x455
.014 84
.0x5x3
.0x543
.0x571
.0x6
.0x639
.0x658
.01687
.0x7 16
.0x7 46
lufiuite.
3437f5
X718.87
X45.92
859-436
687.549
572-957
491. X06
29.718
38X.97X
343-774
12.521
286.478
64.44X
45-552
329.182
14.858
02.219
190.984
8a 032
X71.885
637
56.259
49465
43237
137-507
32.219
27.32X
22.774
18.54
X14.389
XOL892
07.426
04.X7X
01.107
98.2179
5-4895
3.9085
0.4633
88.1436
85.9398
3-8435
1.847
79-9434
8.X263
76-39
4-7292
3- "39
X.6131
0-X533
6&7SOX
7-4019
6.1055
4.858
3-6567
63.4092
X.3820
0*3058
5*2659
8.36x2
57-29
J2
CO-TAS*. TaMQ.
80O
.01746
.01775
.01804
.018 33
.01862
.01891
.0192
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.019
.02007
.02036
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.02095
.021 24
.02153
.021 82
.022 II
.0224
.02269
.02298
.02328
.02357
•02386
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•02473
•02502
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.0256
.02589
.02610
.02648
.0^77
.02706
.02735
.02764
•03793
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.03851
.02881
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•03939
.03968
.03997
.03026
•03055
.03084
.03x14
•031 43
.03x72
.032 ox
.0323
.03259
.032 88
•033 « 7
.03346
.03376
•03405
•03434
•03463
.03492
and. Co-tungents.
20 30
Tano. ! Co.T*NO.
TaMS. I CO-TANO.
I:
57.29
6.3506
5.44>5
4.5613
3.7086
53.8821
3.0807
X.3032
0.5485
49.8157
40. 1039
8.4121
7.7395
7.0853
6.4489
45.8294
5. 2261
4-6386
4.0661
3- 5081
42.964X
2-4335
X.9158
X.4106
0.9174
40-4358
399655
6177
38.1885
7.7686
7-3579
6.956
6.5627
36.1776
5.8006
54313
50695
4-7151
34.3678
40273
36935
3-3662
3-0452
32.7303
2.4313
3.xx8z
1.8205
1.5284
31-^16
0.9599
0.6833
0.41 16
O.X446
39.8823
9.6245
9-37i«
?<X22
.877X
38.6363
.03492
-035 21
•0355
.03579
.03609
.03638
.03667
.03696
03725
.03754
.037 83
.038 12
.038 42
.03871
.039
.039 20
.03958
•03987
.040 16
.04046
•04075
.04104
.04133
.04162
04191
0422
0425
•04279
.04308
.04337
.04366
•04395
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•044 54
•04483
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0457
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0493
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•05X 53
• 05x82
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28.636:)
8.X664
79372
7.7X17
27.4899
7.2715
7.0566
6.84s
6.6367
26.4316
6.2296
6.0307
5-8348
5.6418
254517
5.2644
5.0798
4.8978
4-7185
24.5418
43675
4- 1957
4-0263
3-8593
236945
3-5321
33718
3-2137
30577
22. 9038
2.7519
3. 603
2.4541
3.3081
32. 164
2.0217
X.8813
Z.7426
X.6056
21.4704
■1.3369
<x.3049
10747
0.046
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0.6932
0.5691
0.4465
0.3253
802056
0.0872
19. 0702
9-8546
9^7403
X9.6373
9.5156
9-4051
9.2059
91879
19.08x1
Co^AiiB; Tamo.
88O
Co-TARO. Tamo.
i 87°
•05241
.0527
.05290
.05338
•053 57
.05387
.054 x6
•05445
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.062 91
.06321
.0635
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laoStx
8.9755
8. 87 IX
8.7678
8.6656
18.5645
8.4645
8.3655
8. 2677
8.1708
x8.075
7.0802
7.8863
7-7934
7-7016
17.6106
7-5205
74314
73432
72558
17. 1693
7.0837
6-999
6-Q15
6-8319
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6.6681
6.5874
6-5075
6.4283
16-3499
6.2722
6. 1952
6.x 19
6-0435
15.9687
5-8945
5.8211
57483
5-6762
15.6048
5-534
5.4638
5-3943
5-3254
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51893
5. 1222
5-0557
4.9898
14.9344
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4-7954
4-7317
4-6685
14.6050
4-5438
4.4833
4-42x2
4.3607
14-3007
60
5
57
56
55
54
53
52
51
50
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47
46
45
44
i43
42
41
40
3
37
36
35
34
33
32
31
30
2
27
26
25
24
23
22
21
20
\i
17
x6
15
14
13
X2
XX
10
7
6
5
4
3
3
z
Co-TAMO. Tamo. ■ '
86°
NATUE&L TANtiKNTS AND CO-
4
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'SKh
JTATUAAL TANGENTS AND CO-TANGENTS.
417
8©
TAJr«. C<vrAire.
o
I
2
3
4
5
6
7
8
9
xo
XX'
X2
13
14
X5
x6
17
x8
«9
ao
3X
a3
«3
24
25
26
27
28
30
31
32
33
34
35
36
37
38
39
40
4»
4a
43
44
45
46
*2
48
49
50 i
52 ]
53
54
55
56
57
58
12
4054
4084
4H3
4M3
4' 73
4203
4232
4262
429"
4321
43 51
43 8x
441
444
447
4499
4529
45 59
4588
46x8
4648
4678
4707
47 37
4767
4796
4826
4856
4886
49^5
4945
4975
5005
5034
5064
5094
5124
5153
5183
52x3
5243
5272
5302
5332
5362
5391
5431
545«
5481
55"
554
557
56
563
566
5689
5719
5749
5779
5«oo
5838
II
90
Tamo. Co«avo.
7- "5 37
.10038
.08546
.07059
•05s 79
7.041 05
.02637
•oxx 74
6.907 18
.98268
6.96823
.95385
•939 52
.92525
.91104
6.89688
.88278
.86874
.85475
.84082
6.82694
.81312
•79936
.78564
6.75838
•74483
•73«33
.71789
•7045
6.691 16
.67787
.66463
.65x44
.63831
d.625 23
.612 19
.59921
.58627
•573 39
6.56055
•547 77
.53503
•52234
.5097
6.497 I
•484 56
.47206
•45961
•4472
643484
'422 53
.4x036
•39804
•38587
6.37374
.36165
•34961
.33761
.32566
6.31375
CoHMir«. Tamo.
81 9
5838
5868
5898
5928
5958
5988
6017
6047
6077
6107
6137
6x67
6196
6226
6256
6286
6316
6346
6376
6405
6435
6465
6495
6525
6555
6585
66x5
6645
6674
6704
6734
6764
6794
6834
^54
6884
69x4
6944
6974
7004
7033
7063
7093
7123
7153
7183
7213
7243
7273
7303
73 33
7363
7393
7423
74 53
7483
7513
7543
7573
7603
7633
6.31375
.30189
.29007
.27829
.26655
6.25486
.24321
.2316
.22003
.20§5I
6. X97 03
.18559
•17419
.X6283
•15151
6.X4023
.12899
.11779
.X0664
•09552
6.084 44
TAIie. I Co-TA«G.
•79944
•789
'75941
•74949
•7396
•72974
s 719 92
•71013
•70037
.69064
.68094
5.67X 38
Co.«AlfO. TAMO.
80O
7633
7663
7693
7723
77 53
7783
7813
7843
7873
7903
7933
7963
7993
8023
8053
8083
8x13
8143
8173
8203
8233
8263
8293
8323
8353
8383
84x4
8444
8474
8504
8534
8564
8594
8624
8654
8684
87x4
8745
8775
8805
8835
8865
8895
8925
8955
8986
9016
9046
9076
9106
9136
9x66
9197
9227
9257
9287
9317
9347
9378
9408
9438
67128
66165
65205
64248
63295
62344
61397
60452
59511
58573
57638
56706
557 77
54851
53927
53007
5209
51176
50264
49356
48451
47548
46648
45751
44857
43966
43077
42192
41309
40429
39552
38677
37805
36936
3607
35206
34345
33487
32631
31778
30928
3008
29235
28393
27553
26715
2588
25048
242x8
23391
22566
21744
20925
20107
19293
184I
X767I
X6863
16058
15256
14455
110
Tamo. | Co^amo.
19438
19468
19498
19529
19559
19589
X9619
19649
1968
1971
1974
1977
X980X
19831
198 61
19891
19921
19952
19982
200 X2
20042
20073
30103
20133
30x64
30x94
SOS 34
30354
30385
203x5
20345
30376
304J06
30436
20466
20497
30537
20557
20588
20618
20648
30679
20709
20739
2077
3o8
2083
30861
30891
30931
30953
30983
310x3
SX043
21073
31x04
211 34
3x164
3x195
313 25
.31356
C<HEAK». XAMa.
790
514455
.13058
.12862
.12069
.11279
5.1049
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.081 39
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5-065 84
.05809
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5.Q27 34
.019 71
.012 X
•00451
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4.9894
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4.95201
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4.915x6
•90785
.90056
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4.87882
.871 62
•86444
•85727
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4.80769
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•74534
473851
•7317
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4- 704 63
60
59
58
57
56
55
54
53
52
51
50
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
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418
MATUBAI. TAKafHTg AJTD CO-TANGKNTB.
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3.98607
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420
NATUBAL TANGBliTS AND CO-TANGENTS.
200 1
210
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Co-TAMO.
Tamo. C
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2.74748
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18
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20
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58
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Co-TAMO.
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Co-TAMO.
0
90
680
220
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40572
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40674
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40945
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410 13
41047
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41217
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417 28
41763
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41831
41865
41899
41933
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42207
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2.404 32
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2.38473
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2.37504
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2.35585
Co-TAHO. Tamo.
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2.35585
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Co-TAMO.
Tamo.
6
60
60
59
58
57
56
55
54
53
52
5>
50
49
48
47
46
45
44
43
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37
36
35
34
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31
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27
26
25
24
23
23
21
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NATURAL' TANGENTS AND CO-TANQKNTS.
421
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9
3
4
5
6
7
8
9
10
II
13
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14
15
16
17
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20
31
23
83
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25
36
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4«
43
43
44
45
46
47
48
49
50
S«
52
53
54
55
56
57
58
59
60
240
Tamo. | Co-tan«.
260
Taito. Co4ar«.
44523
44558
44593
44627
44662
44697
44732
44767
44802
44837
44872
44907
44942
44977
45012
45047
45082
45117
45«52
45187
45222
45257
45292
45327
45362
45397
45432
45467
45502
45537
45573
45608
45643
45678
457 '3
45748
45784
45819
45854
45889
459 JH
4596
45995
4603
46065
461 01
46136
461 71
46206
46242
46277
46312
46348
46381
46418
46454
46489
46595
4656
46595
46631
24604
24428
24252
24077
23903
23727
235 53
23378
23204
2303
22857
22683
2251
22337
22164
21992
218 19
21647
21475
21304
211 32
30961
2079
20619
20449
30278
20108
9938
9760
95 .«
943
9261
9092
8923
8755
8587
8419
8251
Bo 84
79 «6
7749
7582
7416
7249
7083
6917
6751
6585
642
6255
609
2.
5925
576
5596
5432
5268
5104
494
47 77
4614
4451
Co^AKo.; Taxo.
650
46631
46666
46702
46737
46772
46808
46843
46879
46914
4695
46985
47021
47056
47092
47128
47163
47199
47234
4727
47305
473 41
473 77
474"
47448
47483
47519
475 55
4759
47626
47663
47698
477 33
47769
47805
4784
47876
47912
47948
47984
48019
48055
48091
48137
48163
48198
48234
4827
48306
48342
48378
48414
4845
48486
48521
48557
48593
48629
48665
48701
48737
48773
144 51
14388
M'25
"3963
138 01
13639
>34 77
13316
13154
12093
12832
126 71
125 II
1235
121 9
1203
I1871
117 II
11552
1 13 92
"233
1 10 75
109 16
10758
106
10442
10284
lOI 26
09969
098 1 1
09654
09498
09341
091 84
09028
08872
087 16
0856
08405
0825
08094
07939
077 85
0763
07476
07321
07167
07014
0686
06706
06553
064
■06247
06094
05942
057 9
05637
05485
05333
05182
0503
260
Tamo. | Co-taiw.
Co-tamo. Tano.
640
48773
48809
48845
48881
48917
48953
48989
49020
49062
49098
49134
4917
49206
49242
49278
49315
49351
49387
49423
494 59
49495
49532
49568
49604
4964
49677
49713
49749
49786
49823
49858
49894
49931
49967
50004
5004.
50076
50113
50149
50185
503 22
50258
50295
50331
50368
50404
504 41
50477
50514
5055
50587
50623
5066
50696
50733
50769
50806
50843
50879
50916
50953
0503
04879
04728
04577
04426
04276
0*135
"39 75
03825
03675
03526
03376
03227
03078
02929
0278
02631
02483
02335
03187
02039
018
91
01743
01596
01449
01302
01155
010 08
00862
007 IS
00569
00423
00277
001 31
99986
99841
99695
9955
99406
99261
99' 16
95272
98828
98684
98s 4
98396
98253
981 1
97966
97823
9768
97538
9739s
97253
971 II
96685
96544
96402
96261
CO-TAMO.I XaNU.
630
270
1
Tamo. | Co-tano.
•509 SS I
.96261
.50989
.961 2
.51026
■95979
-51063
.95838
.51099
.95698
.51136 1
95557
.51173
95417
.51209
95277
•51246
95137
.51283
94997
94858
.51319 I
.51356
94718
.51393
94579
.5143
9444
•51467
94301
•51503 I
94162
•5154
94023
•51577 '
93885
.51614 .
93746
.51651
93608
.51688 I.
93^7
•51724 ■
93332
.51761 .
93195
.51798 •
.51835 •
93057
9293 .
.51873 I.
92782
.51909 .
92645
•S1946
92508
.51983
92371
.5302
92235
.52057 I
92098
•52094
91962
91026
.53131
.521 68
9169
.52205
9'5 54
914 18
.52243 I
•52279
91282 1
.52316
91147
•52353
910 12
•5239
90876
.52427 I
90741
.52464
90607
•52501
90472 1
.52538
90337
•52575
90203
.52613 I
•5265
Q0069
29235
89801
.52687
•52724
.89667
.52761
89533
.52798 1
■894
.52836
.89266
•52873
89133
.5291
•52947
'8i867
•52984 1
S23^
.53022
.88602
•53059
.88469
.53096
•88337
•53134
88305
■53171 1
88073
Co-TAMO.i
Taao.
6*0
60
59
58
57
56
55
54
S3
52
5"
50
Ji
47
46
45
44
43
42
4«
40
3
37
36
35
34
33
32
3x
30
31
27
36
25
24
23
33
31
30
:i
17
16
15
14
13
12
II
10
t
I
5
4
3
a
I
o
422
NATtJBAL TAKGENTS AND CO-TANGENTS.
o
I
2
3
4
5
6
7
8
9
lO
II
12
13
M
15
i6
>7
i8
19
20
31
22
a3
24
25
36
39
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
28©
Taho. Co-tak«.
5317"
53208
53246
53283
5332
53358
53395
53432
5347
53507
53545
53582
5362
53657
53694
53732
53769
53807
53882
5392
53957
53995
54032
5407
54»o7
54M5
54183
5422
54258
54296
543 33
543 7'
54409
54446
54484
54522
5456
54597
54635
54673
547 « I
54748
54786
54824
54862
549
54938
54975
550x3
55051
55089
55127
55165
55203
55241
55279
553 > 7
553 55
5539?
554 3'
• 88073
.87941
.87809
87677
.87546
1.874 15
• 87283
,871 52
,87021
.86891
Z.8676
.866
.864
863 _^
,86239
X.861
859
.858
.857.
•8559'
8546:
13 33
1204
853
,852«,
85075
?4r -^
^99
169
39
09
79
5
2
84S
©46
^48 18
84689
84561
84433
•84305
,84177
,84049
.83922
83794
83667
8354
■834 '3
.83286
831 59
•83033
1.82906
,8278
■ 82654
.82528
.82402
1.82276
8215
82025
81899
81774
z. 816 49
81524
81399
81274
.8115
z. 81025
,80901
80777
80653
,80529
X. 804 05
COTAiia. Tah«.
610
290
Tako. Co-tavo.
55431
55469
55507
555 45
55583
55631
55659
55697
55736
55774
55812
558 s
55888
55926
55964
56003
56041
56079
561 17
56156
56194
56232
5627
56309
56347
56385
56424
56462
56539
56577
56616
56654
56693
56769
56808
56846
56885
56962
57
57039
57078
57n6
57*55
57«93
57232
57271
57300
57348
57386
57425
57464
57503
575 4«
5758
57619
57657
57696
577 35
80405
8028^
8015s
80034
799"
79788
79665
79542
794x9
79296
79«74
Co-TAire. TAxa.
I 000
\
30O
Tahs. Co-tano.
57735
57774
57813
57851
5789
57929
57968
58007
580 a6
58085
58124
58162
58201
5824
58270
58318
58357
58396
58435
58474
585x3
58552
58591
586 3X
5867
58709
58748
58787
58826
58865
58904
58944
58983
59023
59061
59x01
59M
59»79
592x8
59258
59297
59336
59376
594x5
59454
59494
59533
59573
596x2
59651
596 9z
597 3
597 7
59809
5988
59928
59967
60007
60046
60086
CO-TAMA.
73205
73089
72073
72857
72741
72625
72509
72393
72278
72163
72047
Taks.
ago
310 {
Tak«. Co-tako.
60086
601 26
60165
60205
60345
60284
60324
60364
60403
60443
60483
60533
60563
60602
60642
60681
60721
60761
608 ox
60841
608 8r
60921
6096
6x
6x04
6108
6ll9
6x1 6
613
6134
6138
6133
6x44
6148
6153
."61561
.61601
.616 41
.61681
.61721
.61761
61801
61843
61883
61933
61963
.63003
.63043
.63003
.631 34
63164
.63304
.633 45
63385
.63335
.63366
.63406
• 634 46
.62487
CO-TAlf«.
1.66438
.66318
.66309
.66099
.6509
X.65881
•65772
.65663
•65554
•65445
1-65337
.65328
.6513
.65OIZ
.64903
1.64795
.64687
•64579
.64471
.64363
1.64356
.641 48
.64041
•63934
.63826
X.637 19
.636 Z3
•63505
.63398
.63393
X.631 85
.63079
.62973
.62866
6376
X. 636 54
.62548
.63442
62336
6223
1.62135
.63019
.6zoz4
.61808
.61703
z. 61598
•6x493
.61388
.61383
.6zi 79
z. 610 74
.6007
.60865
.60761
.60657
«6os53
•60449
•6034s
.6CK14X
•60X 37
1.60033
Tami
580
60
%
57
5<f
55
54
53
52
5x
50
Ji
47
46
45
44
43
42
4X
40
n
37
36
35
34
33
32
3x
30
37
36
25
24
»3
sa
sx
«o
:i
12
«5
X4
X3
X3
ZX
ZO
I
7
6
5
4
3
t
NATUBAL TANSXNTS AND CO-TANOBNTS.
423
o
I
3
4
I
I
9
10
XI
13
13
»4
«o
31
a3
as
3:
39
30
3»
33
33
34
3§
36
3
39
40
4"
43
43
44
45
♦6
49
5«
51
53
S4
P
57
58
320
330 II
340 II
350 1
Tano. Co-TANa.
Tana.
d<VTAKO.
Tano.
Co^TANO.
Tahs.
CO-TAHO.
.62487 I
60033
.64941
,.53986
•674 51
1.482 56
.70021
1.42815
.625 27
S9826
.64982
.53888
•67493
.48163
.70064
.427 26
.62568
.65023
•53791
•675 36
.4807
.70107
.42638
.62608
59723
.65065
.53693
•67578
•47977
•47885
.70151
•4255
.62649
.5962
.65106
•53595
.6762
.70194
.70238
.42462
.62689 <
59517
.65148
.65189
153497
,67663
1.47792
1.42374
.42286
.6273
.594 '4
•534
.67705
•47699
.70281
.6277
593"
.65231
•53304
•67748
.47607 1
70325
.421 98
.628 II
.59208
•652 72
.53205
.6779.
•47514 !
.70368
.421 I
.62852
.59x05
•653 14
.53107
.67832
.47422
.70412
.420 22
.62892 I
.59002
•65355
1.5301
.67875
«4733 [
•70455
"•41934
.62933
.589
•65397
.65438
.52913
.52816
.679 ,7
.47238 1
•70499
.41847
.62973
•58797
.6796
.68002
.47146 1
.70542
.70586
•417 59
.630 14
•58695
.6548
.52719
.47053
.41672
•63055
.58593
.65521
.52622
.68045
.46962
1.4687
.70629
.41584
.6^095 r
t^%^
•65563
1.52525
.68088
•70673
1.41497
.631 36
.65604
•52429
.6813
•46778
.70717
.41409
.631 77
.58286
.65646
.52332
•S* 73
.46686
.7076
.70804
.41322
.63217
.63258
.58184
.65688
.52235
.682 15
•46595
.41235
.58083
•65729
52139
68258
•46503
.70848
.41148
•63299 I
579 8 1
•65771
1.52043
.68301
1.464 11
.70891
X.41061 '
.6334
•6338
.57879
•57778
•55^3
.51046
.5185
•?S3^3
-4632
•70935
.:si? !
.65854
.68386
.46229
.70979
.6342*
57676
.65896
.51754
.68429
•461 37
.71023
.408
.63462
•575 75
.65938
.51658
.684 71
.46046
.71066
.40714
.63503 X
574 74
.6598
1.51562
.685 14
14595s
•45864
.711 1
X. 406 27
•63544
57372
.00021
.51466
,.68557
•7" 54
•4054 i
•63584
5727'
.66063
•5137
.686
45773
.45682
.71198
.40454 1
.636 25
5717
.66105
.51275
.68642
.71242
.40367
.63666
.57069
.66,47
.51179
1.5,084
.68685
•45592
.71285
.40281
.63707 I
56969
.66189
.68728
'•45501
71329
1.40195
.63748
36868
.6623
.50088
• 50893
.68771
.688 14
•4541
•71373
.40109
•63789
56767
.66272
•4532
.71417
.40022
•5383
.63871
56667
56566
.66314
.66356
.50797
.50702
.68857
•45229
•451 39
.71461
•71505
.39936
.3985
.63912 I
56466
.66398
1.50607
.68942
.68985
1.45049
•71549
1.39764
•63953 '
56366
.664^
.66482
.50512
•44958
44868
•7'593
•39679 1
.63994
56265
.50417
.69028
•71637
.39593 I
•64035
56165
.66524
.66566
.66608
.50322
.69071
•44778
716 81
•39507
64076
56065
.50228
.69114
.44688
•71725
V 394 21
641 17 1.
55966
I 50133
69157
1.44598
.71769
'•39336
.641 58
55866
.6665
.50038
■692
.44508
.71813
.3925
.641 99 ,
55766
.66692
.49944
.49849
•69243
•44418
•71857
.39165
.6424
55666
.66818
.69286
•44329
.71901
.39079
.38994
.64281
55567
•49755
.69329
•44239
.71946
.643 22 I.
55467
1.496 61
•69372
1.441 49
.7199
1.38909
.38824
•64363
55368
.6686
.49566
.69416
.4406
•72034
.64404 .
55269
.66902
•49472
69459
•439 7
.72078
.38738
.64446
5517
■^'^
.49378
.69502
.43881
.72122
.38653
.64487 .
55071
.49284
.69545
•43792
.72166
.38568
'64528 I
54972
.67028
1.491 9
.69588
1-43703
.722x1
1.38484
•64569
54873
.67071
.49097
.69631
•436 14
•72255
•38399
•6461
54774
.671 13
.49003
.69675
•43525
•72299
.383 14
.646 52
54675
.671 55
.48900
.48816
.69718
.43436
.72388
.38^29
.64693
54576
.671 97
.69761
.43347
.3?» 45
.64734 '•
54478
.67239
.67282
1.48722
.69804
'•432 18
.43169
•72432
X.3806
•647 75 •
S4379
54281
.48629
.48536
.69847
•72477
.37976
.3789*
.64817
■%v^
.69891
.4308
.72521
.64858
54183
•48442
•69934
.42992
.72565
.37807
.64899 .
54085
53986
.67409
•48349
.69977
•42903
1.42815
.7261
•37722
•^494' '
.67451
1.48256
.70021
•72654
'•37638
Co4:Aa«.
liAJia.
Co-TAXA.
Tamo.
Co-TAN«.
Tamo.
CO-TAKO.
Tans.
«7o
6
60
6
6<5
6
40
60
5
57
56
55
54
53
52
5«
50
%
47.
46
45
44
43
42
41
40
3'
37
36
35
34
33
32
31
30
I
2
2
25
24
23
22
2Z
20
\%
;i
'5
14
13
12
xz
10
%
7
6
5
4
3
2
z
o
414
NATURAL SECANTS AND CO-SSCANTS.
440
SiCAira. Co-nc'T.
I
4A^ \
4«
SCCANT.
Co-ac*r.
1.4065
1.4221
42
.4069
.4217
43
.4073
.42x2
44
•4077
.4208
45
1.4081
1.4204
46
.4085
•^' .
47
.4089
.4196
48
•4093
•t:?s
49
.4097
SO
X.4IOZ
1.4183
51
.4105
•4»79
52
.4109
•4»75
53
•4"3
.4171
54
.4117
.4167
55
1.4122
1.4163
56
.4126
•4«59
57
•413
•4154
58
•4»34
.415,
?9
.4«38
.4146
60
1.4142
1.4142
Co-«BCt.
Sbcamt.
450 1
II
17
16
>s
X4
"3
12
II
10
I
7
6
5
4
3
2
I
o
i
Co-*kc't. I Secant.
450
Preceding Table contains Natural Secants and Co-secants for evei7
minute of the Quadrant to Radius i.
If Degrees are taken at head of column, Minutes, Secant, and Co-seeant
must be taken from head also; and if they are taken at foot o( column.
Minutes, etc., must be taken from foot also,
Illustration —1.05 is secant of 17O 45' and cosecant of 72° 15'.
To Compvite Secant or Co-seoant of* Any Angle.
RuLB. — Divide i by Cosine of angle for Secant, and by Sine for Co-secant
ExAMPLK L— What is secant of 25O 25' ?
Cosine of angle = .903 21. Then i -r- .903 21 = 1. 1072, Secant
2.— What is CO- secant of 64O 35'?
Sine of angle = .903 21. Then t -?- .903 21 = 1. 1072, Co-gecant.
To Compute D«*grees9 !Minntes, and Seconds of* a Secant
OP Co-seoant.
When Secant it given,
Proceed as by Rule, page 402, for Sines, substituting Secants for Sines.
ExAMPLB. — What is secant for 1.1607?
The next less secant Is i.x6o6, arc for wkxchrssyp -y/.
Next greater secant is 1.1608, differe^ncc between which and next lest it 1.1608—
1.1606^.0002.
Difference betioeen less tab. secant and one given is 1. 1607 — x. 1606 = .0001.
Then .0002 : .0001 :: 60 : 30, which, added to 30O y/ssyP 30' 30"^.
When Co-tecant it given^
Proceed m by Rule^ page 40a, srubstitutlng Co-secants for Cosfamk
»ATtraAL TANGBNTS AND CO-TANGENTS.
415
IQ'atiiral Xangexxts
00
1° II
f
Taho.
C0.TAN0. 1
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176 71
16863
16058
15256
14455
11°
Tamo. I Co-tako.
19438
19468
19498
19529
19559
19589
196 19
19649
1968
1971
1974
1977
19801
19831
19861
198 91
19921
19952
19982
20012
20042
20073
20103
20133
20164
20194
20234
20254
20285
20315
20345
20376
20406
20436
20466
20497
20527
20557
20588
20618
20648
20679
20709
20739
2077
208
2083
20861
20891
20921
20952
20982
21013
21043
21073
21104
21134
211 64
211 95
21225
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5- 144 55
.13658
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4.99695
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470463
CO^TAKO. TAIfOk-
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56
55
54
53
52
51
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46
45
44
43
42
41
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35
34
33
32
31
30
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27
26
25
24
23
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21
20
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16
15
14
13
12
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NATURAL TANGSNTft A^TD CO-TANGSKTB.
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53
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Tams. Gs-*AMa.
21256
21286
21316
21347
21377
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21469
21499
21529
2156
2«5 9
21621
216 51
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32017
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231 69
233
22231
22261
32292
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223 53
32383
22414
33444
23475
33505
32536
22567
22597
32628
32658
33689
32719
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NATUfiAL TANGENTS AND CO*TANOENTS.
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Tamo. Co-taro.
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1
2
3
4
5
6
7
8
9
20
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12
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20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
5'
52
53
54
55
56
57
58
59
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36397
3643
36463
36496
36529
36562
36595
36628
36661
36694
36727
3676
36793
36826
36859
36892
36925
36958
36991
37024
37057
3709
37124
37157
3719
37223
37256
37289
37322
373 55
37388
37422
374 55
37488
37521
375 54
37588
37621
37654
37687
3772
377 54
37787
3782
37853
37887
3792
37953
37986
3802
38053
38086
3812
38153
38186
3822
38253
38286
3832
38353
38386
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2.72281
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2.68653
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2.67462
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2.66281
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2.65109
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2-63945
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2.62791
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2.61646
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2.60509
210
TaKO. I CO^AMO.
Co-TAMO. Tamo.
690
38386
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38453
38487
3852
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38587
3862
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38687
38721
38754
38787
38821
38854
38888
38921
38955
38988
39022
39055
39089
39122
39156
3919
39223
39257
3929
39324
393 57
39391
39425
39458
39492
39526
395 59
395 93
39626
3966
39694
39727
39761
397 95
39829
39862
39896
3993
39963
39997
40031
40065
40098
40132
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402
40234
40267
40301
40335
40369
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2.60509
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60057
59831
59606
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58932
58708
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58261
58038
57815
57593
57371
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56707
56487
56266
56046
55827
55608
55389
5517
54952
54734
54516
54299
54082
53865
53648
53432
53217
53001
52786
52571
52357
52142
51929
51715
51502
51289
51076
50864
50652
5044
50229
50018
49807
495 97
49386
49177
48967
48758
48549
4834
48132
47924
47716
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Cu-TAMo. Tamo.
680
220
Tamo. I Co-tano.
230
Tano. I Co-tamo.
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2.47509
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2. 464 76
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2.45451
•40775
.45246
.40809
•45043
•40843
.44839
.40877
.44636
.40911
2-444 33
•40945
•4423
.40979
•44027
.41013
43825
41047
.43623
.41081
2.43422
.41115
■4322
.41149
.430 19
.41183
.42618
.41217
.41251
2.42418
.41285
.422 18
•41319
.42019
.41353
•41819
.41387
.4162
.41421
2.41421
•41455
.41223
.4149
.41025
.41524
.40827
•41558
.40629
41592
2.40432
.41626
•40235
.4166
.40038
.41694
•39841
41728
.39645
•4»763
2^39449
•41797
-39253
.41831
.39058
.41865
.38862
.41899
.38668
•41933
2.38473
.41968
.38279
.42002
.38084
.42036
37891
•4207
•37697
.42105
237504
•42139
•37311
•42173
.37118
.42207
• 36925
.42242
.367 33
.422 76
2.36541
.4231
•36349
.36158
■42345
■42379
.35967
•42413
•35776
42447
235585
CO-TAKO.
Tamo.
6
70
.42447
235585
.42482
•35395
.425 16
• 35205
•425 51
•35015
-42585
• 34825
.426 19
2.34636
.42654
•34447
.42688
•34258
.42722
.34069
•42757
.33881
.42791
2.33693
.42826
.33505
4286
•33317
.42894
3313
.42929
•32943
.42963
2.32756
.42998
•3257
•32383
•43032
.43067
•32197
.43101
.32012
■431 36
2.3x826
•4317
.31641
.43205
•31456
-43239
.31271
•43274
.31086
•43308
2.30902
•43343
.30718
43378
■30534
.43412
-30351
•434 47
30167
.43481
2.29984
435 i6
298 01
.4355
.29619
.43585
29437
•4362
-29254
•43654
2.29073
.28891
43689
•43724
.2871
•43758
.28528
.43793
.28348
-43828
2.28x67
.43862
•27987
.27806
43897
•43932
.27626
•439^6
27447
.44001
2.27267
.44036
.27088
•44071
.26909
.44105
•2673
•4414
26552
.441 75
2.26374
.4421
.261 96
•44244
26018
44279
2584
•44314
.25603
443 '59
2.25486
■44384
.25309
.444 i3 .
.25132
444 53
.24956
44488
.2478
•44523
2. 246 04
Co-TAMO.
Tawq.
60
5
57
56
55
54
53
Sa
51
50
:i
47
46
45
44
43
42
41
40
3'
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
23
21
20
19
18
>7
16
15
«4
13
12
XI
10
7
6
S
4
3
a
t
a
66©
NATtlRAL' TANGENTS AND CO-TANGBNTS.
421
o
I
3
3
4
5
6
7
8
9
xo
II
13
'3
»4
15
16
17
x8
«9
so
31
33
23
«4
25
36
37
38
39
30
3'
33
33
34
35
36
37
38
39
40
4x
42
43
44
45
46
47
48
49
50
5X
52
53
54
55
56
57
58
59
60
240
Tamo. Co-tamo.
44523
44558
44593
44627
44662
44697
44732
44767
44802
44837
44872
44907
44942
44977
45012
45047
45082
4b* >7
45152
45«87
45222
45257
45292
45327
45363
45397
45432
45467
455 o3
45537
45573
45608
45643
45678
45713
45748
45784
45819
45854
45889
45924
4596
45995
4603
46065
461 01
46136
461 71
46306
46243
46277
46313
46348
46383
46418
46454
46489
46525
4656
46595
46631
24604
24428
24252
24077
23902
23727
23553
23378
23204
2303
22857
33683
2251
22337
32164
21992
218 19
21647
21475
21304
211 32
20961
2079
30619
30440
30378
30108
9938
9760
95 V9
943
9361
9092
8923
8755
8587
8419
8351
8084
7916
7749
7582
7416
7349
7083
6917
6751
6585
643
6255
609
5925
576
5596
5432
5268
5104
494
47 77
4614
4451
260
Tamo. Cotamo.
CkKTAMo.i Tamo.
65°
46631
46666
46702
46737
46772
46808
46843
46879
46914
4695
46985
47021
47056
47092
47x28
47163
47199
47234
4727
47305
47341
47377
47412
47448
47483
47519
47555
4759
47626
47662
47698
477 33
47769
47805
4784
47876
47912
47948
47984
48019
48055
48091
48x27
48163
48198
48234
4827
48306
48342
48378
484x4
4845
48486
48521
48557
48593
48629
48665
48701
48737
48773
4451
4288
4125
3963
3801
3639
34 77
3316
3154
2993
2832
2671
25 II
235
21 9
203
1871
1711
1552
1392
1233
1075
0916
0758
06
0442
0284
0x26
09069
098 II
09654
09498
09341
09 1 84
09028
00872
08716
0856
08405
0825
08094
07939
07785
0763
07476
07321
071 67
07014
0686
06706
06553
064
06247
06094
05942
0579
05637
054 85
05333
05182
0503
Co-XAKo. Tamo,
640
260
Tamo. | Co-TAMe.
48773 i 2.0503
48809 I .04879
48845 .04728
48881 .04577
48917 .04426
48953 2.04276
48989 .04x35
49026 .03975
49062 .03825
49098 .03675
49134 2.03526
4917 .03376
49206 .03227
49242 .03078
49278 .02929
49315 2.0278
49351 .02631
49387 .02483
49423 .02335
49459 .02187
49495 2.02039
49532 .01891
49568 .01743
49604 .01596
4964 .0x449
49677 2.0x302
497x3 .0x155
49749 .01008
497 86 .008 62
49822 .00715
49858 3.00569
49894 .00423
499 31 .00277
49967 .00x3,
50004 1.99986
5004. 1. 99841
50076 .99695
501 13 -9955
50x49 99406
50185 .99261
50222 X.99116
50258 .980 72
50295 .98828
50331 .98684
50368 .9854
50404 X.98396
504 41 .98253
504 77 .981 1
50514 -97966
505 5 -978 23
50587 X.9768
50623 .97538
5066 .9739s
50696 .97353
50733 -97111
50769 X. 969 69
50806 .96827
50843 .96685
50879 96544
50916 .96402
50953 1.962 61
CO-XAMO.I T>no.
630
270
Tamo. I Co-tano.
50953
50989
51026
51063
51099
51136
51173
51209
51246
51283
51319
51356
51393
5143
51467
51503
5154
51577
516x4
51651
51688
51724
51761
51798
51835
51872
51909
51946
51983
5202
52057
52094
52131
52168
52205
52243
52279
52316
52353
5239
52427
52464
52501
52538
52575
526x3
5265
52687
52724
52761
52798
52836
52873
5291
52947
52984
53022
53059
53096
53134
53171
96261
961 2
95979
95838
95698
95557
95417
95277
95137
94997
94858
94718
945 79
944 4
94301
94162
94023
93885
93746
93608
9347
93332
93195
93057
9292
92782
92645
92508
92371
92235
92098
9x962
91826
9169
91554
91418
91282
91147
910x2
90876
90741
90607
90472
90337
90203
90069
89935
89801
89667
89533
894
89266
89133
88867
88734
88602
88469
88337
88205
88073
Co-TA^o.l Tako.
1 1 62°
60
5
57
56
55
54
53
52
51
50
:i
47
46
45
44
43
42
41
40
li
37
36
35
34
33
32
31
30
2
27
26
25
24
23
22
21
20
\t
17
16
15
14
13
12
IX
10
t
I
5
4
3
a
I
natdbal takqbhts and (.
«,il
>'i!!
li:;i
|,.„
;!3 ;;
X-'
s ;;
NATUBAL TANGENTS AND CO-TANGENTS.
423
320
TaNO. I Co-VLItQ,
I
o
z
3
4
i
9
10
fi
12
X3
»4
31
a3
"4
as
^
3:
39
30
3«
33
33
34
35
36
li
39
40
41
43
43
44
45
49
5«
53
54
55
56
II
59
63487
62527
62568
62608
62649
63689
6273
6277
628 II
62852
62893
63933
62973
63014
63055
63136
63» 77
63217
63258
63399
6334
6338
63431
63462
63s 03
63544
63584
636 25
63666
63707
63748
63789
6383
63871
63912
•63953
63994
64035
64076
641 17
641 58
64199
6434
64381
643 22
64363
64404
64446
64487
64538
64569
6461
64652
64693
64734
64775
64817
64858
64899
^494'
CO-VAMA.
60033
5993^
59826
59723
5962
59517
594 »4
593"
59208
59105
59002
589
58797
58695
58593
5849
58388
58286
58184
58083
579 81
57879
57778
57676
57575
57474
57372
5727*
5717
57069
56969
56868
56767
56667
56566
56466
56366
56265
56165
56065
55966
55766
55666
55567
55467
55368
55269
5517
55071
54972
54^73
54774
54675
54576
54478
i43 79
54281
54' 83
54085
53986
570
IAMB.
330
Tama.
.64941
.64982
.65023
.65065
.65106
• 65148
.651 89
.65231
.652 72
•653 14
•65355
•65397
•65438
.6548
.65531
•65563
.65604
.65646
.65688
.65729
.65771
.65854
.65896
.65938
.6598
.66021
.66063
.661 05
.661 47
.66189
.6623
.66272
.66314
.66356
.66398
.6644
.66482
.66534
.66566
.66608
.6665
.66693
•667 3A
.66776
.66818
.6686
.66903
!669^
.67038
.67071
.671 X3
-671 55
.67x97
.67339
.67282
tin
.67409
•6745'
CO-TANO.
53986
53888
537 9»
53693
53595
53497
534
53302
53205
53107
5301
52913
52816
52719
52622
52525
52429
52332
52235
52139
52043
51046
S185
51754
51658
51562
51466
5137
51275
511 79
51084
50988
50893
50797
50702
50607
50512
504x7
50333
50228
50x33
50038
49944
49849
49661
49566
49472
49378
49284
4919
Co.TAJi«. Tamo.
660
340
Tamo.
67451
67493
67536
67578
6762
67663
67705
67748
6779-
67832
67875
67917
6796
60002
68045
68088
6813
68173
68215
68258
68301
68343
68386
68429
68471
68514
68557
686
68642
68685
68728
68771
68814
68857
689
68942
68985
69028
69071
69x14
69157
692
69243
69286
69329
69372
69416
69459
69503
69588
69631
6967s
69718
69761
69804
69847
69891
69934
69977
70031
Co-TAHtt.
48256
48163
4807
47977
47885
47792
47699
47607
475 M
47422
4733
47238
47146
47053
46962
4687
46778
46686
46595
46503
464 II
,4632
46229
46137
46046
459 55
45864
45773
45682
45592
45501
4541
453 a
45229
45139
45049
44958
44868
44778
44688
44598
44508
444x8
44329
44239
44M9
4406
439 7
4.-)88i
43792
43703
43614
43525
43436
433 47
43258
43169
4308
42992
42003
428x5
Co-TAM«. TaNQ.
660
350
Tam«.
0021
0064
0107
0151
0194
0238
0281
0325
0368
0413
0455
0499
0542
0586
0629
0673
0717
076
0804
0848
70891
0935
0979
1023
1066
II 1
"54
1198
1242
1285
1329
1373
14x7
X461
15 OS
1549
1593
1637
16 81
1725
1769
18 13
1857
19 01
1946
199
2034
2078
21 22
2X66
22 1 1
2255
2299
2344
2388
2432
2477
2521
2565
261
2654
Co-TANO.
42815
42726
42638
4255
42463
42374
42286
42198
421 1
42022
41934
41847
41759
41672
41584
414 97
41409
41322
41235
41148
410 61
40887
408
40714
40627
4054
40454
40367
40281
40195
40109
40022
39936
398 5
39764
39679
395 93
39507
39421
39336
3925
39165
30079
38994
38Q09
38824
38738
38653
38568
38484
38399
383*4
38^29
38145
3806
37976
37891
37807
37722
37638
Ck>-TAM«. Tamo.
640
60
5
57
56
55
54
53
52
51
50
J?
45
44
43
42
41
40
3'
37
36
35
34
33
32
31
30
25
24
23
22
21
20
15
«4
13
13
XI
10
i
7
6
5
4
3
3
I
o
424
NATURAL TANGENTS AND CO-TANGENTS.
o
I
2
3
4
5
6
7
8
9
lO
II
12
13
»5
i6
»7
i8
»9
20
21
23
23
24
25
26
37
28
29
30
31
32
33
34
35
36
37
38
39
40
41
43
43
44
45
46
\l
49
50
51
53
53
54
55
56
57
58
«6o
370
Tano. C
O-TANO.
Taro. G
O-TAHO.
•72654 >
•37638
•753 55 I
•32704
.72699
375 54
.75401
•32624
•7^7^12
•374 7
•754 47
•32544
.72788
■37386
•75492
•32464
.72832
•373 o3
•75538
•32384
.72877 I
.37218
.75584 J
.32304
.72921
•37134
•75629
.32224
. 729 66
3705
•75675
33144
7301
36067
36883
•757 21
32064
7305s
•75767
31984
•731 '
368
.75812 I
31904
•73' 44
367 16
.75858 .
31835
•73189
.36633
•75904
31745
•73334
36549
•759 5,
31666
.73278 X
36466
.75996
3x586
•73333
36383
.76042 I
31507
•73368
363
.76088
3X427
•73413
36317
.76134 .
3x348
•734 57
36133
.7618
3x269
•73503
36051
.76226
3x19
•735 47 I
35968
.76272 I
311 I
•73592
35885
.76318
3X031
•73637
35802
.76364 .
30953
30873
.73681
35719
.7641
•73736
35637
.76456
30795
•73771 I
.73816 .
355 54
.76502 I.
307x6
35472
.76548
30637
.73861
35389
•76594 •
30558
.73906
35307
•7^5 L •
3048
•73951 •
35234
.76686
30401
.73996 I
35M2
•76733 »•
30333
74041
3506
•76779 •
30344
.74086
34978
34896
.76825 .
30166
•741 31
.76871 .
30087
.74176
34814
.76918 .
30009
.74221 I
34732
.76964 I.
39853
-74267
3465
.7701
•743X3
34568
•77057 •
39775
•743 57
34487
.77103 .
29696
•744 OS'
34405
.77149 .
29618
•74447 '
34323
.77196 I.
395 4x
•74492
34343
.77242
39463
•74538;
3416
.77289! .
39385
•74583,
.74638
34079 }
33998
'77335 •
•77383
29307
29229
.74674 1
33916
•33835
.77428 I
39152
•74719
•774 75 1
29074
28997
•74764
•337 54 1
•77521 1
.7481
■33673 1
•77568 1
289 19
•74855
•33592 1
■77615 '
28842
•749 »
335"
.77661 I
28764 •
•74946
334 3
.77708
28687
•74991
33349
33268
•777 54
2861
•75037
.77801
28533
.75083
33187
.77848 1
•284 56
.75128 I
33107
•77895 I
283 79 1
•75173
33036 1
•7794' -
•77988
38302 1
.75219
l^tt
28225 1
•75364
•78035
281 48 '
•7531
33785
.78082
28071
•753 55 I
33704
.78129 I
.27994
Co-Tijra.
Tamo.
CO-TAMO.
Tax0.
530
029
380
Tano. Co-tah«.
781 29
78175
78222
78269
783x6
78363
7841
78457
78504
7855/
78598
78645
78692
78739
78786
78834
78881
78928
78975
79022
7907
79117
79164
79212
79259
79306
79354
79401
79449
79496
79544
795 9x
79639
79686
797 34
79781
79829
79877
79924
79973
8oo2
80067
801 15
80163
802 II
80258
80306
80354
80402
8045
80498
80546
80594
80642
8069
80738
80786
80834
80882
8093
80978
27994
27917
27841
27764
27688
27611
375 35
27458
27382
37306
2723
27x53
27077
27001
26925
26849
26774
26698
26622
26546
26471
26395
26319
26244
261 69
26093
26018
25943
25867
35793
25717
25642
35567
35492
35417
35343
25268
35x93
251 18
35044
24969
34895
2482
34746
34672
34597
34533
34449
34375
24301
24227
24x53
34079
34005
339 3 X
33858
33784
337 X
33637
33563
3349
3go
Tano. Co^amo.
Co-TAHO. Tano.
51©
80978
81027
81075
811 23
81271
8122
81268
81316
81364
8x4x3
81461
815 1
81558
81606
8x655
81703
81752
818
81841
8189
81946
8«995
82044
82092
821 41
821 9
82238
82287
82336
82385
82434
82483
82531
8258
82620
82678
82727
82776
82825
82874
82923
82972
83022
83071
83x2
83160
83218
83268
833x7
83366
834x5
83465
835x4
83564
83613
83662
83712
83761
838x1
8386
839'
CO-YANO.
2349
234 16
23343
2327
23196
23123
2305
22977
22904
22831
22758
22685
32612
22539
22467
22394
22321
22249
221 70
22104
22031
3x059
21886
918x4
21742
2167
21598
21526
2x454
21382
3x31
2x238
21166
21094
21023
20051
20879
30808
20736
20665
20593
20522
20451
20370
20308
30237
20166
20095
20024
198x1
X974
196 69
X9599
X9528
X9457
19387
193x6
192 46
19x75
6a
^
57
56
55
54
53
52
5x
50
47
46
45
44
43
43
4X
40
P
37
36
35
34
33
33
31
30
a?
26
25
34
33
32
21
20
15
»4
»3
xa
zi
zo
I
I
5
4
3
a
z
o
Tamo.
000
irATUBAL TAN6BNTS AND CO'TAliaBNTS.
425
40O
410
420 II
43P
/
Taxs. C
ovAira.
Tamo. C
O-VAV0.
Tamo.
Co^TAna.
Taho.
Co-tAim.
*
0
.8391 I
19175
.86939 1
15037
.9004
1.11061
•932 5»
107237
"6^
X
.8396
19105
.8698
14969
.90093
•10996
•93306
.07174
n
3
.84009
1Q035
18964
.870 3X
.87082
14003
14834
.90146
:;3i;
•9336
.071x3
3
:i:°s .
.90199
•93415
.07049
.06987
57
4
'??94
•87133 •
14767
•90251
.10803
•93469
56
5
.841 58 X.
18834
.871 84 X
14699
•90304
1.10737
.93524
•93578
1.06935
.06863
55
6
.84308
18754
.87336
.87387 .
X4633
•90357
.10673
54
7
.84358 .
18684
14565
.904 X
.10607
•93633
.068
53
8
.84307 .
186x4
.87338 .
14498
.90463
.10543
.10478
.93688
.06738
5«
9
•84357 -
'8544
•87389 <
1443
.905x6
•93742
.06676
51
10
.84407 1
18474
.874 4x X.
14363
•90569
1104x4
•937 97
1.066x3
50
zx
•84457
18404
.87493
14296
.90621
.10349
.93852
•065 sx
»
Z3
.84507 .
'?3§^
.87543
14229
.90674
.10385
.93906
.06489
X3
.84556 .
18364
•87595 -
14x63
.90737
.xo3a
.93961
.06437
47
»4
.84606
X8194
.87646
X4095
.907 8x
•90834
.10x56
.94016
.06365
46
X5
.84656 X.
X8135
.87698 X
14038
X.X009X
94071
X.06303
45
x6
.84706
'^§1
.87749
.878 ox
.X396X
.X3838
.90887
.10037
.941 25
.06341
44
«7
S^zsf .
17986
•9094
•09963
.09899
.9418
.06179
43
z8
.84806
17016
X7846
.87853
•90993
.9x046
•94235
.o6x X7
4»
»9
.848 56
.87904
137 6x
•09834
.9439
.06056
41
30
.84906 X
17777
.87955 >
•13694
•91099
1.0977
•94345
105994
40
31
.84956
X7708
.88007
.13637
.91153
.09706
•944
.05932
■0587
?
33
.85006
17638
.88059
.13561
.91306
.09643
.94455
23
•85057 •
17569
.88xx
•13494
.13438
•91259
•09578
•9451
.05809
37
24
.85x07
X75
.88x63
.913 13
•09514
•94565
•05747
36
as
.85x57 X.
«743
.883x4 1
. 13361
.91366
X.0945
.9462
X. 056 85
35
36
.85307
.X736X
.88365
•13295
.13338
•914 19
.09386
.94676
.056 34
34
37
.85257
. Z73 93
.88317
•91473
.09333
•94731
.055 62
33
s8
• 55307
.X7333
.88369
.X3x68
.91526
.09358
•94786
•94841
.055 ox
3a
29
•!5358
>7i54
.884 3X
.13096
.9158
.09x95
•05439
105378
3>
30
.85408 X
.17085
•88473 »
.13039
.9x633
X.0913X
.94896
30
3»
.85458
.X7016
•S5524
13963
.X3897
.91687
.09067
•94952
•053x7
H
32
•85509
tdjl
.88576
.9174
.00003
•95007
.052 55
33
•85559
.88638
.X383X
•91794
.91847
•**!2*
.95063
•05194
27
34
■85609
.16809
.8868
.X3765
.08876
.951 18
•051 33
36
35
.8566 I
.X674X
.88733 X
.88888
12699
.91901
1.088x3
.951 73
1.05073
25
36
.8571
X6673
12633
•91955
:^ll
.95229
.0501
24
37
.857 6x
.858 XX
X6603
13567
.92008
.95284
■.^m
23
38
.X6535
135 ox
.93062
.08633
•9534
33
39
.85863
.X6466
•8894
12435
.931 16
•08559
•95395
.04837
3X
40
.85913 X
16398
.88993 X
13369
•9217
X.08496
•95451
X.047 66
30
4x
•85963
.16339
.89045 .
12303
.932 33
.08433
.95506
•04705
:i
42
.86014
16361
.89097
12238
.93277
.08369
.08308
•95562
.046 44
43
.86064
16193
.89149
X2X 72
•92331
.956 18
•04583
17
44
.86115
16134
16050
.89201
13106
•92385
.08243
•95673
.045 32
16
45
.86166 X
.892 53 «
12041
•9*439
x.o8z 79
•957 29
X.O446X
15
46
.86316
15987
.89306 .
11975
•92493
.o8xx6
•95785
.04401
14
47
•?5*^
15919
158 5x
.89358 .
11009
11844
11778
•92547
•08053
.95841
•0434
13
48
.86318
.8941
.92601
•0799
•95897
.042 70
.04318
13
49
.86368
15783
.89463 .
•92655
•07927
X.07864
•95952
XX
50
.864 Z9 X.
>57«5
.895 15 1.
117x3
.92709
.96008
X.O4X 58
xo
51
•SS^7
15647
.89567 .
11648
.92763
.078 ox
.96064
•04097
i
52
.865 3X
X5579
.8963 .
11583
.92817
.07738
.96x8
.04036
53
•K|72 .
155"
.89673 .
11517
.928 73
.07676
.96176
.03976
7
54
.86633
15443
.89725 ■
"452
.92926
.07613
.96333
.96288
•039 15
103855
6
55
.86674 I
15375
.89777 X
11387
.9298
10755
5
56
157 »5
15308
.'89813 .
11321
.93088
•07487
•96344
•03794
■4
57
•J527^
1524
11356
.07435
•964
•03734
3
58
•!S*2 ■
15x72
Zu ■
XXX 9x
•931 43
.07363
•96457
•03674
a
^
.86878
151 04
XIX 26
.93197
.07399
•96513
.036 13
X
60
.86929 I
15037
.9004 1,
xxo6x
.932 53
1.07337
.96569
1.035 53
Taro.
0
/
Co^TAM*.
Tang.
CivTAiia.
Tans.
Co-TAao.
Tanq.
CO-TANO.
^
490
480
4
70
4
CO
Nh»
42a
NJLTUBAX TAN6BNTS AND CO-TANGBSTTS,
o
z
a
3
4
5
6
7
8
9
lo
IX
19
»3
»4
«5
i6
»7
i8
«9
4o
4«o
Takv.
.96569
.96625
.96681
•96738
.96794
.9685
.96907
.96963
.9703
.97076
•971 33
.97x89
.97246
•97309
•973 59
.974 16
•97472
975 89
•97586
•97643
•977
Co^TAHS.
CkHTAHO.
1035 S3
103493
103433
X. 033 72
X.O33 Z2
X. 033 52
I 03X 92
I.03I 32
z. 030 72
X. 030 12
X.OI952
X.O2892
1.03832
X.O2772
1.02713
z. 036 53
X09593
109533
X.02474
X.094 14
«-093 55
TaI«9.
450
60
57
56
55
54
53
58
51
50
%
47
46
45
44
43
42
4»
¥>
31
93
23
24
25
36
27
28
99
30
31
32
33
34
35
36
37
38
39
40
440
TaII«. I CkHTABC.
97756
97813
^787
97937
97984
98041
98098
98»55
98313
9827
98397
98384
J98441
98499
98556
98613
98671
98798
98786
98843
' I Oo-TANe.
1.03395
I.033 36
I.03I 76
I.02X 17
X.03057
X.OX998
1. 019 39
1.0x879
x.oxSs
X.OI76I
X.OX709
Z.0I6 42
1-01583
Z.OZ594
Z.OI465
I.OI406
101347
X.OI388
X.OI339
X.OXX 7
Tama.
460
44« 1
»
»
41
Tah*.
C04AII».
12
.9890Z
I.OIX X3
42
•98958
1.01053
37
43
.990x6
100994
36
44
•99073
1.00035
X. 008 76
35
45
.99131
.991 8^/
34
46
x.oq8x8
33
%
•99247
100759
32
•99304
X.0070X
31
49
.99363
X. 006 43
X.005 83
30
50
•994a
39
51
,99478
x,oo5 35
38
52
.99536
z. 004 67
27
53
•99594
Z.00408
36
54
•99652
X.O03 5
25
55
•997 «„
X. 003 91
24
S6
.99768
X. 003 33
23
57
.99836
z.ooi 75
29
58
.998 84
z.ooi x6
3X
59
•99942
1.00058
ao
60
X
z
f
CO-TARO.
TAxe.
450 1
*7
z6
15
»4
»3
13
iz
xo
I
\
5
4
3
9
z
o
Preceding Table contains Natural Tangents and Oo-tangenta for every
minute of the quadrant, to the radius of i.
If Degrees are taken at head of columns, Minutes, Tangents, and Co-tan-
gents must be taken from head also \ and if they are taken at foot of ool-
ftmns, Minutes, etc., must be taken from foot alsa
Illustration.— .1974 te tangent tor n© j©', and co-tangent for 78® 50'.
a?o Compute T»UKe*^ts »nd Co-taixgents fbr Seconds.
Ascertain tangent or co-tangent of angle for degrees and minutes from
Table ; take difference between it and tangent or co-tangent next below it.
ITjen as 60 seconds is to difference, so are seconds given to rfesult required,
which is to be added to tangent and subtracted from co-tangent
lLLUSTRATios.<^What \% the tangent and co-tangent of 54O 40' 49"?
Tangent of 540 40', per Table =^ z. 4x0 61 ) ,^« dur^nm^
Tangent of 54O 41', " =? z.4zx 48 } "^ ^7 dxffermct.
Then 60 : .00087 :*• 40 : .00058, which, added to z.41061 =? 1.411x9 tangent
Coungentur54^4o' perTftble=.7o8 9i J ^^.^aiffere^io'
Co tangent of 54041', '■ =.708^8 / '^^^'^ 3 <"il^«^ '«*«<'
Then (xP : .00043 : : 40 : .00039, which, subt'd nrom .70891 = .70863 co-tangeitL
70 Compute rPang^xit or Co^taiigent of* any A.nele in
Degpees, ^iiztites, and Seconds.
Divide Sine by Cosine for Tangent, and Cosine by Sine for Co-tangent.
ExAJtfUE.>^What is tangent of 95^^ x8'f
Sine = .497 36; cosine := .904 08. Then
•42736
=3.4727 tangmt
.90408
rro Compute ^umt>er of Degrees, ^dinutee, and Seoonda
of a grivez\ Taitg:ent or Co-tangent.
When Tangent w o&cn.— Proceed as by Bule, page 402, for Sines, substi-
tuting Tangents for Sines.
ExAi(PLB.^What is tangent for Z.41Z z9t
Next less tangent is z.41061, cm: y^ which it 54° Ao^ Next greatest tangent is
z. 41 1 48, difference between which and nesst less it .ooo8v.
inference between U*$ tabtUar temgeiU and one given t$ z.41061—- Z.41Z 19S.00058.
Then .000 87 : .ooq 58 : : 60 : 40, whid), added to 54O 40 = 54° 40' 40".
When Otk-tangent is given* — Proceed as by Rule, page 403, for CosineSi
ibstituting Co-tangents for Cosinesi .
AEROSTATICS. 42/
AEROSTATICS.
Atmospheric Air consists, by volume, of Oxygen 21, and Nitrogen 79
parts ; and in 10 000 parts there are 4.9 parts of Carbonic acid gas.
by weight, it consists of 23 parts of Oxygen, and 77 of Nitrogen.
One cube foot of Atmospheric Air at surface of Earth, when barome-
ter is at 30 ins., and at a temperature of 32^, weighs 565.0964 grains s=
x)8o728 lbs. avoirdupois, being 773.19 times lighter than water.
Specific gravity compared with water , at 62.418 =s .001 293 345.
Mean weight ot a column of air a foot square, and of an altitude
equal to height of atmosphere (barometer 30 ins.), is 2124.6875 lbs. =
14. 7548 lbs. per sq. inch = support of 34.0393 feet of water.
Standard pound is computed with a mercurial barometer at 30 ins. ; hence,
as a cube inch of mercuiy at 60° weighs .490 776 9 lbs., pressure of atmos-
phere at 60°= 14.723307 lbs. per square inch.
12.3873 cube feet of air weigh a pound, and its weight varies about
I gr. for each degree of heat.
Extreme hxk^i of barometer in latitude 30° to 35<> N.^3a2i ins.
Rate of expansion of Air, and all other Ehttic Fluids for all temperatures,
is essentially uniform. From 32° to 212° they expand from 1 to 1.3665
volumes = .002036 or yirirra^^ P*'* "^ '^^''* *^"^^ ^^^ every degree of heat
From 212° to 680° they expand from 1.3665 to 2.3192 = .002036 for each
degree of heat.
Thus, if volume of air at 132° is required, 132° — 32° 3= xoo, and i ^
100 X xx>2 036 = 1. 2036 volumes.
Height, at Equator is estimated at 300 feet greater than at Poles, its
mean height at 45° latitude.
In like latitudes, air loses 1° for every 340 feet in height abpve level'
of sea.
Below surface of Earth, temperature increases.
Elasticity of air is inversely as space it occupies, and directly as its density.
When altitude of air is taken in arithmetical proportion, its Rarity will be
in geometric proportion. Thus, at 7 miles above surface of Earth, air is 4
times rarer or lighter than at Earth's surface; at 14 miles, 16 times; at 21
miles, 64 times, and so on.
Density of an aeriform fluid mass at 32° and at <° will be to each other
as I + .002088 (<° — 32°) is to I.
For Volume, Pressure, and Density of Air, see Heat, page 521.
Altitude of Atmosphere at ordinary density is = a column of mercury 30
ins. in height, divided bv specific gravity of air compared with mercury.
Hence 30 ins. = 2.5 feet, which, divided by .0000949871 specific gravity
of air compared with mercury, = 26 z^gfeet = 4.985 miles.
Gay Lussac, Humboldt, and Boussingault estimated it at a minimum of
30 miles. Sir John Herschell 83, Bravais 66 to 100, Dalton 102, and Liais at
x8o or 204 miles.
The aqueous vapor always existing in air, in a greater or less quantity,
being lighter than air, diminishes its weight in mixing with it ; and as, other
things equal, its quantity is greater the higher the temperature of the air, its
effect is to be considered by increasing the multiplier of t by raising it to
.00222.
Glaisber and Ooxwell, in 1862, ascended in a balloon to a height of 3700^
feet
428
ASBOSTATICS.
At temperature of 32^, mean velocity of sound is 1089 feet per second. It
is increased or diminished about one foot for each degree of temperature
below or above 32°.
Velocity of sound in water is estimated at 4750 feet per second.
Velocitjf of Sound cU Various Temperatures.
O PwSMond. o Per Second.
5
23
Feet.
1056
1070
»079
32
50
59
0
Per Second.
68
77
86
Feet.
1 122
X132
1142
1 0
Per Second.
Feet.
95
1 152
104
1161
"3
1171
Motions of air and all gases^ by force of gravity^ are precisely alike to
those offtuids.
Sensation of hearing, or sound, cannot exist in an absolute vacuum. The
human voice can be heard a distance of 3300 feet.
Echo. — At a less distance than 100 feet there is not a sufficient interval
between the delivery of a sound and its reflection to render one perceptible.
Xo Compute Distaxioes \>y^ Velooitjr of Sound in Aiv,
1089 X T V Y + [• 002 088 (J— 32°)] = dutance in feet per second^ T repruenUng tipge
Off ore report was heard, and t temperature of air.
Illustration. — Flash of a cannoD from a vessel was observed 13 seconds before
report was beard; temperature of air 60°; what was distance to vessel?
1089 X i3>/x + [. 002 088 (60° — 32°)] = 1089 X 13 X 1.029 = '4 567.55/««*=^- 76m<te».
The<Mretical velocity with which air will flow into a vacuum, if wholly vm-
obstructed, is V^gh=i 1347.4 yec< per second. In operation, however, it is
1347.4 X .707= 952.61 ycc<.
Xo Compixte Velocity of* Air Flowing into a Vacuoim.
y/zgh X c = r in feet per second, c representing coefficient ofefflvx.
Coefficients for openings are as follows :
Circular aperture in a tbui plate 65 to .7
Cylindrical adjutage 92 | Conical aciyutage 93
Velocity of Sonnd in Several Solids.
Velocity in Air^=i.
\jeaA ,. 3.0 I Zluc 9.8 I Pine 12.5 I Glass
... 5.6 Oak 9.9 I Copper . .
Gold
11.2
Pine.
II. 9
"•5
steeL . . .
Iron . . .
«4-3
15. X
To
Compute Slevations l>y a Barometer.
Approximately* 60000 (log. B — log. 6) C = fieight in feet; B and b representing
heights of barometer at lower and upper stations, and C correction due to T -{- 1 or
temperatures qfUnoer and upper stations.
Values of C
or T-t-e.
0
C
40
•973
42
.976
44
.978
46
.98
48
.982
50
.984
52
.987
54
.989
56
.991
58
•993
0
60
62
64
66
C
.996
.998
I
1.002
68
1.004
70
1.007
7a
1.009
74
78
I. on
1. 013
1. 016
0
c
1.0x8
82
1.02
84
86
88
1.02a
1.024
1.027
90
1.029
92
I.03X
98
»-033
1.036
1.038
0
C
100
X.04
102
1.042
104
106
X08
1.044
1.047
1.049
110
1.051
1X2
VA
".053
1.056
1.058
1.06
0
c
0
140
<= 1
0
160
X20
X.062
X.084
122
1.064
142
087
162
124
1.067
144
080
164
126
1.069
146
091
166
128
1.071
148
093
168
130
'•073
«50
096
170
132
1.076
152
.098
172
134
1.078
"54
.1
174
136 1.08
156
.102
176
138
1.082 1
>58
104
178
I.X06
I.X08
I. XXX
1.1x3
I.XI5
X.IX7
x.ia
X. 12a
1.X24
x.ia6
* For more «s»ct forinulM, ••« TtM^ And FormuUs, by Captt T- 3< I'««i U. S. Top. Eng ., 1S53.
ABB08TATICS.
429
Their vakies vary approximately .001 1 per degree.
Upper Station. Lower StetiOB.
Illustratio.x.— Thermometer 70.4 77.6
Barometer 23.66 30.05
0 = 77.6 + 70.4 = 1.093, log. 8 = 1.4778, log. 6 = 1.374.
Then 60000 x (1.4778 — 1.374) x 1.093 =6807. 2 /at
To Conapu.te Klevations "by a Th.eriiaometer.
520 B -|- B" X C = fieight in feet B rlpi'etenting temperature of water bmling at
ttevated station deducted from 212°.
Correction for temperatures of air at lower and npper stations, or T -f <, to be taken
firom table, page 428, as before.
Illustratiox.— Temperature of water boiling'at upper station 192^; temperatare
of air 50° and 32°, C = 1.02.
a
Then 520X212 — 192 -|- 212 — 192 x i.oa= xq&o&JuL
To Compute Capacity of a BaUoon, etc.y see page 218.
Barometer.
Elevations by Baroixieter Readiugs*
Mean Temperature of Air soP.
For correction for temperature, see note at foot
Height.
-Feet.
4000
4250
4500
47SO
5000
5250
5500
5750
6000
6250
6500
6750
(AHronomer SoyaL )
Height.
Berom.
Height.
Barom.
Height.
Barom.
Feet.
Ins.
Feet.
Ins.
Feet.
Ins.
0
31
600
30-325
1500
29.34
50
^ill
650
30.269
1600
29.233
100
700
30-214 .
1750
29.072
«50
30^83
750
30.159
1800
29.019
28.807
200
3<^773
800
30.103
2000
250
30"7«7
850
30.048
2250
*5-514
300
3a 661
900
29993
29.883
2500
28.283
350
30.604
1000
2750
28.025
400
30.548
1100
29774
3000
27.769
450
3p.ig2
1200
29.665
3250
27-5'5 ;
500
30.436
1300
29-556
3500
27.264 i
550
30.381
1400
29.448
3750
27.015 i
Barom.
Ins.
26.769
26.524
26.282
26 042
25.804
25-569
25335
25.104
24-875
24.648
24423
24.2
Height.
Barom.
Feet.
Ins.
7000
23.979
7SOO
23-543
. 8000
23- "5
8500
22.695
22.282
9000
9500
21.877
10000
21.479
10500
21.089
IIOOO
2a 706
II 500
20.329
12000
19.959
12500
19.952
Saroxneter.
CwrredHonfoT CapUlary Attraction to be added in Indus,
Diameter of tube. . . .
Correction, unboiled.
Correction, boiled . . .
.6
.55
•5
.45
•4
•55
•3
•25
.9
.004
005
.007
.01
.014
.02
025
04
059
002
.003
UU4
005
.007
ox
.0x4
.02
029
.1
087
044
To Compute Height.
RuLK.— Subtract reading at lower station ftvm reading at upper station, difference
is height in feet.
Table assumes mean temperature of atmosphere to be 50O F. or iqO C. , For other
'temperatures following correction must be applied.
Add together temperatures at upper and lower station If this sum, in degrees
in F., is greater than xoo^, increase height by | A> part for every degree of excess
by ^^ part for every degree of defect from aoP.
Saroxneter Iiidioations.
Increasing storm.— If mercury falls during a high wind Arom S. W., S. S. W., W.,
orS.
Violent but short ~If fall be rapid.
IjCss violent but of longer continuance.— If fkll be slow.
Snow. — If mercury iklls when thermometer is low.
Improved weather.— When a gradual continuous rise Of mercury occurs with a
fklling thermometer.
430 ABBOSTATICS.
Heavy gales fh>m V.—Soon kUbt first rise of tnercnry fh>m a very low point.
Unsettled weather. — ^With a rapid rise of mercury.
Settled weather. — With a How rise of mercury.
Very fine weather.— With a continued steadiness of mercury with dry air.
Stormy weather with rain (or snow). — With a rapid and considerable fall of mer
cury.
Threatening, unsettled weather. — With an alternate rising and falling of mercury
Lightning only. — When mercury is low, storm being beyond horizon. .
Fine weather. — With a rosy sky at sun^t.
Wind and rain.— When sky has a sickly greenish hue.
Bain. — When clouds are of a dark Indian red.
Foul weather or much wind. —When sky is red in morning.
"WeatJgier Grlasses.
£:xplana.tor3r Card. Vice-AdmirtU Fitzroy, F. R. S.
Barometer Rises for Northerly wind (including from N. W. by N. to E.), for dry,
or less wet weather, for less wind, or for more than one of these changes —
Except on a few occasions when rain, hail, or snow comes from N. with strong wind.
Barometer Falls for Southerly wind (including from S. E. by S. to W.), for wet
weather, for stronger wind, or for more than one of these changes —
Exc^t on a few occasions when moderate wind with rain (or snow) comes from N.
For change of wind toward Northerly directions, a Thermometer /(Ms.
For change of wind toward Southerly directions, a Thermometer rises.
Moisture or dampness in air (shown by a Hygrometer) increases If^fbre rain, fog,
or dew.
Add one tenth of an inch to observed height for each hundred feet Barometer is
above half-tide level.
Average height of Barometer, in England, at sea-level, is about 20.94 inches; and
average temperature of air is nearly 50 degrees (latitude of London).
Thermometer fklls about one degree for each 300 feet of elevation from ground,
but varies with wind.
** When the wind shifts against the sun,
Trust it not, for back it will run.''
First rise after very low I Long foretold— long last,
Indicates a stronger blow. | Short notice— soon past.
Rare/cu^^ion of Air,
In consequence of rarefaction of ait, g^ loses of its illuminating power x cube
Inch for each 2.69 feet of elevation above the sea. {M Bretnond.)
Clo-ads.
Classification. — i. CiVrwa— Like to a feather, commonly termed Mare'*s
tails. 2* Oirro-aqmdus — Small round eloudfi, termed mackerd sky.
3. Cirro-strattis — Concave or undulated stratus. 4. Cumtilus — Conical,
round clusters, termed wool-packs and cot(on balls, 5, Cumulo^ratus —
Two latter mixed. 6. Ninums — ^A icumulus spreading out in anns, and
precipitating rain beneath it. 7. Stratus — ^A level sheet.
NoTS. — Cirrus is most elevated.
Height, — Clouds have been seen at a greater height than 37000 feet.
Velocity. — At an apparent moderate speed, they attain a velocity of 80
miles per hour.
Xii^h.tn.iiig.
Classification. — i Striped or Zigzag — Developed with great rapidity.
2. Sheet — Covering a large surface. 3. Olobtdar — When the electric
fluid appears condensed, and it is developed at a comparatively lower
Telocity. 4. P^ufsphanC'-^Wh&i the flash appears to rest upon the
edges of the clouds.
/
ABBOSTATICS. — ATMOSI
WEATHBB Iin>ICA1
Weather.
Fioe and
Fair.
CUmdt.
Soft or delicate-looking and in-
definite outlines.
WiDd.
Hard - edged, oily - loolcing, and
tawny or copper-colored, and the
more bard, '"greasy," and ragged,
the more wind.
Wind only.
Light scud alone.
Rain.
' Small and inky
Wind and
Ratn.
Light scud driving across heavy
masses.
Rain and
Wind.
Hard defined outlinea
Change of
Wind.
High upper, cross lower in a di-
rection different to their course or
43J
Sky.
Grav in morning and light^
dellc&le tints and low dawn.
High dawn, and sunset of ft
bright yellow.
Sunset of a pale yellow.
Orange or copper color.
Gaudy unusual bnea
that of wind.
Fair. — When sea-birds fly early and far out, when d^w is deposited, and when a
leeoh, confined in a bottle of water, will curl up at the bottom.
Rain.— Clear atmosphere near to horizon and light atmospheric pressure, or a
good ''hearing day," as it is termed.
Storm.— When sea-birds remain near to 'Shore or fly inland!
Rain, Snow^ or Wittd.^When a leech, confined in a bottld of water, will rise ex-
citedly to the surface
'Thunder.— When a leech, confined as above, will be much excited and leave the
water.
Value of Indications of* Fair Weather, in T^aym^ Ooxo*.
pared to one of Rain.
From an extended series of observations. {Loufe.y
Proflise Dew. 4.5
White Stratus in a valley 7. 2
Colored Clouds at sunset a.9
Solar Halo 1.9
Sun red and rayless. 10.3
Sun pale and sparkling. i
White Frost 4.2
Lunar Halo. i
Lunar burr, or rough-edged 2.8
Moon dim a
Moon rising red. 7
Mock Sun or Moon. .«...■..,.«.... 3.3
Stars falling abundant. 3.21
Stars bright 3.4
Stars dim 1.5
Stars scintillated 6
Aurora borealis z.8
Toads in evening. 2.4
Landrails noisy.. 13
Ducks And Geese noisy 2.3
Fish rising .* 1.5
Smpke rising vertically 5
For weather-foretelling plants, see page 185.
ATU08PHKBIG AIB.
Very pure air contains Oxygen 20.96, Nitrogen 79, and Carbonic Acid .04.
Air respired by a human being in one hour is about 15 cube feet, produc-
ing 500 grains of carbonic aci<^ corresponding to 137 grains carbon, and
during this time about 200 grains of water will be exhaled by the lungs.
Daring this period there would be consumed about 415 grains of oxygen.
In one hour, then, there would be vitiated 73 cube feet pure air.
A man, weighing 150 lbs., requires 930 cube feet of air per honr^ in' order
that the air he breatbei mav itot<sontain more than i per 1000 of cavbonic
acid (at which proportion its imparity becomes sensible to the nose)-; he
ought, ^eref ore, to have Soo cube feet of well ventilated space.
432
ATMOSPHEBIC AIE. — ANIMAL POWER.
An adult human being consumes in food from 145 to 165 grains of carbon
per hour, and gives off from 12 to 16 cube feet of carbonic acid gas.
An assemblage of 1000 persons will give off in two hours, in vapor, 8.5
gallons water, and nearly as much carbon as there is in 56 lbs. of bitumi-
nous coaL
Proportion of Oxygen and. Carloonio A.oid at fbllovtrin^;
Xuooations.
Pure Air represented by Oxygen 20.96.
Street in Glasgow saSQs
Regent Street, Ijondon 20.865
Centre Hyde Park 21.005
Metropolitan Railway (underground) . . sae
Pi t of a Theatre • • ao. 74
Gallery of a Theatre aa63
Carbonic Acid .04 Per cent
Open field, Manchester 0383
Churchyard. ...» 0323
Market, Smithfield 0446
Factory mills 283
School-rooms 097
Pitt of theatre, zi P. M 32
Boxes " 12 *' 218
Gallery " 10 " ....
XOI
Top of Monument, London 0398
Hyde Park 0334
Metropolitan Railway (underground).. .338
Lake of Geneva 046
Boys' school 31*
Girls' " 723t
Horse stable 7
Convict prison 045
t PeltenhoflSBT*'
Consumption of A.tmo8ph.erio ^ir. {Coathupe.)
One wax candle (three in a lb.) destroys, during its combustion, as much
oxygen per hour as respiration of one adult.
A lighted taper, when confined within a given volume of atmospheric air,
will become extinguished as soon as it has converted 3 per cent, of given
volume of air into carbonic acid.
Carbonic Acid Exhaled per Minute by a Man. (Dr. Smith.)
During sleep 4.99 per cent, lying down 5.91, walking at rate of 2 miles
per hour 18. i, at 3 miles 25.83, tiard labor 44.97.
ANIMAL POWEB.
'Worls.
Work is measured by product of the resistance and distance through
which its point of application is moved. In performance of work by
means of mechanism, work done upon weight is equal to work done by
power.
Unit of Work is the moment or effect of i pound through a distance
of I foot, and it is termed a foot-pound.
In France a kilogrammetre is the expression, or the pressure of a
kilogramme through a distance of i meter =r 7.233 foot-pounds.
Result of observation upon animal power furnishes the following as maximum
daily eiibct:
z. When effect produced varied fh)m .2 to .33 of that which could be produced
without velocity during a brief interval.
2. When the velocity varied fh>m .16 to .25 for a man, and firom .08 to .066 for a
horse, of the velocity which they were capable for a brief interval, and not involv-
ing aay effort.
3. When duration of the daily work varied from .33 to .5 for a brief interval,
during which tixe work could be constantly sustained without prejudice to healtb
of man or animal; the time not extending beyond 18 hours per day, however lim-
ited may be the daily task, so long as it involved a constant attendance.
ANIMAL POWBB. 433
Mien..
Mean effect of power of men working to best practicable advantage, is
raising of 70 lbs. i foot high in a second, for 10 hours per da,y:= 4300 jfoot-
pounSa per minute.
Windlass. — Two men, working at a windlass at right angles to each other,
can raise 70 lbs. more easily than one man can 30 lbs.
Labor. — A man of ordinary strength can exert a force of 30 lbs. for 10
hours in a day, with a velocity of 2.5 feet in a second ^4500 lbs. raised one
foot in a minute ^ .2 of work of a horse.
A man can travel, without a load, on level ground, during 8.5 hours a day,
at rate of 3^7 miles an hour, or 31.45 miles a day. He can carry 11 1 lbs.
II mUes in a day. Daily allowance of water, i gallon for all purposes ; and
he requires from 220 to 240 cube feet of fresh air |)er hour.
A porter going short distances, and returning unloaded, can carry 135 lbs.
7 miles a day, or he can transport, in a wheelbarrow, 150 lbs. 10 miles in a '
day.
0*ane. — The maximum power of a man at a crane, as determined by Mr.
Field, for constant operation, is 15 lbs., exclusive of frictional resistance,
which, at a velocity of 220 feet per minute = 3300 foot-pounds, and when
exerted for a period of 2.5 minutes was 17.329 foot-pounds per minute.
PUe^rimng.-^-G. B. Bruce states that, in average work at a pile-driver, a
laborer, for 10 hours, exerts a force of 16 lbs., plus resistance of gearing, and
at a velocity of 270 feet per minute, making one blow every four minutes.
Rowing. — A man rowing a boat i mile in 7 minutes, performs the labor
of 6 fuUy-worked laborers at ordinary occupations of 10 hours per day.
Drawing or Pushing. — A man drawing a boat in a canal can transport
1 10 000 lbs. for a distance of 7 miles, and produce 156 times the effect of a
man weighing 154 lbs., and walking 31.25 miles in a day ; and he can push
on a horizontal plane 20 lbs. with a velocity of 2 feet per second for 10 hours
per day.
TVeadrmill. — A man either inside or outside of a tread-mill can raise 30
lbs. at a velocity^of 1.3 feet per second for 10 hours, := 1 404 000 foot-pounds.
PuUeif»—A man can raise by a single piUley 36 lbs., with a velocity of .8
of a foot per second, for 10 hours.
Walking.— A man can pass over 12.5 times the space horizontally that he
can vertically, and, according to J. Robison, by walking in alternate directions
ui)on a platform supported on a fulcrum in its centre, he can, weighing 165
lbs., produce an effect of 3984000 foot-pounds, for 10 hours per day.
Pump, Crank, Bell, and 2iatcing.—Mr. Buchanan ascertained that, in work-
ing a pump, turning a crank, ringing a bell, and rowing a boat, the effective
power of a man is as the numbers 100, 167, 227, and 248.
Pumping.— A practised laborer can raise, during 10 hours, 1000 000 IbSc
water i foot in height, with a properly designed and constructed pump.
Crank, — A man can exert on the handle of a screw-jack of 11 inches ra-
dius for a short period a force of 25 lbs., and continuously 15 lbs., a net
power of 20 lbs. Mr. J. Field's tests gave 11. 5 lbs. as easUy attained, 17.3 ai
difficult, and 27.6 with great difficulty.
Mowing. — A man can mow an acre of grass in i day.
Reaping. — A man can reap an acre of wheat in 2 days.
Ploughing, — ^A man and horse .8 of an acre per day.
Oo
434
ANIMAL POWSB.
Day's "Work. (D. K. Clark.)
iSa&orer.— Carrying bricks or tiles, net load io6 Ibs.=:6cx> lbs. i milai
Carrying coal in a mine, net load 95 to 115 lbs. :^ 342 lbs. x mile.
Loading coke into a wagon, net load 100 lbs. =2270 lbs. t mile.
Loading a boat with coal, net load 190 lbs.= 1230 lbs. i mile, or &o cube yardfl ot
earth in a wagon.
Digging stubble land .055 of an acre per day, or ^000 cube feet of superficial earth.
Breaking 1.5 cube yards hard stone into 2 inch oabes.
Quarrying.— A. man can quarry tvom 5 to 8 tons of rock per day.
A foot-soldier travels in i minute, in common time, oo steps £=; 70 yards.
tie occupies in ranks a ft'ont of 20 inches, and a depth of 13, without a knapsack:
interval between the ranks is 13 inches.
Average weight of men, 150 lb& each, and five men can stand in a space of i
square yard.
SjfFeotivd Po-wei* of Afexi fbr a Sliort Period*
Manner of AppUtMiolk.
Bench-vice or Chisel. . . .
Drawing-knife or Auger.
Uand-pUme
Hand saw
form.
Lbs.
73
100
50
36
Manner of ApfpUcatioii.
Screw-driver, one hand
Small screVt- driver
Thumb and fingers
Windlass or Pincers . . .
ionw.
Lbs.
84
14
14
60
The muscles of the human jaw exert a force of 534 lbs.
Mr. Smeaton estimated power of an ordinary laborer at ordinary work was equiv-
alent to 3763 foot-pounds per minute. But, accordiDg to a particular case made by
him in the pumping of water 4 feet high, by good English laborers, their power was
equivalent to 3904 foot-pounds per minute; and this be assigned as twice that of
ordinary |>er8on8 promiscuously operated with.
Mr. J. Walker deduced from experiments that the power of an ordinary laborer, in
turniug a crank, was 13 lbs., at a velocity of 320 feet per minute forS hours per day.
A.movmt of l^aV>or prod voiced, "by a ]&£axi> (Morin.)
For 10 hours per day.
MANNER OF APPUGATION.
Throwing earth with a shovel, a height of 5 feet. .
Wheeling a loaded barrow up an inclined plane,
I to la.
Raising and pitching earth in a shovel 13 feet
horizontally
Pushing and drawing alternately in a vertical
dirpction
Transporting weight upon a barrow, and return-
ing unloaded.
For 8 HorRS per DaY.
Asceuding a slight elevation, unloaded
Walking, and pushing or drawing in ahoriiontal
dinnUion
Turning a crank
I'lwu a tread mill*
Ku w I ng
For 7 Hours pbr Dat.
Walking with a load upon his lx\ck
For 6 Horaa per Day.
Trausportinff a weight upon his back, and return-
ing unloaded
Trun8p<)rtiug a weight U{M>n his back up a slight
olovailon. and returning unloaded
Raialng a woight by his hands
Power.
Vel«dty
per
Second.
Lbe.
Feet.
6
1-33
132
.625
6
2.85
13
2-5
132
X
143
•5
26
2
18
2-5
140
26
•5
5
88
2-5
140
>-75
140
.2
44
•5
Weight
miaed.
Feet per
Bf^inute.
Lbs.
480
4950
810
1950
7920
4290
3120
2790
4200
7800
13200
14700
fS»r
Period
((iven.
No.
90
«4-7
35-5
144
6a
45. a
61. X
113
x6ow5
X60.5
•Morin fflvM aiN«>NMl »>r Uln^r of a m»n upon trMMt-mill, io an
iMtly of .5 ^i per «Kxu»d for 8 lK>ttn fer day :x ;o Ite. at x Ibofc
1680 19
X 320 14.4
aa Individoal case, at 140 Iba., At a 're>
pcrMMBdt heaea 70 -i- 1.3 fc«t m
ANUf AL POWBB.
435
<ro Compute Number of* M.en. to Ferfbrm WotIs. upon
a Xread-mill or Pile-cl river.
Rule. — To product of weight to be raised and radius of crank, add fric-
tion of wheel, and divide sum by product of power and radius of wheel.
ExAMPLK. — How many men are required upon a tread-mill, 20 feet in diameter,
to raise a weight of 9233.33 lbs., crank 9 inches in length, weight of wheel and its
load estimated at 5cmx> lbs., and friction at .015.
Weight of a man assumed at 25 lbs. Radius of crank .75 feet
Eflbct of a man on a tread^mill, page 433, 30 Iba at a velocity of i. 3 feet per second,
= 1.3 X 60 = jS feet per mintUe.
9233.33 X .75-I-5CXX3 X .oi5 = 7cxx> lbs. resistance of load and wheels and 7000-^
^ X 10 X 30 = 7000 = load and weight -i-prodaci of power inoretued by its
20 X 3-i4'6
vdocity over loadj raditu of wheel and power = 7000 ^ 1.241 X xo X 30 = 18.8 men.
Horse.
Amount of I^abor pro<ix\cecl t>y a Horse under dififereut
. OirouxustaiiceH. {Morin.)
For 10 how'i per day.
lUMIflB OF AFPUOATIOII.
Drawing a 4-wheeled carriage at a walk
With load upon his back at a walk
Transporting a louded wagon, and returning un-
loaded at a walk
Drawing a loaded wagon at a walk
For 8 Hodbs pkr Dat.
Upon a revolving platform at a walk
For 4.5 HorRs per Dat.
Upon a revolving platform at a trot
Drawing an unloaded 4 wheeled carriage at a trut.
Drawing a loaded 4-wheeled carriage at a Irut
Power.
154
364
1540
1540
100
66
97
770
Velocity
per
Second.
WeiKht
drawn.
Feet per
Minute.
H»
for
Period
i;iven.
Feet.
3
3-75
t
3-75
6.75
7-35
7- 25
Lbe.
27 720
59400
184800
346500
18000
26730
43>95
334 950
No.
504
1080
3360
6300
260.8
218.7
353-5
2741
If traction power of a horse, when continuously at a walk, Is equal to 120 lbs.,
and grade of road i in 30, resistance on a level being one thirtieth of load, be can
draw a load of I30 X 30 -f- • 2= 1500 iba
Street Raila or TrauiAways, {Henry Hughes.)
Cars, 26 lbs. per ton, or i to 86 as a mean.
Perfbrmaiioe of Horses in ITreuiioe. {M. Charii-Marsaims.)
•BASOH.
Winter. . ,
Sammer .
Road.
WoiRht
Horte.
Speed
per
Hour.
Pavement
Macadam
Pavement
Macadam
Toot.
1.306
.851
I-39S
X.14X
Mile*.
2.05
1.91
».i7
2.16
Work per
Hour, drawn
One Mile.
Ton-mile*.
2.677)
1.625 J
a. 464)
Ratio of
Pavement to
Macadam.
1.644 ^ I
1.229 ^ '
Average daily woric of a Flemish horse in North of France, where country is flat
and loads heavy, is, on same authority, as follows:
Klven In example k S3'8 Iba., from which a dcdnetion U to be made for exeeea of amount t>f labor that
can be performed In Slioon over 10. Or, at 10 : 8 : .' 53.8 : 43-04 ibt., which doaa not etaentiaH^ dift-
fr«n amct of 30 Iba. for that of an average performaaoo.
43^ ANIMAL POWBS.
Greatest mechanical effect of an ordinary horse is produced in operating a
gin or drawing a load on a railroad, when traveilin^^ at rate of 2.5 miles per
hour, where he can exerl a tractive force of 150 lbs. fur 8 hours per day.
Horse upon Turnpike Hood,
At a speed of 10 miles per hour, a horse will perform 13 miles per day tor
3 years. In ordinary staging, a horse will perform 15 miles per day.
To Compute Tractive Power of a Horse Team^ see Traction^ page 848.
Assuming maximum load that a horse can draw on a gravel road as a
standard, he can draw,
On best-broken stone road a to 3 times.
On a well-made stone pavement 3 to 5 '"■
On a stone trackway 7 to 8 '•
On plank road 4 to 12 "
On a railway 181020 "
NoTB.— Track of an iron railway compared with a plank-road is as 27 to'^a
To Compxite Power of Draught of a Horse at IDifierent
S^levatioxis.
Let ABC represent an inclined plane, o weight
of a horse which, being resolved into two com-
ponent forces, one of w^ch, n, is perpendicular to
plane of inclination, and other, r, is parallel to it.
Hence, r represents force which horse must over-
come to move his own weight.
Then, by similar triangles, A B or / : B C or A : : o : r. Or, '7^ = r.
Ifnepresents tractive power of horse, upon a level, of 100 lbs., t tractive
power upon a plane of inclination, and r that part of force exerted by hurse
which is expended upon his own body, then f = « — r, or < - ^ = <' in Ws.
Illustration.— If inclination is i in 50.
Assume t = 100, weight of horse 900 lbs., and I = 50.01.
Then, 100 — ^~^ = 100 — 17.99 = 82.01 lbs.
Assuming load that a horse can draw on a level at 100, he can draw upon
loclinations as follows :
I in 100..... 91
I " 90. .... 90
I " 80 89
On his back a horse can carry from 220 to 300 lbs., or about 27.5 \mr cent,
of his weight
Z,a5o»\--The work of a horse as assigned bv Boulton A Watt, Tredgold,
Reniiie, Beardmore, and others, ranges from 20600 to 39320 foot-pounds per
minute for 8 hours, a mean of 27 750 lbs. r r
A horse can travel, at a walk, 400 yards in 4.5 minutes ; at a trot, in a
minutes ; and at a gallop, in i mmute. He occupies m ranks, a front of 40
uis., and a depth of 10 feet; in a staU, from 3.5 to 4.5 feet front; and at a
picket, 3 feet by 9 ; and his average weight = 1000 lbs.
Carrying a soldier and his equipments (225 lbs.) he can travel 25 miles
\\\ a day of 8 hours. ^ ^ ^ j
cli;de*d *"^^'"^**"^ *^ ^^*^ ^^^ ^^^' ^^ ^^^^ * ^*^' ^^^**^ °^ carriage in-
I in 75 88
I " 70 87
I '• 60 85
X in 50 82
I " 45 80
' " 40 77
'10 35 74
X " 30 70
« •• 25 64
I in 20 55
I " x5 40
I '* 10 10
AmUAL POWBB.
437
Ordinary work of a horse may be stated at aa 500 lbs., raised x foot in u
minute, for 8 liours per day.
In a mill, be moves at rate of 3 feet in a second. Diameter of track should not
be less tban 25 feet
Reiinie ascertained that a horse weighing 1233 lbs. could draw a canal-boat
at a speed of 2.5 miles per hour, with a power of 108 lbs., 20 miles per day.
This is equivalent to a work of 23 760 foot-lbs. per minute, He estimated
that the average work of horses, strong and weak, is at the rate of 22 000
foot-lbs. per minute.
From results of trials upon strength and endurance of horses at Bedford, Eng., it
was determined that average worlr of a horse =: 20000 foot-lbs. per minute. A good
horse can .draw i ton at rate of 3.5 miles per hour, fVom 10 to 12 hours per day.
Expense of convoying goods at 3 miles per hour, per horse teams being i, expense
at 4.33 miles will be 1.33, and so on, expense being doubled when speed is 5.135 miles
I)er hour.
Strength of a horse is equivalent to that of 5 men, and his dally allowance of
water should be 4 gallons.
A^xnount of* "Lteibov a Horse of average StrexxKtb. is capa-
ble of peribrxning, at difiereut Velooities, oix Canal,
Railroad, and Xumpike.
Veloei-
typer
Hoar.
MUee.
2-5
3
4
5
Dara-
UW9IO
1 bneci, ara
tion of
Ona
On a Rail-
Work.
Canal.
road.
Hoor*.
Toot.
Tona.
11.5
520
"5
8
243
93
45
103
73
2.9
52
57
Traction atimaUd at 83.3 Ibt.
irn I Mile.
On a Tarn-
pike.
Tona.
14
13
9
7.8
Veloci-
ty per
Hour.
Dnra-
tion of
Work.
uteiui
Ona
Canal.
cncct, ara
On a Rail-
road.
Miiee.
6
Hoan.
3
Tona.
30
Tona.
48
I
ID
15
1.125
•75
13.8
6.6
4«
36
28.8
On a Turn-
pike.
Tona.
6
5-»
4-5
3-6
Actual labor performed by horses is greater, but they are injured by it.
Tractive Power of a horse decreases as his speed is increased, and within limits
of low speed, or up to 4 miles per hour, it decreases nearly in an inverse ratio.
For 10 Hourt per Day.
Milea.
Traction.
Mllea.
Traction.
Per Hoar.
75
X
'^5 .
Lbe.
330
250
200
Per Hoar.
«-5
'•75
3
Lba.
165
140
X35
Milea.
Traction.
Per Hour.
Lba.
2.35
no
2-5
100
3.75
90
Mil«e.
Per Hour.
3
3-5
4
f^r Ordinary or Short Periodt. (MoUsworth.)
Miles per hour 3 3 3*5 4
Power in lbs z66 135 104 83
4-5
63
Traction.
Lba.
82
70
62
5
41
Miule. (D.K. Clark.)
Load on hack, 170 to 220 lbs. day's work = 6400 lbs. i mile ; 400 lbs. at 2.9
miles per hour =: 5300 lbs. i mile, and 330 lbs. at 2 miles per hour = 5000 lbs.
I mile.
Upon a revolving platform, at a velocity of 3 feet per second, = n 880 lbs. raised
one foot per minute, or 172.2 H* for 8 hours per duy
Load on back, 176 lbs. carried 19 miles day's work = 3300 lbs. 1 mile.
In Syria an ass carries 450 to 550 lbs. grain.
Upon a revolving platform, at a velocity of 3.75 feet per second, = 5280 lbs. raised
one foot per mlnaie, or 76.5 ff for 8 hours per day.
Oo*
438
ANIMAL POWBB.
Ox. I
An Ox, walking at a velocity of 2 feet in a second (1.36 mfles per honrX
eOLerts a power of 154 lbs., = 18480 lbs. raised one foot per minute, or
a68.8 W for 8 hours per day.
A pair of well-condilioaed bullocks in India have performed work =s 8000 foot-Ib&
per minute.
Camel.
Load on back^ 550 lbs. carried 30 miles per day for 4 days, 4 daya^ work
165CX) lbs. I mile, fur 5 days 130CX} lbs. i mile = 44 H* for xo hours per day
Load of a Dromedary, 770 lbs.
Xjlaxxxa.
Load on hach^ no lbs., day's work 2000 to 3000 lbs. i mile = .5 to .75 H*
for 10 hours per day.
Birds and Insects.
Area of their wing surface is in an inverse ratio to their weight.
Assuming weight of each of the folIowiDg IMrds to be one pound, and each Insect
one ounce, the relative area of their wing surface proportionate to that of their act-
ual weight would be as follows (if. 2>« Lucy) :
Sq.ft.
Swallow .... 4.85
Sparrow .... 2. 7
Turtle-dova . 2. 13
Sq.ft.
Pigeon 1.27
Vulture 82
Crane, Australia, .41
Sq.ft.
Gnat 3.05
Dragon -fly, sm'U, 1.83
Lady-bird 1.66
Sq.fL
Cockchafer.. .33
Bee 33
Meatfly 35
Crooodile and X>os.
The direct power of their jaws is estimated at 120 lbs. for the former and
44 for the latter, which, with the leverage, will give respectively 6000 and
1500 lbs.
PERFORMANCES OP MEN, HORSES, ETC.
Following are designed to furnish an authentic summary of the fastest or
most successful recorded performances in each of the feats, etc., given.
MAN. 'Wallrine.
1874, Wm. Perkins, London, Eng., .5 mile, in 2 min, 56 ««c.; x, in 6 mxn. 23 «ec;
1877, 20, in 2 hourz 39 min. 57 sec
1881, C. A. Harriman, Chicago, 111., 530 miles, in 5 days 20 hours 47 mm.
1878, W. Huwes^ London, Eng.. 50 miles, in 7 hours 57 min. 44 see.; 1880, 57 miles,
in 13 htturs 7 min. 27 sec, and 100, in 18 hours 8 min. 15 sac,
i8oi, Capt. R. Barclay, Eng., country road, 90 miles, in 20 hours 22 min. 4 «c., in-
cluding rests; 1803, .25 mile, in 56 sec, and Charing Cross to Newmarket, 64, in lo
hours, including rests; 1806, 100, in lO hours, including i hour ^omin. in rests, 1809,
1000, in 1000 consecutive hours, walking a mile only at commencement of each hour.
1877, D. O'Leary, liOudon, Eng., 200 mijes, in 45 /tours 21 min. 33 sec
1818, Jos. Eaton, Stowmarket, Eng., 4032 quarter miles, in 4032 consecutive quar-
ter hours.
1877, Wm. OaU, London, Eng., 1500 miles, in 1000 consecutive hours, 1.5 miles
each hour; and 4000 quarter miles, in 4000 consecutive periods of 10 minutes.
1882, Chas. RoweU, New York, N. Y., and running, 80 miles 1640 yards, in lahours.
1882, Geo. Hazad, New York, N. Y., and running, ^ miles 220 yards, in 6 days.
1883, J. W. Raby, London, Eng., 2 miles in 13 min. 14 sec; 3, in 20 mxn. 21.5 tee.;
4, in 27 min. 38 sec ; 5, in 35 min. 10 sec; and 10, in 1 hour 14 min. 45 sec
1882, John Meagher, New York, N. Y., 8 miles in 58 min. 37 sec
W. Franks, London, Eng., 2$ miles in 3 hours 55 min. 14 sec
1885, W. Cummings, Ix)ndon, Eng., 10 miles in 51 min. 6.6 sec
1884, J. E. Dixon, Birmingham, Eng., 40 miles in a hours 46 min. 54 sec
1883, Peter Golden, Brooklyn, N. Y., 50 miles in 7 hours 29 min. 47 sec
"Rxxxtrtixxg,
1844, Geo. Seward, of U. S., Manchester, Eng., flying start, 100 yards, in 5.25 aea
1864, Jas. NutaXl, Manchester, Eng., 600 yards, in i min. 13 sec.
1881, L. E. Myers, New York, N. Y., 1000 yards, in a min. 13 sec.
1863, Wm. Lang, Newmarket, Eng., 1 mile, in 4 lat'li. 2 sec, descending giound}
Manchester, a, In 9 min, 11. 5 sec; 1865, 11 miles x66o7ardB, iQ « ho/ur a min. a.5
AifriM Ai. ^owBB. 439
mMs^Wm. Howta, " AnMrioan D«er,*' f.andon, {Sng., 15 mltos In i how aa vUm.
1863, L. Bennett, " Deerfoot," Hackney Wick^ Eng. , 12 m. , in i hour a min. 9- 5 M&
1879, Patrick Bymes, Haliikx, N. S., ao miles, in i Aour 54 min.
1880, Z>. I>(movan, Providence, R. I., 40 miles, in 4 hows 48 min. 23 sec
17—, j1 Oourter, fSast Indies, loa miles, in 34 hour:
1889, H. if. Johnson, Denver, CoL, 50 yards, in 5 sec
1884, if. JBT. KitUemany Oakland, Cal., 150 yards (twice), in 14 min. 6 tee.
1890, James Grant, Cambridge, ICaas., 5 miles in 35 min. 32.35 see.
JvLvapir^jg^ X^eaping, oto.
1854, J. Howard, Chester, Eng., i jump, board raised 4 ins. in front, running start,
^ivh dumb-bells, 5 lbs., zgfeet 7 ins,
1868, Geo. M. KeUey, Corinth, Mass., running, and from a spring board, leaped
ovur 17 horses standing side by side.
1879, G. W. HamiUon, Romeo, Mich., dumb-bells, 23 lbs., standing jump, 14 feet
5.5 ins.
1886,/. PurceU, Dublin, running long jump, z^feet 11. 5 ins.
1889, J. Darby, Ashton- under- Lyne, Eng., two standing jumps, wMth weights, 26
^«^8.5»«8.
H. M. Johnson, St. Louis, Mo. , without weights, 22 feet 6. 75 ins. 10 standing long
Jnmps, without weights, 114/eet 8.5 ins.
J. F. Kearny, Walpole, Mass., 3 standing long jumps, with weights, 42 feet 3 trw.;
without weights, at Boston, Mass- , 35 feet 6 ins. Boston, Mass. , running high jump,
with weights^ 6jfeet 5.25 ins,; backward jump, with weights, heel to toe, lafeet 1.35
ins. Oak Island, Mass., standing high leap, with weights, sj^ef 9.5 ins.
Uiftixig*.
1825, Thomas Gardner, of New Brunswick, N. S., a barrel of pork, 320 lbs., under
each arm; also transported across a pier an anchor, 1200 lbs.
1868, Wm. B. Curtis^ New York, N. Y., 3239 Ws., in harness.
1883, D. L. Dotod, Springfield, Mass., by hands, 1442.25 lbs.
1870, JDL JHnnie, New York, N. Y., light stone, 18 lbs., 43 /<^; heavy stone, 24 lbs.,
34ye«f 6 ins.; heavy hammer, 24 llis., B^/eet 6 ins.; iSjz^ Aberdeen, Scotland, l^il
hammer, ijfifeet; mn, x6 IbSL, 162,^.
1887, Fet0' Mey, Milwaukee, Wis., 56 lbs., wHbout foHow, y/eet 5 int.
S 'vvizxi xn i n §:•
1835, S. Bruck, 15 miles. In rough sea, in 7 hxturs 30 min.
1846, A Native, off Sftndwjch Islands, 7 miles at sea, with a live pig under one arm.
1870, Patdine JRohn, Milwaukee, Wis-, ^50 fpet, still water, in 2 min. 4 \ .ncc.
1872, J. B. Johnson, lx)ndon, Eng. , remained under water 3 min. 35 sec.
1875, Capt M. Webb, Dover, Kng., to Calais, France, 23 miles, crossing two ftiU
tod two half tides ^ 35 miles, in 21 hov>rs 45 min. 1880, Afloat 60 hours.
x886, J. Haggerty, Blackburn Baths, Eng., 100 yards, 4 turns, in i min. 5.5 teo.
1800, J. NuUally London, Eog., jooo yards, 23 turns, in 13 min. 54.5 sec
1885, J. J. ColHerf London, Eng., i mile in 26 min. 52 sec
Skating.
1877, John Ennis, Chicago, 111., 9 laps to a mile, 100 miles, in n hours 37 min. 45
tec; and 145 inside of 19 houra
1887, T. Donoghue, Jun., Newbargh, N. Y., 1 mile, with wind, in 2 min. 12.375 sec
i88a, S. J. Montgomery, New York, N. Y., 50 miles, in 4 haurt 14 mxa. 36 sec
Nora. — The Sporting Magazine, London, toI. fx., pafr« 135, reporU 11 mao in 1767 to have akatod a
iniio upon th« Serponune, Hyde Park, London, in 57 eeconds.
HCmSB. Trotting.
2814, "Boston Bine," Lynn turnpike, one mile, sulky, in 2 mn. 54 sec
1875, "Steftl tiwjy," Yorkshire, Eng., lo m'les, saddle, in 27 min. 56.5 sec.
1867, ''John Stewart," Boston, Mass., half-mile track, 20 miles, harness, in 58
min. 5-75 sec, and 2a5 miles in 59 min. 31 see.
>830, "Top Gallant," Philadelphia, Penn., 12 miles, harness, in 38 min.
1829, "Tom Thnmb," Sunbury Common, Eng., 16.5 miles, harness, 248 lbs., ih 56
min. 45 tec; and 100 miles, in 10 hours 7 min., including 37 min. in rests.
1869, "Morning Star," Doncaster, Eng., 18 miles, harness (sulky 100 lbs.), in 57
min. 27 tec
1835, " Black Jok«," Providence, R L, 50 mites, saddle, 175 lbs., in 3 hourt 57 min.
440 ANIMAL POWJBB,
1855, "Spangle," LoDg Island, N. Y., 50 miles, wagon and driver 400 lbs., in 3
hour$ 59 min. 4 sec.
1837, "Mischief," Jersey City, N. J., to Philadelphia, Penn., 84.35 miles, harness,
very hot day and sandy road, in 8 hours 30 min.
1853, ''Conqueror," Long Island, N. Y., 100 miles, harness, in 8 houn 55 min, 53
<ec., including 15 short rests.
1873, M. Delaney''s mare, St. Paul's, Minn., 200 miles, race track, harness, in 44
hours 20 min.^ including 15 hours 49 min. in rests.
1834, ''Master Burke" and '' Robin," Long Inland, N. Y., 100 miles, wagon, in 10
hours^ 17 min. 22 «ec., including 28 min. 34 sec. in rests.
Stage-coaoliiMg.
1750, By the Duke of Queensberry, Newmarket, Eng., 19 miles, in 53 min. 24 sec
1830, London to Birmingham^ Eng.^ "Tally-ho," 109 miles, in 7 hours 50 min..
including stop for breakfast of passengers.
J^eapiixg.*
1821, A horse of Mr. Mane, at Loughborough, Leicestershire, Eu^., 173 lbs., over a
hedge 6 feet in height, -isfeet.
1821, A horse of Lieut. Green, Third Dragoon Guards, at Inchinnan, Eng., ridden
by a heavy dragoon, over a wall 6/«*'< in height and ijfbot in width at top.
1847, "Chandler," Warwick, Eng., over water, yjfeet.
1901, '• Heather bloom," Chicago, 111., over a bar, jfeet 4-5 ins.
NoTB. — The maximum stride of a horse is estimated to be 28 ftet 9 %n». ; " Eclipse " haa oovarad ac
fttt. The maximum stride of an ellc is 34 fttt, and of an elephant 14 feet.
X701, Mr. Sinclair, on the Swift at Carlisle, a gelding, 1000 miles, in 1000 consecu-
tive hours.
1731, Geo. OsbdUleston, Newmarket, 156 lb&, 100 miles, by 16 horses, in 4 hours xg
min. 40 sec, and 200. by 28 horses, in 8 hours 3^ min., including i hour 2 min. 56 sec
in rests; i horse, "Tranby," 16 miles, in 33 twtn. 15 sec
1752, Spedding^s mare, 100 miles, in 12 hours 30 min., for 2 consecutive days.
1754, A Galloway mare of Daniel Corker's, Newmarket, 300 miles, by one rider,
67 lbs., in 64 hours 20 min.
1761, John Woodcock, Newmarket, 100 miles per day, by 14 horses, one each day,
for 29 consecutive days.
1814, An Officer of 14^ Dragoons, Blackwater, 12 miles, i horse, in 25 min. n sec
1868, N. H. Movrry, San Francisco, Cal., race track, x6o lbs., 300 miles, by 30 horses
^Mexican), in 14 hours 9 min., including 40 minutes for rests; the first 200, in 8
hours 2 min. 48 sec, and the fastest mile in 2 min. 8 sec.
1869, Nell Coher, San Pedro, Texas, 61 miles, in 2 hours 55 min. 15 sec, including
rests.
1870, John Faylor, Carson City, Nevada, 50 miles, by 18 horses, in i hour 58 min,
33 sec; and Omaha, Neb., 56 miles, in 2 hours 26 witn., including rosta '
1876, John Murphy, New York, N. Y., 155 miles, by 20 horses, in 6 hours 45 min.
7 sec
1878, Caf*t. SaJvi, Bergamo to Naples, Italy, 580 miles, in 10 days.
x88o, " Mr. Brown," Rancocas, N. J., aged, 160 lb&, xo miles, in 26 min. 18 sec
1828, "Chapeau de Paillc" (Arabian), India, 1.5 miles, xx5 lbs., in 2 min. 53 sec
1 83-, Capt. Home (Arabians), Madras to Bunga^ore, India, 200 miles, in less than
xo hours.
DOOS. Coursixis and. CHaeing.
A Greyhound and Hare ran 12 miles in 30 min.
1794, A Fox, at Brende. Eng., ran 50 miles in 6.5 hours.
A Greyhound, at Bushy Park, Kng., leaped over a brook y^feet 6 ins.
BIRDS. Flying.
Jn Miles per hour: Swailow. 65; Marten, 60, Carrier Pigeon and fiScoZ DueXe,
50; Wild QotK^e, 45; Quail, 38; Crow. 25.
1870, Carrier Pigeons, I'esth to Cologne, Germany, 600 iu 8 hours. 1875. Dundee
Lake to I'aterson, N. J., 3 in 3 7iiin. 24 sec.
Non.— At so miles the prassur* on a pinne surfitce ia 12.1; lbs. per sq. foot; and at •00, 50 lbs.
* A Salmon can leap a dam i^/tet in htlghU— Sporting Jfo^ostiM, London, Tol. sti., paf* 79.
HOB8E-POWKS. — BELTS AND BELTING.
441
HORSE -POWER.
Horge-power, — ^H* is the principal measure of rate at which work is per-
firmed. One horse-power is computed to be equivalent to raising of 53000
lbs. one foot high per minute, or 550 lbs. per second. Or, 33 000 foot-lbs. of
work, and it is designated as being Nonimal, Indicated, or Actual.
A ^ in work la estimated at 73 000 Iba , raised i foot in a minute ; bat as a horse
can exert tliat rorce for only 6 Hours per day, one work W is equivalent to that of
4.5 horses, at a rate of 3 miles per hour.
C^eval-vapeur of France is computed to be equivalent' to 75 kilogram-
meters of work per second, or 7.233 foot-lbs., or 75 x 7.233 = 542.5 foot-lbs.^
which is 1.37 per cent, less than American or English value.
BELTS AND BELTING.
Capacity of belts to transmit power is determined by extent of their
adhesion to surface of pulley, and it is very limited in comparison with
tensile strength of belt.
Resistance of a belt to slipping depends essentially upon character
uf surface of pulley, its degree of tension, and width, and as adhesion
i.s in proportion to pressure on surface of pulley, long belts, by having
greater weight, give greater adhesion.
TJltiinate Tensile Strengtlx of Seltiug per Sq,. Inch.
of* Section.
Merchantable Oak-tanned, of first quality. Belts, 6 ins. in width.
Single, .2 inch in thickness, gi8 lbs. per lineal inch, and 4536 lbs. per sq. inch of
section. Double, .35 inch, 1396 lbs. per lineal inch, and 4101 per sq. inch.
Ratio of 8in(?Ie to double/giB -=-1396 = .658.
Elongation in two Inches of length and four in width for a load of 2000 lbs. Sin-
gle, 9.09; double, 5.79.
The resistance and elongation of double belting is roorc uniform than that of sin-
gle, f^om the irregularities in each layer cuuuteructiug each other.
Belt
Dwtnictive
Streu.
Jointing.
Stress
per sq. inch of
Mction.
Lbs.
3940
3000
3545
1792
5560
per lineal inch
of width.
Lbs.
709
611
762
.407
1112
Elongation.
Per cent
75
7-5
75
7-5
7
Riveted Joints failed at rivet holes. Riveting of dohble belts was shown to be
objectionable. Riveted Joints of single belts have one-third less strength than the
average of different manners of hieing.
A double staggered laced Joint, i strand only in each hole (5 of. 1875 inch punched),
broke in belt at a stress equal to that of resistance of it per area of section.
Transzniasion of Po-v^er.
A single belt, 4 ina in width and .2 inch in thickness, over drums 3 feet in di-
ameter, running at a speed of 868 feet per minute, with a tension of 88 lbs. per lineal
inch of width on the driving face, and 29 Iba, or one-fourth, on the driven, devel-
oped an average of 7 horse-power, with a slip of but s feet per minute = .0058 per
cent. Co efficient of friction. . 14, and number of sq. feet of surface of belt, per IP
per minute, 41.8, and factor of safety assumed at 10.
Hence, one lineal inch of belt of sutflcient strength (3000 to 4 000 lbs. per sq. inch)
at a velocity of 1000 feet per "minute, less slip, with a power of 50 lbs. per sq. inch,
will give X.3 net IP, inclusive of co-efficient of friction of .14. The power in this
case, including friction, was 3a 6 lbs. per sq. inch.
— Prom Eletnents of Prof. Chas. H. Benjamin.
44^ BKLTS AND BELTING.
Commutation ttfW.
<^(S~*)_;g^868(88X4-aaX4)_g fl.
33000 33000
V reprezenting velocity of bdt in feet per minrUe, S on « stress on belt per lineal
inch of width on upper or driving side and underneath or returning side.
To Compute Widtti of a JJeather :Belt.
Assiiniin<; a well-defined case (where limit of adhesion was ascertained),
a belt of ordinary construction Haced). and 9 inches in width, transniitt^
the power of 15 horses over a pulley ^ feet in diameter, at a velocity of 1800
feet pr miiitite, with &n arc of adliesion of 210°, or oi .6 or 7.54 fw^ of cir-
cumference, and with an area of 95 square feet of belt {ter Ip.
Hence, p szw{ to represenfinff vndth of belt in inches, d di-
ameter ofpuUey in feet, and v velocity of belt in feet per minuttt
NoTK.— Tliirkness of belt should be added to dimneter of palley. Applying thefie
eleineuts 10 the formulas of 13 difl'ereot authors, the result varies from 7.85 to 13.5
ius., mean of which is 10 675. For double belting width = .66 to.
iLLCSTRATiovs.— If H* 25, afid vc'loclty of belt^^so feet per minute, what
should bo width of belt^ diameter of pulley 4 feet?
-— I2.S ins. for ordinary thickness of lijti in.
4X2250 :> -f 9 J /:>
Xo Cottipiite IClem«kats oV ^tf^lting.
vw H» 33000 „ 33 006 IP _-_ Wrir ^ a ^ .
1000* vw V 33000 t a
1' 1000 laeedf 550 riveted (fbr a thickness of . 1875 inch), with variations according
to the character and condition of the belt, diameter of pulley, and arc of adhesion
of belt. P representing power traniferred, W loeight or stress in Ws., t thickness of
belt in ins., v velocity cfit in feet per minute, and S stress on belt per lineal inch of
width w, in lbs.
Single belts at their relative thickness with double, of ,2 to .35 Inch, will sustain
oue-tenth more stress per sq. inch of belt.
To Compute tb.e A.iigle of tlie A.ro of Cout^aot of a Belt.
Sin^ (R — r-r-d) X 2 + 180° for large pulley or driver and — 180° for small.
R and r representing radii of pulleys, d distance between their centres — a/2 in feet
or inches.
iLLrsTRATiox. — Assumo pulleys 11.2 feeit and 4 feet in diameter find distance
apart 15 feet.
Sin/./*-' '~"^-r- 15 J X 2-f- 180° = 207° A^'for large pulley and 152° ia' for smail.
India H.ubber Belting:. {Vutcanixed.)
EstuUs <tf JBsqaeriments upon Adhesion of India Rubber and Leather Belting,"^
{J. H. Cheever).
LtM.
Rubber belt slipped on iron pulley at 90
»» " leather " 128
Leather belt slipped on iron pulley at 48
" " leather " 64
Hence it appears that a Rubber Belt for equal resistances with a I.eather Belt
may be reduced respectively 46, 50, and 30 per cent.
/ran Wire,^^A wire rope .375 inch in diameter, over a pulley 4 feet in di-
ameter, running at a velocity of 1250 feet t^er minute, will transmit 4.5 H*.
tn order to avoid undue bending of Wires, diameter of pulley should not be less
than 140 times diameter of rope.
Bff Expei'imeiitH of H. R. Towne ami Afr. Kirkaldy. {England.)
Tensile utreuffth of Single leather belting per square inch 0/ section.
Laced, 960 Uts* = i. Rivete<l, 1740 lbs, s= 1.8. Solid, 3080 lbs.
BELTS AND BBLTIKO. — BLASTING. 443
By the experiments ofF W Taylor, M,R,the tmuOe strength o/bdia
JPer Square Inch of Section.
Oak-tanned 192 to 329 lbs. Raw hide 353 to 284 Ibt.
Leather Bdis— Are best when oak- tanned, should be frequently oiled,* and when
run with hair side over pulley will give greatest adhesion.
Ordinary thickness .1875 inch, and weight 60 lbs. per cube Toot.
Relative effect of different puileyn and belts:
I^eather surface., i. Rough iron. ... 41 Turned iron... 64 Turned wood. .. .7
Morin assigned 50 lbs. as a proper stress per inch.of width of good belting.
Presence of small holes io a belt will prevent its slipping or squealing.
To increase adhesion, coat driving surface with boiled oil or cold tallow, and then
apply powdered chalk.
When new, cut them .1875 inch short for each foot in length required, to admit
of the stretch that occurs in their early operation.
Helbs should be set as nearly horizontal as practicable, in order that the sag may
increase adhesion on pulley, and hence power should be communicated through
under side.
The ''creeping" or lost speed by belts is about .006 per cent., hence, to maintain
a uniform or required speed, driver must be Increased in diameter pro rata with slip.
A double belt, 75 ins. in width and 153.5 feet in length, transmitted 650 IIP.
{See page 989).
BLASTING.
In Blasting^ rock requires from .25 to 1.5 lbs. gunpowder per cube
yard, according to its degree of hardness and position. In small blasts
2 cube yards have been rent and loosened, and in very large blasts 2 to
4 cube yards have been rent and loosened, by i lb. of powder.
TuMids and tha/U require 1.5 to 2 lbs. per cube yard of rock.
Q-vxii powder has an explosive force varying from 40000 to 90000
fbs. per sq. inch. That used for blasting is much inferior to that used for
projectiles, the proportion being fully one third less.
N'itro-slyoerine is an unctuous liquid, which explodes bj concussion,
an extreme pressure (aooo lbs. per sq. inch), or a temperature exceeding 600°
if quickly applied to it^ it will inflame, however, and bum gradually.
At a temperature below 40® it solidifies in crystals.
Its explosion is so instantaneous that in rock-blastlng tamping is not nec-
essanr ; its explosive power by weight is from 4 to 5 times raat of gun-
powder.
i:)3ri&axnite is nitro-dycerme 75 parts, absorbed in 25 parts of a sili-
ceous earth termed kieselguhr; it also explodes so instantaneously as to
render tamping in blasting quite unnecessary.
It is insoluble in water, and may be used m wet holes ; it congeals at 40°,
is rendered ineffective at 212°, and has an explosive force by weight of 3
times that of gunpowder, and by bulk 4.25 times.
<3-xm - oottoix is insoluble in water, and has an explosive force by
weight of from 2.75 to 3 times that of gun|)0wder, and by bulk 2.5 times.
It may be detonated in a wet state with a small quantity of dry material.
Tonite is nitrated gnn-cotton, and is known also as eoUon powder. It
is produced in a granulated form.
J^itho-fVetoteiir is a nitro-glycerine compound in which a portion of
the base or absorbent material is made explosive by the admixture therein
of nitrate of baryta and charcoal.
• Sm CemenU, «te., fgb 871, for compMitioM, eU
444
BLASTING.
Cellulose Dsrziaxnite is when gan-cotton is used as tlie absorbeni
for nitro-glycerine ; it will explode frozen dynamite, and is more sensitive tc
percussion than it.
To Coxnptite Cb.arge of Ounpowder fbr Roolz Blasting:.
Rule. — Divide cube of line of least resistance by 25, as for limestone, tc
32 for granite, and quotient will give charge of iwwder in lbs.
Or, L3 -1- 32 = lbs.
Example. — When line of least resistance is 6 feet, what is charge required?
6^-7-32 = 6.75 lbs.
Line of least resistance should not exceed .5 depth of hole. *
Tamping. — Dried clay is the most effective of all materials for tamping; Broker.
Brick toe next, and Loose Sand the least.
Relative Costs of a Tunnel and Shaft in England, {Sir John Burgoyne.)
Iron find steel 8.98
Smiths and coal 6
Fuses 7. 18
Powder ^9*^4
Labor 4o-8
100
Diam.
Weight of Eirplosive Materials in Holes of Dijei'enl Diameters.
Per Inch of Length.
Powder
or Gun- Dynamite. Diam. or Gun- Dynamite. Diam.
cotton. ~~" —
Ins.
I
1.25
1-5
Oi.
.419
•654
.942
Oz.
.67
1.046
1-507
Ins.
'•75
2
2.25
Oz.
1.283
1-675
2. 12
Oz.
2053
2.68
3393
Ins.
2-5
2-75
3 •
Powder
or Gun-
cotton.
Dynamite
Boring Holes in Granite.
Diam.
of
Jamper.
Depth
of
Hole.
Men.
Ins.
I
1-75
2
Ins.
I t02
2.5 to 6
4 to 7
No.
I
3
3
Depth bored
per Day.
Ham-
mer.
Diam.
of
Juniper.
Depth
Hole.
Men.
Feet.
8
12
8
Lbs.
6
14
14
Ins.
2.25
2.5
3
Ins.
5 to 10
9 to Z2
9tOx5
No.
3
3
3
Oz.
2.618
3.166
3769
Depth bor«d
per Day.
Feet.
6
5
4
Oz.
4.189
5.066
6.03
Ham-
mer.
Lbs.
x6
x6
18
Drt^-^Width of bit compared to stock .625.
Charges of Fowder,
Usual practice of charging to one third depth of hole is erroneous, inasmuch as
volume of charge increases as square of diameter of hole. Hence holes of 1.5 and
2 inches, although of equal depths, would require charges in proportion of 2.25 and 4.
Line of
least re-
sistance.
Feet.
I
2
Powder.
Oz.
•75
Line of
least re-
sistance.
Powder.
Line of
least re-
sistance.
Powder.
Feet.
3
4
Lbs. Oz.
13- 5
a
Feet.
5
6
Lbs. Oz.
3 145
6 12
Line of
least re-
sistance.
Feet.
7
8
Powder.
Lbs. Oa.
xo it.5
16
Effects.
Gunpowder. — ' From its gradual combustion, rends and projects rather than
sb a Iters.
A hole 5.5 ins. in diameter and ig feet 7 ina in depth, filled to 8 feet 10 ins. with
75 lbs. powder, has removed and rent 1200 cube yards, equal to 2400 tons. The
labor expended was that of 3 men for 14 days.
Temj)erature of gases of explosion 4000°.
Gun-cotton.— From the rapidity of its combustion, shatters.
Di/namile.— from the greater rapidity of its combustion over gun cotton, i« morf
shuttering in its explosion.
BLASTING. — BLOWING ENGINES. 445
Drilling.
Chum-drilling.— A churn-driller will drill, In ordinary hard rock, from 8 to ja
^eet. 2 inch holes of 2.5 feet depth, per day, and at a cost of from 12 to 18 cents per
foot, on a basib of ordinary labor at $1 per day. Drillers receiving $2. 5a
One man can bore, with a bit i inch in diameter, fVom 50 to 100 inches per day
of xo hours in granite, or 300 to 400 inches per day in l>mo8tone<
Tamping.— Two strikers and a holder can bore, with a bit 2 mnhcs in diameter,
10 feet in a day in rock of medium hardness.
Composition for watmproof charger or fuse consists by weight of Pitch, 8 parts,
Beeswax and FuUow each i part.
A£iiiin{i;. (Lefioy''s Handbook.)
In demolition of walls line bf least resistance L = half thickness, and C is a co-
efficient depending on structure.
Charge in lbs. = C x L^.
In a wall without counterforts, where interval between the charge is 2 L, 0 = .15.
In a wall with counterforts the charge to be placed in centre of each counterfort
at junction with wall, G = . 2.
Where the charge is placed under a foundation, haviug equal support on both
sides, C = .4.
A leather bag, containing 50 to 60 lbs. powder, hung or supported against a gate
or like barrier, will demolish it
For ordinary mines in average rock charge in ounces =rL3 -h j6a
BLOWING ENGINES.
For Smelting.
Volume of oxygen in air is different at different temperatures. Thus,
dry air at 85° contains 10 per cent, less oxygen than when it is at tem-
perature of 32°; and when it is saturated with vapor, it contains 12
per cent. less. If an average supply of 1500 cube feet per minute is
required in winter, 1650 feet will be required in summer.
Smelting of Iron Ore.
Cohe or Anlhracite Coal, — 18 to 20 tons of air are required for each ton
of Pig Iron, and with Charcoal 17 to 18 tons are required.
(i ton of air at 34^ = 29 751, and at 60° ^ 31 366 cube feeL)
Pressure. — Pressiure ordinarily required for smeltinj? purposes is equal to
a column of mercury from 3 to 10 inches, or a pressure of 1.5 to 5 lbs. per
8quar» inch.
i&»crw»V.— Capacity of it, if dry, should be 15 to 20 times that of cylin-
der if single acting, and 10 times if double acting.
Pipes, — Their area, leading to reservoir, should be .2 that of blasi cylinder,
and velocity of the air should not exceed 35 feet per second.
A smith's forge requires 150 cube feet of air per minute. Pressure of
blast .25 to 2 lbs. per square inch. A ton of iron melted per hour in a cu-
pola requires 3500 cube feet of air per minute. A finery forge requires
100 000 cube feet of air for each ton of iron refined. A blast furnace re-
quires ao cube feet per minute for each cube yard capacity of ftiruace.
A Ton of Pig Ircm requires for its reduction from the ore 310000 cube
feet of air, or 5.3 cube feet of air for each pound of carbon cou:iumed.
Pressure, .7 lb. per square inch.
P P
^5 BLOWING EKOINES.
To Compute Po-wer Iie<iuir«d. to IDrlvo a Blo'wlx^
.0000509
^Ki + 3^0^^33ooo=».
d'=z\ / . V representing velocity of air in fret per <«©-
V .01 X .78S4 XV
ond, d and d diameUrs of pipe and of nozzle infeet^ =yj ^
35
.7854 X 500
= .309.
Illustration.— What should be power of a steam engine to drive 35 cube feet of
air at a velocity of 500 feet per second, through a pipe i foot in diameter and 30c
feet in length ?
c = ratio between power employed and effect produced by it=zin a wellconttrudcd
engine . 5, and C = .93. d — . 2974, assumed at . 3.
:^??1^5£9 ^ 333 /^+ 4^\ 60-- 330cx> = 2263i.625 X 60^33000 ;t.4X.i5 IP.
To Compute Req.uired Po-wer of* a Bloxvii&s finsine.
— ^^ i=zW. P representing pressure of blast in Ws, per sq. inck;
33.000
a area of cylinder in sq. itis. ; v velocity ofpi^on inj'eetper minute ; ffric^
tion of piston and from curvaturesy etc,^ estimated at 1.25 per sq. inch of
piston.
NoTK.— If cylinder is single acting, divide result by 2.
Illustration. — Assume area of blast cylinder 5600 sq. in&, pressure of blast 2.25
lbs. per sq. inch, and velocity of oi^ton 96 feet per second.
2.25 -|- 1.25 X 5600X96 i88t6oo , ^, . J » J
~— ^ — ^ 2_=3 =: 57 horses, the exact power developed in
33000 33000
this case.
To Compute Dimensions of a Driving Sngine.
Rule i. — Divide power in lbs. by product of mean effective pressure upon
piston of steam cylinder in lbs. per sq. inch, and velocity of piston in feet
per minute, and quotient will give area of cylinder in sq. ins.
2.— Divide velocity of piston by twice number of revolutions, and quotient
wiU give stroke of piston in feet.
Volume of air at atmospherio density delivered into reservoir, in oonsequeDce of
escape through valves, and partial vacuum necessary to produce a current, will b«
about .2 less than caiMicity of cylinder.
Example.— Assume elements of preceding case, with a pressure of 50 lbs ste&m.
cut off at .375, and with 12 revolutions of engine per minute, what should he area
of cylinder of a non^condensing engine?
Mean effective pressure of steam with 5 per cent clearanoe = 50 lbs., and 50 —
/♦ -f- '4- 7 = 50 — 9- 5 4- 3-33 + «4-7 — 29-47 W»»., and velocity of piston =s 1^2/eet
56ooX2.25-|-i.25X9€ 1881600 .192 o .* * *_ 1.
— — ' — ^ ' — ^ = — r-5— = 332-5 *9' »»»»•. and — ^ — *= B/eet siroke.
29.47 X 192 5658 33 :> ^ . 12 X 2 "^
Area of cylinder in this case was 324 sq. ins.
For Volame, Preamre, and Density of Air, see Heat, page s-ji.
• 8m formqU ud not* for pow«r of ooi»-eond«Britig wgtao, pift 7^
BLOWING EKGINEg. 44^
To Compute Slements ot a Slo-vring Kn^ne*
Single Stroke.
930 33000 3 4Pa '
D'sn
-«! ^=V^ 5^ = V,«.d34P + 3»=fc
40 r * P-f/ 9a
y repreaenting wjiume of air in wbe feet per minuU^ Ppresflirs of air and
f frictional resistance in lbs. per sq, tnchy A area of cylinder and a area
of its valves in sq. ins.., s stioke ofpision infset^ n number of single strokes
of piston p^ minute^ L length of air-ftipefrom reservoir to discharge infeet^
a aiameUr of air or blast pipe and I) diameter qf cylinder in ins.., v veiucitg
of blast in feet per second, and t temperaiwe of bUist consequent upon eontr-
pression in degrees^
iLLrsTRATiONs. — Assume blowing cylinder 50 ins. in diam., stroke of piston 10
feet, number of single strokes 10 per minute, pressure by mercarial manometer
6.12 iB&, frictloiuil resistanos .4 lb., leDgih of pipe 35.85 feet, and areaof vaivea
^5 sq. iji&
V= 1363.54 ett&e/e0t, P=3 3 26«., As 1963.5 iqf^tni.
The„336i5lXi±5««^,6ff, Wd x963.5XioXioxIT;;^^
230 33000
3 40X95 40X65-8 '
T*o Compute Volume of* A.ir transmitted tty an Sngine*
When Pressure, Temperature, etc., are given.
1^. ^ W h ( A i^H ) C = IT. Then avx6o ^ V in cube feet per minute,
(\ and h representing height of barometer and pressure of blast in ins, of
vtercttry f t uinperature of Uast ; and v vfiocit^ in feet per second.
Illustbation.— A ftimace having 3 ftayeres of s in& diameter, pressure and tem-
perature of blast 3 ins. aiui 350O, f^^ barometer 30 ins. ; what is volume of air trans-
mitted per minute T
C for a oonieal opening •= .94.
■■Ill »^i i^m ^ |i>i-T . ^^^^^^
34-5V 3 (^^^"1,^ X -94 = 34-5 ^3 (^) =p 34-5 X .467 X .94 ;=* «5.i4
f^H vsUmty ptr st99n$,
Then, area 5 in8.= 19.635, which X » =? 39«»7 *«*! "P** 39-27 X i5' 14 X 60-J- 144.^
^47. 73 cube feet,
Xo Compnte Pressure of Hiast from "Water or Mercurial
C>-aug;e.
RuLB. — Divide Water and MereuriAl Gauge in ina. by 37.67 and a.04 re-
spectively, and quotient will give prtes^re in lbs. per aq. inch.
Fan-l>lowers,
Proportions of Parts, B^m.— Theff width sod kngtb should be ^t least
equal to .4 pr .5 radiua of ian,
Openings. — Inlet should be equal to radius of fan ; and opttet, or dia*
ehar|>e, sBooid be in depth not less than .135 diameter, its width being aqua)
to width of fan.
Eccentrici^, — .1 of diameter of fan. Journals, 4 diameters of shafts
44B BLOWING ENGINES.
By the experiments ci MnBncMO) he deduoed
1. That velocity of periphery of blades should be .9 that of their tkeoreticcd
velocity ; that is, velocity a body would acquire in falling height of a homo-
geneous column of air equivalent to required density.
2. That a diminution of inlet from proportions here given involved a
greater expenditure of power to produce same density.
3. That greater the depth of blade, greater the density of air produced
with same number of revolutions.
To Coxnpute XCleznents o£ a Fan^'blower.
a V 60 .rr ^ d a V
400 i
(^:;o) ^93945 = ^; 244Vrf=»; ~— -- = V; and = IH».
\0.02/ 100 400 _
V represenfinff velocity of periphery of fan in feet per second^ d inches of
mercury ^Y volume of air in cube feet ^ and a area of discharge in sq, ins.
Illustration.— Assume velocity of periphery of fan 123 feet per second, density
of blast .25 inch, volume of air 1845 cube feet^ and area of discharge 40 sq. ina
i23-T-5.o2-7-939.454 = .25inc*. 244Vl25=i22/5e«. lS2Li|l2i52 — ,845 cuft.yt
242 X 40 X 12^ ____
— = 2.g7lW, independent ofJrictionqfbUut in pipes cMd tuyeres.
400
. To Compute I^o-wer of* a Centrifugal Fan.
V* -f- 97 300 = P. V representing velocity of tips of fan in feet per second.
(See also p. iQi 8. 1
JMemoranda.
Operation of a blower requires about 2.5 per cent of power of attached
boiler.
An increase in number of blades renders operation of fan smoother, but
does not increase its capacity.
Pressure or density of a blast is usually measured in ins. of mercury, a
pressure of 1 lb. per sq. inch at 60° ^ 2.0376 ins.
When water is used, a pressure of i lb. 1=27.671 ins.
Cupola blast .8 lbs., and Smithes forge .25 to .3 lbs. per sq. inch.
An ordinary Eccentric Fan, 4 feet in diameter, with 5 blades 10 ins. wide
and 14 in length, set 1.5 ins. eccentric, with an inlet opening of 17.5 ins. in
diameter, and an outlet of 12 ins. square, making 870 revolutions per min-
ute, will supply air to 40 tuyeres, each of 1.625 ^"s* ^^ diameter, and at a
pressure per sq. inch of .5 inch of mercury.
An ordinary cccEntric fan-blower, 50 ina in diameter, running at 1000 revoluiioDB
per minutCj will give a pressure of 15 ins. of water, and require for its operation a
power of 12 horsea Area of tuyere discharge 500 sq. ins.
A non -condensing engine, diameter of cylinder 8 ins., stroke of piston i foot, press-
ure of steam 18 Iba (mercurial gauge), and making loo revoFufions per minute, will
drive a fan, 4 feet 1^ 2, opening 2 feet by 2*, 500 revelations per minute.
Such a blower was applied as an exhausting draught to smoke-pipe of steamer
Keystone Slate^ cylinder 80 ina by 8 feet, and eva])oration was doubled over that
of when wind was calm.
In French blowing engines, volume of air discharged 75 per cent that of
volume of piston space in cylinder, stroke equal diameter of cylinder, and
velocity of piston 'h'om 100 to 200 feet per minute.
Area of admission valves from .066 to .0S3 of that of cylinder for apeeds
of 100 to 150 feet |)er minute, and from ,\ to .111 for higher speed& ArBt
of exit viUves from .066 to .05 of cylinder, (if. C^cmieL)
BLOWING ENGINES. — CENTBAL FOBCES. 443
By some experiments lately concluded in England with boilers of two
•teamers, to determine relative effects of natural and forced draught furnaces,
the results were as follows {R, J, Butter) i
Per Sq. Foot of Grate Surface, — NvUural Draughty 10 to ia87 IIP; Steam
Blasts 12.5 to 13 ; Forced or Blast DraugfUj 15 to 16.
Heating Surface per IH*. — Natural Draught; 2.44 to 2.61 ; Steam Blasty
1. 71 to 2,86; Forced or Blast Draughty 1.56 to 2.5.
Tube Swfa^eper IH* in Sq. Feet. — Natural Draught.^ 2.03 to 2.18; Steam
Blasts 2.02 to 2.08; Forced or Blast Draught, 1.3 to 2.8.
IH? per Sq, Foot of Grate in the^e Trials. — Natural Draughty 10.15 to
10.87 » Steam Bla^f, 12.76 to 13.1 ; Forced or Blast Draught, 10.6 to 16.9.
Booths Rotarg Blower — Is constructed from .125 to 14 nominal IP, supplying
from 1 50 to 10 800 cube feet of air per minute. Delivery pipe 2.5 to 19 ins.
jn diameter. Efficiency 65 to 80 per cent, of power.
For VentUatiow of Mines — From 40 to 280 revolutions per minute, equal
to discharge of 12 500 to 200000 cube feet of air per minute. 15.5 to 189 IP.
Steam cylinder from 14 x i3 ins. to 28 x 48 ins.
For other details of Blowing Engines see page 898L
CENTRAL FORCES.
All bodies moving around a centre or fixed point have a tendency to
fly off in a straight line: this is termed Ceidiifugal Force; it is op-
posed to a CentHpetal Force^ or that power which maintains a body in
*ts curvilineal path.
CenJtrifngal Force of a body, moving with different velocities in same
eircle, is proportional to square of velocity. Thus, centrifugal force of
a body making 10 revolutions in a minute is 4 times as great as centrif-
ugal force of same body making 5 revolutions in a minute. Hence, in
equal circles, the forces are inversely as squares of times of revolution.
If times are equal, velocities and forceg are as radii of circle of revolution.
The squares of times are as cubes of distances of centrifugal force from
axis of revolution.
Centrifugal forces of two unequal bodies, having same velocity, and at same dia.
Uince from central body, are to one another as the respective quantities ol matter
*& the two bodies.
Centrifugal forces of two bodies, w^hicb perform their revolutions in same time,
the quantities of matter of which are inversely as their distances from centre, are
equal to one another.
Centrifugal forces of two equal bodies, moving with equal velocities at different
distances firom centre, are inversely as their distances from centre.
Centrifugal forces of two unequal bodies, moving with equal velocities at different
distances from centre, are to one another as their quantities of matter, multiplied by
their respective distances from centre.
Centrifugal forces of two unequal bod'cs. having unequal velocities, and at differ-
ent distances from their axes are in compound ratio of their quantities of matter,
■l|oares of their velocities, and their distances from centre.
Ceotrifiigal force is to weight of body, as double height due to velocity is to radiu?
of rotation.
A Badius Vector is a line drawn fh>ra centre of force to moving body.
Pp*
45© CENTBAL FOBCBS.
To Compute CentrifVieal Foroe of azi^r Body.
Rule i. — Divide its velocity in feet per second by 4.01, also square of
auotient by diameter of circle ; this quotient is centrifugal force, assuming
le weight of body as 1. Then this quotient, multiplied by weight of body,
will give centrifugal force required.
ExAMFLfL — What is the ceotrit'ugal force of the rim of a fly-wbpel having a diam-
eter of 10 feet, and runumg with a velocity of 30 feet per second?
30^-4.01 = 7.48, and 7.48^-7-10 = 5.59, or timts weight o/rim.
W n' VR^ + t'
Or, ■■ = C. rrq»r€ientingr(iuiituo/iiiHerdiamtterofrkui.
4100 ^ w
NoTK.— Diameter of a fly-wheel should be measured fVom centres of gravity of rim.
When great accuracy is required, ascertain centre of g}Tation of body, and
take twice distance of it from axis for dianieter.
Rule 2. — Multiply square of number of revolutions in a minute by diam-
eter of circle of centre of gyration in feut, and divide product by constant
number 5217 ; quotient is centrifugal force when weight of body is i. Then,
as in previous Rule, this quotient, njultiplie4 by weight of body, is centrif-
ugal force required.
n'd
Or, — - X W. n repretenting number of rtwAy^ioM pet n^ni^ d du^fuUr of
circle of gyration infict, and W weight of revolving body in lbs.
ExAMPLB.— What is centriftigal force of a griodstone weighing 1200 lbs., 42 inches
in diameter, and turning with a velocity of 400 revolutions in a minute?
Centre of gyration = rad. (42 -H 2) x .7071 = 14.85 int., which -4-12 and X 2 =
a.475/e«< at diameter of circle of gyration. Then — ?^^ x 1200 = 91 080 Ibi.
5217
Formulas to I>eterxuiiie Various K|en&en.ts«
Wv^ WRn^ wT, , _ 0 32.166 R
C* = rr-o; = ; =WRij'i.225; W = — ^
32.166 tt' "" 2925 ' — "' "" »" '
2930C. _ Wv' , /2930C. /CR 32166. _. ««'Il:
*-w^' -^2:1660' "-yiTR"' ''-v — w — ' •~6»8«'«-
C repreienting centrifugal farce, W mo** or weight (^revolving body^ both in Ibs.^
R radius of circle of revolving body in feet, n number of revolutions per minuley and
V and v' linear or circumferential and angular velocities of body in feet per second.
iLLUfTTRATioN.— Wbai is centrifugftl force of a sphere weighing 30 Ibe., rievolTlng
around a centre at a distance of 5 feet, at 30 revolutions i>er secondT
60 ^ I -> 32.166X5
CeniriJug<U forces of two bodies are as radii qf circles of revolviion directly^ and
as squares of times inversely.
Illustration. — If a fly-wheel, 12 feet in diameter and 3 tons in weight, revolves
in 8 seconds, and another of like weight revolves in 6, what should be the diameter
of the second when their centrifugal forces are equal ?
12 sv 12 X 6'
Then 3 : 3 :: ^3 : -r^] or xz= — - — =6.75.^, x = unknown element
o* O* o*
CenirijSigal forces of two bodies, when weights are unequalj are direcliy at squares
of times.
Illustration.— What should be the ratio of the weights of the wheels in the pre-
ceding case, their forces being equal?
Then 3 : * :: 6» : 8», or » = 5-^= ^-^ = 5.333 «»«»•
Moletworth gives .000 34 W R n^ = G.
* This k t«mi«d th« rU TtVa, or IlTing fore*.
CENTRAL FOBGSS. — FLT-WHBBI*. 4^1
FLY-WHBBL.
A Flt-whbxl by its inertia becomes a reservoir as well as a regulator
of force, and, to be fully effective, it should have high velocity, and its diam-
eter be from 3 to 4 times that of stroke of driving engine.
Coefficient of fluctuation of its energy ranges from .015 to .035.
Weight of a fly-wheel in engines that are subjecte<l to irregular mo-
tion, as in a cotton-press, rolling-mill, etc., must be greater than in others
where so sudden a check is not experienced, and its diameter should range
from 3.5 to 5 times length of the stroke of the piston.
A single-acting engihe requires a weight of wheel about 2.5 times greater
than that for a double-acting, and 5 times for doable engines of double action.
To Compute "WeigUt of R.im of a Fljr-iKrheel.
RuLB.-^Multiply mean effective pressure upon piston in lbs. by its stroke
in feet, and divide' product by product of square of number of revolutions,
diameter of wheel, and .000 33.
KoTK.— If a light wheel, multiply by .ocx>3 ; and if a heavy one, by .ocx> 16.
Example l— A non-condensing engine (double-acting), having a diameter ofcyl.
inder of 14 ins., and a stroke or piston of 4 feet, working full stroke, at a pressure
of 65 lbs. mercurial gauge, and making 40 revolutions per minute, develops about
65 £P ; what should be the weight of its flywheel when adapted to ordinary work t
Area qf cylinder 154 sq. ins. Mean pressure assumed 50 Ws. per sq. inch. Diam-
eter o/imeel = 4 /^ stroke of piston X 35, assumed as above, = i^Jedt.
so X 154 X 4 = 30 8<»» which -r- 40' X 14 X .000 23 = 5978 lbs.
3. ^If a fly-wheel, 16 feet in diameter and 4 tons in weight, is sufficient to regulate
an engine (double-acting), it revolving in 4 seconds, what should be the weight of a
wheel of 12 feet, revolving in 2 seconds, so that it may have like centrifugal force?
NoTR.— The centrifugal forces of two bodies are as the radii of the circles of revo-
lution directly, and as squares of times inversely.
Thenl2<L6 = ^2^ Or, «^ 4 X .6x2^^4 X 16X4 ^,,333,0^.
4» a' 12 X 4' ' la X 16 *'*'^"*
7o Coraptite IDim^tiAions of R.ixn.
Rule. — ^Multiply weight of wheel in lbs. by .1, and divide product by
mean diameter of rim in feet ; quotient will give sectional area of rim in
square inches of cast iron.
Assume elements of example x. 5978 X • x -r* 13.25 = 45. 13 tg. ivu.
PS W
Or, — — = W, and — — = A. I* represefUing pressure oti piston and ?f tdeight of
ufkeel iM <6ff., d Hrohe of pistm, and D mean diameter ofwhtel^ both in feet, tmd A
area ofse<Uion ojrim in sq. ins.
Or, — — — — — = W. C coefficient, varying frofm 3 to 4 ordinarily, increasing
to 6 tnth great regularity of speed and n numher of revolutions per minute.
N0T8. — Maximum safe velocity for cast iron is assumed at 80 feet per second.
For engines at high expansion of steam, or with irregular loads, as with a rolling-
mill, mufltply W by 1. 5, or pat W 100 lbs. for each W. iMolesworth.)
In com or like mills, the velocitv of periphery of fly-wheel should exceed that «f
tb« atones, to arrest backlash.
452 CENTRAL FOBC£S. — GOVEENOJJS. — PENDULUMS*
GOVERNORS.
A 60YBRNOR or Conical Pendulum in its operation depends upon the
principles of Central Forces.
When in a Ball Governor the balls diverge, the ring on tertical shaft
raises, and in proportion to the increase of velocity of the balls squared,
or the square roots of distances of ring from fixed point of arms, cor-
responding to two velocities, will be as these velocities.
Thus, if a governor makes 6 revolutions in a second when ring is 16
ins. from fixed point or top, the distance of ring wil[ be 5.76 ins. when
speed is increased to 10 revolutions in same time.
For 10 : 6 : : \^ 16 : 2.4, which^ squared =. 5.76 tw«., duUance of nna
from top. Or, 6' ; 10* : : 5.76 : 16 im.
A governor performs in one minute half as many revolutions as a
pendulum vibrates, the length of which is perpendicular distance be-
tween plane in which the balls move and the fi.xed point or centre of
suspension.
ITo Compvite ^vim'ber ot Re-volutioiis of* a Ball Ghovernor
per Alinute to maintain 3alls at any given HeigUt.
188 -H y/H = revoltUiom. H I'epresmtir^ verticai height between plane of beUl*
and points of their napension in int.
Illustration. —If the rise of the balls of a centrifugal governor is 32 in&, what
are the number of revolutions i)er minute ?
1 88 -r- v'za = 40.09 revolutions.
To Compute Vertical Height between Flane of Sails
and. tlieir "Points of Suspension.
(188 -^ r) a = vertical height in ins. r representing number of revolutions per minute.
Illustratiox.— If number of revolutions of a centrifugal governor is 100, what
will be rise of balls ?
188 -7- 190= i.88« = 3.53 in*.
To Compute A.ngle of A^rms or Plane of Balls Mritli
Centi-e ©haft.
r-i-l = 8in. ^. r representing distance of bails Jrom plane of centre shaji^ an4 I
distance between balls and point of suspension measured in plane of shaft
iLLtTSTRATiON.— Distance of balls ftom plane of centre shaft is 10 inches, and
their distance from point of suspension is 25; what is the angle?
10 -^ 25 = .4, and sin. .4 = 23© 35'.
When Number of Revolutiona are given, ^~~r — *^- ^•
Illustration. —Revolutions of a governor per minute are 50, and length of its
arms a feet; what is their angle with plane of shaft?
(54.16-7-50)* 1. 173 „^ n ,,
i^2 Z_L = — LI = .5865 = co#. 54O 6'.
a 2
PENDULUMS.
Pendulums are Simple or Compound^ the former being a material
point, or single weight suspended from a fixed point, about which it
oscillates, or vibrates, by a connection void of weight ; and the latter,
a like body or number of bodies suspended by a rod or connection.
Any such body will have as many centres of oscillation as there are
given points of suspension to it, and when any one of these centres are
determined the others are readily ascertaine\L
I
OBNTBAL FORCES. — PENDULUMS. 453
Thus, * o y » ^ = a corutant product,, and * r = V« o x sff^ s g o and r
represfintiwj jmnts ofauspetmon, grcanty^ mciUation,, and gyration.
Or, any body, as a cone, a cylinder, or of any form, regular or irregular,
80 suspended as to be capable of vibrating, is a compound pendulum, and
distance of its centre of oscillation from any assumed point of suspension is
considered as the length of an equivalent simple pendulum.
The Amplitude of a simple pendulum is the distance through which it
passes from its lowest position to its farthest on either side.
Conu^eie Period of a pendulum in motion is the time it occupies in making
two vibrations.
All vibrations of same pendulum, whether great or small, are performed
very nearly in same time.
Number of Oscillations of two different pendulums in same time and at
same place are in inverse ratio of square roots of their lengths.
Length of a Pewlulum vibrating seconds is in a constant ratio to force of
gravity.
Time, of Vibration is half of a complete period, and it is proportional to
square root of length of pendulum. Consequently, lengths of pendulums for
different vibrations arc —
Latitude of Washington.
39.0958 ins. for one secuud. | 4- 344 for third of a second.
9.774 ins. for half a second. | 2.4435 for quarter of a second.
JLtexkgtlxa of ir^encLixltixxis vil^rettins Seconds at X..evel of
tlxe Sect iu several flaoes.
Ins.
Ekinator 39-0152
Washington 39*0958
Ina.
New York....... 39.1017
Lttt. 45O. 39* 127
Puris 391284
London 39«393
1?o Compute I^eugth. of a Simple Pendulum for a givetx
Uatitude.
39. 127 — .099 82 coa 2 L = ^ L representing latitude.
Illubtration. — Required the length of a simple pendulum vibrating seconds in
the latitude of 50^' 31'.
L = 50° 3rcos. 2 li = 2 X 50° 31* = cos. 180O — 5o0 3i'X3=: cos. 78° 58' = . 191 38
— 39. 127 -|- . 191 38 X 099 82 {two — or negative = an affirmative or-f ) = 39. 1461 ins.
ITo Coiupute L«cngtli or a Simple Feudiilum Tor a g;iven
Nvitiiber of* Vibrations.
ljt' = l. L representing length Jor latitude, I time in seconds, and I length of pen-
dulum in ins.
Illustration.— Required vibrations of a pendulum in a minute at New York, an
60; what should be its length?
39. loi 7 X I ' = 39- 101 7. Or, -^ = I. n representing number o/vibratums per seeond.
To Compute dumber of Vibrations of* a Simple Pendu-
lum in a griven rTime.
—,j- = w, - rqtresenting time of one vibration in seconds.
To Compute Centre of Q-ravity of a Compound Pendu*
luxn of 'P-wo "^^eiglits connected in a Higlxt I^ine.
When Weights are both on one Side of Point of Suspension.
WW-u>
o=:distance oj centre of gravity /irom point of suspension.
454 UlCNTBAL FORCES. — PENDULUMS.
When Weighty are on Opponte Sides qf Point of Suspension,
= c = distance qf centre of gravity qf greater weight from jmrU qfsuS'
W •»]— w
peruioH.
Note.— To obtain strictly isochronous Tibrations, the circular arc must be sub-
stituted for the cycloid curve, which possesses the property of having an inclinar
tion, the sine of which is simply proportional to distance measured on the curve
from its lowest point.
For construction of a Cycloidal pendulum, see Deschaniers Phy^ics^ Part I. , pp.
71-a.
To Compute Xjength, of a Sin)ple Pendulum 9 'Vibration a
or "wrliich. -will be same in Number as Xncliies in ita
Xjengtb.
^(^L X 60)* = / in inches.
Illustration. — What will be length of a pendulum in New York, vibrations oi
which will be same number as the in& in its length?
V (>/39.ioi7 X 60)' = 7.21X* = 52 ins.
To Compute Time of Vibration of a Simple Penduluzn,
Uength. being given.
Vi -^ L = < in seconds.
iLLUSTRATioir. --Length of a pendulum is 156.4 ins. : what is the time of its vibiBr
tion in New York?
156.4
A
ssateoonds.
39.XOX7
Or, ^— X 3. 1416 = t I representing length of a pendtUum vibrating seconds i«
ins. J g measure offeree of gravity^ and t timt of one oscillation.
Illustration — Length of a simple pendulum vibrating seconds, and measure of
force of gravity at Washington, are 39.0958 ins., and 32. 155 feet.
/ 39-^953
3Mi6^ ^^^^ ^ ^- = 3.1416 X V'oi3 = 3*416 X .3183 = I second.
/
To Compute Number of Vibrations of a Simple Pen-
dulum in a given Time.
y X i = »». n represevUing number of vibrations.
Illustration.— The length of a pendulum in New York is 156.4 Ins., and time of
its vibration is 2 seconds; what are number of its vibrations?
)3Q.IOI7 /6.2S'? ^ 60
./^^^— X2 = . / — ^X2 = .sX2 = i vibration. Hence, i X— = 30 vi-
V '50.4 V »«-5o6 a ^
brationsper minuie.
To Cotnputa Measure of Ghravity, Length of Pendulum
and X umber of its Vibrations Deing given.
.82846 In'
^a =g. g representing measure of gravity in feet
To Compute TQ'umber of Revolutions of a Conioal Pen.
dulum per Alinute.
y^
933-5
~j^ — = *• * representing distance betvoeen point of suspension amd plane qf
revolutions in ins.
NoTB.— Number of revolntions per minate are constant for any given heigbk and
Che time of a revolution is directly as square root of height
CBAITBS.
455
VVlieil Post is
Fig.
r. —
o^-
CRANEa
Usual foim of a Crane is that of a right-angled triangle, tbe sides
being post or jib, and stay or strut, which is hypothenuse of triangle.
When jib and post are equal in length, and stay is diagonal of a sqUare,
this form is theoretically strongest, as the whole stress or weight is borne by
stay, tending to compress it in direction of its length ; stress upon it, com>
pared to weight supported, being as diagonal to side <^ square, or as 1^143
to I. Consequently, if weight borne by crane is 1000 lbs., thrust or com-
pression upon stay will be 1414.2 lbs., or as a 6 to e W, Fig. i.
Supported, at laotlx Head and Foot^ A»
B'igf* 1.
Weight W is sustained by a rope or chain,
and tension is equal upon botii parts of it ; that
is, on two sides o| square, i a and e W. Conse-
quently jib, i a, has no stress upon it, and serves
merely to retain stay, a e.
If foot of stay is set at n, thrust upon it, as
compared with weight, will be as an to aw;
and if chain or rope from i to a is removed, au^
weight is suspended from a, tension on jib will
be as t a to a W.
If foot of stay is raised to o, thrust, as compared with weight, will be as
line a o is to a W, ahd tension on jib will be as line ar.
By dividing line representing weight, as a W or a u^, into equal parts, to
r^resent ton^ or potmds, atid using it as a scale, stress upon any other part
may be measured upon described parallelogram.
Thus, as length of a W, compared to a «, is as 1 to 1.4143 : if a W is di-
vided into 10 parts representing tons, a e would measure 14.142 parts or tons.
Wlxeii Post is Supported at IToot only.
If post !« wholly nnsuppnrted at head, and its foot is secured up to line
o W, then W, acting with leverage, e W, will tend to rupture post at c, with
dame effect as if twice that weight was laid uiwn middle ef a beam equal to
twice kn^h of e W, e being at middle of beam, which is assumed to be sup-
ported at both ends, and of like dimensions to those of post.
Or, force exerted to rupture post will be represented by stress, W, multi-
plied by 4 times length of lever, e W, divided by depth of post in line of
stress, squared, and multiplied by breadth of it and Valve* of its material
Post of such a crane is in condition of half a beam supported at one end,
weight suspended from other; consequentlv, it must be estimated as a beam
of twice the length supiK)rted at botli ends,' stress applied in middle.
To Compute Stress 6\\ Jitj^ and on Stay or Strut—ITig. S.
^^fr *• -^K» On diaffrahi of crane, Fig. 2, mark off 6rt line of
chain, fl W, a distance, a b, representing weijifht on
chain \ from point b draw a line, b c, parallel to jib,
a «, and where this intersects stay or strut, draw a
vertical line, e o, extending to jib, and distances
from a to points b c and o c, measured upon a scale
of equal parts, will represent proportional strain.
iLLtJSTRATioir.— In figure, weight being 10 tons, stress
on stay or strnt compressing, a c, will be 31 tons, and
on Jib or teDalon-rods, a 0, 26 tons.
* For Value of MatoriaU, we p«f« j^
456
CBANES.
To Compnte Diuiexisions of I*08t of et Craxie.
When Post is Supported at Feet only. Rule. — Multiply weight or stress
to be borne in lbs. by length of jib in feet measured upon a horizontal
plane ; divide product by Value of material t^ '^ used, and product, divided
by breadth in ins., will give square of depth, aiso in ins.
ExAMPLR.— Stress upon a crnne is to bo 22400 lbs., and distance of it ttom centie
of post 20 feet; what should be dimonsiou of post if of American white oak?
Vcdtie of American white oak 5a Assumed breadth
ms.
22 400 X 20
50
^8960, and
8960
12
746.67. Then V746-67 = 27.32 tn».
When Post is Supported at both Ends. Rule. — ^Multiply weight or stress
to be borne in lbs. by twice length of jib in feet measured upon a horizontal
plane ; divide product by Valtie of material to be used, and product, divided
by four times breadth in Ins., will give square of depth, also in ins.
Example.— Take same elements as in preceding case. Assumed breadth zo iua
Then
22 400 X 20 X 2
50
= 17920,
17920
4 X 10
448, and V448 = 21. 166 in*.
In Fig. 3, angle abe and ebc being equal, chain or rope is represented
^ by ab c, and weight by W ; stress upon stay b u, as
^*fr 3- ^^ compared with weight, is as 6 (i to a 6 or 6 c.
In practice, however, it is not prudent to consider
chain as supporting stay ; but it is proper to disreP^.d
cliain or ro|)e as forming part of system, and crane
should be designed to support load independent of it.
It is also proper that angles on each side of diagonal
stay, in this ease, should not be equaL If side a 6 is
fr)rnied of tension-rods of wrought iron, point a should
be depressed, «o as to lengthen that side, and decrease
angle abe; but if it is of timber, point a should be
laise I, and angle abe increased.
Fig. 4. g Fig. 4 shows a form of crane very generally used;
angles are same as in Fig. 3, and weight suspended nrom
it, being attached to point t(, is represented by line bd.
The tension, which is equal to weight, is shown by length
of line 6 c, and thrust by length of line 6 a, measured by
a scale of equal parts, into which line 6 d, repi esenting
weight, is supposed to be divided.
But if b e be direction of jib, then b g will show ten-
sion, and bf the thrust {df being taken parallel to b e).
both of them being now greater than before; line b a
representing weight, and being same in both casea
To Ascertain Stress on Jit), 021 Strut
of a Crane. ^TTig. 5,
Through a draw a a, parallel to jib or tension-rod
o r, and also s u parallel to strut a r ; then r « is a
diagonal of parallelogram, sides of which are equal to r a and r u,
Pig -^ ^--^'* ^^ ^^^ ^ * represents a stress of 20 lbs.,
^^"^ the two forces into which it is decoin-
posed are shown by r u and ra; or ia
equal to r u, as each of them is equal to
a «, and r « is equal to o a. Hence, 20
represented by a o, stress on jib will be
represented by o r, tind that on strut by
ra.
Assuming then o r 3 feet, a r 3.5, and
o a I, stress on jib will be 60 lbs., and on strut 70.
CB^NBS.
457
Thus, in all cases, stress on jib or tension-rod and on strut can be deter-
ramocl by relative proportiomj of sides of triangle formed.
VCo Compute Stress upon Strut of* a Crane.
Rule. — Multiply length of strut in feet by weight to be borne in lbs. ; di>
vide product by height of jib from point of bearing of strut in fee% and
quotient will give stress or thrust iu lbs.
ExAMPLK. — Length of strut of a crane is 28.284 ^t, height of post is 26.457 feet,
and weight to be borne is 22 400 lbs. ; what is stress?
28.284X23400 633561.6 _^
"* - ""^ = 23947 Iftf.
26.457
26.457
Ciiains and Ropes.
Chains for Cranes should be made of short oval links, and should not ex*
ceed I inch in diameter.
Short -linked Crane Cl&ains and Ropes sho-wiug I^i-
niensions and '%Veigh,t of eaoli, and Proof* or Chain
in rTons.
Dlmm.
Weight
Circamr.
WeijthtJ
Diam.
Weight
of
per
Proof
of
of Rope
of
per
Proof
Chains.
Fathom.
Straio.
Rope.
per Path.
ChaiBi.
Fathom.
Strain.
iDB.
Lba.
Tod*.
In*.
Lto.
loa.
Lbe.
Tom.
•3«25
6
•75
2.5
1-5
.6875
28
6-5
•375
8.5
x-5
3-35
3-5
.8125
32
7-75
•4375
11
a- 5
4
3-75
36
9.35
•5^
«4
3-5
4-75
5
•875
44
»o-75
.5625
18
4-5
5-5
7
•9375
5?
13.5
.625
34
5-35
6.25
8.7
I
56
«4
Circamf.
Weight
of
of Rope
Rope.
per Fath.
Int.
Lbe.
7
las
Z-5
12
8.25
15
9
>7-5
9-5
19s
10
22
Ropes of circumferences given are considered to be of equal strength with
the chains, which, being short-lmked, are made without studs.
A crane chain will stretch, under a proof of 15 tons, half an inch per fathom.
Alaohinery of Cranes.
To attain greater effect of application of power to a crane, the wheel-work
must be properly designed and executed.
If manual labor is employed, it should be exerted at~a speed of 220 feet
per minute.
Proportioru.—Cnpaciftf of Crane^ 5 tons.
Radius of winch or handle 15 to 18 ins. Height of axle from flook 36 to 39.
iBt pinion, 11 teeth, 1.25 ina pitch. I 2d pinion, 12 teeth, 1.5 ina pitch,
ist wheel, 89 '• 1.25 " " | 2d wheel, 96 " " " "
Barrel 8 ins. x n teeth x 12 teeth X 11 200 ?6*. = 30800 ,^ ....
- - — -...-_.___._ "i = 20.35 '6«« = statical re-
Winch 17 %tu. X 80 teeth X 96 teeth x 4 men = 1513 ^'
B'.stance to each of ine 4 men at winches.
An expenment upon capacity of a crane, geared i to 105, dcvelo|: 2d that
a strong man for a period of 3.5 minutes exerted a power of 27 562 foot-
pounds per minute, wnich, when friclion of crane is considered, is fiilly equal
to the power of a horse for one minute.
' In practice an ordinary man can de>'elop a power of 15 lbs. upon a crane,
handle moved at a velocity of 220 feet per minute, which is equivalent to
3300 foot-pounds.
For Treatise on Cranes, see Weales^ Scries, No. 33.
458
COMBUSTION.
CJOMBUSTION.
Combustion is one of the many sources of heat, and denotes combi-
nation of a body with any of the substances termed Supporters of Com-
bustion ; with reference to generation of steam, we are restricted to but
one of these combinations^ and that is Oxygen.
All bodies, when intensely heated, become. luminouB. When this heat
is produced by oombination with oxygen, they are said to be ignited ;
and when the body heated is in a gaseous state, it forms what is termed
Flame.
Carbon exists in nearly a pure state in charcoal and in soot. It com-
bines with no more than 2.66 of its weight of oxygen. In its combus-
tion, I lb. of it produces suificient heat to increafie temperature of 14 500
lbs. of water 1°.
Hydrogen exists in a gaseous state, and combines with 8 times its
weight of oxygen, and i lb. of it, in burning, raises heat of 50 cxx> lbs.
of water 1°.*
An increase in the rapidity of combustion is accompanied bj a dimi-
nution in the evaporative efficiency of the combustible.
Mr. 0. K. Clark Aimishes the fbllowing: When coal is exposed to beat in a Air-
nace, the carbon and hydrogen, associated in various chemical unions, as hydrocar-
bons, are volatilized and pass off. At lowest temtterature, napbthalioe, resins, aod
fluids with high boiling-points are disengaged; at a higher teuiperature, votetile
fluids are dJseugagcd; and still higher, oTetiunt gas, followed by light carbaretted
hydrogen, which continues to be given off after the coal has rea<died a low red beat
As teuiperature rises, pure hydrogen is also given off, until flnally, in the fifth or
highest stage of temperature for distillation, aydrogen alone Is discharged. What
remains after distillatory process is over, is coke, which is tbe^xed or solid carbon
of ooal, with earthy matter or ash of the coaL .
The hydrocarbons, especially those which are given off at lowest temperatures,
being richest in carbon, constitute the flame-making and amoke-makiog part of th«
coal. When subjected to beat much above the temperatures required to vaporize
them, they become decomposed, and pass successively into more and more perma-
nent forms by precipitating portions of their carbon. At temperature of low red-
ness none of them are to be found, and the oleQant gas is the densest type that
remains, mixed with carburetted and f^ee hydrogen. It is during these trans-
formations that the great volume of smoke is ms^i/e, consisting of precipitated car-
bon passing off uucotubined. Even defiant gas, at a bright red heat, deposits half
its carbon, changing into carburetted hydrogen; and this gas, in its tarn, may
deposit the last remaining equivalent of carbon at highest furnace heata^ a^d be
converted into pure hydrogen.
Throughout all this distillation and transformation, tho element of hydrogen
maintains a prior claim to the oxygen present above the fuel; and until it is satis-
fled» the precipitated carbon remains unburned.
Svimixiary of Products of IDeconapoeitioii in the Furnaoe.
Reverting to statement of average composition of coal, page 485, it ap-
pears that the fixed carbon or coke reniaming in a furnace after volatile
portions of coal are driven off, averages 61 per cent, of jp-oss weight of the
coal. Ttiking it at 60 per cent, proportion of carbon volatilbed -in com-
bination with hydrogen will be 20 per cent., making total of 80 per cent, of
constituent carbon in average coal.
Of the 5 per cent, of constituent hydrogen, i part is united to the 8 per
cent, of oxygen, in the combinlfig pro()ortious to form wat^r, and r^maimne
4 parts of hydrogen are found partly united to the volatilized carbon, ana
pjutly free.
* Mmui sffKt.
coMBusTioir. 459
These particulars are embodied ki following snmmary of condition of
elements of loo lbs. of average coal, after having been decomposed, and prior
to entering into combustion-^
loo Lbs, of Average Coal in a Furnace.
Composition Lbft. Lb*. DecompMitioD.
n.riw>n ( Fixed 60
caroon j volatilized. . . . ao
Hydrogen 5
Sulphur t.BS
Oxygen 8
Nitrogen 1.3
Ash, etc 4-55
100
forming
60 fixed carbon.
24 hydrociirfoons and f^ee hydrogen
1.25 Bulphar.
9 water or steam.
I. a nitrogen.
4-55 "sh, etc
*• 100
showing a total useful combustible of 85.25 per cent., of which 25.25 per
cent is volatilized. While the decomposition proceeds, combustion proceeds,
and the 25.25 per cenL of volatilized portions, and the 60 per cent of fixed
carb(m, successively, are burned.
It may be added that the sulphur and a portion of the nitrrgen are dis-
engaged in combination with hydrogen, as sulphuretted hydrogen and am-
monia. But these compounds are small in quantity, and, for the sake of
simplicity, they have not been indicated in the synopsis.
Vohtme 0/ Air chemtcalUf consumed in complete Combustion qfCocU.
Assume 100 H>8. of average coal. Then, by following
80 + 3 (s ~~o) +'4 X '"S ^ 152 = 1^060 cube feet of air at 62° for 100 lbs. co(U.
For volatilized portion, Hydrogen (H), 4 lbs. X 457 = 1 828 cube feet
Carbon (C), 20 " Xi52= 3040
Sulphur (S), 1.25 " X 57= 71
4939
For fixed portion, Carbon, 60 Ib6.Xi53= 9120
ii t(
i( (I
ii it
Total ttsefol combustible, 85.25 *' 14059 " *^ for con-
plete eomlmstion of 100 lbs. coal of averts composition at 62°.
To Comprtte Volume of A.ir at 6S3°, under One A.t*
xxiosplielTe, ctxemioally conBuxned in. Complete Com*
l>-u8tion of* 1 J-Aim of* a given iCr'uel.
Rule. — Express constituent carbon, hydrogen, oxygen, and sulphur, as
percentages of whole weight of ftiel ; divide oxygen by 8, deduct quotient
from hydrogen, and multiidy remainder bv 3 ; multiply sulphur by .4 ; add
pro<lucts to the carbon, ana multiply sum by 1.52. Final product is volume
of air in cube feet
To compute foeight of air chemicaUy conttimed. — Divide vcrfume thus fbund
by 13.14 ; quotient ia weight of air in lbs.
Or,x.5a(C + 3 (H — -)+.4S)^Air. O Oxygen,
Non.— In ordinary or approximate computations, sulphur may be neglected.
Example.— Assume x lb. Newcastle ooaL 0 = 82.24, H = 5. 42, 0^=6.44, and
8 = 1.35-
-^ =r .805, 5.42— .805 =4.615 X 3 = i3-845» x-35 X .4 = -54i i3-845 + -54+8*ai
^ 96.635, and 96.635 X 1-53 = 146.87 cube feet
Then 146.87 -r 13. 14 s II. x8 Oft
460
COMBUSTION.
To Compute Total AVeiglit ofO-aseous Products of* Coxn-
plete Cotnbustioix of* 1 X^b. of* a given, Fuel.
Rule. — Express the elements as per-ceiitages of fuel ; multiply carbon bv
.126, hydrogen by .358, sulphur by .055, and nitrogen by .01, an^ add prod-
ucts together. Sum is total weight of gases in lbs.
Or, .ia6C-|-.358H-|-.o53S + .oi ii = WeighL
ExAMPLS. — AssQme as preceding case. N = j.6i. -
82.24 X -"6+5 42 X. 358 + 1- 35 X 0534-1.61 X 01 = 12.39 lbs.
To Compute Total "Volume, at 6S% of Ghaseouf* Pi'oduota
of* Complete Comloustioii of* 1 I j1>. oT g^iveu It^uel.
Rule. — Express elements as per-centages ; nmltiply carbon by 1.52, hy-
drogen by 5.52, sulphur by .567, and nitrogen by .1*35, and add products
together. Sum is total volume, at 62° F., of gases, in cube feet.
Or, 1.52 C + 5.52 H -f- .567 S + . 135 N = Volume.
To Compute Volume of tlie several Gl-aseii separately
fVom their Respective Quantities.
Rule. — Multiply weight of each gaseous product by volume of 1 lb. in
cube feet at 62°, as below.
Volume of I Lb, 0/ Gases al 62° undei- a Pressure of i^.'j Lhs,
Cube f«et. Cube feet. Cube feet-
Aqueous Vapor or J I Oxygen 11.887 I Nitrogen 13-501
Gaseous Steam .)'■ "5 I Hydrogen 190 | Carbonic Acid 8.594
Air 13 141 cube feet.
For a lb. of oxygen io combustion, 4. 35 lbs. air are consumed; or, by volume, for
a cube fuoi of o.xygen 4.76 cube feet of air are consumed.
I lb. Hydrogen consumes 34.8 lb&, or 457 cube feet, at 62^.
I *' Carbon, completely burned, consumes.... 11.6 " " 152
1 " '' partially " " 5.8 " " 76
I '^ Sulphur consumes 4-35** " 57
1;
It
I.
Composition
GASES.
and Equivalents of* Oases, oonibined in
Combustion of* IT'uel.
KLKMKNTS.
Oxygen
Hydrogen
Carbon
Sulphur
Nitrogen
COMPOUNDS
^Atmospheric Air
(mech. mixture)
Aqueous Vapor or
Water.
..{
Element*.
By
Weight.
Eqniv-
Hleote.
0. 1
8
H. I
I
C. 1
6
S. I
16
N. I
«4
0.23
26.8}
N.77
0. 1
?}
H. I
OASES.
COMPOUNDS.
Light Carbaretted
Hydrogen
Carbonic Oxide. . . .
Carbonic Acid
01efiantna8(Bi-car-\
bu retted Uyd. ..
Sulphurous Acid. .
Eleaaeole.
EqniT-
•leate.
C.2
H.4
O. 1
C. I
O. 2
C. I
S^
H.4
0. 2
a I
By
WeiKht
"I
I!
1!
Weights of products in combustion of i lb. of given fbel, are—
C = .o366. H=:.09. S = .o2. N = .o893 C-I-.268 H-f.0335 S+.oi N.
Cubt FtH.
.0366 X 8.59= .315 volume carbonic
acid.
.09 X190 =17.1 *' steam.
Oubt Feet.
.02 X 5.85 = .117 volume sulph. acid.
.0893 4- 268 + .03354- .01 X X3-50I =
5.409 volume nitrogen.
Volume of Air or Oases at higher temperatures than here given (62°) is ascer-
tained by, V ^ ^W = v. V representing volume of air or gas at temperature <,
e-f-461
and V at tempercUure V.
* By Volume i OzygeD, 3.769 Nitrofen.
COMBUSTION.
461
Cliexnlcal
Composition, of* sotxie
bustibles.
CO)fBU>nBLB.
Carbonic oxide.
Light carburetted hydrogen . . .
OleQant gas, Bicarburetted hyd.
Sulphuric ether.
^Icoliol
Turpentine
Wax
OI'veoil
Tailow
Compound Com*
Oxy.
Per Cent.
57- »
CombiniDK equivalenta. <
In xoo
parte by -n
Car.
Hyd.
Oxy.
Car.
Hyd.
Per Cent.
Per Cent.
I
—
z
42.9
—
a
4
—
75
as
4
4
—
857
«4-3
4
5
I
64.8
J3-5
4
6
a
52.3
'3«
ao
16
—
88.3
11.8
—
—
—
81.6
'3-9
—
—
—
77.3
»3-4
—
—
—
79
11.7
21.7
34^8
4-5
9-4
9-3
Heating powers of compound bodies are approximately equal to sum of
heating powers of their elements.
Thus, carburetted hydrogen, which consists of two equivalents of carbon and four
of hydrogen, weighing respectively 2X6 = 13 and 1 x 4 = 4, in proportion of 3 to i,
or .75 lb. of carbon and .35 lb. of hydrogen in one lb. of gas. Elements of heat of
combostiou of one lb. are, then-
Unite of heat.
For carbon 14 544 X -75 = 10908
For hydrogen *. 63 033 X .35 = 15508
Total heat of combustion, as computed 26 4x6
Total heat, by direct trial 335x3
£Ceatiiie I*o"wers of Coxxxbustiloles*
(MM. Favre and SUbermann, D. K. Clark aand others)
1 Lb. ov
CouBOvnsLB.
Hydrogen
Carbon, making 1
cartx>uic oxida )
Carbon, making i
carbonic acid . . )
Carbonic oxide
Light carburetted \
hydrogen )
Oleflant gas
Sulphuric ether. . . .
Alcohol
Turpentine
Sulphnr
Tallow
Petroleum. ........
Coal (average)
Coke, desiccated. . .
VTood, desiccated . .
VTood - charcoal, )
desiccated )
Peat, desiccated. . . .
peat-charcoal, de- )
siocaied )
Lignite.
Asphalt
Oxygen
coneuraed
par lb. of
Com-
bnetible.
8
«-33
3.66
•57
4
3-43
a. 6
3.78
329
1
2-95
4.12
3.46
2-5
«-4
3.35
«-75
3.38
3.03
2.73
Weiftht and Volnme
of A ir cooeumed per
lb. of Coiiibuatible.
Lba.
34-8
5-8
XI.6
3.48
«7-4
»5
"3
12. 1
14-3
4-35
13.83
«7-93
10.7
10.9
6.1
9.8
7.6
9.9
8.85
11.87
C'ai>f Feet
«i6a*.
457
76
153
33
339
196
'49
188
57
169
235
'4'
>43
80
X39
zoo
Z39
ZI6
156
Total Heat
of Combua-
tioii of z lb.
of Combtu-
tible.
EquivHient evaporative
Power of I lb. of Coni-
bualiltlc, uiider one At'
uiuepbere.
Unlta.
63033
1.ha. ofwa-
tar at (a*.
55.6
Lbe. of wa-
ter at 312*.
64.3
4452
4
4-6i
14500
»3
15
4325
3.88
448
23513
3Z.07
2434
21343
16249
12929
19534
4032
Z8028
Z9.Z9
M-56
1Z.76
3-6i
Z6.15
22.09
16.83
1338
20.23
4 »7
18.66
27531
i4«33
13550
7792
Z3.67
Z3.I4
6.98
28.5
14.6a
14.03
8.07
'3309
xi.93
«3.«3
9951
8.91
za3
12325
ZX.04
X3.76
1x678
16655
—
Z3.Z
X7.24
When carbon is not completely burned, and becomes carbonic oxide, it prodacet
less than a third of heat yielded when it is completely bH.med. For heating powei
of carbon an average of X4500 units is adooted.
402
COMBUSTION.
To Compute J^eatin^ J*o'wer of* 1 ZjIj, of a 8fi"^e»^ Coxn-
l>u8tible.
When proportions of Carbon, Hydrogen, Oxygen^ and Sidphur are given.
Rule. — Ascertain ditt'erence between hydn.gen and .125 of oxygen ; multi-
ply remainder by 4.28 ; multiply sulphur by .28, add products to the carbon,
multiply sum by 14 500, divide by 100, aud product is total heating power
in units of heat.
Or, 145(0-1-4.28 H— Ox.i25-i-.28S) = »«afc
Illustration.— Assume as preceding case.
5.42 'V82.28 X -125 X 4-28-|- 1.35 X .28 -{-82.28 X 14 500-T- 100 ■« 15005.
To Concipute Svaporative Power of* 1 JJXim of a GS-iveii
Combustible.
When Proportions of Carbon^ Hydrogen, Oxygen, and Sulphur are given.
Rule. — Ascertain dilFerence between hydrogen and .125 of oxygen, multiply
remainder by 4.28 ; multiply sulphur by ,28, add products tu the caxbon, and
multiply sum by .13, when water is supplied at 62Siuid ,i$ when at 913°;
product is evaporative power in lbs. of water at 212*^.
Or, When total heating power is known, divide it by 11 16 when water u
at 62*^, or 996 when at 212 .
Txa.C8THATiu.v.— .By table, heating power of Tallow is 18028 unita
Hence, 18 028 ^ i xi6 = 16. 15 U>9. wcUer evaportUed at 62^.
Temperature of Coiii"biistion.
Temperature of combustion is determined by product of volumes. and
specific heats of products of combustion.
Illustration.— i lb. carbon, when completely burned, yields 3.66 lb& carbonic
acid and 8.94 of nitrogen. SpeciQc heats . 2164 and .244.
3.66 X .2164 = .792 units of heat for 1°.
8.94 X -244 =
12.6
2.181
(I
t(
((
it
2.973 * •
Consequently, products or combustion of i lb. carbon absorbs 2.973 nnlta of heal
in producing 1° temperature.
VC^eigb-t and Specifio Heat of Frodiiots of Combustion,
and Xemperature of Combustion. {D. K. CUtrh.)
I Lb. Of COHBUSTIBLK.
Hydrogen «
Sulphuric ether. . . . ,
Oletiant gas (Bi carburetted hyd.)
Tal lo w
Coal (average)
Carbon, or pure poke.
Wax
Alcohol
Light carburetted hydrogen
Sulphur
Turpentine
Coal, with double supply of air..
Qui
Weight.
wous Produc
Menn
sp«ciiie
Heat.
Lbs.
Water = x.
35-8
11.97
.302
.256
150
»3-84
•257
.256
11.94
12.6
.246
.236
15.21
.257
10.09
18.4
•27
.268
5-35
.211
12.18
22.64
•257
.242
Hent to raise
tiie Tempnra-
ture 1 .
Units.
10.814
3.063
4.089
3 54
2.935
2.973
2.68
4-933
1. 128
3.127
5.478
Tmperatort o|
CoinbusUfl*.
O
5744
5305
5219
5093
4879
4J77
4836
482s
4766
3575
3470
2614
Rati*.
100
93
§8.7
85
85
84
83
62
60
45
Whence it appears, that mean specific heat of products of combustion, omitting
hydrogen .302 and sulphur .211, is about .25.
Hence. To Ascertain Temperature of Comhustion. — Divide total heat of
combustion in units by anit3 of heat for i^, and quotient will give tem^
^erature.
COMBUSTION. 463
Illustration.- ^ What is tempentart of combuetiou of coal of aventse oompoei-
tiont
Gaseous products as per preceding table xx.94, which X .246 specific heat = 2^935
units of heat at i^.
Hence, 14 133 units of combustion (fh>m table, page 461) -r- 2.935 = 4812^ temper-
ature of ccfmhAttion uf average coal.
If surplus air is mixed with products of combustion equal to volume of air chem-
ically combined, total weight of gases fur one lb. of this coal is increased to 22.64.
See following table, having a mean specific heat ot .24a.
Then 22.64 X -242 = 5-478 uniUfor 1°.
Hence, 14 133 total heat of combustion -4- 5.478 zrasBo^^ temperature of combOB-
tiou. or a little more than half that of undiluted products.
Taking averaffeSf it is seen that the evaporative efficiency of coal varies
directly with vwume of eonstituent carbon, and inversely with volume of
constituent oxyg<en : and that it varies, not so much because there is more or
lew carbon, as,* chictiy, because there is less or more oxj^^en. The per-cent-
ages of constituent hydrogen, nitro^iY, sidphur, and ash, taking averages,
■i.e nearly oimstant, though there are individual exceptioiis, and their united
eti'ect, as a whole, appears tu be nearly constant also.
Meat of Conibiiation.
Or, number of times in combustum of a substance^ its equivalent weight of water
wou.d be raised 1°, by heat evolved in combustion of substance.
Alcohol 12 930 I Ether 16 246 I Olefiant gas 21 340
Charcoal 14545 I Ohveoil 17750 | Hydrogen 62030
CorobuBtion of ITuel.
Constituents of coal are Carbon^ Hydrogen, Azote, and Oxygen.
Volatile products of combustion of coal are hydrogen and carbon, the
unions of whicli (relating to combustion in a furnaee) are Carburetted
hgd)'ogen and Bi-carbtiretted hydrogen or Olefiant ga^^ which, upon com-
bining with atmosplieric air, becomes Carbonic acid or Carbofiic oxide^
Steamy and uncombined Nitrogen.
Carbonic oxide is result of imperfect combustion, and Carbonic acid
that of perfect combustion.
Perfect combustion of carbon evolves heat as 15 to 4.55 compared
with imperfect combustion of it, as when carbonic oxide ia produced.
I lb. carbon combines with 2.66 lbs. of oxygen, and produces 3.66 lbs.
of carbonic acid.
Smeke is the combustible and incombustible products evolved in combustion of
AmI, which pass off by flues of a fUraace, and it is composed of sueh fiortions of
hydrogen and carbon of the Aiel gas as have not been supplied or combined with
oxygen, and contequently have not been converted either into steam or carl)onic
acid; the hydrogen so passing away is invisible, but the carbon, upon being sepa-
rated firom the hydrogen, loses its gaseous character, and returns to its elementary
atate of a black pulverulent body, and as such it becomes visible.
BKomfnous portion of coal is converted into gaseous state alone, carbonaceous
portion only into solid state. It is partly combustible and partly Incombustible.
To effect oombnstlon of i cube foot of coal gas, 2 cube feet of oxygen are required;
and, as locotM feet of atmospheric air are necessary ta supply this volume of oxy-
gen, I cube foot of gus requires oxygen of 10 cube feet of a.r.
In fnmaces with a natural draught, volume of air required exceeds that
when the draught is produced artificially.
An insufficient supply of air causes imperfect combustiop ; an excessive
auppl^f a waste of heat.
464
COMBUSTION.
Volame of atmospheric air that is chemically required for combnstioii of
1 lb. of bituminous coal is 150.35 cube feet. Of this, 44.64^^ cube feet com-
bine with the gases evolved from the coal, and remaining 105.71 cube feet
combine with the carbon of the coaL
€k)mbi nation of gases evolved by combustion gives a resulting volume
proportionate to volume of atmospheric air required to furnish the oxygen,
as II to 10. Hence the 44.64 cube feet must be increased in this proportion,
and it becomes 44.64 + 4146^49.1.
Gases resulting from combustion of the carbon -of coal and oxygen of the
atmosphere, are of same bulk as that of atmospheric air requiretl to furnish
the oxvgen, viz., 105.71 cube feet. Total volume, then, of the atmospheric
air and gases at bridge wall, flues, or tubes, becomes 105.71 4- 49.1 ^ 154.81
cube feet, assuming temperature to be that of the external air. Conse-
quently, augmentation of volume due to increase of temperature of a fur-
nace is to be considered and added to this volume, in the consideration of the
ca|)acity of flue or calorimeter of a furnace.
There is required, then, to be admitted through the grates of a furnace for
combustion of i lb. of bituminous coal as follows :
Coal containing 80 per cent. 0/ carbon, or .7047 per cent of coke.
I lb. coal X 44-64 cube feet of gas = 44.64
7047 lb. carbon x 150 cube feet of air . . . = 10S71
150.35 cube feet.
For anthracite, by observations of W. R. Johnston, an increase of 30 per
cent, over that for bituminous coal is required = 195.45 cubefcet»
Coke does not require as much air as coal, usually not to exceed 108 cube
feet, depending upon its purity.
Heat of an ordinary furnace may be safely considered at 1000^ ; hence air
entering ash-pit and gases evolved in furnace under general law of ejLpan-
sion of i)ermanently elastic fluids of ^^^^ths of its volume (or .002087) ^^^
each degree of heat imparted to it, the 154.81 is increased in volume from
100° (assumed ordinary temperature of air at ash-pit) to 1000° ^ 900^ ; then
900 X .002087 = 1.8783 times, or 154.81 +154.81 X 1.8783 = 445.59 cvbtfeet.
If the combustion of the gases evolved from coal and air was complete,
there would be required to give passage to volume of but 445.59 cube feet
over bridge wall or through flues of a furnace ; but by experiments it ap-
pears tliat about one half of the oxygen admitted beneath grates of a furnace
passes off uncombined ; the area of the bridge wall, or flues or tubes, must ctm-
sequcntly be increased in this proi)ortion, hence the 445.59 becomes 891.18.
Velocity of the gases passing from furnace of a proper^proportioned boiler
maj' be estimated at from 30 to 36 feet per second. Then zr-—, ~ 7 =
•^ 001- 60x60x36
.00687 sq. feet, or .99 sq. ins., of area at bridge wall for each lb. of coal con-
sui^ied ))er hour.
A limit, then, is here obtained for area at the bridge wall, or of flues or
tubes immediately behind it, below which it must not be decreased, or com-
bustion will be ini|)erfect. In orduiary practice it will be found advan-
tagiH)us to make this area .014 sq. feet, or 2 sq. ins. for every lb. of bitu-
minous coal consumed per sq. foot of grate per hour, and so on in propcfftioo
for any otlier quantity.
Volumes of heat evolved are very nearly same for same substance, what-
ever temperature of combustible.
* ^•>P*rim«Bt, 4.464 c«b« «Mt of gu art •ToWad from i Ih. of bUambioai coal, raqslilBf 44.64
COMBUSTION.
465
BdoHve Volumes of Air required Jbr Oombu^ion ofFuds.
Lb*. ! Lbs.
Vi^arlich^s patent... 13.1 ! ADtbraclte Coal . . . . 12.13
Charcoal 11. 16 Bituminous** .... 10.98
Coke 11.28 Bitum.Coal, average 10.7
Bitum. Coal, lowest. . 5.92
Peat, dry 7.08
Wood, dry 6
Perfect combustion ci 1 lb. of carbon i;eauires 11. 18 lbs. air at 62°, and
total wei^^ht^ J2.jg38. Total heat of combustion of i lb. carbon or char-
coal is 14 500 thennal units ; mean specitic heat of products of combustion
is .25, which, multiplied by 12.39 ^^ above = 3.0975, and 14 500* -r- 3.0975 =
4681° temperature of a liiniace, assuming every atom of oxygen that was
ignited in it entered into combination.
1^ however, as in ordinary furnaces, twice volume of air enters, then
products of combustion of i lb. of cual will be 12.39-}- ii*i8 = 23.57, which,
multiplied by its specific heat of .25 as before, and if divided into 14 500^
quotient will be 2461°, which is temperature of an ordinary furnace.
Ratio of Oombustum. — Quantity of fuel burned per hour per sq. foot of
grate varies very much in different classes of boilers. In Cornish boilers it
is 3.5 lbs. ijer so. foot ; in ordinary Liand boilers, 10 to 20 lbs. ; (Itlnglish) 13
to 14 lbs. ; in Marine boilers (natural draught), 10 to 24 lbs. ; (blast) 30 to
60 lbs. ; and in Locomotive boilers, 80 to 120 Ib^,
Volumes of air and smoke for each culie foot of water converted into
steam, is for coal and coke aooo cube feet, for wood 4000 cube feet ; and for
each lb. of fuel as follows :
Coal 307 I Cannel coal... 315 | Coke......... 216 | Wood 173
Calorific power or 1 lb. good coal = 14 000 X 772 = 10808000 lbs.
Relative Evaporation of Several Combustibles in X^ba.
of "Water, Keated 1° by 1 Lb. of Miaterial.
Comboitible.
Alcohol..... .813
BitaminoQS coal. . .
Carbon
Coke
Hydrogen (mean). .
Oak wood, dry ....
(t
u
green.
Compmttion.
Hyd.
Carb.
Hyd. 04 )
Carb. .75 J
•45 J
Carb. .84
(Hyd. .06)
I Carb. .53}
(Hyd. .08)
{Carb. .37f
Water.
Lb*.
8120
9830
14220
9028
SO 854
6018
5662
Combuatible.
Olive Oil
Peat, moist
" dry
Pine wood, dry....
Sulphuric ether.. 7
Tallow
Composition.
IHyd.
( Carb.
(Hyd.
( Carb.
iHyd.
( Carb.
(Hyd.
\ Carb.
(Hyd.
(Carb.
•*3
•77
.04
•43)
.06
.58
.06
•7
•13
.6
W»t«r.
14560
3481
3900
36>8
8680
14560
I lb. Hydrogen will evaporate 62.6 lbs. water ftom 212° = 60.509 lbs. heated t^.
I lb. Carbon '' 14.6 lb& ^' 212°, or raise 12 lbs. water at
5o^ to steam at 120 lbs. pressure.
I lb. of Oxygon will generate same quantity of beat whether in combustion with
bydrogen, carbon, alcohol, or other combustible.
Relative Volumes of Gases or Products of Combustion per Lb, of FwL
T«mp.
Air.
Supply e
xalbt.
Volnm*
per lb.
0
CateFMt
II
150
i6x
104
313
393
173
ao5
3S9
18 lb*.
Volome
p«r Ih.
Cnlie IVft.
225
241
258
389
of Fael.
24lb«.
Temp.
Vol nine
Air.
p«r lb.
Cub« Feet.
0
300 ^
572
322
752
344
ZXZ3
409
1472
5'9
2500
Sapply of Air per lb. of Fad.
X3 tbe.
Volume
per lb.
Cube Feet.
3>4
369
479
588
906
tSlbe.
34lba.
Volume
Volume
per lb.
per lb.
Cube Feet.
Cube Feet.
471
628
553
738
718
957
883
1 176
1359
x8z2
* Mean 0/ all ezperimenti 13964.
466 COMBUSTION. — EXCAVATION AND EMBANKMENT.
To Compute Conauxnption of* I^uel to Keat Air*
Rule. — Divide volume of air to be heated by volume of i lb. of it, at ita
temperature of supply ; multiply result by number of heat-units ne^^essary
to raise i lb. air through the range of tem|)erature to which it is to be heated,
and product, divided by nuuiber of heat-taiits of fuel used, will give result
in lbs. per hour.
ExAMPLK.— What is required congumption per hour of cool of an average compo-
sition to beat 776400 cube feet of air at 54^^ to ii4<'?
Coal of an average composition (Table, page 461) = 14 133 heat-units. Volume ol
I lb. air at 54° (see formula, page 522) = li-'tSi ^ ,^.94 cube feet i X114--54
X •''S?? (specific beat of air) = 14.262 heat-uniU.
776400
^^— — X 14.262 -5- 14 133 =s 6a55 »».
12.94 -r -/^ .in*
Loss of heat by conduction of it to walls of apartment is to be added to ttila
EXCAVATION AND EMBANKMENT.
JLiabor and "Work upon Kxoavatioii and B^mbankmenb
Elements of Estimate of Work and Cost,
Pier Day of 10 Hours.
Cart. — One horse. Distance or lead assumed at 100 feet, or 200 feet f»
a tripf at a speed of 200 feet per mnute.
Earths. — Of gravelly, loam, and sandy, a laborer will load per day hito a
cart respectively 10, 12, and 14 cube yards as measured in embankment, and
if measured in excavation, .11 more is to be added, in consequence of tho
greater density of earth when placed in embankment than in excavation.
Note. — Earth, when first loosened, increases in volume about .2. but when settled
in embankment it has less volume than when in bank or excavation.
Carting. — Descending, load .33 cube yard. Level, .28, and Ascending .25,
measured in embankment ; and number of cart-loads in 9, cube yard of em*
bankment are, Gravelly earth 3, Loam 3.5, and Sandy earth 4.
Lnosening — Loam, a three-horsed plough will loosen from 250 to 800 cube
yards |»er day.
Tnmming. — Cost of trimming and superintendence i to 2 cents per cubt.
yard.
• Scoopmff, — A scoop load measures about .1 cube yard in excavation ;
time lost in loading, unloading, and tummg, 1.125 minutes per load; in
double scoopinff it is i minute. Time occupied for every ico feet of dis-
tance from excavation to embankment, 1.43 minutes.
Time. — Time occupied in loading, unloading, awaitmg, etc., 4 minutes pei
load.
To Compute Nnm1>«r of X^ocula or Trips in Cube Yard*
per Cart per Day.
f =;— — ; — I jk -f" y = n. E repi-esenting average distance of carting from em-
\E-!- 1004-4/
batiicmeni in stations of 100 feel each, y number of cartloads to cuhe yard ofetcona^
tion, and n number of cube yards in embankment, hauled by a cart per day to di»
tonoeE.
SXCAVATION AND EMBAKKMKNT, 467
Illustration. —What is number of cube yards of loam that can be removed by
one cart ft-om an embankment on level ground for an average distance of 950 feet?
E = 250 -r- joo = 2.5, and y = 3.5.
; — X io-i-3.5 = -— X lorT- 3.5 = 26.37 cube yards,
2.5 + 4 °'5
Substituting for 3, 3.5, and 4 number of cart-loads in a cube yard of embank
meai, 30, 17.14, and 15,= 60 minutes, divided respecMvely by these numbers.
* X 20 . , -. ,. 17.14 X A . , , J 'SXfe
-="1 — =f^tn descending carting; - '-. = n, m level, and -5-. — ^ n, m
"•■T4 *' + 4 «' + 4
ascending, h representing number of hours actuaUy at work.
To Compute Cost of* Hixoavatins enid. ^vatyantaing per
Cube Yard.
L e
1 (-/-|-' = 'V. L rq>resenting pay 0/ laborers, v tJcUue or result of loading
V WW t
in different earths, OJ 10, 12, and 14, c 0/ one cart and driver per day, l cost of loosen-
tng material per cube yard, and s cost <\f trimming and superintendence, both per
cube yard, and aU in cents.
Illustration.— Volume of excavation in loam 30000 cube yards. Level carting
650 feet &= 6. 5 trips or courses. Loosening by plough 1.7 cents per pube yard,
laborers xo6 cents per day, carts 160, and trimming and superintendence 1.5 cents
per cube yard.
c = i2, and -^ — -r- — =^i6.3^numberof loads per da}f by preceding formula
Then 1- -^ |-i-7 + i-5 — 8.833 + 9.707 + J-7 + «-5 = 2i-83 cents per cube
12 10.33
yard.
Earth^v^ork .
By Carts.— A laborer can load a cart with one third of a cube yard of sandy
earth in 5 minutes, of loam in 6, and of heavy soil in 7. This will give a result, fbr
a day of 10 hours, of 24, 20, and 17.2 cube yards of the respective earths, after de-
ducting the necessary and indispensable losses of time, which is estimated at .4.
^ It is not customary to alter the volume of a cart- load in consequence of any dif-
TCreoce in density of the earths, or to modify it in consequence of a slight inclina-
tion in the grade of the lead.
In a lead of ordinary length one driver can operate 4 carts. With labor at $1
per day, the expense of a horse and cart, including harness, repairs, etc., is $1.25
per day.
A laborer will spread flrom 50 to 100 cube yards of earth per day.
The removal of stones requires more time than earth.
The cost of maintaining the lead in good order, the wear of tools, superintend-
ence, trimming, etc., is fiiHy a>5 cents per cube yard.
By Wheel-barrows. — A laborer in wheeling travels at the rate of 200 feet per mih-
ot«. and the time occupied in loading, emptying, eta., is about 1.25 minutes, with-
ont including lead. The actual time of a man in wheeling in a day of 10 hours is .9
or t.35 minutes per lead of 100 fl3et Hence,
To Compute Ntxxnber of* Bapro-w-Loads rexnoved. by a
X^aboper per J^&y.
— "^ = n. n' r^esenting number of leads of 100 feet
A barrow-load is ali^oat .04 of a cube yard.
Roolc.
By Carte.— Quarried rock will weigh upon an average 4250 lbs. per cube yard,
and a load may be estimated at .2 cube yard, and weighing a very little more than
a load of average earth.
Hence, the comparative cost of carting earth and rock is to be computed on the
basis of a cube yard of earth averaging 3.5 loads and one of rock 5 loads, with the
addition of an increase in time of loading, and wear of cart.
4e>b
EXCAVATION AND EMBANKMENT.
Ijat»or.
For labor ofa man, see Animal FoWer, pp. 433-34.
By Wheel-barrow.— A barrow-load may be assumed at 175 Iba — 2 cube feci of
space.
Bleating. — Wben labor is $1 per day, bard rock in ordinary position may bd
blasted and loaded for 45 cents per cuoe yard.
The cost, however, in consequence of condition, position, etc., may vary ft-om ao
cents to $ I
See Blasting page 443.
17 cube yards of hard rock may be carted per day over a lead of 100 feet, at a cost
of 7.29 cents per yard.
The preceding elements are esMTitiaUy deduced from notes Jurnished by Bflwood
Morris, C.E., and tlie valuable treatise of John C. TrautwinCj C.E., Phila., 1873.
Stone.
Hauling Stone. — A cart drawn by horses over an ordinary road will travel 1.15
miles per hour of trip = 2.3 miles per hour.
A four-horse team will haul from 25 to 36 cube feet of stone at each load.
Time expended in loading^ unloading, etc., including delays, averages 35 minutes
per trip. Cost of loading and unloading a cart, using a horse-crane at the quarry,
and unloading by hand, when labor is $ i 25 per day, and a horse 75 cents, is af
cents per perch = 24.75 cube feet= i cent per cube foot
Work done by an animal is greatest when velocity with which he moves is .125
of greatest with which he can move when not impeded, &nd force then exerted .4>r
of utmost force the animal can exert at a dead puU.
XGartli-work. {Moletuforth.)
Proportion of Getters^ Fillers^ and Wheelers in different mlSy Wheekrt being oal-
culated at 50 yards run.
In loose earth, sand, etc.
" Compact
"Marl
6«U'i.
Fill's.
Wheel's.
G«tt's.
FUl's.
Wheel's.
z
X
z
z
3
2
z
3
2
In Hard clay
'' Cknnpact gravel
" Rock, flrom . . . .
z
z
3
z
z
z.as
A.verage 'Weigh.t o€ Sartlis, H.ool&Sf etc.
Per cube yard.
Lbs.
Sand 3360
Gravel 3360
Mud 3800
Lbs. I Lbs.
Marl 29Z2 Sandstone . . . 4368
Clay 3472 Shale. 4480
Chalk 4033 I Quartz. 4492
Lbi.
Granite...... 4700
Trap... 4700
Slate. 47Z0
Sulk of* R,ock, S^arth-worlc, etc., Origizial Kxoavatlou
aatsuxned at 1.
When in En^>ankment.
Rock, large z.5 z.6 z.7
Medium z.25 to z.7
Metal 4... X.2 to Z.8
Sand and gravel z.07
Clay and earth after subsidence . . . 1.08
ti
(t
before
t(
z.a
In small stones, per cent of interstices to total volume is 44 to 48, which is an
increase in volume of solid rock to fragments of 79 and 92 per cent
The relative proportions of Earth in Bank and Embankments, as given by differ-
ent authorities, are so varied and so opposite that it is evident the difference is acci-
dental, depending, primarily, u|ion the season, location, and character or condition
of the earth, and then upon the height of the embankment, the manner and durar
lion of time of raising it
Thus, Eilwood Morris, ante p. 466, makes the embankment less, and Mole8wor(l^
B8 above, gives It greater
FRICTION. 469
FRICTION.
Friction is the force that resists the bearing or movement of one sur-
face over another, and it is termed Stidhig when one surface moves
over another, as on a slide or over a pin ; and Rolling when a body ro-
tates upon the surface of some other, as a wheel upon a plane, so that
new parts of both surfaces are continually being brought in contact with
each other.
The force necessary to abrade the fibres or particles of a body is
termed Meature of friction ; this is detcimined by ascertaining what
portion of the weight of a moving body must be exerted to overcome
the resistance arising from this cause.
CoffficierU of Friction expresses ratio between pressure and resistance of
one surface over or upon another, or of surfaces upon each other.
Angle of Repose is the greatest angle of obliquity of pressure between
two planes, consistent with stability, the tangent of which is the coefficient
of friction.
Erperiments and Invesfigations have adduced the following observations
and results :
1. Amount of friction in surfaces of like material is very nearly propor-
tioned to pressure perpendicularly exerted on such surfaces.
2. With equal pressure and similar surfaces, friction increases as dimen*
sions of surfaces are increased.
3. A regular velocity has no considerable influence on friction ; if velocity
is increased friction may be greater, but this depends on secondary or inci-
dental causes, as generation of heat and resistance of the air.
M. Morin'&«xperiments afford the principal available data for use. Though con-
stancy of lyictioD holds good for velocities not exceeding 15 or 16 feet per second,
yet, for greater velocities, resistance of friction appears, fbom ex^ieriraenls of M.
Poir^, in 1851, to be diminished in same proportion as velocity is increased.
4. Similar substances excite a greater degree of friction than dissimilar.
If pressures are light, the hardest bodies excite least friction.
5. In the choice of unguents, those of a viscous nature are best adapted for
rough or porous sur&ces, as tar and tallow are suitable fur surfaces ot woods,
and oils best adapted for surfaces of metals.
6. A rolling motion produces much less friction tlian a sliding one.
7. Hard metals and woods have less friction than soft.
8. Without unguents or lubrication, and within the limits of 33 lbs. press"
ore per sq. inch, the friction of hard metals upon each other may be esti-
mated generally at about one sixth the pressure.
9. Within limits of abrasion friction of metals is nearly alike.
10. With greatly increased pressures friction increases in a very sensible
ratio, being greatest with steel or cast iron, and least with brass or wrought
iron.
IT. With woods and metals, without lubrication, velocity has very little
influence in augmenting friction, except under peculiar circumstances.
12. When no unguent is interposed, the amount of the friction is, in every
case, independent of extent of surfaces of contact ; so that, the force with
which two surfaces are pressed together being the same, their friction is the
Mune, whatever may be the extent of their surfaces of contact
13. Friction of a body sliding upon another will be the same, whether the
body moves upon ite face or upon its edge,
Rr
470
PBICTION.
14. When fibres of materials cross each other, firiction is less than when
they run in the same direction.
15. Friction is greater between surfaces of the same character than be-
tween those of different characters.
16. With hard substances, and within limits of abrasion, friction is as
pressure, without regard to surfaces, time, or velocity.
17. The influence of duration of contact (friction of rest) varies with the
nature of substances ; thus, with hard bodies resting upon each other, the
effect reaches a maximum very quickly ; witli soft bodies, vety slowly ; with
wood upon wood, the limit is attained in a few minutes; and with metal (m
wood, the greatest effect is not attained for some days<
Coefficients of F'riction and A^ngles of Repose.
The CoefflcieDt of Friction is the tangent of the augte of repose Arom a borixontal
plane.
MatikiaL.
Belt on wood, dry
Clay, damp
" wet
Earth
" dry
*' wet clay
Gravel. ,
Hemp on dry oak
" wet "
Sand, fine
Timber on stone
" " timber, dry
" " " soaped.
Metal on Metal, wet,
dry
lubricated.
Wood on wood, dry.
" ♦' stone
ti
((
CoeflliilenL
•47
I
.25 to. 31
.X to .25
.81
323
.81 to I. II
•53
•33
.6
•4
.25 to. 5
.04 to .2
•3
.15 to .2
,08
.4 to .6
•4
Anfcle.
45"
14O to 17O
14O to 43O
17^
i?o
t0 48O
180
30'
3'";
22"
140
t0 260
1^0'
20
to 11°
30'
160
30'
8° to iio
30'
4°
9"
to 22°
22°
1025°
Cotangent of Angle.
Exponent of
Stability.
Surpacbs.
Oak on oak
Wrought iron on oak,
Cast iron on oak.
(t H il
Pressure = t.
Lubrication.
Soap
Wet
Sojip
Wet
.Soap
lny
3.23 to 4
1 to 4
'•«3
•3«
9 to z. 23
t.§9
3
1.67
25
2 t04
2.8 to 4.9
3^3-3
49*07
•«4
a 5 to 6
21 to 3-5
CMflldeot.
.16
.26
.21
»2a
.19
.27
Leather belt on oak
Wheel Gearing. Grooves of wheel, V angle scfi. Compared with leather belts,
under a pressure equal to the tension of the belts, kiis proved to have greater ad-
hesion, equal to 30 per cent, in one instance.
Leather belts over wood drums .47 of pressure, and over turned cast-iron pulleys
28 of pressure.
Coefficients of* ITriction of Alotion.
SawatAXOt*.
Hemp cord^ etc {^j;^
Metal upon wood Mean...
Sole-leather, smooth, upon wood (Raw
or metcU t I'T
Wood upon metal Mean . . .
Wood upon wood ,,,.,,,,,....
Q
Conditi
1
on ofS
•
1
0
nrfiwea
and Ui
ipienta
1
•45
•33
—
—
—
—
—
—
•15
—
.19
—
.18
'^1
.07
.09
.09
.9
•54
•3<>
.16
—
.2
-^
•34
•31
■in
—
•'i
—
.42
.24
.07
.ott
.a
.36
•25
—
,07
.07
•«5
■»3
«4
PSICTION.
47 1
Hel»tive Value
Wood
of* XJnsuexit^ to fieduoe I^riction,.
UMGtTBNTS.
Dry mmp
Lard
Lard and plumbago.
upon
Wood.
•4
.82
Wood
upon
Metala.
3»
•8s
.67
MatoU
upon
Mctola.
•«7
•7
.96
UnociNTs.
Wood
tipOB
Wood.
Olivaoil
Tallow
I
Water
.sa
Wood
upon
MeUb,
•93
•34
M«taU
upon
.8
.18
rPo JDeterzxiiiie CoeffloieAtt of* F'riotioii of Bodies.
Place them upon a horizontal plane, attach a cord to them, and lead it in
a direction parallel to the plane over a pulley, and suspend from it a scale in
which weignts are to be placed until body moves.
Then weight that moves the body is numerator, and weight of body moved
is denominator of a fraction, which represents coefficient required.
lLLU8TRATioif.— If; by a pressure of 320 lbs. fHelion amounts to 80 lbs., its coeffi-
cient of fViction in this case would be 80 -r- 320 = . 95.
Hence, if coefficient of friction of a wagon over a gravel road was . 25, and the load
8400 lbs., the power required to draw it would be B400 x .25 = 2100 lbs.
Coefficients of* ^xle Friction. {M. Mwrim.)
ScanAKCBs.
Condition of Surfaces and UngnenU.
Dry and
a little
Greaay.
Bell metal upon bell metal.. .
Cast iron upon bell metal. . . .
Oist iron upon cast iron. ....
Cast iron upon lignum vit«e
Wrought iron upon bell metal. .
Wrought iron upon cast iron. . .
Wrought iron upon lignuiu-vitn
•••«•«
,194
» • • •
.185
.251
» • a •
.188
Greasy
and wet
with
Water.
.161
.079
• ■ • •
.189
Oil, Tallow, or Lard.
In usual
Continu-
way.
ously.
.097
• • • •
.075
.054
•075
.054
.1
.092
.07s
•054
•075
•054
•J25
■ • • «
Very soft
and puri-
fied Car-
riane
Grease.
.065
• • ■ •
.109
.09
Friction of a journal of an axle which presses on one side only, as in a
worn bearing, is less than whea it [Hreases at all points^ the difference being
about .005.
Friction o/ArUg. — With axles, friction of motion has alone been experi-
mented upon. When weight upon axle and radius of its journal is given,
mechanicai eject oi friction may be readily determined.
The mechaniceU e£ftct absorbed by, or of friction, increases with pressure
or weight upon journal of axle and number of revolutions..
Frictidh of an axle is greater the deeper it lies in its bearing.
If journal of an axle lies in a prismatic bearing, as in a triangle, etc.,
friction is greater, as there is more pressure on, and consequently greater
friction in contact : in a trianguZar baring it ia about double that of a cyl-
indrical bearing.
To Compute Aleclxanical Bffeot of IT'riction on- Journal
of an A^xle.
P.^^ . ** — f*. n rejfre^nting number of revolutions^ and r radius of journal
infeeL
ImtiTBATKUir.— Weight of a wheel, with its axle or shaft resting 00 its journals,
is 360 Iba ; diameter of Journals 2 insj and number of revolutions 30; what Is me*
ffhan*^^ effect of the flriction, the coefficient of it being .x6t
3.I4<^ X 30 X .»6 X 360 X I H- I? _ 452.4 ^ ^ ^^
?o 30
472 FBICTION.
By application of friction-wheels (rollers^ friction is much rednced, and
medbanical ^ect then becomes, when weignts of friction-wheels are disre-
gardedf
i- — X = = F- ^ representing radii of axles of JruMom-vohedM^
30 a' COS. a -T- 2
a' radii of /rietion-wheeli^ and a angle ofUnes of direction between aans of roller
and axis offridion-wkeels.
When a single frictum-vOuel is used, -'^— X / W = F, and -737-7 = F'. F
r^presentkig mechanical effect
iLLUSTRATioir.— A Wheel and its shaft, makiDg 5 revolalions per minute, weighs
3ocxx> Iba ; its diameter and that of its Journals are 32 feet and 10 ins. The joumate
rest upon a ft-iction-wheel, the radius of which is 5 times greater thaa its axle.
I. What is the power at circumference of wheel necessary to overcome friction f
2. What is mechanical effect^ of the friction ? 3. What is reduction of friction by
use of the flriction-wheel ?
^2 "T— 2X12
= 38. 4, ctrcttm. qf wiieel — 38. 4 times thai of axU.
IO-r-2
Coefficient of friction assumed at .075. Hence ^°°°° — '^^ = 58. 59 lbs. = power
38.4
at circum. to overcome friction at axle. 2. — — ^''^' =z 2.6iBfeet = distance passed
by friction.
Consequently, ^^-^- — - = .2181 feet = distance passed by friction in one second.
00
Hence, .2181 X 2250 (30000 X .075) = 490.725. 3. i -^ 5 = .2 •= radius offricHon-
axle-i-by radius offrUAion-wked, and 38.4 X .2 = 7.68 ^fi-UAion referred to ctrcum.
of wheel, and *^^'^ = 98.145 = mechanical effect by application offriction-wheei
= a reduction offourfflhs.
P'rlotion of Pivots.
Friction on Pivots is independent of their velocity, increases in a greater
degree than their pressures, and approximates very near to that of sliding
and axle friction.
Friction on Conical Bearings is greater than with like elements on plane
surfaces.
Figure of point of a pivot, as to its acnteness, affects friction : with great
pressure the most advantageous angle for the figure ranges firom 30° to 45° ;
with less pressure it may 1^ reduced to 10° and ia°.
Relative Value of A^ngles of Pivots.
6° X I is<> 66 I 450 39
Relative Values of difTereiit ^laterials fbr use as Pivots.
Agate 83 I Granite i I Tempered steel 44
Glass 55 I Kock crystal 76 |
BViction. and Rigidity of Corda«ce.
Experiments by Amonton and Coulomb, with an apparatus of Amonton*8,
furnish the following deductions :
1. That resistance caused by stiffness of cords about the same or like pot
leys varies directly as the suspended weight.
2. That resistance caused by stiffness of cords increases not only in direcf
proportion of suspended weights, but also in direct proportion oC diametei
of the cords.
FBICnON.
473
Consequently, that resistance to motion over the same or like pulleys,
arising from stiffness of cords, Is in direct compound proportion of suspend-
ed weight and diameter of cords.
3. That resistance to beudiug vai ied inversely as diameter of sheave or
drum.
g_i_C T
4. That complete resistance is represented by expression — ^ — . S rep-
resaUing conatani for each rope and sheave^ expresiing ttiffnesa of rope ; T
tension of rope which is being bent^ expressed (^ C T; C constant for each
rope ani sheave ; and d diameter of sheave^ inciuding diameter of rope,
5. That stiffuess of tarred ropes is sensibly greater than that of white ropes.
lilxtending results obtained by Coulomb, Morin furnishes following for'
fnuias :
For White Ropes: 12 n-r-d (.00915+001 77 n 4- .0012 W) = R. For Tarred
Ropes : 12 n -^ d (.010 54 -f- .0025 n -f- -0014 W) = R. K representing rigidity in llu. ,
n number of yams, d diameter 0/ sheave in ins. and rope cmnirined^ and W weight
in lbs.
Illustration.— What is valuer of stiffhess or resistance of a dry white rope bav-
iug a diameter of 60 yams, which runs over a sheave 6 ins. in diameter in the
iproove, with an attached weight of 1000 lbs. ?
12 X 60
Assume diameter for 60 yarns to be 7.2 ins. Then (.002 15 + .001 77 x
7.2
60 + -0012 X 1000) = 100 X 1*308 35 = 130.835 lbs.
Value of natural stiffness of ropes increases as the square of number of
threatls nearly, and value of stiffness proportional to tension is directly as
number of threads, being a coustant number. Hence, having the rigidity f(»r
any number of threads, the rigidity for a greater or lesser number is readily
ascertained.
Wire Ropes,
Weisbac|i deduced from his experiments on wire ropes that their rigidity
for diameters capable of supporting equal strains with hemp ropes is con-
siderably less.
Wire ropes, newly tarred or greased, have about 40 per cent less rigidity
tban untaried ropes.
Railing FHcOon.
Rolling Friction increases with pressure, and is inversely as diameter of
rolling liody.
For rolling upon compressed wood,/= .019 to .031.
When a Body is moved upon Rollers and I*ower applied at the Base of the Body,
t/-f-/') — =c p. fandf representing atefficients of friction of two surfaces upon
•which roUers act.
When Power is applied at Circumference of Roller, / W -r- r = F.
When Power is applied at Axis ofRoUer,f\f-^r-7-a = P.
Beariuffs ibr Propeller Shaft. {Mr. John Penn.)
BlARtllOS.
Babbit's metal on iron*. . .
Box 00 brass
Box on troD
Brass on brass
Biaas on Iron
• Rolled oot.
PreMurtf
Tlm«
per
ofOi>-
Sq. Tnch.'eratlon.
Lbs.
Min.
1600
8
4480
5
448
30
448
30
448
30
Biasings.
Brass oh Iron!
Brass on iron t
I.ignnm-vitsB on brass . .
Snalce*wood on brass . . .
Lignumvit» on iron . . .
Preasare
Time
I»«r
Sq. Inch.
of Op.
eretioa
Lbt.
Min.
675
4480
60
4000
5
4000
1250
2z6o
t Abrmded.
BJ4*
tSetful.
474
FEICnON.
Heault of Bxperixnents upon F'riotioxi ofSeVer&l In«tra«
xxxents, (B. S. BcUl)
iNSTHUmNT.
Pulley, single
" 3 sheaves
" iliflerential
Screw
Inclined plane, angle 17O 2'. . . .
Screw Jack
Wheel and Axle
" " Barrel
" " Pinion
Crane
Friction.
Velocity ratio.
Mscbaoical
eiBcieacy.
UmAiI
effsct.
F L
Per C«at.
2.21 -
-•5453
2
>.8
90
a. 36 -
-.238
6
4
64
3.87 --.151
16
6.Z
38
.0 -
h.014
»93
70
36
.09 -
-•55
3^4
1.72
5«
.66 -
-.007
414
1x6
28
.204 --.043
3»
22
70
•5 -
-.169
5-95
5-55
93
2-46 -
-.21
8
^r
51
.0 -
-.056
23
ll
.185-
-.008
137
87
F representing fridion^ and L Zoodl.
Illustration i.--If it is required to ascertain power necessary to raise 200 lbs.
2 feet, by a single movable pulley, 200 x .5453 + 2.21 = 111.27 W>»., which must be
applied as power to raise 200 lbs. 2 feet. 1 11.27 X 2 ^c 222. 54 lot. ' Henoe, for appli-
cation of 222.54 '^s^t 200 or 89.87 per cent are tt$^ftUly or effectively employed.
2.— If it is re<)uired to raise 100 lbs. by a three-sheave pulley, then 100 X -2384-
2.36 = 26.16 lbs, which most be applied as power to raise 100 lbs. 6 feet (3X2 = 6).
26. 16 X 6 = 156.96 lbs. Hence, ibr application of 156.96 lbs., 100 or 63.71 per cent
are effectively employed.
3. — ^The velocity ratio of a crane being 137, and Its mechanical efflciency 87, a
man applying 26 il>s. to it can raise 87 x 26 = 2262 lbs.
^Application, or preoeding Results.
• Illustration. — Tf a vessel, including onidle, weighing 1000 tons, is to be drawn
upon an inclined plane having a risd of 10 feet in 100 of its length, what will be the
resistance to bd overcome, the cradle being supported on wrotight^lron axles in ca^t-
iron rollers, running on cast-iron raild?
= 100 tons ■= power required to draw vessel independent oj friction.
100
Ratio of ft-iction to pressure ef wrought iron on cast, in an axle and its bearing,
.075. Ratio of ditto of cast iron upon cast^ say .005.
Hence .075 -)- .005 = .08 of 1000 tons = 80 tons, which, added to 100 tons before de-
ducted, gives 180 twts, or resistance fn h^ overcome.
Power or effect lost by friction in axles and their bearing may be ex-
pressed by formula
W/dr
230
= P. / repre6enting coefficient of friction^ d diameter of axk in ins. , and
r nuniber of revolutions per minute.
Illustration.— PressHre on piston of a steam-engine Is 20000 tbs., namber of
revolutions 20, and diameter of driving shaft of wrought iron in a brass Journal Is
8 ins. ; what is ihe etl'cct of (Viction ?
20000 X .07 X 8X20
230
= 973- Qi lbs.
Hence P » -5- 33 000 = IP. v representing circumference of shaft in feet X by revo-
lutions per minute.
The power or effect lost by friction in guides or slides may be expressed
by- following formula:
W fs r
jf-— :a P. t representing stroke of cnm-head, and I length of eof^
60 X v(5 '• — * )
nsciing rod infect*
FBICTIOK.
475
SViotional I^esistances.
I^riotion of Steam-engines.
JETriotion oi* Condensing E^ngiiies in Xjbs. per Sq.. Inoh
of Piston.
OwillaUsg
B«ain
Direct-
Diameter
OacUlating
Beam
and
and
actinff and
Vertical.
7
of
and
and
Trunk.
Geared.
Cylinder.
Tmnk.
Geared.
5
6
50
a- 5
a. 7
4
5
6
60
2-4
a.6
3-5
4 -
5
^
2.3
2-5
3
3.6
4-5
a
a. 3
3^
35
4
100
1.6
a. a
a.6
3
35
no
1-5
a
Direct-
actinfc and
Vertical.
3-3
3
a. 7
2.6
a- 5
a- 1
DUuneter
of
Cylinder.
10
15
ao
25
30
35
Experiments upon different steam-engines have determined that friction,
when pressure on piston is about 12 lbs. per sq. incti, does not exceed 1.5 lbs.,
or about one tenth of power exerted.
Friction of double cylinder (50-inch diam.) direct-acting condensing pro-
peller engine is 1.25 lbs. per sq. inch of piston = 10.3 per cent, of total power
developed ; friction of load is .9 lbs. per sq. inch of piston = 7.5 per cent, of
total pressure; and friction of propdier is 1.3 lbs. per sq. inch of piston =
10.8 per cent of total power =s 28.6 per cent
Friction of double cylinder (70-inch diam.) inclined condensing water-
wheel engine with its load is 15 per cent, of total power developed.
In general, when engines are in good order, their efficiency ranges from 80
per cent, for small enginca tc 93 per cent, for large.
Power required to work air-pumps is 5 per cent, and to work feed-pumps
I per cent.
Results of Kxpex^ixnents iipon Kriotion of Alaolilnerjr.
{Davison. )
Sfeam-engine^ vertical beam, one tenth its power ; 190 feet horizontal, and
180 feet vertical shafting, with 34 bearings, having an area of 3300 sq. ins.,
with II pair of spur and bevel wheels; 7.65 H*.
Set ()f ihree-Uirow Pumpg, 6 ins. in diara., delivering 5000 gallons per hour '
at an elevation of 165 feet ; 4.7 £P, or about 13 per cent.
Two pair iron Roiiers and an elevator, grinding and raising 320 bushels
malt per hour ; 8.5 IP.
AUrmaahing Machine, 800 bushels malt at a time ; 5.68 H*.
A rchimedes Screw (ninety-five feet), 15 ins. in diameter, and an elevator
conveying 320 bushels malt per hour to a height of 65 feet; 3.13 Ip.
Friction dutch. — Driven by a leather belt 14 ins. in width ; tace of clutch
5 ins. deep ; broke a cast-iron shaft 6.5 ins. in diameter.
Flax Mill (i/. Otrnut, 1872). — Two condensing engines, cylinders, 12.9
ins. X 44.3 ins. stroke, and 22 ins. x 59.8 ins. stroke. Pressure of steam,
50 lbs. per sq. inch ; revolutions, 25 per minute. Friction of entire machin-
erj*, 20 i^er cent
With ve;^table oil and hand oiling a steam pressure of 62 lbs. per sq.
inch was required, and with mineral oil and continuous oiling a pressure of
50 lbs. only was required.
By continuous oUing, a saving of 44 per cent was effected oyer hand
ofliiiig.
476
FBICTION.
T^spL Mill.
Power required to Drive ICngiite, Shafting, and entire
M!aoliinery. {M. ComtU.)
Parts.
Engines, shafting, and belts
4 cards.
14 drawing frames (29 heads or 156
slivers) \
4 combing machines '.
6 roving frames (330 spindles)
20 spinning frames.
Dry (1480 spindles)
Wet (2080 " )
ToUl 1 5a 1 1 IP.
Total.
30.41
8.42
7.19
2.22
7.78
47-5
46.59
Indieatfld Hon»-pow«r.
One Machine
at work.
empty.
_
__
2.105
'•423
.0934
.0794
•555
.02627*
•151
2-434
.032 1*
0224*
2-515
1.613
Effect of
Mnchine«i
32
15
78
7-3
ai.6
19
* Per 100 spindle*.
Estimate of Morsels Power.— 20S0 8pmd\iX, wet, 34.4 per ff, long flbra
640 " dry, 20.1 " " " »'
840 '* " 14. s " " tow.
}±1
average, 23.7 "
3560 "
The IP per 100 spindles varies inversely as sq. root of their number.
Winding Kngine {O. H. DaglUh).
Shafts 738 to ij^o feet in depth; cylinder 65 X 84 ins. stroke; pressure of steam
19 Mm. per sq. ind^; revolutions 11. i per minule; mean diameter of drum^ 26 feet
H* 313.4; effect 235 = 75 per cent
Tools. {Dr. Bartig).
n t'
Single ehiearing, i •}- -r— =W to drive tool, n represenlting nwmher of
a¥
13? to shear, a representing
26.7
cuts per minute, t thickness of plate, and
1980000
area of surface cut or punched per hour in sq. ins., and F (ii66-f 1691 1) a factor ex-
pressing work requir^ to cut or shear a surface of i inch square.
• Illustratiox.— A shearing machine cutting 4648 sq. ins. of surface per hour, in
plates .4 inch thick, required .68 IP to run and 4.3 to operate it, equal to 5 horses.
▼ -r^i ^ 1 J- 85 000 6 <* I ,j , . , ri-^oobni
Iron r»late-l>endiiig. = Vfor cold pUUes^ and — >
= Pfor red-hot plates, b, t, and I representing breadth, thickness^ and length of plate,
r radius of curvature, all in ins., and P net power of bending.
Power for large rolls when running only .5 to 6 IP.
Ordinary Cutting Tools, in ^letal.
Materials of a brittle nnture. as cast iron, are reduced must economically in power
consumed, by heavy cuts; while materials which yield tough curling shavings are
more economically reduced by thinner cuttings. Following formulas apply to light
cutting work :
Power required to plune cast iron is—
Planing Cast iron, W (.0155 H — | = H*. W representing weight of east
\ II 000 «/
iron removed per hour, in lbs., and s average sectional area of shavings, in sq. ins.
Steel, Wrought iron, and Gun-metal, with cuts of an average character-
Steel 112 W = IP I Wrought iron, .052 W = :ff I Gun-metal, .0127 W = EP
Planing and Iblolding. — Run without cutting. = ff. N rep
3000
reseiUing sum of revolutions of all tite shafts per minute.
FRICTION. 477
Molding. — P*ne, 0566 -|- '.3^^^ and Red Beech, 088 95 + -^^^ = ff. hrep-
resenting depth of wood ad doion to form molding.
Turning. —Steel, .047 W = ff; Wrought Iron, .0327 W = ff: Cast Iron,
0314 \y = w.
For turning off metals, power required is less than for planing, and it is ascer-
tained that greater power is required for small diameters than large.
Light LatheSj .05 -|- .0005 n = IP; 1 or 2 shafts, .05 -)- .0012 n = IP; 3 or 4 shafts,
. 35 -f- .05 n = H?. Heavy LcUhes, .025 -|- .0031 n ; .025 + .053 n ; .025 -f-.iS n.
n rqvresmting number ofrevoluiions of spindle per minute.
Drillinfi;.— Power required to remove a given weight of metal is greater than
in planing. X'olume being taken in place of weight.
Hi^from .4 to 2 ins. in diameter,
Ca8tiron,dry. V /.oi684-~^)=H». Wrought iron, oil. V (.ox68 + l^\=H».
V representing wdume removed in cube ins. per hour^ and d diameter of hole.
Witbont gearing, .0006 n-f- .0005 n'; with gearing, .0006 n -f .001 n'; radial
drills without gearing, .0006 n -f -004 n'; radial drills with gearing, .04 -4- .0006 n -f
.004 n'. n representing number of revolutions per minute of gearing shaft, and n'
of drill.
n s
Slotting.—Stroke 8 ins. .045 -\ = H*. n rqaresenting number of strokes
4000
per minute, and s stroke in ins.
'WoodHsa'wiiig, Circular— A cube foot of soft wood and half a cube
foot uf bard, reduced to sawdust, requires i IP.
Hard wood, — = ff '. Soft wood, — = EP'. A representing area in sq. feet
and W horse-power per sq foot^ both cut per hour, and e width of cut in ins.
From .4 to 4 ins. in diameter.— Vine. V ( 000 125 -f ^ J = H*.
S c
Dry pine timber. .004 28 4-0065 ^ = IP'. S representing stroke of saw in feet,
and ffeed per cut in ins.
n d
- =^Wfor horse-power to run only without cutting, d representing diam,^er
32000
qfsaw in ins., and n number of revolutions per minute.
Net power required to cut with a circular saw is pro|H)rtional to volume of ma-
terial removed. For a saw cutting hot iron, at a circumferential speed of 7875 feet
per minute, and making a cut .14 inch wide, power is expressed by formulas—
.709 A = ff, for red-hot iron. 1.013 A = H*. for reo hot pteel.
A rq^esenting sectional area of surf a: : 3ut through, in sq. feet.
'Vertical Sa^w. .c»4 284- .0065 -^ = ff in dry pine timber per sq. foot
per hour. S representing stroke of saw in feet, c wi^Uh of cut in ins., and ffeed of
cut in ins.
Sand Saw. 0034 + 1^*-^=H»' in i\n«. .oo483-f^5L^=H>'tnOaJfc.
10000/ ^ "' 10000/
.005 76 + — — - — J = W* in Beech, v representing velocity of saw, and f rate of feed,
10000/
In feet per mmule.
Kld3 2(23
Screw Cutting. Screws, =-2 — = H*. Taps, — = H*. d rqpresenHng
64 29
diameter in ins. , and I lengtfi cut in feet per hour.
Machine of medium dimensions, .2 W-
478
FBICTION.
#fe C^ tv
G^rindstones. — — = W. p representing pressu^ upon itone^ v drcum
Jerential velocity ofstorte in feet per minute^ and C coefficient cf friction.
Coefficients of Ft'iction between Grindstones and Metals,
Cast iron, .22 at high speed, .72 at low speedy Wrought iron, .44 at high speed,
X at low; Steel, .29 at high speed, .94 at low.
Power required to run them alone.
Large 0000409^^ = 1? I Small 16 -f. 0000895 dv = H*
or oooiaSd^n r=IP | or. 16-)- .000 28^^11 =IP
G^raiIl Conveyers.
Conveyert of Grain horizontally by Screws and Bands. — A 12-inch screw, having
4 ins. pitch, turning in a trough, with a clearance of .25 inch, revolving with a
speed of maximum effect, 60 turns per minute, will discharge 6.75 tons of grain
per hour, expending .04 H* per foot run. Sectional area of body of grain moved
49 per cent, of that of screw. At speeds above 60 turns per minute, the grain nrill
not advance, but will revolve with screw.
Steatxi-engines.
Friction of a Steam-engine varies as its principal dimensions, and increases
slightly with the load.
Besults q/' re«te.— Engine, cylinder 4 in., 57 per cent.; cylinder 9 In., 13 tu
22 percent. Corliss engine, cylinders 18 and 24 in., xo percent, worthington
large pumping engine, 9 per cent. Compound engine, first cylinders of from 12 u>
21 ins., 80 to 89 per cent. [O. K. Clark.)
Engine^ Unloaded, -^-pr = pressure of steam in lbs. per sq. inch, and D diame-
V *^
ter of cylinder in ins. .
jMariiie B^iij^iue. Vertical Beam. {J.V.Merrick.) In Pressure of Steam.
Air-pump .585 to .7 lb
Cylinder packing 15 ".3 "
Valves, etc ». .169 " .258 '
Weight of parts. 51b.
Air-pump packiug 046 to .092 lb.
Average of all 165 lb.
If journals are kept constantly lubricated, friction of weight will be reduced to
.33, and pressure from 1.65 — .33 to 1.32 lbs. per sq. inch of piston to operate en-
gine without loud. Friction of load, from 2 to 5 per cent
Sore-w Steamer. {Vice- Admiral C. R. Moorsom^ R. N.)
Hull moving 07 | Hotation of screw. . .09 I Hull resistance. 606
Load 063 I Slip of screw 171 | Total x
Locomotives and Railway Trains* See Railways, page 68a.
Friction, developed, in Xjaunoliing of "Vessels.
Experiments made by a committee of Franklin Institute on fViction of launching
vessels gave, when pressure or weight was fVom 2280 to 3560 per sq. foot, a co-
efficient of .0335.
Marine Railway.— To draw 3000 tons upon greased slides a power of 250 tons was
necessary to move it, but when started 150 tons would draw it.
Woollen Machinery. {Dr. Hartig.) When running empty 8. 15 IW^ and at work
32- 97-
The efficiency of the various machines averaging 60.5 per cent.
Friction of* a T<^on-oonden8iixg Steam-ensiiie.
Friction of an Engine. Diameter of cylinder 20 ins. by 40 ins. stroke of pistoik
Revolutions, 15 to 70 per minute.
Engine, unloaded, 2 lb& per sq. inch = x.86 to 8.69 H*.
Stiafling, uuloaded, 2. 5 to 45 lbs. per sq. inch = 2.36 to io.6x "
Total 4.5 to 6.5 lbs. per sq. inch = 4.2a to 88<3 **
FUBL. 479
FUEL.
With equal weights, where each kind is exposed under like advas-
tageous circumstances, that which contains most hydrogen ought, in its
combustion, to produce greatest volume of flame. Thus, pine wood is
preferable to hard, and bituminous to anthracite coal.
When wood is used as a fuel, it should be as dry as practicable.
To produce greatest quantity of heat, it should be dried by direct ap-
plication of heat ; usually it has about 25 per cent, of water combined
with it, heat necessary for evaporation of which is lost.
Different fuels require different volumes of oxygen; for different
kinds of eoal it varies from 1.87 to 3 lbs. for each lb. of coal. 60 cube
feet of air is necessary to furnish i lb. of oxygen; and, making a due
allowance for loss, nearly 90 cube feet of air are required in furnace of
a boiler for each lb. of oxygen applied to combustion.
Clamfica-
lion
ofOoaL
Seml-bltumlii.. . {^f}"^*
! Caking.
Cherry.
Splint
(betni or gaseous.
Situmin.ou.8 Coal.
Lignite. Brown CoiU or Bituminous Wood. — Presents a (Jistinct woody
structure ; is brittle, and bums readily, leaving a white ash, and cuntains
and absorbs moisture in some cases fully 40 per cent.
Caking. — Fractures uneven, and when heated breaks into small pieces,
which afterwards agglomerate and form a compact body. When the pro-
portion of bitumen is great, it fuses into a pasty mass. This coal is unsuit-
ed where great heat is reouired, as the draught of a furnace is impeded by
its caking. It is applicable for production of gas and coke.
Splint or Hard. — Color black or brown-black, lustre resinous and glisten-
ing. It kindles less readily than caking coal, but when ignited produces a
clear and hot fire.
Ckerry or Soft. — Alike to splint coal in fracture, but its lustre is more
splendent. Does not fuse when heated, is very brittle, ignites readily, and
pn'oduces a bright fire with a yellow flame, but consumes rapidly,
Cannel. — Color iet, or gray or brown-black, coni|iact and even texture, a
shining, resinous lustre. Fractures smooth or flat, conchoidal in every di-
rection, and polishes readily.
Experiments upon practical burning of this description of coal in Airnace of a
Bteam-boiler give an evaporation of from 6 to 10 lbs. of fVesh water, under a pressure
of 30 lb& per sq. inch per lb. of coal; Cumberland (Hd., U. S.) coal being most ef-
fective, and Scotch least.
Limit of evaporation from 9ia° for i lb. of best coal, assuming all of heat
evolved from it to be absorbed, would be 14.9 lbs.
Coals that contain sulphur, and are iq proipress of decay, are liable to spootaneoas
combustion.
There are very great variations in the chemical composition and proper-
ties of coals.
AfMTtcdn.
Carbon, ttora 75 to 80 per cent
Hydrogen, tcom 5 to 6.
Oxygen, fi-om 4 to la
Nitrogen, fh>m z to 2.
Sulphur, flrom .4 to 3.
Ash, fliQin 3 to la
Coke, from 48.5 to 79.5.
Brititk.
Carbon, from 70 to 91 per eeni.
Hydrogen^ from 3.5 to nearly 7.
Oxygen, flrom about . 5 to 2a
Kitrogen, from a mere trace to a.s.
Salphur, (h>m o to 5.
Ash, from .3 to 15.
Coke, flrom 49 to 93.
For Volume of Air, etc^ see Combustion, page 465.
48o
FUBI..
Goal*
AntlxrsMjite.
Anthraciie or Glance CoaL, or Culm — Is hard, compact, lustrous, and some-
times iridescent, most perfect being entirely free from bitumen ; it ignites
with difficulty, and breaks into fragments when heated.
Evaporative power, in furnace of a steam-boiler and under pressure, is
from 7.5 to 9.5 lbs. of fresh water per lb. of coal.
Coal from one pit will sometimes vary 6 per cent, in evaporative value.
i^metUs of Various A merican Coals.
Earthy
Matter.
Pm-
C«ai.
— _ ^ 5.a
Illinois, Warren Co.
Bureau '*
Mercer "
Indiana, Clay '^
Cooprlders
Pennsyl- \ Connellsville
vania ) Yongliiogliciiy . . .
Fayette Co
Kentucky, Sardric
Mud River
Ohio, NelsoDville
Colorado. Carbon City
Washington Territory
Specific
Fixed
Volatile
Moiat-
» .. '
Gravity.
Carbon.
MHtter.
Water.
nre.
Aih.
Per
Per
Per
Per
Per
Cent.
Cent.
CenL
Cent.
Cent.
1.23
51-7
*Ii
—
—
—
1.32
57-6
—
XI. 2
2-4
1.26
54.8
31-3
—
8.4
56
1.38
56. 5
32-5
8.5
2-5
Z.38
50.5
435
3
—
4
1.28
65
24
4-5
—
6.5
«-3
55-*
35
X
5.6
1.29
5«
34
3
—
5
1.32
51
42.5
2
—
4-5
1.38
57
37
3-5
—
as
1.27
^H
33-05
6.65
—
X.9
X.2Z
56.8
34-2
4-5
—
4-5
X.33
58.25
3J-7S
7
—
3
Coke.
Coke. — Coking in a close oven will give an increase of yield of 40 per cent,
over cokiiiff in heaps, gain in bulk beiug 22 per cent. Coals when coked in
heaps will lose in bulk.
Cannel and Welsh (Cardiff) coals when coked in retorts will gain from 10
to 30 per cent, in bulk and lose 36.5 per cent, in weight.
Relative costs of coal and coke for like results, as developed by an ex-
periment in a locomotive boiler, are as 1 to 2.4.
Evaporative power in furnace of a steam-boiler and under pressure, is
from 7.5 to 8.5 lbs. of fresh water per lb.
Bituminous coal will vicld from 60 to 80 per cent, of coke. Averaging
66 ])cr cent. It is capable of absorbing 15 to 20 per cent, of moisture.
Heat of combustion lost in cokuig of bituminous coal 40 per cent
Clxarooal.
Charcoal^ properly termed, is not made below a temperature of 536°* The
best quality is made from Oak, Mafde, Beech, and Chestnut.
Wood will furnish, when properly burned, about 23 per cent of coal.
Charcoal absorbs, upon an avera^ of the various kinds, from .8 per cent.
of water for Beech, to 16.3 for Black Poplar, Oak absorbing about 4.28, and
I'ine 8.9.
Evaporative power, in furnace of a boiler and under pressure, is 5.5 lbs.
of fr^ water per lb. of coal.
Volume of air chemically required for combustion of i lb« of charcoal is,
when it consists of 79 carbon, 129 cube feet at 62^.
138 bushels charcoal and 432 lbs. limestone, with 2612 lbs. of ore, will piro-
duce I ton of pig iron.
FUEL.
481
Wood.
Cork
Oak
Beech.
Pine
Poplar roots.
Wood.
Weight.
Larch
Per Cent.
40-31
36.06
34-69
34-59
34-17
CheBtnat
A pple
Elm «..:
Birch
Wood.
produce of Charcoal from Various Woods dried at 300^ and Carbonized
at 572^. {M. VioletU.)
Weight.
Per Cent.
33-75
33-74
33- 61
33.28
3x88
Weight.
Per Ce^t.
62.8
46.09
44-25
41.48
4a 9
Maple
Willow
Black elder.
Ash
Pear
Poplar 3Z.X2 per cent
In a Grem or Ordinary State. ( Weight per cent. )
Apple 23.8
Ash 26.7
Beech 21. i
Birch 24.1
Elm 25.1
Maple........ 22.9
Oak 22.85
*' young... 33.3
Poplar. 2C.S
Red Pine 23
White Pine... 23.5
Willow i8.6
It appears from this that cork, the lightest of woods, yields largest percentage
of charcoal, about 63 per cent. ; and that poplar yields lowest, about 31 per cent.
There does not appear to be any definite relation between density of wood and
volume of yield.
Produce by a slow process of charring is very nearly 50 per cent, greater than by
a quick process.
Xjig-iiite.
Lignite is an imperfect mineral coaL It is distinguished from coal by
its .large proportion of oxygen, being from 13 to 29 per cent Its specific
gravity ranges from 1.12 to 1.35.
Elements of Various A merican Lignites, ( W. M. Barr.)
LocAnoN.
Kentucky
Blandville . . .
Washington Terr'y . . . .
Vancouver's Island. . . .
Colorado, Carbon City . .
Canon City . .
Arkansas... 1
Tesuis, Robertson Co. . .
Spec.
Flzed
Volatile
Total
Grav.
Carbon.
Matter.
Water.
Ash.
Volatile.
Percent.
Percent
Per Cent.
Per Cent.
Per Cent.
X.2
40
23
30
7
53
1. 17
31
48
xi-5
9-5
59-5
38.75
— -
58.25
3«-75
7
3
—
62
35
4
3
35
X.27
^I'l^
46
3-5
9-25
38.7
x.a8
56.8
34-2
4-5
4-5
—
34-5
28.5
32
5
60.5
1.23
45
39-5
XX
4-5
S0.5
Coke.
Per Ceut.
47
405
61.25
65
50-5
61.3
39-5
4^5
A. s p li al t U.ZX1 .
A^haUum contains 1.65 to 10.09 P^^ <^^^ ^^ oxygen.
Wood.
Woodj as a combustible, is divided into two classes, the bard, as Oak, Ash,
Elm, Beech, Maple, and Hickory, and soft, as Pine, Cotton, Birch, Sycamore,
and Chestnut
Green wood subjected to a temperature ranging from 340° to 440° will
lose 30 to 45 per cent, of its weight.
At a temperature of 300°, Oak, Ash, Elm, and Walnut, in a comparatively
seasoned state, lost from 16 to 18 per cent.
Woods contain an average of 56 per cent, of combustible matter.
From an analysis of M. Violette it appears that composition of wood is about
same throughout the tree, and that of the bark also; that wood and bark have about
same proportion of carbon (49 per cent.), but that bark has more ash than wood.
Xieaves and small roots have less carbon than wood (45 per cent.), and more ash,
5 and 7 per cent
Leaves when dried at 2x2^ lost 60 per cent of water, and branches 45 per cent
Ss
482
FUJBL.
Evaporative power of i cube foot of pine wood is equal to that of x cabe
foot of fresh water ; or, in the furnace of a steam-boiler aud under pressure,
it is 4.75 lbs. fresh water for 1 lb. of wood.
Northern Wood. — One cord of hard wood and one cord of 90ft wood, such
as is used upon Lakes Ontario and Erie, is equal in evaporative effects to
sooo lbs. of anthracite coal.
WesUifi Wood.'— Out cord of the description used by the river steamboats
is equal in evaporative qualities to 12 bushels (960 lbs.) of Pittsburgh coaL
9 cords cotton, ash, and cypress wood are equal to 7 cords of yellow pine.
Solid portion (lignin) of all woods, wherever and under whatever circum-
stances of growth, are nearly similar, specific gravity being as i^^6 to 1.53.
Densest woods give greatest heat, as charcoal produces greater heat than
flame.
For everv 14 parts of an ordinary pile of wood there are 11 parts of space ;
or a cord of wood in pile has 71.68 feet of solid wood and 56.32 feet of voids.
Trees in the early part of April contain so per cent more water than they
do in the end of January.
Proportion of Ash in 100 Lbs. 0/ several Woods.
Woons. Wood. Lmves. Woods. Wood. Lmtc*.
Ash. . .
Beech.
Birch .
P«r Cent
.5
•35
•34
PerCant.
5-4
5
Elm ,
Oiik. ,
Pitcb PineL
Percent.
Z.88
.91
as
Per Cent.
1X.8
4
3«5
Peat.
Peat is the organic matter, or soil, of bogs, swamps, and marshes— decayed
moss, sedge, coarse grass, etc. — in beds varying from i to 40 feet in depth.
That near the surface, and less advanced in transformation, is light, spongy,
and fibrous, of reddish-brown color ; lower down, it is more compa<^ of a
darker brown color ; and, in lowest strata, it is of a blackish brown, or almost
black, of a pitchy or unctuous surface, the fibrous texture nearly or alto-
gether transformed.
Peat, in its natural condition, contains from 75 to 80 per cent, of water.
Occasionally its constituent water amounts to 85 or 90 per cent., In which
case peat is of the consistency of mire. It slirinks very nmch in drying ;
and its specific gravity varies from .22 to j.o6^ surface peat being lignteat,
and deepest peat densest.
When peat is milled, so that its fibre is broken up, its contraction in dry-
ing is much increased, and in this condition it is termed condemf-d.
When ordinarily air dried, it will contain 20 to 30 per cent of moisture,
and when effectively dried at least 15 per cent
Products of Distillation of P^at,
Water 31. 4. Tar 2.8* Gas 36.6. Charcoal 29.2.
The distillation of the tar will yield parafiine, oil, gas, water, and chai^
coal, and the water acetic acid, wood spint, and chloride of ammonia.
Evaporative power, in furnace of a steam-boiler and under prtasurei ia
from 3.5 tc 5 lbs. of fresh water per lb. of fuel.
Tan.
Tan, oak or hemlock bark, after having been used in the prooeaa of tan-
ning, is combustible as a fuel. It consists of the fibre oS. the bark, and,
aocordhig to M. Peclet, 5 parts of bark produce 4 parts of dry tan ; and
heating power of it when perfectly dry, or containing but 15 per cent of
ash, is 6100 units ; while that oC tan in an ordinary state of dryness, con-
toiiiing 30 per cent of water, is 4284. Weight of water evaporated at 21a*
W I lb., equivalent to these ooits, is 6w3x Iba. for dry, and 4^4 for moist
VtTBL.
483
Relative V^ues of difibrent 'P'xielm.
Dmemunom. J^uS '^^^ "£>
Peach Mountain, Pa.
Beaver Meadow . . . .
Bituminous.
Newcastle
Pictou
Liverpool
Canneltou, lud
Scotch
Pine wood, dry
t^i
CO h^
•si**
-^.^
•S^r
5
PS
ia7
z
9.88
.923
8.66
.809
8.48
.792
7.84
.733
7-34
.686
6.95
.649
4.69
.436
.982
.776
.738
.663
.616
.625
175
=^g
§
■^50
It
.505
.633
.725
•945
.207
.748
.6
X
.595
588
.887
.418
.346
I
!i^6
.581
z
.333
.852
X
.984
'578
.848
.52X
•499
•649
.909
—
16.4x7
-*.
—
AVeislitSy K-vaporative Po^vtrers per Weietlit and Hulk
etc., of* difiereixt Fuels. (TT. R. Johnion and others.)
FVIIm
BlTmUNOUB.
Camberland, naximum
*' minimum
DaflVyn
Cannel, Wigan
BlossburKh
Midlothian, screened
average
Newcastle, Hartley
Pictoa i
Pi t tabu rgh
Sy d ney •
Carr'8 Hartley
Clover Hill, Ya
Canneltou, Ind
Scotch, Dalkeith
Chill
Japan
AHTHBACITS.
Peach Moantatn
Forest Improvement
Beaver Meadow
Lackawanna
Beaver Meadow, No. 3
Lehigh
Cork.
Natural Virginia
Midlothian
Cumberland
MiSOBLLANBOUS.
Charcoal, Oak...
Peat
Warlich'sftiel
Wylam's '^
Pine wood, dry '.
Specifle
Gravity.
I-3>3
'•337
1.326
X.23
x.3a4
1.283
1.494
X.257
X.318
X.252
1.338
X.362
X.28S
1.273
«.5»9
X.231
X.464
«'477
1.554
X.42X
x.6x
X.S9
1-323
x-5
•53
1. 15
Weight
Steam from
Water at
per
Cbba Foot.
SIS* by 1 lb.
of Fuel.
Lbt.
Lb*.
52.92
xa7
54-29
9-44
53-22
10.14
48.3
7-7
53-05
0.72
8.94
43.72
54-04
8.39
50.82
8.76
49-25
8.41
46.81
8.2
47.44
7-99
7.84
47.88
45-49
7.67
47-65
7'H
51.09
7.08
—
572
48.3
53-79
xaxi
53.66
iao6
56.19
9.88
•48.89
9-79
54-93
0.3I
8.93
55.32
46.64
S-*'
32.7
8.63
31.6
8.99
«4
5.5
09.x
5
'0.4
65
8.9
»i
4-7
Clinker
Cube Feet
from 100 Ibe.
iu a Ton.
Lbt.
No.
2.13
42.3
4 53
41.2
—
42.09
—
46.37
3-4
42.3
3.33
49
8.82
41 4
3-14
44
6.13
^5„
.94
47-8
2.35
47.2
1.86
46.7
3.86
49- 2
x.64
^7«
5-63
43-8
—
*—
—
■"~
303
41-6
81
398
.6
1.24*
45-8
X.OI
40.7
X.08
40.5
5-31
48.3
10.51
68.5
3 55
70^9
A«h.
3.06
104
—
75
2.91
3244
—
— f
•31
X06.6
484
FUEL.
Weiyhta and ComparcUive Values of different Woods,
Woods.
Sbell-bark Hickory .
Red-heart Hickory .
White Oak
Red Oak
Virginia Pine
Southern Pine
Hard Maple
Cord.
Value. 1
Lba.
1
4469
I
3705
.81
3821
.81 ;
3254
.69
2689
.61
3375
•73
2878
.6
Woods.
New Jersey Pine.
Yellow Pine
White Pine
Beech
Spruce
Hemlock
Cottonwood
Cn.4 t Vain*.
Lbs
2»37'
1904
1868
•54
•43
•42
•7
.52
•44
•33
Xiiquid. IFuels.
Petroleixxxi.
Petroleum ia a hydro-carbon liquid which is found in America and Europe.
According to analysis of M. Sainte-CIaire Deville, composition of 15 ))etro-
leums from different sources was found to be practically constant. Average
specific gravity was .87. Extreme and average elementary composition was
as follows :
Carbon 82 to 87. i per cent. Average, 84.7 pei- c^uk.
Hydrogen 1121014.8 " " 13.1 '^
Oxygen 5 to 5.7 " " ^.2 "
• 100
Its heat of combustion is 20^40, and its evaporative power at 212^ 20.33.
Petroleum Oils — Are obtained by distillation from petroleum, and are com*
pounds of carbon and hydrogen, in average proportioti of 72.6 and 27.4.
Boiling-point ranges from 86*^ to 495°.
Schist CH7— Consists of carbon 80.3 parts, hydrogen 11.5, and oxygen 8.2.
Pins Wood Oil — Consists of carbon 87.1 per cent,, hydrogen 10.4, and
oxygen 2.5.
Coal-gas.
Coal Gas — As furnished by Chartered Gas Co. of London is composed as
follows :
Oleflant Gas, )
Bi-carb.hyd. { "
Marsh gas, )
Carb. hyd. J * * * *
Carbonic oxide....
Carbon. ,Hydro(i^n.
3.096
26.445
3.84
•434
8.81S
5-"
Hydrogen . . .
Oxygen
Nitrogen.....
Oxygen.
Hydrogen.
.08
51-8
Nitrogen.
.38
Total xooparta
Heat of combustion at 212° 52 961 units, and evaporative power 47.51 lbs.
Coal-gas. [V. Harcourt.)
Oleflant gas
Marsh gas
Carbonic oxide. .
Carbonic dioxide
Cftfb.
Hyd.
Per ct.
Oxy.
Nit.
Per ct.
Per ct.
Per ct.
IO-5
'•7
—
—
39-7
13-2
—
5-9
—
7-9
—
1.9
^■"
5
^■^
Carb.
Per ct.
58
Hyd.
Oxy.
Hydrogen
Nitrogen
Oxygen
Perct.
8.1
Perct.
•3
Total
23
13-a
Nit
Perct.
5~8
"78~
One lb. of this gas had a volume of 30 cube feet at 62° ; heat of combn»-
tion 22684 units; and of one cube foot 756 units, which is equivalent to
evaporation of .68 lb. of water from 62°. or of .78 lb. from ii2° per cube foot.
wmu
485
Average Composition, of Fuels,
BITUMTNOU8 Ck)AL&
Aaetralian
Borneo
British, lowest
Boghead, dry, average
Chili, Conception Bay
" Chiriqai
Cannel, Wigan
Cumberland, Md
Coke, Garesfield
*' Durham
'' Average
Dofifryn
Formosa Island
French, hard
" caking
*' k>ng &ime
** average*
Indian^ average
" Kotbec
Patagonia.
Russian, Miouchif
Sydney, & W
Splint, Wylam
Glasgow
Cannel, Lancashire .
" Edinburgh.
Cherry, Newcastle. .
Caking, Garesfield . .
Ebbro Vale, Welsh..
IJangcnneck *' ..
Vancouver's Island
t(
tc
(I
t(
ii
I<
Anthragitbs.
Anthracite
French
Russian
Woods.
Beech....
Birch ,
Oak ,
White Pine ,
Woods, average. ,
Charcoal.
Oak ,
Pine ,
If aple
M1SCBLLANK0U&
Asphalt
Lignite, perfect.
imperfect
bituminous . . . .
Colorado
Kentucky
Arkansas
Peat^ dense ~
*^ Irish, average
Patent, Warlich
" Wylam's
4i
(I
i(
t(
it
Specific
Grav-
ity.
Carbon.
Hydro-
gen.
Nitro-
Ken.
Oxygen.
Sal-
pbiir.
Per ct.
Per ct.
Per ct.
Per ct.
Per ct.
I- 31
—
—
—
—
•5
1.28
64.52
4.76
.8
20.75
1-45
—
68.72
—
18.63
1-35
1.18
6394
8.86
.96
4-7
•32
1.29
70.55
5.76
•95
13-24
X.98
38.98
4. ox
.58
13-38
6. 14
1.23
7923
6.08
1. 18
7.24
1-43
x-3«
93.81
1.83
—
2.77
—
—
97.6
—
—
—
■85
—
89.5
—
—
—
X.25
—
93-44
—
•^
—
X.2»
1-33
88.26
4.66
1-45
.6
1.77
1.24
78.26
5-7
.64
10.95
•49
1.32
88.56
4.88
( 4.38)
1.29
87.73
5.08
( 565)
—
1-3
82.94
5-35
( 8.63)
—
1.31
«S
4.5
( 7 )
—
~"~
47-3
62.25
—"
~"~
•■"
"^
—
5.05
.63
17-54
i->3
—
01.45
82.39
4.5
( 405)
—
—
532
1.27 1 8.33
.07
—
74.83
6.18
( 5-09)
—
—
83.92
5.49
(10.46)
—
—
8375
5.66
( 8.04)
—
—
67.6
5-4
(12.43)
—
—
84.85
505
( 8.43)
—
—
8795
5-24
( 5.42)
—
—
89.78
5. 15
3.16
•39
X.03
—
84.97
4.36
1-45
V7
.43
""^
66.93
5.32
X.03
3.2
x-5
88.54
_„
___
_^
•52
«-5
86.17
2.67
( 2.8s)
96.66
X.35
( I
99)
^^
.^
50.17
6.13
X.05
40.38
— _
—
48.13
6-37
'^5
43-95
—
—
48.13
5-25
.83
445
—
—
49.95
6.41
—
43-65
—
—^
49-7
6.06
x.05
41-3
_
87.68
2.83
_
6.43
—
71-36
5-95
—
22.19!
..^
"~"
70.07
4.61
~~
24. 89!
"^
X.06
79.18
9-3
( 8.72)
->
x.2q
69.02
5.05
(8ai3)
—
1.25
60. x8
5.29
( 29.03 )
—
1.18
74.82
7.36
(13-38)
—
1.28
56.8
—
—
—
X.2
40
—
—
—
—
345
—
—
—
—
—
6x.o2
5-77
.8z
32.4
—
.528
58.18
5.96
X.23
3I.2X
—
IIS
9a 02
556
— -
—
X.62
X.I
79.91
569
X.68
6.63
X.25
Aih.
Per ct.
8.38
7-74
21.22
7-52
36. OX
4,84
X.6
1-55
9-25
5-34
336
396
3.19
1-54
3.08
3-5
32.9
4
13-4
3.04
13-91
I- 13
2.55
14-57
X.67
1-39
1-5
5-4
15-83
8.67
8.56
1-77
•48
1-3
•31
X.8
3.06
•4
•43
2.8
5.83
5-57
4-45
4*5
7
5
3-43„
2.91I
4-84
* He«t of Combostion of x Lb. 14 733.
X laelndlng Nitrogen.
Ss*
t Heat of Combtutlon of x Lb. 15651.
I Inciadiog Ozygeo*
486
FUEL.
Average Oompoiiition of* Coals and Fuels, Heat of Com<
l^iastioxi, and Kvaporative Povp^er.
Deduced from analytU and fxperimnUs o/Jietsrt. De La Biche, Plaffairy cmd Peetet
COAW A«D I^ILS.
cOg
Coi(P06inoif.
Carbon.
I 29
1.27
1.26
1.26
1.28
Derbysbire and)
Yorksbire . . . . j
Tiftnoasbire
Neweaatle
Scotob
Welsh
Ayerage of British.
Patent fbels. ' 1.17
Van Diemen's Land
Chili
Lignite, Trinidad..
" French Alps
" Bitnm.,Ciiba
♦' Wasb.Ter*.
Asphalt
Petroleum
•' olla....
Oak bark Tan, dry.
♦* •* moist
Charcoal at 302*3. . .
(1
ti
57a'
810°.
Peat, dry, average.
" moist, t
Coal-gas....
It
1.28
1.2
I 06
.87
•75
«-5
14
1.71
•53
42
Per et.
79.68
77-9
82.12
78.53
83.78
80.4
83.4
65.8
63.56
65.2
70.02
75-85
67
79.18
84.7
475'
7324
81.64
58.18
43 «
3338
Hydro-
Ren.
Peret.
4-94
539
5-31
5.61
4-79
5-19
4 97
3-5
5-43
4.25
5- a
7-25
4-55
9-3
i3^«
6. IS
4-«5
4.96
59*
66! 16
Nitro-
gen.
Per ct.
1.41
x-3
I- 35
X
.98
X.21
1.08
«-3
.82
'•33
Sul-
plinr.
Per ct.
l.ox
«-44
1.24
x.ix
'•43
'•as
X.26
X.I
2.5
.69
Oxy-
gen.
Pepct
ia28
9-53
5.69
9.69
4->5
7.87
2.70
5.58
14.84
21.69
2.2 ^^
(OandN 46.29)
(Oand N 21.96)
(OandN 15.34)
1,23 I — |3'-2»
( 0 and N 21.4 )
.38 I — I .08
^ Muistnre 27.8.
± M
9^
SH
Aeh.
0 0
OS
1^-
Peret.
UBlt*.
Lbs.
2.65
X3860
«4-34
4.88
13 018
14890
X4.56
3-77
«5-3a
4-03
'♦i^
"4-77
4.9X
14858
"5-52
4-Q5
l43«o
14.82
S-93
150Q0
15-66
22.71
1x320
XX. 83
IX.68
13-31
1x030
6.84
X0438
ia87
30X
H790
X2.X
3-94
14568
14.96
3-1
"9538
xa.9x
2.8
»66s5
17.24
^^
20240
90-33
^—
»7 530
610Q
.8.5
15
6.3*
'S
4284
t»*
.8
*ir
8.4
•57
xt86x
12.27
1. 61
14 916
'S43
3-43
995«
8917
10.3
33
9.22
—
529*'
4751
8a1iihup .a.
* Water 7. Oxygen and Nitrogen 17.36.
Klexxxexits o£ ITuels not included in Preceding Xal>Ies.
Bitumintnu CoaL
Welsh ,
Newcastle
Lancashire
Scotch. ,
Boghead
British, average
Irish, lowest
Cumberland, Md. ,
American, average . . . . .
French, average.
Aastrallan
AfUhracUe.
Americar.
French . . .
Miscellaneoui. '
Warlicb's (\jel ,
Coke Mickley
Virginia, ftvenige
Charcoal.
Lignite, perfect ,,...
** imperfect
'* Russian
Asphalt
Woods, dry, average
Heat of
Combustion
off lb
UniU.
14858
14820
X3918
1416^
14478
»4«33
14723
i4 5<»
14038
16495
X5600
X3550
11678
9834
'5837
16555
179?
Evaporatire
Power of I
lb. at 312*,
Lba.
9-05
8.01
794
7-7
7.87
8.13
9-85
14.03
xa.x
XQ^xS
X7.24
8.07
Coke pro-
duced.
Weight
of I
Cub. Foot
Per cent.
IM.
58
54
82
78.3
in
30-94
6x
79.8
64.2
68.27
09.6
84-93
8754
K
93. 78
—
73-5
—
45
47
—
37-5
^~
9
—.
—
•^
Volmneol
X Ton,
Cube Feet
43-7
45-3
45- a
4a
44-52
35-7
424
43-49
40
49-35
69.8
12.7^
- 114
FUEL. — GRAVITATION. 487
!]M[isoellan.eou.0»
Experiment undertaken by Baltimore and Oliio R. R. Co. determined
evai)oratiug effect of i ton of Cumberland coal equal to 1.25 tons of anthra-
cite, and I ton of anthracite to be equal to 1.75 cords of pine wood; aUo
that 2000 lbs. of lAckawanna coal were equal to 4500 lbs. b<Mt pine wood.
One n>. Of anthmclte coal in a cupola niraaee will men (Vom 5 to to lbs. of cast
iron; 8 bushels bttumluoua coal in an air fVimace will melt t ton of cast iron.
Small coal produces lUMUt ^75 effect of large coal of same description.
Experiments by Messrs. Stevens, at Bordentown, N. J., gave following results:
Undkr a pVKimfe ofyt lbs., t lb. pine wood evaporated 3.5 to 4.75 lbs. of water.
I lb. Lehigb coal, 7.S5 to 8.75 lbs«
Bituminous coal is 13 per cent, more effective than coke for equal weights; and
in England effects are alike for equal costs.
RadiatUmfrom JvVi«2.— Proportion which heat radiated ttom Incandescent f\iel
bears to total heat of combustion is,
From Wood..... 4..... .09 | From Charcoal and Peat... 5
I.east consumption of coal yet attained is x.5 lbs. per Iff. It usually varies in
diflbrent engines from 9 to 8 lbs.
Volume of pine wood is about 5.5 times as great as its equivalent of bituminous
coal.
GRAVITATION.
Grayity is an attraction common to all material substances, and
they are affected by it directly^ in exact proportion to their mass, and
inversely, as square of their distance apart.
This attraction is termed terrestrial gravity^ and force with which a
body is drawn toward centre of Barth is termed the weight of that body.
Force of gravity differs a little at different latitudes : the Uiw of variation,
however, is not accurately ascertained ; but following theorems represent it
very nearly :
2^}!Z'^ll,^''2?'th^^les l-a ff'represeniing farce of gravity at lati.
i V^IZ^k S Ihe ^uatori '-^' ^ 45°, ar^ gforc. at otker places,
— / 2H\
Or, 3x171 (lat 45°) (i + •«>5 i33 sin. L) 1 1 —\ = g. L representing latitude^
H height ofeUtntUrti ab&o^ letel qfsea, and R radius oftkirth, both in feet.
NoTS. — If 3 L exceeds 90°, put cos. 180 — 2 L, and R at Equator = 20936063, at
Poles so 853 439, and mean 30 889 746.
Illustration.— What is force of gravity at latitude 45°, at an elevation of 309
feet, and radius = 20900000 feetf
/ aH \
3a. 171 (I + .005 133 sin. 45°) ^i————j = 32.171 X 1.00363 X .99998 = 32.387.
Gravity at Various LoetHiaru at Level of Sea,
Equator. 33.088 I New York 32. 161 I I/)ndon 32. ^89
Washington 33. 155 I Lat. 45° 33. 171 | Poles 32.253
In bodies descending freely by their own weight, their t^locities are as
times of their descent, and tpdcei pAsaed tiirough as square of the times.
TVmM, then, being t, 9, 3^ 4, etc., Velocities will be i, 2, 3, 4, etc.
Spaces passed through will be as square of the velocities acquired at end
of those times, as i, 4, 9, 16^ etc. ; and spaces to: ^acb time as i, 3, 3, 7, 9, et^
488
GRAVITATION.
A body falling freely will descend through 16.0833 ^^^ ^^ first second of
time, and will then have acquired a velocity which will carry it through
32.166 feet in next second.
If a body descends in a curved line, it suffers no loss of velocity, and the
curve of a cycloid is that of quickest descent.
Motion of a falling body being uniformly accelerated by gravity, motion
of a body projected vertically upwards is uniformly retarded in same manner.
A body projected perpendicularly upwards with a velocity equal to that
which it would have acquired by falling from any height, will ascend to
the same height before it loses its velocity. Hence, a body projected up-
wards is ascending for one half of time it is in motion, and descendiag the
other half.
Varioiu Formtdas here given are for Bodies Projected Upwards or
Falling Fredy, in Va,cuo.
When^ "however^ weight of a body i» grecU compared vnth Us volume, cmd velocity
of it is loWy deductions given are si^cienUy accurate far ordinary purposes.
In considering action of gravitation on bodies not far distant from surfkce of the
Earth, it is assumed, without sensible error, that the directions in which it acta are
parallel, or perpendicular to the horizontal plane.
A distance of one mile only produces a deviation Arom parallelism less than one
minute, or the 60th part of a degree.
Relation of* Tixiae,
Space, axid
Velocities.
Time from
Velocity acqaUred
Squares
Space fallen
Soaces
Spaoe fkllen
Beeinuhig of
D«went.
at End of that
of
through in that
Time.
%t
thronrii in last
Second of Falk
Urn*.
Time.
this Time.
Seconds.
Feet.
Seconds.
Feet.
No.
Feet.
z
32.166
X
16.083
z
16.08
2
64333
4
64333
3
48.25
3
965
9
»44-75
5
80.41
4
128.665
16
257-33
7
112.58
5
160.832
25
402.08
9
'44-75
6
193
36
579
788.08
zz
176.9Z
I
225. 166
19
13
209.08
257-333
^
1029.33
>5
241.25
9
289.5
8z
1302.75
17
273-42
10
321.666
100
1608.33
19
30558
and in same manner this Table may be continued to any extent
"Velocity acquired. d.\xe to given !II!eigb.t of B^all and
Xi;eigh.t due to given Velocity.
S.o4y/h = t> ; 32.2 < = i> ;
64.4
= A; and 16.083 <2 — A*
h representing height offdIX in feet^ v velocity acquired in feet per second^ and t
time of fail in seconds.
To Compute -Auction of GJ-ravity.
Time.
When Space is given. Rule.— Divide s^iace by 16.083, ^^^ square root
o£ quotient will give time.
ExAMPLB.— How long will a body be in falling through 402.08 feet?
V402.o8 -r- 16.083 =r 5 seconds.
When Velocity is given. Rule. — Divide given velocity by 32.166, i»ad
quotient will p:ive time.
F.XAMPLB.— How long must a body be in fulling to acquire a velocity of 800 feet
"^r second ? 800 -;- 32. 166 = 24. 87 seconds.
GBAVITATION. 489
When Space u given. Rule. — Multiply space in feet by 64.533, and
square root of product will give velocity.
Example. —Required velocity a body acquires in descending through 579 feet
V579 X 64. 333 = 193/eet
Vehcity acquired at amy period is equal to twice the mean velocity during
thai period.
Illustration.— If a ball fkll through 2316 feet in 12 seconds, with what velocity
wiU it striker
2316 -^ 12 = X93, mean velocity^ which X a = 386/^ = vdocUy.
When Time is given, Hule. — Multiply time in seconds by 32.166, and
product wiU give velocity.
ExAicPLB.— What is velocity acquired by a foiling body in 6 seconds?
32.166 X 6 = i92.996ye«t
Bpaoe.
When Velocity is given. RuiJS.— Divide velocity by 8.04, and square of
quotient win g^ve distance fallen through to acquire tluit velocity.
Or, Divide square of velocity by 64.33.
Example.— If the velocity of a cannon-ball is 579 feet per second, ttom what
height most a body foil to acquire the same velocity?
579 -4- 8.04 =: 72-014, and 72.014' = 5186. 02 ^«t
When TVme is given. Rule. — Multiply square of time in seconds by
16.083, and it wiU give space in feet.
ExAMPLK. — ^Required space follen through in 5 seconds.
53 = 25, and 25 X 16.083 = M^-oSJeeL
Distance follen through in feet is very nearly equal to square of time in fonrtiis
of a second.
Illustration l— A bullet dropped ftom the spire of a church was 4 seconds in
reaching the ground; what was height of the spire?
4 X 4 — 16, and j6' = 256/^
By Rule, 4 X 4 X 16.0833 = 2S7.33/e<f.
2.— A bullet dropped into a well was 2 seconds in reaching bottom; what is the
depthof the well?
Then 2X4 = 8, and 8^ = 64/eet
By Rule, 2 X a X 16.0833 = 64.33 fut
Bjf Iwoertion—ltk what time will a bullet foil through 256 feet?
-^256 = 16, and 164-4 = 4 seconds.
Spaoe fbllen tlxroutflx in last Second of* IHall.
When Time is given. Rule. — Subtract half of a second from time, and
multiply remainder by 32.166.
ExAMPLN.— What is QMUse foUen through in last second of time, of a body foiling
for loaeoonds?
10 —.5 X 3«' «66 = 305. 58 feel
Proxnisouous Bxamples.
z. If a ball is i minute in foiling, how for will it foil in last second?
Space foUen through = square of time, and x minute = 60 seconds.
60' X 16.083 = 57 S6&/eet for 60 seconds. .
S9«X 16.083 = 55 9»4 " ** S9 "
1 914 I
s. Compute time of genenting a velocity of 193 feet per second, and whole space
detcended.
193-^32-166 = 6 jecondt; 6' x 16.083 = 579 ^ixt
>/
49© GRAVITATION.
3. If a body was to fiiU 579 feet) what time would it be in foiling, and how fhi
i^Qld it foU in the last fieooad ?
^Z2^ = -^3$ - 6 ie«m<(», and 6 — .5 X 33. 166 ^ 5, 5 X 33- 166 = I76.9X /«t
B^OFxn.'alas to determine tlie various Kleznexits.
„ / V \« V« VT gT9 _, . «. .
" ^ = (lj^) ' =1^* =T' =V' =^ -^^^ 3 ft=(T^.S)»
T refyreienftn^ Mm« of falling in seconds^ V velocity aegtitlmt <n /;«< jp^y ««OMidL
8 ipace or veri%«s^ heigJU tn/oe^ h ipacejuUm tkr^ugh in latt «9Mnd, 039.166 and
. 5 g and . 35 g representing 16.083 and 8.04.
Retarded Sk^otion*
. A body projected vertically upward is affected inyersely to ita motion
when falling freely and direc^y downward, inasmuch as a lute cause rotarda
it in one case and accelerates it in the other.
In air a ball will not retqm with same velocity with which it started. In
V(icu6 it would. Effect of the air is to lessen its velocity both ascendiug and
descending. Difference of velocities wiU depend upon relative specific grav-
ity of ball and density of medium through which it passes. Thus, greater
weight ci ball, greater its velocity*
To Compnte Motion of Q-ravity "by a Bocly prcdeoted
XJp"warcl or .I>o"WT»."ward. vritb- a given "Velocity.
Spevoe.
When projected Uptoard. Rule. — From the product of the given veloei^
and the time in seconds snbtraet the product of 3s. 166, and half the square
of the time, and the remainder will give the space itl feet.
Or, Square velocity, divide result by 64.33, and quotient will give space
in feet.
ExAMPLB.~If a body te projected upward with a vdocity (^96.5 feet per second,
through what space will it ascend before it stops?
96. 5 -r- 32. 166 = 3 seconds = time to acquire this velocity.
Then, 96.5 X 3-^ ua-J^e X^j » 889.5 -* X44'75 =« ^AA-fSfstL
Time.
Rnij|,-^Divide velocity in feet by 32.1^^ and quotient will giy^.time in
i^condjs*
ExAMPLi.— Velocity as in preceding exampla
^ 5 -^ 38* 106 sa 3 ie«oilda
"Velocity.
Rule. — Multiply time in seconds by 32.166, and product will ^ve velodtf
In feet per second.
EzAXPLi.— Time as in preceding example.
3 X 32. x66 = 96. 5 fset vehcttg.
Space fallen through in la9t Second.
Rule. — Subtract .5 from time, multiply remainder by 32.166, and prodnol
will give space in feet per second,
EzutPUL— Time as in preceding example.
3 — • 5 X 3a. x66 = a. 5 X 3«. 166 = 8o.4i6/«t
GKAVITATION. 49I
When projected Downward.
Space.
Rule. — Proceed as for projectioii upwards and take sum of products.
ExAHPLB I.— If a body is projected downward with a velocity of 96.5 feet per see*
end, through what space will it fall in 3 seconds?
965 X 3+ (32166 X y) = «89.s+ 144.7s = 434.a5>fcrf.
Or, «« X 16.083 + t>X< = *.
3. — If a body is projected downward with a velocity of 96.5 feet per second,
throagh what space must it descend to acquire a velocity of 193 feet per second^
96.5 -f- 33.166 = 3 secondgy time to acquire this velocity.
193 -^ 32. 166 = 6 seconds J time to acquire this velocity.
Hence 6^3 = 3 seeonds^time of body f ailing.
Then 96.5 X 3 = 389.5 z=.prod%ict of velocity of projection and time.
16.083 X 3'= 144-75 = product 0^33.166, and half square oftimt.
Therefore 989. 5 -|- 144. 75 = 434. 35 feet
Time«
Rule. — Subtract space for velocity of projection from space giren, and
remainder^ divided by yelocity of pTojection, will giv» time.
ExAMPLB.— In what time will a body fall throagh 434.35 feet of space, when pro-
jected with a velocity of 96. 5 feet ?
Space for velocity of 96.5= 244.75/^
Then, 434.35 — 144.75-i- 96.ssra89.5-i- 96.5=3 Mcoiidl.
Velocity .
Rule. — Divide twice space fallen through in feet by time in seconds.
EatAMPLB. — Elements as in preceding example.
Space fallen through when prqjeeled ai velocity of 96. sfeet ^^ 144. 75 fe^, and 434. 35
feet = space faUen throi^fh in 3 eeoonds.
Then, 144.75 + 434'a5 =3 579 feet space (iUlen through, and V579 ^16.083 3:6
seconds. .
Hence, 579X3^6 = tr58't-6=ri93/erf.
Space' S^allexi tlirough in last Second.
Rule. — Subtract .5 flrom time, multiply remainder by 33.166, and product
will give space in feet per second.
ExAMPLB.— Elements as in preceding example.
6— .5 X 3a->^= 5-5 X 33.166 = 176.91 feet
Ascending bodies, as before stated, are retarded in same ratio that descending
bodies are accelerated. Hence, a body projected upward is ascending for one hair
of the time It is In motion, and desoendtog the other halt
Illustration i.— If a body projected vertically upwards return to earth in 13
seconds, how high did it ascend ?
The body is half time In ascondiDg. la -^ 3 2 6.
Henoa, by Bttle,.p. 489, 6'X 16.083=579 feetasprodstet i^f square of time and
16.083.
X— If a body is projected upward with a velooity of 96.5 feet per second, it is
required to ascertain point of body at end of zo seconda
96.5-^-38.166=: 3 teconds. time to acquire thie velocity t and s'X 16.083 = 144.75
feet, height body reached with its initial veloeity.
Then 10— 3= 7 seconds left for body to fall in.
Hence, by Rule, as in preceding example, 7* X 16.083=788.07, and 788.07—
144.75 = 643. 3s feet 3s disUmwe below point ofpri^eetion.
Or, 10' X 16.083 ^ t6o8.3/«e^ space faUni through w^dier the ej^set ofgraM^. an''
g6.5 X io=965>W, jpooe \f gravity did not act, He»ce 1608.3 --965 = 643.3/ff
49^ GRAVITATION.
?.— A body is prq|ecte<l vertically with a velocity of 135 foet: what velocity win
iaveat6ofeet?
i35«-r-64.33 = 283.3/<^ 'P<tce projected at that vdocUy^ 135 -r- 33. 16 =54. 197 tee-
ondsz=.tiine of prqjeclion, and 283.3 — 60 = 223. 3 = apace to be passed through ajier
aUainnunt of 60 feeL Hence, V233.3X 64.33 = x »9- 85 fset vdoeUy, and 233. 3 -f 60
= 283.3/«;«t
By Inversion.— Velocity 1x9.85. Hence, ''^ ^ = 223.3 fi^ muse, and 283.3 —
04.33
223.3 = 6oyfee<.
ForxAulas to X>eterxnine IClexnents of Retarded Af otlon.
X. » = V-p7 2. V=-|-— . 3- y^v-^gl
t 2
4. <'=^^. 5. 8 = V«-i^. 6. »="T-7:^'-.s».
2 ^ ^ g N 9^^ g
V representing velocity at expiration of time, t amy less time than T, f less time than
t, s space th rough which a body ascends in Hme ^ Y, T, S, and ha^in previous formu-
las, page 49a
iLLusTRATioir.— A body projected upwards with a velocity of 193 feet per Deoond,
was arrested in 5 seconds. _ ,
T=:o, c =x.
X. What was its velocity when arrested? (i.)
2. What was the time of its passing through 562. 92 feet of space ? (8. )
3. What space had It passed through ? (5. )
4. What was the time of its projection, when it had a velocity of 96. 5 feet ? (4. )
5. What was the height it was projected in the last second of time? (6.)
I. i93-»- 32. 166 X 5 = 32- 17 feet 3. 32.17 -f 32.166 X 5 = 193 velocHy.
56l9?^3»j6«2<5 = „3«to«sr. 4 2213^ = -^^ = 3 ««»<&.
5^2 yj jr t 22,56 32.X66 ^
5. ,93 X 5-32:i51±i!=:56a.92>ket 6. e-jp^-.s x''32.x66 = 48.25
2 jettt
7. S = «i> + flf<»-r-2 = 562. 93 feet a '93 ^ 32- '7 — g seconds.
3x 166
7-
193
^,/_i23! l>^J^?^^6-y/^6:::r^=:KseeondL
V32.x66» 32.X66 ° ^3^ 35 -5 *«»!««.
32.166
G^ravity and ]\Cotion at axi Ixiolination*
If a body freely descend at an inclination^ as upon an inclined plane, by
force of gravity alone, the velocity acquired by it when it arrives at ter-
mination of incllnaticm is that which it would acquire by falling fr^y
Uirough vertical height thereof. Or, velocity is that due to heiglU of in-
clination of the plane.
Time occupied in making descent is greater than that due to height, in
ratio of lengtn of its inclination, or distance passed, to its height.
Consequently, times of descending different inclinations or phines of like
heights are to one another as lengths of the inclinations or planes.
Space which a body descends upon an inclination, when descending by
gravity, is to space it would freely nill in same time as height of inclination
IS to its length ; and spaces being same, times will be inversely in this pro-
portion.
If a body descend in a curve, it suffers no loss of velocity.
If two bodies b^in to descend from rest, from same point, one upon an in-
clined plane, and the other falling freely, their velocities at all eqiud heighta
''>w point of starting will be equal,
GBAYITATION. 493
tLLiTsnunoir— What distance will a body roll down an inclined plane 300 feet
long and 35 feet high in one second, by force of gravity alone?
As 300 : 35 :: 16.083 : 1.34035 yaet
Hence, if proportion of height to length of above plane is reduced firom 35 to 300
to 25 to 600, the time required for body to foil 1.34035 feet would be determined as
follows:
As 35 : 600 :: 1.44035 : 33.166, and 33.166=16.083 X 2 = twice time or space in
which it would /aujre^y required Jmr one ha{f proportion ofhei^t to UngHk.
Or, as — : — :: 1.34035 : 33.166, at above.
' 35 35 ^ -^ ■»
Impelling or accelerating force by gravitation acting in a direction paral*
lei to an inclination, is less than weight of body, in ratio of heicht of in-
clination to its length. It is, therefore, inversely in proportion to length of
inclination, when height is the same.
Time of descent, under this condition, is inversely in proportion to accel*
crating force.
If, for instance, len^h of inclination is five times height, time of making
freely descent at inchnation by gravitation is five times that in whiefa a
body would freely fall vertically through height ; and impelling force down
mclination is .a of weight of body.
When bodies move down inclined planes, the accelerating force is ex-
pressed hjh-T-l, quotient of height -t- length of plane ; or, what is equivalent
thereto, sme of inclination of plane, i. e., sin. a.
Illustration.— An inclined plane having a height of one half it^ length, the space
fallen through in any time would be one half qf that which it would faUjireely.
Velocity which a body rolling down such a plane would acquire in 5 seconds is
80.416 feetk
Thus, 33.166 X 5 = 160.833 ftet, and an inclined plane, having a height one half
of its length, has an angle or sine of zcP. Hence, sin. 30^ = .5, and x6a833 X -5 =
8a4i6/«et.
WoTxaxdaM to Deterxnine vario-as £lexnexits of G-ravita*
tioii on an Inclined Plane.
V«
I. S = .5^T'ctn.a; = ^ ^^ ^ ; =.5TV. 4. y=;«:p^T»'ii. &
a. Vs^TjAta; s= V(a P S lin. a) ; =—. 6. H=---^.
5. S = VT:f .5^T»n».o. Or,
V«
3 g t%n. a
V representing velocity o/prqjeetion in feet per second^ S space or vertical height
of velocity and projection, a an^ of inclination ofj^ne, I lengthy and H height of
plane.
Illustratioh. — Assume elements of preceding illustration. V = 8a4i6, T = 5,
andH^aox.04.
I. sX3a-»66XS'X.5 = aoX'<H/««*- a- sai^^X 5 X .5 = 8oL4i6/Mt
^ .5 X*6!X X 5« "^ aoio4 /<?<<- 7- 4 X SX V^^o4 = 293.42 feet
If projected downward with an initial velocity of 16.083 f^^ P^^ second. V-f-ni
4. 16.083 + 33. 166 X 5 X .5 = ^5/^'
5. 8a4«6 4-i6.o83X5 — •'iX3a«66X5'X.5 = a8i.46/«l
494 GBAVITATIOir.
Illustration.— What lime will it take for a ball to roll 38 fset down an inclined
plane, the angle a = la^ so', and what velocity will it attain at 38 feet flrom its itart-
ing-point?
'=\/^^=N/irSS = *»'*°*^ V = »T»1B.«=3*.66X3..3
X • 2136 = 22. 88 feet per second.
When a body is projected upwftfd it iB retarded in the same ratio that a
descending body is accelerated.
Illustration.— If a body is projected up an inclined plane having a length of
twice its height, at a velocity of 96.5 feet per second,
Then, 1=96. 5 -5-32.166 = 3 «ec<md»' S = .5 32. 166X3' X.5 = 72375 /««*• » =
32.166 X 3 X .5 = 48- 25 feet
Inclined Plane.
Problems on descent of bodies on inclined planes are soluble by formulas
I to 9, page 495, for relations of accelerating forces. Ah a ] n liniinary step,
however, acceleratinflf force is to be determined by multiplying weiglit of
descending body by height of plane, and dividing product by length of plane.
Illustration. — If a body of 15 lbs. weight gravitate fVcely down an inclined
{)lane, length of which is live times height, accelerating force is i5-}-5 = 3 Iba If
ength of plane is xoo feet and height 20, velocity acquired in lUliog firoely (torn top
to bottom of plane would be
'5
Time oocapied in making descent,
« = 8\A^ = 8 >/20 = 3S-776/««t
t = .2SyJ = .25 y/soo = s.S9MComi»,
Whereas, for a finee vertical fall through height of 20 feet, time would be^
tz=2Ul-z=i.ijZ seconds^
32. 160
which is .2 of time of making descent on inclined plane.
Velocities acquired by bodies in falling down planes of like height will all be
equal when arriving at base of plane.
When Length <tf an Inclined Plane and Time qf Free Deaceni art given.
Rule. — Divide square of length by square of time in seconds and by 16 ;
the quotient is height of inclined plane.
EzAXPLB.— Length of plane is 100 feet, and time of descent is 5.59 seconds; then
Tertical height of descent is
——-—^^vffed.
Aooelerated and Itetarded Alotion.
If an Accelerating or Retarding force is greater than gravity, that is,
weight Qf the body, the constant, g^ or 33.166, is to be varied in proportion
thereto, and to do this it is to be multiplied by the accelerating force, and
product divided by weight of body.
Thus, Letf represent acederoHng farce, and 10 weigM of body.
Then, _ii33/ ^^ 3^__/ ^^ >_j — 3/ become the constanta
The Rflme rules and formulas that have been given for action of gravity alone
are applicable to the action of any other uniformly accelerating or retarding force,
'\e numerical constants above given being adapted to the foroei
GRAYITATIOK. 495
A.vera||pe Velocity oi* a Miovine Sody xxxxifbrxxily A.oo.el-
erated or HetArded.
Avenge velocity of a moving body unifonnly acceleiated or retiurded,
during a given time or in a given space, is equal to half sum of initial and
final velocities ; and if body begin from a state of rest or arrive at a state of
rest, its average speed is half the final or initial velocity, as the case may be.
Thus, in example of a ball rolling, initial speed or velocity ifl^ in either
case, 60 feet per second, and terminal speed is nothing ; average speed 10
therefore — ^, namely, one half of that, or 30 feet per second.
When a cannon-tMill is proj^oted at an angld to horiion, there are two forces act-
ing on It at flame tlme^vix., force of charge, which propels it unifonnly in a right
line, and force of gravity^ wbtch eaases it to fall from a right line with an acoel-
erated motion : these two motions (nnirorm and accelerated) cause the ball to move
In the cnrred line of a Parabola
Formulas for Flight of a Cannon-ball,
V = 28oo,/-; P=s-5 ;
V^ 7840000'
- V>8ln.a,coaa ^ Vein, a . V«8ln."a
(s — ; t = : h=: .
w repretenHng ibetg^t ofbaU and P ofprndir in tbs, ; t Hme ofJligJU in tecondt;
b horizontal range^ and h vertical height of range ofprqjection qfbcUl in feet
Illustration. — A cannon loaded to give a ball a velocity of 900 feet per second,
the angle azs4s**\ what is horizontal range, the time t and height of range hf
«=?2i>l^ = .„8««wdi, *=.y°'^W?'i= 6.195 Jtot
32.166 ^* 2X32.166 "■'•'
Note.— As distance b will be greatest when angle 0 = 45°, product of tine and
cosine is greatest for that angles Sia 45<' x voa 45°= S'
•4 lb. ball with a velocity of 2000 feet per second at 45O range 7300 feet
G^eneral IToAuulas for iVcoeleratlns and Retarding
Foroes.
W 10 fff 2gf
V w
2(^8 632.2 ^ V
NoTS I.— When accelerating or retarding force bears a simple ratio to weight of
body, the ratio may, for facility of calculation, be substituted in the quantities rep-
resenting modified constants, for force and weigbt. Thus, if accelerating force Is a
tenth part of weight, then ratio is i to 10, and ^^ — = 3. 3x66 \ or, ^ — ^ s= i.^v
10 * 10
and .±333 _ g ^^^^ . ^^ ij^gg^ quotients may be sabstttated for 16.083, 32. 166, and
64.333 respectively, In formulas for action of gravity i to 9, to fit them for computa-
tion ih an accelerating or retarding force one-tenth of gravity
2.— Table, page 488, giving relations of velocity and height of falling bodies,' may
be employed in solving questions of accelerating force general.
EzAMPLB.— A ball weighing xo lbs. is projected with an initial velocity of 60 feel
Cr second on a level plane, and firictional resistance to its motion is i lb. What dis-
Ace will it traverse before It comes to a state of rest ? By formula 4 :
10 lbs. X 60' ^ ,
64.333 X. lb. °»»»-^
496 GBAYTTATION.
Again, same restitt ma^ be arrived at, according to Note i, by multiplying con-
stant 64.333, in Rule, page 494, for gravity, by ratio of force and weight, which in
this case is ^, and 64. 333 X t'fr = 6.4333- Substituting 6.4333 ^^^ 64. 333 in that
rule, formula becomes
V» 60*
The question may be answered more directly by aid of table for fiUling bodies,
page 488. Height due to a velocity of 60 feet per second, is 55.9 feet; which is to
be multiplied by inverse ratio of accelerating force and weight of body, or -^j or 10;
'**"' '^ 55-9 X 10 = 5S9/««*-
If tlie question is put otherwise— What spaoe will a weight move over before it
comes to a state of rest, with an initial velocity of 60 feet per second, allowing fac-
tion to be one tenth weight? The answer is that flriction, which is retarding force,
being one tenth of weight, or of gravity, space described will be 10 times as great as
is necessary for gravity, supposing the weight to be projected vertically upwards to
bring it to a state of rest The height due to velocity being 55.9 feet; then
55-9 X 10 =ss9 feet.
Average velocity of a moving body, uniformly accelerated or retarded during a
given period or space, is equal to half sum of Initial and final velocities.
T*o Compute Velocity of a Falling Streazxi of Water per
Second at Iiixid of any given Xixne.
When Perpendicular Distance is given.
Example. — What is the distance a stream of water will descend on an inclined
plane 10 feet high, and 100 feet long at base, in 5 seconds f
5* X 16.083 = 402.08.^ = space a body will freely fail in this Hme.
Then, as 100 : 10 :: 402.08 : 40.21 feet = proportionate velocity on a jUane qf these
dimensions to velocity token falling jreeiy.
I^isoellaneouB Illustrations.
s.^What is the space descended vertically by a foiling body In 7 SflOOOda
S=.5yx<'. Then 16.083 X 7' = 788.067 /»«.
9.— What is the time of a fitUing body descending 400 feet, and velocity acquired
at end of that time?
t=z-. Then -^ — ^=z4.d&see. v^VTgxS. Then V64.333 x 400= 160.4 feeL
g 32^ 100
3.— If a drop of rain (kll through 176 feet in last second of its QUI, how high was
the cloud (h)m which it fell?
S = — . Then 2^^^ =482. 75 /eee.
9g 64.166 ^ '^''
4.— If two weights, one of 5 lbs. and one of 3, hanging flreely over a sheave, are
■M free, how fhr will heavier one descend or lighter one rise in 4 seconda
f^ X 16.083 X 4»=^l X 357.3a8 = 64-33/«<-
5 + 3 8
5.— If length of an inclined plane is zoo feet, and time of descent of a body is 6
■econds, what is vertical height of plane or space foUen through?
100' 10 000
6'X.5^ 579
= x'j.vjfeeL
6.—\t a bullet )8 projected vertically with a velocity of 235 (bet per second, what
velocity wiU it have at 60 foet?
» . "35 / »35' 2X60 ^5.
Formal. 9, p.«.49» ^M-\/^,6^—^M=*^^
6UN^£BY. 497
GUNNERY.
A heavy body impelled by a force of projection describes in its flight
or track a parabola, parameter of which is four times height due to
velocity of projection.
Velocity of a shot projected from a gun varies as square root of
charge directly, and as square root of weight of shot reciprocally.
1?o Compute 'Velocity of* a Shot or Shiell.
Rule. — Multiply square root of triple weight of powder in lbs. by 1600 j
divide product by square root of weight of shot ; and quotient will give ve-
locity in feet per second.
ExAXPLX.— Wbat is velocity of a shot of 196 lbs., projected with a charge of 9 lbs
of powder?
V9X 3X 1600 -i-v^i96 = 8320 -7-14 = 594. 3 feet.
To Compute Range fbr a Charge, or Charge for a Range.
When Ba$igefor a Charge ia giren.^Eangea have same proportion as
charges of powder; that is, as one range is to its charge, so is any other
range to its charge, elevation of gun being same in both cases. Consequently,
To Compute Range.
Rule. — Multiply range determined b}' charge in lbs. for range required,
divide product by given cfaar^ and quotient will give range required.
ExAXPLK. —If, with a charge of 9 lbs. of powder, a shot ranges 4000 feet, bow for
wiU a charge of 6. 75 lbs. prqject same shot at same elevation ?
4000 X 6.75 -^9 = 3000 .^t
To Compute Charge.
Rule. — Multiply given range by charge in lbs. for range determined,
divide product by range determine^ and quotient will give charge required.
EzAMPLK.— If required range of a shot is 3000 feet, and charge for a range of 4000
feet has been determined to be 9 lbs. of powder, what is charge required to project
same shot at same elevation ?
3000X9-5-4000=6.7516*.
To Compute Range at one Slevation, when Range for
another is given.
Rule. — As sine of double first elevation in degrees is to its range, so is
sine of double another elevation to its range.
ExAXPLR.— If a shot range 1000 yards when projected at an elevation of 45O, how
Our will it range when elevation is yP 16', charge of powder being same?
Sine of 45° X a = 100000; sine of yP 16' X 2=87064.
Then, as 100 000 : 1000 :: 87064 : 670.64 feet.
To Compute Klevation at one Range, -wrhen Slevation
fbr another le given.
Rule. — As range for first elevation is to sine of double its elevation, so
is range for elevation required to sine for double its elevati(Mi.
ExAMPUL— If range of a shell at 45O elevation is ^750 feet, at what elevation
must a gun be set for a shell to range .aSio feet with a like chaiige of powder?
Sine of 45<^ X 3 = 100 000.
Then, as 3750 : looooo : : 38x0 : 74 933 = rinefor dmMe devotion = 34^ x6'.
Approximate Bute for Time of Flight
Under 4000 yards, velocity of projectile 900 feet in one second ; under
6000 yards, velocity 800 feet ; and over 6000 yards, velocity 700 feet.
Gum and Howitzert take their denomination from weights of their solid
shot in round numbers, up to the 42-pounder ; larger pieces, rifled guns, and
mortars, from diameter of their bore.
Tt»
498
GUNNERY.
Initial 'Velocity and H.feingrBS of Sliot and Shells.
Tbe Range of a shot or shell \b the distance of its flrat gmee upon a horiaontal
plane, the piece mounted upon its proper carriage.
le.
WeiKht.
Abmh and OanNANCB.
rrujeck
DeKription.
Rifle Musket.
Elongated.
Musket, 1841
Round.
6-Ponnd6r. . <
t(
la »* 4.
i(
24 "
(t
02 "
it
42 " :..:::::..
tk
8 inch Coluinbiad...
i«
10 '' "
t«
10 " Mortar.
Shell.
13 '* *'
15 "' Columbiad. . .
((
t(
, . (( t(
n
15 • • •
RIFLBD.
zo-pouDder Parrott. .
n
20 " " ..
(t
JO
i(
iOO " »' ..
Elongated.
100 " " ..
Shell.
200 '\ " ..
11
12- inch Rodman
t(
Hairs Rockets
3-inch.
Graios.
5«o
412
Lbs.
6.13
U.3
2425
323
42.5
65
200
30a
3*5
9-75
19
29
100
xoi
150
Powder.
Initial
Velocity.
Tline uf
Fiigiit.
Eleva-
tion.
R«Bg«.
Grains.
VeeU
SecAndl.
a t
Yarda.
60
963
-♦
—
-^
no
1500
—
Lbs.
(
1.35
*-.
*♦•
$
»S«3
2.5
X826
X.75
X
575
6
X870
a
X147
8
X640
—
z
7»3
10.5
—
—
5
«955
10
—
X4.19
15
3224
«5
•—
^•''
IS
3281
10
—
45
4350
20
—
■*-
45 •
43»5
40
•—
— *
7
2948
50
~~
33.39
as
4680
I
—
31
ao
5000
2
—
17.25
15
4400
3.95
— •
27
as
670D
xo
—
S
as
9^**
10
1250
25
68ao
16
—
—
4
3200
50
"54
55
40
—
—
—
47
1720
16
Penetration of* tShot and Shell.
Experiments at Fort Monroe, 1839, and at West Point, X853.
0
Mean
PBaetral
,lon.
OUONAMCS.
1
0
1
Yds.
13
1
Ins.
Lbs.
Int.
Ins.
32 Lbs. Shot.
8
880
—
i5-«5
3.5
33 " "
IZ
100
60
—
42 " «'
X0.5
100
54-75
18
4
42 " Shell.
7
100
40-75
—
Osdnaucb.
8-inch Howitz *
8 " Columb.>t
10 " " t
10 " '« *
I
Lba
6
IB
18
18
e
Yds.
880
aoo
114
100
Mean PMMinttoo.
1^
Ins.
|-5
0.75
VM
Ins.
8^5
44
I
o
Ills.
X
7-75
* 34 ioa. of Concrete.
• Shell.
t Shot
Solid shot broke against granite, but not against flreestone or brick, and geneml
effect is less upon brick than upon granite.
Shells broke into small fVagments against each of the three materiala
Penetration in earth of shell from a xo-incb Columbiad was 33 ins.
Earpeiiments — England. (HotUy. )
Obdnanci.
xi-inch U. S. Navy.
x5-lnch Rodman...
RIFLED.
7-lnclt Whitworth..
xo.s-inch Armstrong
x3-inch *'
diar^e.
Lbs.
30
60
•5
45
90
Projectile.
Weight.
Velocity.
Range.
Target and Kflhoto.
Shot
Lbs.
X69
400
Feet.
1400
X480
Yards.
50
SO
Iron plates, X4 ina
—loosened,
iron plates, 6 loft.—
destroyed.
Shot
4i
150
307
344-5
1341
1338
X760
300-
soo
300
IngUs^et— dflstr'd.
Solid plates, n ins
thick— destr'd.
* Steel. t 8-inch yertical and 5-lnch horizontal slabs, and 7-inch vertical and <-tn. bortsontal
"^,9 X 5 ins. ribs and 3-inch ribs-
OUNNBBT.
499
JSUmmtt of Rywri of Board of Engineers, far FortifieationSy U. S. A,
ProfMional Papers No. 25. {Brev. Maj.-Gtn. Z. B. Towei:)
Experimental firings for penetration during the past twenty years have
detennined that wrought iron and cast iron, unless chilled, are unsuitable for
projectiles to be used against iron armor; that the best material for that
purpose is hammered steel or Whitworth's compressed steeL
3. That caat'iron and cast-steel armor-plates will break up under the im-
pact of the heaviest projectiles now in service, unless made so thick as to
exclude their use in ship-protection.
3. That wrought-iron plates have been so perfected that they do not break
upf but are penetrated by displacement or crowding aside of the material in
the path ot the shot, the rate of penetration bearing an approximately deter-
mined ratio to the striking energy of the projectile, measured per inch of
shot's circumference, as expressed by the following formula :
yap
— — =^ penetraiion in ins, V rqaresenting velocity in
9gX2rirX 2240 X .86 -"^ *^ » *
Jbctper aecondj P weight of shot in Ws., and r radius of shot in ins.
That such plates can therefore be safely used in ship construction, their
thickness being det«rmiaed by the timit of flot$ition and the protection
needed.
4. That, though experiments with wrought-iron plates, faced with steel,
have not been sufficiently extended to de^mine Uie beiBt combination of
these two materiajs, we may nevertheless assume that they give a resistance
of about one fourth greater thau those of homogenous iron.
5. That hammered steel in the late Spezaia trials proved superior to any
other material hitherto tested for armor-plates. The 19-inch plate resisted
penetration, and was only partially broken up by 4 shots, three of which had
a striking energy of between 33 000 and 34 000 foot-tons each. Not one shot
penetrat^ the plate. Those of chilled iron were broken up, and the steel
projectile, though of excellent quality, Was set up to about two thirds of its
length.
Velocity aixd. iHangee of Sb.ot, {Kmpp's Ballistic Tables.)
Penetiration. iii "Wrought Iron.
*vr^
Vap
— —7^ = penetration in ins. C = 2. 53.
gX^rnX 2240 X C ^ ^^
QVK.
Tona.
Armstrong, 100.
«
ti
81..
Woolwich,
Kmpp, 71..
»' 18..
U.S.* 8-inch....
Velocity
Penetrattoo
Cali-
ber.
Powder.
Shot.
at
Muzzle
Range.
at
Range
per Sec.
3000
Yds.
6000
Mazzle
Coo
3fxx>
Int.
Lbs.
Lbs.
Feet.
Yds.
Ids.
ins.
Ids
1 7- 7*5
550
2022
1715
1424
1 191
34-76
33-2
27-55
>7-75
776
2000
1832
1518
1259
37-52
35- 81
29.66
16
445
1760
1657
'393
xi8x
32.6
31-23
26.04
1575
4«S
I715
1703
1434
1 211
3352
32.12
27.04
r«
165
474
1688
1351
IU3
20.48
"9-31
15-46
35
180
»450
1036
840
10.23
9.22
6.72
60QO
Ins.
22.04
23-47
2»-35
21.89
12. 14
5- 17
* Uncbanibered.
Target.— For loo-ton gun, steel plate 22 ins. thick, backed with 28.8 ins. of wood,
2 wrought-iron plates 1.5 ins. thick, and the fhime of a vessel.
J^ect.~Tota1 destruction of steel plate, and backing entered to a depth of 22 in&,
bat not perforated.
500
GUKKBBY.
Suxninary of Record of* Practice in Burope 'writli IXdittV^
A-rmstrong, Wool^violi, and. Krtipp Gt-tius.
Board of Engineers Jbr FortificcUionSy U. S. A.jProfsmonal Papers ZVb. 25.
Gum.
Armstroxo,
100 Tons, caliber
17 ins., bore 30.5
feet.
Woolwich, 81
Tons, caliber 14.5
iqa , bore 24 feet.
caliber 16 ins. . .
38 Tons,
caliber 12.5 ins.
bore 16.5 feet
Krupp, 71 Tons,
caliber 15.75 in&,
bore 28.58 feet
18 Tons,
caliber 9.45 lbs.,
boro 17.5 feet
!
■■}
Powder.
1. 5- inch cubes,
Wttltham Abbey
Fossano
.75-inch cubes.
1.5 " "
1.5 '* "
1.5 " "
1.5 " "
1.5 " *'
Prism A
" H
" 2 inch. . .
" xhole...
** 3 inch. . .
^
Bneruy
Projectile.
^i
•Si
1 VelodI
Second.
V.
5>
•
ills
i
k
Lb«.
Lbe.
il
Feet.
£ft.
ei
peril
eircon
of a
P
N
n
1
Ft.-tOD».
Fooi-ioiu.
'shot....
330
2000
f446
38990
54405
375
2000
«S43
33000
633
400
2000
1502
3128a
585-74
776
aooo
1832
46580
83532
170
1258
»393
x6q22
20843
371-5
220
1450
1440
457-57
250
1260
1523
20259
34508
444- 7«
310
1466
1553
520.4
Pall, shell
130
800
M5>
II 668
207.64
285.4
n
200
800
1421
II 210
((
t8o
80a
1504
"545
3«9-4
Plain . . .
t
1707
1x84
16602
335-4*
Shrapnel
1725
«703
34503
697.91
Shell . . .
441
1419
1761
30484
616. 14
Plain . . .
132
300
1873
7298
246^03
Shrapnel
145
474
1688
8344
315.66
Shell . . .
165
300
1991
277.6.
9
Penetration in Ball Cartridge Paper, No, i.
Musket, with 134 grains, at 13.3 yards. 653 sheeta
Common rifle, 92 grains, at 13.3 yards. 500 sheeta
X*exietration of Uead Sails in Small A.rzns.
Experiments cU Washington Arsenal in 1839, and at West Paint in 1837.
AXM.
Musket
Common Rifle.
Hairs rifle.
Hairs carbine, musket
Galil)er.
Pistol
Rifle musket
Altered musket
Rifle, Harper's Ferry..
Pistol carbine
Sharpe's carbine
Bumside^B
IMsmeter I Charge
of Bull. I Powder.
((
Inch.
.64
•64
5775
•5775
.685
•5775
•5775
•55
•55
Graina.
«34
>44
100
92
100
70
70
80
90*
lOO*
5"
60
70
40
60
55
Weight
Penetration.
Distance.
of Bull.
White Oak.
WUtePla*.
Yaida.
Gnina.
loa.
lu.
9
397-5 •
1.6
—
5
397-5
3
—
5
219
2.05
—
9
—
X.8
—
5
219
2
^
9
219
.6
—
5
—
'Z
—
5
2x9
.8
—
5
—
x.x
—
5
•
1.2
—
5
S19
.725
—
300
500
—
Zl
200
730
—
10.5
200
500
—
9-33
200
450
—
5-75
30
463
—
7.17
30
350
^
6.15
* Chargea too great for aervice.
Mosket discharged at 9 yards distance, with a charge of 134 grains, x ball and js
buckshot, gave for ball a penetration of 1. 15 ins., bn&luhot, 41 inch.
GUNNEBT.
501
XjOms cr F'oroe \>y "Windagre.
A oomparison of resalts shows that 4 lbs. of powder give to a ball without wind-
Btgfi nearly as great a velocity as is given by 6 lbs. having . 14 inch windage, which
i» true windage of a 24-lb. ball; or, in other words, this windage causes a loss of
nearly one tlard of force of charge.
Venta. — ExperimenCs show that loss of force by escape of gas from vent
of a gun is altogether mconsiderable when compared with whole force of
charge.
Diameter of Vmi in U. S. Ordnance is in all cases .2 inch.
Effect of different Waddings with a Charyeofii Grains o/Poioder,
Wad.
Ball wrapped in cartridge paper and crumpled.
1 felt wad upon powder and 1 upon ball
2 felt wads upon powder and i upon ball
1 elastic wad upon powder and i upon ball . . . .
2 pasteboard wads upon powder.
2 elastic wads upon powder.
Velocit
per
of Ball
ond.
Feet.
1377
1346
1482
II32-
1200
HOC
Felt wads cat from body of a hat, weight 3 grains
Pasteboard vxtds .1 of an inch thick, weight 8 grains.
Cartridge paper 3 X 4-5 ina, weight 12.82 grains.
Elastic toadSy *' Baldwin's indented," a little more than .x of an inch thick,
weight 5.127 graina
Most advantageous wads are those made of thick pasteboard, or of or-
dinary cartridge paper.
In service of eannon, heavy wads over ball are in all respects injurious.
For purpose of retaining the ball in its place, light grommets should be used.
On the other hand, it is of great importance, and especially so in use of small
arms, that there should be a good wad over powder for developing fUU force of
charge, unless, as in the rifle, the ball has but very little windage. {Capt. JUordecai.)
Weij$Iit. aiid. IDimexisioiis or X^ead Balls.
Number of BaUs in a Lh^^frotn 1.67 to .237 of an Inch Diameter,
Ins.
1.67
1. 3*6
1.IS7
X.051
•977
.919
.873
.835
.802
•775
No.
DlMD.
No.
DUm.
No.
Dtam.
No.
IncDe
Inch.
loeh.
X
•75
XX
•57
as
.388
80
2
•73
12
•537
30
•375
88
3
r
13
•51
II
.37a
90
4
.693
«4
•55JS
.359
.348
xoo
5
.677
15
.488
40
XIO
6
.662
x6
.469
45
•338
X20
I
.65
»7
•453
50
.329
130
.637
x8
.426
60
.321
140
9
.625
«9
.405
70
•314
X50
xo
.6x5
ao
.395
75
.307
x6o
Diam.
No.
Diam.
No.
Inch.
Inch.
.301
170
•259
270
.295
x8o
256
280
:.%
190
.252
290
200
249
300
.281
210
.247
310
.276
220
244
320
.272
230
.242
330
.268
240
•239
340
.265
250
.237
350
.262
260
Heated shot do not return to their original dimensions upon cooling, but retaio
a permanent enlargement of about .02 per cent in volume.
A A.
A.
Number of Pellets in an Ounce of Lead Shot of the different Sizes',
No. 6 280
40
50
58
B.
No.x.
9.
75
82
IZ2
No. 3.
4-
5-
»35
X77
218
7-
8.
34»
600
Naz4.
No. 9.
10.
Z2.
984
Z726
2140
3x50
502
GUNNSBT.
Proportion of Po-wd«r to Sliot fbr fblloT«rinK M^uxnber*
of Slxot.
Shot.
No.
Shot.
Powder.
No.
a
3
Oi.
3
«-7S
Druo*.
1-5
1.625
4
5
Powder.
No.
Shot
Rowder.
I>num.
i«75
2.125
6
7
1. 125
DraiiM.
"•375
2.625
Oi.
1-5
1-375
NoTS.— 3 oz. of No. 2 shot, with 1.5 drams of powder, proiduced greatest eflPect.
Increase of powder for greater number of pellets is in consequence of increased
friction of their projection.
Numbers o/Brcumon Capt cotrespotiding mHth Birmingham Ntmhen.
Eley's.
Qirmiugbam.
5
6
7
46
8
"48
9
49
24
50
43
44
xo
IX
53 and 54
x8
55 and 56
13
57
>3
58
»4
58*
51 and 52
Where there are two numbers of Birmingham sizes corresponding with only one
of Eley's, it is in consequence of two numbers being of same sue, varying only in
length of capa
Comparison of S^oroe of* a
Lock.
Ordinary rifle...
tt it
Hall's rifle...*.!!
Hall's carbine. . ,
Jenks's carbine,
Cadet's musket ,
Pistol ,
Cliarge iu. 'variotifii Arms.
Vslocity.
Percussion.
Flint.
Percussion,
ti
Flint
Percussion.
Powd«r«
As.
WiiuUge.
Weight
oTBaII.
Graint.
Inch.
GniuB.
100
.015
219
7P
.015
319
70
.0
319
70
0
319
70
.0
3x9
70
.045
310
ax6.5
35
.015
Fort.
2018
«755
1490
1340
1687
1690
947
Rangetfor Smcdl Arms*
Musket— With a ball of 17 to pound, and a charge of no grainii of powder, eto.,
an elevation of 36' is required for a range of soo yards; and for a range of 500
yards, an elevation oTj,^ 30' is necessary, and at this distance a ball will pass through
a pine board x inch in thickness.
At/I«.— With a charge of 70 grains, an effective range of flrom 300 to 350 yards is
obtained; but as 75 grains can be used without stripping the ball, it is deemed bettor
to use it, to allow for accidental loss, deterioration of powder, etc
Pistol— W\ih a charge of 30 grains, the ball is projected through a pine board
X inch in thickness at a distance of 80 yard&
GhMipo-wd.er.
Gunpowder is distinguished as Musket^ Mortar, Cctntum, Mammothf and
Sportina powder ; it is all made in same manner, of same proporttons of
materials, and differs only in size of its grain.'
Bursting or Explosiw 3n«rgy.— By the experiments of Captain Rodman, U. S.
Ordnance Corps, a pressure of 45 000 lbs. per square inch was obtained with xo lbs.
of powder, and a ball of 43 lbs.
Also, a pressure of 185000 lbs. per sq. inoh was obtained *ohen the powder was
Immed in iU own volume, in a cast-iron shell having diameters of 3.85 and xs ins.
Proof of Powder. {U. S. Ordnance Maaiial)
Powder in magazines that does not range over x8o yards is held to be unservice-
able.
Oood powder averages from 280 to 300 yards; smaU grxUn, flrom 300 to 330 yards.
Restoring UmerviceaMe Powder. — When powder has been damaged by being
stored in damp places, it loses its strength, and requires to be worked over. If
quantity of moisture absorbed does not exceed 7 per cent., it Is sufllcient to dry It
to restore it for servioe. This is done by exposing it to the sun.
When powder has absorbed more than 7 per cent, of water it should be SQlltlOtt
powder mill to be worked over.
UUNNSBT.
503
Properties and Itesults of O-unpo-wder, deterxnixied t>y
ICxperixxiexits. {Ca^in A. Mordecai, U. S. A.)
^USKST PBMOULVM.
Weight of ball 397.5 gnini-
*' «' powder. i«o. "
Windage of ball.. ^.. o9lflch.
a4-P0ITirDBB CrOM.
Weight of ball and wad. ... 34.25 lbs.
" ♦' powder 6 "
Windage of ball....... 135 inoh.
<bunc
Cannon, large. . .
" small . .
Masket
Rifle.....
Rifle......
Musket.'.
Rifle
Cannonruneven.
" large . . .
Sporting
Blasting, uneven
Rifle.
Sporting ,
Rifle
C«mpo«it!on.
Salt,
petre.
I HI 11
75
77
70
75
•Glaied.
Ciutr,
coal.
14
H.5
«3
"5
15
15
Sul-
phur.
12.5
Is}
'}
.0
Ifanafifictur*.
Where from.
•^wvif^
.*^i^wi*»-^**»*.
* Dupont's M-ills,
Del.
t Dupont'a Mill?,
Del.
• Dupont's Mills,
Del.
Loomis, Hazard,
&;Ca, Conn.*
Waltham Abbey,
England.*
Is®
Per c't.
77
«75
2.77
569
314
3-35
i»34
214
—
6174
14a
—
5 344
a83
3-^
1642
—
—
«3i5«
—
• —
,66
"53
3.09
loq
72808
183
100
1. 91
4.42
395
aia
—
2378
204
iz6oo
—
—
I
677
72
808
907
728
834
943
788
756
.82
.888
- - .865
t Rough.
Manufacture of Powder.— TovrdeiT of greatest force, whether for cannon or small
arms, is produced by incorporation in the "cylinder milla"
Efffd ofSiz6 of Chain. —Within limits of difference in size of grain, which occurs
in ordinary cannon powder, the granulatioQ appears to exercise but U^Ue influence
upon force of it, unless grain be e^eeedingly dense and bard.
Effect of Glazing. — Xllazing is favorable to production Of greatest force, and to
quick combustion of grams, by affording a rapid transmission of flam^ through
mass of the powder.
' JBffM €f'Mtvng P^cMtitm- I¥inier». — Inoi^ease of force by use of primers, ^ich
ntarly <ilo»*$ wit,\a ooastant and appreciable in, ameunt, yet not of su£Bcient Talat
to authoriM a reduQtiw of chai)t9.
Jfiafio of Relative Strength of different Powd&'sfor use under water dijfkr
hut little from the reciprocal of the ratio between the sizes of the grains^
ahowmg that the strength is nearig invers^ proportional thereto,*
Mammothf .08; -OliTer, .09; -Cannon, .18; Mortar, t; Mtnket, 1.57;
Sporting a.6if and SaHety Compound 30.63.
I>ualizx is nitro-glycerine absorbed by Schultze's powder.
For other powders and explosive materials see Blasting, p. 443.
Heat and B^jscplosive Po'wer. {Capt. Noble an4 F- A. Abel.)
One gram of fired powder evolves a mean temperature of 730®. Temper-
•tnrt of exptosioD 3970^. Valume ol permanent gas (irhich is in an in-
verse ratio to units of heat evolved) at 32° =250.
The explosive power of powder, as tested in Ordnance, ranges, for volames
of expansion of 1.5 to 50 times, from 36 to ijofooMons per lb. burned.
. A charge of jq Ibd. gave to an 180 lbs, shot a velocity of 1694 feet per
•econd, eooal to a total energy of 3637 /oo^-toiu, and a charge of 100 lbs.
gave a vdocity of 2^189 f^ and an energy of S9^of<totnton8*
* Report of Enertmente and Inveetlgatloiui to deiwlop a tyttem of •vhnarioe mloM. profeaaiopaJ
Fqiani, U. 8. E., No. 33.
504 HEAT.
HEAT.
Ifeaty alike to gravity, is a universal force, and is referred to both as
cause and effect.
Caloric is usually treated of as a material substance, though its claima
to this distinction are not decided ; the strongest argument in favor of
this position is that of its power of radiation. Upon touching a body
having a higher temperature than our own, caloric passes from it, and
excites the feeling of warmth ; and when we touch a body having a
lower temperature than our own, caloric passes from our body to it, and
thus arises the sensation of cold.
To avoid any ambiguity that may arise from use of the same expres-
sion, it is usual and proper to employ the word (Mloric to signify the
principle or cause of sensation of heat.
ffeat Unit. — For purpose of expressing and comparing quantities of
heat, it is convenient and customary to adopt a Unit of heat or ITiermal
unity being that quantity of heat which is raised or lost in a defined
period of temperature in a defined weight of a particular substance.
Tbas, a Thermal unit. Is quantity of heat which eorrespmds to an interval ofi^in
temperature of i lb. of pure liquid waier^ at and near it* temperature of grecUett
dcnrity, 39.1°
Thermal unit in France, termed Caloric, Is quantity of heeU which oorreffNmdt
to an interval ofi° C. in temperature ofx kilogramme of pure liquid watery at and
near its temperature of greatest density.
Thermal unit to Caloric, 3.96833; Caloric to Thermal unit, .351 996.
One Thermal unit or i® in i lb. of water, 773 foot-lba.
One Caloric or lO C. in i kilogramme of water, 433.55 kilogrammetrea
lO C. in I lb. water, 1389.6 fbot-lbe.
Ratio of Fahrenheit to Centigrade, 1.8; of Centigrade to Fahrenheit, .555.
Absolute Temperature, Is a temperature assigned by deduction, as an
opportunity of observing it cannot occur, it being the temperature corre-
sponding to entire absence of gaseous elasticity, or when pressure and vol-
ume =0. By Fahrenheit it is — ^461.2°, by Reaumur — 229.2% and by Cen-
tigrade—274®.
Heat is termed Sensible when it diffuses itself to all surrounding
bodies ; hence it is free and uncombined, passing from one substance
to another, affecting the senses in its passage, determining the height
of the thermometer, etc.
Tenyterature of a body, is the quantity of sensible heat in it, present
at any moment.
Heat is developed by water when it is violently agitated.
Heat is developed by percussion of a metal, and it is greatest at the fitit
blow.
Quantities of heat evolved are nearlv the same for same substance, with-
out reference to temperature of its combustion.
Mechanical power may be expended in production of heat either by fric-
tion or compression, and quantity of heat produced bears the same propor-
tion to quantity of medumical power expended, beinpr i unit for power
necessary to raise i lb. 772 feet in height This number of 772 is termed
the mechamccU equivcU^ of heal (Joules).
HEAT. 505
Specific !Keat.
Specific Heat of a body signifies its capacity for heat, or quantity re-
quired to raise temperature of a body i^, or it is that which is ab-
sorbed by different bodies of equal weights or volumes when their
temperature is equal, based upon the law, That aimilar quantities of
different bodies require unequal quantities of heat at any given tempera-
ture. It is also the qitantity of heat requisite to change the tempera-
ture of a body any stated number of degrees compared with that which
would produce same effect upon water at 32°.
Quantity of heat^ therefore, is the quantity necessary to change the tem-^
perature of a body by any given amount (as 1°), divided by rmantity ol
heat necessary to change an equal weight or volume of water at 32^ by same
amount.
KoTB.— Water has greater specific beat than any known body.
Every substance has a specific heat peculiar to itself, whence a change of
composition will be attended by a change of its capacity for heat.
Specific heat of a body varies with its form. A solid has a less capacity
for heat than same substance when in state of a liquid; specific heat of
water, for instance, bemg .5 in solid state (ice), .622 in gaseous (steam),
and I in liquid.
Specific heat of equal weights of same gas increases as density decreases ;
exact rate of increase is not known, but ratio is less rapid thim diminution
in density.
Change of capacity for heat always occasions a change of temperature.
Increase in former is attended by diminution of latter, and contrariwise.
Specific heat multiplied by atomic weight of a substance will give
the constant 37.5 as an average, which shows that the atoms of all
substances have equal capacity for heat. This is a result for which at
yet no reason has been assigned.
Thus: atomic weights of lead and copper are respectively 1294.5 and 305.7, and
their ^speciflc beats are .031 and .095. Hence 1294.5 X •031 = 4a 129, and 395.7 x
.095 = 37.591.
It is important to know the relative Specific Heat of bodies. The most conve-
nient method of discovering it is by mixing different substances together at dif-
ferent temperatures, and noting temperature of mixture; and by experiments it
appears that the same quantity of heat imparts twice as high a temperature to
mercury as to an equal quantity of water; thus, when water at loo^ and mercury
at 40° are mixed together, the mixture will be at 80°, the 20^ lost by the water
causing a rise of 40^^ in the mercury; and when weights are substituted for meas-
ures, the f^t is strikingly illustrated; for instance, on mixing a pound of mercury
at 4o<' with a pound of water at 160°, a thermometer placed in it will fall to 155O
Thus it appears that same quantity of heat imparts twice as high a temperature to
mercury as to an equal volume of water, and that the heat which gives ^° to water
will raise an equal weight of mercury 1150, being the ratio of i to 23. Hence, if
equal quantities of heat be added to equal weights of water and mercury, their
temperatures will be expressed in relation to each other by numbers i and 23; or,
in order to increase the temperature of equal weights of those substances to the
same extent, the water will require 23 times as much heat as the mercury.
Capacity for Heat is relative power of a body in receiving and re-
taining heat in being raised to any given temperature ; while Specific
applies to actual quantity of heat so received and retained.
Bpeoiilo Keat of* A.ir and other Gt-ases.
Specific heat, or capacity for heat, of permanent gases is sensibly constant
for all temperatures, and for all densities. Capacity for heat of each gas i^
5o6
HSAT.
same for each degree of temperature. M. Kegnaolt proved that capacity
for heat for air was uniform for temperatures varying from —22° to
+437° ; consequently, specitic heat for equal weights of air, at donttant
pressure, averaged .2377.
Metals Jirom 33° to
Antimony... .0508
Bismuth 0308
Brass 0939
Copper 092
Cust iron 1298
Gold 0324
Lead •0314
Mercury 0333
Nickel 1086
Platinum 0324
Speoillo Ueat. Water at 33°
Silver . » 056 : Woods.
z.
Steel. 1165
Tin 0562
Wrought iron .1138
Zinc 0955
Stmei.
Chalk 2149
Limestone... .2174
Masonry 2
Marble, gray. .2694
*' white. 2158
Oak.
Pear
Pine
•57
.65
MinH Stibstances.
Charcoal .2415
Coal 2411
Coke ,. .eo3
Glass 1977
Gypsum. 1966
Phosphorus.. 2503
Sulphur 3036
Liquids.
Alcohol. 658S
Ether 4554
Linseed oil .. .31
Olive oil 3096
Steam 365
Turpentine . . .416
Vin^ar 9a
Solid.
Ice 504
Oases.
3377 I Hydrogen.* »...* 2356
3308
Air ..... -
Oxygen 2412 I Carbonic Acid
ForSquai Weights.
Air. 1688 I Hydrogen 2.4096
Oxygen..... 1559 \ Carbonic Acid.; 1714
Metals have least, ranging fVom Bismuth .0308 to Cast Iron .1298. Stones and
Mineral Substances have 2 that of wa tor. and Woods about .5. Liquids, with e.x
ce^tion of Bromine, are less than water, Olive oil being lowest and Vinegar highest.
Illcstratios. — It 1 lb of co^l will heal i lb. of water to 100°, of a lb. will
.033
of lilte k^ub*.
heat I lb. of mercury to 100°.
a?o Compute 'Peznperature o^ A :Ml3etui>«
stauoeb.
W + w -*' T-f -^' W +^ =^- ^ repressing weight
or volume of a substance of temperature T, w weight or volume of a like substance of
temperature t, and t' temperature of mixture Vf-^w.
Illustration i. —When 5 cube feet of water (W) at a temperature Of 150° (T) Is
mixed with 7.5 cube feet (w) at 50^ (f), what is the resultant temperature of the
mixture?
5X150° + 7- 5.x 50° 1125
5 + 7 5
12.5 ^
2.— How much water at (T) ioo<> should be mixed with 30 gallons (w) at 60*^, fbr
a required temperature of 8o<^?
30(800-^600) 600
To Compute Texupei^atiire of a AliJttur^ of TJnlllK«
Subtitanoes.
WST4-wst ^, ws{t—f) ^ If lWS4-ws)<\jwst „ „ ^
W-a-T = ' ; s^ — :r=»W: — ^ — ' \^ J' • — «=T. W and w
8-l-w* ' S(T — f) ' WS
r^esenting weights^ and S and s specific heeU of substances.
Illustration.— To what temperature should 20 lbs. cast iron (W) be heated to
raise 150 lbs. {w) of water to a temp«ratar« (t) of 50^ to 600 f
' MX .1.911 ..jje *^
HBJlT.
5P?
To Compute Speoifi.o Heat at Constant Voluxne.
Whin Spee\fie ffeat ai OomtatU Presture is htovm, 'ir =^ '■ ^ r^oretent-
%ng specif hecU at constant pressure, p pr<ip(»rtion of heal absorbed at constant vol-
ume^ H iiotal heat absoHted at constarU pressure^ and s specifio heat at constant volume.
Or,
a<r— 0—2.742 (v—D)
t'—t
= «. t and t' represefnJting initial andjinal tempera-
twre qfthe gas and that to which it is raised, and V and v initial and Jinal volumes
o/ths gat under 14.7 <6«. per sq. tnoA, and of it hetUed under constant pressure in
cvMfeet,
Iu.u8TRATioN,-^AasainQ I lb. air at atmoepheric pressure and at 33*^, doubled in
ToluYne by heat 8 =«:. 2377 *,*--«' 5= 32^ «x, 525° = 493° and V — t; = j 2. 387 * ctOie
feet.
•^377 X493-(2. 742 X. 2.387) ^ ^^gg ^^^ ^^
493
For comparative volumes of other gases, see Table, page 506.
To Compute Speoifio Heat for Kq.ual Volume of O-as
and A.ir.
Rule. — Multiply specific heat of the gas for equal weights of gas and air
by specific gravity of gas, and product is specific heat for equal volume.
Example —What is specific heat of air at equal volume with hydrogen ?
Specific heat of hydrogen for equal weigh ta at conslant volume, 2.4096, and speci-
fic gravity of the gas, .0692. (See Table, page 506.)
Then, 2. 4096 X '0692 = ■ 1667 specific heaJtfor equal volumes at constant volume.
Specific heat of steam, air at unity — 1.381.
Capaoity fbr Heat.
When a body has its density increased, its capacity for beat is di-
minished. The rapid redaction of air to .2 of its volume evolves beat
sufficient to inflame tinder, wbicb requires 550^.
Relative Copacityfor Heat of Various Bodies. ( Waier a< 32° = i.)
Eqaal
Volumes.
■oDtSS.
Eaval
NVefichU.
Eqiwl
Volnmw.
BODIU.
Equal
wlfghu.
Equal
Volainet.
Bodies.
Equal
WeiRbto.
Water..
Brasa..
('opper.
Glass. . .
I
X16
114
187
I
.971
1.027
.448
Gold. . . .
Ice
Iron....
Lead...
.05
.126
.043
.966
.993
.487
Mercury
Silver . .
Tin
Zinc. . . .
036
.082
.06
.102
•833
To Asoevtaln. Relative Capacities of Different Hodiea,
ooml>ined witlx experiment,
RuL.B.-^Multiply weight of each body bv number of degrees of heat lost
or gained by mixture, and capacities of bodies will be inversely as products.
Or, if bodies be mingled in unequal quantities, capacities of the bodies
will be reciprocally as quantities of matter, multiplied into their respective
changes of temperature.
Illustration.— If i lb. of water at 156° is mixed with x lb. of mercury at 40°,
resultant temperature is 152°.
Thus, t X 1 56** — I s**? = 40, and i x 40O -x^ 1 52° = 1 1 2°. Hence capacity of water
for beat is to capacity of mercury as 112° to 4C>, or as 28 to i.
Sensible }^eat.
Sensible heat or temperature to raise water from 32° to 2i2°r= i8a9^, or
beat onits.
• See T«blM, pagta 906 aad sao-sx.
5o8
BEAT.
Xiatent Heat.
Latent Heat is that which is insensible to the touch of our bodies,
and is incapable of being detected by a thermometer.
When a solid body is exposed to heat, and ultimately passes into the
liquid state wider its influence, its temperature rises until it attains the
point of fusion, or melting point. The temperature of the body at this
point remains stationary until the whole of it is melted ; and the heat mean-
time absorbed, without* affecting the temperature or being sensible to the
touch or to the indications of a thermometer, is said to become latent. It is,
in fact, ike latent heat of fusion^ or the latent heat of liquiditify and its func-
tion is to separate the particles of the body, hitherto soUd, and change their
condition into that of a liquid. When, on the contrary, a liquid is solidified,
the latent heat is disengaged.
If to a pound of newly-fallen snow were added a pound of water at 172°,
the snow would be melted, and 32° would be resulting temperature.
When a body is fusing, no rise in its temperature occurs, however great
the additional quantity of heat may be imparted to it, as the increased heat
is absorbed in the operation of fusion. The quantity of heat thus made
latent varies in different bodies.
A pound of water, in passing from a liquid at 212^ to steam at 212°, re-
ceives as much heat as would be sufficient to raise it through 966.6 thcr-
mometric degrees, if that heat, instead of becoming latent, had been sensibU.
If 5.5 lbs. of water, at temperature of 32°, be placed in a vessel, communicating
with another one (in which water is kept constantly boiling at temperature of 212°),
until former reaches temperature of latter quantity, theu let it be weighed, and
it will be found to weigh 6.5 lbs., showing that one lb. of water has been received
In form of steam through communication, and reconverted into water by lower
temperature in vessel. Now this pound of water, received in the form of steam,
bad, when in that form, a temperature of 212^. It is now converted into liquid
form, and still retains same temperature of 212°; but it has caused 5. 5 Ibs^of water
to rise from the temperature of 32° to 212°, and this without losing any tempera-
ture of itself Now this heat was combined with the steam, but as it is not sensible
to a thermometer, it is termed Latent.
Quantity of heat necessary to enable ice to resume the fluid state is euual
to that which would raise temperature of same weight of water 140° ; ana an
equal quantity of heat is set free from water when it assumes the solid form.
Su-xxx of* Sensible and I-iatexit jtleats.
From Water ai 32°.
Fren-
ure.
Latent.
Sum.
Prasa-
are.
Latent.
Sam.
Preu-
ure.
Utent.
Sura.
LlM.
0
0
Lbs.
0
0
Lba.
0
0
M-7
964.3
1x46.1
26
943-7
"55-3
55
912
1169
16
962.x
1 147- 4
27
942.2
"55.8
60
908
117a 7
«7
959-8
1148.3
28
940.8
X156.4
65
904.2
1172.3
18
957-7
1 149. 2
29
939-4
"57-1
70
900.8
1173.8
>9
955.7
1150.1
30
937-9
"578
Z5
897-5
1175,2
20
952.8
1150.9
32
935-3
1158.9
80
894.3
1176.5
21
951-3
1151.7
35
931.6
1160.5
85
801.4
888.5
1177.9
22
949.9
"52-5
37
9293
1161.5
90
1179.1
23
948.5
1153.2
40
920
1 162. 9
95
885.8
1180.3
24
946.9
"53-9
45
920.9
1 164.6
100
883.1
1181.4
»5
945-3
1154.6
50
916.3
1167. 1
110
878.3
1183.5
Latent.
Sam.
0
0
873-7
"85.4
869.4
1187.3
865.4
X189
861.5
1190.7
857.9
1 192. 2
854.5
"93?
851.3
ii95.£
848
1196.5
845
1 197. 8
829.2
1200. ■?
831.2
1203. 7
Latent Heat of Vaporizaiionj or Number of Degrees of Heat required to con-
vert foUoioing Substances from their Liquidities to Vapor at Pressure
of Atmo^here.
Alcohol 364°
Ammonia 860*^
Ether (Sulph.) 163O
Ice 142.60
Mercury 157O
Carbonic Acid agB9
Water 966.6a
Zinc
493:
Oil of Turpentine. . 134O
HEAT.
509
SobtUncM.
Xjatent Keat of Fusion, of Solids.
Melt-
Substancen. J»K
Point.
Tin
Bismuth. .
liead
Zinc
Silver . . . .
Mercury. .
Cast iron. .
Melt-
iDg
Specifl<
:Heat.
In Heat-
unitu of
Point.
Liquid.
Soiid.
lib.
0
0
0
44a
•0637
.0562
25.6
507
.0363
.0308
'*L
617
.0402
•0314
9.86
773
1873
—
.0956
5a 6
—
•057
37-9
39
•0333
.0319
5
3400
—
.129
233
Ice.
Phosphorus . . . .
Spermaceti...;.
Wax
Sulphur
Nitrate of soda. .
Nit of potassia .
c
32
113
120
143
239
591
643
{Person.)
IJquid.
•2045
•234
•413
•3319
cHeat.
TnHeai-
unita of
Solid.
zlifc
0
.504
142.85
.1788
mI
—
—
"75
.3026
17
.2782
"3
.2388
85
To Compute I^ateut Heat of Fvisiou. of a ^on-metallio
Bu.l>staxioe.
C'\^c{t-\- 256°) = L. G and c rqpregenling specific heals of 'substance in solid a^^
liquid stalCf t temperature of fusion^ and L kUent heat.
Illustration.— What is latent beat of fusion of ice ?
C = .504; c = i; and< = 32°.
.504 A, I X 33 4- 256 = 142.85° units.
KoTB. — For Latent Heat of Fusion of some substances, see Deschanel's, New York,
1872, Heat, part 3.
Radiation of Heat.
Radiation of Heat is diffusion of heat by projection of it in diverffing right
lines into space, from a body having a h'igner temperature than space 3iir-
rounding it, or body or bodies enveloping it.
Radiation is affected by nature of surface of body ; thus, black and rough
surfaces radiate and absorb more heat than light and poli:shed surfaces.
Bodies which radiate heat best absorb it best.
Radiant heat passes through moderate thicknesses of air and gas without
snffecing any appreciable loss or heating them. When a polislicd surface
receives a ray of heat, it absorbs a portion of it and reflects the rest. The
quantity of heat absorbed by the body from its surface is the measure of
its ahsavbing power^ and the heat reflected, that of its reflectinff prnwr.
When temperature of a body remains constant it is in conso4|uence of
quantity of heat emitted being equal to quantity of heat absori)e(l by body.
Keflecting power of a body is complement of its absorbing power ; or, sum
of absorbing and reflecting powers of all bodies is tlie same.
Thus, if quantity of heat which strilces a body = 100, and radiating and reflecting
powers each 90, the absorbent would be zo.
Ttadlatins or iVbsor'ben.t and Ftefleoting !Po"wers
6uT3stanoes.
Radiating
or Ab-
■erbing.
So
ANCK8.
I^mp Black.
Water.
O.rbonate of Lead
T<ead, white
Writing Paper
Ivory, Jet, Marble
Resin
Glasa
India Tnk
Ice
Shellac
Lead
Cast Iron, bright polished
Platinum, a little polisb'd
Mercury
RadiatioR
or Ab-
•orbinir.
Reflect-
ing.
zoo
—
100
—
zoo
—
100
—
98
93 to 98
96
3
7 to 2
4
fs
85
73
zo
15
IS
28
45
55
25
2*
75
76
23
77
SCBBTANCBS.
IT u*
Wrought Iron, polished..
Lead, polished ,*
Zinc, polished '.
Steel, polished
Platinum, in sheet
Tin
Copper, varnished
Brass, dead polished. . . .
" bright polished. . .
Copper, ham'ered or aist
" deposited on iron
Gold, plated
polished
Silver, polished
cast, polished . . .
i(
23
19
«9
17
17
X5
14
zz
7
7
7
5
3
3
3
of
Reflect*
ing.
77
8z
8z
83
83
85
86
89
93
93
93
95
97
97
97
510
HBAT*
H-adiatinur and. A-IObOrloing Poi^or of varioxis Sodies, in
Units of* Heat per Sq.. f^oot per Hour for a IDiffbrenoe
of 1°. {Pedet)
UuiU
Iron, ordinary 5663
Glass 5948
Iron, cast 648
Wood sawdust 7335
Stone, Brick, etc 7358
Dolt.
Silver, polished. 0366
Copper 0337
Tin 0439
Brass, polished 0491
Ironj sheet 093
Unit.
Woollen stuff 7533
Oil paint .7583
Paper 7706
Lamp-black 8196
Water X0853
To Compute JUoaa of Heat lay Radiation i>er Bq.. IToot.
'"^ ! ~ ' = R T repraenUng temperature ofpipe^ which is anumed tobe .0$
Itn tMn that ofHeam; t temperature of air; I length ofpipt^ and v «eIoc% of heat
in feet per second; d diameter in tnt., and R radieUion in degrees per second.
Illustration.— Assume temperatures of a steam-pipe, steam, 313*, too**, and air
60° length of pipe 30 feet, velocity of heat (steam) 15 feet per second, and diameter
of pipe 16 in& ; what will be loss of heat by radiation?
,.7X20(300-60)^
x6 X IS
Hefieotion.
Reflection of Heat is passage of heat from surface of one substance
to another or into space, and it is the converse of radiation.
Heat is reflected from surface upon which its rays fall in same nuuuier ai
light, angle of reflection being opposite and equal to that of incidence. Met-
als are the strongest reflectors.
RfjUcting Power of various Subsfancet,
Silver. 97
Gold 95
Brass 93
Specular metal 86
Tin 85
Steel 83
Zinc.
Iron .
Lead.
.81
•77
.6
Coznzn-unioation and Tranennission of* Heat.
Communication of Heat is passage of heat through different bodied
with different degrees of velocity. This has led to division of bodies
into Conditctora and Kon-condtictors ; former includes such as metals,
which allow caloric to pass freely through their substance, and latter
comprise those that do not give an easy passage to it, such as stones,
glass, wood, charcoal, etc.
Velocity of cooling, other things being equal, increases with extent of toi^
face conipared with volume of substance ; and of two bodies of same mate-
rial, temperature, and form, but differing in volume.
Transmimon of Heat is passage of heat through different bodies with dif-
ferent degrees of intensity. Gaseous bodies and a vacuum are highest in
•rder of transmittents.
Relative Power of various Substances to TYansmit Heat,
All bodies capable of transmitting heat are more or. less translucent,
though their powers of transmitting heat and light are not in same rel*'
tive proportions.
Air I
Alcohol 15
Crown-glass. . .49
Flint-glass 67
Oypsum 9
Ice 06
Nitric acid ....
Rock-crystal . .
Rape seed oil..
•15
63
Sulphuric acid. .17
Turpentine 31
Water n
Heat which passes through one plate of glass is lest subject to absorptioi»
in passing through a second and a third plate. Of 1000 rays, 451 were in^
teroepted by 4 pUtes as follows :
lit. 3i8x. 2d. 43. 3d. x8. 4th. 9.
BK4.T.
S"
Result* ot Heatinc And K-vaporatlmc '^^atev by
Steam in Copper Pipes and Soilers. {D. K. Otark.)
StaMii «m4«M«l HmI tnuMiBitt«d
P«r iq. foot for i* diflttaaet per hoar.
Cast-iron plate surface. ,
Copper- pUte surrace...<
Oopper-pipe sarface. . . ,
HMting.
.077
.348
.391
Evcporating.
.105
•483
1.07
HMtinf(.
UoiU.
83
376
313
EvaporatiDK
Unita.
xoo
534
X034
Whence. — Efficiency of copper-plate surface for evaporation of water is
double its efficiency for heating ; for copper-pipe surface efficiency is more
than three times as much ; and for cast-iron-plate surface, a fourth more.
Efficiency of pipe surfitice is a fifth more than that of plate surface for
heating, and more than twice as much for evaporation.
Generally, copper -plate surface condenses .5 lb. of steam, copper-pipe
I lb., and cast-iron-plate surface .1 lb. per sq. foot per 1° of temperature pier
hour, for evaporation.
Quantity of heat transmitted is at rate of about 1000 units per lb. of steam
condensed.
Trantmimou qfffeat through Glass of different Colors.
Direct = loa
Plate 65.5
Window 53
Violet, deep. 53
Blue, deep 19
" light 42
Green 36
Yellow 40
Orange 44
Red 53
M. Peclet defines law of transmission of heat as : The flow of heat which
traverses an element of a body in a unit of time is proportional to its sur-
face, and to difterenoe of temperature of the two faces perpoidicular to direc-
tion of flow, and is in inverse of thickness of element.
0r,(<^O^
H. I amd f reprtumHng Umperatures of mrfkeM^ C wmiant for
meUerial 1 ineh thiek^ or quantity of heat transmitted per hour for i^ difference of
tempercUure through 1 unit ftf thtckneti^ T thicknesi^ and H quantity of heal in units
pasted through plate per sq. Jm^ per hour.
Quantities of Heat transmitted iVom Water to "V^ater
thtougli Plates or Beds of* Aletals and. otlier Solid
Bodies, 1 Inoli thiols, per Sq,. IToot.
Far z® Difflerenfis of Temperature between the two Faces per Hour,
Selected firom M, Pwlet^s tables. {D. K. Clark.)
BvMrARcs.
Oold
Platinum
Silver . . .
Copper . .
C or
QuMtlty
OfHMt.
DaiU.
630
555
80:
And.
Iron.
Zinc.
Tin..
Lead.
C or
QuaoUty
ofHMk
UatU.
335
335
177
BUBCTAKCB.
Marble.
Plaster.
Glass..
Sand...
Cor
QuAnllty
ofHMi.
Units.
84
3.6
6.56
3.z6
The conditions are, that the surfaces of conducting material must be per-
fectly dean, that they be in contact with water at both faces of different
temperatni^ and that the water in contact with surfaces be thoroughly and
constantly changed. M. Peclet found that when metallic surfaces became
dull, rate of transmission of heat through all metals became very nearly
the same.
To Compute Units o<* Heat Transmitted.
Illustration l — If aooo lbs. taeet root jnica at 4o<> are contained in a copper
boiler with a double bottom, and heated to 2i2<', with a beating sarface of 35 sq. feet,
and subjected to steam at a temperature of 375°, for a period of 15 minutes, what
will be the total heat, and heat per degree of difference transmitted per sq. foot per
hsiirv
512
HBAT.
ai20— 40® X 60-5- 15 =688o per hour^ and 2000 X 688-4-asi= 55040 tmiit per 9q.
foot per hour.
(212° -f 40°) -f- 2 = 126"^ mean temperature ofjuict, and 275° — 1260 = 149® m^ean
difference of temperature.
Hence, 55 040 -r- 1 49 = 369. 4 uniU per sq. foot per degree of difference per hour.
2.— If 48.2 sq. feetof iron pipe 1.36 ins. in diameter, is supplied with steam at 275^,
and it raises temperature of 882 lbs. water fk*om 46^' to 212^ in a, minutes, what will
bo total heat per sq. foot per hour, total heat per sq. foot per degree, and quantity
condensed per sq. foot per degree per hour ?
212® — 46° X 60-?- 4 = 2490° in an hour: 46° + 212° -r- 2 = 129° mean temper-
ature, and 275O — 129O = 146° difference oftempercUure.
= 45 563 units per sq.foot per hour, 45 563 -4- 146 = 31a. i units per sq.
40.2
foot per degree, and total heat of steam above Z29<' = xo68<'.
Hence ' = .292 lbs. steam condensed per sq.foot per degree per hour.
lOOO
lE^vaporatioxi.
^Evaporation or Vaporization is conversion of a fluid into vapor, and
it produces cold in consequence of heat being absorbed to form vapor.
It proceeds only from surface of fluids, and therefore, other t/iings equaij
must depend upon extent of surface exposed.
When a liquid is covered by a stratum of dry air, evaporation is rapid,
even when temperature is low.
As a large quantity of heat passes from a sensible to a latent state during
formation of vapor, it follows that cold is generated by evaporation.
Fluids evaporate in vacuo at from 120° to 125° below their boiling-point
Heat required, to Kvaporate 1 l"b. "NVater at Teinperatures
IdeloMT S1S° Ironx
a Vessel iii
{Thomas Box.)
open air at 33^.
H s a
is'
Water evapo
per sq foot
sarfacep'rho
0
Lba.
32
.027
42
.04
Sa
.058
62
.083
72
.117
82
.162
92
.223
X02
•303
X12
.406
122
.528
HEAT
1
^Vfe
1
HEAT
lost by radia-
tion from
ti
a
i
Unite.
Total lost
per hour.
5c &I
lost by radia-
tion fW>in
surface.
a
s
to evaporate
X lb. of wa-
ter.
UniU.
Units.
Unite.
0
Lbs.
Unite.
Unite.
Unlta.
—
—
109 1
29
13a
.706
x8a
ao2
XS06
270
424
2788
71
142
.916
158
x62
1445
375
581
2052
119
153
1. 178
'37
127
X392
405
605
2110
»74
162
1-505
X18
97
1346
386
566
205s
239
172
1895
106
72
13x2
358
504
1968
319
182
a.373
r.
50
"79
3»9
434
1862
415
192
2.947
32
1253
280
366
1758
533
202
3-633
V
»4
X228
24s
304
1664
t^'
212
4-471
63
—
X209
211
250
1580
849
—
—
—
—
.2 a
o
Units.
X068
1326
»637
2039
2475
3<H5
3685
4465
5397
To Compute Surfttoe of* a RefVigrerator.
Illustration of Table. — If it is required to cool 20 barrels, of 42 gallons each, of
beer, from 202° to 82"^ in an hour.
Result to be attained is to dissipate 42 X 8.33 (Ib& U. S. gallons) X 20 X 202 — • 82
= 840000 units of heat per hour.
At 202°, 4465 units are lost, and at 82^, 319, hence, average loss for each temper-
ature between extremes = 1850 units per sq.foot per hour.
_, 840000 , ^ . .....
Then —- — = 454 sq.feet »n a sttU air.
X850
The volume of air required per hour in this case would be about xooooo cube fteU
HEAT. 513
To Oompute Area of_0-rate and Consuxn^tion of* Fuel
jfor ICvapo ration.
UkutraUon of Table.— It it is required to evaporate 6 Beer gallons (282 cabe ins.}
of liquid per hour, at a temperature not exceediug 152^'.
6 gallons = 50 lbs. At 152°, water evaporated as per table = 1. 178 lbs. per hour.
^ = 43 gq.feet. Heat required to effect this = 1392 x S© = 69 600 uniU.
Assuming 6000 units as average economic value of coals, then -^— • = »»-6 U>t.
waly on a grate of x sq.foot
When it is practicable to evaporate at a high temperature, as at or above 212^, it
Is most economical
Thus, water requires only 1209 units per lb. if sur£BM;e is exposed, but if enclosed,
heat is reduced (1209 — 63) to 1146 unit&
EvaporaUve Power$ of Different Tubes per Degree ofHeaJt^per Sq. Foot of
Surface. — In Units.
Vertical tube, 230; Double-bottomed vessel, 330; Horizontal tube or Worm, 43a
To Compute "Volutne of "Water Evaporated in a g^iven
Tixne.
Illustratiow.— What is volume evaporated at 212°, In 15 minutes per sq. foot of
surface, in a double- bottomed vessel having an area of heating surface of 17 feet,
and subjected to steam at a pressure of 25 lbs. ?
Temperature of steam at 25 + 14.7 Iba = 96g^. 269° — 2x2° = 57°, and latent
beat = 927.
Then ?3£><lI^il2<Jl = 86.a «» BOfcr.
927 X 60
When Water is at a Lower Temperature than 212°.
If 120 gallons or iocx> lbs. of water were to be evaporated from 42^ in an
hour, from same vessel and under like pressure as preceding :
There would be required 1000 x (2x2° — 42^) 170000 units ofheai. Mean tempera-
tare of water while being heated = ^^ — = 127°.
2
Difference between temperature of steam and water = 267*' — 127<' = i4o<'.
Then, J- :; — =:.2x6 lioar^ztime to raise water to 212°; hence i — .2x6 rx
330 X 140 X 17
.784 hour left for evaporation, and quantity evaporated = 330X57X 17 X -7 4 ^
927
970.4 Ibs.^ or 32.44 gaUons.'
IDessiooatioxi.
Demecaiion, or the drying of a substance, is best effected in a drying
chamber, and it is imperative that to attain greatest effect the hot air
should be admitted at highest point of exposed substance and dis-
charged at its lowest.
Wood, submitted to an average temperature of 300° in an enclosed space
for a period of 2.5 days, will lose jts moisture at a consumption of i lb. of
wootl for 10.5 lbs. of wood dried, and evaporating 4 lbs. of water, equal to
3.66 lbs. of water per lb. of undried wood.
Limit of temperature for drying of wood is 340^.
514
HEAT.
Evaporation of "Water per Sq.- Foot of StiriCkoe p#r HotiA
{Dr. Dalton.)
rempei
of Wi
ater.
33
40
50
60
70
80
ETaporation
Calm. Air.
Brisk
Wind.
Lbs.
Lba.
Lbs.
•0349
•0459
•065s
.0448
.0589
.0841
.055
.0723
.1032
.0917
1257
1746
.1616
.2241
.1441
•1983
•2751
Texaperatare
of Water.
O
100
125
150
175
2CO
2X2
Evaporation.
Calm.
LicM
Air.
Lbs.
Lbs.
.3248
.4169
.6619
.8494
1.296
1.663
2.378
3'053
4.128
5.298
5239
6.724
BrUc
Wind.
Lbs.
• 5"6
X.043
2.043
3-74«
6.502
8.252
The rates of evaporation for these conditions of the air when petfsctly dry are as
I, 1.28, and 1.57.
To Compute Quantity of Water eitposed to Air that vooudd be evap&rated at
above, — Subtract tabulated weight of water corresponding to dew-jwint from
weight of water corresponding to temperature of dry air, and remainder is
weight of water that would be evaporated per sq. foot of surface p^ hour.
IDistillation.
Distillation is depriving vapor of its latent heat, and, though it may
be effected in a vacuum with very little heat, no advantage in regard to
a saving of lael is gained, as latent heat of vapor is increased propor-
tionately to diminution of sensible heat.
A temperature of 70° is sufficient for distillation of water in a vessel ex-
hausted of air.
Conduotion or Convection. o£ Heat.
Air and gases are very imperfect conductors. Heat appears to be
transmitted through them almost entirely by conveyance, the heated
portions of air becoming lighter, and diffusing the heat through the
mass in their ascent. Hence, in heating a room with air, the hot aii*
should be introduced at lowest part. The advantage of double win-
dows for retention of heat depends, in a great measure, upon sheet of ait
confined between them, through which heat is very slowly transmitted.
Convection of heat refers to transfer and diffusion of heat in a fiuid Biass>
by means of the motion of the particles of the mass.
Relative Internal Conducting I^owers of Varioxis
Sul^stanoes.
MeUOs.
Brass 76
Cast Iron 517
Copper 89
Cement 21
Chalk 6
Charcoal. .07
Slate...
Gold
Lead........
Platinum ....
.z8
.98
Minerals.
Porcelain 012
Silver 97
Terra Cotta.. .011
Tin. 3
Wrought Iron .44
Zinc 36
Coal, anth'cite 1.92
" bitnmin. 1.68
Ooke 1.98
Gypsum 3
Lime 34
Marble ..k..,. 1.33
* .t. .08
Apple
Ash..
.68
•73
Cotton 55
f^Mer down. . . .44
Alcohol
Firebrick 61
fireclay 76
Glass.... .96
...... X VTood ash
Woodi with Birch = .41 voUh Silver.
Birch I I Ebony. 5
Chestnut 7 | Elm 73
Hair cmd Pur toith Air s z.
Flannel 2.44 | Hair a | Silk 43
HempCanvaa .28} Hare*« fur 43 | Wool 5
Liquids with Water.
Oak.
Pine.
73
73
Aiconoi 93 I Proof spirit. ,85 I Turpentine ^t
Mercury 2.8 | Sulphxiric acid ..'z.7 (Water. a
BEAT.
515
Practical Deductions from preceding Results^
Asphalt compositions are best for resisting moisture and insuring dryness.
Being a slow conductor of heat, it will help to exclude or retain heat as de-
sired.
8laU is a very dry^ material, but, from its quick conducting power, it is
not adapted for retention of heat.
Cemenfg. — Plaster of Parte and Woods are well adapted for Iming of
rooms, having low conductive powers, while Hair amd Lime^ being a quick
conductor, is one of the coldest compositions.
Fire-brick absorbs much heat, and is well adapted for lining of fire-places,
etc, ; while //on, being a hij^h conductor of heat, is one of the worst of sub-
stances for this purpose. Comtnon brick is not a very slow conductor of heat.
Steam Pipe, — A wrought-iron pipe, 4 ins. in internal diameter, conveying
steam at a pressure of 35 lbs. per sq. inch (280°) and xoo feet in length,
will lose .84 W,
^ Casing to Pipes. — A like pipe with the aljove, cased with following mate-
rials and covered with canvas, to give like radiating power to the outer
surface, gave loss of heat in units per hour, and for t£e thickness given, as
follows :
Caiino.
.5 Inch.
Woollen Felt
71
100
173
Sawdust
Coal-asbes
I Iceh.
3 InchM.
4 InehM.
6 Inches.
36
55
no
16
26
60
7
II
27
4-3
7
16.6
CozidenBation.
Tredgold ascertained by experiment that steam at pressure (absolute)
of 17.5 lbs. per sq. inch, 221°, produced i cube foot of water per hour
by condensation in 182 sq. feet of cast-iron pipe, at a uniform and qui-
escent temperature of 60°. Hence, condensation .352 lb. water per
hour, or .0022 lbs. per degree of diflPerence of temperature (221—60).
From experiments of Mr. B. G. Nichol in England, 1875, it was deduced:
That rates of transmission of heat, between temperature of steam and
that of water of condensation at its exit, at the rate of 150 feet per minute,
may be taken as 380 units for vertical tubes and 520 for horizontal.
Oondensation of* Steaxn in Cast-iron Pipes. (M. BumaJt.)
Av«r«fri
Pr«H. par
Sq. Inch.
23
Temperatara.
Stfl«m.
o
333
Air.
o
365
Dtffereaee.
o
196.5
CoQdenMtioR p«r aq. foot of •ztemal HirfMe of pip*
per hour.
Bara.
Lb.
.581
Straw.
Lb.
.2
Pipe.
Lb.
.239
Waste.
Lb.
386
Plaater.
Lb.
•324
From these data, following constants are deduced for an absolute iiressure of
23 Iba per sq. inch of steam coDdcnsed, and heat passed off per sq. foot of external
surface of pipe per hour of i^ difference or temperature.
SUBFACK or PiFS.
Bare pipe
Straw coat
Cased with clay pipe. . .
steam
condensed
per Sq. Foot.
Lb.
.003
.00103
.001 15
Heat
paeaed
off.
Unite.
2.8l2
.968
f.106
SuRFACB Of Pipe.
Cotton wute i inch. ,
Earth and hair ,
While paint *..
steam
condensed
per Sq. Foot.
Lb.
.00146
.00165
.00156
Heat
pasted
off.
Onils.
1.384
1.568
1.^
5i6
USAT.
Pipes wer* 4.7a Ini. dlain«tor, .as iDcb thick, and had area of 58.5 aq. feet
Bare — rough surface as cast Straw cool— laid lengthwise .6 inch thick and bound.
i'tyj«— laid in clay pipe with an air space between them, the whole covered with
loam and straw. Waste cotton — i inch thick and bound with twine. Platter—
laid in clay and hair 2.36 ins. thick.
A wrought- iron pipe 3.75 ins. in external diameter, .as inch thick, and lagged
with felt and spun yarn .5 inch thick, condensed steam at 345O at rate of .262 lb.
per sq. foot per hour, in an external temt)erature of 6o<^.
Steazn. Condensed per Sq.. F'oot and per Degree per Ko-ur.
Mean Results of severed Erperiments with bare Ca^-iron Pipes, with Steam
at Absolute Pressure 0/20 lbs. per Sq. Inch.
.4 lb. per sq. foot, and .002 39 lb. per degree.
Hence, to ascertain quantity of heat lost by condensation of .002 39 lb. = — of a Ik
Difference of total and sensible heats of i lb. steam at 20 Ib& absolute pressure =
"51° + 32° — 2280 = 955 units, and 955-7-420 = 2.274 un\ts = heat (xmdensed.
The loss of heat fVom a naked boiler in air at 62^, under an absolute pressure of 50
lbs. per sq. inch, was 5.8 units.
Congelation and Xjiquefkotion.
Freezing water gives out 140° of heat. All solids absorb heat when
becoming fluid.
Particular quantity of heat which renders a substance fluid is termed
Hs caloric of fluidity, or latent heat.
Temperature of Solidification of Several Gases. (Faraday. )
Cyanogen 31O I Ammonia 103^ I Sulphuretted Hydrogen, 1230
Carbonic Acid 72® | Sulphurous Acid. . . 105O | Protoxide of Nitrogen. . 148O
Frigoriilo IMixtures.
MiXTOBXS.
Sea salt
Nitrate of ammonia . . .
Snow, or pounded ice. .
Muriate of ammonia )
Nitrate of potash )
Snow, or pounded ice. .
Phosphate of soda
Nitrate of ammonia . . .
Dilute mixed acids . . . .
Snow
Crystallized muriate )
of lime )
Snow
Dilute sulphuric acid . .
Phosphate of soda
Nitrate of ammonia . . .
Dilute nitrieacid
Snow
Dilute nitri« acid
Parta.
12;
5
\
X
8]
10]
3
a
K
Fall of
Temp«rBture.
0
0
—18 to
—25
-Sto
—18
-34 to
-so
—40 to
—73
-68 to
-9>
otO
—34
otO
-46
MiXTCBKS.
Nitrate of ammonia.
Water
Snow
Dilute sulphuric acid
Sulphate of soda. . . .
Diluted nitric acid . .
Nitrate of ammonia.
Carbonate of soda . . .
Water
Sulphate of soda ....
Muriate of ammonia.
Nitrate of potash....
Dilute nitric acid . . .
Phosphate of soda. . .
Dilute nitric acid . . .
Snow.
Muriate of lime
Potash
Snow.
Parts.
:!
6'
4 .
2
4.
J}
w
Fan of
Tempcratar*.
+50 to +4
— xoto— 60
+50 to —3
+3otO -7
4-50 to —10
-f-soto — I a
-f ao to —48
+32 to — sx
A Mixlure of Solid Carbonic Acid and Salphuric Ether, under reoeiver of an air-
pump, under pressures of .6 lbs. to 14 lb&, exhibited a temperature ranging Hrom
•^107® to -^%W*i wl^ich is t))e mOPt iQlpQS^ QPld «s .vet known. {Faraday.)
HBAT.
SI7
^Melting-points.
Mbtals.
Aluminum.,.. •••••
Antimony
Arsenic
Bismuth
Bronza
Calcium at red heat.
Ck>pper
Gold, pure
standard
i(
Iron, cast
2d melting.
It
Wrought.
" malleable forge
Lead
Lithium
Mercury ,
Platinum
Nickel, highest forge heat.
Potassium ,
Silver.
Sodium,
Steel...
Tin....,
Zinc...,
Allots.
Lead 2, Tin 3, Bismuth 5.
" I, " 3, " 5.
1400
810
365
476
1692
1996
(2282
12590
2156
!2000
2250
3479*
!2aoo
2450
3700*
12700
2912
3509*
608
356
—39
3200
136
(1250
(1873
194
2500
446
680
212
8IO
Allots.
Lead i, Tin 4, Bismuth 5
(C
ii
C(
Tin
ti
it
3t
3.
2,
n
(t
((
ti
t(
((
((
3 »••••■
2, Bismuth 5..
I.
1 (solder)
2 (sod solder).
I
2,
8,
Zinc I
Bismuth
ti
ii
Tin
Bism. 4,
I
I
I
Cadm. I
FuRible Plugs.
Lead 2, Tin 2.
it
it
it
6,
7.
8,
ii
it
tt
Various Su'bstanoes.
Ambergris
Beeswax
Carbonic acid
Glass
Ice
Lard
Nitro-Glycerine.
Phosphorus
Pitch
Saltpetre
Spermaceti
Stearine
Sulphur
Tallow
Wax, white.
* Ranklne.
240
334
199
552
475
360
368
155
286
336
39a
399
372
38i
410
MS
151
—108
2377
32
95
45
X12
9Jt
606
112
"4
239
92
143
Volume of Water, Antimony, and Cast iron, in the solid state, exceeds
that of the liquid, as evidenced by the floating of ice on water, and of cold
iron on iron in a liquid state.
Soiling-points. (Under One Atmosphere.)
LiouiiM. o Liquids.
Alcohol, B. g. 813
Ammonia
Benzine.
Chloroform
Ether
Linseed oil
Mercury
Milk
Nitric acid, s. g. 1.42
ii It **!<..
Oil of Turpentine
Petroleum, rectified
PbospboruB
Sea water, average
Sulphur
Sulphuric acid, s. g. 1.848.
it it - .
I.J...
'Hher
173
140
146
100
597
648
213
248
210
315
316
554
213.
570
590
240
100
Turpentine
Water
" in vacuo
Whale oil
Saturated Solutions.
Acetate of Soda.
" " Potash
Brine
Carbonate of Soda
" " Potash
Nitrate of Soda
" " Potash
Salt, common
Various SuBSTAh'CBa
Coal Tar
Naphtha
315
212
630
255.8
336
226
220.3
275
250
240.6
227.3
335
>86
5i8
H}32A1\
Pareaaixre oi Saturated. Vapors ixnder Various temper-
atures. {RegnauU \
Tamper-
atnr*.
o
32
50
68
86
104
183
X40
176
»94
Water.
Alcohol.
Eth«r.
Lb*.
Lb*.
Lbs.
.089
.346
3-53
.178
.466
5-54
•337
.851
8.6
.609
1-52
12.33
. 1.06
8.59
17.67
t.78
4.36
24-53
3.88
6.77
33-47
1§'
10.43
44.67
6.86
«5-72
57-01
xo.z6
23.03
75-41
Chloro-
Tetnpmr-
Chloro-
form.
•tore.
Water.
Alcohol.
Ether.
form.
Lba.
0
Lbt.
Lb*.
Lbe.
LU.
—
313
'4-7
33.6
95- > 7
45-54
2.53
230
20.8
45-5
130.9
58-42
3.68
340.8
25-37
—
'37
Tttrp'line
5-34
348
39.88
63.05
4-97
7.04
366
39-27
83.8
—
6.71
10.14
B76.8
46.87
—
—
'ISZ
384
52.56
109. 1
—
8.94
18.88
303
69.37
140.4
—
11.7
26.46
305.6
73-07
1473
—
—
35.03
330
89.97
—
—
«3-»
Boiling-points of Water corresponding to Altitudes ofBaromeier between
(a and 31 Ins»
Barom.
BoiliTiR-point.
Barmn.
Boiling-point.
Baroin.
Boiling-point.
Barom.
Boiling-point
36
36.5
37
0
304.91
»8S
0
207-55
208.43
209.31
29
29-5
30
0
2iai9
311.07
313
30-5
32
0
313.88
213.76
Boiling-point of Salt water, 2i3»2°. Water may be heated in a Digestei
to 400° without boiling.
Fluids boil in a vacuum with less heat than under pressure of atmosphere.
On Mont Blanc water boils at 187° ; and in a vacuum water boils at 98° to
100°, according as it is more or less perfect
Water may be reduced to 50 If confined in tubes of from .003 to .005 inch !n dtam-
eter: this is in consequence of adhesion of water to surfkce of tube, interfering with
a change In its state. It may also be reduced in its temperature below 390 if it ia
kept perfectly quiescent
Kfibot upon Various Bodies "b^r Heat.
Wedgewood's zero is 1077° (Fahrenheit), and each degree = 130°.
In designation of degrees of temperature, symbol -|- is omitted when temperature
Is above o; but when below it, symbol — must be prefixed.
Degrees.
Acetiflcation ends .... 88
Acetous fermen-) »
tationbegins..} ••• 'O
Air Furnace 3300
Ammonia (liq.) freezes — 46
Blood (hum.), heat of. 98
" freezes. 35
Brandy f^ezea — 7
Charcoal burns 800
Cold, greatest artifia — 166
" " natural —56
Common fire 790
Fire brick. . . .4000 to 5000
Gutta-percha soflena . 145
Heat, cherry red 1500
" (Daniell) 1141
bright red i860
red, visible by I _
day .P°77
white 3900
14
It
Deg
-}
117
293
Highest natural tem-
perature, Egypt
India-rubber and
Gutta-percha vul-
canize
Iron, bright red in)
the dark } 752
Iron, red hot in twi- ) qq
light } ^4
Iron, wrought, welda .3700
Ignition of bodies .... 750
Combustion of do. . . 800
Mercury volatilizes... 680
Milk n^ezes 30
Nitric Acid (sp.gra v. )
1.434) freezes.... J ^
Nitrous Oxide freezes —150
Olive-oil freezes 36
Petroleum boils 306
Proof Spirit freezes. . . — 7
Degrees.
Sea- water ft'eezes.... 38
Snow and Salt, equal )
parts I ^
Spirits Turpen. (feezes 14
Steel, faint yellow. . . . 430
" Aill " .... 470
purple 530
blue 550
fbll blue 560
dark '' 600
polished, blue .. 580
'* straw color 460
Strong Wines freeze. . ao
Sulph. Acid (sp. grav. \
1.641) flreezes.... ) *5
Sulph. Ether fVeezes. .—46
Vinegar ft'eezes 38
Vinous ferment ..60 to 77
Zinc boila 1873
Wood, dried. 340
(t
(t
Volume of Several
Uiq.uid.8
ftttam I Steam. I
I Water 1700 1 x AloohoL sb8 | x £Uier 398 \ x Tiurpentint . . X93
at their 8oilixis*poixit»
Steam. I Steun.
HEAT.
SI9
STeitflxt ooirrespoiidizie to Soiliii^-polixt of Pizva Inciter.
Boiling-poifU at Level of S€a = 2^12°,
DogFM.
Feet.
IHlif
Feet.
Decree.
Feet. 1
Degree.
197
X96
Feet.
Dagref.
211
a 10
521
1569
2625
3689
4224
203
202
20X
200
4761
5300
5841
6384
6929
7476
^5
8576
19s
194
193
192
Feet.
9129
9684
X024Y
10800
Correction for temperature of air same as given at page 428 for Elevation
by a Barometer by multiplying by C.
Illustration.— If water boils at a temperature of xkP and 0 = 1360,
Then 6384 x 108 = 6894. 72 ^t
TJndergrovxnd Temperature.
Mean increase of underground temperature per foot, from observations in
36 mines in various and extended localities, is .01565°^ 1° in 64 feet.
Uiuear ISxpansion or IDilatatio^ of* a Bar or Priam "by
Keat.
For I* in a Length of 100 Feet,
Metals, Minerals, etc.
Inch.
Antiorany. .007 22
Bismuth 009 28
Brass , .oia 5
*^ yellow 0126
Brick 001 44
Cast Iron 0074
Cement : 009 56
Copper flrom o^ to 212° on 5
" trova 32° to 572° 004 18
Fire brick 003 3
Glass 005 74
*' flint 00541
" tube 0612
Gold— Paris standard annealed.. .0x0 x
" " *' unannealed .0103
Granite 005 25
Gun Metal— x6 copper 4- x tin... .0x27
" " 8 copper -}- I tin . . . .0121
Ice 033 3
Iron, Ibrged 008 14
" ft-om o® to 212O 007 88
Inch.
Iron, fl*om 32° to 572° 003 a6
Iron wire ooS 23
Lead .019
Marble 00566
Palladium 00667
Platinum 00571
" from 32° to 572" octtof
Sandstone 013
" 00814
Silver 012 7
Speculum metal .013
Steel, rod 007 63
cast .007 a
tempered 008 26
not tempered .007 19
Tin 014 5
Water 000 222 9
White Solder — tin i -\- 2 lead. . .016 7
Zinc, forged , .0207
sheet 019 6
8-|-itin 0179
u
(«
It
To Compute Xjinear B^xpansion of a Sulsstanoe.
Multiply difference of the temperatures by the decimal in the above table. Or,
Divide x by it, and quotient will give proportion.
Superjicial expcamon is twice linear^ and cubical is three times linear.
Illustration x.— A rod of copper 100 feet In length will expand between tem-
peratures of 33O and 2X2°. 2x2 — 32 = 180 X -ox 15 = 2.07 ins.
a.— A cube of cast iron of x foot will expand in volume between temperatures ol
6aO and 2x2°. 2x2—63 = 150, and 150X . 0074 = 1. xi, which -r- 100 for x foot =
«oixx foot, and .oxxi X 3 = -0333 foot.
Some solids, as Ice, Cast iron, etc., have more volume when near to thefr melting-
point than when melted. This is illustrated in the floating of solid metal In a liquid.
filxpansion of AVater.
Water expands from temperature of maximum density (see page 520),
39.1°, to 46°, at which degree it regains its initial volume of 33°, and from
tbonce it expands under one atmosphere to 212° ; and its cubical expansion
is .0466. that is, its volume is dilated from z at 32^ to 1.0466 at ai2°.
Its expansion increases in a greater ratio thtn that of its temperature*
520
HEAT.
-Xo Coxnp-ate "Dexiaity of^'Water at a sivexx Texxiperatixre.
62.5 X 2
= approziincUe density, t repraenting temperature of water.
t-\-46i 500
500 ' < + 461
Illustration. —What is density
»f pure water at 298° f
62.5X2
298 -\- 461
500
+
500
298 + 461
= 57.43 lb*, or wetght 0/
I cube foot
Expansion of Water. (DaUon.)
Tamp.
Rrpansionr
Temp.
Expansion.
Temp.
0
22
♦46
X.OO09
X
I
0
52
72
92
I 00021
I.ooz 8
1.00477
0
112
132
152
Expansion.
Temp.
EzpADaiOB.
1.0088
I.01367
1.01934
0
172
192
212
1025 75
1.03265
1.0466
Hence, at 72°, water expands
* Greatest density 39.1°.
I
.0018
= 555- 55^b P^ft of its original bulk.
Expansion of Liq.uids from 3fi° to 812°.
Liquids. Volume at 212*. Liqciob.
Alcohol.... »
Linseed oil
Mercury
212° to 392°.
392° to 572°.
Nitric acid
I. II
X.08
I.OIS4
1.018 433 1
1.0188679
I. IX
Volume at 32° = i.
Volume at axa*.
Olive oil
Sulphuric acid
" ether.
Turpentine
Water.
Water sat. with salt
1.08
1.06
1.07
1.07
X.0466
1.05
Expansion of G ases fVo«a 38° to 818°. Volume at 32° = x.
Gasbs.
Air
Hydrogen . . . . i
3.35
Carbonic acid, i
3-32
.. I Atmosphere.'.
3'45 "
Volume
at 312°.
1.36706
1.36964
1.366 13
X. 366 16
1.37099
1-38455
Gases.
Nitrous oxide . . . i Atmosphere
Sulphurous acid, x
X. 16
Carbonic oxide . . x
Cyanogen i
(t
C(
Volara*
at 2ia*.
1.317?
X.3903
X.398
X.3669
'•3877
Expansion of Gases is uniform for all temperatures.
Volume of One Pound of Vaiioiu Gases at 32° under one Atmosphere.
Cube feet.
Air 12.387
Carbonic acid 8. zoi
Ether, vapor 4. 777
JPCxpansion of A.ir. {DaUon.)
Cube iSset.
Hydrogen 178.83
Nitrogen 12.753
defiant 12.58
Cobefeet
Oxygen 12.205
Mercury 1.776
Steam 19-913
EzpftD'
ston.
Temp.
Expan-
sion.
Temp.
Elxpan-
sion.
Temp.
Expan-
sion.
Tempb
Expan-
sion.
Temp.
Expan-
sion.
Temp.
0
0
0
0
0
0
32
X
40
X.021
60
1.066
80
1. 1 10
100
I<X52
392
33
X.002
45
1.032
65
1.077
85
X.X2I
200
1.354
482
34
X.004
50
1043
70
1.089
90
I>X32
212
1-376
680
35
1.007
55
»-o55
75
1.099
95
X X42
302
1.558
772
1.739
1.912
2.028
2.JI2
To Compute Volunne of a Constant Mi^'eight of .A.ir or
i*enmanent Gl-as for any Pressure.
When volume at a given pressure is knaum^ temperature remaining con-
ttant. RuLU. — Multiply given volume by given pressure and divide by
new pressure.
ExAKPLB.— Pressure at 312°=: 18.92 lbs. per sq. inch, and volume X6.9X cube feel;
what is volume at pressure of 13.86 lbs.
X6.9X X x3.86n-x8.93 := xa.39 o/^feet
HSAT.
521
ReUUitfe Densities of some Vapors.
Water X. Alcohol a. 59. Ether 4.16. Spirits of Turpentine 8.06. Sulphur 3.59.
Volume, Pressure, and Density of* A.ir at Various Tezn*
peratures.
Volume and Atmospheric Pressure at 63^ =
I.
Yolnine of
z lb. of air at
Preesnre
ofairiven
weiffht of
Density, or
weight of one
Volume of
I lb. of air at
Pressure
ofairiven
wcipit of
a.\r.
Density, or
weisrht of one
Temper-
atnre.
atmoapberie
preasureof
cube foot
ofi^rat
Temper*
atore.
atmospheric
pressure of
cube foot
of air at
::4.7 »»>••
14.7 lbs.
14.7 lbs.
itti .
14 7 lbs.
0
Cube feet.
Ltie. per
Sq. Inch.
Lbs.
0
Cube feet.
Lbs. per
Sq. Inch.
Lbs.
0
".583
13.06
13-86
.086 331
360
20.63
23.08
.048 476
32
12.387
.080738
380
21. 131
23.64
•047 323
40
12.586
14.08
.079439
400
21.634
34.3
.046 223
50
13.84
'4.36
.077 884
425
32.263
34.9
•04492
63
13-14X
«4-7
.076097
450
32.89
35.61
.043 686
^
13-342
14.93
•07495
475
23.5»8
36.31
.042 52
13.593
1S2I
•073565
500
24.146
37.01
.041414
90
13.845
1549
.07223
525
24-775
37.71
.040364
xoo
14.096
15.77
.070942
550
25-403
38.42
•039365
.038415
X30
14.592
16.33
.0685
575
26.031
39.12
140
«5.»
16.89
.066221
600
36.659
29.82 .
-037 5«
160
15603
»7.5
.064088
650
27.9»5
31-23
.035 822
180
16.106
18.02
.06209
700
29.171
32.635
.03428
300
16.606
18.58
.06021
750
30.428
3404
.032865
210
16.86
18.86
.059313
800
31.684
35-445
.031 561
313
16.91
xa93
.059135
.058443
850
32.941
36.85
.030358
220
17.111
19.14
900
34-197
38-255
.029 242
340
17.613
19.7
.056774
950
35.454
39-66
.028206
360
18.116
3a 37
•0552
1000
36.811
41-065
.027241
380
18.631
30.83
•0537*
1500
49-375
55-115
.020295
300
19. I3X
21.39
.052297
2000
61.94
69.165
.016172
320
19. 634
21-95
•050959
2500
74-565
83.215
013441
340
3ai36
33.51
.049686
3000
87-13
97-265
.011499
To Compute Volume of a Constant 'Weight of Air or
other Permanent G}-as for any otlier Pressure and
Temperature.
Wken volume is htoton at a given pressure and temperature. Rule. — Mul-
tiply given volume by given pressure, and by new absolute temperature,
and divide by new pressure, and by given absolute temperature.
ExAMFLB.'— Given volume 16.91 cube feet, pressure 13.86 lbs., and temperature
32O; what is volume at this temperature?
Temperature fbr volume 16.91 = 212O.
16.91 X 13.86 X 32 4" 461 -^ 13.86 X 212 + 461 = 13.39 cutfeJuL
To Compute Pressure of a Constant "^VeigHt of A.ir or
other Perxnanent G^as ibr any other Volume and,
Temperature.
IVhen pressure is known Jor a given volume and temperature. Rule. —
Multiply given pressure by new absolute temperature, and divide by given
absolute temperature.
NoTK.— Absolute temperature is found by adding 461O to temperature.
EX4MPX.B.— Given pressure 13.86 lbs., and temperature at this volume 33O; what
is pressure at temperature of 212O?
13.86 X 813 +461-?- 32 + 461 :?= 18.93 lbs.
Xx*
522 HEAT.
To Compnt© "Volume of a Constant "Weiglit of Air ov
otlner Permanent O-as at any Temperature.
When volume at a given temperature is kmnon^ pnsswre being contfmu.
Rule. — Multiply given volume by uew absolute temperature, and divide
by given absdute temperature.
Absolute zero-point by different thermometrical scales is: Fahrenheit —461.2^;
Reaumur — 319.2°; Centigrade —374°.
EZAMPLK.— Volume of i lb. air at 32® = 12.387 cube feet; what is its volume at
•120?
12.387 X 212 -1-461-4-32 + 461 = 16.91 cube feet
To Compute Increased Volume of a Constant "Woifflit
of A.ir.
When initial volume at 62® = i under 1 atmosphere. Rule. — To givea
temperature add 461, and divide sum by 523 (62 + 461).
Example. —Assume elements of preceding case.
212^-1-461 -;- 533 = 1.287 cow^arctitive volume to x.
To Compute Pressure of a Constant Weiglit of Air or
other Oas at OS®, and at l^.'T lbs. I»res8ure per Sq.. In.,
witli Coixatant Volume, for a given Temperature.
Rule.— Add 461 to given temperature, and divide sum by 35.5S.
Example. —Temperature is 212^'; what is pressure?
212 + 461-7-35.58 = 18.92 Ws.
To Compute Volume, Fressnre, Temperature, and
IDensity of A.ir.
« + 46i ^ < + 46i « '+46X „ ^ » A
^ - = V; p =V; J^-^ =p; V 3.7074 p— 461 = «; and
|> 2.71 39.8 V2.7I # *-rr -r
3. 71 .F, = D. i rqfraenting temperature, p pressure in lbs. per sq. tncft, V wJ-
ume in cubefeet^ and D voeiglU of x ctibeftyot at 14.7 lbs. per sq. inch.
Product of volume and pressure of a constant weight of air, or any other
permanent gas, is equal to product of absolute temperature and a coefficient,
determined for each gas by its density.
Or,Vjp = C« + 46i.
Coefficients, as determined by volumes and oonseqaent densitieB.*
Air 2.71
Carbonic acid 4. 14
Ether, vapor 7.02
Hydrogen 1875
Nitrogen 2.63
Oleflant 2.67
Oxygen 3.
Mercury 18.
Steam x.68
• Sm D. K. Clark, Londoo, 1877, paga 349.
Deorease of Teniperature by A.ltitude8.
In eUar «hf. Wttk doudf tkf.
From X to xooofeet i°in 130 net.. x^' in 222 feel
X " xoooo " lO " a8§ *♦ jO "
33«
ti
X " 20000 " xO *♦ 365 " lO" 468 "
To Compute Temperature to wliloh. a Stibstanoe of a
given UenstH or Diinexision must be Submitted or
Reduced, to give it a G^reater or Uess Uength or Vol-
ume by £2xpaxksion or Contraction.
Lineai. — TTAen Length is to be increased. ~^^ — \-t=iT L and { nprusnk
ing lengths of increased and primitive substance in like denominations^ T astd t tern
peratures ofL andl^ and G expansion <(f substance fbr eaeh degree qfhtaX.
HSAT. 523
Iiujsnu.TiON.— A copper rod at 39^ Is 100 feet In length; to what temperature
maat it be subjected to increase its length 1.1633 ins. ?
Expansion for a length of 100 feet of copper for z^ = .0115.
.CO X » + .. .633 -ro^X " ^ Lig33 ^ fl.,
.0115 .01X5 ^^
Illustration.-- Take elements of preceding case.
iaoi.x633 — laoo
.0115
133. 16° = loi. 16 — 133. 16 = 3a9.
7o Recluoe Degrees of* Falirenlieit to Reauxnur and Cexi«*
tiisrade, aaxd Contrari-wise.
irabrenlieit to Reaumur. If above zero. — Multiply difference
between number of degrees and 32 by 4, and divide product by 9.
Thus, ai20 — 320 = 180°, and 180O y^^^^ — ^o^
If hdow zero.— Add 32 to number of degrees ; multiply sum by 4, and
divide product by 9.
Thus, — 400 -I- 32O = 72O and 72° x 4 -^ 9 = —32°.
Reaumur to Falirenlieit. If above freezinff-poinl, — Multiply
number of degrees by 9, divide by 4, and add 32 to quotient.
. Thus, 8c^ X 9^'4 ^ «8oO, and 180° -f 32 = 2120.
If below freezinff-point. — Multiply ntuuber of degrees by 9, divide by 4,
and subtract 32 from product.
Thus, —32° X 9 -i- 4 = 72°, and 72° — 32 = — 40O.
Falirenlieit to Centigrade. If above zero. — Multiply difference
between nnmber of degrees and 32 by 5, and divide product by 9^
Thus, ai20— 32OX 5-5-9 = 180^X5-5-9=1000.
//* behw zero, — Add 32 to number of degrees, multiply sum by 5, and
divide product by 9.
Thus, —400-1-320 X 5-^9 = 72° X S-i-9= —40®.
Centigrade to Falirenlieit. If above freezing-point. — Multiply
nmnber of degrees by 9, divide product by 5, and add 32 to quotient
Thus, looPx 9-5-5= 180O, and 1800-^-32=2120.
Ifbehwfreeeinff-poini' — Multiply number of degrees by 9, divide product
by 5, and take difference between 32 and quotient.
Thus, — loO X 9 -T- 5 = 180, and 180 rv 32 = 14O.
Reaumur to Centigrade.— Divide by 4, and add product
Thus, 80O -^ 4 = aoP, and 20O 4- 80O = looo.
Centigrade to Reaumur. — Divide by 5, and subtract product
Thus, jooo -5- 5 = «oO, and xooo — 20 = 80O.
Corretponding Degrees upon the Three Scales.
Fakr. I Cmi. I R«nun. F«hr. Cent. Bcmri. Fthr. Cent. R«Mm..
Renun.
F«hr.
Cent.
Reaam.
Fthr.
Cent.
80
3a
0
0
—40
—40
aza \ lOQ J 00 3a o o — 40 — 40 — 3a
T*o Compute Bxpansion of ITluids in Volume.
RuLB. — Proceed bv preceding formulas for computing length of a sub-
stance. Substitute V and v for volume, instead of L and /, the lengths.
524
HEAT, VENTILATION, BUILDINGS, ETC.
Illustration. — A closed vessel contains 6 cube feet of water at a temperature of
40^; to what height will a column of it rise in a pipe 1.152 ins. in area, when it is
elposod to a temperature of 130^^?
X. 152 in& = .008 sq. Jbot. C for water = .000 222 9.
6 (i -f" 'Ooo 222 9 (130 — 40)) = 6. 120366. and ~ ^-— = 15.047 Hnealfeet
.008
Temperature "by .Agitation..
RaulU of Experiments wWi Water enclused in a Vessel cuid violenUy AgiUiML
Temperature of Air, 60. 5° ; of Water, 59. 5°.
Duration
of Agitation.
Hour.
•5
I
Incnaie
ofTemperatare.
O
10
J4-5
Duration
of AKiUtion.
Honn.
2
3
IncnuiM
ofTemperatare.
O
19s
29.5
J>oration
of Afcitiition.
Hours.
S
6
IncreaM
of Temperatart.
o
39-5
4*5
VENTILATION.
Suildinss, ^pax^znents, eto.
/« Ventilation of AparimenU, — From 3.5 to 5 cube feet of air are required
per minute in winter, and 5 to 10 feet in summer for each occupant In
Hospitals, this rate must be materially increased.
Ventilation is attained by both natural draught and artificial means. In
first case the ascensional force is measured by difference in weight of two
columns of air of same height, the height beingdetermined by total difference
of level between entrance for warm air and its escape into the atmosphere,
llie difference of weight is ascertained from dif)*erence of temperatures of
ascending warm air and the external atmosphere, as by Table, page 521, or
by formula, page 522.
Volumes of Air T)iBoUarged tlirough. a Ventilator One
Koot Square of Opening, at Various Heights and
Temperatures.
Height of
VenUlator
from
Base-line.
Feet.
10
»5
90
30
Ezceu of Temperature of Apartment
above that of External Air.
Height of
VenUlator
EZCM
a
5°
loO
Cft.
164
15°
C.ft
200
20O
Cft.
235
25«
Cft.
260
300
C.ft.
284
Baae-iine.
50
C.ft.
218
C.ft.
116
Feet.
35
142
184
202
232
260
285
318
284
330
368
3i«
368
410
34a
404
450
40
45
50
235
248
260
201
284
347
403
450
493
55
270
Ezceet of Temperature of Apartment
above that of Eitemal Air.
loP
Cft.
306
^41
367
385
15^
Cft.
376
403
427
450
472
200
a5*>
3o<»
Cft.
C.ft
Cft.
436
486
53«
1 46s ! 518
570
493
55«
60s
518
579
635
54»
ftos
66,
Velocity of draft bavine been ascertained Ibr any particular case, together with
volume of air to be suppl^ per minute, sectional area of both air passages may be
computed from these data.
KeatixMS "by I9Cot "Water.
One sq. foot of plate or pipe surface at 200^ will heat from 40 to 100 cube
feet of enclosed space to 70° where extreme depression of temperature is
-10°.
The range from 40 to 100 is to meet conditions of exposed or corner
buildings, of buildings less exposed, as intermediate ones of a cluster or
block, and of rooms intermediate between the front and rear.
When the air is in constant course of change, as required for ventilation
or occupation of space, these proportions are to be very raftterially increased
""s per following rules.
HEAT, YEKTILATIOK, AND HEATING. $2$
In detenniniDg length of pipe for any given space it is proper to include
in Uie computation die character and occupancy of the space. Thus, a
church, during hours of service, or a dwelling-room, will require less service
of plate or length of pipe than a hallway or a public building.
Reduction of Heat by Surfaces of Glass or Metal.— In addition to the
volume of air to be heated per minute for each occupant, 1.25 cube feet for
each sq. foot of glass or metal the space is enclosed with nkust be added.
The communicating power ot<he glass and metal being directly' proportion-
ate to difterence of external and internal temperature of the air. Thus, 80
feet of glass will reduce 100 feet of air per minute.
When Pipes are laid in Trenches in the Earth, — The loss of heat is es-
timated by Mr. Hood at from 5 to 7 per cent.
Circulation of Water in Pipes. — In consequence of the complex forms of
heating-pipes and the roughness of their internal surface, it is impracticable
to apply a rule to detennme the velocity' of circulation, as consequent upon
difference of weights of ascending and descending columns of the water.
For a difference of temperature in the two columns of 30° (190° — 160°)
and a height of ao feet, the velocity due to the height would be 3.74 feet
In practice, not .3, and in some cases but .1, would be attained.
In Churches and I^r^e Public Rooms, with ordinary area of doors aod windows
and moderate veutilation, a large amount of heat is generated by the respiration
of the persons assembled therein. /
In these cases it is not necessary to heat the air above 55°, and a rule that will
meet the ordinary ranges of temperature (Tom lo^ is to divide volume in cube
feet by 200, and quotient will give area of plate in sq. feet or length of 4- inch pipe
in lineal feet
Volume of Air required pei' Hour for each Occupant in an Enclosed Space-
{GenercU Morin.)
CabeFMt.
Hospitals. . . . 3IOO to 3700
Workshops . . 2100 " 3500
Lecture-rooms 1000 to 2100
Theatres. 1400 '' 1800
Ctabe Feet I Cabe Feet.
Prisons x8oc
Schools 424 to 1060
To Coxxxpute Xjensth of Iron Pipe req.uired to Keat A.lr
in axx l£xicloaed Space.
By Hot Water.
RuLR»— -Multiply volume of air to be heated per minute in cube feet by
difference of temperatures in space and external air, divide product by differ-
ence ci temperatures of surface of pipe and space, multiply result by follow-
ing coefficients, and product will give length of pipe m feet
For diameter of 4 ins. multiply by .5 to .55, for 3 ins. by .7 to .75, and for
a ins. by i to i.i.
A pipe 4 ins. in diameter, .375 inch thick, and i foot in length has an
area of internal surface of ix>5 sq.feei,
EzAMFUi — ^Volume of a room of a protected dwelling is 4000 cube feet; what
length of 4 Ina pipe, at 200O, is necessary to maintain a temperature of jcP, when
•xtemal air is at o^* f
42222<5E2x.4 = 862^rf.
200 — 70
In oomptitin^ lenffth of pipe or surface of plate it is to be borne in mind
that the coefficients here given and computation in f dlowing table are based
upon a ventilation or change of air ordinarily of 3.5 to 5 cube feet per
person, and from 5 to 10 cube feet in summer per minute. Hence, whoi
the ventilation U restrictad the coefficient may be correspondingly in-
creased.
526
HEAT AND HBATING.
Uenstlis of XTour-Inoli IPipe to Heat lOOO Cube ITeet
of* ^ir per Adlixxute. {Ckas. Hood.)
Temperature of Pipe soo**.
Tempentnre
of
External Air.
lo
i6
20
26
30
36
40
50
Temperatara af Baildiog.
45^
50°
55°
60°
Feet.
650
70O
75°
80O
Ss'^
Feet.
Feet.
Feet.
Feet.
Feet.
F^t.
Feet
Feet.
136
150
«74
BOO
339
259
293
338
367
«05
127
X51
176
204
323
265
300
337
3J5
9'
XI2
135
160
187
216
347
281
69
90
113
136
162
190
320
253
288
54
75
97
ISO
145
173
303
234
2O9
35
52
73
58
t
1 30
147
«75
306
239
18
37
104
'g?
>57
187
220
—
—
«9
40
62
ZZ3
140
171
90C
Proper Texxiperat-ares of ESnolosecl Spaces.
SPACia.
Temper-
atare
required.
SrAcn.
Work-rooms manufactories, etc.
0
55
55
%
60
65
Dwelling- rooms
Churches and like spaces
Greenhouses v
GraDcries
Hot-houses
Schools. lecture- rooms.
Drying rooms, when filled
*' '' for curing paper..
Halls, shops, waiting rooms, etc.
Dwelling- rooms
Feet.
t^
358
327
3<7
376
25s
204
TeInpa^
atara
required.
o
70
80
70
I30
JBoiler.
Boiler for steam-heating should be capable of evaporatin^ic as much water
as the pipes or surfaces will condense in equal times. Mr. Hood recom-
mends that 6 sq. feet of direct heating-surfisice of boiler should be provided
to evaporate a cube foot per hour. Adopt mean weight of steam of 5 lbs.
above pressure of atmosphere, or ao Ibe. absolute pressure, condensed per sq.
foot of pipe per degree of difference of temperature per hour, viz., .002 35 lb.
(as given by D. K. Clark), the quantity of pipe or {)late surface that would
form a cube foot of condensed water per hour, weight of like volume of
water 62.4 lbs., would be, per 1° difference of temperature,
62. 4 -i-. 002 35 = 26 550 sq.feelj and for differences of 168°, 158°, 148°, and 108**,
required surface would be respectively (36550-^168 = 158) 158, x68, 179, and 246
tq.Jwt,
Henoe, assuming, as previously stated, that 4 sq. feet of direct and effec-
tive heating boiler-surface, or its equivalent flue or tube sur&ce, will evap-
orate 1 cube foot of water per hour, 158 sq. feet of 8tean>-pipe or plate will
require 4 sq. feet of direct surface, etc, for a temperature dt 60^, and cor-
respondingly for other temperatores.
Boiler-power. — One sq. foot of boiler-surface exposed to direct action of
fire, or 3 sq. feet of flue-surfiice, will suffice, with good coal, for heating 50
sq. feet of 4-inch, 66 of 3-inch, and xoo of 2-inch pipe. Mr. Hood assigns the
proportion at 40 feet of 4-inch pipe for all purposes. Usual rate of com-
bustion of coal is 10 or II lbs. per sq. foot of grate-surface, and at this rate,
ao sq. ins. of grate suffice for heating 40 feet of 4-inch pipe.
Four sq. feet of direct heating boiler-surface, or equivalent flue or tnbe
surface, exposed to direct action of a good fire, are capable of eraporating
t cube ifoot of water per hour.
According to M. Grouvelle, x sq. meter of pipe-snrfkce (ia76 sq. feet), heated to
6eP an otriinary room alike to a libniry or office, of ftom 90 to koo cube meteis
(3178 to 3^31 cube feet).
HEAT, WABUINO BUILDINGS, BTC.
527
If a worinhop to be heated to a bif^ temperatiiTe, x sq. meter (11x76 iq. feet) of
Burfifcce is assigned to 70 cube meters. (3473 cube feet) = 4. 35 sq. feet or 5. 11 lineal
feet of 4-iQch pipe per 1000 cube feet.
For beating workshops, having a transverse section of 260 sq. feet, with a window-
surface of one sixth total surface, it is customary in France to assign 1.33 sq. feet
of iron pipe surface per lineal foot of shop = 5.3 sq. feet per 1000 cube feet.
lUusircUiiHts of extensive Heating by Steam. (R- Briffgsy M. J.- O. & )
X. Total number of rooms, including halls and vaults 286
" Area of floor surface 137 370 sq. feet.
" Volume of rooms 1 923 500 cube feet
•* Number of occupants 650
Maximum average of occupants at any time - 1300
Volume per occupant, excludmg vaults 1443 cube feet
Boilers. — 8 with X73 sq. feet of grate surfiu^e and 8000 sq. feet of heating surface.
Furnishing steam in addition to the above, to operate the elevators and electric
dynamos, elevating wator, and supplying steam to heat a distant building, requiring
one third of their capacity.
Sy Steam.
To Ooraptite I^ensth. of Iron I*ipe reqLnired. to Keat A.iv
in an. SSnoloaed. Space, with. Steam at S 1138. per Sq.
Inolx alcove Pressure of* A^tmosphere.
Rule. — Multiply volume of air in cube feet to be heated per minute, by
difference of temperature in space and external air, divide product by coeffi-
cients in preceding table, and quotient will give length of 4-inch pipe in
lineal feet, or area of plate-surface iu sq, feet
Temperature of steam at 5 lbs.-f pressure = 228°. Hence, if temperature of space
required is 60®, 70°, 80®, or 120**, the differences will be 168°, 158°, 148*^, and 108**,
which for a coefficient of .5, as given in rule for hot water, would be 336, 316, 296,
and 2i6, for a pipe 4 ins. in diameter, and for
3-inch pii>e 252
2 " " 168
I " " 84
iLtrsTRATTOW.— Volume of combined spaces of a fectory is socxjo cube feet; what
surface of wrought iron plate at 200° is necessary to maintain a temperature of 50**
when external air is at 0° f
70"
8o»
120"
237
222
163
158
148
108
79
74
54
50000 X 50 — o
200 •
50
X .4 = 6666 square feet
Coal Consunied. per 'H.oxit' to Heat IQO Feet of X^ipe,
{Chas. Hood.)
1^^^ ^ DifliBreDee of Teapentnre of Pipe and A ir In Spwe, In DofpnaM.
PilM.
150
>45
140
135
Lb*.
LU.
Lbs.
Lbs.
l.l
I.I
I.I
I
2-3
2.2
2.2
3.X
3 5
3-4
3-3
3>
4-7
4-5
4-4
4-2
130
"5
Lbs.
Lbs.
I
•9
a
1.9
3
2.9
4.1
3-9
120
US
XXO
>o5
100
95
90
85
80
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
LU.
Lbs.
•9
•9
.8
.8
•7
•7
■7
:6
.6
1.8
X.8
1-7
1.6
1-5
1.4
"•4
1-3
1.2
2.8
2.7
2.5
2.4
2-3
2.2
2.1
2
1.8
3-7
3.6
3-4
3-2
31
2.9
2.8
2.6
2.5
Ins.
I
2
3
4
To warm a ttictory, according to H. Claudel, 43 fbet in width by 10. 5 high, a single
line of hot- water pipe 6.25 ins. in diameter per foot of length of room, api>ears to be
sufBcient, temperature in pipe being IVom 170° to 180°. Also, water being at i8o<>,
and air at 60°, making a diflference of 120^, it Is convenient to estimate from x.5
to 1.75 sq. feet of wator-heated surfkce as equivalent to one sq. foot of steam-heated
surface, and to allow flrom 8 to 9 sq. feet of hot-water pipe-surface per 1000 cube
feet of room.
M. Grouvelle states that 4 sq. feet of cast-iron pipe surface, whether heated by
steam or by water at 176^ to 194°) will warm 1000 cube feet of workshop, main-
taming a temperature of 60^. Steam is condensed at rato of .328 lb. per sq. foot
per hour
528
HEAT, WABMJNG BUILDINGS, BTO.
a. {B.L.Oreme.) Lengthof AronUof buildingB. 2000 lineal fsal
Total volume of rooms 3 574084 cube feet
IU«ll.Uog.«r«««»,^d^r«t,.o8o4.......... ^^,^^ f^
Boilers. — Grate-gurfii^ 180
Heating surface 5 863
11
Volume of A.ir Heated l>y Radiator* ; Coxksuxnption of
Coal ; A.reas of* Cl-rate and Keating-surface of i!3oiler.
(Rob't Briggs.)
Per 100 Sq. Feet of Wartning-wrface of Radiator,
Pressure of steam per sq. iucb + )
almospbere in lbs
Heat from radiators per minute )
in unite. )
Volume of air heated i^^ per min- ) \
ute in cube feet. )
Effloiency of radiators in rcUio ....
Coal consumed per hour in lbs. . . .
Area of grate consuming 8 lbs. )
coal per hour in sq. feet )
do. 12 lbs
Heating surfkce of boiler ; coal )
consumed per hour X2.8 in ^[.fedl
8 lbs. X 2.8
12 lbs. X 2. 8
1 _
3
456
486
25 no
2
304
.38
26772
1.066
324
•405
8.512
9.072
22.4
22.4
10
537
89570
I 178
358
.448
.298
10.03
22.4
336
30
643
35352
1.408
4.28
•357
11.98
336
60
74'
40803
1.625
4-94
.412
13-83
33-6
By Hot-A-ir ITHimaoes or Stoves.
A square foot of heating surface in a hot-air furnace or stove is held to
be equivalent to 7 sq. feet of hot water pipe.
M. Peclet deduced that when the flue-pipe of a stove radiated its heat
directly to air of a space, the heat radiated per sq. foot per hour, for 1°
difference of temperature, were, for: Cast iron, 3.65 units; Wrought iron, 1.45
units, and Terra cotta .4 inch thick, z.42 units.
In ordinary practice, i sq. foot of cast iron is assigned to 328 cube feet
of space.
Open Fires.
According to M. Claudel, the quantity of heat radiated into an apart ■
ment from an ordinary fireplace is .25 oi. total heat radiated by combustible.
For wood the heat utilized is but from 6 to 7 per cent., and for coal 13 per
cent
In combustion of wood, chimney of an ordinary open fireplace draws
from 1000 to 1600 cube feet of air per pound of fuel, and a sectional area
of from 50 to 60 sq. ins. is sufficient for an ordinary apartment.
Proportions of fuel required to heat an apartment are : For orcfinaiy fire-
places, zoo ; metal stoves, 63 ; and open fires, 13 to 16.
fXimaoes.
By D. K. Clark^fnm investiffotions of Mr. J. Lothian BdL
Cupola. — M. Peclet estimates that in melting pig-ir(m by combnstioa
of 30 per cent of its weight of coke, 14 per cent only of the heat of oombu»-
tion is utilized.
Mietallurgical. — According to Dr. Siemens, i ton of coal is consumed
in heating 1.66 tons of wrought iron to welding-point of 2700°, and a ton
of coal is capable of heating up 39 tons of iron ; from which it appears that
only 4.5 per cent of whole heat is appropriated bv the iron. Similarly, he
estimates 1.5 per cent of whole heat generated is utilized in melting pol
' HEAT AND HEATING. — HYDRAULICS. 529
■ted in ordinary furnaces, whilst, in his regenerative furnace, x ton of sted
is melted by combustion of 1344 lbs. of small coal, showing that 6 per cent,
of the heat is utilized.
BIaat-fVirxxaoe.«^Mr. Bell has formed detailed estimates of appro-
priation of the heat of Durham coke in a blast-f uniace ; from which is de-
duced following abstract :
Diurham coke consists of 92.5 per cent, of carbon, 2.5 of water, and 5 of
ash and sulphur. To produce i ton of pig-iron, there are required 1232 lbs.
of limestone, and 5588 lbs. of calcuied iron-stone ; the iron-stone consists of
2083 lbs. of iron, 1008 lbs. of oxygen, and 2509 lbs. of earths. There is
formed 813 lbs. of sh^, of which 123 lbs. is formed with ash of the coke,
and 690 lbs. with the limestone. There are 2397 lbs. of earths from the iron-
stone, less 93 lbs. of bases taken up by the pig-irou and dissipated in fume,
say 2314 lbs. Total of slag and earths, 3127 lbs.
Mr. Bell assumes that 304 per cenL of the carbon of the fuel, which es-
capes in a gaseous form, is carbonic acid; and that, therefore, only 51.27
per cent, of heating power of fuel is developed, and remaining 48.73 per
cent, leaves tunnel-head undeveloped. He adopts, as a unit of heat, the
heat required to raise the temperature of 112 lbs. of water 33.8°.
HYDRAULICS. •
Descending Fluids are actuated by same laws as Fallmg Bodies.
A Fluid will fall through i foot in .25 of a second, 4 feet in .5 of a
second, and through 9 feet in .75 of a second, and so on.
Velocity of a fluid, flowing through an aperture in side of a vessel,
reservoir, or bulkhead, is same that a heavy body would acquire by fall-
ing freely from a height equal to that between surface of fluid and
middle of aperture.
Velocity of a fluid flowing out of an aperture is as square root of
height of head of fluid. T^heoretical velocity, therefore, in feet per sec-
ond, is as square root of product of space fallen through in feet and
64.333 = **^2^ A; consequently, for one foot it is v' 64.333 = S.02 feet.
Mean velocity, however, of a number of experiments gives 5.4 feet,
or .673 of theoretical velocity.
In short ajutages accurately rounded, and of form of contracted vein,
{vetia c(mtracta)y coefficient of discharge := .974 of theoretical.
Flaids subside to a natural level, or curve similar to Earth's convexity; apparent
level, or level taken by any instrument for that purpose, is only a tangent to Rarth's
circumference; hence, in leveling for canals, etc., difference caused by Earth's cur
valnre must be deducted fh>m apparent level, to obtain true level.
r>ed.uotioiis fVom Kxperixnents on Disoliarge of* Fl-uida
iVojti Reservoirs*.
1. That volumes of a fluid dischar^^ed in equal times by same apertures
from same head are nearly as areas of apertures.
2. Hiat volumes of a fluid discharged in equal times by similar apertures,
under different heads, are nearly as square roots of corresponding heights
of fluid above surface of apertures.
3. That, on account of friction, small-lipped or thin orifices discharge pro-
portionally more fluid than those which are larger and of similar figure^
under same height of fluid.
Y Y
530
HYDRAULICS.
4. That in consequence of a alight augmentation which contractimi of tlie
flnid vein undergoes, in proportion as the height of a fluid increases, the flow-
is a little diminished.
5. That if a cylindrical horizontal tube is of greater length than its di-
ameter, discharge of a fluid ia much increased, and may be increased with
advantage, up to a length of tube of four times diameter of aperture.
6. That discharge of a fluid by a vertical pipe is augmented, on the priii-
ciple of gravitation of falling bodies ; consequently, greater the length of a
pipe, greater the discharge of the fluid.
7. That discharge of a fluid is inversely as square root of its density.
8. That velocity of a fluid line passing from a reservoir at any point is
equal to ordinate of a parabola, of which twice the action of gravity (3 er)
is parameter, the distance of this point below surface of reservoir being the
abscissa.* Or, velocity of a jet being ascertained, its curve is a parabola,
parfuneter of which = 46, due to velocity of projection.f
9. Volume of water discharged through an aperture from a prismatic
vessel which empties itself, is only half of what it would have been during
the time of emptying, if flow had taken place constantly under same head
and corresponding velocity as at commencement of discharge ; consequently,
the time in which such a vessel empties itself is double the time in whidi
all its fluid would have run out if the head had remained uniform.
10. Mean velocity of a Jluid flowing from a rectangular slit in side of a
reservoir is two thirds of that due to velocitv at sill or lowest point, or it is
that due to a point four ninths of whole heiglit from surface of reservoir.
XI. When a fluid issues through a short tube, the vein is less contracted
than in preceding case, in proportion of 16 to 13 ; and if it issues through
an aperture which is alike to frustum of a cone, hase of which is the aper>
ture, the height of frustum half diameter of aperture, and area of small end
to area of large end as 10 to 16, there will be no contraction of the vein.
Hence this form of aperture will give greatest attainable discharge of a fluid.
12. Velocity of efllux increases as square root of pressure on sur&ce of a
fluid.
13. In efllux under water, difference of levels between the sur&ces must
be taken as head of the flowing water.
14. To attain greatest mechanical effect, or vis viva, of water flowing
through an opening, it should flow through a circular aperture hi a thin
plate, as it has less frictlonal surface.
ITrom Conduits or I*ipes. {SosnU.)
1. Less diameter of pipe, the less is proportional discharge of fluid.
2. Discharges made in equal times by horizontal pipes of difl^erent lengths,
b'Jt of same diameter, and under same altitude of fluid, are to one another
in inverse ratio of sq. roots of their lengths.
3. In order to have a perceptible and continuous discharge of fluid, the
altitude of it in a reservoir, above plane of conduit pipe, must not be less
than .082 ins. for every 100 feet of length of pipe.
4. In construction of hydraulic machines, it is not enough that elbows and
contractions be avoide<1j but also any intermediate enlargements, the in-
jurious effects of which are proportionate, as in following Table, for like
volumes of fluid, imder like heads in pipes, having a diftereni number of
enlarged parts.
HJ^ HS^ Wa
Velocity.
No.
of P«rU.
Velocity.
Vo.
ofPartfc
Velocity.
No.
of Parts.
Velocity.
No.
of Partt.
0
X
I
•74>
3
.569
5
• See D'AubQlifon, page ^
•454
tH«iBbOT,iM|rtS7.
HTDBAUUCS.
531
ITrlotion.
Flowing of liquids through pipes or in natural channels is materially af-
fected by friction.
If £qual volumes of water were to be discharged through pipes of equal
diameters and lengths, but of following figures :
Fig. 1. Fig. a- ^ Fig. 3.
F^«. X.
The times would be as 1,
And velocities as i,
3. 3-
1. 1 1, and 1.55.
.72, and .64.
Disoliarges from Compound or Dividecl lieser-voirs.
Velocity in each may be considered as generated by difference of heights
in contiguous reservoirs ; consequently, square root of ditl'eience will rep-
resent velocities, which, if there are severed apertures, must be inversely as
their respective areas.
NoTK.— When water flows into a vacuum, 33.166 feet must be added to height of
ii; and when into a rarefied space only, height due to difierence of external and
internal pressure must be added.
VELOCITY OP WATER OR OF FLUIDS.
Coefficients of IDiscliarge.
CoefficietU of Discharge or Efflux is product of coefficients of Contraction
and Velocity.
It is ascertained in practice that water issuing froin a Circular Aperfw'f
in a thin plate contracts its section at a distance of .5 its diameter from
aperture to very nearlv .8 diameter of aperture, so as to reduce its area
from I to about .61.* Velocity at this point is also ascertained to be ahovtt
.974 times theoretical velocity due to a body falling from a height equal
to head of water. Mean velocity in aperture is therefore .974, which, x
.61 = .594, theoretical discharge ; and in this case .594 becomes coej^ient of
discharge^ which, if expressed generally by C, will give for discharge itself
ay/2gkxC=iV. a representing area of aperture, and V volume discharged per
seconeL Or, 4.97 a V* = V. Or, 3.91 d^ y/h s= V. d representing diameter in feet
Hence, for cube feet per second, 4.97 a y/k, or 3.91 d' y/h.
Illustratioh.— Assume bead of water 10 feet, diameter of opening 1.227 feet,
area i sq. foot, and C = .62.
Tben X Va p 10 X .6a = 15.72 cube feet. 4.97 x 1 X V«o = i5-7« cube feety and
3.91 X I.127 XV 10 =15- 7 ««*«/««*.
For square aperture it is .615, and for rectangular .621.
Volume of water or a fluid discharged in a given time from an aperture
of a given area depends on head, form of aperture, and nature of approaches.
= ^ h representing height to centre of opening in feet
64-333 * = »', and - —
64333
Nora. — Head, or height, h, may be measured from surface of water to centre of
apertvre without practical error, for it has been proved by Mr. Neville that for cir
cnlar apertures, having their centre at the depth of their radius below the surface,
and therefore circumference touching the surface, the error cannot exceed 4 pet
cent in excess of the true theoretical discharge, and that for depths exceeding three
* Bajw, .6u ObMTTvd diicharRM of water colncida
to tukit at Boyer tluui Uiat of til oihon.
532 HTDBAULIOS.
times the diameter, the error is practically immaterial. For rectangular apertaras
it is also shown that, when their upper side is at sur&ce of the water, as in notches,
the extreme error cannot exceed 4. i? per cent in excess ; and when the upper is
three times depth of aperture below the surface, the excess is inappreciable.
For wOches, toeirs, sliU, etc., however, it is usual to take ftill depth for head, when
.666 only of above equation must be taken to ascertain the discharge. .
Experiments show that coefficient for similar apertures in thin plates, for
small apertures and low velucities, is greater than for lar^e apertures and
high velocities, and that for elongated and small apertures it is greater than
for apertures which have a regular form, and which approximate to the
circle.
When Discharge of a Fluid is under the Surface if another body of a
like Fluid. — The difference of levels between the two surfaces must be taken
as the head of the fluid.
Or,Va^(/i— /0 = ».
When Outer Side of opening of a discharging Vesselis pressed by a Force,
— The difference of heignt of head of fluid and quotient of pressures on two
sides of vessel, divided by density of fluid, must be taken as heads of fluid.
Or, y/2 g (h — /^""Pj^''^A ^ ^ g representing density of fluid.
Illustration.— Assume head of water in open reservoir is 12 feet above wftter-
line in boiler, and pressures of atmosphere and steam are 14.7 and 19.7 Iba.
Then ^/^P^^^MI^^. \A-333x(»-ig|i) = 3.56/«t
When Water fUms into a rarefied Space^ as into Condenser of a SteamF-
engine^ and is either pressed upon or open to A tmosphere. — The height due to
mean pressure of atmosphere within condenser, added to height of water
above mtemal surface of it, must be taken as head of the water.
Or, V2^(A4-A')=:r.
Illustration.— Assume head of water external to condenser of a steam-engine to
be 3 feet, vacuum gauge to indicate a column of mercury of 26.467 ins. (= 13 Iba),
and a column of water of 13 lbs.== T^gfeet
Then V'2flf (3-I-29.9) = V64.333X 32.9 = -/anS- 57 = 4<5 feet.
Relative Velocity of Disoliarse of "^Vater tlirotisl^ differ-
ent A-pertures and under like Heads.
Velocity that would result from direct, unrHarded action of^ke column of
water which produces it, being a constant, or i
Through a cylindrical aperture in a thin plato 635
A tube from 2 to 3 dinmeters in length, projecting outward 8125
A tube of the sanie length, projecting inward 68xa
A conical tube of form of contracted vein 974
Wide opening, bottom of which is on a level with that of rsBervoir;
aluice with walls in a line with orifice ; or bridge with pointed piers. 96
Narrow opening, bottom of which is on a level with that of reservoir;
abrupt proJe<>.t{ons and square piers of bridges 86
Sluice without side walls 63
IDisoliaree or ICfflux of "Water ibr various Openings and
A.pertures.
Rectangxilar "Weir.
Weirs are designated Perfect when their sill is above surface of natural
stream, and Imperfect y Submerged^ or Drowned when it is below that surfiaoo.
HVDRAULIOS. 533
Height meamredfrom Surface of Water to Sill. {Jas. B. Francis.)
Mmii Head.
.6a to 1.55 feet
Length of Opealng.
10 feet.
Mean Discharfce per Second.
32.9 cube feet.
Mean Coeflcient.
.623
Principal causes for variation in coefficients derived from most experi<
ments giving discharge of water over weirs arises from,
1. Depth being taken from only one part of surface, for it has been proved
that heads on, d/, and above a weir should be taken in order to determine
true discharge.
2. Nature of the approaches, including ratio of the water-way in channel
above, to water-way on weir.
When a weir extends from side to side of a channel, the contraction is
less than when it forms a notch, or Poncelet weir, and coefficient sometimes
rises as high as .667.
When weir or notch extends only one fourth, or a less portion of width,
coefficient has been found to vary from .584 to .6.
When wing-boards are added at an angle of about 64^, coefficient is greater
than even when head is less.
Computation, of* Volume of Disolxarge.
Mean velocity of a fluid issuing through a rectangular opening in
side of a vessel is two thirds of that due to velocity at sill or lower
edge of opening, or it is that due to a point four ninths of whole height
from surface of fluid.
Height measured from Surface of Head of Water to Sill of Opening.
Rule. — Multiply square root of product of 64.333 ^"^ ^^ 'g^* or whole
depth of the fluid in feet, by area in feet, and by co^cicnt for opening, and
two thirds of product will give volume in cube feet per second.
t representing time in seconds and V volume in cube feet.
ExAMPLB.— Sill of a weir is i foot below surface of water, and its breadth is xo
feet; what volume of water will it discbarge in one second?
C = .623, ■\/64.33X I X lolJo = 80. 2, and f 8a 2 X • 623 = 33. 32 cube feet.
-^OTK.— Mean coefficient of discharge of weirs, breadth of which is no more than
Ihird part of breadth of stream, is two thirds of .6 = .4 ; and for weirs which extend
^hole width of stream it is two thirds of .666 = .444.
Or, 214 VP = V in cube feet per minute. When h is in ins., put 5.15 for 214.
Or, CbhV29b = V. C for adepth .1 of length = .4x7, and for .33 of length=:.4.
8
Or, by formala of Jas. B. Francis: 3.33 (L — .1 n H) H'S^= V.
L representinff length of weir and H depth of water in caned, suf^ciently far from
weir to be unaffected by depression caused by Ote current, both in feet, and n number
of end contractions.
NOTS.— When contraction exists at each end of weir, n :t=: ? ; and when weir is of
width of canal or conduit, end contraction does not exist, and n - o.
This formala is applicable only to rectangular and horizontal weirs in side of a
dam, vertical on water-side, with sharp edges to current; for if bevelled or rounded
off in any perceptible degree, a material effect will be produced in the discharge;
tt is essential hIso that the stream, after passing the edges, should in nowise h
nstricted in iUi (low and descent.
Y Y*
534 HYDRAULICS.
In cases in which depth exceeds one third of length of weir, this formula is not
applicable. In the observations iVom which it was deduced, the depth varied from
7 to nearly 19 ins.
With end contraction, a distance from side of canal to weir equal to depth on
weir is least admissible, in order that formula may apply correctly.
Depth of water in canal should notl>e less than three times that on weir for ac-
curate computation of flow.
Illustration. ->If an overfull weir has a length of 7.94 feet and a depth of .986
(as determined by a hook gauge), what volume will it cfischarge in 24 hours?
s
3-33 (7-94 — -2 X. 986) .986^ = 3- 33 X 7-94 — -1972 X. 97907 = 3-33 X7'74a*X
.97907 = 25.243 875, which X 60 X 60 X 24 = 2 181 061 cubefuL
By Logarithms.— Log. 3. 33 = ^522 444
7.7428 = .888898
a _
.986^=1.993877
3
2) 1.981 631
1.990815 = 1. 990815
x.4oa 157
Log. 34 hours = 86 400 uconda. 4.936 5x4
6.338671
I^fr 6. 338 67 =^ 2 181 073 eulbe feet. C in this case = .6x5.
Or, 2141/113 and 5.i5-\/A3 = V, if stream above the sill is not in motion. H
representing height of surface of water above sill in feet^ h in inches; and
314 VH3-f- .035 1)2 H3 = V, if in motion, v representing velocity of approach of
water in feet per secondhand V volume in cuJbefeet discharged over each lineal foot
of sill per minute.
In gauging, waste-board must have a thin edge. Height measured to level of sur-
Ikce not affected by the current of overfall. {Molesioorth.)
To Compute Deptli of Klo^w over a Sill that -will IDis-
cliarge a given Volvmae of "Water.
(3V 8\8 t>*
— — — -\-ki\S^Jc = d. * = — representing height due to velocity (t>) as U
Hows to the weir.
Note.— When back-water is raised considerably, say 2 feet, velocity of water ao-
proaching weir (h) may be neglected.
Xleotangular iNotolies, or Vertical Aperture» or Slita.
A Notch is an opening, either vertical or oblique, in side of a vessel reser-
voir, etc., alike to a narrow and deep weir.
Vertical Apertures or Slits are narrow notches or weirs, running to or
near to bottom of vessel or reservoir.
Coefficient for opening, 8 ins. by 5, mean .606 (JPoncelet and LeArot).
Coefficient increases as depth decreases, or as ratio of length of notch to
its depth increases.
When sides aud under edge of a notch increase in thickness, so as to be converted
mto a short open channel, coefficients reduce considerably, and to an extent beyond
wbat increased resistance from friction, particularly for^mall depths, indicatea
Poncelet and l^esbros found, for apertures 8 x 8 ina, that addition of a horiaontal
Moot 21 ins. long reduced coefficient from .604 to .601, with a head of about 4 feet;
but for a head of 4. 5 ina coefficient fell from Tsti to .483.
For Rule and Formulas, see precedin^f pa|^e,
HYDRAULICS. 535
Jkieotatigular Openings or Slixioes, or Horizontal Slits.
ReigM measured from Surface of Head of Water to Upper Side and to SiU
of Opening,
( Opening, i inch by i inch. Head, 7 to 33 feet = .621.
Coefficient for { " 3 " "3 »' '* 7 " 23 " =.614.
( «' ft feet " ifoot '* 1 *' « " =.641.
Poneelet and LesbroB deduced that coefficient of discharge increases with small
and very oblong apertures as they approach the surface, and decreases with large
and square apertures under like circumstances.
Coefficients ranged, In square apertures of 8 by 8 ins., uuder a head of 6 ins. to
rectangular apertures, 8 by 4 ins. ; under a head of 10 feet, from .572 to .745.
In a Thin FlaU, C = .6x6 (Bozsut) ; C = .6x (MiohdoUi).
Xo Compute Disoliax^Bre.
Rule. — Multiply square root of 64.353 and breadth of opening in feet, by
coefficient for opening, and by difiereuce of products of heights of water and
their square roots, and two thirds of whole product will give discharge in
cube feet per second.
Or,— b^Tg ih^/h—h'Jh') C = V; — = ^ = <; and
3 \b y/Tg {h y/h^h'^/h') C
V
— == o. h and h' reprueniing depth to sill and opening in feet, and v velocity
b(k—h')
in feet per second.
ExAMPLB.— SiU of a rectangular sluice, 6 feet in width by 5 feet in depth, is 9 feel
below surface of water; what is discharge in cube feet per second?
C = .625, 9 — 5 = 4, and ~ Vai X 6 X .6as X (9V9--4 X y/4) = 380.95 cubefsO.
Or, Vagd a C = V. d representing depth to centre of opening in feet
d = 9 — 3.5 = 6.5, a = 6x 5 = 30. and V64.33 X 6^5 x 30 X .6b5 =383.44 cubejl
Sluice "Weirs or Sluices.
Diacharge of water b^ Sluices occurs under three forms — viz., Unimpeded,
Impeded, or Partly Unimpeded,,
7o Compute Disoharge M^lien. Unimpeded.
Cdb VTgh = V. d representing depth of opening and h taken from centre oj
opening to surface ofweUer.
If velocity, k, with which water flows to sluice is considered,
— (rrmiJ — * = *i :==i = d: and — = d.
h' representing Jieig:u to which noater is raised by dam above sill
lLU78rBiiTioir.>-How high most the gate of a sluice weir be raised, to discharge
tso cub* IMI of water per second, its breadth being 24 feet and height, A', 5 feet?
C by «cp0rtment =: .6. d ai^proxfmately = x.
. ^===: = ~ = 1.0204/eet
.6X«4V64.33(5-i) *^4X?7«4
^O Compute X>i8oliarise wlien Impeded*
y
Cdby/2gh = V, and — =d.
CbVagh
A rfpresenting d^gftrmce qfkoel between supply and back-water.
536 HYDRAULICS.
To Coznpute IDiscHarge Mrlien. partly Impeded.
C b yfTg \d yjh \- d V^) = ^' <*' r^re^enting depth of back-wcUer above
upper edge ofsUL
Illustration. — Dimensions of a slaice are z8 feet in breadth by .5 in depth:
height of opening above surface of water .7 feet, and difference between levels of
supply and surface water Is 2 feet; what is discharge per second?
.6 X x8 X 8.02 (-7 'v/a — ~ + 5 vA = 86.62 X . 896 -f. 707 = 138.85 cube feet
CoefHcients of Ciroular Openings or Sluioes.
Height measured from Surface of Head of Water to Centre of Opetiing.
Contraction of section (yom i to .633, and reduction of velocity to .974; hence
.633 X .974 = .617 (Neville).
In a Thin PlcUe, C = .666 {Bossut)] .631 iVenturi); .64 {Eytehoein).
Qflindrical Ajt^ages^ or Additional Ttibes^ give a greater discharge than
apertures in a thin side, head and area of opening l^ing the same ; but it
is necessary that the flowing water should entirely fill mouth of ajutage.
Mean coefficient, as deduced by Castely Bossut^ and Eyteltoetn^ is .82.
Slxort rrul>es, Aloutli-pieces, and Cylindrical Prolonga-
tions or A.J\itages.
F^fr 4- If an aperture be placed in side of a
vessel of from 1.5 to 2.5 diameters in
thickness, it is converted thereby into a
short tube, and coefficient, instead of being
reduced by increased friction, is increased
from mean value up to about .815, when
opening is cylindrical, as in Fig. 4 ; and
when junction is rounded, as in Fig. 5, to form of contracted vein, coefficient
increases to .958, .959, and .975 for heads of i, 10, and 15 feet.
Conioally Convergent and Diverge*^ t T\x"bes.
Fig. 6. In conically divergent tube. Fig. 6, cocffi-
I cient of discharge is greater than for same
P^^VM£_ tube placed convergent, iluid filling in both
l»— » I ^"Ull-r^--— 0 cases, and the smaller diameters, or those at
' — ' " same distance from centres, O O, being used
in the computations.
^m^tm^r''
Fig. 7.
©-«-----:::::
A tube, angle of convergence, O, of which
is 5*^ nearly, with a head of from i to 10
feet, axial length of which is 3.5 ins., small
diameter i inch, and large diameter 1.3 ins.,
gives, when placed as at Fig. 6, .921 for co-
efficient ; but when placed as at Fig. 7, co-
efficient increases up to .948. Coefficient of velocity is, however, larger for
Fig. 6 than for Fig. 7, and discharging jet has greater amplitude in falling.
If a prismatic tube project beyond sides into a vessel, coefficient will be re-
duced to .715 nearly.
Form of tube which gives greatest discharge is that of a truncated cone,
lesser base being fitted to reservoir, Fig. 7. Yenturi concluded from bia ex-
HTDBAULICS.
537
periments that tube of greatest discharge has a length 9 times diameter of
lesser opening base, and a diverging angle of 5^ 6' — ^charge being 2.5
greater than that tlirough a thin plate, 1.9 times greater than through a
short cylindrical tube, and 1.46 greater than theoretic discharge.
Ooxxipouxicl I^outli-pieces And. AJutases.
Fig. 8.
Flg.9-
Fig. la
Coeffioients fbr Afoutlx- pieces, SHort 1?ube8, ai&d. Cyl-
indrical Ir'rolongatione.
Computed and reduced by Mr. Neville, f ram Venturi^s EzperimenU.
Description of Aperture, llouth-piece, or Tube.
1. An aperture i. 5 ins. diameter, In a thin plate
2. Tube 1. 5 iu& diameter, and 4.5 ins. long. Fig. 4
3. Tube, Fig. 5, having junction rounded to form of coulracled
vein
4. Short conical convergent mouth-piece. Fig. 6
5. Like tube divergent, with smaller diameter at junction with
reservoir; length 3.5 ins.,or = i in., and 06 = 1.3 ^^^- •••
6. Double conical tnbe, ao,S T, r b. Fig. 9, when a& = ST = i.5
ina, or =1.21 ina,ao = .92 in., and oS = 4. i ins
7. Like tube when, as in. Fig. 8, ao rb=:oS Tr, and aoS-s
1.84 ina
8. Like tube when S T= 1.46 ins. , and 0 S = 2. 17 ina
9. Like tube when ST=3 ina, and 08 = 9.5 ins
10. Like tul)e when o S = 6.5 ins., and S T = 1.92 ins
11. Like tube when ST = 2.25 ins., and 08 = 12.125 ins
12. A tube, Fig. 10, when os = rt — 3 ina, or-=^stf=. 1.21 ina,
and tube o S T r, as in No. 6, S T = i. 5 ins. , and s 8=4. i ins.
c. for
Di«m. a b.
.622
.823
.611
.607
.561
.928
.823
.823
.911
1.09
1. 215
.895
C. for
Diam. o r.
•974
.823
.956
•934
.948
1.428
1.266
1.266
1-4
1.569
1-855
1-377
Mean of various experiments with tubes of .5 to 3 insi in diameter, and
with a head of fluid of from 3 to 20 feet, gave a coefficient of .813 ; and as
mean for circular apertures in a tliin plate is .63, it follows that under
similar circumstances, .813 -4- .63= 1.29 times as much fluid flows through
a tube as through a like aperture in a thin plate.
Preceding Table gives coeflicients of discharge for figures given, and it
will be found of great value, as coefficients are calculated for large as well
as small diameters, and the necessity for taking into consideration form of
junction of a pipe with a reservoir will be understood from the results.
Circular Sluices, etc.
To Compute X)i8cliarefe.
Height meamtred from Surface of Head of Water to Centre of Opening.
Rule. — ^Multiply square root of product of 64.333 and depth of centre of
opening from surface of water, by area of opening in square feet, and this
product by coefficient for the opening, and whole product will give discharge
in cube feet per second.
Or, y/TgHf aC = Y. a rq^ennting area in tq. feet, and d depth qf aur/ace <^
JIuidfrom centre of opening vn fe^.
538 HYDRAULICS.
ExAVPLB —Diameter of a circular sluice is i foot, and its centre is 1.5 feet below
surface of the water; what is discharge in cube feet per second?
Area of i foot = .7854 ; C = .64, and V64.333X1.5 X .7854 X .64 = 4.938 cfibtfeeL
When Circumference reaches Surface of Water. VTgr, .9604 o C = V.
r representing rctfHus of cireie in feet.
Illustration.— In what time will 800 cube feet of water be discharged through a
circular opening of .025 sq. foot, centre of which is 8 feet below surface of water?
p_ >; 800 800
^ — •°^- , — -, — = ^^z:o V r^. sy z;^ = 2239.58 = 37 min. 19.6 sec.
V2gdX.025X'63 22. 68 X. 025 X. 63 ^^ ^ j/^ v
NoTB.— For circular orifices, the formula y/Tgd a C = V is sufficiently eiact for
all depths exceeding 3 times diameter; the finish of openings being of more effect
than extreme accuracy in coefficient.
Semicircular Sluices,
W^e« Diameter is either Upward or Downward. VTgd a C = V. d repre-
senting depth of centre of gravity of figure fr&m surface.
When Diameter as above is at Depth d, hehto Surface. -y/Tgd i. x88 a C = V.
Circvilar, SexuioircTxIar, Triangular, Trapezoidal, Pris-
zuatio W^ edges. Sluices, Slits, etc.
See Neville, London^ i860, pp. 51-63, and WeUbach, vol. \. p. 456.
For greater number of apertures at any depth below surface of water,
product of area, and velocity of depth of centre, or centre of gravity,'
if practicable to obtain it, will give discharge with sufficient accuracy. '
IDischarge fVozu Vessels not Receiving any Supply.
For prismatic vessels the general law applies, that twice as much would
be discharged from like apertures if the vessels were kept full during the
time which is required for emptying them.
To Compute Time. -^^ = ?>* = <.
CaV2^ ^
Illustration.— A rectangular cistern has a transverse horizontal section of 14
feet, a depth of 4 feet, and a circular opening in its bottom of 2 ins. in diameter- in
what time will it discharge its volume of water, when supply to it is cut off* and
cistern allowed to be emptied of its contents?
A = 4/ce<, a — 2«x. 7854 -^144 =0218, C = .613, and VagkXaxC = .214^1
2X14X4
cube foot per second. Then — - = 522. 6 seconds.
.2143
To Compute Time and ITall.
Depression or subsidence of surface of water in a vessel, corresponding to
a given time of efflux, is A — h'. h' representing lesser depth.
;;^(VA-*') = t inversely, Uk^^^ t)' = K'.
Qay/:ig \ 2A/
Illustration, — In what time will the water in cistern, as given in precedins
case, subside 1.6 feet, and how much will it subside in that 4im« ?
A =14. C = .6, O = .o2i8, %/««» = 8.02, ft = 4, A'=s4-.j.$~a.4.
a8
.1049
.6X.L8'x8.o2^^^^""V'2.'|)=;^X(2-i.5s) = ,2aiW«md*
/ ,6 X .0218 X 8.02 \a
V* 2x14 * ^'^'y =*— •45 = 2.4/««*; hence,4-2.4 = x.6/e«i
When Supply is maintained,— VWida result obtained as preceding by 3.
HYBBAULIOS. 539
iDisplxarge, -^s^liexi VoTtti and I>inaensioiia of* VeAsel or
fijfflux are not kno'ivn.
Volume discharged may be estimatetl by observing heads of the water at
equal intervals of time; and at end of half time of discharge, head of water
will be .25 of whole height from surface to delivery.
When t = mch interval. For openingi in Mtom or Hde, Gaty/^g (^ "rv i\
= Y,Jbr ^ depth; C a t V J^ (^^ "*" '^ ^^ ' "^ ^* -) = V /or 2 depUu ; and
NoTK.— At end of half time of discharge, head of water will be .25 of whole height
firom surface to delivery.
"Weirs or ^N'otch.es.
- Cbty/ng {y/h3 -j- 4 y/h^i -\- y/h^i) = V. 6 representing breadth in feet
9
Illustration.— A prismatic reservoir 9 feet in depth is discharged through a
notch 2.222 feet wide, surface subsiding 6.75 feet in 935 seconds; what is volume
discharged ?
C = .6, *,=9— 6.75 = 2.25yfec<, and - 6 X 2.222 X935 X 8.02 (>/93-|-4
V2.253-I- Vo3) = 2221.6 X 4a 5 = 89 974. 8 cube feet
When there m an Infivx and Efflux.
If a reservoir during an efflux from it has an influx into it, determination
of time in which surface of water rises or falls a certain height becomes so
complicated that an approximate determination is here alone essayed.
A state of permanency or constant height occurs whenever head of water is in-
creased or decreased by — ( — j = Jfc. I reprewiUing influx in cube feet per fecond.
Ai V
Time (t) in which variable head («) increases by volume (0) = i q ^ , ;
Aft)
and time in which it sinks height, fc, by — _^^ . Time of efflux, in which
CaV^ gx — l
subsiding sarlace falls fW>m A to Ai, eta, and head of water flrom h to Ax, when
k is represented by = >/*i 1^
Cay/i g
*— *4 / ^ I 4Ai . 2Aa ■ 4A3 . A4 \
i2Cav^W*-Vfc'^VAi-VA"^VA2-v'*"*'V*3-V*'^VA4-V*/'"
Illustratiox. — Tn what time will surface of water in a pond, as in a previous
example, CblII 6 feet, if there is an influx into it of 3.0444 cube feet per second?
flo— 14 / 600000 ■ 4 X 495000 t ' X 410000 I 4 X 325 OOP
" X. 537 x'SBJex 8.02 V4-472— 8"*" 4.301— .8 "*^ 4123- 8 "•" 3-937 — -8
26$ OCX) \ 6 - «, J » . >.
-I- — - -)= ^ X i48o2oi = i94486«econd«=54 A., I mtfk, 26«ee.
3.742 — .a/ 45-ooS
PrimuUic Vends^
U rtmssk has a uniform transverse section, A,
Then— i4=f>/*—V*i + V*X hyp. log. (^,^^^jA]=t=zUmeinwhM»
G a V 2 17 L >v *i — V */ J
head qf water Jlawtjiwn htoh^
540 HYDBAULICS.,
lLLuaTRATiO!7.->A reservoir has a sarface of 500000 sq. feet, a depth of 30 feet; it
16 fed by a stream affording a supply of 3.0444 cabe feet per second, and outlet has
an area of .8836 sq. foot; in what time will it subside 6 feet?
2 X 'JOO 000 I
y/k^ as before, =,. 8, C = . 537, and ^ x V20 — 'V/14-J-.8 X hyp. log.
Cay/zg l
l-y — ZTg) ^ *• 3°3 1 ~ ^3® ^^^ fecondt = 66 A. 13 min. 34 «c.
To Compute Fall in a. given Time.
This is determining head hi at end of that time, and it should be sub-
tracted from head h at commencement of discharge. Put into preceding
equation several values of hi, until one is found to meet the condition.
iLLusTRATiox. — Take a prismatic pond having a surface of 38750 sq. feet, a depth
to centre of opening of sluice of 10. 5 feet, a supply of 33.6 cube feet, and a discharge
of 40 cube feet per second.
-^^ = .84.
Putting these numerical values into the equation, and assuming different values
for Ai, u value which nearly satisQes the equation is 4. Consequently, 10.5 — 4 =
6. 5 feel, faU.
(- Y = *^> arc (tang. = y, arc tangent of which = y, and I as preceding.
tCby/^g/
According as A: is ^ A, and influx of water, l^^Cl Vsgh^^ there is a rise or fkll
of fluid surface, the condition of permanency occurring when hi — k, and time cor-
responding becomes cxs.
Illustration.— In what time will water in a rectangular tank, 12 feet in length
by 6 feet in breadth, rise from sill of a weir or notch, 6 inches broad, to 2 feet
above it, when 5 cube feet of water flow into the tank per second P
fc, = 2, A = o, A= 12X6 = 72, I = 5i '' = •5) C = .6.
* = (ir-7 — - — r—'\^ = '&^3."7« = 2.1338.
Vf .6 X 5 X 8.02/
— . 73 X 2.1338 r. , ,^. 2 + ^2 X 2. 1338 -|- 2. 1338 , - /
'"" 3X5 l*"^ "*"'""° (V»-V. .3T8)' +^" *" ('"'«■ =
-) = 10.2423 X hyp. log. -^^^ 3.4641 X arc (tang. "^ \ =
2/ J 002162 \ 4- 335V
2 v/2. 1338 4-^2)
ia2423 X [7.961 — (3.461 X arc, tangent of which = .56497, or 29° 28' = 29.466,
length of which = .5143) = 1.781] = ia2423 — 7.961 — x.781 = ia2423 X 6.18 =
63.297 seconds.
X>isoliarge of "Water under "Varia^ble Pressures,
To Compute Time, Xtise and. Fall, and Volume.
~--y/2 gx = v. X representing variable Aea<2, A and a areas oftramverie Aomofi-
A
tal seUion of vessel and discharge, and v theoretical velocity ofeffLviz.
To Compute "Volume.
A y = y. y repretei^ng extent of fall, and V volume of water dis^of^td, ai
h~—h .
Illustration.— Assume elements of preceding case.
A = x4. y = 4feet. Then $6 X ^ = 224 evbefttt
HTDBAULICS.
It of that In supply, tbrou^ B pipe a ina In dituu-
Bupplyf
M X V4 S6_ _ ^^
.oaiBxB.m~.ioji '^ '^
Ihal, tod I feet below ouIlBi o; in wbHt time will
Kiel ill vussel ruD out aud aver al a Ihruugb a pipe,
i=0"=
^^ — ^^ = J. A' TfpTfunting tectum oJttcHvirtg vtuet, t Ane in whicA
Ca(A + ATv'ip ^ _
Ikt Ini Rir/ii«t r^nUfl- oUsin hmi 1«vI; and '** V*~V^ ~ i Umi wUMn
Ca{A + A-)v^
»Aie* In>rf/aUl/™« * <o »'.
.8iX-78MX^XS.oa ■'™
DlBohaPBe fVom a Mocoh* In Side of s Vease).
iLLmTunon.— ira menolr ottiUfr. iid r«t in tengtb by tain bimdib, bxa
noub Id end or g ios. in widih; In ntasiiime will head DrwaUrofij ine. lUl la 6?
NoTS.— For dMtarBS of rnwis in motion, see Welsbacb. toL t, pp. J94-»(L
Reeervoira or Cistei-ns.
Xo Compote Time of K>]IIi>k and of KmptylnB a Renap.
^~g = T, and ^--g = (. V rrpriieBling votume of vnel, S fimply ef maltr,
and D ditdmroi of mater, boa prr minalt. and in cute fat. T timi itfJUUmg tatO,
«ihI t time of diarAarging if, boU in minitfet.
542
HYDBAUUGS.
Irregn^ilaivSliapedL "Vessels, as a Pond, Hiake, eto.
Xo Compute rTime and 'Volume XDisoharged.
Operation, — Divide whole mass of water into four or six strata of equal
depths. •
Then, /br 4 StraJUx, =r X (-7r+^7ri + -7T- + ^^ + -7ril =* I *, *,
etc., r«pre«en<in^ dep^Aa o/ Araia cU a, ai, etc., commencing at surface; o^, aa,
etc., 6et9i^ areai of first, second, etc., transverse sections of pond, etc. ; and
12
X a-|-4at + 2aa+4o3-f a*=V.
**'**" A « % Illustration. —In what time
C will depth of water in a lake,
A 6 C, Fig. 12, subside 6 feet, sur-
faces of its strata having follow-
ing areas, outline of sluice being
a semicircle, i8 ins. wide, 9 deep,
and 60 feet in length?
Then
a at 20 feet {h ) depth of water = area of 600000 sq. feet
ai " 18.5 " (hi) " " = " 495000
aa '.♦ 17 " (A2) " " = " 410060
o3 " 15.5 " (A3) « " = " 325000
a4 " 14 " (h4) " «' = «' 265000
a = area of 18 -r- 2 = .8836 sq. feel ; (j = .537.
20—14 \, /600000 4X495000 , 2X410000
(1
(600 OOG
4-473
4- 301
4- 123
"X. 537 X. 8836 X8.O8
265 ooo\ 6
-f J = — — X 1 194 431 = 156 938 »«c. = 43 A. , 35 »*n. 38 tea
6
4X325000
3-937
3742
And discharges: — X (600000+4 X 495000-f a X 410000+4 x 325 000+365000)
12
= ■5 X 4965000 = 2482 500 cti&e/ee&
For 6 Strata, put a a4, instead of a4, ^d 4 as and at additional, and divide by
x8 instead of 22.
inow of "Water in. Beds.
Flow of water iu beds is either Uniform or Variable. It is uniform when
mean velocity at all transverse sections is the same, and consequently when
areas of sections are equal ; it is variable when mean velocities, and there-
fore areas of sections, vary.
To Compute Fall of Flow.
G — X — = A- C representing coefficient of friction, I length offiow, p perimeter
a ng
of sides and bottom of bed, and hfaU infeeL
Illustration.— A canal 2600 feet in length has breadths of 3 and 7 (bet, a depth
of 3 feet, with a flow of 40 cube feet per second ; what is its fidi ?
G = aa per table below .007565; p = "\/3a + 2*X2 + 3=ia2; 0=15;
and
0 = 40 4- 15 = 2,66. Hence ,007 565 x
2600 X X0.2 ^ 2.66*
»S 64.33
To Conapute Velocity of Flow. ^— iL
= 1.47 7&ct
2 jirA=«.
Illustration.- A canal 5800 feet in length has breadths of 4 and 12 feet, a depth
of 5, and a fall of 3; what is velocity and volume of flow?
^ = Vp+V X 2+4 = x6.8, and a = 4a
Then
J:
40
.007 565 X 5800 X 16.8
TOlttme = 40 X 3. 23 = 129. 2 cu6e feei.
X 64. 33 X 3 = V.0542 X 193 = 3. 23 feeu Henoe
HYDBAUUCS.
543
Ooe£Aoi«nt« o£ IPriotion. of Srio-w of '^Varter in. Bods,
ill R.i\rex«9 Canals, Streams, eto.
In Feet per jSecond.
Velocity.
•3
■4
•5
.6
C.
.<y>8i5
.00707
.00785
.007 7B
Velocity.
•7
.8
C.
•00773
.00769
.00766
.Q0763
Velocity.
C.
Vdodty
* 1-5
.00759
5
2
.00752
8
a.5
.00751
ID
3
.00749
13
c.
•0074s
.00744
•00743
.00742
Forms of Transverse Sections of Canals, eto.
Resistance or friction which bed of a stream, etc., opposes to flow of water,
in coiisequence of its adhesion or viscosity, increases with surface of contact
between bed and water, and therefore with the perimeter of water profile, or
of that portion of transverse section which comprises the bed.
Friction of flow of water in a bed is inversely as area of it.
Of all r^^ar fi^i^ures, that which hss greatest immber f^ sides has for
same area least perimeter ; hence, for enclosed conduits, nearer its trans*
verse profile approaches to a regular figure, less the coefiScient of its friction ;
ocmseqaently, a circle has the pnofile which presents minimum of friction. -
When a canal is cut in earth or sand and not walled up, the slope of its
sides should not exceed 45°.
'Varia'ble IVXotion..
Variable motion of water in beds of rivers or streams may be reduced to
rules of wiiform motion when resistance of friction for an observed length
of river can be taken as constant.
To Compute Voluzxke of "Water ilo-wing izi a River.
y/zgh
Va^
■^C
ip
Aa A, -I- A
W,'^A=)
= V. A and A^ representing areas of upper
and, lower transver^ sections of
flow.
Illustratiom. ^A stream having a mean perimeter of water profile of 40 feet for
a length of 300 feet has a fall of 9.6 ins. ; area of its upper seclion is 70 sq. feet, and
of Its lower 60; what is volume of its discharge?
To obtain C for velocity due to this case, 92.35
ooefficient for which, see Table above, = .007 44.
V64.33X(9.6-j-i2) _
sjl
+ 60X
9^
12
40 X 300
= 8.59/««<,
7174
V^
6o»
+ 00744
300X40
7o-|-6o
\7oa"'"6o='/
V-ooo33o89
= 394.6 cube feet;
and mean velocity = ^^' . - ' = 6.07 fea^ C for which is . 007 45.
70-f-uo
FRICTION JN PIPES AND SETWEES.
Friction in flow of water through pipes, etc., of a uniform diameter is in-
dependent of pressure, and increases diiecdy as length, very nearly as square
of velocity of flow, and inversely as diameter of pipe.
With wooden pipes friction is 1.75 times greater than in metallic
Time occupied in flowing of an equal quantity of water through Pii)es or
Sewers of equal l^igths, and with equal Leads, is proportionaUy as foUows :
In « Right Line as 90, in a True Curve as 100, and in a Right Angle as 140.
544
HYDBAULICS.
To Compute Head neoesaary to overooxna B^riotion, of
Pipe. (Weitbach.)
Loi44-f '°'/^ ) X ^ X — = h\ h' representing head to overcome JriOion of
flow in pijpe, I length of pipe, and v velocity of water per second, aU in feet^ and d
intemdt diameter of pipe in ins.
Illustration. — Length of a condait-pipe is looo feet, its diameter 3 ins., and the
required velocity of its discharge 4 feet per second; what is required head of water
to overcome fViction of flow in pipe?
(. .017 46\ 1000 16 , ^ , .
•0144 + -77-] X -y >< 57;= -^^a *3 X 333-333 X a. 963 = 32. 845 /cct
Head here deduced is height necessary to overcome friction of water in
pipe alone.
Whole or entire head or fall includes, in addition to above, height between
surface of supply and centre of opening of pipe at its upper end. Conse-
quently, it is whole height or vertical distance between supply and centre
of outlet.
To Compute -^vliole Head, or Heiglit fVom. SurfiaMse of
Supply- to Ceutre of Disoliarge.
I ^
(Cx^+i.5)X— = A.
X.5 is taken as a mean, and is coefficient o^riction for interior orifice, or that of
upper portion of pipe.
To obtain C or coefficient, (.0144 + - — 7-^) = C.
For facilitating computation, following Table of coeffici^ts of resistance
is introduced, being a reduction of preceding formula :
Coefficients of BViotion. of 'Water.
In Pipes at IDiffereixt "Velocities.
V.
C.
V.
C.
V.
C.
V
C.
V.
Ft. In*.
Ft. In*.
Ft. Ins.
Ft. Ina.
Ft. Ina.
4
•0443
2 8
.025
5
.0221
7 4
.0208
II 6
8
•0356
3
.0244
5 4
.0219
7 8
.0206
12
I
■0317
3 i
.0339
5 8
.0217
8
.0205
12. 6
I 4
.0294
3 8
.0234
6
.0215
8 6
0204
13
X 8
.0278
4
.0231
6 4
.0213
9
o2oa
14
9
.0266
* ^
.0227
6 8
.0211
10
0199
15
2 4
.0257
4 8
.0224
7
.0209
II
0196
16
.0195
.0194
.0193
.0191
.OIBQ
.0188
.0187
iLLrsTRATioN I.— Coefficient due to a velocity of 4 feet per second is .0231.
s.— Take elements of preceding casa
16
^^ 1000 X 12 , , A'
(.0231 X : |-«-5)X ^
= 93-9 X
= 23-35yfe«<-
3 ' "64.33 ''•'■'"' 64.33
Note.— In preceding formula I was taken in feet, as the multiplier of 13 for ins.
was cancelled by taking 5.4 Ibr 2 g, but in above formula it is necessary to restor«
this multiplier.
Radii of Curvatures.
When Pipes branch off from Mains, or when they are deflected at right
angles, radius of curvature should be proportionate to their diameter. Thua,
Ina.
Ina.
Ina.
In*.
Ina.
Diameter
2 to 3
18
3*04
so
6
30
8
Radius
10
60
nyi/HAULICS.
545
Cnrvea and. Bends*
Reaifltance 0/ Voss of head due to curves and bends, alike to that of friction,
increases as square of velocity ; when, however, curves have a long radius
and boids are obtuse, the loss is small
Carved Circular Pipe, ( WeUbach). -^ x [. 131 -f i. 847 (^ *1 x ^ = *•
a repr^te^ng angle ofcurve^ d diameter ofpipcj r raditu of curve, and h height
due to friction or vetiitance of curve, aU in feet.
For c*eilHy of compatations, foUowing values of .131 + 1.847 f — ) "^ intro-
dUOftd-
Coefficients of* Resistaxiod.
lr%. Curved. Pipes -^vitlx Section of a Circle.
d ] '^ *
— { '5 •«
i3>
33
38
•25
•145
•4
.206
.6
•44
•75
.806
•9
•3
.158
•45
.244
.65
•54
.8
•977
•95
•35
.178
•5
.294
•7
.661
•«5
x,i77
I
1.408
I.674I
1.978
Illustration. — If in a pipe 18 ina in diameter and i mile in length there is a
rigbt-angled curve of 5 feet radius, what additional head of flow should be given to
attain velocity due to a bead of 20 feet?
a=9oP, V for such a pipe and head = 4 feet per second; 18=1.5 <uid -^^
*X 5
= . 15, and . IS by table = . 133.
Hence, -^ X .133 X ~— = .5 X .133 X T^ = .016 53>oe.
»8o 64.33 64.33
NoTK.~If angle is greater than 90*', head shoald be proportionately increased.
Bent or A^ngular Circular Pipes.
Coeflteient A>r angle of bend = .9457 sin.^ x -(- 2.047 ^^^-^ ^' Hence,
70O
X
loO
200
300
400
45°
50°
55°
60O
65°
C
.046
•«39
•364
•74
.984
1.26
«-556
i.86x
2.158
2.43«
and — X C = /u X repreteniing haif angle of bend,
aff
QO°
iLLDSTRATioir. — Assumo « =r 4 fset, and angle = 90° ; a? = ^—- = 45°.
Then
4'
64.33
X .984 ■= .24^7 foot additional head required.
In "Valve Oates or Slide "Valves.
In Rectangular Pipes,
r
t
•9
.8
•7
.6
•5
•4
•3
.2
.z
C
.0
.09
•39
•95
2.08
4.02
8.12
17.8
44-5
«93
r = ratio oferou tection.
In Cylindrical Pipes,
h
0
•125
•25
•375
•5
.625
•75
•875
r
C
I
.0
•948
.07
.856
.26
.1}
.609
9. 06
.466
5-52
•3'5
«7
.159
97.8
h = relatite height of opening.
In a Throttle Valve. Tn Qflindrical Pipes.
r
C
5°
.913
•24
loO
150
20O
25O
30O
35°
400
45°
50°
60O
.826
•52
•74«
•9
.658
«54
•577
a.51
•5
3-9*
.426
6.22
•357
xa8
.293
18.7
•234
32.6
XI8
70^
.06
75«
A = angU (/potiUon.
546
ttTDAAtTLlOB.
In a GlAok Of Trttp Vfedve.
Angle of <»pMiing.
«5*
90
62
*5°
42
300
30
35*
30
4<^
45*
9-5
50°
&6
55*
4.6
«n«>|
«5^ t<^
3-a
a. 3
«»r
Iix a Cook. /» Qfi/nirfrttfti/ Pip^.
▲
5*
xoo
r
0
.936
OS
•85
.29
«5*
.772
75
.692
1.50
25^
.613
3* |5'47
30^
535
35'
•458
9.68
_4o"
•385
«7«3
45'
•3>5
3i.a
50^
•95
Sa.6
55'
,19
k«i6
60°
137
65'
.091
486
In a Conioal Valve. ( x-645 — — 1) =C. a^mda' = arecuofpipe
andopetwug.
Ixx Izxipexrfeot Contraotiotxa. (;r~>'~'') '*^^' c=ia/act9r^ttuiif
J, tt a
inif/rom .624/or —, = .ito ijbr -7 = x, being greater the gireei/ter the nUia.
CI A
iLLrsTRATioN— If a slide valye is set in a oyliodfictt pipe 3 ins. in diatneter and
500 feet in length, is opened to .375 ofdiameter of pipe (hence, .625 diameter closed),
what volume of water will it disclMiiBe ubdef' a lieftd of ta» fiset) ootfflcStai of en-
trance of pipe assumed at .5 ?
C, by tabUiP. 5iS»P^P^ ^'^ -^S cU>9ed=:S'S^
y/ig y/h
= «.
C z=from tabUj p. 544,/OT' an asmnud velocity qf 11 feet 6 ins. = .0195.
8.03 X xo
Then
'\^64.33X Vioo
^ ^^i 5 + 5- 52 + otgs — - — )
^80.3
500 X ia\ "" V^(7-oa + 39) " 6- 78
:3£ XI.85.^et
Hdnce, area of 3 fna = 7.07, and 7.07 x la X 11.8J = X005.4 ci^fietperKcand,
Valves. (Conical, Spherical, or Flap.)
Oouioal or Spider ioal Valve £*uppet.
v^
Height due to resistance or loss 0/ head of waler =11—. v repreaetUing
vehcitg of water infuU diameter of pipe or vessel.
(-^ — x) = C. A and A' r^^esenHng traasvene areas of vessel and of valve
dperUng, and (x.645 p — ») = C qf contraction in general
Illustration. —If A' = . 5 of vessel, C = f i. 645 X ~ — i j = 3. 29" 5= 5. 34.
Clack or Trap VcUve. — C decreases with diameter of vesseL
iLLOSTRATi^f.— If aeingle-acting force-pump, 6 ins. in diameter, delivers at each
stroke 5 cabe feet of water in 4 seconds, diameter of vulve seat 3.5 in«., and of valv*
4.S> what resiBtance has water in its pMsage, and what is loss of mechanical effect T
a = . X96. (~ ) = . 34 nUio of transverse area of opening, x — \~r) = • 44 w^^^e
qfaxwular oirUxaciUm to transverse Area of vessel
Hence, -34+ -44^ ^^ fii^^ifi ^^^^^ ^m^ confident of rssislanee correspvmdinff
thgrtU>= (i^ -xy = 3.8a»=xa37.
4X.196
^ 6.37 veloe&y per second.
!
HTOBA.UI.ICS.
547
2-^ = .63 height due to velociiy. Consequently, lasj X .63 = 6.53 height due to
04.33
fiMUtaNee o/valve^ and - X 62. 5 X 6.53 = 5io< iS ^- n^echaniccU fffect lost
I>isoliarge of "V^ater in. Pipes.
For any X^euffth. and Kead, and. for Dianxeters fVom
1 Incli to 10 Keet. In Cube Feet per Minute. {BearUmore.)
T*b. No. L Di«B. Tab. No. Dbun. Tab. No.
DUm.
Tab. No.
1 DUm.
Tab. No.
DUm.
Int.
Ft.
In*.
Ft. Ina.
I
til
9
1 147.6
I II
1.25
10
1493-5
1894.9
3
1-5
13.02
II
3 Z
I 75
19.15
2356
2 3
a
26.69
I
2876.7
2 3
«-s
46.67
9
34633
2 4
3
73-5
3
4115-9
a 5
3-5
108.14
4
4836.9
3 6
4
151.02
5
562^5
3 7
4-5
194.84
6
6493.1
3 8
5
263.87
7
7 433
8449
3 9
6
416.54
8
3 10
I
612.32
9
9544
3 II
85499
10
10722
3
1 1 983
»3328
16278
17889
19592
31 390
33282
35270
27358
29547
3«834
34228
3P725
Ft. Ins.
2
3
4
5
6
I
9
10
II
t ?
39329
42040
44863
47 794
50835
53995
57265
60648
64156
67782
71526
75392
87730
101207
Ft. Ina.
4 9
5
5 S
5 6
I '
6 6
I 6
8
8 6
9
9 6
10
"5 854
131 703
148 791
167 139
186786
207754
253 781
305 437
362 935
426481
496275
572508
655 369
745038
xn
This Table is applicable to Sewers and Drains by taking same proportion
of tabular numbers that area of cross-section of water in sewer or drain
bears to whole area of sewer or drain.
Formula upon which the table is constructed is, 9356^-?- xd'^=^y in
ing hei^ of fall qf water artd d diameter of pipe und I lengthy cUl in feet.
To Compute DisoliarKe.
{Egtelwein. ) yj -~- 4.71 a= V, and k/-^ . 538 = d. d =:: diameter of pipe v
<M., I length of pipe and h head of water ^ boih in feet
(ffawksley.) yj—r- — = <*i and ij ^^-r — = ^- ^ = number of Imperial
gallons per hour, and I length of pipes in yards.
(Heville. ) xio y/r « — 1 1 ^r7 = v in feet per second, r = hydraulic mean depth
iufutj and t sine of the indination or total fall divided by toted length.
V 47.124 d^ = V, and « 293.7286 d' = Imperial gallons per minute^ d ■=■ diameter
of pipe in feet.
To CoTnpute "VolnTne disoliarfced.
When Length of Pipe^ Height or Fatt^ and Diameter are given. Rule.
— Divide tabular number, opposite to diameter of tube, by square root of
rate of inclination, and quotient will give volume required in cube feet per
minute.
EzAMPLB. — ^A pipe has a diameter of 9 ins., and a length of 4750 feet; what is
Its dlschaiip per minute under a head 0117.5 (bet?
XrU. No. 9 ina = 1147 6, and
1147.61 1x47.61
/475
V »7-
4750
5
16.47
=s 69.67 cubofkeL
54^ BTDRAtLIOa
To Coxnpvite IDiazneter.
When Lengthy Head, and Volume are given. Rule.— Multiply discharge
per minute by square root of ratio of inclination ; take nearest coiresponding
number in Table, and opposite to it is diameter required.
Example.— Take elements of preceding case.
69.67 X -v/^^ = "47-6i, and opposite to this is 9
ins.
^^' WTs^h "^ ** *"/*'«'■ " representing velocity in feet per second and I length
in feet.
To Compute Head.
When Length, Discharge^ and Diameter are given. Rule. — Divide
tabular number for dia^neter by discharge per minute, square quotient, and
divide length of pipe by it ; quotient will give head necessary to force given
volume of water through pipe in one minute.
Example.— Take elements of preceding cases.
1147.61 .- ^ ,
^^^ = 16.47; 16.472 = 271.3; 47So-^27i.2 = i7.5ye«t
To Compute -whole Kead xieoeasarsr to furnish. req.ui8ite
X>isoliarg'e.
See Formula and Illustration, page 544.
To Compute Velooity.
When Volume and Diameter alone are given. Rule. — Divide volume
when in feet per minute by area in feet^ and quotient, divided by 60 will
give velocity in feet per second. *
Example.— Take elements of preceding case.
— ft^^a ^6o = 2.63/egt.
•75^ X. 7854
When Volume is not given. Rule. — Multiply square root of product of
height of pipe by diameter in feet, divided by length in feet, by 50, and
product will give velocity in feet per second. (Beardmore.)
To Compute Inolitiatioii. of a I*ipe.
When Volume, Diameter, and Length are given. I ^^ — — — .
\8356/ d* I
Illustration. — ^Take elements of preceding case.
{l^y^::^='°^^7iX4'2i4 = . 00368, and iZl^ = .003 68, or 4750 X. 003 68
=ziy.^g feet head.
To Compute Elements of Xjong* Pipes.
V 4 V V / , , /,'\ v=* . V77h
5 / V2
and 4787 ^ {1. 505X d -^ c I) -^=z din ins.
V^'+c + Cj
= «•
This latter formula will only give an approximate dimension fn consequence of
unknown element d, and also of C, as v = 1 .
' 3.1416 xd'
For Illustration, see Miscellaneous lliustratiou. ^uge 556.
HYDBAULies. 549
To Compute Vertical Height of a Stream prcgeotecl &om
Pipe of a Fire-engiixe or Pump.
Rule. — Ascertain velocity of stream by computing volume of water run-
ning or forced through opening in a second ; then, by Rule in Gravitation,
page 488, ascertain height to which stream would be elevated if wholly un-
obstructed, which multiply by a coefficient for particular case.
In great heights and with small apertures, coefficients should be reduced.
In consequence of the varying elements and conditions of operation of fire-
engines, it is difficult to assign a coefficient for them. Difference between
actual discharge and that as computed by capacity and Stroke of cylinder,
as ascertained by Mr. Lamed, 1859, was 18 per cent := a coefficient of .82.
A steam fire-engine of the Portland Company, discharging a stream 1.125 ins. in
diameter, through 100 feet 3.5 iueh hose, gave a theoretical head, computed fVom
actual dischaive, of 225 feet, and stream vertically projected was 300 feet; hence
coefficient in this case was .88.
EzAMPLs.-— If a flre-engine discharges 14 cube feet of water vertically throug?) a
pipe ,75 inch in diameter in one minute, bow high will the water be projected?
14 X 1728 -5-. 4417 area of pipe, -?- la ina in a foot, -i- 60 seconds = 76.07 /;«/ le-
locity ; and as coefficient of such a stream =: at .85, then 1x4.1 x .85 = i^.^Jiu,
~^ —. .0022 H'
Or, H -^ — = A. H representing head at nozgU^ and d height ofjtt, lt«th in
feet^ and d diameter ofnoxzU in im. (R F. Hartfbrd)
Illustbation.— /iffiume head of no feet and diameter of nozzle .75 inch.
.0022 X no' , .
J ,0 _ = 1 10 -^ 35. 5 = 74- 5/««'-
•75
NoTK. — The loss of head is greater with ring than with smooth nozzlea E. B.
Weston, Am. Soc C. E., puts the difference at .000 171 v*.
The loss of head increases with the absolute height of the Jet, and is less with an
increase of its diameter. This loss increases nearly in ratio of square of height of
Jet, and varies nearly in inverse ratio to its diameter
Cylindrical Ajutage.
Mean coefficient as determined by Mariotte and Bos8ut= .003066 square
of effective head for cylindricid ajutages ; hence, for co&ical, alike to that of
an engine pipe, coefficient ranges from .72 to .9, or a mean of .81.
By formula of D'Anbuisson, .003 047 K* = V,
Effective head, or A, in preceding examples 114.1. Then 114.1— .003 047 x
■ 14. 1 » = 1 14. 1 — 39.67 = 74.43 feet height of jet.
Hence, for a conical or engine pipe, 74. 43 x .8x = 6a 2g feet, or a coefficient of . 535.
To Compute l^ietanoe a Jet of ^Vater -^will l:>e prcxjeoted
Arozxi a Vessel through an Open ins in its Side.
AMFw^ ^ ^» ''^fr '3' '^ «Qi»l to twice square root of A o X 0 B.
' 'S- >3- ^^S If « is 4 times as deep below A as a is, < will discharge
twice volume of water that will flow (h}m a in same time,
as 2 is v^ of A < and i is -y/ of A a.
NoTK.— Water will spout fluthest when o is equidistuit
from A and B; and if vessel is raised above a plane, B most
bo taken upon plana
^ Volumes of water passing through equal apertures in
time are as square roots of their depths (Tom surfkce.
Rui«c. — Multiply sqiuire root of product of distance of opening from sur-
face of water, and its height from plane upon which water flows, in feet by
a, and produet will give distance in feet
EXAUPLV.— A vessel zo feet deep is raised 5 feet above a plane; how far will a Jet
reach that is 5 feet ttom bottom ot vessel ?
ao — 5X5 + 5 = '5o> and V150 X a = a4.49s/eet
HYDBAULICB.
e Tolaiiie o{ discharge tbcoiigh a tylindiical (qpaDuig
Jets d'Kku. (Fit. 14-1
Tliat a jet may ascend- to greatest practicable height,
conimunicatiiin with aupply ahavld be perfectly free.
Short lubes shaped aliks to contracted fluid vein, and
conically converj.'CDt pipes, big those vhich give gitalieBt
vdocilieB of efflux. Uanx^ to attain eieatoit effect, u in
fire-eni^nea, lone and eli^lly conical^ coavttgtail tubes
or pipes should be appUe).
In order t^ diniioish rpsUUnce of descending valer, a
4ed with a slight iiiclioaUoo bom vcitical.
With cylindrical tobea, vdocity being rediu»d in ratio of i to .8a, and as
btightH of jets are as squares of these coefBcicDts or rRtios. or as i to .67,
height of a jet through a cylindrical tube is two thirds that of head of
water (rom whidi it flows.
H C = A. H reprtiBiting head </ wolcr, C coffficient, and H luigkl qfjtL < Jtoli*-
VhendsH-r- 300,0 = . 9^ I When d = H -!- lyn, C = .B.
PLOW OP WATER IN KrVERS, CAITAIS, AND BTBBAlCa.
^nnti^ ITiUcr.— Water flows either in a natural or artifirial bed
or course. In first case it forma Streams, Brooks, and Bivers ; in
second, Drains, Cuts, and CanaU.
Bed of a water-coiiiBB la formed of a Bottom and two Baakt or Skertt.
7VaHiE«rM Section is a vertical plane at ri|^t angles to course of the
flowing wBt«ri Penmeter is length of this section in its bed.
La^Uvdinid StcHan or Pn^ is a vertical plane in the course or Ikrtai
of cutrnic of flowing water.
Slope or Dti^vitf is the mean angle of ioclinatian of surface of the water
to the horizon.
FiM is vertical distance of the two estreme points of ■ defined length o(
the flowiuR course, measured upon a horizontal plane, and this fall assigns
anf-le for defined length of the course.
Une or Thrtad of Cutrenl is the pomt where Bowing water attains ita
maxiuiutn vdoclty.
Wid-channel is deepest point of the bed in thread of current. ftliKit/ is
rratest at surface aivd in middle of current ; and surface of flowing; water
higheet iti current, and lowest at hanha or shore.
A River, Canal, etc.. is in a stale of pfnaimmey when an equal quantity
irf WHlor flows through each of its traiuverae sections in an equal timf^ or
when V. product of area of lection, (aid nkoh ntonfy tinmsi vialt 4SUM
q/" lie ffrcum, ii a ootutant number.
HYDRAULICS, 55 1
Vo Ooxnp'at# ^ean X>eptH of* ^Flo'wing "Water »
BuLE. — Set off breadth of the stream, etc., into any convenient number of
divisions ; ascertain mean depths of these divisions ; then divide their sum
by number o£ divitioiis, and quotient is the mean depth.
To Coxiapixte ISCean. A.rea of* Flo-^ving "Water.
Rule i. — Multiply breadth or breadths of the stream, etc., by the mean
de|)th or depths, and product is the area*
2. — Divide the volume flowing in cube feet per second by mean velocity
in feet per second, and quotient is area in sq. feet.
To- CoTOpiate "Voliznae of Flo-wing "^^ater.
Rule. — Multiply area of the stream, etc., in sq. feet, by the mean veloclty^
of its flow in feet, and product is volume in cube feet
To Compute ACean 'Velocity of IFlowing '^^ater.
RuLJU-^Divide smrfiice velocity of flow in feet per second by area of the
stream, etc., and quotient, multiplied by coefficient of velocity, will gm
mean Telocity in feet
Mean velocity at half depth of a stream has been ascertained to be as .91c to t,
and at bottom of it as .83 to s, compared with velooity at snrflftce. , Again, the ve-
locity diminishea flrom line of current toward banks, and, to obtain mean superficial
velocity, „,^„,-j.V3
n
= .915 w; hence,
To Complete M,eQii. "Velooity in -vvlxole Profile of a 19'avi-
ga'ble River, eto,,
V-J-j ^ 9 V^ ~ velocity at Mtom, and V-f-s — V V = mean vel^icUjf.
In rivers of low velocities multiply mean velocity by .8.
Obstrnotion In Rivere. (JtHtl^sworth.}
-rr^ -f 05 X ( — I -«- 1 =3 B. V rqpresetUing velocity in int. per ucond previow
58.6 \a/
to obstrueiiony A. and a areas of river unob§tnieted and ai obstruction in «?. feet, and
R rise in feet.
Illustbation. — Velocity of ol)8tructed flow of a river is 6 feet per second, and
areas of soctioa before and after obstmetion are xoo and 90 sq. feet; what would be
life in feet ?
^+05X^— j - 1^.664 X.a34=«i55/«<-
Blew of "Watev in X<ined Channels. (Bagin.)
/?^ _- V ; = C. D rqmsentinff mean kydmulie depth i» fMy P
^ ^ • x(v4-^ ^^ ^ i€«^& of channel to fall of i, x and
\^ ' D/ y as per toJble^ and C as per table p. 543.
.9
Plastered 0000045
Cut Stone .000013
zaio
4-354
X
Rubble Masonry 00006
Earth 000 35
y
1. 219
"4
For Sections of Um/vrm Area^ at Canab, Seioers^ etc, \J^ 2 D = v. A =^
area of fUm in sq. feety P toet perimeter of section, and D fall of stream per mile
vnfeeL
Illcbtbation.— Area of transverse section of a sewer is 50 sq. feet, Its wet perim.
eter 20 feet, and its ttB\ 5 feet per iniM.
/ (— X 2 X 5) =s V^S = 5 f^^ ^^ Sections of Rivers. 12 ^D p = v.
iiLDSTMAtiOH.— Assume area goo eq. feet, wet perimeter aoo, and ikll 5 feet per mUa
13 W 5 X ~ = la V»* 5 = 49-4 /««•
V 300
552 HYDEAULiCS.
• . • ■
Hydraulic Radius or Mean Depth is obtained by dividing area of^traot-
verse section by wet perimeter, both in feet.
To Compvite Fall per A^Iile for a. required 'M.eeaa. 'Velooity.
(V X I2\'
—J -j- a r = D. r representing hydraulic radius in feet
Upper surface of flowing water is not exactly horizontal, as water at Its sarfkce
flows with different velocities with respect to each other, and consequently exert
ou each other different pressures.
If V and vi are velocities at line of current and bank of a stream, the difference
of the two levels is = A.
2g
Illustration. —If v=s f^^i and « x 9 w ; then '^ — - = ^^ =0738 JbaL
zg 64.33
A velocity of 7 to 8 ins. per second is necessary to prevent deposit of slime and
growth of grass, and 15 ins. is necessary to prevent deposit of sand. .
MaoBimum velocity of water in a canal should depend on character of bed of the
channeL
Thus, Mean Velocity should not exceed per second over
Fine clay 6 ins.
A slimy bed 8 "
Common clay. 6 "
River sand i ft.
Small gravel i **
Large shingle 3 "
Broken stonea 4 fL
Stones 6"
Loose rocks xo "
To Compute Velocity of Flow or T>ia6h.ane^ee of-TVater in
Streaxns, Pipes, Oeiiials, etc.
I. When Volume discharged per Minute is given in Cube Feet, and A rea of
Canal, etc, in 8q. Feet, Rule. — Divide volame by area, and quotient, di-
vided by 60, will give velocity in feet per second.
3. When Volume is given in Cube Feet, and A rea in Sq, Ins, Rule. — Di-
vide volume by area ; multiply quotient by 144, and divide product by 60.
3. When Volume is given in Cube Ins,, and Af^ea in Sq. Ins. Rule. — Di«
vide volume by area, and again by 12 and by 60.
To Compute Flo-w or Vol-ume of X>iaoliaree.
1. When Area is given in Sq. Feet, Rule. — Multiply area of flow by its
velocity in feet per second, and product, multiplied by 60, will give volume
in cube feet per minute.
2. When Area is given in Sq. Ins, RuLfi. — Multiply area by its velocity,
and again by 60, and divide product by 144.
NoTB L— Velocities and discharges here deduced are theoretical, actual results de-
pending upon coeflicient of efflux used. Mean velocity, however, as before given,
page 529, may be taken at y/Tg .673 = 5.4 feet, instead of 8.02 feet.
2.— As a rule, with large bodies, as vessels, etc., their floating velocity is some-
what greater than that of flow of water, not only because in floating they descend
an inclined plane, formed by surface of the water, but because they are but slightly
affected by the irregular intimate motion of water: the variation for small bodies
is BO slight that it may be neglected.
a?o Comptite XXeifflit of Head of Flowing "Water.
When Volume and Area of Flow are given in Feet, Rule. — Divide vol-
ume in feet per second by product of area, and f coeflicient for opening, and
square of quotient, divided by 64.33, will give height in feet.
BxAXPLK Assume volume 266.48 cube feet, area 40 sq. feet, and C zl 4a^
_. / 266.48 \» . ^ 257.28 . .
Then ( "* ^ 1 -^64.33 = -^^ — ^±feeL
\4oX*.6a3; *" 64.3a
HTDBAUUCS.
553
SubxxxerKed. or r>rovrxied OrifioeB and. "Weirs.
When wholly submerged (Fig. is).-Available pressure at any poipi in depth
of orifice is equal to diflference of pressure on
Fig* 15- ■ each side.
Whence, C y/Tgh = t>, and C a y/Tffh = V.
a repraenting area ofduice in sq.feet.
_^_^^^_ ^_ ^^^^___^ Illobtratick.— Assuino opening 3 foet by 5,
/-T^-r^r^T ^r S--^fA Then, 5 X 3^5 V64.33X4 = 7-5 X 16.04 =
120. 2 cube feet per second.
When partly submerged iFig 16). h' -h = d = subroerged depth, and *--
*^ ^ ^ fc" =; d' — remaining portion of depth; whence
Fig. j6. -
L'Sjssj^gj.l.jjy
^ -|- d — entire depth, and
^^ss-si,-.^^ . iLLrsTRATiON.— Assume opening as above, fc=
^^^^5^-wi_ 4/fe<rf,fc' = 6,A" = 3,andC = .5. Thend = 6~
^^'T 1 r^ri Then .5 X 5 X 8.02 (2 V4+1 X 4>/4 - 3>/3)
— -=2ao5X 5 869 = 117.67 CM6«/ec< per •flcond.
TV%m drowned (Fig. 17).
.-- ^^«B CZ>/7?A(d+f A) = V.
S^^^J Illustration. -»• Assume opening as above,
^|g^ h=z4feet, d = a, and C = .52.
Then, .52 X 5 X V64.33 X 4,X (2 + f 4) = a-6
X 16.04 X 4-66 = 194.34 cw^ /ee< j>«r tecond.
CANAL LOCKS.
Single Hjooks.
WTiMi iL fliiM msses from one level or reservoir to another, through an
irJ^re ?overed?v^e mad in the latter, eflfective head on each point of
:K and^^uently head due to velocity of efflux at each instant, is
the diffSence of levels of the two reservoirs at that instant.
Hence C a V7^=V per second, h' repretentina difference of levels.
To Compnte Time of KilUns and IDisolxargiiiK a Single
Xjoclr.— Fig. 18-
When Sluice in Ujype^ G<^ « ^*''^^y "'•^ ^"^^^ "^^^ '**^'' ^^"^ ^^
AV
Oay/Tgh
= time of filing up to centre of sluice.
Fig. 18.
I
h repremUbing height of centre of sluice in uppar ^^
aaU from surface of canal or reservoir, and fi height ^^ .
^^ VsluiceUn upper g^Ue fro^U^iur- M^^^^Sk
face, or loiur infhelockoT river, aU tnfeet; and ^S^^^^^^B
aAh
^;^=«me ofjaiing the remaining space,
Uppw
?C A»l£
6«I4«K^ U'^oS &-4M UIC' CSLt
Zha-ea^gradual diminution of head of water occurs.
ConsequenUy, (A'±^^ = t time qf fitting a single tock
Cay/Vgh
When Aperture or Sluice in Lower Gate is entirely under Water, and above
Lower Level. — ^^^"^ '^- = time of emptying or discharging it. a' representing
mrea of lower Ouice.
SS4
and or lowi
diiwgln^
h^mtof^r
IlXIlHiUUCS.
enaloDB oT tt IMk, Dg. >8, trs ido ftet Ifa tetaph by 14
or upstMiB or rtuioe irom upper Md lower surtHiMB i»
asd kuter sluices Is i. j reet; hsigbiof up|>er is 4 f«sl,
r water.-; feet; required the tlmee ot Ullmg aad die-
" = !45,59 iwrndi = (iwt ../Jiiting UxkHpIo caUn 0/
I o/ilaia, and »4S»+ 49i'8 = 73«-77 '«™d», "^ote
^ = ,j6,iT«K.=«iiieofJlttiKF. 'X«8mv^H^
or'x-t:
1X4B00X
.S4iX.<.xV.
_303S _ 55^.j ,(„„,),_ j,^yi(i^arji^.
If Aen .iJperturs orShice in Upper Gale is eatirdy under Water and bdoa
Loioer Level. -^-- = liiiif o/^Ung Mk.
fV&eu Sluice in the Loaei- Gate it is pari oiove Surface of Lamer Level
and in part belwi it. —. — — ■ = K"" vf •'w-
chdrairig. <E and if rt^if^mf^ni^ ditfanov ly" por^ cf aperivrt atjove dnd qf httov
lurfice o/Wer loafer, A breadlh ofaprrOtre, anil * nnd A' at b^fiiri.
[LLEtTTUTioH.—Asenme sluice in precedLOg eiainpte lo be 1 Toot sboie loner
leiel or water, or tbat of lower canal: wbat is time uf d.ecbarge of lock, distance
of pan of aperture ■ font and of Itist below lurlkoe of water 4 l^elt
- = SsB-i "COnd*.
Double X>otdE. (J. D. Vmi Barm, Jr.]
.. double loek is not a duplication of
lower chamber supply of water _
LB from upper one, having no •
Influx, inetesilof aunirorm sup- s
ply lowing dimctlj from 8Ui- (
face level of canal or feeder.
Operation, therefore, of ■ fl
double lock is complex, addiUon ?
to formula for a sinsle lock be- i
iu^thatof ilisdiatviiiKuf water .
in iii>iiar lock to All lower, the
head 0! water cradually depreas-
iuR in the chamber, which is
c]i««i from upper reach (luring diaobarge into lower.
Xo Compute Time required ftjr 'Watep to ITolI iVom
tJlkp«r to UalAimi Wktiu Ubv«1.
'■ cwo'^-^''"''''*"^'*""'^"'' ^'^''''''^'^ll'nriimtaiareiKifloa^
and a arra o/iiufce upening, both in iq. fiet. C n)fjfc*i« hf diichargt = .Ki^Jbr
tftntngi uiilA iquart arriia, g acciltralim of gravily, / drpA ef ctMn »f Mfkx
HTDBAUUOS. 555
belmo uniform level, k depth of centre sluice opening Mow upper water level, and d
height of centre of sluice above Tower water level, all infect^ and t tCmefor water to
fall from upper to uniform toater tevel, in seconds.
Illustration— A =c20oo«qf./<«5«/ C=.54S; ^^^S; /=*6; h^n^ JmUcJ^?
afeeL (Fig. 19.)
Then, 2000 ^ ^:^2E^X77i- 4-9 = 367-6 seconds.
.545X5X567 »5'45
a. ira^o, caVP .545X5X5-67 iS-45
Note —/is never greater than I (lift in feet); it is equal to / when dr=:o; /a is
eonal to I when /i = o, never greater. In each caae it is the unbalanced beaa above
sluice, however far below the lowest water level the sluice is.
To Fill Upper X^ools or Blxnpty rjovror.
To fill upper lock or empty lower, when the sluice is below the lowest water-line,
in either case, takes the same time; for the head diminishes at the same rate, one
from the upper surface, the other from the bottom.
3. ^^^-f — t, Ber^jflteing below loioest water level 0/ ioc*= 8 /jct, as <ii=o,
Co y/g
aooo '1/2 X 8 8000 « ■»
attdf=zwhoU lift= '"""^^^ -> = 517.8 seconds.
•' •' .545X5X5.67 15-45
To Discharge a like Volume under a Constant Head
^ GayfTg Ga\/ ^g ^ .545X5V 64.33 ^^
Or, one half the time given by preceding case.
The times deduced by preceding formulas are in the foUowing proportions in
order, as i : v« • » or i : V2 : -7^-
If sluice of upper lock, through which it is filled, is above lowest water level,
thtoB, by combiniBg formulas 3 and 4, the time is thus deduced.
To jm from Lottfest Water l^el of said Lock to Level of Centre of Sluice,
5. .^^'^ . ss e'. /' representing height cfcewtn of sluice above said lowest water
G a yf%g leveL
To Jill remaining Portion of Loch above Sluice,
5. ?^.^J =s f\ /" repreaenibng depQi, hetaw upper woter levd of centre of
i^ayfTg
dmce or remaining portion of lift Hence, «* + <" = (y/f + 2 V/") = t
\j a 'v 2-ff
TofiU iMoer Lock under Constant Head from Upper Canal LeveL
8, If both lifts are the same, h — /= J, and — ^ — (^ + T "" ^-v / ) — ^'
CaV2fl»^ " ^ i2A
If lower lock is filled from upper one under a constant head, when latter is dtuwn
down to lowest level, formnia 7 will apply by making h =/, and
— ^^z=z (» y/f+ -ttY which te lde^Ucal with 7, for/=/8 apd d =/, the CM^f
Cay/^g V v//
bein^ the same-
556 HTDBAULICS.
MISCELLANEOUS ILLUSTRATIONS.
1. If external height of fresh water, at 60^. above injection opening in condensei
of a steam-engine, is 3 feet, and the indicated vacuum at 23 iua , velocity of watei
flowing into*oondenser is thus determined. {FonniUa page 532J
V = Vap (A-j-fc')- A' representing height of a cohunn ofwaler equivalent to press-
ure o/atmo^here vnthin condenser.
Assuming mean pressure of atmosphere = 14. 7 Ws. per sq. tncA, height of a column
of fresh water equivalent thereto =: 33.95/eet.
Then, if i inch = .4913 Uu., 23 ins. = ix.3 lbs.; and if 14.7 ibs. = 33.9s f^t ii-3
lbs. = 26. 1 feet
Hence v = Va 9 (3 4- 36. i) = 43. 37 feet^ less retardation due to coefficient of both
influx and efflux.
2. What breadth must be given to a rectangular weir, to admit of a flow of 6 cube
feet of water, under a head of 8 ins. ? {FonntUa page 533. )
_ =r — = 2.21 feet
fX.easVaT^ .4*7 X 6.56
3. It being required to ascertain volume of water flowing in a stream, a tem-
porary dam is raised across it, with a notch in it 2 feet in breadth by i in depth,
which so arrests flow that it raises to a head of 1.75 feet above sill of notch; what
is volume of flow per second ? {Formula page 533. )
C = .635. - X. 635X a X 1.75 >/2flfX>.75- 1-481 X 10-6 = 15 7 cu6«/«et
3
4. A rectangular sluice 6 feet in breadth by 5 in depth, has a depth of 9 feet of
water over its sill, and discbarges, as per example page 535, 380.95 cube feef per
second ; what is velocity of flow t (Formula page 535. )
38o,9J 38095^^^
6x(9-4) 30 '
2 / — ■Jh^ — 'Jh'^
If volume was not given : — C v a ^ x . _ /, — = «. C = .eaj.
Then -^ x .635 X 8.02 X v^^Q — V 4_ ^^^^ ^ 3.8 = ia.7/e«^.
3 9 — 4
5. If a river has an Inclination of 1. 5 feet per mile, is 40 feet in breadth with nearly
vertical banks, and 3 feet depth ; what is volume of its discharge ? (F<yrmulap. 542. )
Perimeter 40 + 3 X 3 = 46 f^et; hydraulic mean depth ^ =r 2.61 feet;
46
a 3= tao feet; C per tdble^ page 543, ^r assumed velocity of 2.$ feet = . 0075.
Then W -^^ — -^^^—— x 64.33 X 15 = V. 0659 x 96. 5 = 2.52/e«< velocity.
Hence 120 x 2.52 = 302.4 tmbefeet
6. What is head of water necessary to give a discharge of 25 cube feet of water
per minute, through a pipe 5 ins. in diara. and 150 feet in length? {Formulap. 548.)
Tabular number far diameter 5 ins.^p<xge 547, = 263.87.
— *
Then 263.87-^-25 = 111.3, and 150-^ 111.3 = 1. 35 /««<.
If this pipe bad 2 rectangular knees or bends, what then would be head of water
requ ired t (Foi-mula page 545. )
C) P«^« 545./o»' — = .984, area of $ ins. = .i36/€e^ and -^ -J- 60 = 3. 06 /eel
2 " . I 30
? 06'
velocity. Then ^ — X 984 X 2 = .2863, which, added to 1.35 = 1.64 >^1
64.33
By formulas foot of page 548, € = .024, and c .505 velocity = 3.06 feet ; head=:
i.^qfett^ and volume 26.38 cube feet,
7. If a stream of water baa a mean velocity of 2.25 feet per second at a breadth
of 560 feet, and a mean depth of 9 feet, what will be its mean velocity when it baa
t br«adth of 390 feet, and a mean depth of 7.5 feet? (Rule page 548.)
560x9x2.25^11340^ ^^^^^^
320 X 7-5 24«?
HTDBAULtCS. 557
8. What volume will a pipe 48 feet in length and ? ins. in diameter, under a head
of 5 feet, deli ver per second f { Formula page 547. )
Tabular number for diameter 2 tyu., page 547, = 26.69.
^— = 3- »• Then ^-^ = 8.61, w^ich -i- 60 = . 143 cube/eeL
If this pipe had 5 curves otqaP, with radii — = - =.5; what would be it»diB-
2 r 4
charge per second ?
V = .i43; a = 2-hi44=.oi39; Cper tabU=2^ = .2g4; v = -^^^:=: 10. agfiet.
90® 10.29'
Then .294 X ^^ X j~- = .147 X 1.64 = 241, which Xs/or 5 curvet = i.a =s
height due to resistance of carves. h = s — 1.2 = 3. 8.
Henc«, if V2 ^ 5 s= . 143 ; V2 ^ 3.8 =s . 125 cu^e/stft
9. If a slide stop valve, set in a cylindrical conduit 500 feel in length and 3 ins. m
diameter, is raised so as to close .625 of conduit; what volume will it discharge
under a head of 4 feet ? {FormtUa page 546. )
Cfor conduit = .s, for friction .025, and for dide valve .375 open. taJbJ^pagt 545,
5. 52, d = . 25, and a = 7.07 sq. ins.
Then '. = .. ' , — r = 2.13 ftei velocity^ aad
3. 13 X 13 X 7-07 s= x8o, 71 cube ins.
ta If a single lock chamber is 200 feet In length by 24 in breadth, with a depth
of 10 feet, centre of up'per gate, which is 4 feet in depth by 2. sin breadth, is at
middle of depth of chamber, lower gate, k feet in depth by 2.5 in breadth and wholly
immersed; what is time required for filling and discharging it? {Formula p. 553.)
C = .6i5, A=5, A'=s, A ^200X24 = 4800, 0 = 4X2.5 = 10, and a' = 5
X 2.5 = 12.5
(2X5 + 5)4800 _ ^ 7£0oo ^ 3 ^^^^ ^ .^^
.615X10^64.33X5 "°-'7
2X4800XV5 + 5 _ ^^ = 491.4 seconds time of emptying.
I "i'73
.615 X 12.5 V2flr
XX. In a moderately direct and uniform course of a river, the depths and velocities
are as follows ; what is the volume of its flow and what its mean velocity ? {p. 55X.)
F«et. Feet. Feet. Feet. Feet.
Distances 5 12 20 15 7
Area of profiles = 5X34-
Depths 3 6 11 8 4 12 x6-f 20X n -f 15 X 8-f
Mean velocity 1.9 2.3 2.8 2.4 2.1 7 X 4 = 455 ^S'-/^^^'-
15 X x.9 4-72X2.3-}-22oX2.8 + x2oX2.4 + 28X2.i = xx56.9 citbefeet volume,
and — =-^ = 2.SAfeet velocity.
455
Alixier's Inoh..
A * Miner's inch " is a measure for flow of water, and is an opening one
inch square through a plank two inches in thickness, ander a head of six
inches of water to upper edge of opening.
It will discharge 11.625 U. S. gallons water in one minute.
Theoretical IP under diff&'ent Beads.
xoo 90 |8o 170 |6o so 40 ho (20 I15 |xo | sj- 3I x
3.25 3.61I 4.061 4.64I 5.41 6.5 8. i2lia8|i6.2l2i.6|32.5|65|io8|325
Heads in flset.
Ins. per W. . .
Water Inch (Pouce ePeau). — Circular opening of i inch in a thin plate is
equal to a discharge of 19.1953 cube meters per 24 hours.
a A*
558 HYDRODYNAMICS.
HYDRODYNAMICa
Hydrodynamics treats of the force of action of Liquids or Inelastic
Fluids, and it embraces Hydraulics and Hydrosiaiics .-^ the former of
which treats of liquids in motion, as flow of water in pipes, etc., and
latter of pressure, weight, and equilibrium of liquids in a state of rest.
Fluids are of two kinds, aeriform and liquid, or elastic and inelastic,
and they press equally in all directions, and any pressure communicated
to a fluid at rest is equally transmitted throughout the whole fluid.
Pressure of a fluid at any depth is as depth or vertical height, and
pressure upon bottom of a containing vessel is as base and perpendicu-
lar height, whatever may be the figure of vessel. Pressure, therefore,
of a fluid, upon any surface, whether Vertical, Oblique;, or Horizontal, is
equal to weight of a column of the fluid, base of which is equal to sur-
face pressed, and height equal to distance of centre of gravity of sur-
face pressed, below surface of the fluid.
Side of any vessel sustains a pressure equal to its area, multiplied by .
half depth of fluid, and whole pressure upon bottom uuU against sides
of a cubical vessel is equal to three times weight of fluid.
Pressure upon a number of surfaces Is ascertained by multiplying
sum of surfaces into depth of their common centre of gravity,' below
surface of fluid.
When a body is partly or wholly immersed in a fluid, vertical press-
ure of the fluid tends to raise the body with a force equal to weight of
fluid displaced ; hence weight of any quantity of a fluid displaced by a
buoyant body equals weight of that body.
Centre of Pressure is that point of a surface against which any fluid
presses, to which, if a force equal to whole pressure were applied, it
would keep surface at rest. Hence distance of centre of pressure of
any given surface from surface of fluid is same as CerUre of Percussion.
Centres or Pressuxre.
PlBiraUelogram^ Sidt^ Base, Tangent, or Vertex of Figure at Surfhce ofFlmid, \b at
.66 of line (meaflariag downward) that Joins centres of two horizontal 'sides.
} Triangle, Base ujmermogt, is at centre of a line raised from lower apex, and join-
' ing it with centre or base; and Vertex uppermost, it is at .75 of a line let fall from
{ vertex, and joining it with centre of base.
' Right-angled Triangh, Base uppermost, is at intersection of a line extended (Vom
t centre of base to extremity of triangle by a line ranning horizontally from centre
1 of side of triangle. Vertex or Extremity uppermost, is at intersection of a line ex-
tended fYx)m the centre of the base to the vertex, by a line running horizontally flrom
I 375 of side of triangle, measured from base.
; TrapeMoid, either of parallel Sides at Surface, - ' ■ , X a - d * and 6' repre-
• senting breaiUhs ofjlgure, d distance from surface of fluid, and a length ofUne join-
ing opposite sides.
Circle, at 1.95 of Its radias, measured from upper edge.
"i pr
Semicircle, Diameter ai Surface of Fluid,— =d. r representing ra4liusqfciirdl»
10
and j» =3.1416. Diam. dmanward, '^ *^ *" ^ -rsd.
n j>— 10
HTPBQDYNAMICS, 559
Side, ^aae, or T^T^f^^nt of F'igure Iselo-w Surface of*
n ^ , « ,. > . 2 ^'3 — A3 \rAo4-m^ , .m* ,,,
Rectangle or PardUelog^m. - X irr—t ^ =* d ; or, ' = d : and — = d .
h and &' ngit^enA^n^ dcjiifti qf upper an4 lovudr. wr/aoes offyfv^t a{a4i d d^pth.
both from surface of fluids m JuUfifipt^ of figure, o depth 0/ centre of gravity of
figure fron^ suxfau^ of fluid, d' distance from upper side of figure, and d" distance
Jrom centre of gravity.
Triangle. — Vertex Uppermost — *— = a: —r — = d\ Base Uppermost.
z8 o 18 o "^
' ' ° =: d. I representing depth offigw-e, d distance from smfuce of fluid upon
a line from vertex to centre of base, and d' distance from centre of gravity of figure,
Cirde. ■ — = d. or — = distance from centre ofdrde.
Semidrde. — Diam. Horixontal and Upward «>r DowMMrd. <— --~ -^ — ^ 4- Q =3 d;
'xnl — A.l 4,1 I' 16P
^^ ^— = d': -^— =ad", and -; — =aft d fwretcnHng di^anoe from
surface of fluid, d' diftanct of centre of gravity from, centre of arc, d'* distance of
centre qf gravity fnm, diameter when it is uppermost, and c centre of pressure.
I^ressure.
To Compute ^Pressure of a IB^luid upon Bottom, of its
' Oontainingp 'Vesael.
Rule. — Multiply area of base by he!£;ht of flttid ia feet, and .product by
weigbt of a cube foot of fluid.
To Compute Pressure of a F'luid upon a Vertical, In-
clined, Curved, or any. Surface.
Rule. — Multiply area of surface by height of centre of gravity of fluid
in feet, and product by weight of a cube foot of fluid.
ExAMPLB I.— What is pressaro i)p«a a ploping 9ido of. a pond of flresh water 10 feet
square a^drifr feet in depth ^
Centre of ^ayit^, 8 -4- 2 — 4feHfrom surface, irhen io« X 4 X 62. 5 == 25 060 lbs.
2. — What is pressure upon staves of a cylindrical reservoir when filled with fresh
water, depth being 6 f^t, an4 diameter of base 5 feet ?
5X3. 1416 = isjdi feet curved mrface of reservoir, which is coQSidered as a plane.
15.708 X 6 X 6-7-2 = 282.744, which X 62. 5 = 17 671.5 lbs.
3. — A rectangular flood-gate in ftesh water is 25 feet in length by 13 feet deep;
what is pressure upon it?
85 X 12 X i2-r-2= 1800, which x62.5=ii2 5oo Ihs.
When water presses against both sides of a plane surface, there arises from
resultant forces, corresponding to the two sides, a new resultant, which is
obtained by subtraction of f omter, as they are opposed to each other.
iLLrsTRATior ^Depth of water in a canal is 7 feet; in its ac^olning lock it 18^
feet, and bi^dtn of gates is 15 feet; what mean pressure have they to sustain, anp
what is depth of point of its application below surface f
7 X 15 = "OS, and 4 X 15 =60 sq.feet. (105 X - —60X2) X 62. 5 == 15468. 75 itt.,
Then 15468.75--- 62. 5 = 247. 5 = cube feet pressing uptm gates upon high, side, and
•47. 5-r-i5X7 = 3.3S fket =. depth of centre of gravity of mean pressure.
To Compute Pressure on a Sluioe.
Awd — V, and C P = P*. A representing area of shHce in sq. fket, w weight qf
Ufaterpercuhefbot, d mean depth of sluice betma suTfaoe, infoet, F pressure <tn sluioef
and r power required to operate it^ both in lbs.
C= .68 when sluice is of wood, and .31 when of irpo.
560 HYDRODYNAMICS.
Example — What Is pressure on a sluice-gate 3 feet square, its centre of gravity
being 30 feet below surface of a pond of flresh water?
3 X 3 X 30— 270, which X 62.5= 16875 Ibt.
«
To Coxxipnte Fressiire or a. Coluxxizx of a Fluid per
6q.. Inoli.
Rule. — Multiply height of column in feet by weight of a cube foot ot
fluid, and divide product by 144 ; quotient will give weight or pressure per
sq. inch in lbs.
NoTit ^When height is given in Ins., omit division by 144.
PIPES.
To Compute required Tlxiokness of a Pipe.
Rule. — Multiply pressure in lbs. per sq. inch b^ diameter of pipe in ins.,
and divide product by twice assumed tensile resistance or vahte of a sq.
inch of material of which pipe is constructed.
By experiment, it has been found that a cast-iron pipe 15 Ina in diameter, and
.75 of an inch thick, will support a head of water of 600 feet; and that one of oalc,
of same diameter, and 2 ins. tbiclc, will support a head of x8o feet?
Example i.— Pressure upon a cast-iron pipe 15 ins. in diameter is 300 lbs. per sq.
inch ; what is required tbiclcness of metal?
300 X IS = 4500. which -T- 30Q0 X 2 = . 75 inch.
Note. — Here 3000 is taken as value ot tensile strength of cast iron in ordinary
small water-pipes. This is in consequence of liability of such castings to be im-
perfect from honey-combs, springing of core, etc.
2 Pressure upon a lead pipe i inch in diameter is 150 lbs. per sq. inch; what IB
required thickness of metal ?
Here 500 is taken as vaZue of tensile strength.
150 X I = 150, which -r- 500 X 2 = .15 inch.
Cast-iron Fipes.
To Compute TliiokiiesB, etc., of* flangred !Pipe0*
For 75 lbs. Pressure. For 100 Jbs. Pressure.
.025 D-f .25 =T
.03 D-|- .3 =J
.05 D -f- I'lS = *
.03 I>+ -35 =/
1.05 D4-4.25<l-l- 1.25=0
X.05 D-|-2Xd+i =0'
.03 D-j- .3 =T
.035 D-- .45 =r«
.05 D+ 1.15 =1
.04 DH-^^6 =/
I.I D + 5 X d-f i.S =0
I.I DH-2.5Xd4-x.4 =0'
.7D + 2.2 = n; — ^^-^- = a, and ^/— 5 — \-C = d.
' ^ 4000 V 7854
D representing diam. of pipe, T tiiickness 0/ metal, t tiiickness and I len^ qfboss^
f thickness offiangt, o diam. of flange, 0* diam. of centres at boU holes, and d diam.
iffboUSj cUl in ins.; A area of pipe and a area of bolt at base of its tftread, in sq. ins.,
p pressure in lbs. per sq. inch, and C a coefficient due to diam. of bolt
Thus, diam. .125 -f. 032, .25 4- .064, .5 + . 107, x + .i6, 1.5-}-. 214, and 2 + . 285.
Illustration.— What should be dimensions of a flanged pipe, 10 ins. in diameter,
for a pressure of 100 lbs. per sq. inch ?
.7 X xo + 2.2 = 9. 2 = 10 number of bolts, and diam. 10 int. = 78.54 ins. area = A.
Z?Jl^±i2 = ..^35,and,/^ + C = V.>s = .5: hence, .5+ .07 =
607 i= .625 lbs. diameter ofboUs ; .03 X lo-f- .3 = .6 = thickness qf metal; .035 X 10
4-. 4s = '^ = thickness of flange; .05X 10+ 1.15 = 1.65 = ggwgtfft of boss; .04X10
4- .6 = I =s thiekness of flange; i.i X 10 -f- 5 X .625 + x. 5 = 15.635 = diameter qf
flange ; and 1. 1 X 10 + 2. 5 X .625 -+- 1. 4 = 13. 9625 = diameter ofboU hdsi.
For Tables of Cast-iron Pipes, see page 132.
HYDB0DYNAMIC8. 5^^
fTo Compxite ICleznents of* 'V^ater-pipes.
xx»ia4 5Pd + C = «; or, .000054 H d-f- C = «; .4336H-=P; and
02^ijPX a- 45 = W. P representing pressure of water in lbs. per sq. inch, D and d
tsBtemal and internal diameters ofpipe^ and t thuSeness ofmetal^ all in ins. , C coejgl-
dentfar diameter ofpipe^ and H head ofwaler infiet.
C ss . 37 for pipes less than 12 in& in diameter, . 5 flrom 12 to 30. and 6 (torn 30 to 50
To Compute "Weight of Fipea.
To Diameter add thickness of metal, multiply sum by 10 times thickness,
ind product wiU give weight in lbs. per foot of length.
Weight of Faucet end is equal to 8 ins. of length of pipe.
Hydrostatic I*ress.
Vo Compute Elements of a Ujrdroatatio Press*
Tlk „ Wra , Wi'a „ PA« r, *.-
y^ = W; -^^ = A; -^-^ = P; ^^ = a. V repremOxng pouter or pren-
ure appliedy W toei^t or resistance in lbs. ^ I and V lengths of lever and fiUcrum in
ins. or/eety a$id A and a areas ofrwrn andpiston in sq. ins.
Illustration.— Areas of a ram and piston are 86.6 and x sq. ins., lengths of lever
and fulcnim 4 feet and 9 ins., end power applied 20 lbs. ; what is weight that may
be sustained?
ao X TXi^ X 86. 6 83 136 .,
= ■ = 9237.3 lbs.
9X1 9
To Compute ^Fliiokuess of "M-etal to Resist a given
Pressure.
Rule. — Multipl}'' pressure per sq. inch in lbs. b^ diameter of cylinder in
ins., and divide product by twice estimated tensile resistance or valtte of
metal in lbs. per sq. inch, and quotient will give thickness of metal required.
Example.— Pressure required is 9000 lbs. per sq. inch, and diameter of cylinder is
5.3 in& ; what is required thicl^ness of metal of cast iron?
VcOue of metal is taken at 600a 9p°.^J'J. - 47 7oo __ ^^
6000X2 12000
Values of Different Metals in Tom, (JUolesuforih.)
Cast iron. 41 1 Gun metal 22 | Wrought iron.. .14) Steel 06
Hydraulic Ham.
Useful effect of an Hydraulic Ram, as determined by Eytelwein, varied
from .9 to .18 of power expended. When hei<^ht to which water is raised
compared to £all is low, effect is greater than with any other machme ; but
it diminishes as height increases.
Len^ of supply pipe should not be less than .75 of height to which
irater is to be raised, or 5 times height of supply : it may be much longer.
To Compute Klements.'
.ooii3V* = H»; ^^ = V; 1.45VV-D; .75v/V = d; and |x^ =
effidencjf. V and v represetUing vohtmes expended and raised, in cube feet per
minmUf h and h' keighiU from unUcft water is drawn and eUwUed in feet, D and d
diameters ofs%qpply and discharging pipes in ins.^ and IP effective horse-power.
Illustration. — Heights of a fall and of elevation ars 10 and 26.3 feet, and vol-
umes eqwnded and raised per minute are 1.71 and .543 cul>e feeW
.001X3X 1-71 X 10 =.0193 ff; ' — — = 1.71 cube feet; 1.45^1.71 = 1.89
tm.; .75V»-7«=-975<«.; tnA ^ X ^^^^ = .6g^ efficiency.
S02
HTDBOPTHAtfJCa
Re«ult9
of* Operationei of ^srdirAv&Ue HaiSRfl*
Strokes
FaU.
Eleva-
WAter
Usefnl
Strokes
FaU.
Eleva-
Water |
{Mr M.
tion.
Expen'd.
Raited.
Effect.
perM.
tion.
ExfenM.
Raised.
C, * t.
No.
Feet.
Feet.
C. Ft.
C. Ft.
No.
Fe»t.
Feet.
C Ft.
66
iao6
26.3
1.71
•543
%
15
3-«2
38.6
1.98
.058
50
9-93
•38.6
«-93
.421
10
1.97
38.6
1.58
.014
36
6.05
38.6
1-43
.169
%
—
22.8
196.8
.38
.029
3>
5.06
38.6
X.29
.113
—
8-3
52.7
2
.186
UMftll
Efltet.
•35
.18
.67
•57
NoTB.— Volume of air vessel = volume of delivery pipe. One seveQtb of w^er
may be raised to about 4 times head of fall, or one fourteenth 8 times, or one twenty-
eighth 16 times.
WATER POWER.
Water acta as a moving power, either by its weight or by its f^s vivat, and
in latter case it acts either by Pressure or by Impact.
Natural Effhct or Pmoer of a fall of water is equal to weight of its volume
and vertical height of its fall.
IfSvater is made to impinge upon a machine, the velocity with which it
impinges may be estimated m the effect of the machine^ Result or effect,
however, is in nowise altered ; for in firfit case P sm V «» A, and in latter ^
— Y Iff, V representing volume in cube feet^ to v>eighi^ in lbs,f and v velocity
2 g
of flow in feet per second.
62. s V A = P, and 3. a * a ^A =s= V. P represe^tifM pressure in {Ifs. , a Ckv^ <if vpm-
ing in sq./eet, and A height of flow infect per second.
To Compnte Power of a FalJ of "Water-
RuLK. -^Multiply volume of ilowin*; water in cube feet per minute by
62.5, and this product })y vertical height of fall in feet«
if OTE.— When Flow is over a Weir or Notch, height Is nreaSnred from surfkce of
tail race to a point four ninths of height of weir, or to centre of velocity or pressure
of opening of flow.
When Flow is through a Sluice or Horizontal Slit^ height Is measured from sur
face of tail-race to centre of pressure of opening.
Example. — What is power of a stream of water when flowing over a weir 5 feel
in breadth by i in depth, and having a fall of 20 feet from centre of pressure of flow?
By Rule, page 533, -5X1 V^gi X .625 = 16,73 cube J^et per «ecan<i
16.68 X 60x62.5 X 20 = 1 251 000 ?&«., which -f- 33 000:^=37.91 htrrses'' power.
Or, . 1 1 35 V A = theoretical H*. A representing height from, race in feet.
Illustration.— If flow of a stream is 17.9 cube feet per second, to what height
and area of flow of i foot in depth should it be dammed to attain a power of 10
horses. i
33 000 X 10 __ ^^^^ ^^^ ^^ ucond^'dnd y* • aaSS cube feet per second.
60 02.5
88
17.9
4.92 ^( heighti H^oe,-- .6 V2 gx i = 3-9, and r7.9-r-3»2 = 5.59 sq.feeL
Water sometimes acts by its weight and vis viva simultaneously, by com-
bining effect of an acquired velocity with fall through which it nows upon
wheel or instrument.
In this case h, + ^ j V x 62.5 = mtckanieal effect.
* 4a determlMd \ff - O,
HYI>RODYNAMIC8. 563
WATEK-WHEEL8.
Water-wheels are divided into two classes, Vertical and Horizontal.
Vertical comprises Overs/iot^ Breast^ and Uiiderthot ; and Hori;&outai,
Turbifiey Impact^ or Reaction wheels.
Vertical wheels are limited by construction to falls of less than 60 feet
Turbines are applicable to falls of any height from i foot upward.
Vertical wheels applied to a fall of from 20 to 40 feet give a greater
effect than a Turbine, and for very low falls Turbines give a greater effect.
Slxiices. — Methods of admitting water to an Overshot or Breast
Wheel are various, consisting of Overfall^ Guide-hiicket^ and Penstock.
An OverfaU Sluice is a saddle-beam with a curved surface, so as to direct the
current of water tangentially to buckets ; a Chiide-bttcket is an apron by which
water is guided in a course tangential to buckets; and a Penstock is sluice-board or
gate, placed as close to wheel as practicable, and of such thickness at its lower edge
as to avoid a contraction of current. Bottom surface of penstock is formed with a
parabolic lip.
Sb.rovidinR: of a wheel consists of plates at its periphery, which
form the sides of the bucket.
Height offaU of a water- wheel is measured between surfaces of water in penstock
and in tail-rcux, and, ordinarily, two thirds of height between level of rcQcrvoir and
point at which water strikes a wheel is lost for all effective 0))^ration.
Velocity of a wheel at centre of percussion of fluid should be fbom .5 to .6 that
of flow of the water.
Total effect in a fall of water is expressed by product of its weight
and height of its fall.
Ratio of Kflteotive I*ower of "Water ^otprs.
Overshot and high I m^^ ^g »„ ^ .^
breast *; } ft«m .68 to .6 to i
Turbine " .6 to .8 to i
Breast... " .45 to .65101
Hydraulic Ram " .6 to i
Undershot, PoDcelet'-s, from .6 to .4 to i
Undershot. .» . . " .^27 to .45 to i
Impact and Reac-') „ • to c tot
tion f * ">-5 *aj
Water-pressure engine ** .8 toi
Oversliot-AVh.eel,
OvEBSHOT-wHEEL. — The flow of water acts in some degree by iippact,
but chiefly by its weight.
Lower tiie speed of wheel at its circumference, the greater will be mechan-
ical effect oi the water, in some cases rising to 80 per cent. ; with velocities
of from 3 to 6.5 feet, eflSciency ranges from 70 to 75 per cent. Proper ve-
locity is about 5 feet per second.
Number of buckets should be as great, «nd should retain water as long, as
practicable. Maximum effect is attained when the buckets are so numerous
and close that water surface in the bucket commencing to be emptied should
come in contact with the under side of the bucket next above it. Moles-
worth gives 12 ins. apart.
Curved buckets give greatest effect, and Radial give but .78 of effect of
Elbow buckets. Wheel 40 feet in diameter should have 152 buckets.
Small wheels give a less effect than large, in consequence of their greater
centrifugal action, and discharging water from the buckets at on earlier
period than with larger wheels, or when their velocity is lower.
When head of water bears to faXL or height of wheel a proportion as great
as I to 4 or 5, ratio of effect to power is reduced. The general law there-
fore is, that ratio of effect to power decreases as proportion of hecui to toiaJ
head andfaU increases.
564
HTBBODTNAHICS.
Wheel with shallow Shrouding acts more efficiently than one where it is
deep, and depth is usually made lo or 12 ins., but in some cases it has been
increased to 15.
Breadth of a wheel depends upon capacity necessary to give the buckets
to receive required volume of water.
Form, of Buckets.— ^KA\a\ buckets— that is, when the bottom is a right line— in-
volve so great a loss of mechaDical effect as to render their ase incompatible with
economy; and when a bucket is formed of two pieces, lower or inner piece is
termed bottom or floor, and outer piece arm or torut. Former is usually placed in
a line with radius of wheel.
Line of a circle passing through elbow, made by junction of floor and arm, is
termed division circle, or bwket pUch, ana it is usual to put this at one half depth
of shrouding.
When arm of a backet is included in division angle of buckets, that is, ^ — , n
It
representing number of buckets, the cells are not suflSciently covered, except for verj'
shallow shrouding; hence it is best to extend arm of a backet over x.2 of division
angle, so as to cover or overlap elbow of backet next in advance of It.
Construction of Buckets (Fig. i) Capacity of bucket should be 3 times volume
of water.
^'S- >• Fairbaim gives area of opening of a backet in a
— ^ r — .— T--,-. wheel of great diameter, compared to the volume of it,
^..-AVV \ A Ms to 24.
'"f'- \ \ ' / \ Backets having a bottom of two planes, that is, with
a' V'^V*--/ I two bottoms, and two division circles or bucket pitches
and an arm, give a greater effect than with one bottom.
When an opening is made hi base of buckets, so as
to afford an escape of air contained within, without a
loss of water admitted, the buckets are termed ven-
tilated, and effective power of wheel is much greater
than with closed bucketa
D = distance apart at periphery = d, d depth of
shrouding, i length of radial start = .33 d, Z length of
backet curve = x. 25 d in large wheels, and i in wheels
under 25 feet, a angle of radius of carve of bucket,
with radial line of wheel at points of backet = 15^.
(Midesivorth.)
To Compute Radius and Revolutions of* an Oversliot—
^wlieel, and Heiglit of*' Fall of Water.
When whole Fall and Veldcity of Flow, etc., are given, —— = r,
— n, — 1.1=*', and ^'**' = c h representing height of whole
3.1416 r ig fc
faU, h' height between the centre of gravity of discharge and half depth of bucket
upon which water flaws, v velocity of flaw in feet per second, a ang^ tMck point qf
entrance of water into a bucket makes with summit of wheel, n number qf revolutions
per minute, c velocity of wheel ctt its circumference per second, and r its radius.
NoTK.— Height of whole fall is distance between surface of water in flume and
point at which lower buckets are emptied of water, and as a proportion of velocity
of flow is lost, it is proper to assume height ft' as above given.
Illustration.— A fall of water is 30 feet, velocity of its flow is 16 feet per second,
angle of its impact upon backets is 12^, and required velocity of wheel is 8 feet per
second ; what is required radius, number of revolutions, and helriit of fall nnou
wheel?
*'=^X 1.1=4. 38/'«*/ «>8- "*' = -978; ^^P^==^ = ia.95/«rfradM«;
»ff i-f.978 1.978 ^ '
3.Z416X 12.95 40.68 """
HTDBODTKAMICS. 565
Wheu Number of RevoluHons and Ratio between Velocifiea of Flow and at
Circumference of Whed are given.
\/.cxx>772 (»n)*A-(-(i-|-cos. a)2 — i-fcos. a) v 3.i4i6nr
.000386 «n)» ' c ' 30
iLLCSTRATiOH.— If Dumber of revolutions are 5, x => 2, and fiiU, etc. , as in previous
case, what is radius of wheel, velocity of flow, and height of fall?
V:^77i { g X 5')' X 30 + ( I 97»)' - '978 ^ ^518^ ^ y^^
.000386(2X5)* .0386 ■*"* •'
3_i4i6 X 5 X 13-4' _, ^ ^^^ ^^^^6 7.03 X 2 = 1406 vdocitif of flow, and ^^^
30 04.33
X I i=y^^feei
Xo Compute "W^xdtli of an Oversliot-'svheel.
C V
— ; = 10. G rejTresetiImp a coefficient =■ 3, toAeu buckets arefUed to an excess, and
9 C
5 when they are deficiently fllled, V volume of water in cube feet per second, s depth
of shrouding, w width of buckets, both in feet, and c' velocity of wheel at centre of
Arouding, in feet per second
' iLLUSTRATioM ~A wheel is to be 31 feet in diameter, with a depth of shrouding of
I foot, and is required to make 5 revolutions per iriinute under a discharge of 10
cube feet of water per second , what should be width of buclcets?
A«iumeC-4,andc'r.3^^^X3-4»6X5^y854. Then * ^ ' ° 509/«^
60 . 1 X 7054
Xo Compute Nuin"ber of BuoUeta.
7(1 + — J — 12 = d, and ^ = n. D representing diameter of wheel, d dis-
tance between centres of buckets, in feet, and n number of buckets.
Illustration —Take elements of preceding case.
Then 7 (, + -J-) =. 7 X 2.2 - ,2 = 1.283, and 31I=i^3_L4i6X_i ^ „.^^ g^y 73
buckets; hence - — ^=50, angle of subdivision of buckets.
72
Xo' Compute Il2fi*eot of au Overshot-'wlieel-
v*'»-(gv«+/)
^.^ — - ' = p. 10 representing weight of cube foot of water in lbs. ,
1/ velocity of it discharged at taU of wheel, in feet per second, V vatum/e of flow in
cube feet, and f friction of wheel in lbs.
Illustratiok. -—A volume of 13 cube foet per second has a fiUl of 10 feet, wheel
Ming bttt 8.5 feet of it, and velocity of water discharged is 9 feet per second; wha^
Is effect of fiill?
Friction of wheel is assumed to be 750 lbs.
ja X 8.5 X 62. 5_- (g^ X la X 62.5 + 750^
6375 — (1.26 X 75o-h7S0)_ 4680 ^
12X10X62.5 7500 7500
.6»4 t:i ratio of effect to power ; and 4680x60 Meofidf-^ 33 000 - 8.51 H^.
Xo Compute l*0"^^er of an. Oversliot--wlieel.
Rule.*— Multiply weigbt of water in lbs. discharged upon wheel in one
minute by height or distance in feet from centre of opening in sate to sur-
face of toil-race; divide product by 33000, and multiply quotient by as-
•umed or detennined ratio of effect to power. Or, for general puiposeai
divide product by 50000, and quotient is W.
Or, .0853 V /t = H», and ^ inVper second; or, ^^^ ^W per minitte.
aB
566 HYDBODYNAMICS.
Mechanical £lffect of water is product of its weight into height from which
it falls. .
Example. — Volume of water discharged upon an oversbot-wheel is 640 cube feet
per minute, and effective height of fkllis 22 feet; what is ^ ?
-i2 J — ?? = 36.67, which, X .75 = assumed ratio of effect to power = 20 ff.
33000
XJsefiil JbSfibot of an Overshot-'wrb.^el.
With a large wheel ranning in most advantageous manner, .84 of power
may be taken for effect .
Velocity of a wheel bears a constant ratio, for maximum effects, to that
of the flowing water, and this ratio is at a mean .55.
Ratio of effect to power with radial-buckets is .78 that of elbow-buckets.
Ratio of effect decreases as {proportion of head to total head and fall increases.
Thus, a wheel 10 feet in diameter gave, with heads of water above gate,
ranging from .25 to 3.75 feet, a ratio of effect decreasing from .82 to .67 of
power.
Higher an overshot-wheel is, in proportion to wfade descent of walef,
greater will be its effect Effect is as product of volume of water and its
perpendicular height.
Weight of arch of loaded buckets in lbs. is ascertained by multiplying
444 of their number by number of cube feet in each, and that product by 40.
XJxvderslxot-'wlieel,
Undershot-whrbl is usually set in a curb, with as little clearance for
escape of water as practicable ; hence a curb concentric to this wheel is more
effective than one set straight or tangential to it
Computations for an undershot-wheel and rules for construction are near-
ly identical with those for a breast-wheel.
Buckets are usually set radially, but they may be inclined upward, so as
to be more effectively relieved of yater upon their return side, and thev are
usually filled from .5 to .6 of their volume. Dej)th of shrouding should be
from 15 to 18 ins., in order to prevent overflow Of water within the wheel,
which would retard it
Velocity of periphery should equal theoretical velocity due to head of
water x .57.
NoTB.— "When constructed without shrouding, as in a current-wheel, etc, buckets
become blades.
Sluice-gate should be set at an inclination to plane of curb, or tang^tiid
to wheel, in order that its aperture may be as close to wheel as practicable ;
and in order to prevent partial contraction of flow of water, lower edge of
sluice should be rounded.
Effect of an undershot-wheel is less than that of a breast-whed, as tbe
fall available as weight is less than with latter.
rTo Ooxnpxite Po-wer af an. Uxiderehot-'urlieel.
Proceed fts per rule for an overshot-whed, using 937S0 for 50000, imd ^
for ,75.
_ M — ^ T^3
Or, V k .ooo66 = H»; or, -—^ — ±= V. ' V repretmdn^ volyime o/uxtter in eu^
/bet ppr nf^Nnte, wnd K Kemd of\tfaier in feet
HYDRODTNAMlCfd. tfij
Fonoelet's "WTieel*
PoNCBLET*s Whkbi* — Buckets are curved, so that flow of water is in
course of their concave side, pressing upon them without impact; and effect
is greater than when water impinges at nearly riglit angles to a plane sur-
face or blade.
This wheel is advantageous for application To fails Uttder 6 feet, as fts
effect is greater than that of other undershot wheels with a curb, and for
falls from 3 to 6 feet its effect is equal to that of a Turbine.
For falls of 4 feet and less, efficiency is 65 per cent, for 4.25 to 5 feet, 60
per cent, and from 6 to 6.5 feet, 55 to 50 per cent
In its arrangement, aperture of sluice should be brought close to fkce of
wheeL First part of course should be inclined from 4° to 6° ; remainder of
course, which should cover or embrace at least three buckets, should be car-
ried concentric to wheel, and at end of it a quick fall of 6 ins. made^ t* guard
against eff'ect of back-water. Sluice should not be opened over i foot in any
caaO) add 6 ins. is a suitable height for &lls of 5 and 6 feet
Distance between two buckets should not exceed 8 or 10 ins., and radius
of wheel should not be less than 40 ins., or more than 8 feet
Plane ot stream or head of water should meet periphery of wheel at an
angle of from 24° to 30°, Space between wheel and its Curb shouM no| ex-
cecit .4 of an inch.
Depth of shrqudinff should be at least .35 depth of head of water, or such
as to pr^ent W^ter m)m flo#in^ through it and ovet» the backets, 4ud width
of wheel should be equal to that of stream of impinging water.
«
Eff'ect of this wheel increases with depth of water flow, and, therefore,
other elements being -eqnal, as Ailing of buckets, to obtain maximum effect,
water should flow to buckets without impact, and velocity of wheel BlMUld
be only a little less than half that of velocity of wat^.r flowing upou wheel.
170 Compute P«>oportions of a, Poki omelet "^l^lieel.
Note.— As it is Impracticable to arrive at the results by a direct formula, they
must be obtained by gradufU approximation.
ExAMPLX. — Height or fall is 4.5 feet: volume of water 40 cube feet per second;
radiusof wbeel = 2^or9feet; depth or the stream ==. 75 /ee^; and C assumed at .9.
V riprtati^ng voUim€ qf water in cuiffefsetper Koond, h height o/faUy 4 d^th q^
throuding = — . 1- d' ; d' opening of and e wicUh oftluice, r radi-As of curva-
iure of buckets ^= , and a ofwheelj all in feet; n number qfrcwltUiom = - —
per nUn^ ; e ieSoeit^ oftiraMi^renee of vtlhed 4nd « ^Oocify cf water ^ ft«M imfeet
par tecond; C cOejfic€eM of tiHstdnie dfjlow ofwalet; a) angle bditetn plane of
'Sfc
Jlowimg water and Otat qf circuntference qf wheel at point of contact^ sin. of -■=.
•>Acoa « ; * a^le made by cirdwnfir&nce ofwhtel with end ofbuckd9=.^ lang. y;
and y angU of direetim <if wdktfrdtn eircmt^fortncB ofwkita sz ^ I- ^,
Then © = •9'vA g\^ ) = -9 X 16.29 = »4-^ f^ •'• velocity of wheel, being
568 HYDB0DYNAM1C8.
1MB than half velocity of water •, c r= ^ — ^ — = 7 feet;
2
.95, angle corresponding to which = 14O 30'; n = ^° ^ = 7.43 revoluHofu;
« = 2 tang, y = 2 X .25862 = .517 24 .-. « = 27° 20'; e =z—^-—=z 3.63 feet;
r = — — ^ — > = -55l — =^1.7^ feet; fl; = 8in. - = Vcoe. t = Vcoe. 27® 90' = .943
COB. 27O 20' .88835 ' -^ ' 3
=r8in. of 70° 34' .'. X = 141° 8'. Effect is a maximum when c = .5 « cos. y.
Fi^. 2. Construction 0/ Buckets (Fig. 2). (^otewoortt.)
From point of bucket, a, draw a line, a 6, at an angle of 26^
/ with radial line, point 6, where this line cuts an imaginary cir-
' cle, drawn at a distance of « X x.tj fh>m periphery of wheel, is
ib centre from which bucket is struck with radius, b a. Radius of
; ^ wheel should not be less than 7, or more than 16 feet
; '^ Curb should fit wheel accurately for 18 or 20 ins., measured
1" ' back fh>m perpendicular line which passes through axis of
\ wheel, the breast should then incline i in 10, or x in 15 towards
sluice.
\ After passing axis of wheel in tail-race, curb should make a
sudden dip of 6 in&
To Compute Power of* a £*oixoelet AVhieel.
880 ^P
V k .001 13 = IP, and — 7 — = V. V = velocity of theoretical periphery = . 55. ♦
A
Number of buckets 1.6 D + 1.6, D = diameter of wheel in feet Shrouding . 33 to
.5 depth of head of water, and D ■= 2 A, and not less than 7 or more than x6 feet
B reas t-Tvlie el .
Breast-whbbl is designed for fails of water varying from 5 to 15 feet,
and for flows of from 5 to 80 cube feet per second, 'it is constructed with
either ordinary buckets or with blades confined by a Curb,
Enclosure within which water flows to a breast-wheel as it leaves the sluice
is termed a Curb or Mantle,
When blades are enclosed in a ctir5, they are not required to hold water ;
hence they may be set radicU^ and they should be numerous, as the loss of
water escaping between the wheel and the curb is less the greater their num-
ber ; and that they may not lift or carrv up water with them from tail-race,
it is proper to give them such a plane that it may leave the water as nearly
vertical as may be practicable.
Distance between two buckets or blades should be from 1.3 to 1.5 times
head over gate for low velocity of wheel and more for a high velocity, or
equal to depth of shrouding, or at from 10 to 15 ins.
It is essential that there should be air-holes in floor of buckets, to prevent
air from impeding flow of water into them, as the water admitted is nearly
as deep as the interval between them ; and velocity of wheel should be SQcli
that buckets should be filled to .5 or .635 of their volume.
When wheels are constructed of iron, and are accurately set in masoniy,
a clearance of .5 of an inch is suflliclent.
* ^9 g k i% /tit p*r MMmA,
HYDRODYNAMICS. 569
High Breast-wkeel is used when level of water in iail-raoe and penstock
or fortbay are subject to variation of heights, as wheel revolves in airection
in which water flows from blades, and oach^oater is tlieref ore less disad-
vantageonSf added to which, penstocks can be so constructed as to admit of
an adjustable point of openuig for the water to flow upon the wheel.
Efi^ect of this wheel is equal to that of the overshot, and in some instances,
from the advantageous manner in which water is admitted to it, it is greater
when both wheels have same general proportions.
Under circumstances of a variable supply of water, ^reasHtfh^el is better
designed for efl^ctive duty than Oversfiotj as it can be made of a greater
diameter; whereby it affords an increased facility for reception of water
into its buckets, also for its discharge at bottom ; and further, its backets
more easily overcome retardation of back-water, enabling it to be worked
for a longer period in back-water consequent upon a flood.
Id a well-constructed wheel au efOciency of 03 per cent was observed by M.
Morin, and Sir Wm. Fairbairn gives, at a velocity of circumference of wheel of
5 feet, an. ^Bciency of 75 per cent, velocity usually adopted by him was from a
to 6 feet per second, both for high and low falls; a mfnimum of 3.5 feet for a foil of
40 and a maximum of 7 feet for a foil of 5 to 6 feet.
When water flows at flrom 10° to 12° above horizontal centre of wheel, Fairbairn
gives area of opening of buckets, compared with their volume, as 8 to 24.
The capacity between two buckets or blades should be very nearly double that of
volume of water expended.
1*0 Compute Proportioixs and Sfieot of* a Sreast-'wlieel.
lUtUSTKATioN. — Flow of Water is 15 cube feet per second; height of fall, measured
flrom centre of pressure of opening to tail-race, is 8.5 feet; velocity of circumference
of wheel 5 feet per second; and depth of buckets or blades i foot, filled to .5 of their
volume.
V IS
Width of wheel = — , d r^reseiUing deptA, and v velocity of bucketi ; — ^— = 3 ;
and as buckets are but . 5 filled, 3 -i- . s = 6fuL Assume water is to flow with double
velocity of circumference of wheel ; v = 5 x 2 = lofeet ; and foil required to gen-
^3 100
erate this velocity = — xi.i = *' = z X 1. 1 = 171 fut. ,
2 9 64.33
Deducting this height ftora total fall, there remains for height of curb or shrood-
ing, or foil daring which weight of water alone acts, ft — h' = 8.5 — 1.71 zz^t.-j^fut
Making radius of wheel 12 feet, and radius of bucket circle ix feet, whole mechan-
ical effect of flow of water = 15 x 62.5 X 8.5 = 7968.75 26a, Arom which is to be de-
ducted ft'om 10 to 15 per cent, for loss of water by escape.
Theoretical efibct, as determined by M. Morin, velocity of circumference about
.5 of that of water, and within velocities of 1.66 to 6 feet
/(pcoaa— t>)t> ^ ^,\ ^ ^^^ ^ repnwnting wngU of direction of velocity vnik
ufhick toaUr fiows to takeel at centre of thread offlovt and directum of velocity of
wheel at this line, and h*' h—h' in feet
a Is here assumed at 20^. See Weisbach, London, 1848, vol. ii. page 197, and for
tbe necessarily small value of a, its cosine may be taken at x. Go& ao° = .94.
Then (^'°^ ^7 ^^^ + 6.79^ X xsX62.5 = 7.474X 15X62.5 = 7006.9 Mw., which
\ 32- "o /
is to be reduced by a coefficient of .77 for a penstock cluice, and .8 for an overfall
Blnice.
Theoretical effect, as determined by Weisbach, 7273 Ihs.^ from which are
to be deducted losses, which he computes as follows :
TiOfls by escape of water between wheel and curb = 916
Loss by escape at sides of wheel and curb = x8o
Friction and resistance of water = 2. 5 per cent. = 160
1256 Vb».
3B*
570 HYPBODYNAMICS.
Frlotton ofwbMl m per fbrmala, page 571, sc WmC .0686; aas.048 /--> =
^llSSZss 4. 36 WW.; and n = ^^^ — 2 = 4 rMtuttont. C = 08.
r=4.36-r-a = 2.xa Then x6 goo X 3.18 X 4X .08 X. 9086 =^98.99 Ux.
Whence, ^ ^^"^ "r9-9 __ ^^ efficiency^ upon assumption of losses as com-
7968.75
puted by Weishach.
To Compute 1P<%-v^&t of" A Breast-'^^lieel.
Rule. — Proceed as per rule for an overshot-wlieel, using 55000 and .65
with a. high breast, and 62 500 and .6 for a low breast
Or, High breast, .0612 V A = ff , and ^^4 — = ^ J *•*<* ^'^^ breast 0546 V * =
n
ff, anditAi^^v
iLLusTRATHur.^Aasume elements of preceding case. Then 'SX *5X .sX —
33000
= 14-49, ^hich X .7 = 10. 14 liartei.
7006.9 ~ "564- igg:6X6o ^ ^^ ^^^
33000
Openings ofBuek$ts or Blades.— High Breast, .33 sq. foot, and Lone Breast, .9 so.
foot for each cube foot of their volume, or generally 6 to 8 in opening in a. high
breast and 9 to 12 in a low breast.
f\)nns of Buckets.— Two Part. dt^D, »= 5 d, 1 1.*5 d in large wheels, and =d
In wheels less than 25 fbet in diameter.
Three Part Buckets.~d divided into 3 equal parts; J = .25 d, d = D, » = .33 d, i =3
d in large wheels, and .75 d in wheels less than 35 feet in diameter.
Ventilating Buckets (Fairbaim^s). Spaces are about i Inch in width.
NoTsa.— A Committee of the Franklin Institute ascertained that, with a high
breast wheel 20 feet in diameter, water admitted under a head of 9 1n&, and at 17
feet above bottom of wheel, elbow buckets gave a ratio of effect to power ol .731 at
a maximum, and radial blades .653. With water admitted at a height of 33 feet
8 ina., elbow-buckets gave .658, and radial blades .638.
At iaQ6 feet above bottom of wheel, with a head of 4.29 feet^ elbow-buoketa gave
. 544, ana bladee . 329.
At 7 ^t above bottom of wheel, and a head of 2 ftet, a >f»e *treast gave for
elbow-buckets .62, and for blades .531.
At 3 feet 8 Ins. above bottom of wheel, and a head of i foot, elbowbnoketa gare
.555, and blades. 533.
Cnrrent-'WT'lieel.
CuRRENT-WHRBU^D. K. Clark assigns the most saitable ratio of v«loo
ity of blades to that of current as 40 per cent.
Depth of blades should be from .35 to .3 of radius : it should not be less
than 13 or 14 ins. Diameter is usually from 13 to 16.5 feet, with 13 l)lades ;
but it is thought that there might be an advantage in applying x8 or even
34. The blades should be completely submerged at lower side, but not mpre
tliaii 3 ins. under water, and not less than 3 at one time.
*L- (tj _ »)» = H». a r^ftesenting area of tertical section of imnersed btadet in
»5o
sq. feet, s velocity of wheel at drwi^fermcey amd « ofttremm, Mk infest ptr mcqmL
Or, . 38 — V 6a. 5 = iu</W effeeL Henoe, efflolenoy = . 3a
HYDBOt^TKAMIGS. 57 1
Flutter w Setw-mUi Wheel — Is a small, low breast-wheel operating under
a high head of water ; the design of its construction, water i>eing plenty, is
the attainment of a simple api)Tication to high-speed (KHinections, as a gang
or circnlar saw. In efiect it is from .6 to .7 that of an overshot-wh^ of
like head of faU.
v«
— (v^t)=zl3P. V and t oi preceding.
150
PViotion of* Journals or <3-udg:eon.s.
A very considerable portion of mechmiical effect of a wheel is lost in ef-
fect absorbed by friction of its gudgeons.
To Compute ITriotion of* Jourxietls or Qudgeoxus ot a
AVater->vlieel .
W rn C . 0086 =/ W representing weight of wheel in lbs. , r raditu 0/ gudgeon in
ms., asid n number qf revolutions ofwheaper mimUe.
For well-turned surfaces and good bearipgs, C=:.o7s with oil or tallow; when
best of oil is well supplied = .054 ; and, as in ordinary circumstances, when a black-
lead unguent is alone applied = . ix.
IU.U8TRATI0N. — A wheol Weighing 25 000 Ib& has gudgeons 6 ina in diameter, and
makes 6 revolatlons per minute; what is loss fA effect?
A8SumeG = .o8. ThenasoooX - X 6X08 X. 0086 =309.6 ^.
'W«igpfait«.~/rM» Mtkeds of x8 to ao feat in diameter wiU weigh fimn 800 to
1000 Iba per H*.
Wood wheels of 30 feet in diameter, 2000 to 2500 lbs. per H*-
rro Compute Diameter and JonmalB of* a Shaft, Stress
lAid iuiifbxrml3^ alons its X^enstb.
Casilnm, — r-^**- Wood,6.ia3/ — zsd. W representing weight or load in
lbs.. I length qfsk^ between jowmals in Jetty emd d diameter of she^ w its bedy
in
Journals or Gudgeons C^t Iron^ .048 / — =d.
When Shaft has to rteiet both Laieral and Torsionai Streu.—Aacettahk
the diameter for each stress, and cnbe root of sum of their cubes will give
diameter.
To Compute T>inaenslot&s ot i^rms.
CadJrm^^^^w. d nprtsenting diameter ^sk(\ftt and w width 0/ am, bath
ifn
w
in isu.^ n numter of ariM, — =s<, and t thickntse ^arm,
Whfn Arm is j/Oak^ w should be 1.4 times that of Iron, and thickness .7 that
of width.
Al Axnoranda.
A volome of wator of 17. 5 cube feet per second, with a ftill of 25 fttet, applied to an
andeilhoA-wheel will drive a hammer of 1500 Iba in weight fh>m loo to lao blows
per minute, with a lift of f^om i to 1.5 feet*
A Tohime of water of 3x<5 cube feet per second, with a fall of 12.5 feet, applied to
a wheel having a great height of water above its summit, being 7.75 feet in diame-
ter, will drive a hammer of $00 lbs. in weight 100 blows per minute, with a Uft of 9
feet xo Ina Estimate of power 3x. 5 horses.
e Tolam* of water raqBlrtd for • bammeV lacrMUM In 11 maeli grwtor r»tfo tluui Ttlodiy to >• glTW
to It. it boinf BMrly m c«b« of Tolocity.
572 HYDROBTKAMIOS.
A Stream and Overshot Whee\ of following difnensions— ti2., height of head to
centre of openiDg, 24.875 ina ; opening.' 1.75 by Bo ins. ; wheel. 22 feet in diameter
by 8 feet foee; 53 buckets, each i foot fn depth, making ^5 revolutions per niinvte
-^rove 3 run of 4.5 feet stones 130 revolutions per minute, with all attendant ma-
chinery, and ground and dressed 25 bushels of wheat per hour.
4.5 bushels Southern and 5 bushels Northern wheat are required to make i bar-
rel of flour.
A Breast-wheel and Stream of following dimensions— viz.^ head, 20 feet ; height
of water upon wheel, 16 feet; opening, 18 feet by 2 ins. ; diameter of wheel, 26 feet
4 ins. ; face of wheel, 20 feet 9 ins. ; depth of buckets, 15.75 ins. ; number of buck-
ets, 70; revolutions, 4.5 per minute --.drove 6144 self-acting mule spindles; 160
looms, weaving printing-cloths 27 ins. wide of Ko. 33 yarn (33 hanks to a lb.), and
produeing 24ocx> hanks in a day of n hours.
Horizontal AVlieels,
In horizontcd water ■■ wheels^ water produce its effect either by Impact,
Pressure^ or Reaction, but never directly by its weight.
These wheels are therefore classed as Impact, Pressure, and Reaction, bat
are now designated by the generic term of Turbine.
Tu.r"bines.
Turbines, being operated at a higher number of revolutions than Ver-
tical Wheels, are more generally applicable to mechanical purposes ; but
in operations requiring low velocities. Vertical Wheel is preferred.
For variable resistances, as rdllng-mills, etc., Verticiil Wheel is far
preferable, as its mass serves to regulate motion better than a small
wheel.
In economy of construction there is no essential -difference' between
a Vertical Wheel and a Turbine. When, however, fall of water and
volume of it are great, the Turbine is least expensive. Variations in
supply of water affect vertical wheels less than Turbines.
Durability of a Turbine is less than that of a Vertical Whtol ; and it is
indispensable to its operation^that the water should be free from sand, silt,
branches, leaves, etc.
With Overshot and Breast Wheels, when only a small quantity of water is
available, or when it is required or becomes necessary to produce only a por-
tion of the power of the fall, their efficiency is relatively increased, from the
blades being but proportionately filled ; but with Turbines the effect is con-
trary, as when the aluioe is lowered or supply decreased water enters the
wheel under circumstances involving greater loss of effect. To produce
maximum effect of a -stream of water upon a wheel, it must flow without im-
pact upon it, and leave it without velocity ; and distance between point at
which the water flows upon a wheel and level of water in reservoir should
be as short as practicable.
Small wheels give less effect than large, in consequence of their making a
greater number of revolutions and having a smaller water arc.
In Higk-presture Ttvtbines reservoir (of wheel) is enclosed at top, and water
is admitted through a pipe at its side. In Lou>preuure, water flows into res-
ervoir, which is open.
In Turbines working iinder water, height is measured from surface of
water in supply to sur&ce of dischai*ged water or race ; and when they work
in air, height is measured from surface in supply to centre of wheel.
In order to obtain maximum effect from water, velocity of it, when leav-
ing a Turbine, should be the least practicable.
HYDBODYNAMTCS. 57 J
Efficiency is greater when sluice or" supply is wide open, and it is less af-
fected by head than liy variations in supply of water. It varies but -little
with velocity, as it was ascertained by experiment that when 35 revolutions
gave an effect of .64, 55 gave but .66.
When Turbines operate under water, the flow is always full through them ;
hence they become Reaction-ieheelsy which are the most efficient.
Experiments of Morjn gave efficiency ;of Turbines as high as .75 of power.
Angle of plane of water entering a Turbine, with inner periphery of it,
shottld be greater than 90^, and angle which plane of water leaving reservoir
makes with inner circumference of Turbine should be less than 90^^
When Turbines are constructed without a guide curve*^ angle of plane of
flowing water and inner circumference of wheel = 90°.
Great curvature involves greater resistance to efflux of water ; and hence
it is advisable to make angle of plane of entering water ratlier obtuse than
acute, say 100° ; angle of plaue of water leaving, then, should be 50°, if in-
ternal pressure is to balance the external ; and if wheel operates free of
water, it may be reduced to 25^ and 30^.
If blades are ^iven increased length, and formed to such a hollow curve
that the water leaves wheel in nearly a horizontal direction, water then boUi
impinges on blades and exerts a pressure upon them; therefore effect is
greater than with an impact-wheel alone.
Turbines are of three descriptions : Outward, Downward, and Inward flow.
OutTvard-flovr rrux^bizies.
FouRNBTRON TuRBiNif, as reccntlv constructed, may be considered as one
of the most perfect Of horizontal wheels; it opiates both in and out of
back-water, is applicable to high or low ^lls, and is either a high or low
pressure turbine.
In hi^-pressure, the reservoir is closed at top and the water is led to it
through a pipe. In low-pressure, the water flows directly into an open res-
ervoir. Pressure upon the step ia confined to weight of wheel alone.
Fonmejrron makes angle of plane of water entering =90°, and angle of
plane of water leaving = 30*^.
Efficiency is reduced in proportion as sluice is lowered, for action of water
on wheel is less favorabk' exerted. M. Morin tested a Foumeyron turbine
6.56 feet in diameter, and he found that efficiency varied from a minimum
of 24, to 79 per cent., when supply of water was reduced to .25 of full supply.
In practice, radial length of blades of wheel is .25 of radius, for falls not ex-
ceeding 6.5 feet, .3 for falls of from 6.5 to 19 feet, and .66 for higher falls.
To Coxxxpute Eitlexneiits aiad Reeul-ts.
Bigh Pretturef6.6y/h = v; -=A; ^ ;/ =Dt; 12.6 =^ = V; and
.079 yk = W. h TtpresenHmg head o/uxUer, v vetocUjf oftMrbine at peHphery per
«i»ntf<e, and D internal diameter of turbine, aU in feet, V volume of water in cube feet
per second, A titm of area of orifices in sq. feet, and W effective horsepovfer.
I. a 0 = external diameter of turbine in feet, when it is more than 6 feet, and 1.4'
when it is less than 6 feet Number of guides = number of blJEtdes t when less than
34t and number-^ 3 when greater than 24. Area of section of supply pipess .4 V.
For construction of blades and guides, see Molesworth, Londun, 1882, page 540.
■ I ■ ■ — II. . ... 1. II ■ ■» ■ II ■ - ., ■ >i... ! ■ I 1 1
• OoUe canras utm plalM a|H>p ecnti* bodjr of • TarbiM, wiiich glT« flncUoti to flowtag water,
or to Madat of whaal wUch anrrooud tham.
t Ib astr«na cataa of T«ry hifch fall* diamatar ftfvan by tiiU fonnala may ba increaiMd.
i Wwtntjton'* rala for the oombar of bbidaa ia eooatant nvmbar 36, irrMpaetiT* of iIm of tarbtM* '
574
BTDBOOTHiLiaCS.
Operation of Hi«b-
Pressure '
Purl^inea
•
h
V
«
4a
36
40
31
42
50
2-5
47
60
2.1
5>
7®„
1.8
55
80
1.6
59
90
63
100
1.37
xao
1.05
73
140
78
k6o
.8
84
180
8,'
30O
.63
94
hszhead ofuMiUir infeet^ V vo^mt qfioater in eubtfut requirtdfar eifch xo ff,
and V velocity ofpfriphery ofturbiiu infut per second.
BoYDBN Turbine. — Mr. Boyden, of Massftchngetta, designed an
oojtirflurd-flow turbine of 75 H*, which realized an eflkien<7 of 88 per cent
Peculiar features, as compared with a Fuumeyron turbine^ are, ist, and most
important, the conduction oC the water to turbine through a vertical tnm-
cated eon^ concentric with the shaft The water, as it descends, acquires a
gradually increasing velocity, together with a spiral movement in direction
of motion of wheel. The spiral movement is, in fact, a continuation of the
motion of the water as it enters cone. — sd. Guide-plates at base are inclined,
so as to meet tangentially the approaching water. — 3d. A ** diffnser," or annu-
lar chamber surrounding wheel, into which water from wheel is discharged.
This chamber expands outwardly, and, thus escaping velocity of water, is
eased off and reduced to a fourth when outside of diffuser is reached. Efifect
of diffuser is to accelerate velocity of water through machine; and gain of
efficiency is 3 per cent Diffuser niuit be entirely submerged. {D. K. GtaTk,\
PoNCELRT TuKBiNE. — This whccl IS alike to one of his undershot-wheeb
set horizontally, and it is the most simple of all horizontad wheels.
To Compute Klemeiits of G^eneral Proportion, and
Reaulta. {tA F. A. Malum, U. & A.)
.o^sD'hy/h = Wi 4-85^j^ = I>; .5l'V* = V; .iD = H; 4-49V'* = «;
3(D+,o) = N; ? = «>; ^ = W;
V
SD _ ... „ d
— = d; .5Nto.75N = »; - -w ;
and C coefficient for V in terms of V = — . X> and d rqpretenfing exterior and ini-
terior diameUn ofv^eel, H atid h heights of orifices efdisdwrge at onUer ciroum-
ference and of fail acting on tohfel, to and w shortest didances b^ween ttoo a4s<tcent
biades and ttoo adjacent guides, all in feet, V, T' and v vdocities due tofaU of water
passing through narrotoest section of wheel, and of interior drcwMferenee ofvoheel^
all in fset per second, N and n numlMrs of Ua4ie$ wnd guides, mtd W aetml Aorte-
pouter.
For lUis of fh>m 5 feet to 40, and diameters not leas than 3 feet, n to should be
equal to diameter of wheel. H equal to . i D, nio' — d, and 4 w = width of crown.
For fUls exceeding this, H should be smaller, in proportion to diameter of wheel
IDownward-flo'w Tur"bin.e8.
In turbines with downward flow, wheel is placed below 'an annular series
of guide-blades, by which water is conducted to wheeL The water strikes
curved blades, and falls vertically, or nearly so, into tail-race ; consequently,
centrifugal action is avoided, and downward flow is more compact.
FoNTAiME Turbine yiehls an efficiency of 70 per cent, when fuU^
charged. When supply of water is shut off to .75, by sluice, efficiency is
57 per cent Best velocity at mean circumference of wheel is equal to 55
per cent of that due to height of fall, it may vary .35 of this either way,
without materially affecting efficiency.
In operation the water in race is in immediate contact with wheeL and its
effieien<rjr is greatest when sluice is fully opened. Its efficiency, also, is lesa
affected by variations of head of flow than in volume of water supplied;
heooe they are adapted for fi^mlU,
sn>Boi>Tir&ttic6.
sn
J&ttrAL TtmBtNfi.— TMs wheel ni essentially tliks in its princip^ropoiv
tioiiB to Fontaine's, and in principle of operation it is the same, ^^ter in
race must be at a certain depth bdiow wheel.
For convenience, it is placed at some heiffht above level of tail-race, within
an air-tight cylinder, or " draft-tube," so that a partial vacuum or reduction
of pressure is induced under wheel, and eifect of wheel is by so much in-
creased. Besulting efficiency is same as if wheel was placed at level of tail-
race; and thus, while it may be placed at any le%'el, advantage is taken of
whole height of fall, and its efticiency decreases as volume of water b di-
minished or as sluice is contracted.
To Compute Slenxents and Result.
Low Pteuure.—For fiiUs of 30 feet «b4 less.
6y/h
= I = A;
and .079 V & = BP.
h representing head oftoater, v velocity of turbine eU periphery per minute^ and D
mtemcU diameter of turlrine, all in feet, V volume of water in cube feet per second^
A sum of area of orifices in iq.feelf and ^ ^B^Mive horse-power.
i.s D =«xlenial diameter of turbine in (bet, when it is more than 6 feet, and 1.4
when it is less thaa 6 feet. NuiiU)er of guides = number of blades f when less than
24, and number -i- 3 when greater than 24. Area, of section of supply-pipe ^ .4 V.
For oonslructioa of blades and guides, see Moles worth, London, 1882, page 540.
UO'^v-JPressure rTuk-bixxes. {Molesworth.)
1
SH» 1
10
IP
15 >
B?
V
V
V
R
V
R
a- 5
9.48
25
50
24
75
20
5
13-38
*i!-5
81
35
57
3«
47
7-5
16.38
8.5
136
»7
92
as
79
to
fR.06
6.3
180
ta.6
k«8
«9
105
»5
93. M
4-«
3*9
«.4
836
18. 6
««5
ao
96.88
—
—
<>'3
3«9
9-3
rj
95
y'^u
—
—
—
—
7-5
30
32.88
■^
—
—
—
—
—
ao
IP
30
ff
40
V
R
V
R
V
100
>7
— .
50
■ 33
a
75
51
U
100
68
«5
90
3«
75
SO
'^
160
«S
\3i
33
X2.6
a3a
1^9
*9i
as
to
310
'5^
253
3Q
^4
380
IS.O
310
17
R
28
48
«4
"3
164
230
268
50
W
V
R
J. ^
~^
126
26
85
ti
63
42
roo
3«
1*8
25
196
21
240
9 representing wlocitif ^f^anire <^yb»Ast infeei and V voUtme of aoofef, in esAe
fietf Mhper second, R revolutions jper minute^ and IP effective horse-power.
rsfi«inUSha0. ^^^SsiOKm^erofsKt^inint.
In-warcL-flow TTurlDiiie,
iNWAtiD-FiiOW Turbine. — Inward-flow or vortex wheel is made with
radiating blades, and is surrounded by an annular case, closed externally,
■nd open internally to wheel, having its inner circumference fitted with fbur
oarred guide-passages. Tiis water is admitted by one m* more pipes to tlie
caae, and it issues ccntripetally through the guide-passages upon circum-
ference of wheel. The water acting against the curved blades, wheel is
driven at a velocity dependent on height of fall, and water having expended
its force, passes out at centre. This wheel has realized an efficiency as high
as 77.5 per cent. It was origmally designed by Prof. James Thomson.
SwAUf Tuiu»MB.~Coabine» an inward and a downward discharge. Re-
ceiving edges of buckets of wheel are vertical opposite guide-blales, and
lower portions of the edges are bent into form of a quadrant. Each budost
thus fonns> with the sumee of adjoming bucket, an oudet which combines
ma inward and a downward discharge. One, 73 ins. in diameter, was tested
• la
citM of v«ry Uftli Uls dhm«t«r giva by tlii* formnU may b« incrMMd.
'• raU for th* namlwr of Uadti b coastant nambar 36, lmfep<KUT« of slBa of tarUsa.
S76
HTDBODTKAMiipS.
by Mr. J. B. Francis, for several heights of gate or sluice, from a to 13.08
ins., and circumferential velocities of wheel raqgine from 60 to 80 per cent
of respective velocities due to heads acting on whed.
For a velocity of 60 per cent., and for heights of gate varying within limits al-
ready stated, efficiency ranged from 47.5 to 76.5 per cent, and for a velocity of 80
per cent, it ranged from 37.5 to 83 per cent Maximum efficiency attained was 84
percent, with a 12-inch gate and a velocity ratio of 76 per cent ; butlVx)ra 9-inch
to 13 inch gate, or fh>m .66 gate to full gate, maximum efficiency varied within
very narrow limits— ft*om 83 to 84 per cent,—v8looity-rati08 bemg 72 per cent for
9-inch gate, and 76.5 per cent for full gate. At half-gate, maximum efficiency was
78 per cent, when velocity-ratio was 68 per cent At quarter-gate, maximum effi-
ciency was 61 per cent, and velocity-ratio 66 per cent
Tremont Turbine, as observed by Mr. Francis, in his experiments at
Lowell, Mass., gave a ratio of effect to power as .793 to i.
Victor Turbine is alleged to have given an effect of .88 per cent under
a head of 18.34 feet, with a discharge of 977 cube feet of water per minute,
and with 343.5 revolutions.
Tangential 'Wh.eel.
Wheels to which water is appUed^at a portion only of the circumference
are termed tangential. They are suited for very high falls, where diameter
and hi^h tangential velocity may be combined with moderate revolutions.
The G%r€ard turbine beloings to this class. It is employed at Groeschenen
station for St. Gothard tunnel , it operates imder a head of 279 feet. The
wheels are 7 feet 10.5 ins. in diain., halving 80 blades, and their speed is i6o
revolutions per minute, with a maximum charge of water of 67 gallons per
second. An efficiency of 87 per cent, is claimed for them at the Paris
water-works ; ordinarily it is nrom 75 to 80 per cent. (J). K, Ctark,)
Impact and. Reaction "Wh-eel.
Impact-wheel. — Impact Turbine is most simple but least efficient form
of impact-wheel. It consists of « series of rectangular buckets or blades,
set upon a wheel at an angle of 50*** to 70*^ to horizon ; the water flows to
blades through a pyramidal trough set at an angle of 26° to 40°, so that
the water impinges nearly at right angles to blades. Effect is .5 entire me-
chanical effect, which is increas^ by enclosing blades in a border or frame.
If buckets are given increased length, and formed to such a hollow curve
that the water leaves wheel in nearly a horizontal direction, the water then
impinges on buckets and exerts a pressure upon them; effect therefore is
greater than with the force of impact alone.
By deductions of Weisbach it appears that effect of impact is only half
available effect under most favorable circumstances.
Reaction-wheel. — Reaction of water issuing from, an orifice of leas
capacitv than- section of vessel of supply, is eqtml to loeiffht of a colnmn of
water ^ oasig of which is area of oHJtce or of stream^ and height of which it
twice height dm to vdocitg of water discharged.
Hence, the expression is 2. — a to = R. w representing weight of a cube foot of
water in lbs.y and a area of opening in sq.feet
Whitelaw's 'is a modification of Barker's j the arms taper from centre
towards circumference and are curved in such a manner as to enable the
water to pass from central openings to orifices in a line qearly ri^t and
radial, when instntment is operating at a proper velocity ; in order that very
little centrifugal force may be imparted to the Water by the revolution of
the arms, and consequently a minimum of frictional resistance is opposed
to course of the water.
HYDRODYNAMICS. 577
A Turbine 9.55 feet in diameter, with orifices 4.944 ins. in diameter, oper*
ated by a fall of 25 feet, gave an efficiency of 75 per cent , including friction
of gearing of an inclined plane.
When a reaction wheel is loaded, so that height due to velocity, corresponding to
velocity of rotation v, is equal to fall, or — — A, or v = -\/2 ^ A, there is a loss of 17
per cent, of available effect; and when — = 2 A, there is a loss of but 10 per cent. ;
and when — = 4 ^t there is a loss of but 6 per cent. Consequently, for moderate
falls, and when a velocity of rotation exceeding velocity due to height of fall may
be adopted, this wheel works very effectively.
Eflaciency of wheel is but one half that o/an undershot- wheel.
When sluice is lowered, so that only a portion of wheel is opened, efficiency
ot a Reaction-wheel is less than that of a Pressure Turbine.
Ratio of Effect to Pbwer qf several Turbines is as follows: ■
Poncelet 6510 75 to i I Jonval , 6 to 7 to x
Foumeyron ,,, 6 to .75 to i | Fontaine... 6 to 7 to i
Barker's Mill. — Effect of this mill is considerably greater than that
which same quantity of water would produce if applied to an undershot-
wheel, but less than that which it would produce if properly applied to an
overshot-wheel.
For a description of it, see Grier^s Mechanics^ Calculator^ page 234; and for its
formulas, see L&Mmi Artisan^ 1845, page 229.
IMPULSE AND RESISTANCE OF FLUIDS.
Impulse and Resistance of "Water. — Water or any other fluid,
when flowing against a body, imparts a force to it by which its condition of
motion is alter^. Resistance which a fluid opposes to motion of a body
does not essentially differ from Impulse.
Impulse of one and same mass of fluid under otherwise similar circum-
stances is proportional to relative velocities c :f » of fluid.
For an equal transverse section of a stream, the impulse against a surface
at rest increases as square of velocity of water.
Impulse against Plane Surfaces. — The impulse of a stream of water de-
pends principally upon angle under which, after impulse, it leaves the water ;
it is nothing if the angle is o, and a maximum if it is deflected back in a
line parallel to that of its flow, or 180°, 2 -"^^ V w := P*.
When Surface of Resistance is a Plane, and = 90°, then • V w = P, and
for a surface at rest, zahw^P, a representing area of opening in sq.feet.
P = 2 A A to-; c a«»d v representing velocities of water and of surface upon which it
impinges infutper seconA, to weight of fluid per cube foot in lbs. , A transverse section
of stream in sq. ins. , and c if v relative motions of water and surface.
* Normal impulse of water against a plane surface is eq'.nvalent to weight
of a column which has for its base transverse section of stream, and for
altitude twice height due to its velocity, 2^ = 2 — .
Resistance of a fluid to a body in motion is same as impulse of a fluid
moving with same velocity against a body at rest.
* Weubach, New York, 1870, ▼ol. i. page leoS.
578 H YDROD YN Aif ICS.
Maximum Effect of ImpuUe. — Effect of impulse depends principally on
velocity v of impinged surface. It is, for example, o, both when t; = c and
v^o; hence there is a velocity for which eifect of impulse is a maximum
t= (c — 9) v; that is, v = — , and maxinmm effect of impulse of water is ob-
tained when surface impinged moves from it with half velocity of water.
Illustration. — A stream of water having a transverse section of 40 sq. Ins., d's
charges 5 cube feet per second against a plane surface, and flows oflT with a velocity
of x3 feet per second ; effect of its impulse, then, is ^^^ Vwzs:F]c= - — — = 18;
^ = 32.16; 10 = 62.5; 2- X 5X62.5= 58.38 a*.
32.10
Hence mechanical effect upon surface = P o = 58.28 x 12 = 699.36 Ibt.
C I ^ X ld,A, I 18'
Maximum effect would be « = - = - X = — = 9 feet, and - X — X 5 X 62.5
2 2 40 2 3 ff
= - X 5036 X 312.5 = 786.87 lbs.; and hydrauHepretmrezzi^--^ ==87.44 lbs.
2 9
When Surface it a Plane and at an AngU^ then (i — cos. a) — V «?= P.
y
Illustration.— A stream of water, having a transverse section of 64 sq. ins., dis
charges 17.778 cube feet per second against a fixed cone, having an angle of con-
vergence from flow of stream of 50°, hydraulic pressure in direction of stream;
then c = -—Prr^ = 40; coa 50° = .642 79. (1 — .642 79) -1°-- X 17- 778 X 62. 5 =
04 -r- 144 32.10
.357 21 X 1382.2 = 494.26 Ibt.
When Surface of Resistance is a Plane at 90°, and has Borders added to
its Perimeter^ effect will be greater, dei^emyng upon height of border and
ratio of transverse section between stream and part confined.
Oblique Impulse. — In oblique impulse against a plane, the stream may flow
in one, two, or in all directions over plane.
VThen Stream is coi\fiMed at Three Sides, (1 00& a) V 10 =s P.
When Stream is cor^fined at Two Sides, sin. a' V w = P.
Normal impulse of a stream increases as sine of angle of incidence; par-
allel impulse as square of sine of angle ; and lateral impulse as double the
angle.
When an Inclined Surface is not Brndered, then stream can spread over
it in all directions, and impulse is greater, because of all the angles by
which the water is deflected, a is least ; hence each particle that does not
move in normal plane exerts a greater pressure than particle in that plane,
, 2 sin. a' c — 1> -, -.
*nd — r-TT — 5 X V «? = P.
1 -f- sin. a' g
Impulse and Instance against Surfaces.
Coefficient of resistance, C, or number with which height due to velocity is to be
multiplied, to obtain height of a column of water measuring this hydraulic press-
ure, varies for bodies of different figures, and only for surfaces which are at right
angles to direction of motion is it nearly a definite quantity.
According to experiments of Du Buat and Thibault, € = 1.85 fbr impulse of air
or water against a plane surfkce at rest, and for resistance of air or water against a
surface in motion, G =« i. 4. In each case about .66 of effect ia expended upon fhmt
■urfkce, and .34 upon
HYDBODYNAMIC8. 579
Coxzxparison iDet-veeen. Xvirl^ines axxd otlier 'Water-'%vlieel8.
Turbineg are applicable to falls of water at any height, from i to 500 feet.
Their efficiency for very high falls is less than for smaller, in consequence
of the hydraulic resistances involved, and Which increase as the square of
the velocity of the water. They can only be operated in clear water.
With Fourneyron's, the stress and pressure on the step is that of the wheel
in motion ; with Foataine^s, the whole weight of the water is added to that
of the wheel ; they are well adapted, however, for tide-mills. Experiments
on Jouval's gave equal results with Fontaine's.
Vertical Water-Wheels are limited in their application to falls under 60
feet in height.
For falls of from 40 to 20 feet they give a greater effect than any turbine ;
for falls of from 20 to 10 feet, they are equal to them ; and for very low
&lls, they have much less efficiency.
Variations in the supply of water effect them less than turbines.
"Water-pressure ISngine.
By experiments of M. Jordan, he ascertained that a mean useful effect of
.84 was attainable.
Weisbach, London, 1848, vol ii. page 349.
PERCUSSION OP FLUIDS.
When a stream strikes a plane perpendicular to its action, force with
which it strikes is estimated by product of area of plane, density of fluid,
and square of its velocity.
Or, A d v3 = P. A represerUing area in sq. feetj d toeigJU of fluid in Ibs.^ and v
vdoeity in feet per aeeond.
If plane is itself in motion, then force becomes A d (v — v')^ = F. V representing
velocUy ofj^ne.
If C represent a coefficient to be determined by experiment, and h height
due to velocity r, then v' ^ 9 g h^ and expressiou for force becomes
AC2gh = V.
CENTRIFUGAL PUMPS. {D. K. Clark.)
i^ppold Puxnp, made with curved receding blades, is the form of
centrifugal pump most widely known and accepted. M. Morin tested three
kinds of centrifugal or revolving pumps :
ist, on model of Appold pump; 2d, one having straight receding blades
inclined at an angle of 45° with the radius, and jd, one havmg radial blades.
They were 12 ins. in diameter and 3.125 ins. in length, and had central open-
ings of 6 ins. Their efficiencies were as follows :
.1. Curved blades. . 48 to 68 per cent | 2. Inclined blades. . 40 to 43 per cent
3. Radial blades 24 per cent
Height to which water ascends in a pipe, by action of a centrifugal pump,
would, if there were no other resistances, be tiiat due to velocity of circttm-
ference of revolving wheel, or to — . Results of experiments made by the
author on two pumps, in 1862, yielded following data, showing height to
which water was raised, without any discharge:
(bladM partly rmdial, /vTn^^nVSS^
eurr^UMidi). (bl»det, curved).
Diameter of pomp- wheel 4 feet 4 feet 7 ins.
Revolutions per minute..... 177 95.4
Veloctty of circumference per second. . . 37.05 feet 22.9 feet
Head due to the velocity 21.45 '^ 8->94 **
Actualhead ia2i " 5.833 "
Do. do. in parts of head due to velocity, 85 per cent 71.2 per cep(.
JSO HYDRODYNAMICS. — IMPACT OR COLLISION.
Mr. David ThomBon made similar experiments with Appold pumps of from 1.25
to 1. 71 feet in diameter, the results of which showed that the actual head was about
90 per cent, of the head due to the velocity.
M. Tresca, in 1861, tested two centrifugal pumps, 18 ins. in diameter, with a cen-
trul opening of 9 ins. at each side. The blades were six in number, of which three
sprung trom centre, where they were .5 inch thick; the alternate three only sprung
at a distance equal to radius of openiug from centre. They were radial, except at
ends, where they were curved backward, to a radius of about 2.25 ins. ; and they
joined the circumference nearly at a tangent. Width of blades was taper, and they
were 5.75 ins. wide at nave, and only 2.625 ^^^- ^^ ends: so designed that section of
outflowing water should be nearly constant.
M. Tresca deduced from his experiments that, in making fi*om 630 to 700 revolu-
tions per minute, efficiency of the pump, or actual duty in raising water, through a
height of 31.16 feet, amounted to from 34 to 54 per cent, of work applied to shaft;
or that, in the conditions of the experiment, the pump could raise upward of x6aoo
cube feet of water per hour, through a height of 33 feet, with about 30 H* applied
to shaft, and an efficiency of 4 5 per cent
According to Mr. Thomson, maximum duty of a centrifugal pump worked by a
steam-engine varies from 55 per cent, for smaller pumps to 70 per cent for larger
pumps. They may be most effectively used for low or for moderately high lifts, of
from 15 to 20 feet; and, in such conditions, they are as efficient as any pumps that
can be made. For lifts of 4 or 5 feet they are oven more efficient than others.
At same time, larger the pump higher lift it may work against. Thus, an 18-inch
pump works well at 20 feet lift, and a 3-feet pump at 30'feet lift A 21 inch wheel
at 40-feet lift, has not given good results: high lifts demand very high velocities.
Efficiency is influenced by form of casing of pump. Hon. R. C. Parsons made exper-
iments with two 14- Inch wheels on Appold's and on Raiikine's forms. In Rankine's
wheel blades are curved backwards, like those of Appold's, for half their length;
and curved forwards, reversely, for outer half of their length. Deducing results or
performance arrived at, following are the several amounts of work done per lb. of
water evaporated from boiler :
Work don« p«r lb. of
watfir evapontfld.
Foot-lbs. Ratio. .
Appold wheel, in concentric circular casing 11 385 1.06
'''■ '* in spiral casing 15996 1.5
Rankine wheel, in concentric circular casing xo 748 x
" '* in spiral casing 12954 1.2
Thes* data prove:-— ist, that spiral casing was better than concentric casing; 2d
that Appold's wheel was more efficient than Rankine's wheel.
IMPACT OR COLLISION.
Impact is Direct or Oblique. Bodies are Elastic or Inelastic. The
division of them into hard and elastic is wholly at variance with these
properties ; as, for instance, glass and steel, which are among hardest
of biodies, are most elastic of all.
Product of mass and velocity of a body is the Momefitum of the body.
Principle upon which motions of bodies from percussion or collision are
determined belon«:s both to elastic and inelastic bodies ; thus there exists in
bodies the same momentum or quantity of motion, estimated in any one and
same direction, both before collision and after it.
A ction and reaction are always equal and contrary. If a body impinge
obliquely upon a plane, force of blow is as the sine of angle of incidence.
When a body impinges upon a plane surface, it rebounds at an angle equal
to that at which it impinged the plane, that is, angle of reflection is equal to
that of incidence.
Effect of a blow of an elastic body upon a plane is double that of an in-
"^tic one, "reloctty and mass being equal in each , for the force of blow
IMPACT OB COLLISIOK. ^gl
from inelastic body is as its mass and velocitv, which is only destroyed by
resistance of the plane ; but iu an elastic body that force is not only destroyed,
being sustained by plane, but another, also equal to it, is sustained by pfane,
ill consequence of the restoring force, and by which the body is repelled with
an equal velocity ; hence intensity of the blow is doubled.
If two perfectly clastic bodies impinge on one another, their relative ve-
locities will be same, both before and after impact ; that is, they will recede
from each other with same velocity with which they approached and met.
If two bodies are imperfectly elastic, sum of their moments will be same,
both before and after collision, but velocities after will be less than in case
of perfect elasticity, in ratio of imperfection.
Effect of collision of two bodies, as B and b, velocities of which are differ-
ent, as V and v\ is given in following formulas, in which B is assumed to
bave greatest momentom before impact
If bodies move in same direction before and after impact, sum of their
momenta before impact will be equal to their mm after.
If bodies move in same direction before, and in opposite direction after
impact, mm of their momentt before impact wiUbe eqttm to difference of their
nam after.
If bodies move in opposite directions before, and in same direction after
impact, difference of their moments before impact will be equal to their
sum after.
If bodies move in opposite directions before, and in opposite directions
after impact, difference of their moments before impact toiU be equal to their
difference after.
rro Coxnpiate Velocities of Inelastic I3odies after Ixxipaot.
When Impelled in Same Direction. pT^. = r. B and b representing
vfeight* of the. two bodies, V and v their velocUies before impact, and r velocity of bodies
afUr impacty aU infeeL
Consequently, ■ X 6 = velocity lost by B, and -- - x B = velocity gained by b.
B -f- 0 D -J- 0
KoTK.— In these formulas it is assumed that V>v. If V<v the result will be
negative, but may be read as positive it lost and gained ure revei'sed in places.
Illustration. — An inelastic body, 6, weighing 30 lbs., having a velocity of 3 feet,
is struck by another body, B, of 50 lbs., having a velocity of 7 feet; the velocity of
b after impact will be ,
50X7 + 30 X 3 _ 440 . , A*#
— — , — -n — — J- 5 /*».
50 + 30 tio *'"'•[
When Impelled ir. Opposite Directions* ■ pT. =»'■
iLUJSTRATioir.— Assume elements of preceding case.
50X7 — 30X3 _ 260 _
50 4-30 80
B V
When One Body is at Best. » -I- ft "***
Illusthation. —Assume elements as preceding.
50 X 7 _ 350 _ ^ ^ . ^
So+lo-fo-'^'^ys/eet
When Bodies are inelastic, their velocities after impact will be aliks.
582 IMPACT OB COLLISION.
To CoznpTxte Velocities of* Silastic Bodies after Impact
fTTj: T J7J- ^ rvr ^- B^^V + 2 6t» _ 2BV— B^w
When ImpelUd »n One Dtrectton, „ ^ . = R, and ^ '■ . = r.
Illustration. — Assume elements as preceding.
5o-3oX7 + :»X3oX3^3go^^^^JaX5oX7-5o-3oX3^^_8/.^t
50+30 80 ^-^ ' • 50-1-30 80
ttb =7 ...» . . 2 B
Or, V — V — » = velocity of iv, and w + V — « xs^ocity of r.
Wiften Impelled in Opposite DtPtcfioni.
B — bVro2bv „ ^zBV-l-B — 6w
— r+ 6 — = ^' ""** — B+fr — "''•
Illustration.— Assume elements as preceding.
5o--3oX7'^2X3oX3_'40'^'8o_ /fcct and ' ^ ^°^ ^"^^^"^^"^ ^ =
50 + 30 80 "" •5«'**» 50 + 30
700+60 . . _ 2 6(V+i)) t ., t *v » A„ 2X30X7 + 3 60c
Z-^ = 9.5^«t Or,-^qj;^ = t«toct<yto«*6yB. As — ^-p^ = —
=^7.5 feet.
V B — 6 2 B V
PF^en (?»e Boc^ is at Rest, ^ = R, and ^-^=r.
Illustration.— Assume elements as preceding.
7 X 50 — 30 140 ,. .2X50X7 700 o J..
50+30 80 '•'•'' 50+30 80
To Compxite "Velocities oriixiperfeot Silastic Bodies af^er
Ixxxpaot.
Effect of Collision is increased over that of perfectly inelastic bodies, but
not doubled, as in case of perfectly elastic bodies ; it must be multiplied by
I + — or "* , when — represents degree of elasticity relative to both per-
fect inelasticity and elasticity.
Moving in same Direction, V ^t_ x g^^; (V— »)=:R; and v-|
•D
X ( V — «) ~ r, m and n repretetOing ratio ofperfeU to imperfsct elaatidty,
B + ft
Illustration. — Assume elements as preceding. m and n= 9 and z.
- * + "- 30 X7-3 = 7 — 1-5X^X4 = 7-2.25 = 4.75 yw<, and 3 +
' 2 "50+30''' " ' --"^80
^i^X— ^x7^ = 3 + 3.75 = 6.75/«««•
2 50 + 30
When Moving in Opposite Directions,
v(B-n6) BV{. + ^)
When One Body is at Rest. — ^ = R, and — ^ = r.
Illustration.— Assume elements of preceding case.
7X(50— -X30) ^ 50X7xfi+-)
_V_a /^7X5o— 5^ ^^^^ ^ V »/
35oXf 5
80
= 6.5625 ftel.
LIGHT.
S83
LIQHT.
Light is similar to Heat in many of its qualities, being emitted in
form of rays, and subject to same laws of reflection.
It is of two kinds, NtUural and Artificial ; one proceeding from Sun
and Stars, the other from heated bodies.
Solids shine in dark only at a temperature from 600^ to 7CX>°, and in
daylight at IOOo^
Intensity of LigJu is inversely as square of distance from luminous
body.
Velocity of Light of Sun is* 185 000 miles per second.
Standard of Intensity or of comparison of light between different methodi
of illumination is a Sperm Candle *' short 6," burning 120 grains per hour.
Can.dles.
A Spermaceti candle .85 of a inch in diameter consumes an inch in length
in I hour.
X>eooncipo8itioxi of I^iglit.
Coi.OBa.
Violet...
Indigo. . .
Blue
Green . . .
Yellow . .
OfRDge . .
Red
MaxiiDom
Ray.
Chemical.
Electrical.
Light
Heat.
Primary.
Contrasts.
Second'y.
Blue.
Yellow.
Red.
Green.
Orange.
Purple.
TerUary.
Brown.
Green.
Broken.
Green.
Primary.
CombinaUoos.
S«condary.
Blue. . . )
Yellow, j
Blue... I
Red. ... J
Yellow. \
Red.... 1
Green. . »
Purple. )
Orange. 1
Green. . )
Purple.
Orange
•}
Tortlary.
Dark.
Green.
Gray.
Brown.
All colors of spectrum, when combined, are white.
Consumption nnd Comparative Intensitsr of ILiiglxt
oi* C and lea.
Candlb.
Wax.
Spermaceti
it
Tallow
(I
it
No. In a
Lb.
Diameter.
Lenirth.
Inch.
Int.
3
3
.875
12
15
3
.9
15
4
6
•84
135
8.5
3
I
"•5
3
4
:I
15
13-75
Consomptlon
per Hour.
Gmins.
135
156
204
light comp'4
irith Carcel.
.09
.09
.07
Compared toith icx» Cube Feet of Gas.
Cavdlb.
Oassx.
Con-
sump-
tiOD.
Light.
C«a- 1
samption,
for equal
LliKlit.
Piarafflne.
Sperm . . .
.098
.095
Lba.
3-5
3-9
Lbt.
35-5
41. 1
103
lao
Candlb.
Oassi.
Con-
sump-
tion.
Light.
Adamantine.
Tallow.
.108
.074
Lbs.
51
5"
Lbs.
47-3
53-8
Coo-
aainptloD
for equal
Lifcht.
137
'55
In combastion of oil in an ordinary lamp, a straight or horizontally cut wick
glTes great economy over one Irregularly cut.
584
LIGHT.
Relative Iix tensity-, ConsiaxKiption, Ill-axnxnatioii, and
Cost of* variovis Alod.es of* Illunaiuation.
Oil at II cents, Tallow at 14 cents, Wax at 52 cents, and Stearioe at 32 cents pel
lb. 100 cube feet coal gas at 14 cents, and 100 cube feet of oil gas at 52 cents.
iLLmnNATOB.
Carcel Lamp
Lamp with in- )
, verted reserv'r. |
Astral liamp
Wax Candle 6 to lb.
Illumi-
nation.
Carcel
Lamp
= 100.
ZOO
57.8
48.7
61.6
Actual
Cost
per
Hour.
Genu.
.87
.89
.56
.92
Coit for
equal
Inten-
sity.
PerH'r.
.87
•99
1.78
6.31
Illvmikatob.
Stearine Candle 5 to lb.
Tallow '* 6 "
Sperm " 6 "
Coal Gas.
Oil Gas
niumi.
nation.
Cartel
Lamp
= 100.
Actual
Coat
Hoar.
66.6
Cento.
•59
.25
.89
1.22
I.2S
Coatfoi
equal
Inten-
sity.
PerH»r.
4«3
2-34
.96
.98
1000 cube feet of 13- candle coal gas is equal to 7.5 gallons sperm oil, 52.9 lbs. mold)
and 44.6 lbs. sperm caudles.
Candles, I^amps, Fluids, and Ghas.
Comparison of severed Varieties 0/ Candles^ Lamps, and Fluids^ xoith Coal* €hu, de-
duced from Reports of Cmn, of Franklin Institute^ and of A. Frye, JU.D.y etc
Caxdli.
V3
Lieht
at Equal
Costs.
Coat com-
pared with
Oaafor
Equal Light.
Canolb.
Intensity
of
Li^ht-t
Ifl
Coat com-
pared with
Gas for
Equal Light.
.58
.5
•54
.85
15.1
16.2
7-5
Tallow, short 6's,)
double wick . . }
Wax, short 6 's....
Palm oil
X
.8
7
X
.6x
•77
7-x
»4-4
las
Diapbane
Spermaceti, short 6*8.
Tallow, short 6'8, )
single wick... ) '*
* City of Philadelphia. t Compared with a fish-tail jet of Edinburgh gas, containing la per cent,
of condensable matter and consuming i cube foot per hour.
Lamt and Fluid.
Carcel.
Sperm oil, max^m
mean.
mtn'm
Urd oil.
Inten-
sity of
Light.
2.15
J. 22
.69
•77
Light
at
Equal
Coat.
Time of
Burning
zPint
of Oil.
Hours.
1,8 i 6.32
'•35 '
1.2
•97
9.87
14. 6
"•3
Lamp and Fluid.
Gas
Semi-solar, Sperm oil
Solar, Sperm oil
Camphene
Inten-
sity of
Ught.
Light
at
Equal
Coat.
z
1.76
»-75
X
•93
Time of
Baming
I Pint
ofOU.
Hours.
6.75
8.4a
9.31
Loss of Light by Use of Glass Globes.
Clear Glass, 12 per cent | Half ground, 35 per cent. | Full ground, 40 per cent
RefVaotion .
Relative Index of Refraction—lB. Ratio of sine of angle of incidence to sine of
angle of refhiction, when a ray of light passes fVora one medium into another.
Absolute Index or Index of Refraction — Is, When a ray passes ftx>m a vacuum into
any medium, the ratio is greater than unity-
Relative index of refVaction (torn any medium, as A, into another, as B, is alwaya
equal to absolute index of B, divided by absolute index of A.
Absolute index of air is so small, that it may be neglected when compared with
liquids or solids; strictly, however, relative index for a ray passing fit>m air into a
given substance must be multiplied by absolute index for air, in order to obtain
like index of reft'action for the substance.
Alean
Air at 52° 1
Alcohol 1.37
Canada balsam ...... x. 54
Crystalline lens x.34
Indices
Glass, fluid. .
i(
crown
of RefVaotion.
Humors of eye. ... x.34
Salt, rock x.55
Water, fresh x.34
sea........ x.34~-
1 1.58
) 1.64
(I
LIGHT.
585
Gras.
Retort, — A retort produces about 600 cube feet of gas in 5 hours with a
charge of about 1.5 cwt. of coal, or 2800 cube feet in 24 hours.
In estimating number of retorts required^ one fourth should be added for
being under repairs, etc
Pressure with which gas is forced through pipes should seldom exceed 2.5
ins. of water at the Works, or leakage will exceed advantages to be obtauied
from increased pressure.
The average mean pressure in street mains is equal to that of i inch of
water.
When pipes are laid at an inclination either above or below horizon, a cor-
rection will have to be made in estimating supply, by. adding or deducting
431 inch from initial pressure for every foot of rise or fall in the length of pipe.
It is customary to locate a governor at each change of level of 30 feet.
Illuminating power of coal-gas varies from 1.6 to 4.4 times that of a tallow
candle 6 to a lb. ; consumption being from 1.5 to 2.3 cube feet per hour, and
specific gravity from .42 to .58.
Higher the flame from a burner greater the intensity of the light, the
most effective height being 5 ins.
Standard of gas burning is a 15-hoIe Argand lamp, internal diameter .44
inch, chimney 7 ins. in height, and consumption 5 cube feet per hour, giving
a light from ordinary coal-gas of from 10 to 12 candles, with Cannel coal
from 20 to 24 candles, and with rich coals of Virginia and Pennsylvania of
from 14 to 16 candles.
In Philadelphia, with a fish-tail burner, consuming 4.26 cube feet per hour,
iUumioating power was equal to 17.9 candles, and with an Argand burner,
consuming 5.28 cube feet per hour, illuminating power was 20.4 candles.
Gas, which at level of sea would have a Value of 100^ would have but 60
in city of Mexico.
Internal lights require 4 cube feet, and external lights about 5 per hour.
When large or Argaud burners are used, from 6 to 10 are required.
An ordinary single-jet house burner consumes 5 to 6 cube feet per hour.
Street-lamps in city of New York consume 3 cube feet per hour. In some
cities 4 and 5 cube feet are consumed. Fish-tail burners for ordinary coal
gas consume from 4 to 5 cube feet of gas per hour.
A cube foot of good gas, ftom a jet .033 inch in diameter and height of
flame of 4 ins., will burn for 65 minutes.
Resin Gas. — Jet .033, flame 5 ins., 1.25 cube feet per hour.
Purifiera. — Wet purifiers require i bushel of lime mixed with 48 bushels
of water for lodbo cube feet of gas.
Dry purifiers require i bushel of lime to 10 000 cube feet of gas, and i
sup^cial foot for every 400 cube feet of gas.
Intensity pf . X^ight -witli Kqiial Volumes of* G}-as frozu
different 13 timers.
EqtmL to Spermaceti Candle, burning 120 Grains per Hour.
Bobs saa.
Sfncle-Jet, x foot
FiS-tail No. 3 .
BaVswing
Ezpenditare in Cube
Feet per Hour.
2.6
35
3
4
4*
4.2
4-3
4-5
BUBMKBS.
Argand, 16 boles....
Argaud, 24 holes
Argand, 28 holes. . . .
Expenditure in Cube
Feet per Hoar.
4
3-8
•32
•33
•34
1.9
2.2
2.3
3-3
3-4
3-5
ii
586
LIGHT.
Volnxne of* O-as obtained fVoixi a Ton of Coal» Itesin^ eto.
Ifntorial.
Boghead Cauoel...
Wigan Cannel
CanneL |
Cape Breton, )
"Cow Bay,"} ..
etc J
Cab«
Feet.
13334
15426
8960
15000
9500
Material.
CnmberlaDd
English, mean
Newcastle j
Oil and Grease ....
Pictoa and Sidney. ,
Pine wood ,
Cube
Feet.
9800
IIOOO
9500
10000
23000
8000
II800
Material.
Cube
Feet.
Pittuburgb
Resin
Scotch ....
Virginia.
West'n..
Walls-end .
9520
15600
10300
15000
8960
9500
Z2000
I Chaldron Newcastle coal, 3136 lbs., will furnish 8600 cube feet of gas at
a specific fi^vity of .4, 1454 lbs. coke, 14. i gallons tar, and 15 gallons am-
moiiiacal liquor.
Australian coal is superior to Welsh in producing of gas.
Wigan Cannel, i ton, has produced coke, 1326 lbs. ; gas, 338 lbs. ; tar,
250 lbs. ; loss, 326 lbs.
PecUt 1 lb. will produce gas for a light of one hour.
Fuel, required for a retort 18 lbs. per 100 lbs. of coal.
In distilling 56 lbs. of coal, volume of gas produced in cube feet when
distillation was effected in 3 hours was 41.3, in 7, 37.5, in 20, 33.5, and in
F'lO'^v of* Q-as ill l:*ipe8.
Flow of Gas is determined by same rules as govern that of flow of water.
Pressure applied is indicated and estimated in inches of water, usually from
.5 to I inch.
Volumes of gases of like specific gravities discharged in equal times by a
horizontal pipe, under same pressure and for different lengths, are inversely
as square roots of lengths.
Velocity of gases of different specific gravities, under like pressure, are in*
versely as square roots of their gravities.
By experiment, 30000 cube feet of gas, specific gravity of .42, were dis-
charged in an hour through a main 6 ins. in diameter and 22.5 feet in length.
Loss of volume of discharge by friction, m a pipe 6 ins. in diameter and i
mile in length, is estimated at 95 per cent.
Diameter and. Uengtli of* O-as-pipes to transmit given
Volumes of* Gi-as to Branoli-pipes. {Dr. Ure,)
Volnme
per Hour.
Volume
per Hour.
Diameter.
Length.
Volume
per Hour.
Diameter.
Length.
Cube Feet.
Im.
Feet.
Cube Feet.
Ine.
Feet.
50
•4
100
1000
3.16
1000
250
z
200
1500
3.87
1000
500
1.97
600
aooo
5- 33
2000
700
2.65
xooo
2000
6.33
4000
Diameter.
Length.
los.
7
7.7s
Q.2Z
8.9s
Feet.
0000
1000
2000
1000
Cube Feet.
2000
6000
6000
8000
Regulation or X>iekmeter and Bxtreme JLiengtK of* Xu'bo
ing, and l^uml^er of Burners permitted.
Bamen.
Diameter
Capacity
Diameter
Capacity
of
Length.
of
Burners.
of
Length.
of
Tnblnir.
Meters.
Tubing.
Meters.
Ina.
Feet.
Light
No.
Ina.
Feet.
Light.
•95
6
3
9
•75
50
30
.375
20
5
IS
I
70
^5
•5
30
10
30
1.25
100
60
.625
40
20
60
^•5
150
100
No.
90
LjaHT.
587
Temperaiure of Gcuea, — Combustion of a cube foot of common gas will
heat 650 lbs. of water 1°.
Services for Xjaxnps.
LAmps.
from Msin.
Diaowter
of Pipe.
No.
2
t
Feet.
40
40
50
Ins.
•375
•5
.635
Lamp*.
No.
10
>5
ao
L«wth Diameter
om Main, of Pipe.
from
Feet.
100
130
150
Ins.
•75
I
1.25
Lamp*.
No.
25
30
Leofftb
from Main.
Feet.
x8o
aoo
Diameter
of Pipe.
In*.
1-5
«-75
Volumes of*Oas XDisoliarged per Hour under a Pressure
of Half an Inoli of "Water.
Specific Gravity .42.
Dfaun.of
Opening.
Volame.
Dlam. of
Opening.
Volume.
IMam. of
Opening.
Volume.
In*.
•25
•5
Cab* Feet.
80
321
In*.
•75
I
Cube Feet.
723
1287
In*.
1.12$
'•25
Cube Feet
1625
aoio
Diam. of
0|i6nin(;.
Ins.
1-5
5
Volume.
Cube Feet.
2885
46150
Xo Coixipute "Volume of d-as Disoliarged. through, a Pipe.
yd-i h /V« G I
YTT = V", and 063 1 / — ^ — = d. d representing diameter ofpipe^ and
k height of wcUer in tn«., denoting pressure upon gas^ I length of pipe in yards, Q
specific gravity of gas, and V volume in cuf>efeet per hour.
Q may be assumed for ordinary computation at .42, and A .5 to i inch.
Illustkatiox.— Assume diameter of pipe x inch, pressure 1.68 ina, and length
of pipe 1 yard.
/i X 1.68 /iM I ^ _.
1000 X . / — = 1000 X ^ / = 2000 cube feet,
V •4a X X V '43
-«j < v^ e /4000000X.42X I e/x 680000
Nora. —For tables deduced by above formulas see Molesworth, 1878, page 326.
I>ixxien8ions of Adainsy -^^ith. "Weight of One Hiength.
Diameter in ina ....
Length in feet
Thickness in ina . . .
Weight in lbs
4
6
8
9
10
"4
18
9
9
9
9
9
9^
9
•375
•375
•5
.5
•5
.625
•75
288
234
400
454
489
,868
1316
20
9
1484
•75
GAS ENGINES.
In the Lenoir engine, the best proportions of air and gas are, for common
gaSf 8 volumes of air to i of gas, and for cannel gas, 11 of air to i of gas.
The time of explosion is about the 27th part of a second.
An engine, having a cvlinder 4.625 ins. in diameter and 8.75 ins. stroke of
piston, making 185 revolutions per minute, develops a half horse-power.
Disttibtaion o/Beat Generated in the Cylinder, {M. Tresca.)
Per cent. Per cent.
Losses.
27
too
PlHfpated by the water and prod-
ads (tfcombosiion. 69
Ccmverted Into work 4
Hence efficiency as determined by the brake = 4 per oenk
Atmospheric Gas Engine,
A single-acting cylinder 6 ina in diameter, making 81 strokes per minute, devel-
oped .456 H*, and the gas consumed per minute for cylinder 20 cube feet and for in-
timing 2 cube feet. {M- Tresca )
S88 LIMES, CEMENTS, M0BTAB6, AND CONCRETES.
LIMES, CEMENTS, MORTARS, AND CONCRETES.
Essentially from a Treatise hy Bng.'Gen'l Q. A. Gillmore, U.S.A.*
Xiizue.
Calcination of marble or any pure limestone produces lime (quick-
lime). Pure limestones burn white, and give richest limes.
Finest calcareous minerals are rhombohedral prisms of calcareous
spar, the transparent double-reflecting Iceland spar, and white or statu-
ary marble.
Property of hardening under water, or when excluded from air, con-
ferred upon a paste of lime, is effected by presence of foreign sub-
stances— as silicum, alumina, iron, etc. — when their aggregate presence
amounts to .i of whole.
Limes are classed : i. Common or Fat limes, which do not set in water.
2. Poor or Meagre, mixed with sand, which does not alter its condition.
3. Hydraulic Lime, containing 8 to 12 per cent, of silica, alumina, iron,
etc., set slowly in water. 4. Hydraulic, containing 12 to 20 per cent, of
similar ingredients, sets in water in 6 or 8 days. 5. Eminently Hydraulic,
containing 20 to 30 per cent, of similar ingredients, sets in water in 2 to 4
days. 6. Hydraulic Cement, containing 30 to 50 per cent, of argil, sets in a
few minutes, and attains the hardness of stone in a few months. 7. Natural
Pozzuolanas, including pozzuolana properly so called. Trass or Terras, Ar^nes,
Ocbreous earths, Basaltic sands, and a variety of similar substances.
Indications of Limestones. They dissolve wholly or partly in weak acids
with brisk effervescence, and are nearly insoluble in water.
Rich Limes are fully dissolved in water frequently renewed, and thev
remain a long time without hardening; they also increase greatly in vol-
unie, from 2 to 3.5 times their original bulks, and will not harden without
the action of air. They are rendered HydratMc by admixture of pozzuolana
or trass.
Rich, fat ^ or common Limes usually contain less than 10 per cent, of im-
purities.
Hydraulic Limestones are those which contain iron and clay, so as to en-
able them to produce cements which become solid when under water.
Poor Limes have all the defects of rich limes, and increase but slightly in
bulk, the poorer limes are invariably basis of the most rapidly - setting
and most durable cements and mortars, and they are also the csAy limes
which have the property, when in combination with silica, etc., of indurating
under water, and are therefore applicable for admixture of hydraulic cements
or mortars. Alike to rich limes, they will not harden if in a state of paste
under water or in wet soil, or if excluded from contact with the atmosphere
or carbonic acid gas. They should be employed for mortar only when it is
impracticable to procure common or hydraulic lime or cement, in which case
it is recommended to reduce them to powder by grinding.
ffydraidic Limes are those which readily harden under water. The most
valuable or eminently hydraulic set from the 2d to the 4th day after immer-
sion ; at end of a month thev become hard and insoluble, and at end of six.
months they are capable of being woi4ced like t^ hard, natural limestones.
They absorb less w^ater than pure limes, and only increase in bulk from 1.75
to 2.5 times their original volume.
• See also hi* TreatiMt on Limet, HydnuUc Cementt, and Mortars, io Paper* on Practical Enginee»>
bug, Engineer Department, U. S. A. "
LIMES^ CEAi:fiNTS, HO&TABS, AND CONCRETES. 589
Inferior grades, or moderately hydraulic^ Tcquire a period of from 15
«o 20 days' immersion, and continue to harden for a period of 6 months.
Resistance of hydraulic limes increase if sand is mixed in proportion
of 50 to 180 per cent, of the part in volume ; from thence it decreases.
M. Vicat declares that lime is rendered hydraulic by admixture with it o( from
3^ to 40 per cent of clay and silica, and that a lime is obtained which does not
slake, and which quickly sets under water.
Artificial Hydraulic Limes do not attain, even under favorable circum-
stances, the 8anie degree of hardness and power of resistance to compression
as natural limes of same class.
Close-grained and densest limestones furnish best limes.
Hydraulic limes lose or depreciate in value by exposure to the air.
Pastes of fat limes shrink, in hardening, to such a degree that they can*
not be used as mortar without a large proportion of sand.
Ar^nes is a species of ochreous sand. It is found in France. On account
of the large proportion of clay it contains, sometimes as great as .7, it can be
made into a paste with water without any addition of lime ; hence it is some-
times used in that state for walls constructed en pisi, as well as for mortar.
Mixed with rich lime it gives excellent mortar, which attains great hardness
under water, and possesses great hydraulic energy. .
Pozzuolana is of volcanic origm. It comprises Trass or Terras, the Arbnes,
some of the ochreous earths, and the sand of certain craywackes, granites,
schists, and basalts; their principal elements are silica and alumina, the
former preponderating. None contain more than 10 per cent, of lime.
When finely pulverized, without previous calcination, and combined with paste
of fat lime in proportions suita-ble to supply its deficiency in that element, it pos-
sesses hydraulic energy to a valuable degree. It is used in combination with rich
lime, and may be made by slightly calcining clay and driving off the water of com-
bination at a temperature of i2oo<^.
Brick or Tile Dust combined with rich lime possesses hydraulic energy.
Trass or Terras is a blue-black trap, and is also of volcanic origin. It
requires to be pulverized and combined with rich lime to render it fit for
use, and to develop any of its hydraulic properties.
General Gillmore designates the varieties of hydraulic limes as follows: If, after
being slaked, they harden under water in periods varying from 15 to 20 days after
immersion, tlighUy hydrauUc; if from 6 to 8 days, hydraulic; and if from i to 4
days, eminently hydravUc
Pulverized silica burned with rich lime produces hydraulic lime of ex-
cellent quality. Hydraulic limes are iniured by air-slaking in a ratio vary-
ing directly with tHeir hydraulicity,ana they deteriorate by age.
For foundations in a damp soil or exposure, hydraulic limes must be ex-
clusively employed,
Bydraulic Lime of Teil is a silicious hydraulic lime; it is slow in setting,
requiring a period €€ from 18 to 24 hours*
Cements.
Hydraulic Cements contain a larger proportion of silica, alumina, magnesia,
etc., than any of preceding varieties of lime ; they do not slake after calcina-
tion, and are superior to tlie very best of hydraulic lime?, as some of them
set under water at a moderate temperature (65*^) in from 3 to 4 minutes;
others require as many hours. They dry not shrink in hardening, and make
an excellent mortar without any admixture of sand.
590 LDUBS, CXMBNTS, MOBTAB8, AND CONCBBTS8.
When ezpond to air, thejr absorb moistnre and cartwaic add g^utd are
rapidly deienanled thenhy.
Bomam CemetU is made from a lime of a peculiar character, found m Eng-
land and France, derived from aTgillo-calcareoiis lddney-«haped stonm termed
It is about .33 strength of Portland, and is not adapted for use with sand.
Rotendaie CemetU is from Roeendale, New Twk.
Pmrtiand Cement is made in England, Germany, France, and the United
States. It requires less water (cement i, water .29) than Roman cement,
sets slowly, and can be remixed with addiiwncd water c^ter an interval ofii
or even 24 hmtrsfrom itsjtrtl mixture.
Propertj of setting slow may be an obstacle to nee of some desigmitions of this
cement, as the Boulogne, when reqaired for iocalities having to contend against
immediate causes of destmction, as in sea constructions, having to be executed un-
der water and between tides. On the other hand, a quick-setting cement is always
difficult of use ; it requires special workmen and an active supervision. A slow-
setting cement, however, like natural Portland, possesses the advantage of being
managed by ordinary workmen, and it can also be remixed vaiik additional water
ajler an interval 0/12 or even 24 hours Jrom itefint mixing.
Conclugions derived from Mr. Grantg Experiments.
X. Portland cement improves by age, if kept firom moisture.
3. Longer it is in setting, stronger it will be.
3. At end of a year, z of cement to i sand is about .75 strength of neat cement;
I to 2, .5 strength; i to 3, .33; x to 4, .35; t to s. ->6.
4. Cleaner and sharper the sand, greater the strength.
5. Strong cement is heavy; blue gray, slow-setting. Quick-setting has generally
too much clay in its composition— is brownish and weak. .
6. Less water used in mixing cement the better.
7. Bricks, stones, etc., used with cement should be well wetted before use.
8. Cement setting under UUl water will be stronger than if kept dry.
9. Bricks of neat Portland cement in a few months are equal to Blue bricks,
BramleyFall stone, or Yorkshire landings.
10. Bricks of x cement to 4 or 5 of sand are equal to picked stock bricks.
1 1. When concrete is being used, a current of water will wash away the cement
Artificial Cement is made by a combmatioD of slaked lime with unbumed
clay in suitable proportions.
Artificial Pozmolana is made by subjecting clay to a slight calcination.
Salt water has a tendency to decompose cements of all kinds, and their
strength is considerably impaired by their mixture with it
IVIortax*.
Lime or Cement paste is the cementing substance in mortar, and its pro«
portion should be determined by the rule that Fo^ume of cementing subttanot
should be somewhat, in excess of volume of voids or spaces in sivna or coarst
material to be united^ the excess beuig added to meet imperfect manipulation
of the mass.
Hydraulic Mortar^ if re-pulverized and formed into a paste after having
once set^ immediately loses a great portion of its hydraulicity, and descends
to the level of moderate hydraulic limes.
The retarding influence of sea-water upon initial hydraulic induration is
not very great, if the cement is mixed with fresh water. The strength of
mortars, however, is considerably ini))aired by being mixed with sea-water.
Pointing Mortar is composed of a paste of finely-ground cement and clean
sharp siliceous sand, in such proportions that the volume of cement paste is
"lightly in excess of the volume of voids or spaces in the sand. The volume
LIMES, CEMBNTS, MOBTABS, AND CONCBBTES. 59I
of sand varies from 2.5 to 2.75 that of the cement paste, or by weight, i oi
cement^powder to 3 to 3.33 of sand. The mixture should be made under
shelter, and in small quantities.
AH mortars are much improved by being worked or manipulated ; and as rich
limes gain somewhat by exposure to the air, it is advisable to work mortar in
large quantities, and then render it fit for use by a second manipulation.
White lime will take a larger proportion of sand than brown lime.
Use of salt-water in the composition of mortar ii^ures adhesion of it
When a small quantity of water is mixed with slaked lime, a stiff paste
is made, which, upon becoming dry or hard, has but very little tenacity, but,
by being mixed with sand or like substance, it acquires the properties of a
cement or mortar.
Proportion of sand that can be incorporated with mortar depends partly
upon the degree of fineness of the sand itself, and partly upon character of
the lime. For rich limes, the resistance is increased if the sand is in pro-
portions varying from 50 to 240 per cent, of the paste in volume ; beyond
this proportion the resistance decreases.
Lime, i, clean sharp sand, 2.5. An excess of water in slakmg the lime
swells the mortar, which remains light and porous, or shrinks in drying ; an
excess of sand destroys the cohesive properties of the mass.
It is indispensable that the sand should be sharp and clean.
Stone Mortar, — 8 parts cement, 3 parts lime, and 31 parts of sand ; or i
cask cement, 325 lbs., .5 cask of lime, 120 lbs., and 14.7 cube feet of sand:=
18.5 cube feet of mortar.
Brick Mortar, — 8 parts cement, 3 parts lime, and 27 parts of sand; or i
cask cement, 325 lbs., .5 cask of lime, 120 lbs., and 12 cube feet of sand=
16 cube feet of mortar.
Brown Mortar, — Lime i part, sand 2 parts, and a small quantity of hair.
Lime and sand, and cement and sand, lessen about .33 in volume when mixed
together.
Calcareous Mortar^ being composed of one or more of the varieties of lime
or cement, natural or artificial, mixed with sand, will vary in its properties
with quality of the lime or cement used, the nature and quality of sand, and
method of manipulation.
Xurkish. Plaster, or Kydraulio Cexnent.
100 lbs. fresh lime reduced to powder, 10 quarts linseed-oil, and i to a
ounces cotton. Manipulate the lime, gradually mixing the oil and cotton, in
a wooden vessel, until mixture becomes of the consistency of bread-dough.
Dry, and when required for use, mix with linseed-oil to the consistency of paste,
and then lay on in coats. Water-pipes of clay or metal, Joined or coated with it,
resist the effect of humidity for very lobg perioda
Stuooo.
Stucco or Exterior Platter is term given to a certain mortar designed for
exterior plastering; it is sometimes manipulated to resemble variegated
nuurUe, and consists of x volume of cement powder to 2 volumes of dry sand.
In India, to water for mixing the plaster is added i lb. of sugar or molas-
•es to 8 Imperial gallons of water, for the first coat ; and for second or finish-
ing, X lb. sugar to a gallons of water.
Powdered slaked lime and Smith's forge scales, mixed with blood in suit*
able proportions, make a moderate hydraulic mortar, which adheres well to
masonry previously coated with boiled oiL
592 LIMES, CEMENTS, MOBTABS, AND CONCRETES.
Plafiier should be applied in two coats laid on In one operation, first coat being
thinner than second. Second coat is applied upon first while latter is yet soft.
The two coats should form one of about 1.5 inches In thickness, and when fin-
ished it should be kept moist for several daya
When the cement is of too durk a color for desired shade, it may be mixed w*4i
white sand in whole or in part, or lime paste may be added until Its volume equals
that of the cement paste.
K.h.ora8sa.r, or Xixrlsish. Miortetr,
Used for the construction of baildings requiring great solidity, .33 pow-
dered brick and tiles, .66 tine sifted lime. Mix with water to requir^ con«
sistency, and lay between the courses of brick or stones.
Miortara.
Mortars used for inside plastering are termed Coarse, Fine, Gauge or hard
finish, and Stucco.
Plasia-ing. — i bushel, or 1.35 cube feet of cement, mortar, etc., will cover 1.5
square yards .75 inch thick. 75 volumes are required upon brick work fbr 70 upon
laths.
When full time for hardening cannot be allowed, substitute flrom 15 to 20 per
cent, of the lime by an equal proportion of hydraulic cement
For the second or In-own coat the proportion of hair may be slightly diminished.
Coarse StxiflT. — Common lime mortar, as made for brick masonry,
Jvith a small quantity of hair ; or by volumes, lime paste (30 lbs. lime) i
part, sand 2 to 2.25 parts, hair .16 part.
Kiiie Sttiff (lime putty). — Lump lime slaked to a paste with a mod-
erate volume of water, and afterwards diluted to consistency of cream, and
then to harden by evaporation to required consistency for working.
In this state it is used for a slipped coat^ and when mixed with sand or plaster of
Paris, it is used tor finishing coat
O-atige, or Hard Kiiilsli, is composed of from 3 to 4 volumes fine
stuff and i volume plaster of Paris, in proportions regulated by rapidity re-
quired in hardening i for cornices, etc., proportions are equal volumes of
each, fine stuff and plaster.
Scrdtch (7oaf.— First of three coats when laid upon laths, and is from .25 to
•375 o^ ^" i"^^^ i" thickness.
One-coat Work, — Plasteringln one coat without finish, either on masonry
or laths — that is, rendered or laid.
Two-coat Woi*k. — Plastering in two coats is done either in a laid cocU
and set, or in a sci'eed coat and set.
Screed coat is also termed a Floated coat. Laid first coat ir two-coat
work is resorted to in common work instead of screeding^ when finished sur-
face is not required to be exact to a straight-edge. It is laid in a coat of
about .5 inch in thickness.
Laid coat, except for very common work, should be hand-floated.
Firmness and tenacity of plastering is very much increased by hand:floating.
Screeds are strips ci mortar 6 to 8 inches in width, and of required thick«
ness of first coat, applied to the angles- of a room, or edge of a wail and paral-
lelly, at intervals of 3 to 5 feet over surface to be covered. When these have
become sufiiciently hard to withstand pressure of a straight-edge, the inter-
spaces between the screeds are filled out fiush with them.
Slipped Coat is the smoothing off of a brown coat with a snuiU quantity
of lime putty, mixed with 3 per cent, of white sand, so as to nu^e a compar*
atively even siurface.
This finish answers when the sorCue is to be finished in distemper, or paper .
LIMES, CEMENTS, MOBTABS, AND CONCRETES. 593
Concrete 01* Betoxi
Cs a mixture of mortar (generally hydraulic) with coarse materials, as
^avel, pebbles, stones, shells, broken bricks, etc. Two or more of these
hiaterials, or all of them, may be used together. As lime or cement paste is
the cementing substance in mortar, so is mortar the cementing substance in
concrete or beton. The original distinction between cement and beton was,
that latter possessed hydraulic energy, while former did not.
Heraldic, — 1.5 parts unslaked hydraulic lime, 1.5 parts sand, i part
gnvfii, and 2 parts of a hard broken limestone.
This mass contracts one flflb m volume. Fat lime may be mixed with concrett,
without serious prejudice to its hydraulic energy.
'Various Com positions of Concrete.
ffydraulic.^'yiS lbs. cement = 3.65 to 3.7 cube feet of stiff paste. 12 cube
feet of loose sand = 9.75 cube feet of dense.
For Stmeratnicture. — 11.75 cube feet of mortar as above, and 16 cube feet
of stone fragments.
Sea Wall. — Boston Hai'hur. — Hydraulic. — 308 lbs. cement, 8 cube feet of
sand, and 30 cube feet of gravel. Whole producing 32.3 cube feet.
Superstructure.-^ 30S lbs. cement, 80 lbs. lime, and 14.6 cube feet dense
sands. Whole producing 12.825 cube feet.
Pise fs made of clay or earth rammed in layers of lYom 3 to 4 ins. in depth. In
moist ctimates, it is necessary to protect the external surface of a wall constructed
in this manner with a coat of mortar
A-splialt Composition.
Aiphaltum 3 parts, residuum oil or soft bitumen i part, powdered stone or fine
sand 12 parts.
Ashes 2 parts, powdered clay 3 parts, sand t part Mixed with soft bitumen
makes a very fine and duruble cement, suitable for external use.
Flooring. — 8 lbs. of composition will cover i sup. foot, .75 inch thick. Asphaltic
limestone 55 \bs. and gravel 28.7 lbs. will cover 10.75 sq. feet, .75 inch thick.
Agpkallic Mastic. —Mix hot asphaltic limestone 8 parts, asphaltum i part; add
sufficient sand for density needed for floor, roof, or walk.
WaUrproofing. — Asphaltum 4 parts, linseed oil 2 parts, sand 14 parts, pulverized
limestone 14 parts, by weight. Materials to be well dried, liot, and apply to dry
surface.
For Roads. — Asphaltum 12.5 parts, soft bitumen or maltlKi 2.5 parts, powdered
limestone 5 parts, sand 80 parts, mixed at temperature of 300^. Thickness, s ina
ArtifieuA lfa<^— -Gomposftion of i square yard .9 inch thick:
Mineral tar. 905 cube in&
Pitch 165 " "
Sand 549 '* "
Gravel 275 cube iu&
Slaked lime 55 " '^
1249 cube ins.
Adiiral Efflorescence. —White alkaline efflorescence upon the surface
of brick walls laid in mortar, of which natural hydraulic lime or cement is the basia
Mortar mixed with animal fat in the proportion of .025 of its weight will prevent
its formation.
Crystallization of these salts within the pores of bricks, into which they have
been absorbed fh>m the mortar, causes disintegration.
Distemper is term for all coloring mixed with water and size.
Growtfng. — ^Mortar composed of lime and fine sand, in a semi-fluid state,
poured into the upper beds and internal joints of masonry.
Laitance is the pulpy and gelatinous fluid, of a milky hue, that is washed
from cement upon its being deposited in water. It is produced more abun-
dantly in sea water than in fresh ; it sets very imperfectly, and has a ten-
dency to lessen the strength of the concrete.
3D*
594 LI^SS, CEMENTS, MOBTABS, AND C0NCB3ETXS.
SlcOcins.
SlciXxd Lime is a hydrate of lime, and it absorbs a mean of 3.5 times its
volume, and 2.25 times its weight of water.
Lime {quicklime) must be slaked before it can be used as a matrix for
mortar.
Ordinary method of slaking is by submitting the lime to its full propor-
tion of water (previously known or attained by trial) in order to reduce it to
the consistency of a thick pulp. The volume of water required for this pur-
pose will vary with different limes, and will range from 2.5 to 3 volumes
that of the lime, and it is imperative that it should all be poured upon it so
nearly at one time as to be in advance of the elevation or the temperature
consequent upon its reduction.
This process, when the water used is in an excessive quantity, is termed
" drowning," and when the volume of lime has increased by the absorption
of water it is termed its " growth."
If too much water is used, the binding qualities of the lime is injured by
its semi-fluidity ; and if too little, it is injurious to add after the reduction of
the lime has commenced, as it reduces its temperature and renders it granu-
lar and lumpy.
While lime is in progress of slaking it should be covered with a tarpaulin
or canvas (a layer of sand will suffice), in order to concentrate its evolved
heat.
The essential point in slaking is to attain the complete reduction of the
lime, and the greater the hydraulic energy of a lime, the more difficult it be-
comes to effect it.
Whitewash or Grouting, — ^When lime is required for a whitewash or for
grouting, it should be thoroughly " drowned," and then run off into tight ves-
sels and closed.
Slaking by Immersion is the method of suspending lime in a suitable ves^
sel in water for a very brief period, and withdrawing it before reduction
commences. The lime is then transferred to casks or like suitable receptacles,
and tightly enclosed, until it is reduced to a fine powder, in which condition,
if secured from absorption of air, it may be preserved for several months
without essential deterioration.
Spontaneous or Air Slaking. — When lime is not wholly secured from ex-
posure to the air, it absorbs moisture therefrom, slakes, and' falls into a powder.
Umes and Cements. — A Cask of Lime = 240 lbs., will make from 7.8 to
8.15 cube feet of stiff paste.
A Cask of Cement = 300 * lbs., will make from 3.7 to 3.75 cube feet of
stiff paste.
A Cask of Portland Cement = 4 bushels or 5 cube feet ^420 lbs.
A Cask of Roman Cement = 3 bushels or 3.75 cube feet = 364 lbs.
•5 inch. .75 inch. x incli.
A Bushel of cement will cover 2. 25 yards x. 5 yards 1. 14 yardlb
From experiments of General Totten, it appeared that
I volume of lime slaked with .33 its volume of water gave 2.27 volumes of powder.
1 " " " .66 " " 1.74 " "
I »* " " I " " 3,06 " '*
One cube foot of dry cement, mixed with .33 cube foot of water, will make . 63 to
635 cube fbot of stiff paste.
Lime should be slaked at least one day before it is incorporated with the
sand, and when they are thoroughly mixed, the mortar should be heaped into
one volume or mass, for use as required.
* 900 Ibt. net h aUndard ; it otaally OTtrmoa 8 lb*.
JilMES, CSMSNTS, MOBTABS, AKD CONCBBTBS. 595
BdCortar, Cement, Aco. {MoUi%oortk.)
Mbrtetr, — i of lime to a to 3 of sharp river sand.
Or, I of lime to a sand and i blacksmith's ashes, or coarsely ground coke.
Cdarse Mortar. — 1 of lime to 4 of coarse gravelly sand.
Concrete.^-1 of lime to 4 of gravel and 2 of sand.
Hydraulic Mortar,-^i of blae lias lime to 2.5 of burnt clay, ground to?
gether.
Or, I of blue lias lime to 6 of sharp sand, i of pozzuolana and i of calcined
ironstone.
Beton. — I of hydraulic mortar to 1.5 of angular stones.
Cement, — i of sand to i of cement. — If great tenacity is required, the ce-
ment should be used without sand.
Portland (IJenient
Is composed of clayey mud and chalk ground together, and afterwards cal-
cined at a high temperature — after calcining it is ground to a fine powder.
Strengtli or JVXortars, Ceznexits. un.d Concretes.
Deduced from, Experiments of Vicaty Paisley ^ Treuuart^ and Voisin.
Tensile
Weight or Power required to Tear asunder Otie Sq. Inch.
Cement ^Mortar. (43 days old.)
Proportion of Sand to x of Cement.
Roman..,
Portland. .
284
142
284
142
199
113
166
92
4
5
6
7
8
9
xo
142
79
128
67
116
57
106*
42
99
35
92
25
95lba
Briolz, Stone, and. d-ranite Af asonrsr. (320 days old.)
Experiments of General GiUmore, U. S. A.
Cement on Bncks,
Pure, average 30.8
Sandx )
Cement i )
Saodx \
Cement 2 )
Sandz )
Cement 3 )
'5-7
X2.3
6.8
Ddajleld and Baxter. Lba.
Pure cement 68
Cement 4 \ ^
Sand X
Cement 8 '
Siftings I
Cement x
Siftings I
Cement x
Sifting! 9
Lawrence Cement Co.
Pure cement 87
" 54
80
82
74
Cement on Granite.
Pure.
Sandz )
Cement z )
Sand z 1
Cement 2 )
Sand z )
Cement 3 )
Lb*.
27-5
2a8
Z2.6
9.2
James River. Lbs.
Pure cement 87
Cement 4 ) ^
Sandz } ^»
Newark Lime and Cement
Co.
Pure cement 93
Cement z )
Sand 2 ] ^°
Newark ana Rosendale.
Pure cement 75
Cement t\ ,
Sandx } *^
Sand z )
Cement 4 )
Water z I
Cement 2 )
Water .42
Cement
Water .33 )
Cement x )
n
Lbi.
7-9
2a5
3725
29. X5
Newark and Rosendale.
Cement z I
Sand 3 )
Pure, without )
morter, mean )
Mortar.
Lime paste z, sand 2. 5,
Lta
7
45
6
t
2
3
1, " 3.
cement paste 5 m
tt
(t
(t
59^ LIMSS, CBMENTS, MORTAJtS, AKD CONGBBTBS.
Aire CemaU,
Lbs.
Boulogne loo, water 50 112
Portland, natural, i year 675
" artificial, Eng., I year... 462
'' ' English, 320 days 1152
" " I month 393
Newark and Rosendale 339
Lbs.
Portland, In sea- water, 45 days 366
' * English, 6 months 424
Roman ''Septaria," X year 191
" masonry, 5 months 77
Rosendale, 9 months. ycx:
Lawrenoe Cement Co. 1210
Transverse.
Reduced to a uniform Measure of One Inch Square and One Foot in Length,
Suppoiied at Both Ends.
Experiments of* Gl-eneral Grillmore.
Formed in molds under a pressure of 32 lbs. per sq. inch, applied until mortar
had set. Exposed to moisture Tor 24 hours, and then immersed in sea-water.
Prisms zbyzbyB ins. between supports.
z W
Reduced by Formula -
portion of prism L
Cement,
James River.
Thick cream.
Thin paste
Stiff paste
Rosendale *' Hoffman. "
Thin paste
Stiff paste
" Delafleld and Baxter."
Thin paste
Stiff paste
English.
Portland, pure
Stiff paste
Cumberland, Md., pure . . . .
High Falls, U1-)
8terCo.,N.Y./
Complete calcination. . . .
3 4 6 d' 2 ~" *
C coefficient of rupture, and a wetfj^t of
Mortar.
•
<
1
Days.
Lbs.
59
320
59
It
6.9
320
320
8.9
320
320
8.5
12
320
320
320
16
13
13.2
95
8.4
95
4.2
Matkrial.
Portland, Eng., stiff paste
Roman, " " "
(t
t(
((
Cumberland, Md.
Akron, N. Y
James River, Va
Pulverized and re- )
mixed after set. . . . )
Fresh
Kingston and Rosendale.
High Falls, Ul- )
8terCo.,N.Y.}
Fresh water to a stiff )
paste j
Sea- water to a stiff paste
Lawrence Cement Co.
Fresh
<
Days.
320
20
100
320
320
O09
Lbs.
13
2-5
6
12.8
&8
320 I 8.6
3 I 3-6
320
320
95
95
95
320
9
76
laa
J8
On
xo
7.8
8.4
8.8
6.6
3-2
4-4
3.6
Crush-lns;.
Cements, Stones, etc. (Crystal Palace, London.)
Reduced to a uniform Measure of One Sq. Inch,
Matcbial.
Portrd cemU, area x, height i.
cement )
sand. , . )
(C
" stone
DflstnictiTe
PrssBure.
Lbs.
1680
X244
"44
Matirial.
Portland cement i
" sand 4
'' cement x'
" sand 7
Roman cement, pare. ,
DflstractiT*
Preuurit.
Lbs.
X244
693
34a
GS-eneral Deductions.
X. Particles of unground cement exceeding .0125 or an inch in diameter may hs
<iIlowed in cement paste without sand, tf> extent of 50 per cent, of wUole, without
detriment to its properties, while a curresixinding proportion of sand injures the
strength of mortar about 40 per cent.
lilMES, CEMENTS, MORTAES, ETC. — MASONRY. 59/
9 WbMi these uogroand particles exist in cement paste to extent of 66 per cent
of whole, adhesive strt-ngih is diminished about 28 per cent. For a corresponding
proportion of sand the dimiuution is 68 per cent.
3. Addition of siftings exercises a less ii\jarioas effect upon the cohesive than upon
the adhesive property of oemeot. The converse is true when sand, instead of sift-
ings, is used.
4. In all mixtures with siftings, even when the latter amounted to 66 per cent of
whole, cohesive strength of mortars exceeded their adhesion to bricks. Same re-
sults appear to exist when siftings are replaced by sand, until volume of the latter
exceeds 20 per cent of whole,, after which adhesion exceeds cohesion.*
5. At age of 320 days (and perhaps considerably within that period) cohesive
strength of pure cement mortar exceeds that of Croton front bricks. The converse
:b true when the mortar contains 50 per cent or more of sand.
6. When cement is to be used without sand, as may be tlic case when grovling is
resorted to, or when old walls are to be repaired by injections of thin paste, there is
no advanta^ in having it ground to an impalpable powder.
7 For economy it is customary to add lime to cement mortars, and this may be
done to a considerable extent when in positions where hydraulic activity and
strength are not required in an eminent degree.
8. Ramming of concrete under water is held to be injarious.'
9. Mortars of common lime, when suitably made, set in a very few day^, and with
euch rapidity that there is no need of awaiting its hardening in the prosecution of
work.
Kire Clay.— The fUsibillty of clay arises from the presence of impurities^
such as lime, iron, and manganese. These may be removed by steeping the clay in
hot muridtic acid, then washing it with water. Crucibles from common clay may
be made in this manner
iViotes by General Gillmort, U. 8. .i.-^Recent experiments have developed that
most American cements will sustain, without any great loss of strength, a dose of
lime paste equal to that of the cement paste, while a dose equal to 5 to 75 the vol-
ume of cement paste may be safely added to any Rosendale cement without pro-
ducing any essential deterioration of the quality of the mortar. Neither is the
hydraulic activity of the mortars so far impaired by this limited addition of lime
paste as to render them unsuited. for concrete under water, or other subntar ue
masonry By the use of lime is secured the double advantages of slow setting and
economy
Notes by OenercU TotUn^ U. S. A.— 240 lbs. lime=: i cask, will make from 7.8 to
8. 15 cube feet of stiff paste.
I cube foot of dry cement powder, measured when loose, will measure 78 to 8
cube foot when.packed, as at a manufactory.
For composition of Concretes, at Toulon, Marseilles^ Cherbourg, Dover, Aldemey,
etc., see Tretttiae of General Gillmore, pp. 253-2561
MASONRY.
£ond is an arrangement of bricks or stones, laid aside of and aboye
each other, so that the vertical joint between any two bricks or stones
does not coincide with that between any other two.
This iB termed " breaking Jointa^'
I/ectder is a brick or stone laid with an end to face of walL
Stretcher is a brick or stone laid parallel to face of wall.
Header Course or Bond is a course or courses of headers alone.
Stretcher Course or Bond is a course or courses of stretchers alone.
Closers are pieces of bricks inserted in alternate courses, in order to obtain
ft bond by preventing two headers from being exactly over a stretcher.
£ngHeh Bond is Uiying of headers and stretchers in alternates courses.
598
MAftONBT.
f^miah Bond is lapng of headers and stretchers alternately in each coorsa
Gauged Work. — Bricks cut and rubbed to exact shape required.
String Course is a horizontal and projecting course around a building.
CorbeiUng is projection of some courses of a wall beyond its face, in order
to support wall-plates or floor-beams, etc.
Wood Bricks^ Pallets, Plugs^ or Slips are pieces of wood laid in a wall in
order the better to secure any woodwork that it may be necessary to fasten
to it.
Reveals are portions of sides of an opening in a waU in front of the recesses
for a door or window frame.
Brick Ashlar. — Walls with ashlar-facing backed with brick.
Grouting is pouring liquid mortar over last course for the purpose of filling
all vacuities.
Lxxrrying is filling in of interior of thick walls or piers, after exterior faces
are laid, with a bed of soft mortar and floating bricks or spawls in it.
Rendering (Eng.) is application of first coat on masonry, Laging if one
or two coats on laths, and *^ Pricking up " if three-coat worK on laths.
Srioks sboald be well wetted before use. Sea sand shoald not be used in the
composition of mortar, as it contains salt and its grains are round, being worn by
attrition, and consequently having less tenacity than sharp-edged grains.
A common burned brick will absorb i pint or about one sixth of its weight of
water to saturate it. The volume of water a brick will absorb is inversely a test of
its qufdity.
A good brick should not absorb to exceed .067 of its weight of water.
The courses of brick walls should be of same height in flront and rear, whether
ft-ont is laid with stretchers and thin joints or not
In ashlar- facing the stones should have a width or depth of bed at least equal to
height of stone.
Hard bricks set in cement and 3 months set will sustain a pressure of 40 tons
per sq. foot.
The compression to which a stone should be subjected should not exceed .1 of its
crushing resistance.
The extreme stress upon any part of the masonry of St. Peter's at Rome is com-
puted at 15.5 tons per sq foot ; of St. Paul's, London, 14 tons ; and of piers of New
York and Brooklyn Bridge, 5. 5 tons.
The absorption of water in 24 hours by granites, sandstones, and limestpnes of a
durable description is i, 8, and 12 percent, of volume of the stone.
Color of Bricks depends upon composition of the clay, the molding sand, tem-
perature of burning, and volume of air admitted to kiln.
Pure clay free of iron will burn vMte, and mixing of chalk with the clay will
produce a like elHect.
Presence of iron produces a tint ranging from red and orange to light yelloio,
according to proportion of iron.
A large proportion of oxide of iron, mixed with a pure clay, will produce a bri^
red, and when there is from 8 to 10 per cent., and the brick is exposed to an intense
heat,, the oxide fUses and produces a dark blue or purple, and with a small volume
of manganese and an increased proportion of the oxide the color is darkened, even
to a black.
Small volume of lime and iron produces a cream cotor, an increase of iron pro-
duces red, and an increase oflime brown.
Magnesia in presence of iron produces yellow.
Clay containing alkalies and burned at a high temperature produeesa bluish gran.
For other notes on materials of masonry, their manipulation, etc., see ** Limes,
Cements, Mortars, and Concretes," pp. 588-597.
Pointing. — Before pointing, the joints should be reamed, and in olose ma-
sonry they must-be open to 3 of an inch, then thoroughly saturated with water,
and maintained in a condition that they will neither absorb water Arom the mortar
or impart any to it Masonry should not be allowed to dry rapidly after pointingi
but it should be well driven in by the aid of a calking iron and hammer.
Jn pointing of rubble masonry tbe Sfiipe p^eper^l 4ireotions are to be observed.
ICASONBT.
599
Sand is ArgiUaeeout, SilieMut, Or CcUcareouSy according to its composition.
Its use is to prevent excessive shrinking, and to save cost of lime or cemeut Or-
dmarily it is not acted upon by lime, its presence in mortar being mechanical, and
with hydraulic limes and cements it weakens the mortar. Rich lime adheres better
to the surfitce of sand than to its own particles; hence the sand strengthens the
mortar.
It is imperative that sand should be perfectly clean, Areed fh)m all imparities,
uid of a sharp or angular structure. Within moderate limits size of groin does
not affect the strength of mortar; preference, however, should be given to coarse.
Calcareous sand is preferable to siliceous.
Sea and River sand are suitable for plastering, but are deficient in the sharpness
required for mortar, fh)m the attrition they are exposed to.
Clean sand will not soil the hands when rubbed upon them, and the presence of
salt can be detected by its taste.
Scoriae, Slag, Clinker, and Cinder, when properly crushed and used, make good
liubstitutes for sand.
Concrete.— In the mixing of concrete, slake lime first, mix with cement, and then
with the chips, etc., deposit in layers of 6 in&, and hammer down.
IB ricks.
Variations in dimensions by various manufacturers, and different d^^ees
of int^isity of their burning, render a table of exact dimensions of different
manufactures and classes of bricks altogether impracticable.
As an exponent^ however, of the ranges of their dimensions, following
averages are given :
Dbscriftior. Ink DBscHiPTtoit. Int.
Baltimore fh>nt
Philadelphia "
Wilmington "
Croton "
Colabaugh
Eng. ordinary...
" Tx>nd. stock
Dutch Clinker...
J 8.25X4125X2.375
8.5 X4 X2.25
8.25X3.625X2.375
O X4-5 X2.5
8.75X4-25 X2.5
6.25X3 X 1.5
Maine. ......
Milwaukee . .
North River.
Ordinary
Stourbridge 1
fire-brick )
Amer. do>,N. Y. .
X 3-375 X 2.375
X 4125X2.375
X 3-5 X 2.25
X 3-625X2.25
X 4- 125 X2.5
9.125X4-625X2.375
8.875X4-5 X '2.625
7-5
8.5
8
(7-75
18
In consequence of the variations in dimensions of bricks, and thickness of
the layer of mortar or cement in which they may be laid, it is also impracti-
cable to give any rule of general application for volume of laid brick-work.
It becomes necessary, therefore, when it is required to ascertain the volume
of bricks in masonry, to proceed as follows ;
Xo Compute Volume of Bricks, and 14'umber in. a. Cube
Foot of Afaeonry.
RuLB. — To face dimensions of particular bricks used, add one half thick-
ness of the mortar or cement in which they are laid, and compute the area ;
divide width of wall by number of bricks of which it is composed ; multiply
this area by Quotient thus obtained, and product wUl give volume of the
mass of a brick and ita mortar in ins.
Divide 1728 by this volume, and quotient will give number of bricks in a
cabefoot
"* ExAMPLS.— Width of a wan is to be 12.75 ina, and tront of it laid with Philadel-
phia bricks in courses .25 of an inch in depth; how many bricka will there be in
fiu;« and backing in a cube foot?
Philadelphia front brick, 8.25 x 3.375 ina foca
8.25 -{-.25X2-7-2 = 8.25 -|-. 25 = 8.5 zslength of brick €mdJ4nfU;
2.375 -{-.25X2-^2 = 2.375 -f .25 =2.625 = «»<tt* of brick and joint.
Then 8.5 X 2.625 = 22.3x35 ti«. = carta of face; 12.75 -r- 3 {number of bricks in
wkUh of watt) =z 4.35 tiw.
Hence 33.3125 x 4.35=94.83 cube im. ; and 1738-^94.83= 18.33 brickt.
6oo
MASONRY.
One rod or brick masonry (Eng.) = 11.33 ^^^ yards and weighs 15 tons, or 373
superficial feet by 13.5 thick, averaging 4300 bricks, requiring 3 cube yards mortar
and 120 gallons water.
Bricklayers' hod will contain 16 bricks or .7 cube feet mortar.
Fire-Tjriolxs.
Fire-clay contains Silica, Alumina, Oxide of Iron, and a small proportion
of Lime, Magnesia, Potash, and Soda. Its fire-resisting properties depend-
ing upon the relative proportions of these constituents and character of its
grain.
A good clay should be of a uniform structure, a coarse open grain, greasy
to the hand, and free from any alkaline earths.
The Stourbridge clay is black and is composed as follows :
Silica 63.3 I Alumina 23.3 { Lime 73 } Protoxide of iron. ... x. 8
Water and organic matter la 3
Newcastle clay is very similar.
rrixiclExiess of* Briok IV alls for 'W'areliouses in Feet.
{Holenoortfu)
Height in Feet
100
90
80
70
60
50
40
30
as
Length Unlimited. . . .
Thickness in Ins. ....
34
70
30
34
30
a6
36
26
21.5
17.5
»3
Length in Feet
Thickness in Ins
70
30
60
26
45
21.5
30
17-5
50
21-5
70
31.5
60
17-5
50
—
Length in Feet
Thickness in Ins
55
26
60
36
45
21.5
35
17-5
40
17-5
30
13
45
X3
—
Stone Miasoiiry.
Masonry is classed as Ashlar or Rubble.
>\shiar consists of blocks dressed square and laid with close joints.
Coursed Asfdar consists of blocks of same height throughout each course,
Iivibt>le is composed of small stones irregular in form, and rough.
Rubble Ashlar is ashlar faced stone with rubble backing.
A.slilav.
Fig. 2.
Fig. I.
:i:^Av<-^|
wm
g
^^^aiaa
P^"?.|lSm53|g^^^B
mti^imm^
^istsism^smi^i
Fig. x.^Coursed^ with chamfiered and
rusticated quoins and plinth.
Fig. ^.—Coursed, with rock nu:e and
draft, edges.
Fig. 3.
:^-^'^,*^
^g>.lf^' :>^:yx:
Fig. 4.
Fig. 3.— (7our«e(2, with rock face.
I
I
I
I
Fig. ^—Regular Cowrnd.
MASONRY.
60I
Fig. 5-
III
1 1 1 1 I
J
- I 1 1 1 >
' 1 ' 1 1 1 >
III \
Randomed Ashlar.
Fig. 6.
Fig. ^,^Irregular Coursed.
Fig. 6.— Random Coursed.
Fig. 7-
Fig. 8.
Fig. T-— Hanged Kandom, level, and
broken coursea
R,tal3"ble.
*'ig- 9- rrrrvr~nr-\i^-TT<rnn Fig. la
Fig. 8.—Randomj level, and broken.
Fig. . 9. Bfodt Coursed. — f jirge blocks
in courses (regular or irregular), Beds
and Joints roughly dressed.
Fig. XI.
Fig. 10.— Ovrxed and Ranged
Random.
i<JV
Fig. 12.
"- IC
Fig. XI. itanflwd iZandoiH.— Squared Fig. 12. Coursed Random.-^ioneBl&\^
rubble laid in level and broken in courses at intervals of from 12 to 18
courses. ins. in height.
Dry Rubble
is a wall laid without cement or mortar.
Fig. 13- S V " rgTV^^^^iH'^^ ..wx^'vj ^'&
14.
Fig. 13. I>ry .Rudb^e.— Without mor-
tar or cement.
Fig. 15.
yig. 14. Rustic or Rag.— Stonea of
irregular form, and dressed to make
close Joints.
Fig. 16.
Fig. 15. Uneoursed or Random. —
Beds and Joints undressed, projections
knocked off, and laid at random. In-
terstices filled with spalls and mortar.
NOTS. —Rustic or Rag work is frequently laid in mortar.
3E
Fig. 16. Zrac^d Cottrxed.— Horizontal
bands of stone or bricks, interposed to
give stability.
UASONRT.
., „ — Pirint»,Fig.is,onaM;hBide,
trom whicb srcb epriii|p).
Omen. — Higheat point of arch.
Hii««ie*«.--8iiles of arch, from Bpringing
., ce between e:tlrailo9,aho>
izonUI line drawn through crown and a ver-
tical line through upper end oS skewback.
Siaidact U Hp[>er surface of an abul-
nient or pier from which an arch sprinKS,
uiil its face ia on a line radiating frraa centre nf arch.
Abu/iaeni ia outer body that supports ari'li and from whic
Pkr is the intermediate support for two or more arches.
Jambi are sides of abutments or piers.
rouwoir) are the bhicks forming an arch.
Keg-tlone is centre voussoir at
Span is horizontal distance from springing to Bpringing of arch.
^«.-Heighl from Bj.rinf ■ ■■ - ■ -
t^eni/th 19 that of springin(
It key-stone. ■
Bing-count of a wall or arch is parallel to face of it, and in directioa of
Slrmg and Collar courtn are projecting ashlar dreseed broad stones at
right angles to (ace of a wall or arch, and in direction of its length,
dimfter is a slight rise of an arch as .laj lu .35 of an inch per foot of
ilHorn is the external angle or course of a wall.
PHidh is a pnijecting base to a waU.
Foolmg is prmecting course at bottom of a wall, in order to distribute its
weight over an mcreased area. Its width shouhl be double thai of base of
wair, diininisliing in regular offsets .5 vidth of tlieir height.
Blocking OmrK.—K course placed on top of a cornice.
Piirapel is a low wall, over Mge of a roof or terrace.
Erfrndw.— Back or upper and outer surface of an arch.
fnlradoi or <?a^ is underside of lower surface of arch or an opeuiog.
Groirttil is when arches intersect one another.
laserl. — An inverted arch, an arch with its intrados below axis or spring-
ing line.
Athlar fBOjOBty requires .125 of its volume of mortar. SubbU, 1.3 cube
yards stone and .35 cube yard mortar for each cube yard.
ftiiiife miuonn/ m cement, 160 feet in haghl, will stand and hear 3000a
lbs. per SI). inch-
Stones should he laid with their strata horizontal.
When " through " or " thorough .bonds " are not introduced, headers ahould
cverlap one another fn>m opposite sides, known ba 'l"if$' /oolb bond.
Aggregate surface "f ends of bond stones should be from .135 to .95 of
area of each face of wall.
Weak alonea, as sandstone and granular limesione. should not have a
length over 3 times their depth. Strong or bard stones amy have a leogU
MASONRY.
603
GcUlets are small and sharp pieces of stone stuck into mortar joints, in
which case the work is termed gaUeted.
Snapped work is when stones are split and roughly squared.
Quarry or Rock-faced, — Quarried stones with their faces undressed.
Pitch-faced. — Stones on which the arris or angles of their face, with their
sides and ends, is defined by a chisel, in order to show a right-lined edge.
Drafted or Drafted Margin is a narrow border chiselled around edges of
faces of a block of rough stone.
Diamond-faced is when planes are either sunk or raised from each edge
and meet in the centre.
Squared Stones, — Stones roughly squared and dressed.
RubUe. — Unsqnared stones, as taken from a quarry or elsewhere, in their
natural form, or their extreme projections removed.
Cat SUmet, — Stones squared ami with dressed sides and ends.
Dressed. Stones. ,
The following are the modes of dressing the faces of ashlar in engineering:
Rnuyh Pointed. — Rough dressing with a pick or heavy point
Fine Pointed, — Rough dressing, followed by dressing with a fine point.
Crandalled. — Fine pointing in right lines with a hammer, the face of
which is close serried with sliarp edges.
Cross Q'andalled. — When the operation of crandalling is right angled.
Hammered. — The surface of stone may l)e finished or smooth dressed by
being Axed or Bushed ; the former is a finish by a heavy hammer alike to a
craodall, the latter is a final finish by a heavy hammer with a face serried
with sharp points at right angles.
Tliiokiiess of Brick Walls for
AVarelxouses. (Molesworth.)
Lenfcth.
Height.
ThickneM.
Length.
Height.
Thickness,
Length.
Height.
Thickness.
Faet.
Feet.
In*.
Feet.
Feet.
Ins.
Feet.
Feet.
Ins.
Unlimitod.
25
13
Onlimit'd.
100
34
45
30
>3
do.
30
175
60
40
^7-5
30
40
13
da
40
215
70
50
ai-5
40
50
175
da
50
a6
SO
60
2>-5
35
60
17s
do.
60
26
45
70
21-5
30
70
'75
da
70
26
60
80
26
45
80
21.5
da
80
30
70
90
30
.60
90
26
do.
90
34
70
100
30
55
100
26
For drawings and a description of stone-dressing tools, see a paper by J. R Cross,
W. E. Memll, and E. B. Van Winkle, ''A. S. Civil Engineer Transactions," Nov. 1877.
Walls not exceeding 30 feet in height, upper story walls may be 8.5 ins. thick.
From 16 feet below top of wall to base of it, it should not be less than the space
deflne<l by two right lines drawn trom each side of wall at its base to x6 feet trom
top
Thiokness not to be less in any case than one fourteenth of height of story.
IL«atli8.
Laths are 1.25 to 1.5 ins. by 4 feet in length, are usually set .25 of an inch
upart, and a bundle contains 100.
to4
MASOK&T.
Matouai.
Cobe Feet.
Cement i
Cement i,BaDd i.
Cement i, sand 2.
Plastering*
Volumei required/br Vcurums Thiekntn.
Square Yards.
Ina.
2.25
4-5
6.75
75
Ins.
3
4-5
Ins.
2.25
3-33
Matsual.
Cobe Feet.
Lime 1, sand 2, )
lw"f3-75- j •*
Square Tanli.
•75 I
In*.
Ina. f Ina.
75 yard8.8up'l ren-
dered and set on
brick or 70 on lath.
Kstimate of Afateriale and. I^a1:>or fbr lOO Sq.. Yards of
Xjatlx and Plaster.
Mnteriala
and I<abor.
Thre» Cnata
Hard Finish.
Lime
4 casks.
66 "
.5 "
20CX>.
4 bashela
7 luad&
Lump lime
Plaster of Paris. .
lAths. . .
Hair.
Sand
Two Coats
Slipped.
3. 5 casks.
2000.
3 bushcte.
6 loads.
Materiala
and Labor.
White sand.
Nails
Masons . . . .
Lqjwrer. . . .
Cartage....
TbreeCoaU
Two CoaU
Hard Finuh.
Slipped.
2.5bashel6.
islha
islba.
4day&
3.5<»ay8-
3 "
3 "
I «
.75 "
Rougli Caa^ is washed gravel mixed with hot hydraulic lime and
water and applied io a semi-fluid condition.
i^jx^Ues and ^'butments.
To Compute I>epth. of* Keystone of Circular or Slliptio
\/K-}-*-=-2
+ .25 = d. R represmting raiUuSj s span, and d depths aU infuL
This is for a rise of abont . 25 of span ; when it is reduced, as to . 125, add . 5 instead
of . 25.
iLLrsTRATiox.— Arch of Washington aqnednct at "Cabin John** has a span of 230
feet, a rise of 57. 25, and a radius of 134-25; what should be depth of its keystone f
■>/l34.25-|-220-r-2 , 15-63 , ^^^»%it.t ^1.*
— ^^ ^ 1-.25 = -2— ^ + .25 = 4.i6./fe«t I>epth is 4.16 feet
Viaducts of several arches increase results as determined above by add-
ing .125 to .15 to de])th.
For arches of 2d class materials and work, and for spans exceeding 10
feet, add .125 to depth of keystone, and for good rubble or brick-work
add .25.
NoTK. — It is customary to make the keystones of elliptic arches of greater depth
than that obtained by above fonnula. Trautwine, however, who is high authority
in this case, declares it is unnecessary.
To Compute Radius of an A.Tcih., Circular or Sllips«.
I —A -f-r'-s-ar = R r rqprttmting rite.
Railtvay A^rches.
For Spans between 25 and 70 feet Rise .2 of span. Depth of arch .055 of spao.
Thickness of abutments .2 to .25 of span, and of pier .14 to .16 of span.
A.l>utment8.
Wh^n height does not exceed 1.5 time$b€ue. R-^s-f-.i r -\- 2 z= thickness at tpring
qf arch in feet. ( Trautvoine. )
Batter. — From .5 to 1.5 ins. per foot of height of walL
MASONBY.^-MECHANICAL CENTEKS. — GRAVITY. 605
To Coxnpute 13epth of ^rolx. (Hurst.)
Cv^R = D. c = Stone (block) .3. Brlck = .4. Rubble=:.45.
When there are a series of arches, put . 3 = . 3-5, . 4 = . 45, and . 45 = . 5.
AI!in.izxiuxxi rTliickness or A.l3utTneiits for Sridge and
similar, Arclies of ISO©. (HursU)
When depth of crown does not exceed 3 feet. Computed from formula
yjt R -f- (^ ) — ^ = T. H representing height of abutment to springing in feet
Height of Abutment to Springinff.
lUdiiu
HfliKht of Abatment to Sprin|clnf(> {
Radius
Heig
of Arch.
5
7-5
ID
ao
30
of Arch.
5
Feet.
Feet.
Feet.
Feet,
Feet.
Feet.
Feet.
Feet.
4
3-7
4-2
4-3
4.6
4.7
12
5.6
4-5
3-9
4-4
4.6
4.9
5
15
6
5
4.2
4.6
4-8
5-5
5.2
20
6.5
6
4-5
4-7
5-2
5-6
5-7
25
6.9
7
4-7
5-2
5-5
6
6.1
30
7.2
8
4-9
5-5
5.8
6.4
6.5
35
7-4
9
S-i
5- a
6.1
6.7
6.9
40
^t
zo
5-3
6
6.4
71
7-3
45
7.8
11
5.5
6.2
6.6
7-3
7.6
50
7-9
7-5
xo
Feet.
Feet.
6.4
6.9
7
7-5
Z-7
8.4
8.2
9.1
8-7
9 7
9.1
10.2
9.4
ia6
9-7
IX
10
11.4
20
30
Feet.
Feet.
7.6
8.4
9.6
10.5
7-9
8.8
10
II.X
11.4
13
II.8
12.8
12.9
13.6
134
14
14.3
15
XoTB. —Abutments in Table are assumed to be without counterforts or win^>
walls. A sufficient margin of safety must be allowed beyond dimensions here
given.
Culrertc for a road having double tracks are not necessarily twice the
length tor a single track.
For other and foil notes, tables, etc., see Trautwine's Pocket Book, pp. 593-7za
MECHANICAL CENTRES.
There are four Mechanical centres of force in bodies, namely, Centre
of Gravity, Centre of Gyration, Centre of Oscillation, and Centre of
Percussion.
Centre of* GJ-ravity.
Centre or Grayitt of a body, or any system of bodies rigidly con-
nected together, is point about which, if suspended, all parts will be in
equilibrium.
A body or system of bodies, suspended at a point out of centre of gravity,
will rest with its centre of gravity vertical under point of suspension.
A body or system of bodies, suspended at a pcjint out of centre of gravity,
and successively suspended at two or more such points, the vertical lines
through these points of suspension will intersect each other at centre of
gravity of body or bodies.
Centre of gravity of a body is not always within the body itself.
If centres o? gravity of two bodies, as B C, be connected by a line, dis-
tances of B and C from their common centre of gpravity, c, is innernely as
the weights of the bodies. Thus, B :C::C c:e B.
To Ascertain Centre of Gravity of any Plane Figure MechamcaUy.
Suspend the figure by any point near its edge, and mark on it direction
of a plumb-line hung from that point ; then suspend it from some other
point, and again mark direction of plumb-line. Then centre of gravity of
«urfa<^'e will pe at point of intersection of the two marks of plumb-line.
3E*
6o6 MECHANICAL CENTBBS. — GBAVITy.
Centre of gravity of parallel-sided objects may readily be found in this
way. For instance, to ascertain centre of gravity of an arch of a bridge,
draw elevation upon paper to a scale, cut out figure, and proceed with it as
above directed, in order to find position of centre of gravity in elevation of
the model. In actual arch, centre of gravity will have same relative position
as in paper model.
In regular figures or solids, centre of gravity is same as their geometrical
centres.
I-iine.
r c
Circular Arc. -z- z= distance from centre^ r representing radius^ c chord, and I
length of arc
Surflatces.
Square^ Rectangle, Rhombuty Rhomboid, Gnomon, Cube, Regular Pobfgon,
Circle, Sphere, Spheroid or Ellipsoid, Sphercidal Zone, Cylinder, Circular
■ Ring, Cylindrical Ring, Link, Helix, Main Spiral, Spindle, all Regular Fig-
ures, and Middle Frusta of aU Spheroids, Spindles, etc.
The centre of gravity of the surfaces of these figures is in their geometri-
ccU centre.
Triangle, — On a Une drawn from amy ang^ to the middle of opposite side,
at two thirds of the distance from angle.
Trapezium. — Draw two diagonals, and ascertain centres of gravity of each
of four triangles thus formed ; join each opposite pair of these centres, and it
is at intersection of the Unes.
Trapezoid. ( rrrrr) ^ ~ = di^ance from B on a Une joining middle of two
parcUlel sides Bb,m represeiUing middle Une.
c r
Circular Arc -^ = distance from centre ofcvrdit,
V
Setoff of a Cirde. . 4344 r = distanee from cenk^ of eirde, c npresenHng chord.
Semicircle. .4244 r = distance from centre.
Semi-semicircle. .4244 r = distance from both base and height and at their inters
section.
c3
Segment of a Cirde. = distance from centre, a reprewnting area of segment
Sector of a Circular Ring. — x — -^ 7" X -x tz = distance from centre of
•^ 3 arc ^ r^ — r^ '
arcs, r and t' representing the radii.
Illustration.— Radii of surfoces of a dome are 5 and 3.5 feet, and angle (^ al
centre = 130°.
4 ^ Sin^ ^ !?5zi4i87S = i X :i^ X '*•'-'' = 3.43>«t
3 arc 130° 15 — 12.25 3 3.2689 *2-75
Hemisphere, Spherical Segment, and Spherical Zone^ At centre of their
heights, ^
Circular Zone, — Ascertain centres of gravity of trapezoid and segmenta
comprising zone; draw a line (equally dividing zone) perpendicular to
chords; connect centres of segments by a line cutting perpendicular to
chords.
Then centre of gravity of figure will be on pernendictdcar, toward lesser
chord, at such proportionate distance of difference between centres of gravity
of tr(q)ezoid and line connecting centres of segments, c(s area of smtents
ocQrs to area of trapezoid, ^
M£CUANIGAX CENTRES. GRAVITY. 607
Prism and Wec^e,— When end is a Parallelogram, in their geometiicaX
centres; when the end is a Triangle, Trape/^iuiu, etc., it is in middle of its
lefufth, iU scum distance from base, as that of triangle or trapezoid of which
it u a section.
Parabola in its a.cis=..6 distance from vertex,
Prismoid,—At samt distance from its base as that of the trapezoid or
trapezium^ which is a section of it.
Lune. — On a line connecting centres of gravity of arcs ai a proportiotiate
^ ^ point to respective areas of arcs,
■ordinates. (r4-r* ; — -A - =«,
V •■+r7 3
Co-
and (^) * =
Kr + r'/ 3
X.
Solids.
CiUfe, ParaUelopipedon., Hexahedron^ Octahedron., Dodecahedronj Icosahe-
drony Qflinder, Sphere, Right Spherical Zone, Spheroid or Ellipsoid, Cylin-
drical Ring, Iawc, Spindle, ail Regular Bodies, and Middle Frusta of aU
Spheroids and Spindles, etc. Centre of gravity of these figures is in their
geometrical centre.
Tetrahedron.— In common centre of centres of gravity of the triangles made by a
section through centre ofeacli side ofl/iejigures.
Cone and Pyramid. .25 of line joining vertex and centre of gravity ofbase=rdis-
tancefrom base.
Frustum of a Cone or Pyramid. \ — 7—77..-' , X - h = distance from centre
\r-\-rY — rr 4
of lesser end, r and r', in a cone representing nuin, and in a pyramid sides., and h
height.
Cone, Frustum of a Cone, Pyramid^ Frustum of a Pyramid^ and Ungula. —
At same distance from base as in that of triangle, parallelogram, or semicir^
de, which is a right section of them.
Hemisphere. . 375 r = distance from centre.
Spherical Segment 3.1416 M'fr J -r- v z=: distance from centre, vs repre-
senting versed sine, and v volume of segment ( ^~^ .) x * = distance from
\i2 r — 4 »*/
vertex.
Spherical Sector. .75 (r — . 5 *) 1= distMioe from centre. ' ^o^ = distance
from vertex.
Spirals. — Plane, in its geometrical centre. Conical, aJl a distance from the
hose, .25 of line joining vertex and centre of gravity of base.
Frustum of a Circular Spindle. -—7 — =r— ^ = dista ce from centre of spindle.
2 {h — D.s)
h representing distance between two bases, D distance of centre of spindle from centre
efcirde, and z generating arc, expressed in units ofraditu.
r»
Segment of a Circular Spindle. — -r — =r-T = dwtatice/rom centre of spindle.
2 (» — u.t)
Semi-spheroids. — Prolate. .375 o.— 06/afe. .^ys<'^=^ distance from centre
Semi-spheroid or ElUpsoid and its Segment— See HasweWs Mensuration, pages
a8i mod 282.
Frusta of Spheroids or Ellipsoids. Prolate. .75 ^^ ~ — ' = distance from
3 a' — «'
eentre of spheroid, a reprsunting semi-transverse diameter in a prolate fruUum^ and
semi-conjugate in an oblate frustuM.
HyperboUnd of Be.voluUon. ^ . , ^ . X % = dUtanoe from vertex^ b represenUng
608 MECHANICAL CENTBES. — GRAVITY.
Segmentt of Spheroids.— Prolate, ./s ^"t^.— O&tefe. .75^^i^ = <«i<afiOft
3a-|-a 20+0
^om centre ofspheroidf d and d' rqpretetUing distancei of bate of segments from.
centre of spheroid.
3(1* — » -f-d a-f-O"*
roid, d and d' representing distances of base and end of segments from centre of the
spheroid.
Segment of an Elliptic Spindle cU two thirds of height from verieas,
ParoUfoloid of Revolution, at two thirds of height from vertex.
Segment of a Hyperbolic Spindle^ at 75 of height from vertex.
2 r'4-r h
Frustum of Paraboloid of Revolution. — ^ ,. , X - = distancefrom baae^ r astd
r -j~ r 3
r' representing radii qfbase and vertex.
Segment of Paraboloid of Revolution, at two thirds of height from vertex.
Segments nj a Circular and a Parabolic Spindle. — See HasweWs Mensuration^
pages 192 aDd 199.
Parabola. .4 of height =: distance from base,
Hyperboloid oj
diameter of base.
(d 4- dO (2 o* — d'« + <l»)
Frustum of Hyperboloid of Revolution. . 75 ^_' ^-^,> j r. ^2 = distance
fi'OM centre of base, a representing semi-transverse axis, or distance from centre of
curve to vertex of figure ; d and d' distances from centre of curve to centre of lesser
and greater diameter of frustum.
Segment of Hyperboloid of Revolution. ^. , ^- X A = distancefrom vertex.
o O-f-4 »
Of Two Bodies. = distance from V or volume or area of larger body, d rg>.
resenting distance between centres of gravity ofbodieSy and v volume or area of less
body.
Cycloid. — .833 of radius of generating circle := distance from centre of
chord of curve.
A ny Plane Fif/ttre. — Divide it into triangles, and ascertain .centre of grav-
ity or each ; connect two centres together, and ascertain their common cen-
tre ; then connect this common centre and centre of a third, and ascertain
the common centre, and so on, connecting the last-ascertained common centre
to another centre till whole are included, and last common centre will give
centre required. .
Of an Irregular Body ofRofaiion.
Divide figure into four or six equidistant divisions ; ascertain volume of
each, their moments with reference to first horizontal plane or base, and
then connect them thus :
h
(A-f-4 Ai + 2 Aa-f 4 A3-f A4) — = V, A Ai, etc., representing volume qf ditis-
12
ton*, and h height of body from base ;
A-f 4Ai-f 2 Aa + 4A3-|-A4 4 ^ ^
gravity from base.
MBGHANIOAL CENTRES. — GTBATION. CX)9
Centre of Gryration.
Centre of Gyration is that point in any revolving body or system
of bodies in which, if the whole quantity of matter were collected, the
Angtdar velocity would be the same ; that is, the Momentum of the body
or system of bodies is centred at this point, and the position of it is a
mean proportional between the centres of Oscillatioti and Gravity
If a straight bar of wiiform dimensions was struck at Uiis point, the
stroke would communicate the same angular velocity to the bar as if the
whole bar was collected at that point.
The A ngular velocity ot a body or system of bodies is the motion of a line
connecting any point and the centre or axis of motion : it is the same in all
parts of the same revolving body.
In different unconnected bodies, each oscillating about a common centre,
their angular velocity is as the velocity directly, and as the distance from
the centre inversely. Hence, if their velocities are as their radii, or distances
from the axis of motion, their angular velocities will be. equal.
When a body revolves on an axis, and a force fe impressed upon it suffi-
cient to cause it to revolve on another, it will revolve on neither, but on a
line in the plane of the axes, dividing the angle which they contain ; so that
the sine of each part will be in the inverse ratio of the angular velocities
with which the bodies would have revolved about these axes separately.
Weight of revolving body, multiplied into height due to the velocity with
which centre of gyration moves in its circle, is energy of body, or mechaui>
cal power, which must be communicated to it to give it that motion.
Distance of centre of gyration from axis ot motion is termed the Radius
of gyration ; and the moment of inertia is equal to product of square of
radius of g3rration and mass or weight of body.
The moment of inertia of a revolving body is ascertained exactly by as-
certaining the moments of inertia of every particle separately, and adding
them together ; or, approximately, by adding together the moments of the
small parts arrived at by a subdivision of the body.
To Compute Alomeiit of Inertia of a Revolving Body.
Rule.— Divide body into small parts of regular figure. Multiply mass
or weight of each part by square of distance of its centre of gravity from
axis of revolution. The sum of products is moment of inertia of body.
NoTB.— The value of moment of inertia obtained by this process will be more
exact, the smaller and more numerous the parts into which body is divided.
To Compute Radiiis of O-yration of a Revolving Body
about its A.xia of Revolution,
Rule.— Divide moment oi mertia of body bv its mass, or its weight, and
square root of quotient is length of radius of gyration.
NoTB.— When the parts into which body is divided are equal, radius of gyration
naav be determined by Uking mean of all squares of distances of parts from axis
of revolution, and taking square root of their suol
Or, VR^ + r'-r- 2 = 0. R and r rcprenrntimj radii.
ExAMPLB.— A straight rod of uniform diameter and 4 feet in length, weighs 4 Iba ;
what is ita inertia, and where is its radius or centre of gyration ?
Each foot of length weighs i lb., and if divided into 4 parta, centre of gyration of
6«ch is respectively .5, 1.5, 3.5, and 3.5 feet Hence,
IX .51= .25 1
1 X 1. 5 = 225 21 =^ inertia, which -J- 4 = 5.25, and A/s-as = a.9a»
iXa.5»=: 6.25 feetradiui. ^
«X3-5' = xa.2S J
5lO MBCHANICiiL CENTRSS. — GYRATION.
Following are distances of centres of gyration from centre of motion io
various revolving bodies :
Straight, uniform Bod or Cylinder or tfiin RectangtUar Plate revolving about one
end; length, x 5773, ^nd revolving ubout their centre; ler^^ x .2886.
The general expression is, when revolving at any point or its length,
Circular Plane, revolving on its centre; radiM of circle X -7071 , Circle Plane, as
a W/teel or Disc of uni/bi-m Thickness^ revolving about one of its diameters as an
axis; radius x -s-
Solid Cylinder y revolving about its axis; radius x •7071.
Solid S]^rej revolving about its diameter as an axis; radius x .6325.
Thin, hollow Sphere, revolving about one of its diameters as an axis; radius
X -8164. Surface of sj^ere .96is r.
Sphere and Solid Cylinder (vertical), at a distance from axis of revolution =s
Vt'-^.^r' for sphere, and Vl^-i- • 5 r^ Jor cy Under ^ I representing length qf connec-
tion to centre of sphere and cylinder.
Cone, revolving about itg axis; radius of hose X .5447; revolving about its ver-
tex = V12 A2-4-3 r^ -H 20^ A representing height, and r radius qf base, revolving
about its ba£es= V2 h^^^ r^-j-zo.
Circular Ring, as Rim of a Flywheel or Hollow Cfylinder, revolving about its
diameter = VR*-|-r«-r-2, R rqpresenting radius of periphery, and r of inner circle
of ring.
Fly-wheel = J ^ ■ — ^^^ — ^ ■ — -, W and w representing toeights of
rim and of arms and hub, and I length of arms from ojbu of wheel
I A d^ -\- c'
Section of Rim. J- — yr^-^-rd. d representing depth and c periphery
of rim.
i=V^+»'
Parallelopiped, revolving about one end, distance flrom end= « /^ — — — , b rep- .
V 12
resenting breadth.
Illustration.— In a solid sphere revolving about its diameter, diameter being
2 feet, distance of centre of gyration is 12 x -6325 = 7.59 ins.
Xo Compute ICleznents of G-y ration.
GWr „ Pr«o ^ GWv Vrtg _ GWt> ^
-— ~ = t>. G representing distance of centre of gyration from axis of rotation^
i» w
W weight of body, t Ums power acts in seconds., v velocity in feet per second acquired
by revolving body in thai time, and r distance of point ofapplioatian of power from
axis of body, as length of cranky etc
Illustration i What is distance of centre of gyration in a fly-wbeel, power
224 lbs., length of crank 7 feet, time of rotation 10 seconds, weight of wheel 5600
lbs., and velocity of it 8 feet per second?
224X7X'OX3».«66^S04373^ eyeet
5600X8 42800 ' '
2.— What should be weight of a fly-wheel making 12 revolutions per minute. lU
diameter 8 feet, power applied at 2 feet fV-om its axis 84 lbs., time of rotation 6 sec-
onds, and distance of centre of gyration of wheel 3.5 feet?
8X31416X12 , -^ , .^ -- 84X2X6X32.166 „ __
^-7^ = 5.0265 feet = velocity. Then -^-^ ^^ = 1843. « *•
°^ 3.5 X 5.0265
MECHANICAL CENTRES. — GYRATION. 6l I
When the Body is a Compound one. Rule. — Multiply weight of several
particles or bodies by squares of their distances in feet from centre of mo-
tion or rotation, and divide sum of their products by weight of entire mass;
the square root of quotient will give distance of centre of gyration from
centre of motion or rotation.
ExjkXPLB.— If two weighu, of 3 and 4 lbs. respectively, be laid upon a lever (which
is here assumed to be without weight) at the respective distances of i and 2 feet,
what is distance of centre of gyration fVom centre of motion (the fulcrum} ?
3X1^ = 3; 4X2»=i6; ^^^=^ = 2.71, and ^"2.71 = 1.64 /erf.
3"r4 7
That is, a single weight of 7 lbs., placed at 1.64 feet from centre of motion, and re-
volving in same time, would have same momentum as the two weights in their
respective places.
When CerUre of Gravity is given. Rule. — Multiply distance of centre of
(»ciUation from centre or point of suspension, by distance of centre of grav-
itv from same point, and square root of product will give distance of centre
of g}'ration.
Example.— Centre of oscillation of a body is 9 feet, and that of its gravity 4 feet
ft-om centre ef rotation or point of suspension ; at what distance from this point is
centre of gyration ?
9 X 4 = 36, and ^36 = 6 feet.
To Compute Centre of Ghyration of a Water-wlaeel.
Rule. — Multiply severally twice weight of rim, as composed of buckets,
shrouding, etc., and twice that of arms and that of water in the buckets
(when wheel is in operation) by square of radius of wheel in feet ; divide
sum by twice sum of these several weights, and square root of quotient will
give distance in feet.
ExAiiPLB. — In a wheel 20 feet in diameter, weight of rim is 3 tons, weight of
arms 2 tons, and weight of water in buckets i ton; what is distance of centre of
gyration Trom centre of wheel?
.Rim =3 tonsx lo^x 2= 600 3-f a + i X 2 = 12 «uin o/wetiyAte.
Buckets = 2 tons x los x 2 = 400
Water =:iton X io» = 100 _ ^ /noo , . . ^
Hence ^ ^^ -^/9i.67 = g. $7 feet.
1100
Gknsral Formulas.— P represmting power., H horset^ power, F force applied to
rotate body in //>«., M mass of revolving body in Ihs.^ r radiiis upon which F atis in
feet, d distance from axis of motion to centre of gyration in feet, t time force is ap-
pliejl in seconds, n number of revolutions in time t, x angular velocity, or number of
32. i66 F 7*^
revolutions per minute at end of time ty and G = — xr a'J — "'
'4prn ^ 2pr^x , Majd» _ Mwd* 2.56e'Fr
y
O ~ » 6o(} ~ ' i53-5tr~ ' 2,56«»F ' M d=
i53.5«F»*_ 244 t P _ „ g' M d« *!^<*'_H
Md« -*' x^d'~ * 244^ ' i34ioot
iLLrsTBATioy.— Rim of a fly-wheel weighing 7000 lbs. has radii of 6.5 and 5 75
feet; what is its centre of gyration, and what force must be applied to it 2 feet
from axis of motion to give it an angular velocity of 130 revolutions per minute in
40 seconds? bow many revolutions will it make in 40 seconds? and what is its
power?
±3o'X7o°oX6.,4' ^ 4459 862680 ^ ^^^
234100X40 5364000
Centre of gyration-^ M±k2^ ^t.t^feet. Then Fz.^^^^^"^^^'^'^
^ V 2 **^ 153-5X40X2
34306636 _ . 2.56 X 40* X 2793.7 X 2 -, , - ^.
" « = 2793.7 '^•i *nd - - —^ :r == 86. 67 revolutions.
W38o '^"" 70ooX6.i4» '
6l2 MECHANICAL CKNTKES.— OSCILLATION, ETC.
Centres of* Oscillation and I*erotission.
Centre of Oscillation of a body, or a system of bodies, is that point
in axis of vibration of a vibrating body in wliicb, if, as an equivalent
condition, the whole matter of vibrating body was concentrated, it would
continue to vibrate in same time. It is resultant point of whole vibrat-
ing energy, or of action of gravity in producing oscillation.
As particles of a body further from centre of its suspension have greater
velocity of vibration than those nearer to it, it is apparent that centre of
oscillation is further from its centre than centre of gravity is from axis of
suspension, but it is situated in centre of a line drawn frcmi axis of a body
through its centre of gravity. It further differs from centre of gyration
in this, that while motion of oscillation is produced by gravity of a body,
that of gyration is caused by some other force acting at one place only.
Radius of oscillation, or distance of centre of oscillation from axis of sus-
pension, is a third proportional, to distance of centre of gravity from axis
of suspension and radius of gyration.
Centre op Percussion of a body, or a system of bodies, revolving
about a point or axis, is that point at which, it resisted by an immov-
able obstacle, all the motion of the body, or system of bodies, would be
destroyed, and without impulse on the point of suspension. It is also
that point which would strike any obstacle with greatest effect, and
from this property it has been termed percussion.
Centres of Oscillation and Percussion are in same point. — ^If a blow is
struck by a body oscillating or revolving about a fixed centre, percussive
action is same as if its entire mass was concentrated at centre of oscillation.
That is, centre of percussion is identical with centre of oscillation, and its
position is ascertained by same rules as for centre of oscillation. If an ex-
ternal body is struck so that the mean line of its resistance passes through
centre of percussion, then entire force of percussion is transmitted directly
to the external body ; on the contrary, if a revolving body is struck at its
centre of percussion, its motion will be absolutely destroyed, so that the body-
will not incline either way.
As in bodies at rest, the entire weight may be considered as collected in
centre of gravity ; so in bodies in vibration, the entire force may be consid^
ered as concentrated in centre of oscillation ; and in bodies in motion, the
whole force may be considered as concentrated in centre of percussion.
If centre of oscillation is made point of suspension, point of suspension
will become centre of oscillation.
Angle of OsdUation or Percussion is determined by angle delineated by
vertical plane of body in vibration, in plane of motion of body.
Velocity of a Body in Oscillation or Percussion through its vertical plane
is equal to that acquired by a body freel}' falling through a vertical line
equal in height to versed sine of the arc.
Xo Coxnpvite Centre of* Oscillation or Percussion of a
Body of Uniform Density and. Figure.
Rule.— Multiply weight of body by distance of its centre of gravity from
point of suspension; multiply also weight of body by square of its length,
and divide product by 3.
Divide this last quotient by[ product of weight of body and distance of
its centre of gravity, and quotient is distance of centre irora point of sus-
pension*
MBCUANIGAL CEKTBBS. — OSCILLATION, ETC. 613
tir 12
Or, j- W X p = distance frcm axis. Or, square radioB of gyration of body
3
Vid divide by distance of centre of gravity from axis of suspension.
ExAJfPLB.— Where is centre of oscillation in a rod 9 feet in length fkt)m its point
of suspeosion, and weighing 9 lbs. ?
Q X - = 40. 5 = product of weight and its centre of gravity ; 2 — 2- z= 243 = quo-
V 24?
tient of product of weight of body and square of its length -r- 3 ; — - = 6 feet.
40-5
. When Point of Stispension is not at End of Rod. Rule. — To cube of
distance of point of suspeiision from top of rod or bar, add cube of its dis-
tance from tower end, and multiply sum by 2.
Divide product by three times difference of squares of these distances, and
quotient is distance of point of oscillation from ])oint of suspension.
ExAMPLK.— A homogeneous rod of uniform dimensions, 6 feet in length, is sus-
pended 1.5 feet from its upper end; what is distance of point of oscillation from
that of suspension ?
2 (4.5' + 1.5') 189
6—1.5=4.5. 2 a= -^ = 3S/«<<'
3 14-5" — x-5') 54
Centres of Oscillation, and. Peroussioii iix Bodi'es of
"Various ITiguves.
When Axis of Motion is in Vertex of Figure, and when Oscillation or Motion
is Facewise.
Right Line, or any figure of uniform shape and density = .66 /.
Isosceles Triangle = .75 A. Circle = 1.25 r.
Parabolas = . 714 A. Cone = .Bh.
When Axis of Motion is in Centre of Body. Wheel = .75 radius.
When Oscillation or Motion is Sidewise. Right Line, or any figure of urn-
form shape and density = .66 i. Bectangle, suspended at one angle = .66 0/ d»-
tMffonaL
Parabola, if suspended by its vertex =7 14 of axis -f- 33 parameter; if suspended
by middle of its base = . 57 of axis -{- . 5 parameter.
"i arc r
Sector of a Circle = , c representing chord ofarCj and r radius of base.
4 ^
CircU=7sd. C<m« =s - rxls -f-
5 5 axis
2 /•'
Sphere = >"f-*'4'C> c representing length of cord by which it is suspended.
Xo A.8certain. Centres or Oscillation and f*ercu8sion
experimentally.
Suspend body very Areely from a ftxed point, and make it vibrate in small arcs,
noting number of vibrations it makes in a minute, and let number made in a min-
ute be represented by n; then will distance of centre of oscillation fh)m point of
140850
suspension be = ^ = tns.
For length of a pendulum vibrating seconds, or 60 times in a minute, being
^9.125 ins., and lengths of pendulums being reciprocally as the squares of number
of vibrations made in same time, therefore n« : 6o» : : 39. 1 25 : ^- — = '^^,^°
n^ n
being length of pendulum which vibrates n timss in a minute^ or distance of centre
ofoscUlation bdow axis nf motion.
3F
6l4 MSCHANICAL CENTBBS. — ^MBCHANICS.
To Oompute Centres of Osoillation or Peronssion. of a
System of JParticles or Dodies.
Rule. — Multiply weight of each particle or body by square of its distance
ttom point of suspension, and divide sum of their products by sum of weights,
multiplied by distance of centre of gravity from point of suspension, and
quotient will give centre required, measured from point of suspension.
^'"' WfyH-W"y~ ^ ^"^"^ qf centre.
ExAMPLR I. — Length of a suspended rod being 20 feet, and weight of a foot in length
of it equal 100 oz., has a ball attached at under end weighing 100 oz. ; at what point
of rod from point of suspension is centre of percussion ?
20
100 X 20 = 2000 = weight of rod; 2000 X — = 20000 =£ momentum ofrod^ mrprod-
2 y a
uctofiU weighty and distance of Us centre of gravity; ■ =a66666.66 =
3
force of rod ; 1000 X 20' = 400 000 ■=. force of balL
_. 266 666. 66 4- 400 000 ^ ^^ - .
Then -^-^ — — = 16.66 /cet
20 000 -f- 20000
2. — Assume a rod 12 feet in length, and weighing 2 lbs. for each foot of itsjength,
with 2 balls of 3 lbs. each^one fixed 6 feet fVoni the point of sus|)ension, and the
other at the end of the rod; what is the distance between the points of suspension
and percussion ?
,2 X 2 X Jjf = f44 = n,amentom of rod. ^_4Xr^ ^ 3456 ^„ y^,^^^ ^^^^
3X6 = 18= " ofistbaU. 3 3
3XJ2 =_36= " qf^ball. 3X 62 = 3X36^108= '' qfistbaU.
igS sum of moments. 3X12*= 3X144=432= ^''ofadbaU.
Then 1 693 -r- 1 98 = 8. 545 feet. 1692 sum qf forces.
MECHANICS.
Mechanics is the science which treats of and investigates effects of
forces, motion and resistance of material bodies, and of equilibrium:
it is divided into two parts — Statics and Dtnamics.
Statics treats of equilibrium of forces or bodies at rest. Dynamics
of forces that produce motion, op bodies in motion.
These bodies are further divided into Mechanics of Solid, Ftuid, and Aeri'
form bodies; lience the following combinations :
I. Statics of Solid Bodies^ or GeosfcUics.
'2. Dynamics of Solid Bodies, or Geodyncanics.
3. SicUics of Fluids, or Ht/drostatics. .
4. Dynamics of Fluids, or Hydrodynamics,
5. Statics of A eriform Bodies, or A erostatics.
6. Dynamics of Aeriform Bodies, Pneumatics or Aerodynamics,
Forces are various, and are divided into moving forces or resistances ; as
Gravity, Heat or Caloric, IneHia,
Muscvlar, Magnetism, Cohesion,
Elasticity and Contractility, Percussion, Adhesion,
Central, Expansion, and Explosion,
Couple. — Two forces of equal magnitude applied to or operating upon
same oody in parallel and opposite directions, but not in same liue of action,
constitute a couple, and its force is sum or magnitude of the two equal forces.
Moment, — Quantity of motion in a moving body, which is alwa3'S equal
to product of quantity of matter and its velocity.
When velocities of two moving bodies are inversely as their quantities of
er, tlieir momenta are equal.
XSCHANICS. — STATICS.
6lS
Fig. I.
STATICS.
Oompositioxi and. Resolutioxx of Woroen,-
When two forces act upon a body in same or in an opposite direc-
tion, effect is same as if only one force acted upon it, being sum of
difference of the forces. Hence, when a body is drawn or projected in
directions immediately opposite, by two or more unequal forces, it is affected
as if it were drawn or projected by a single force equal to difference between
the two or more forces, and acting in direction of greater force.
This single force, derived from the combined action of two or more forces,
is their RemltatU.
The process by which the restdiatU of two or more forces, or a single
force equivalent in its effect to two or more forces, is determined, is termed
the Composition of Forces^ and the inverse operation ; or, when combined
effects oi two or more forces are equivalent to that of a single given force,
the process by which they are determined is termed the Decomposition or
Resolution of Forces. Two or more forces which are equivalent to a smgle
force are tcnrmed Components,
When two forces cut on scune point thdr intensities are repres&ated by sides
of a paraUelograniL, and their combined effect will be equivalent to that of a
single force acting on point in direction of diagonal of parallelogram^ the
intensity of which is tnroportiofial to diagoimL
Illustbation. — Attach three cords to a fixed point, c. Fig. i ; let c a and c b pass
over fixed rollers, and su^end weights A and B tbereflrom.
Point c will be drawn by the forces A and B fn directions a o
and 6 c. Now, in order to ascertain which single force, P, would
produce the etane eOect upon it, set ofl* the distances c m and
c n on the cords in the same proportion of length as weights
of A and B; that is, so that cm: en:: A: B; then draw par*
allelogram cm on and diagonal o c, and it will represent a sin-
gle fbrce, P, acting in its direction, and having same ratio to
weights A or B as it has to sides e m or c n of parallelogram.
Consequently, it will produce same effect on point c as com
bined actions of A and B.
A parallelogram, constmcted from lateral forces, and diagonal of which is
Fig. 2. a mean force, is termed a Parallehgixim of Forces,
^ Illustration. — Assume a weight. W, Fig. 2, to be
suspended trom a; then, if any distance, a o, is set
off in numerical value upon the vertical line, a W,
and the parallelogram, or as, is completed, a s and
a r, measured upon the scale, a 0, will represent
# strain upon a e and a « in same proportion that a 0
W bears to weight W.
If several forces act ujwn same point, and their intensities taken in order
are represented by sides of a polygon^ except one, a single force proportioned
to and acting in direction of that one side will be their recant.
To Resolve a Single Farce into a Pair of Forces. — Figs. 3 and 4.
The ends of a cord, Fig. 3, are led over two points, a and h, and in centre of
cord at e a weight of 4 lbs. is suspended. If distances ac^hc, are each \_ foot, dis-
Fig. 3. tance a h should be 18 Vna
When cord is in this posi-
tion, weight at c draws upon
c a and c b with a force of
3 lbs. ; hence c of 4 lbs. is
equal to two forces of 3 Iba
each in direction of a c and b c
Apply end£ of cord to «/, Fig. 4, distance being 22 ins., then the strain on ee,cji
are eadi 5 lbs. ; hence one force of 4 lbs. is equal to two of 5 Iba each.
6 1 6 MBCHANICS. — STATICS.-^D YNAMICS.
!Kquili"briiim of* IForces.
Two bodies which act directly against each other in same line are iii eqiii>
librium when their quantities of motion are equal ; that ia, when product of
mass of one, into velocity with which it moves or tends to move, is equal to
product of mass of other, into its actual or virtual * velocity.
When the velocities with which bodies are moved are same, their forces
are proportional to their masses or quantities of matter. Hence, when equal
masses are in motion, their forces are proportional to their velocities.
Relative magnitudes and directions of any two forces may be represented
by two right lines, which shall bear to each other the relations of the forces,
j;,. and which shall be inclined to each other in an angle
*■ ** - ^ equal to that made by direction of the forces.
Illustration. — Assume a body, W, to weigh 150 lbs., and
resting upon a smooth surface, to be drawn by two forces, a
and 6, Fig. 5. = 24 and 30 lbs., which make with each other
an angle- a W 6 = 1050, in which direction and with what
acceleration will motion occur?
^ a W 6 = 1050, and cos. 180^ — 105O = cos. 75®, mtam
P = V3o''-l-a4' — g X 30X 24 COB- 75° = V900 -\r 576 —,1440 COS. 7^
= >/ 1476— (1440 X 2ii88^=s'\/iio3.3 = 33.8i Wfc
The acceleration Is ^ = ^^i^ii^J?:!^ = 7.i2xs/«e<.
W 150
Angle of Hepose is greatest inclination of a plane to horizon at which a
body will remain in equilibrium upon it.
Hence greatest angle of obliquity of pressure between two [danes, consist-
ent with stability, is the angle tangent of which is equal to coefficient of
friction of the two planes.
Inertia is resistance which a body at rest offers to an external power to
be put in motion or to change its velocity or direction when in motion.
To Compute Inertia of a Revolvins Body.
Divide ft into small parts of a regular figure, multiply weight of each pan
by square of its distance of its centre of gravity from axis of revolution,
and sum of products will give moment of inertia of body.
DTNAHICS.
Dynamics is the investigation of the laws of Motion of Solid Bodie$^
or of Matter^ Force, Velocity, Space, and Time,
Mass of a body is the quantity of matter of which it is composed.
Force is divided into Motive, Accelerative, or Retardative.
Motive Force, or Momentum, of a body, is the product of its mass and
its velocity, and is its quantity of motion. This force can, therefore, be
ascertained and compared in any number of bodies when these two
quantities are known, f
Accelerative or Retardative Force is that which respects velocity of
motion only, accelerating or retarding it ; and it is denoted by cpiotient
of motive force, divided by mass or weight of body. Thus, if a body
* Virtaal wtoeity Is tha Telocity which > body In «qailibrlnin would aeqairo wtra tba eqaiUbriaa
to be dtetorbed.
t It It eomiwred. bocsoM It b not referable to any standard, aa a ton, poand, etc. That, rappos*
a cannon-ball wrigfaing 15 Iba., projected with a Telocity of 1500 fset per lecond, atvike a reautta*
Hody. it! momentnn, aeoerdin^ to the above rule, woald bo 15 X 1500 b aa 500 1 not pooods, for walfU
pressure wltb which It cauuot be compared.
HSCHA19ICS. — DYNAMICS. 617
of 5 lbs. is impelled by a f oroe of 40 lbs., accel^ating force is 8 lbs. ;
but if a force of 40 lbs. act upon a body of 10 lbs., accelerating force
is only 4 lbs., or half former, and will produce only half Telocity.
With equal masses, velocities are proportional to their forees;
With equal forces, velocities are inversely as the masses.
With equal velocities, forces are proportional to the masses.
Work is product of force, velocity, and time.
Motion. — The succession of positions which a body in its motion pro-
gressively occupies forms a line which is termed the trajectory, or path
of the moving body.
A motion is Uniform when equal spaces are described by it in equal
times, and Variable when this equality does not occur. When spaces
described in equal times increase continuously with the time, a variable'
motion is termed accelerated^ when spaces decrease, retarded, and when
equal spaces are described within certain intervals only, the motion is
termed periodic, and Intervals periods. Uniform motion is illustrated
in progressive motion of hands of a watch ; variable in progressive ve-
locity of falling and upwardly projected bodies ; and periodic by oscil-
latioD of a pendulum or strokes of a piston of a steam-engine.
TJnifbrxzx Amotion.
roBMmJLB. /», Y» Hsso, and y = P; ~, y, and -^=/; -,
- •, and 77 = 9; vt, -y, -7, and — =~ — = «; •'
/» / ' /<~ * ^ /* /' / — ' P' r' /«'
md
W
•"* g^='5 ^'^ °5So<, P«. and /!.<:= W; ^-, {l, I^*» *»*
±1550 550 550 5Sot
-r = H. P rq^retenting power in effect^ pody, or momentum,fJbrce m 26f. , v and
M velocity and tpace in feet per second, t Hme in seconds, H horsepotoer, and W work
inJboUws.
If two or more bodies, etc., are compared, two or more corresponding letters,
as *I',p,p'i V, V, rf, etc., are enqfloyed.
Illustration i.— Two bodies, one of 20, the other of 10 lbs. , are Impelled by same
momentum, say 60. They move uniformly, first for 8 seconds, second for 6; what
are the spaceB described by both ?
60 -f- 20'= 3 = V, and 60 -r- xo = 6 = ».
ThenT V = 3 X 8 = 24 = 8, and tv=6x6 = s6=zs,^paces respectively.
a. — If a power of la 800 eifectB has a velocity 0^10 feet per second, what is its
force? xa 800 -3- xo = X38o lbs.
XJnlfbrm Varlat>le IMotlon.
Space described by a body having uniform variable motion is represented
by sum or difference of velocity, and product of acceleration and time, ac-
cording as the motion is accelerated or retarded.
Illustration l— A sphere rolling down an inclined plane with an initial Telocitf
of 25 feet, acquires in its course an additional velocity at each second of time of 5
feet ; what will be its velocity after 3 seconds ?
^5 + 5X3 = 40 feet.
2 — A locomotive having an initial velocity of 30 feet per second is so retarded
that In each second it loses 4 feet; what is its velocity after 6 seconds?
6l8 MECHANICS. — ^DYNAMICS.
XJxilfbnii IMtotioYi ^ccdlefEkt^d.
In this motion, velocity acquired at end of any time whatev^er is equal to proct
net of accelerating force into time, and space descriDed is equal to product of half
accelerating force into Bqiiiup» of time, or balf product of vekt^ity and time of ac-
quiring the velocity.
Spaces described in sacoessiTe seconds of time are as the odd numbers, z, 3, 5, 7,
9, etc.
Gravity is a constant force, and Its effect upon a body fklling ft-eely in a vertical
iUxe is represented by g^ and the motion of such body is uniformly accelerated.
The following theoremfi are appticable to aik caces of motion uniformly aooeler-
ated by any constant force, F :
2^F V g F y .sg¥
~p — gTt^y/2gTsT^v. -- = —--1= = P.
t gt gi'^ zg»
When gratify acts alone^ as token a hcdyfaUs in a vertical line^ F is omit-
ted. Tkus^
t representing time in seconds, and s velocity infect per second.
If, instead of a heavy body falling freely, it be projected vertically upward
or downward with a given velocity, », then 8=ztv^:.sgt'', aa expression
in which — must be taken when the projection is upward, and + when it is
downward.
Illustration i. — If a body in 10 seconds has acquired a velocity by uniformly
accelerated motion of 26 feet, what is aocelerating foroe, and what space described,
in that time?
26 -^10 Si 9.6 ^oecder^UingfMrci'} ^ Xto*ssty>fBet^^pacedeseribed.
2
2.— A body moving with an acceleration of 15.625 feet describes in 1.5 seconds a
3 — A body propelled with an initial velocity of 3 feet, and with an acceleration
of 5 feet, describes in 7 seconds a siwice = 3X7-l-sX — = lA^-sJcet
4.— A body which in 180 seconds changes Its velocity fh)m 2.5 to 7.5 feet, trav-
erses in that time a distance of '•5'r7-5 ^ 180 = ^00 feet.
5.— A body which rolls up an inclined plane with an initial velocity of 40 fbet per
second, by which it suffers a retardation of 8 feet, ascends -only — = 5 secondSy and
4o»-i- 2 X 8 ^ iQo/Mt in height, then rolls back, and returns, after 10 seconds, with
a velocity of 40 feet, to its initial point; and after 12 seconds arriTOs at a distance
of 40 X 12— :4 X i2'=<j6feet below point, assuming plane to be extended backward.
Ciroular Miotiou..
2prn^2prn'^^ 55ooff^^_^^ frn_f_»prn
60 t ' rn 2prn' •'' 5500 ~ 550 X 60 "" ^»
f2pr n' 8= — ^^ c W. r teprtdtnting radius infect, n number of revolutions
2^/.!rfJf..2r '**"**^ **' '""'"^ revolutions, f force in tot., t time in seconds, and W
MECHANICS. — DVNAMXCS. 619
ACotion on an Iii.oUn.ed !Plane.
To Ascertain Conditions of Motion by Graviijf,
Fig. 6. 0 A ^^'^^^^ A B, Fig. 6, an inclined plane, B C its base,
/Tn ^^ A C iU height, and t> a body descending the plane ; from
OrJ^fr"^ dot, centre of gravity of body, draw 6 a perpend. cular
to BG, representing pressure of b by gravity ; draw bo
parallel and 6 r perpendicular to A B, and complete
„ parallelogram ; then force 6 a is equal to both 6 o, & r,
Qi which b r te sustained by reaction of plane, and
force 5 o is wholly effective in accelerating motion of body.
' Let this force be rqpretenUd by/, and bc^by g or force of gravity, then by similar
triangle,/: gy.bo: ba: AC: AB. Hence, ^^^=/
Put AB = /, AC=:A and ^ A B 0 = a, then force which produces motion on the
plane on /becomes g -j , and ^ sin. a.
Therefore, accelerating force on an inclined plane is constant, and eqaations of
motion will be obtained by substituting its value of /for g in equations x, 3, and
3, page 6x8.
^——f — r, 'Stv. .sgt^BMLo^ and — - — =1.
at* agh* ^ * ^*' ^ 3^ sin. a
as ght hghs ^ . . , -.
T' ^~* \/"~^ — » fir* sin. a, and va^pf sin. a=:o.
When a Body is projected down or up an Inclined Plane^ with a given Ve-
lority, — llie distance which it will be from point of projection in a given
time will be ght* i
tv±.- — r-,and —A2lv±.ght)=zs.
a I a I
iLLusTRAnoN I.— Ijongth of an inclined plane is 100 feet, and its angle of inclina-
tion 60^ \ what is time of a body rolling down it, and velocity acquired ?
8in.6oO = .866.
' X v>°tr^ = yf7' «8 = 2.68 seconds^ and 32. x6 x 2.68 x 866 = 74.64/^.
3x16 X -866 ^' I J IT -t^
3. — If a body is projected up an Inclined plane, which rises i in 6, with a velocity
of 50 feet per second, what will be its place and velocity at end of 6 seconds y
6 X 50— ^^-T.-g^^ — =203.52 feet from, bottom, and 50 — (33.16 x 6 x -^ J =
50 — 33.x6 = i7.84yec<.
To effect an ascent up an inclined plane In least time, its length, to its height,
must be as twice weight to power.
TVork A.oou.TOi:ilated in I^oving Sodiea.
Quantity of work stored in a body in motion is same as that which would
be accumulated in it by gravity if it fell from the height due to the velocity.
Accumulated work expressed in foot-lbs. ia equal to product of height so
found in feet, and weight of body in lbs. Height due to velocity is equal
to square of velocity divided by'64.4, <^"d work and velocity may be de-
duced directly from each other by following rules :
Xo Compute i\.oonmulated "Work.
Bulk. — ^Multiply weight in lbs. by square of velocity in feet per second,
and divide by 64^ and quotient is accumulated work in foot-lbs.
Or, W = --— — , or, = 10 X A- W repretenUng workf w weight in <&«.. ar^
64.4 ^ *
h heipht due to veloett^ in /eet per feotfRd
V3
620
MECHANICS. — DYNAMICS.
TVorlr "by IPercvissive Force.
If a wedge is driven by strokes of a hammer or other heavy mass, effect
of percussive force is measured by quantity of work accumulated in stricken
body. This work is computed by preceding rules, from weight of body
and velocity with which a stroke is delivered, or directly from height of
fall, if gravity be percussive power.
Useful work done through a wedge is equal to work expended upon it,
assuming that there is no elastic or vibrating reaction from the stroke, as if
the work had been exerted by a constant pressure equal to weight of strik-
ing body, exerted through a space equal to height of fall, or height due to
its final velocity.
If elastic action intervenes, a portion of work exerted is absorbed in an
elastic stress to resisting body ; and the elastic action may be, in some cases,
so ^eat as to absorb the work expended.
The principle of action of a blow on a wetlge is alike applicable to action
of the stroke of a monkey of a pile-driver u{)on a pile.
If there be no elastic action, the work expended being product of weight
of monkey by height of its fall, is equal to work {performed in driving the
pile: that is, to product of resistance to its descent by depth through which
it is driven by each blow of monkey.
Illustration. — If a horso draws 200 lbs. out of a mine, at a speed of 2 miles per
hour, bow many units of work does he perform in a minute, coefflcieDt of friction .05 ?
— "2^ — = ij6 feet per mintUe. Hence, 176 x 200 + .05 X 200 = 35 aio unUs,
00
Deooiia position, of Foroe.
By parallelogram of force it is il-
lustrated how a vessel is enabled to
be sailed with a free wind and against
one.
Assume wind to be free or in direction
of arrows, Fig. 7, and perpendicular to
line A B, the course of vessel.
Let line m4) represent directiou and
force of wind, and rs plane of sail ; from
o draw o u perpendicular to r s, and
fVom m perpendicular, m o on r «, and
m u on 0 u.
By principle of parallelogram of forces,
force m 0 may be decomposed into o v
and ou, since they are the sides of parallelogram of which m 0, representing force
of wind, is diagonal. Force of wind, therefore, is measured by o u, both in magni-
tude and direction, and represents actual pressure on sail.
Draw u n and u x parallel to o A and o m, thus forming parallelogram unox.
Hence force o « is equal to the two, o n
Fig. 7.
Fig. 8.
and o X. Force o n acts in a direction
perpendicular to vessel's course and that
of o a; is to drive vessel onward.
It can thus be shown that when di-
rection of sail bisects angle m o B, the
effect of o z is greater than when sail is
in uny other position.
Assume wind to be ahead as in direc-
tion of arrows, Fig. 8. Let o m repre-
sent direction and force of wind, and r a
direction of sail ; from o draw o m, and
proceed as before, and 0 u represents the
effective force that acts upon the saiL
o n that which drives her to leeward, and
o X that which drives her on her course.
Vox fall treatlsM ott this aabjoct, see John C. Tniatwlne's Englneer'i PuckeUbook, 1873 ; Ball'* Ez«
?erlv>enUl Mechanic*, L^DdoD, 1871 ; «Qd Pyn»qil«t> C^nitrPCliW of Mftcbinery, «tc, by G, FladM
MBCHANIC^.— MOHSNTS OF STBE3S OK GIRDEBS^STC. 6il
Fig.z.
MOlfEKTS OF STRESS.
To iDeaoribe and Coxxipute Aloments of Stress on Ghird«
era or Seams.
Supported at Both Ends.
Loaded in Centre^ Fig. x. — Assume
A B, a beam. At centre erect W c =
Wi
— . Connect A e nnd e B, and any
vertical dtstance between them and
B A B will give moincut required at that
= M at any point. W rqaresetU-
ing weight or Uxzd^ I length ofvpan^ x horizonUU distance from nearest support at
vihich M, the moment of stress, is required.
Illustratiox. — Assume { = lo feet, W == lo |ba, and as = 3 feet
Then, W c = ^— — ^— = as Vbs. at centre of span ; and ^^ - = 15 ;6s. a< a
Loaded at Any Pointy Fig. 2.—
Proceed as for previous figure.
— ~. — or W c= moonmiiin load.
Fig. 3.
a representing least distance ofWto mppwty
ajnd h greatest distance.
Wxb
I
Wxa
= M between A and W.
riH H between W and B.
iLLusTRATioir.— Take elements as before with a = 3 feet, x 1.5, smA x' 3.5 feet.
Then, W c = '° ^ ^ ^ ^ = 31 Jbi. at point of stress ; ^^ ^ 'l^ ^ ^ = la^ »*. at x
10
10
between A and W, and '°X35X3 ^ ^^ 5 «». a< a; 6<< w«en W ami B.
10
NoTB.— <0 and re' must be taken flrom the pier, which is on the same side of W as
that of the stress desired.
Loaded with Two Equal Weights at Equal Distances from Supports, alike to a
Transverse Girder in a Single Line of JRailuxiy.^Fig. 3.
Fig. 3. c d At point of stress of weights
^ ""^ erect W c and W d, each = W a.
Connect Aed and B, and vertical
- — I distances l)etween them and A B
-^ will give moments required.
7
W
-II .
4. — h--
Yf {l — o)
= War=: Wb = M a<
any point between weights.
%
hoadsd wUK Four Equal Weights, symmetrically hearing from Centre, alike to, a
Transverse Girder in a Double Line of Railway— ¥\g. 4.
Fig. 4. ,. At W and w" erect Wc. and
w"i — 2Vfa, and at w and w'
erect w d, lo' e, each =: W (2 a -f a').
Connect A c d « t and B, and or-
dinates from them to A B will give
-| moments required.
^ W (2 a + o') = M at u> and to';
.ai
%
10'
^
w
w'
3 W a = M at W and w' .
iLLusTiuTioK. — Assumo W oacb
TO Iba 2 feet apart, and 1 10 feet.
nieD, 10 (3 X 3-f 2) = 60 at 10 or w\ and 3 x xo x 2 ^ 40 at W or ui".
^22 MBOHANICS.— MOMBKTS OT STRESS ON GIRDEES, ETa
Fig-S
---"f?
H--
-l-
Loaded at Differ eni Points.— T\g. 5.
Locate three werghta, W, w, and
to', as at a b, a, b,, a, 6,.
Draw A c B, A (2 B, and A « B, ag
three separate cases, by fonnala,
Waft _.
Produce W c until W 0 = W r, W *,
;» and Wc; Wd until wu = wn,w9
^ and u;d, and w' e to to'm in like
manner.
:..fc j^ Connect A q urn, and B, and an or-
^^...J^ dinate tbereA-om, to A B will give
moment ofstress at the poinj, taken.
Fig. 6.
Illustration. —Take a = 2 feet, o, = 4. 0^=6, 6 = 8, 6, = 6, 6a = 4> W, w, and
v» each 10 lbs., and /= 10 feet, carefiilly observing Note to Fig. 2.
Then -i (W&aj + w6, »-f«'63») = M at a>.
Take« = a. Then i.(io X 8 X 2 + 10X 6 x 2 + 10X 4 X 2)=^=36 »t.
10 . 10
»' = 4. ^ (10 X 2 X 6 -I* 10 X 6 X 4 + 10 X 4 X 4) = — = 52 ««.
'" 10
•"«6. ^(ioX2X4+«oX4X4-f ioX4X6) = ^ = 48»#.
*" xo
Loaded with a Rolling Weig^.—
Fig 6.
Define parabola A c B as deter-
Vf I
mined by — = the ordinate at c,
1b and vertical distances between A B
^ will give moments.
Yfx{l — x) „
^ = M at any point
Loaded Unijormbjf ifo MnUre LengOL-^De^na parabola as at Pig 6, ordinate of
which at c = -g- . L representing stationary or dead load per unU of length.
— (l—x) = M (rf any point, and -— = M a< centre.
o
Load^ with Two Connected Weights, moving in either Direction, aWcetoa Locomo-
twe or Car on a Bailway.--Fig. 7.
Define parabola A e B as deter-
mined by "^+""'=.c.
4
At A and B erect A «, B t = to d,
connect At and Be, and yertical
distances between A o B and A c B
will give moments.
f [(W + ta) (I-»)-^ = M
at any point
Position o/W at greatest moment^ when x=-±—:^^ — . Or if Wand to ara
2 2 (W-|-to) "
equal, when x=: -± — .
2 4
iLLusTRATioK.— ABsame «= 3, d = 4, and W to each 10 Ih&, and 2 zo ftet
Then —(10+ 10 x lo— 2 — 10X4) = U at any point, as at W r, tor.
M£CHANIC&.— MOmSNTS OF STRESS ON 6IBDSBS,,ETC. 62$
Sliearing; Stress.
To IDetenxiixie Slieafing Stress at any Fart of a d-irder
or GeanoL and -under any X>lstributioxx .of Xuoad.
Fig. 8.
A
^—^^
^
Required to determine stress of a
beam at any point as c, Fig. 8.
Assume Vs=load between A and
c, and u) that between B and o.
Then 9x at.c = P — W, or F — w.
The greater of the two values to be taken.
S X repruenting shearing stress at any point as, P and P' the reaction on supports
due to total load on beam between supports^ W and v) loads or stress concentrated at
any point
To Describe
and A.so«sFtaln Sliearins Str«s« in at
GMrder or Beam.
Supported or Fixed at Both Ends.
Loaded Uniformly. Fig.^
At A and B, erect A c, B «, each
equal to — . Connect c and e at
a
middle of span as at n, and vertical
distances between A B and cne will
give shearing stresses as determined
by the ordi nates to en e.
{H=
S. Sign of result to
be disregarded. L representing distributed load per unit of length.
Illustration.— Assume L = xo lb& per foot, I = lo, and x = 3.5 fbet.
Then 10 (-- — 2.5 j = 25 ibi.
NoTK— The moment of rupture at any point, prodnoed by several loads acting
simultaneously on a beam, is equal to the sum of the moments produced by the
several loads acting seiMrately.
For other Formulas and Diagrams sec Strains in Girders, by William Humber,
A..1.C.E., London, 1872.
Operation deduced by Cfraphic Delineation of Chreate&l Sfresa^ with a
Uni/wnUy Distributed load of 14 000 X^.-^Fig. la
T\M, xa
Determine mommt of weights by
formulas
Wmii vfrs
and
w ov
I ' t ' I
Assume W = 7ooo lbs., 10 = 4000,
and w' = 3poo, m =: 7 feet, n = 13,
r = 13, *=s7, 0=3, !>=: 17, and l=v>.
Then
^_7oooXi3X7_^
20
31850,
w = ^??^ ^1^ = 18 aoo, and vT = 3«»X3Xi7 _ ^^^^ ^^ ,g^ j^j, ^j^^^^^.
ulars thereto, as 3 d, 2 c, and x h.
Connect d, c, and h with A B, and sum of distances of intersections of these lines
upon perpendiculars, flrom 3, 2, and i respectively, will give stress upon A B at
these pointa
To determine Ortate$t Stress at Greatest Load.
Stress at X bc3 <7 ; 7650 : 5=5 x 350
Stras at 3 d = 31 850
" *' ac=x3 : 18200 : 7= 9800
43000
43000 + l2lll — 4000 X -5 _ j^ j^ 2^^ concentrated load at W, and proportion
20
of uniformly distribated load of 4000 lbs.
1
624 MZCHANICAli POWKBS. — ^LEVEB.
MECHANICAL POWERS.
Mechakical Powkb is a compound of WeigM^ or Force and VdocUy:
it cannot be increased by mechanical means.
21ie Powers are three in number^~-y\z.y Leyer, Incunid Plane, and
Pullet.
Note.— A Wheel and Axle is a continuotu or revolving lever j a Wedge a double in-
dined plane, and a Screw a revolving inclined plane.
LEYEB.
JJevers are straight, bent, cnrved, single, or oompomid.
To Compnte Hiengtli of* a Xjever.
When Weight and Bower are given, Rqle.— Divide weight by power,
and qaotient is leverage, or distance from fulcrum at which power supports
weight,
w
Or, — = jj. W representing weight, P power^ and p distance of power fhmJiUcrum.
ExAMPLB.— A weigbt of 1600 lbs. is to be raised by a power or finrce of 80; re-
quired length of longest arm of lever, shortest being i foot
1600 -i- 80 = -ioftet.
To Compute 'Weigh.t tliat oaix "be raised \yy a Xjever.
When itt Length, Power, and Position of its Fuicrum are given. Rule. —
Multiplv power by its distance from fulcrum, and divide product by dis-
tance of weight from fulcrum.
Pp
Or, -^ = W. w representing distance of weigM from fkdervm.
ExAVPLK.— What weight can be raised by 375 lbs. suspended ftt)m end of a lever
8 feet flrom fulcrum, distance of weight flrom /ulcrum being 2 feet?
375 X 8 -7- 2 = 1500 M>«.
To Compute Position of* IT-uloruxn.
When Weight and Power and Length of Lever are givent and when Ful-
crum ia between Weight and Power, Rule. — Divide weight by power, add
I to quotient, and divide length by sum thus obtained,
/w \
Or, L -r- f jj + I J = w. L representing entire length of lever.
Example. —A weight of 2460 Iba is to be raised with a lever 7 feet long sod a
power of 300; at what p^rt of lever must fUlcrum be placed ?
2460-7-300 = 8.2, and 8.2 + 1 = 9- 2- l^en 7 X ia-i-9-3 = 9.x3<n«i
When Weight is between Fulcrum and Power, Rule. — ^Divide length
by quotient of weight, divided by power. ,
Or,L-5-- = ia
To Compute luength. of A.rrxx of* I^ever to virfaiioli
"Weight is attadied.
When Weight, Power, and Length of Arm of Lever to which Power is op-
plied are given. Rule. — Multiply power by length of arm to which it is
applied, and divide product by weight
MECHANICAL POWBBS. — LBYSB.
625
Erucpuc— A weight of 1600 lb&, suspended firom a lever, is supported by a power
of 80, applied at other end of arm, 20 feet in length ; what is length of arm ?
80 X 20-4- 1600 = I fool.
Note. — ^Theae rules apply equally Whenfvlcrwm. (or WLpporVs of lever is bettoeen
weight and power ;* when fiUcrum is at one extremity of levers and power, or weight,
at Uie oitier ;t and when anm of lever are eqiuUiy or uneqtuiUy bent or curved.
To Compute Po'wer Reqiaired. to Raise a given "Weiglxt.
When Length of Lever and Position of Fulcrum are given. Rule. — Mul-
tiply weight to be raised by its distance from fulcrum, and divide product
by distance of power from fulcrum.
^ Ww „
Or, = P.
P
ExAMPLB length of a lever is 10 feet, weight to be raised is 3000 lb&, and its
distance from fhlcrum is 2 feet; what is power required?
3000 X 2 6000 ,-
10
8
To Compute I^ength. of Anaa. of* Lever to "wliicli Fo'wrer
is applied.
When Weighty Poicer^ and Distance of Fulcrum are given, Rulk. — Mul-
tiply weight by its distance from fulcrum, and divide product by power.
Or, -p- =j).
Example.
Fig. I
-A weight of ^00 lbs., suspended 15 ins. flrom fUlcrum, is supported by
a power of 50, applied at other; what is length of the arm ?
400 X 15 -^ 50= 120 ins.
When A rma of a Lever are bent or curved^
Distances taken from perpendiculars, drawn
from lines of direction of weight and power,
must be measured on a line running horizon-
tally through fulcrum, as a 6 c, Figs, i and 2.
When Arms of a Lever are at Right Angles,
and Power and Weight are applied at a Right
Angle
Fig._ 3
to each other.
The moments
_ are computed directly aa ab to be.
Thrust, or presB^
' »' - ure on fulcrum,
is in this case less
than sum of pow-
er and weight;
and it may be
determined bv
drawing a paral-
lelogram upon
the two lurms of
O/^ lever, arms repre-
_ ^senting inverse-
ly theif respec-
tive forces. That is^ab represents magnitiide and dbection of weight W,
and 6 c of power P. Diagonal 0 6 of parallelogram represents magnitude
and direction of third force, or thrust upon fulcrum.
* Pwnrt apon ftilcrbm !■ eqoAl to sam of weight and power,
t Pmnare apon ftilcram it eqiwl to diifereuce of weiglit tnd power
1 G
626 MECHANICAL POWEBS. — ^LBTEB. — WHEEL.
Fig. 4.
When seme Lever is borne into an Oblime
Position, Potcer continuing to act HorizofUwly^
lEjP Fig. 4, Draw ^-^rtical a v through end o of
lever, and produce the power line |> c to meet
it at a. Complete parallelogram avhr; then
sides r h and 0 v are perpendiculars to direc-
tions to power and weight, on which moments
are computed.
Consequently, moment P x r ft = moment
W X 6 t^, and a diagonal, b a, is resultant thrust
at fulcrum.
O
Fig. 5.
0 —
When Powei' does not act Horizon-
tally, Fig. 5, but in some other direc-
tion, a p, produce the power - line p a
and draw 0 c perpendicular to it ; dra^
p b o, then moments are computed on
perpendiculars be, bo, and P x c 6 =
Wxbo.
If several weights or powers act
upon one or both ends of a lever, cou-
/^ dition of equilibrium is
^ Vp + P'p' + P"p ", etc, = W w H-
W to', etc.
In a system of levers, /Bither of similar, compound, or mixed
kinds, condition is Ppp* p'
w w w'
= W.
Illustration.— Let P= i lb, p and p' each 10 feet, p" i foot; and if to and w'
be eacb i foot, and w" i inch, then
= laoo; that is, x lb. will support laoo, with levers
I X I20 X 120 X 12 _ 172800
12 x 12 X 1 ~ 144
of the lengths above given.
NotE.— Weights of levers in above formulas are not considered, centre of gravity
being assumed to be over flilcruus.
General Rule, therefore, for ascertaining relation of Power to
VVeigiit in a lever, whether straight or curved, is. Pmcer multiplied by its
distance from fulcrum is equal to weight multiplied by its distance from
fulcrum. Or,P:W::M;:p,orPp = Ww; and
P to
Wto
3- -T5-=l'-
4. ^=«^
WHEEL AND AXLE.
A. "Wheel and Axle is a revolving lever.
Power, multiplied by radius of wheel, is equal to weight, multiplied by
radius of axle.
As radius of wheel is to radius of axle, so is efD^ct to power.
Or,PR = Wr. Or,PV = Wt>. Or, B : r :: W : P. Or.P^saW; ?^=r{
- = R. R and r representing radii, and V and v velociHes 0/ wheel and aaUe,
HBCHAKICAL POWERS.— WHEEL AXD AXLE. 627
When a series of wheels and axles act upon each other, either bv belts or
teeth, weiji^ht or velocity will be to power or unity as product of radii, or
circumferences of wheeb. to product of radii, or circumferences of axles.
«
I1X.U8TRATION.— If radii of a series of wheels are 9, 6, 9, zo, and la, and their pin-
ions have each a radius of 6 ins., and power applied is to lbs., what weight will
they raise?
10 X 9 X 6 X 9 X 10 X 12 583 200 _
6X6X6X6X6 7776 '^
Or, if zst wheel make 10 revolutions, last will make 75 in same time.
To CoxnpYite I»ower of* a Cozn'binatioii of "Wlieels and an
.A.xle or ^xles, as in OrancM, etc.
Rule. — Divide product of driven teeth by product of drivers, and quo-
tient is their relative velocity ; which, multiplied by len^h of lever or arm
and power applied to it in pounds, and divided by radius of barrel, will give
weight that can be raised.
Or. = W; Or, W r = w J P; Or, — =- = P, I repretenting length of leoer or
arm^ r radnu ofbarrd^ F power j v velocity^ and W voei^
ExAMPLK I.— A power of 18 lbs. is applied to lever or winch of a crane, length of
it being 8 ins., pinion having 6 teeth, driving-wheel 72, and barrel 6 in& diameter.
^ = 12, and 12X8X18 = 1728, which, -r- 3, raditu ofbarrd, = 576 lbs.
6
2.— A weight of 94 tons is to be raised 360 feet in 15 minutes, by a power, velocity
of which is 220 feet per minute; what is power required?
jl£K>-^xs=z2^futperminuie. Hence —^ — ^=10.2545 fotu.
220
Coxapouiid. .Ajcle, or Cliizxese "Windlass.
Axle or drum of windlass consists of two parts, diameter of one
being less than that of the other.
The operation is thus : At a revolution of axle or drum, a portion of sus-
taininii^ rope or chain equal to -circumference of larger axle ih wound up, and
at same time a portion equal to circumference of lesser axle is unwound.
Effect, Uierefore, is to wind up or shorten rope or chain, by which a weight
or stress is borne, by a length equal to difference between circumferences of
the two axles. Consequently, half that portion of the rope or chain will be
shortened by half difference oetween circumferences.
rFo Compute Slexnents of a \^lipel and Compound
AjLie^ or dxinese AViiidlasH.^^ITi^. 6.
Bulk. — Multiply power by radius of wheel, arm, or pig. 6.
bar to which it is applied, and divide product by half
difference of radii of axle, and quotient is weight that ^\
can be sustained. ^
P R
Or, 7: = W. R representing radius of wftedy etc, and r and r'
radii of axle ai its greatest and least diameters. L^""^
EZAMFLB.— What weight can be raised by a capstan, radius of its bar, a,
5 tMi, power applied 50 Iba, and radii, r r', of axle or drum 6 and 5 ins. ?
O
S£2<.5Xia^3ooo
.5(6-^5) .5 W
^
628 MECHANICAL POWEBS, — IKCLIKED PLANE.
"Wlieel and Pinion Com'binations, or Complex
"Wheel- work.
Power, multiplied by product of radii or circumferences, or number of
teeth of wheels, is equal to weight, multiplied by product of radii or circum-
ferences, or number of teeth or leaves of pinions.
Or, P R R' R", etc., = W r r' r", etc.
Note. — Cogs on face of wheel are termed teeth, and those on surface of axle are
termed leaves; the axle itself in this case is termed & pinion.
m
I^ack and. Pinion.
To Compute Fo^^ver of a Rraok and Pinion.
Rur.E. — Multiply weight to be sustained by quotient of radius of pinion,
divided by radius of crank, and product is power required.
Or,W^ = P.
When Pinion on Crank Axle communiccUes with a Wheel and Pinion.
Rule. — Multiply weight to be sustained by quotient of product of radii of
pinions, divided by radii of crank and wheel, and product is power required.
rr'
ExAMPLK. — If radii of pinions of a Jack-screw are each one inch; of crank and
wheel lo and 5 ins. ; what power will sustain a weight of 750 lbs. ?
^1X1 750 ,.
750 X — TT- = ^^ = 15 Ws.
10X5 50
mCLINED PLANE.
To Compute Length of* IBase, Heiglxt, or Uengtli.
When any Two of them are given, and when Line of Direction of Power
or Traction is Parallel to Face of Plane. — Proceed as ih Mensuration or
Trigonometry to determine side of a right-angled triangle, any two of three
being given.
To Compute Power necessary to Support a Weight on
an Inclined Plane.
When Height and Length are given. Rule. — Multiply weight by height
of plane, and divide product by length.
Or, — T— = P. h and I representing height and length of plane.
Example.— What is power necessary to support xo(x> lbs. on an inclined plane
4 feet in height and 6 feet in length?
1000 X 4 -i- 6 = 666.67 M>«.
Xo Compute "^Veiglit that may he Sustained, hy a given
Po-wer on an Inclined. Plane.
When Height and Length of Plane are given. Rule. — Multiply -power
by lengtli of plane, and divide product by height.
Or,- = W.
Example. —What is weight that can be sustained on an inclined plane 5 feet jn
height and 7 feet in length by a power of 700 lbs. ?
700 X 7 -J- 5 = 980 lbs.
KoTK.— In estimating power required to overcome resistance of a body being
drawn up or supported upon an inclined plane, and contrariwise, if body is de-
scending; weight of body, in proportion of power of plane (t. «., as its length to its
height), must be added to resi^awXy if being drawn up or supported, or to the mo-
ment if descending.
MECHANICAL POWERS. — INCLINED PLANE. 629
Xo Compute Heiglit or I^ength, of* an Inolixiecl Plane.
When Weight uml Po\oer and one nf required Elements are f/iven, and
when Height is i^equired. Rule. — Multiply power by length, and divide
product by weight.
When Length is reqiw-ed. Rule,— Multiply weight by height, and divide
product by power.
Or, ^ = A, and -p-='.
To Comptite Pressure on an Inclined Plane. -
Rule.— Multiply weight by length of base of plane, and divide product
by lengtii of face.
W b
Or, — — = pressure, b representing length of bcise of plane.
EZAMPLK. — Weight on an inclhied plane Is 100 lbs., b»se of plane is 4 feet, and
length of it 5 ; required pressare on plane.
xoo X 4 -^ 5 = 80 »#.
When Two Bodies on Ttoo Inclined Planes sustain each ot/tevy as by Connection
of a Cord over a Pulley^ their Weights are directly as Lengt/is of Planes.
Illustration. — If a weight of 50 lbs. upon an inclined plane, of 10 feet rise in 100
of an inclination, is sustained by a weight on another plane of 10 feet rise in 90,
what is the weight ortbe latter?
xoo : 90 :: 50 : 45 = toeigfU that on shortest plane would sustain thai on largest.
When a Body is Simported by Two Planes, as Fig. 7, pressure upon them
Pjg _ will be reciprocally as sines of inclinations of planes.
^1^ . D Thus, weight is as sin. A B D.
A 1^ ^^^^/ Pressure on A B as sin. D B i.
PNy^BHP^ Pressure on B D as sin. AB h.
I ^X!^/ Assume angle A B D to be 90° and D B f, 60°; then angle
i B i ^^^ ^'** ^ 3°**» ^^^ ^ ^'°®^ ^^ 9°°' ^°' ^^^ 3°*^ *'® respec-
tively .1, .866, and .5, if weights 100 lbs., then pressures on
A B and B D will be 86.6 and 50 lb&, centre of gravity of weight assumed to be in its
centre.
When Line of Direction of Power is parallel to Base of Plane^ power is
to weight as height of plane to length of its base.
Or,P: W::A2 6.
H»cP=!L"; w=^, »=^; »=!;*.
When Zine of Direction if Power is neither paraUel to Face of Plane nor
to its Base, but in some other Direction, as P, Fig. 8, power is to weight as
sine of angle of phine's elevation to cosine of angle wliich line of power or
traction describes with face of plane.
Fig. a 9\ Thus,P': W::sln. Arcos.P'ec
P* Sin. Arcos. Fee::?*: W.
o CoB.P'ecrsin. A::W: P*.
Illustration.— A weight of 500 lbs. is required to be
sustained on a plane, angle of elevation of which,
c A B, is 10°; line of direction of i)ower or traction,
A n B P' e c, is 50 ; what is sustaining {tower required r
Cos. P* « c (5°) = .996 19 ; sin. A (iqO) = .173 65 :: 500 : 87. 16 lbs.
Or, draw a line, B *, perpendicular to direction of power's action from end
of base line (at back of phine), and intersection, of this line on length, A &
will determine length and height (n r) of the plane.
3G«
632 MECHANICAL POWERS. — SCBEWS. — PULLEY.
Difierexxtial Sove^v.
When a hollow screw revolves upon one of less diameter aqid pitch (as
designed by Mr. Hunter), effect is same as that of a single screw, in which
the distance between threads ^s equal to difference of distances between
threads of the two screws.
Therefore power, to effect or weight sustained, is as difference between
distances of threads of the two screws to circumference described by power.
Illustration. — If external screw has ao threads, and internal one at threads in
pitch of I inch, and power applied describes a circumference of 35 ina, the result or
Hence —^^=14706.
power is as — 00 — = — ,or 00238.
2x 20 420
.00238
PULLEY.
Pullets are designated as Fixed and MovaHe, according as cord is passed
over a fixed or a movable pulley. A movable pulley is when cord passes
through a second pulley or block in suspension ; a single movable pufl^ is
tsi^med a runnet*; and a combination of pulleys is termed a tgttem cfpuueyt.
A Whip is a single cord over a fixed pulley.
To Compute I*ower Required to Raise a given WeigHt,
When Number of Parts of Cord supporting Ijoirer Block are ffiven, and
when oidy one Cord or Hope is used. Kulk. — Divide weight to be raised by
number of parts of cord supporting lower or movable block.
Or, W -i- n = P. Or, n P = W. n representing mmber of parts of cord suOain
-Mg lower block.
Example.— What power is reqaired to raise 600 lbs. when lower bl6ck contains
jix sheaves ?
600
6x2
When Cord is aUaehed to Upper or Fixed Block,
= 50 lbs. = weight -7- number of parts of rope sustaining lower blode.
600
6X2 + 1
When Cord it attached to Lower or Movable Block,
1 46. Z5 lbs, = weight -r number qf parts qf Trope sustaining lower bloek,
To Compute 'Welglit a given Po'wer "will Raise.
When Nunyber of Parts of Cord supporting Lower Block are given. Rule.
— Multiply power by number of parts of cord supporting lower block.
Or, P n = W.
To Compute Number of Cords necessary to Sustain
I^o'%v-er Block.
When Weight and Power are given. Rule. — Divide weight by power.
Or,W-J-P=n.
When more than one Cord is used.
In a Spanish Burton^ Fig. 10, where ends of
one cord, a P, are fastened to support and power,
and ends of the other, c o, to lower and upper
blocks, weight is to power as 4 to i.
In another, Fi^. 11, where there are two cords,
a and 0, two movable pulleys, and one fixed
pulley, with ends of one rope fastened to sup-
port and upper movable pulley, and ends of
other fastened to bwer Uock «nd power, weight
is to power as 5 to i.
rH^ii.
Hechanical powkes. — pcllky.
633
}r. Hulttply power eucceealvel]
KiiurLB [.— irbBtneigblKill
ihroe niovabie pulleys, ihB cci
1, flicil block b«
men fired Ihtllei/i, e e. are used in Place
0/ Hoots, to Allach Endt of Rope to Sup-
W port— Fig. 14.
W*3«=P; 3"XP = W; W-:-P=3''. 9
WhenEadiofOrdoiFiiiiedPuUtyaTrfattejitdlo Weiijlu^aaby aa Inver-
HDB Of tie last Figwei, pall lug Support! for ^Veighrl, and con/rarivriic, —
Figs. 13 and 14.
Flg-.j. "— = P; (a"~i)P = W; ^ = lJ•_I^
Flg.,4. jj^^=P; (3»_,|P=W; ^=(3--,^
lurSTBiTiox.— Wbal welgbt »iU a po«er of 1 lb. BusUln In a syfllr^m on wo mat-
WAtii (hrdi lUilainUg Pullegi are not in a Vertical Diiteli'on.—Fi
F.g n, (o.Flp 15,1a ventcal line Ihrough whicb weight be
' D draw D r, 0 1 parallel tn D « ami A a
'▼f i portioDB. Hence Ihewpighl Kill always full inlQlbepoBii!oa
I W ID wbleh ihB mo pana of cnril A < anil e D will be equally
'X P IndlaMl lo gertlcal line, and It will bear lo power ume rain
of conl, U polBl of nupenBton ot wi
coa. .je : I. t repreiaUine anete Ar D.
Thai la. iwica p«wer, maUiplied bf coiiD* of batf angle
1 f~.i.i.. i- equal to weigh!.
634
METALS. — ALLOYS AND COMPOSITIONS.
Illustbatioh.— Wbal weight will be suBtained by a power of 5 lbs., with an ob-
lique movable pulley, Fig. 15, having an angle, A e D, of ;^^ ?
5 X 2 X .965 93 = 9-6593 lbs. = twice power X cos. 15°.
When Direction of Cord is Irregular^ Weight not resting in Centre of it.
W
sin. a
Psin (a-f-6)
sin. (a 4- ^) ' sin- a
greater and U$ter cmglu of cord at e.
= W;
W sin. a
sin. (a -f 6)
= P a and b representing
METALS.
ALLOYS AND COMPOSITIONS.
Alloy is the proportion of a baser inetal mixed with a finer or purer,
as copper is mixed with gold, etc.
A.xxialgazxi is a compound of Mercury and a metal — a soft alloy.
Compositions of copper contract in admixture, and all Amalgams ex-
pand.
In manufacture of Alloys and Compositions, the less fusible metais
should be melted first.
In Compositions of Brass, as proportion of Zinc is increased, so is
malleability decreased.
Tenacity of Brass is impaired by addition of Lead or Tin.
Steel alloyed with one five-hundredth part of Platinum, or Silrer, is
rendered harder, more malleable, and better adapted for cutting instru-
ments.
Specific gravity of al toys'** does not follow the ratios of those of their
components ; it is sometimes greater and sometimes less than the mean.
Coin position fbr 'Welding* Oast Steel.
Borax, 91 parts-, Sal ammoniac, 9 parts. Grind or pound them roughly together;
Aise them in a metal-pot over a clear fire, continuing heat until all spume has dis-
appeared fVom surface. When liquid is clear, pour composition out to cool and con-
crete, and grind to a fine powder; then it is ready for use.
To use this composition, the steel to be welded should be raised to a bright yellow
heat; then dip it in the welding powder, and again raise it to a like heat as before;
it is then ready to be submitted to the hammer.
F'usible Compotincls.
COMFOUNDB.
Rose's, fusing at 200^
Fusing at less than 200^
Newton's, fusing at less than 312°.
Fusing at 150° to 160°
Zinc.
Tin.
LMd.
Biamuth.
—
as
as
SO
33-3
—
33-3
33-4
—
^9
3»
50
—
12
25
50
Cadmiam.
13
Solders.
Solder is an alloy used to make joints between metals, and it must be
more fusible than the metals it is designed to imite, and it is distinguished
as hard and soft, according to the temperature of its fusing.
The addition of a small portion of Bismuth increases its fusibility.
* For ■ tabl« of Alloys, hsTing drailtlM diffvreot from • mMD of tholr eompoa«iU» ••• D. K. Cfaurk^
niud, London, 1877, pMge 20X.
MKTALS. — ALLOTS AKD COMPOSITIONS.
635
Alloys and Compositions.
Aiigentan
AlumiDum, brown
Babbitt's meUl*.
BrasB, common. . .
4i
li
H
«t
«t
u
•I
u
u
u
M
t«
t(
4(
*' hard, . . . .
instruments
locomot. bearings.
Pinchbeck
red Tombac
rolled
Tutenag
very tenacious...
wheels, ralves....
white
it
wire
yellow, fine ......
Britannia metal
Wb«n rated add ......
Bronze, red.
4» ^ ^
yellow
Gan metal, large
** small
*' soft.
Cymbals ,.
Medals
Statuary
Chinese silver
** white cop|)er...
Church bells
M
««
•i
«(
U
({
I(
Clocks, Miisicia beUs. . . .
Cloi^k bells
German silver
i(
" fine
Gongs
House bells.
Lathe bashes
Machinery bearings
hard.
Metal that etpands in)
cooling 5
Mantz metal
Pewter, best..
Sheathing mcUil
Speculum "
it (t
^^ • . . . . . •
Telescopic mirrors
Temper t.
Type metal and stereo- i
typeplatea j
White metal
" *' hard
Orefde
Copperi
55
95
3-
84.
75
79-
92.
88.8
74-3
50
88.9
90
10
3
7
67
66
87
86
67.2
90
93
95
80
93
91.4
58.1
40.4
80
^7-5
72
33-3
40.4
49-5
81.6
77
80
87-5
77-4
60
56
66
50
66.6
33.4
41
73
Zinc
24
5-8
25
6^4
I
20
II. 2
22.3
31
3.8
80"
90
33
34
13
II.X
31.2
55
17.9
25-4
5.6
33-4
aS-4
34
40
45
ax
7-4
25. »
xa.3
Tin.
89
las
143
7-8
9
3-4
10
10
25
1.6
xo
7
5
20
7
1-4
2.6
tax
31
X2.S
26.5
18.4
93
ao
15.6
86
80
92
29
33-4
66.6
Nickel.
21
4-4
(Mai
IISaF
»9
Lead.
46
tx.6
31.6
33-3
V-6
24
28.4 —
Anti-
mony.
7-3
7
47
25
25
Bie-
moUu
Ala-
minam.
25
«-7
4-3
75
90
75
87-5
16.7
«4
CO
2
0
g
s
8.3
Magnesia
SaHunmoniac
4-4
2-5
25
12-5
56.8
Cream of tartar .6.5
Quicklime..... .x.?
ri.x
g
«-5
9.6
X9 '
• 8w page 636 for dlractiou.
i For addiag ma$H qutntitiee of ooppw.
636
MJiTALS. — ALLOTS AND COMPOSITIOKS.
Copper.
Tin.
Solders
L«ad. Zinc.
>
Silver.
Bis-
naath.
Gold.
Cad-
miam.
Anti-
mony.
rill
•
65
13
50
47
4
20
12
66
S3
25
58
33
67
33
33
50
33
25
67
50
25
66
40
47
11
67
33
6^
45
25
67
75
33
50
25
34
20
SO
35
5
50
47
34
33
82
6
7
80
67
16
22
25
40
89
Mi 1 1 1 1 1 1 1 1 1 1 i II M 1 1 1 St 1 1
<( •
Ytf^
" coarse, melts )
at 5000 . . . j
" ordi'y, melts)
at 360°.. . )
Spelter, soft
♦' hard
T^ad
♦
Steel
Brass or Copper.. .
Fine brass
Pewterers' or Soft.
•
Plumbers' pot- )
metal.. )
" coarse . . .
" fine
" fUslble...
" very " ...
Gold
—
" hard
" soft
—
Silver, hard
" soft
Pewter
—
Iron
Copper
t
A Plastic Metallic AUoy. — See Journal of Franklin Institute, vol. xxtix., page 55,
for its composition and manufacture.
Soldering Fluid for use with Soft Solder.
To 2 fluid oz. of Muriatic acid add small pieces of Zinc until bubbles cease to riM.
Add . 5 a teaspoonfbl of Sal-ammoniac and two fluid oz. of Water.
By the application of this to Iron or Steel, they may be soldered without their sar-
fluses being previously tinned.
Muxes for Soldering or Welding.
Iron Borax.
Tinned iron Resin.
Copper and Brass Sal-ammoniac.
Zinc Chloride of zinc.
Lead Tallow or resin.
Lead and tin Resin and sweet oil.
Sab'bitt's ^iiti -attrition IVIetal.
Molt 4 lbs. copper : add 12 lbs. Banca tin, 8 lbs. Regulus of antimony, and 12
lbs. more of Tin. After 4 or 5 lbs. Tin have been adde^i reduce heat to a dull
red, then add remainder of metal as above.
Tbis composition is termed hardening ; for lining, melt i lb. of this hardening
with 2 lbs. tin, which produces the lining metal for use.
As this metal was introduced in 1839, it is now maintained by engineers that
the increased weight of machines and the velocity of engines and dynamos
require an appropriate alloy ; and it is claimed by engineers that Phoenix Metal
meets existing requirements.
I3ra8s.
Brass is an alloy of copper and zinc, in proportions varying with purpose
of metal required, its color dependinp^ upon the proportions.
It is rendered brittle by continued impacts ; more malleable than cop]>er
when cold, but is impracticable of being forged, as its zinc melts at a low
temiterature. Its fusibility is governed by the proportion of zinc in it; a
mail quantity of phosphorus gives it fluidity.
METALS. — ALLOYS AND COMPOSITIONS. — lEON. 637
Bronze.
Bronze is an alloy of copper and tin ; it is harder, more fusible, and
stronger than copper. It is usually known as Gun-metal.
Aluminum Bronze contains 90 to 95 per cent, of copper, and 5 to 10 per
cent, alarainum.
Phosphor Bronze contains copper and tin and a small proportion of phos-
phorus. It wears better than bronze.
IRON.
Foreign substances which iron contains modify its essential proper-
ties. Carbon add^to its hardness, but destroys some of its qualities,
and produces Cast Iron or Steel, according to proportion it contains.
Thus, .25 per cent, renders it malleable, .5 steel, 1.75 is limit of weld-
ing steel, and 2 is lowest limit of cast iron. Sulphur renders it fusible,
difficult to weld, and brittle when heated, or ** hot short." F/imphoj'us
renders it " cold shoi't^''^ but may be present in proportion of .002 to
.003, without aflFecting injuriously its tenacity. Antimony^ Arsenic^ and
Copper have same effect as sulphur, the last in a greater degree. Sili-
con renders it hard and brittle. Manganese^ in proportion of .02, ren-
ders it " cold sJiort^" and Vanadium adds to its ductility.
Cast Iron-
Process of making Cast Iron depends much updh description of fuel used ;
whether charcoal, coke, bituminous, or anthracite coals. A larger yield from
same furnace, and a great economy in fuel, are ^fected by use of a hot blast.
The greater heat thus produced causes the iron to combine with a larger
percentage of foreign e^ubatances.
Cast Iron for purposes requiring great strength should be smelted with
a cold blcuf. Pig-iron, according to proportion of carbon which it contains,
is divided into Foundry Iron and Forge Iron, latter adapted only to conver-
Bion into malleable iron ; while former, containing largest proportion of car-
boDf can be used either for castings or bars.
High temperatnre in melting injures gun-metal.
There are many varieties of Cast Iron, differing hj almost insensible
shades; the two principal divisions are gray and white, so termed from
color of their fracture. ITieir properties are very different.
Gray Iron is softer and less brittle than white ; it is in a slight degree
malleable and flexible, and is insonorous ; it can easily be drilled or turned,
and does not resist the file. It has a brilliant fracture, of a gray, or some-
times a bluish-gray, color; color is lighter as grain becomes closer, and its
hardness increases. It melts at a lower heat than white, and preserves its
fluidity longer. Color of the fluid metal is red, and deeper in proportion as
the heat is lower ; it does not. adhere to the ladle ; it fills molds well, con-
tracts less, and coptains fewer cavities than white ; edges of its castings
are sharp, and surfaces smooth and convex. It is used for machinery and
ordnance where the pieces are to be bored or fitted. Its tenacity and specific
gravity are diminished by annealing.
White Iron is vety brittle and sonorous ; it resists file and chisel, and is
susceptible of high polish ; surface of its castings is concave; fracture pre-
sents a silvery appearance, generally fine grained and compact, sometimes
radiating or lamellar. When melted it is white, throws off a great number
of sparks, and its qualities are the reverse of those of gray iron ; it is tbere^
fore unsuitable for machinery purposes. Its tenacity is increaaed, and its
specific gravity diminished^ by annealing.
^ H
638
METALS. — ^IBON.
Mottled Iron is a mixture of white and ^ay ; it has a spotted appear-
ance ; flows well, and with few sparks ; its castings have a plane surface,
with edges slightly rounded. It is suitable for shot, shells, etc. A fine mot-
tled is only kind suitable for castings which require great strength. The
kind of mottle will depend much upon volume of the casting. A medium-
sized grain, bright gray color, fracture sharp to touch, and a dose, compact
texture, indicate a good quality of iron. A grain either very large or very
small, a dull, earthy aspect, loose texture, dissimilar crystals mixed together,
indicate an inferior quality.
Besides these general divisions, the different varieties of pig-iron are more
particularly distinguished by numbers, according to their rektive hardness.
No. I. — Fracture dark gray, crystals large and highly lustrous, alike to
new surface of lead. It is the softest iron, possessing in highest degree the
qualities belonging to gray iron ; it has not much strength, but on account
of its fluidity when melted, and of its mixing advantageously with scrap
iron and with the harder kinds of cast iron, it is of great use to a foundry.
No. a is harder, closer grained, and strongs than No. i ; it has a gray
color and considerable lustre. It is most suitable for shot and shells.
No. 3 is harder than No. 2. Fracture white, crystals lar^r and brighter
at centre than at the sides ; color gray, but inclining to white ; has consid-
erable strength, but is principaUy usea for mixing with other kinds of iron
and for large castings.
No. 4 or Bright. — Fracture light gray, with small crystals and little lustre,
and not being suificieutlyfusible for castings It is used for conversion to
wrought iron.
No. 5. Mottled. — Fractare dull white, with gray specks, and a line of
white around edge or sides of fracture.
No. 6. White. — Fracture white, with little lustre, granulated with radiat-
ing crystalline surface. It is hardest and most brittle of all descriptions,
and is unfit for use unless mixed with other grades, or for being converted
to an inferior wrought iron.
Qualities of these descriptions depend upon proportion of carbon, and upon
state in which it exists in the metal ; in darker kinds of iron, where propor-
tion is sometimes 7 per cent., it exists partly in state of grapliite or plumbago,
which makes the iron soft. In white iron the carbon is thoroughly com-
bined with the metal, as in steel.
Cast iron frequently retains a portion of foreign ingredients from the ore,
such as earths or oxides of other metals, and sometimes sulphur and phos-
phorus, which .are all injurious to its quality.
Foreign substances, and also a portion of the carbon, are separated bj*
melting iron in contact with air, and soft iron is thus rendered harder and
stronger. Effect of remelting varies with nature of the iron and character
of ore from which it has been extracted ; that from hard ores, such as mag-
netic oxides, undergoes less alteration than that from hematites, the latter
being sometimes changed from No. i to tchite by a single remelting in an
air furnace.
Color and ^exture of cast iron depend greatly upon volume of casting and
rapidity of its cooling ; a small casting, which oools quickly, is almost always
wAiVe, and surface of large castings partakes more of the qualities of white
metal than the interior.
All cast iron expands at moment of becoming liquid, and contracts in cool-
ing ; gray iron expands more and contracts less than other iron.
Remelting iron improves its tenacity : thus, a mean of 14 cases for two
fusions gave, for ist fusion, a tenacity of 29284 lbs. ; for 2d fu!«ion, 33790
lb9. For two cases— for first fusion, i<s 129 lbs. ; for 9d fusion, 35 786 lbs*
MBTALS. — IBON. 639
AdCallea'ble CBBtings.
Halleable cast iron is made by subjecting a casting to a process of anneal-
ing, by enclosing it in a box with hematite iron ore or black oxide of iron,
and maintaining it in an equable heat for a period depending upon form and
volume of casting.
^W'roiogh.t Iron.
Wrought iron is made from pig-iron in a Bloomei'y Fire or in a Puddling
Furnace — generally in latter. Process consists in nieltmg and keeping it
exposed to a great heat, constantly stirring the mass, bringing every part of
it under action of the flame until it loses its remaining carbon, when it be-
comes malleable iron. When, however, it is desired to obtain iron of best
quality, pig-iron should be rejined.
Refining. — This operation deprives iron of a considerable portion of its
carbon ; it is effected in a Blast Furnace^ where iron is melted by means of
charcoal or coke, and exposed for some time to action of a great heat ; the
metal is then run into a cast-iron mold, b^^^ which it is formed into a large
broad plate. As soon as surface of plate is chilled, cold water is poured on
to render it brittle.
A Bloomtrg resembles a large forge fire, where charcoal and a strong blast
are used ; and the refined metal or pig-iron, after beuig broken into pieces of
proper size, is placed before the blast, directly in ccmtact with charcoal ; as
the metal fosea, it falla into a cavity left for that purpose below ^ blast,
where the ^* bloomer " works it into the shape of a haU^ which he places again
before the blast, with fresh charcoal ; this operation is generally again re-
peated, when ball is ready for the ** sbingler.
Shingling is performed in a strong squeezer or under a trip-hammer. Its
object is to press out as perfectly as practicable the liquid cinder which a
ball contains ; it also forms a ball into shape for the puddle rolls. A heavy
hammer, weighing from 6 to 7 tons, effects this object most thoroughly, but
not so cheaply as the squeezer. A ball receives from 15 to 20 blows of a
hammer, being turnexi from time to time as required : it is now termed a
Bloom, and is ready to be rolled or hammered ; or a ball is passed once
thrimgh the squeezer, and is still hot enough to be passed through the puddle
rolls.
A Puddling Furnace is a reverberatory furnace, where flame of bituminous
coal is brought to act directly upon the melted metal. The " puddler " then
stirs it, exposing each portion in turn to action of flame, and continues this
as long as he is able to work it. When it has lost its fluidity, he forms it into
balls, weighing from 80 to 100 lbs., which are then passed to the "shingler."
Puddle Rolls. — By passing through different grooves in these rolls, a
bloom is reduced to a nmgh bar from 3 to 4 feet in length, its term convey-
ing an idea of its condition, which is rough and imperfect.
Piling. — To prepare rough bars for this operation, thev are cut, by a pair
of shears^ into sucn lengths as are best adapted to the volume of finished bar
required ; the sheared bars are then piled one over the other, according to
volame required, when pile is ready for bailiff.
Balling. — This operation is performed in balling furnace, which is similar
to puddling furnace, except that its bottom or hearth is made up, from tiute
to tinoe, with sand ; it is used to give a welding heat to piles to prepare
them for rolling.
Finishing Rolls. — The batts are passed successively between rollers of va-
rious forms and dimensions, according to shape of finished bar required.
QftaUlg of iron depends upon description of pig-iron used, skill of the
** puddler,*' and absence of deleterious substances in the furnace.
640
METALS. — IRON. — 1.ELD. — Simah.
Strongest cast irons do not produce strongest malleable iron.
For many purposes, such as sheets for tinning, best boiler-plates, and bars
for converting into steel, chmH:oal iron is used exclusively ; and, generally,
this kind of iron is to be relied upon, for strength and toughness, with greater
contidence than any other, though iron of a superior quality is made from
pigs made with other fuel, and with a hot blast. Iron for gun-barrels has
been lately made from anthracite hot-blast pigS.
Iron is improved in quality by judicious working, reheating, hammering,
or rolling : other things being equal, best iron is that which has been wrought
the most.
Best quality of iron has greatest elasticity.
Tests. — It will not blacken if exposed to nitric acid. Long silky fibres in
a fracture denote a soft and strong metal ; short Mack fibres denote a badly
refined metal, and a fine grain denotes hardness and condition known as
" cold short." Coarse grain with bright and crystallized fracture, with dis-
colored spots, also denotes " cold short " and brittle metal, working easily and
welding well. Cracks upon edges of a bar, etc,, indicate " hot short." Good
iron heats readily, is worked easily, and throws off' but few sparks.
A high breaking strain may not be conclusive as to quality, as it may be
due to a hard, elastic metal, or a low one may be due to great softness.
When iron is fractured suddenly, a crystalline surface is produced, and
when gradually, a fibrous one. Breaking strain of iron is increased by heat-
ing it and suddenly cooling it in water. Iron exposed to a welding or white
heat and not reduced by hammering or rolling is weakened.
Specific gravity of iron is a good indication of its quality, as it indicates
very correctly its relative degree of strength.
LEAD.
Sheet Lead is either Cast or MiUed^ the former in sheets 16 to 18 feet in
length and 6 feet in width ; the latter is rolled, is thinner than the former,
is more uniform in its thickness, and is made into sheets 25 to 35 feet in
length, and from 6 to 7.5 feet in width.
Soft or Rain Water, when aerated, Silt of rivers. Vegetable matter, Acids,
Mortar, and Vitiated Air will oxidize lead. The waters which act with
greatest eff'ect on it are the purest and most highly oxygenated, also nitrites,
nitrates, and chlorides, and those which act with least effect are such as con-
tain carbonate and phosphate of lime.
Coating of Pipes^ except with substances insoluble in water, as Bitumen
and SuliJhide of lead, is objectionable.
Lead-encased Pipes. — An inner pipe of tin is encased in one of lead.
STEEL.
Steel is a compound of Iron and Carbon, in which proportion of latter
is from i to 5 per cent., and even less in some descriptions. It is dis-
tinguished from iron by its fine grain, and by action of diluted nitric
acid, which leaves a black spot upon it.
There are many varieties of steel, principal of which are :
Natural Steely obtained \y^ reducing rich and pure descriptions of iron
ore with charcoal, and refinmg cast iron, so as to deprive it of a sufficient
portion of carbon to bring it to a malleable state. It is used for files and
other tools.
Indian Steely termed Wootz, is said to be a natural steel, containing a small
portion of other metals.
METALS* — STEEL. 64 1
Blittered 8t6d, or Steel of Cementai^^m^ is prepared by direct combination of
iron and carbon. For this purpose, iron in bars is put in layers, alternating
with powdered charcoal, in a close furnace, and exposed for 7 or 8 days to
a high temperature, and then put to cool for a like period. The bars, on
being taken out, are covered with blisters, have acquired a brittle quality,
and exhibit in fracture a uniform crystalline appearance. The degree of
carbonization is varied according to purposes for which the steel is intended,
and the very best qualities of iron are used for the finest kinds of steel.
Tilted Steel is made from blistered steel moderately heated, and subjected
to action of a tilt hammer, by which means its tenacity and density are in-
creased.
Shear Steel is made from blistered or natural steel, refined by piling thin
bars into fagots, which are brought to a welding heat in a reverberatory
furnace, and hammered or rolled again into bars ; this operation is repeated
several times to produce finest kinds of shear steel, which are distinguished
by the terms of HcUfshectr^ Single shear, and Double shear, or steel of i, 2, or
3 nmrkSy etc., according to number of times it has been piled.
Spring Steel is blister steel heated to an orange red color and rolled or
hammered.
Cast or Cmclhle Steel is made by breaking blistered steel into small pieces
and melting it in close crucibles, from which it is poured into iron molds ;
ingot is then reduced to a bar by hammering or rolling. Cast steel is best
kind of steel, and best adapted for most purposes ; it is known by a very
fine, even, and close grain, and a silvery, homogeneous fracture ; it is very
brittle, and acquires extreme hardness, but is difficult to weld without use
of a flux. Other kinds of steel have a similar appearance to cast steel, but
grain is coarser and less homogeneous ; they are softer and less brittle, and
-weld more readilv. A fibrous or lamellar appearance in fracture indicates
an imperfect steel. A material of great toughness and elasticity, as well as
hardness, is made by forging together steel and iron, forming the celebrated
Damasked Steely which is used for sword-blades, springs, etc. ; damask ap-
pearance of which is produced by a diluted acid, which gives a black tint to
the steel, while the iron remains white.
With cast steel, breaking strength is greater across fibres of rolling than
with them.
Heath's Process Is an improvement on this method, and consists in adding to
molten metal a small quantity of carburet of manganese.
HeaJUnCs Process consists in adding nitrate of soda to molten pigiron, in order to
remove carbon and silica.
JUusheVs Process. — Malleable iron is melted in crucibles with oxide of manganese
and charcoal.
Puddled Steel is produced by arresting the puddling in the manufacture
of the wrought iron befoi*e all the carbon has been removed, the small
amount of carbon remaining, .3 to i per cent., being sufficient to make an
inferior steeL
Mild Steel contains from .2 to .5 per cent, of carbon ; when mo*e is pres-
ent it Is termed Hard SteeL
Bessemer Steel is made direct from pig-iron. The carbon is first removed,
in order to obtain pure wrought iron, and to this is added the exact quantity
of carbon requirea for the st«el. The pig should be free from sulphur and
phosphorus. It is melted in a blast or cupola, and run into a converter (a
pear-shaped iron vessel suspended on hollow trunnions and lined with fire-
orick or clay), where it is subjected to an air blast for a period of 20 min-
utes, in order to dispel the carbon, after which from 5 to 10 per cent, of spie-
^releiaen is added.
3H*
642 METALS. — ^STESL.
The blast is theo resumed for a short period, to incorporate the two metala^
when the steel is run off into molds. The moment at which all the carbon
has been removed is indicated by color of the flame at mouth of converter,
inhe ingots, when thus produced, contain air holes, and it becomes necessary
to heat them and render them solid under a hammer.
Siemen's Process. — Pig-iron is fused upon open hearth of a regenerative
furnace, and when raised to a steel-melting temperature, rich and pure ore
and limestone are added gradually, whereby a reaction is established between
the oxygen of the ferrous oxide and the carbon and silicon in the metaL The
silicon is thus converted into silicic acid, wUch with the lime forms a fasible
slag, and the carbon, combining with oxygen, escapes as carbonic acid, and
induces a powerful ebullition.
Modification of this process.— The ore is treated in a separate rotatory fa mace
with carbouaoeous material, and converted into balls of malleable irun, which are
transferred from the rotatory to the bath of the steel-melting fUmace.
This process is adapted to the production of steel of a very high quality, becaase
the sulphur and phosphorus of the ore are separated Arom the metal in the rotatory
furnace.
Siemen^ 8 -Martin Process. — Scrap-iron or steel is gradually added in a
highly heated condition to a bath of about .25 its weight, of highly heated
pig, and melted. Samples are occasionally taken from the bath, in order to
ascertain the percentage of carbon remaining in the metal, and ore is added
111 small quantities, in order to reduce the carbon to about .1 per cent.
At this stage of the process, siliceous iron, spiegeleisen, or ferro-manganese
is added in such proportions as are necessary to produce steel of the required
degree of hardness. The metal is then tapped into a ladle.
Landore-Siemen's Steel is a variety of steel made by the Mod^ation of
Siemens Process, Its great value is due to it^ extreme ductility, and its
having nearly like strength in both directions of its plates.
Whitioortk^s Compressed Steel is molten steel subjected to a pressure of
about 6 tons per square inch, by which all its cavities are dispelled, and it is
compressed to about .875 of its original volume, its density and strength be-
ing proportionately increased.
Chrome and Tungsten Sted are made by adding a small percentage of
Chromium or Tungsten to crucible steel, the resiut producing a steel of
great hardness and tenacity, suitable for tools, such as drills, etc.
Homogeneous Steel is a variety of cast steel containing .25 per cenL 0/
carbon.
Remarks on Manufacture of Steel, and Mode of Working it.
(D. Chr.rnoff, 1868).
Steel, when wist and allowed to cool quietly, assumes a crystalline structure.
Higher temperature to which it is heated, softer it becomes, and greater is liberty
its particles possess to group themselves into crystals.
Steel, however hard it may be, will not harden if heated to a temperature lower
than what may be distinguished as dark cherry -red, a, however quickly it is cooled-,
on contrary, it will become sensibly softer, and more easily worked with a file.
Steel, heated to a temperature lower than red, but not sparkling, 5, does not
change its structure whether cooled quickly or slowly. When temperature has
reached &, substance of steel quickly passes from granular or crystalline condition
to amorphous, or wax-lUce structure, which it retains up to its melting-point, c
Points a, &, and c have no permanent place in scale of temperature, but their posi-
tions vary with quality of steel ; in pure steel, they depend directly on quantity of
constituent carbon. Harder the steel, lower the temperatures. Tints above speci-
fied have reference only to hard and medium qualities of steel; in very soft kinds
of steel, nearly approaching to wrought iron, points a and b range very high, and in
wrought iron point b rises to a white heat.
METALS. — STEEL. 643
AsBQinptlon of the crystalline structure takes place entirely In cooling, between
temperatures c and b: when temperature sinks beloMr b there is no change of struc-
ture. For successful forging, therefore, heated ingot, after it is taken out of furnace,
must be forged as quickly as practicable, so as not to leave any spot untouched by
hammer, where the steel might crystallize quietly, as formation of crystals should
t>e hindered, and the steel should be kept in an amorphous condition until tem-
perature sinks below point b.
Below this temperature, if piece is cooled in quiet, mass will no longer be disposed
to crystallize, but will possess great tenacity and homogeneousness of structure.
When steel is forged at temperatures lower than &, its crystals or grains, being
driven against each other, change their shapes, becoming elongated in one direction,
and contracted in another; while density and tensile strength are considerably in-
creased. But available hammer-power is only sufficient for treatment of small steel
forgings; and object of preventing coarse crystalline structure in large forgiugs
is more easily and more certainly effected, if, after having given forging desired
shape, Its structure be altered to an homogeneous amorphous condition by heating
It to a temperature somewhat higher than 6, and the condition be fixed by rapid
cooling to a temperature lower than &, the piece should then be allowed to finish
cooling gradually, so as to- prevent, as far as practicable, internal strains due to
sudden and unequal contraction.
Alloys of steel with Silver, Platinum, Rhodium, and A luminum have been
made with a view to imitating Damascus steel, Wootz, etc., and improving
fabrication of some finer kinds of surgical and other instruments.
Properties 0/ Steel— After being tempered it is not easily broken ; it welds
readily ; does not crack or split ; bears a very high heat, and preserves the
capability of hardening after repeated working.
Hardening and Tempering. — Upon these operations the quality of manu-
factured steel in a great measure depends.
Hardening is effected by heating steel to a cherry-red, or until scales of
oxide are loosened on surface, and plunging it into a cooling liquid ; degree
of hardness depends upon heat and rapidity of cooling. Ste&I is thus ren-
dered so hard as to resist files, and it becomes at same time extremely
brittle. D^ree of heat, and temperature and nature of cooling medium,
must be chosen with reference to quality of steel and purpose for which it
is intended. Cold water gives a greater hardness than oils or like sub-
stances, sand, wet-iron scales, or cinders, but an inferior degree of hardness
to that given by acids. Oil, tallow, ^tc., prevent cracks caused by too rapid
cooling. Lower the heat at which steel becomes hard, the better.
Tempering, — Steel in its hardest state being too brittle for most purposes,
the renuisite strength and elasticity are obtained by tempering— or " letting
d^wn the temper " — which is performed by heating hardened steel to a certain
de^ee and cooling it quickly. Requisite heat is usually ascertained by color
which surface of the steel assumes from fUm of oxide thus formed. Degrees
of heat to which these several colors correspond are as follows :
At43o<3, very faint yellow.. (Suitable for hard instruments ;■ as hammer • faces,
At 450^, pale straw color. . . . ( drills, lancets, razors, etc.
At 47o*>, full yellow ( For instruments requiring hard edges without elastici-
At 490°, brown color ( ty ;^as shears, scissors, tumingtools, penknives, etc.
^'«^te ^^^""^ '^'^*' ^"""^^^ i^«»" ^^ f«»" <^«"'°8 ^««^ »°^ soa metals; such as
At M8°i purple '.'.'.', ! .'!."!.*!( P'*°® ''^°°®' ^*^^' J^^'^es, etc.
At 550^, dark blue (For tools requiring strong edges without extreme
At 560^, fkill blue ( hardness; as cold-chisels, axes, cutlery, etc.
At 600°, grayish blue, verg- (For spring- temper, which will bend before breaking;
fog on black. t ^ saws, sword-blades, etc.
If steel is heated to a higher temperature than this, ^ect of the hardening
process is di*8tr(Hred.
A high breaking strain may not be conclusive as to quality, as it may bo
due to a hard, eUstic metal, or a low one may be due to great softness.
644
METALS. — TIN. — ZIWC. — ^MODELS.
Case-liardenixis.
This operation consists in converting surface of wrought iron into steel,
by cementation, for purpose of adapting it to receive a polish or to bear fric-
tion, etc. ; it is effected by heating iron to a cherry-red, in a close vessel, in
contact with carbonaceous materials, and then plunging it into cold water.
Bones, leather, hoofs, and horns of animals are generally used for this pur-
pose, after having been burned or roasted so that they can be pulverized,
aoot is also frequently used.
The operation reduces strength of the iron.
TIN.
Tin is more readily fused than any other metal, and oxidizes very slowly.
Its purity is tested by its extreme brittleness at high temperature.
T%n plate is iron plate coated with tin.
Block Tin is tin plate with an additional coating of tin.
ZINC.
Zinc, if pure, is malleable at 220° ; at higher temperatures, such as 400°,
it becomes brittle. It is readily acted upon by moist air, and when a film
of oxide is formed, it protects the surface from further action. When, how-
ever, the air is acid, as from the sea or large towns, it is readily oxidized to
destruction.
Iron, Copper, Lead, and Soot are very destructive of it, in consequence of
the voltaic action generated, and it should not be in contact with calcareous
water or acid woods.
The best quality, as that known as *' Vielle Montagne," is composed of zinc
.995, iron .004, and lead .001. Its expansion and contraction by differences
of temperature is in excess of that of any other metaL
STRENGTH OF MODELa
The forces to which Models are subjected are^
I. To-draw thehi asunder by tensile stress. 2. To break them by trans-
verse stress. 3. To crush them by compression.
The stress upon side of a model is to corresponding side of a structure as
cube of its corresponding magnitude. Thus, if a structure is six times greater
than its model, the stress upon it is as 6^ to i = 316 to i : but resistance of
rupture increases only as squares of the corresponding magnitudes, or as
6' to I =: 36 to I. A structure, therefore, will bear as nmch less resistance
than its model as its side is greater.
Vo Coznpu.te X>ixxien8ioxi8 of a Seam, etc., '^vhicfai a
Strnottiro can "bear.
Rule. — Divide greatest weight which the beam, etc. (including its weight),
in the model can Mar, by the greatest weight which the structure is required
to bear (including its weight), and quotient, multiplied by length of beam,
etc, in model, will give length of beam, etc., in structure.
EzAXPLS.— A beam in a model 7 inches in length is capable of bearing a weigbl
of 36 lbs., but it is required to sustain only a weight or stress of 4 Iba ; what ia tba
grMrte«t leofth that a corresponding beam can be made in the structure?
«6 -f- 4 = 6. 5, and 6. 5 X 7 = 45- 5 <««•
\
MODELS. — ^MOTION OF BODIES IN FLUIDS. 645
Resistance in a model to crushing increases directly as its dimensions ;
but as stress increases as cubes of dimensions, a model is stronger than the
structure, inversely as the squares of their comparative magnitudes.
Hence, greatest magnitude of a structure is ascertained by taking square
root of quottent, as obtained by preceding rule, instead of quotient itself.
EXAMPUB. — If greatest weight which a colamn in a model can sustain is 26 lbs.,
and it is required to bear only 4 lbs. ; height of column being 18 in&, what should
be height of it in structure?
/(— j = V^-s = 2.55, and 2.55 X 18 = 45.9 iris., height of column in structure.
If, when length or height and breadth are retained, and it is required to
give to the beam, etc., such a thickness or depth that it will not break in con-
sequenoe of its increased dimensions.
Then /f — j = y/6.s — 2.55, which, X square of relative size of model = thick-
ness required.
To Coxxipiite Itesietance or a Bridge fVoxn a Alodel.
n* W — I — (n — i) 11; = load bridge wiU bear in its centre.
Example.— Tf length of the platform of a model between centres of its repose
upon the piers is 12 feet, its weight 30 lbs., and the weight it will just sustain at its
centre 350 lb&, the comparative magnitudes of model and bridge as 20, and actual
length of bridge 240 feet; what weight will bridge sustain ?
ao*X35o— I — X(20— i) Xsol =: 140000 — 3800 X 30=26000/6*.
MOTION OF BODIES IN FLUIDS.
If a body move through a fluid at rest, or fluid move against body at
rest, resistance of fluid against body is as square of velocity and density
of fluid ; that is, R = c? v^. For resistance is as quantity of matter or
particles struck, and velocity with wbAch they are struck. But quan-
tity or number of particles struck in any time are as velocity and density
of fluid; therefore, resistance of a fluid is as density and square of
velocity.
o' a d v^
— = A, and = R. h ratresenting height due to velocity , d density ofjlwd,
3 g ^ g
and R resistance or motive force.
Resistance to a plane is as plane is greater or less, and therefore resistance
to a plane is as its area, density of medium, and square of velocity; that is.
Motion is not perpendicidar, but oblique, to plane or to face of body in any
angle, sine of which is » to radius i ; then resistance to plane, or force of
fluid against plane, in direction of motion, will be diminished in triplicate
ratio of radius to sine of angle of inclination, or in ratio of i to s\
Hence, = R, and = F. to representing weight of body, and F
39 2 gto
retarding force.
Progression of a solid floating body, as a boat in a channel of still water,
gives rise to a displacement of water surface, which advances with an un-
dnlation in direction of body, and this undulation is termed Wave of Di9-
pkuxmerU.
646
MOTION OF BOPIBS IN FLtJlDS.
Resistance of a fluid to progression of a floating body increases as velocity
of body attains velocity of wave of displacement, and it is greatest when the
two velocitie:) are equal.
In the motion of elastic fluids, it appears from experiments that oblique
action produces nearly same effect as in motion of water, in the passage of
curvatures, apertures, etc.
H.e8i'stanoe to an A.rea of* One SqL. Foot moving tlirougli
AVater, or Contrari-w-ise.
Angle of
Snrface
with
PiaDe of
Current.
o
6
8
9
lO
'5
20
25
30
35
40
Drtuurf ptr 8q. Fbat for feOoteing Vt-
ioeittet per Ifhtd per MintUe.
X20
.09
133
.156
.179
•355
608
94
I 353
1.798
2258
\r aq. pw* jar jouawvn
I per that per MintUe.
040 480
Uw.
•359
53
624
.718
X42
2.434
376
5 4'3
7.192
9032
Lb*.
1-435
a. 122
2.496
2.87
5.678
9-734
15038
21.653
28.766
36.13
900
Um.
5.046
7-459
8.775
10.091
19.963
34. 222
52.869
76.123
101.132
127.018
Angle of
Snrface
with
Plane of
Current.
45
50
55
60
6S
70
75
80
85
90
iVetntr* jper Sq. Font far foJlotring
loeittee per Foot per MtniUe.
120 240 480 ! ge
re-
Lbs.
2.66
2.995
3249
3-455
3-607
3.728
3.81
3-857
3.892
3-9
Lbe.
ia639
11.981
12-995
13.822
1443
14.914
15-241
15.428
15-569
15-6
480 ! goo
LtM.
42- 557
47923
51 979
55286
57-72
59-654
60.965
61.714
62.275
62.4
Lbs
149.614
168.48
182.739
194.366
202.922
209.722
214.329
216.926
218.936
219.375
Resistance to a plane, from a fluid acting in a direction perpendicular to
its face, is equal to weight of a column of fluid, base of which is plane and
altitude equal to that which is due to velocity of the motion, or through
which a heavy body must fall to acquire that velocity.
Resistance to a plane running through a fluid is same as force of fluid in
motion with same velocity on plane at rest. But force of fluid in motion is
equal to weight or pressure which generates that motion, and this is equal to
weight or pressure of a column of fluid, base of which is area of the plane,
and its altitude that which is due to velocitv.
»
Illustration. — If a plane i foot square be moved through water at rate of 32. 166
feet per second, then ^ ^ 16.083. space a body would require to fall to acquire
64. 333
a velocity of 32.166 feet per second; therefore i x 62.5 (weight of a cube foot ot
32. 166'
water) x = 1005 Ibt. •= retittance of plane.
64-333
Resistance of different ITii^-ures at different "V^elocities in
A.ir.
Veloci-
ty per
Second.
Feet.
3
4
5
8
9
10
Cone.
Sph«K.
Cylln-
■ aer.
~ 0«'.
Hemi-
■pbere.
Round-.
Oi.
Veloci-
ty per
Cone.
Bjken.
Cvlin-
der.
Vertex.
Base.
Second.
Vertex.
Bum.
o«.
o«.
Os.
Feet.
Oi.
0*.
(H.
Oi.
.028
.064
.027
•05
.02
12
-376
.85
•37
.826
.048
.109
.047
.09
039
14
.512
1. 166
•505
I-M5
.071
.162
.068
•M3
.063
»5
.589
1-346
.581
1.327
.168
.382
162
.36
.16
16
673
1-546
.663
1.526
.211
.478
.205
456
.199
18
.858
2.002
.848
1.986 .
26
-5«7
255
-565
.242
20
1.069
2-54
1.057
2.528
Hemi.
•phere
Roand.
Ob.
•347
47a
552
634
818
033
Diameter of all the figures was 6.375 ins., and altitude of the cone 6.625 iQB.
Angle of side of cone and its axis is, consequently, 25° 42' nearly.
From the above, several practical inferences may be drawn.
' That resistance is nearly as sur&ce, increasing but a very littla «bov«
proportion in greater surfaces.
MOTION OF BODIES IN FLUIDS. 647
s. Resistance to same surface is nearly as square of velocity, bat gradu*
ally increasing more and more above that proportion as velocity increases.
. 3. When after parts of bodies are of different forms, resistances are differ-
ent, though fore parts be alike.
4. The resistance on base* of a cone is to that on vertex nearly as 2.3 to
I. And in same ratio is radius to sine of angle of inclination of side of cone
to its path or axis. So that, in ttiis instance, resistance is directly as sine
of angle of incidence, transverse section being same, instead of square of sine.
Resistance on base of a hemisphere is to that on convex side nearly as
2.4 to I,, instead of 2 to i, as theory assigns the pro^wrtion.
Sphere. — Resistance to a sphere moving through a fluid is but half re-
sistance to its great circle, or to end of a cylinder of same diameter, moving
with an equal velocity, being half of that of a cylinder of same diameter.
2gx- dx = V. d representing diameter of gphere^ and N and n ipe-
ei^ gravities 0/ sphere omd retisting fluid.
— X - <2 = S. S representing space through which a sphere passes while acquir-
n 3 . *
ing its mtxximum velocity, in falling trough a resisting fluid.
Illustration. — If a ball of lead i inch in diameter, B|)eciflc gravity 11.33, ^ set
free in water, specific gravity i, what is greatest velocity it will attain in descend-
ing, and what space wUl it describe in attaining this velocity f
^ = 32.166, d = — fbot, N = 11.33, *>id n=st.
y.
Then
/ ~ 4 Ti 11.33 — X ,
^aX32i66X^of-X— ^^ = V7. 148 X la 33 =
Hence, ^^^ x — of — = 1.259 feet q vt ,=/= retardive force =
3 12 ' SgHd "^ 3gs
n a v^ n a v^
Cylinder. = R, and =/ a representing area or p r^. and
^g ' igw "^ "^ " ^ *
w weight of body.
Illdstratiox. — Assume a = 3? sq. feet, v = 10 feet per second, and n = .0013.
Tben*^ 2~^ = .06 of a cube foot of water = .06 of 62.5 = 3.75 lbs.
64.33
^ . , ^ ^. notes' _ , npd^v^s' _ . npd'v^s^
Conical Surface. = R, also — ^— = R, and -^
2 g Sg Sgw
sssf. s representing sine of inclination, and a convex surface of cone.
pnv^ d'
Ciiirved Snd as a Sphere or Henaisplierioal Sud. =- — - — —
16 y
= R, and Circle .5 of spherical end.
In general, when n is to water as a standard, result is in cube feet of water, if
a is in sq. feet; and in cube in& of water, if a is in sq. ins., v in ins., and g in ins.
Iff! is given in lb& in a cube foot, a is in sq. feet, v and g are in feet, result is in lb&
To Compute A.ltitnde of a Column of Air, I*ress-ure of
vtrlxiolx slxall l>e eq.ual to Resistance of a Sody moving
througb, it, with, any Velocity.
■f- X — = » = aUituie infect ax — vchtme ofaUumn infect, and — a » = toeight
o a 5
in ounces, a representing area ofseUion of body, similar to any in table, perpen-
dicular to direction of motion, r resistance to velocity in table, and x altitude sought
4ffa column of air, base of which is a, and pressure r.
* Tklf to n rafuUtion of th« popalar MMdion tbnt a Uper tf*r mb b« tow«d in w«Wr vailMt wbw
1^9 b«M la forftmoct.
648 MOTION OF BODIES IN FLUIDS.
3 IK
When a = — of a foot, as in all figures in table, x becomes ~ r when r^re^
9 4
tistance in table to similar body. ^
Illustration.— Assume convex face of hemisphere resistance = .634 oz. at a Te-
locity of 16 feet per second.
Then r = .634, and aj = — r = 2. 3775 feet = altitude 0/ column of air ^ pressure oj
4
which = resistance to a spherical surface at a velocity of 16 feet.
Xo CJotnpute -wheii Pressure of Air in rear of a I*rojeotile
is Inferior to i*ressvire due to its "Velocity,
Assume height of barometer = 2. 5 feet, and weight of atmosphere = 14.7 lb&
Weight of cube inch of mercury = -^^ = .49 lbs., and weight of cube inch of air
30
= .000043 57 1^' > hence, .49 -^ .000043 57 = " 246, which X 2.5 feet = 28 115 feet
Then y/i6.d& : V28 115 :: 32.16 : x, andx=:^^^^ — \ "^ = 1^^1.6 feet.
Xo Compute "Velocity witli whioU a Plane Surface must
"be projected to g;enerate a H^esistance Just eq.ual t;o
Pressure of A-tmospliere upon it.
By table, resistance on a circle with an area of .222 sq. foot (2 -7-9) = .051 oz., at a
velocity of 3 feet per second. Hence 3^ : i* : : .051 : .0056 oz. at a velocity of i foot,
and I X 144X 14-7 X i6x 2-^9= 7526.4 oz. Hence, v^.c»56 : ■y/7526.4 :: i : 1160 feet.
To Compute Velocity lost "by a Projectile.
If a body is projected with any velocity in a medium of same density with itself,
and it describes a space = 3 of its diameters,
Then x = -id, and b =r — — r= — .
' Q C**~"' 2.08
Hence, 6 « = -|- , and — r — = -^—- = velocity lost nearly .66 ofproffctile velocity.
c = base of Nap. system of log. ; hence c&» = number corresponding to Nap. log.
b X. Hence, if 6 x x -43^3) result = com. log. of c&«.
b X =1 = 1. 125, which X -4343 = -488 587 5, and namber to thiscom. log.= 3.0803.
8
_ , .X 1 » ' 30803 — I 2.08
Hence, velocity lost = ^ = — - .
3.0803 3.08
Illustration. — If an iron ball 2 ins. diam. were projected with a velocity of 1200
f«etper second, what would be velocity lost aftor moving through 500 feet of space?
d = — = - , aj = 5oo, N = 7l, and n = . 0012.
12 6 ^ ' '¥'
„ . 3«* 3X12X500X3X6 8i . 1200 „ - ,
Hence, 6 aj = |^ r = — r— — ^ = — , and v = -— - = 998 /ee/ per
' 8Na 8 X 21X10000 440 c 81 J^ -^ «'
second, having lost 202 feet, or nearly — of its initial velocity.
13 3 6 22 . 1
= .0012, — and — = — and — • inverted, b«c«nM N and « are in denominator.
xoooo 33 • 3 6
To Compute Time and. "Velocity.
T- (-• — — J = '*'^*i ?Tr3= ^ ^^^ -r- = *•
b \v a) ' 8 N d c6« .
Illustration.— If an iron ball 2 ins. in diameter were projected in air with a ve-
locity of 1200 feet per second, in what time would it pass over 1500 feet, and what
its velocity at end of that time?
. 3X12X3X6 X ^j. 1500 , I 2716 I 1
b = = — 2 » *nd 6 as = ^ , : hence — = — — ; — = . and
8x22X10000 2716' 2716' b I ' a 1200
I cf>» 1.7372 I , , ^ , ,/i l\
= — = = 2 — nearlv. :. t> = 6qo and <=27i6 x 1 7 1 = 1.67
a I200 600 ^690 xaoo/ '
NAVAL ARCHITECTUBE.
649
NAVAL ARCHITECTURE.
I^esults of* Experiments upon f onxL o£ "Vessels.
{Wm. Bland.)
Cu'bical ACodele. Head RemiManee. — Increases directly with area
of its surface. WeigJU Resistance. — Increases direct!}' as weight.
'Vessels' Alodels. Lateral Resistance. — About one twelfth of
length of body immersed, varying with speed.
(h'der of Superiority of Amidship Section, — Rectangle, Semicircular,
Ellipse, and Triangle.
Centre of lateral resistance moves forward as model progresses.
Centre of gravity has no influence upon centre of lateral resistance.
lielative Speeds.
Length. — Increased length gives increased speed or less resistance.
Depth of Flotation, — Less depth of immersiun of a vessel, less the resistance.
A midship Section, — Curved sections give higher speed than angled.
Sides. — Slight horizontal curves present less resistance than ri^^ht lines.
Curved sides with one fourth more beam give equal speeds with straight
sides of less beam. Keel, — Length of keel has greater effect than depth.
Stem, — Farallel-sided after bodies give greater speed than taj^er-sided.
0r4«r of Speed.
Form or Bow.
I
2
Isosceles triangle^ sides slightly convex
" " " right lines ,
'* *' " slightly concave at entrance and' running)
oat convex )
Spherical eqmkUertd triangle compared to Equilateral triangle^ speed is
as 1 1 to 12. EquUaieral triangle, with its isosceles sides bevellal off at an
angle of 45°, compared to bow with vertical sides, is as 5 to 4.
When bow has an angle of 14^ with plane of keel, compared with one of
7°, its speed is greater.
Bodies Inclined Ufmards from Amidship Section,
I. Model with bow inclined from !St has less resistance than model with-
out any inclination.
a. Model with stem inclined from iS, has less resistance than model with-
out any inclination.
Model I had less resistance than model 3. Model with both bow and
stem inclined from iS, has less resistance tlian either i or 3.
Stability.
He«»ults of Kxperixnents upon Sta'bility of* Reotansvilar
Blocks of* Wood of XJniforiu Hiengtli and I>epth, "bxit
of X>ifieren.t Breadths. {Wm. Bland.)
Length 15, Dq^ 2, and Depression i inch,
lUkio of Stability.
Width.
Wetgfai.
A« ObMrved.
With nice
Wtighu.
By Squares of
Breadth.
By Cabes of
Breadth.
In*.
Oi.
3
34
I
I
z
I
15
35
a- 5
24
2- 25
V"
6
45
7
3-7
4
7
55
XI
4.8
6.25
15625
3l
650
NAVAL ABGHITJEGTURB.
Hence it appears that rectangular and bomogei\eou8 bodies of a uniform
length, depth, weight, and immersion in a fluid, but of different breadths, have
stability tor uniform depressions at their sides (heeling) nearly as aquartt
of their breadth ; and that, when weights are directly as their breadths,
their stability under like circumstances is nearly as cubes of their breadth.
With equal lengths, ratio of stability is at its limit of rapid increase when
width is one third of len^h, being nearly in cube ratio ; aft^wards it ap-
proaches to arithmetic ratio.
Results of* Ifixperiments upon Stalsility^ and Speed of
]Nd[odel8 Yiarvitxss A-xnidsliip Sections ordifierent WoTixxet^
"but XJniibrm JJengtli, Bread til, and TVeifflits. {W.Bland.)
Immersion different^ depending upon Form of Section.
Form oV Immbkbbd Sbction.
Half-depth triangle, other half rectangle
Rectangle.
Right-angled triangle *
Semicircle
13
«4
7
9
* Dnnf ht of water or ImoMriion dovble thai of rMtaogle.
Stability.
Speed.
4
3
3
a
Statical Stability is moment of force which a body in flotation exerts to
attain its normal position or that of equilibrium, it having been deflected
from it, aud it is equal to product of weight of fluid displaced and horizontal
distances between the two centres of gravity of body and of displacement, or
it is product of weight of displacement, height of Meta-centre^ and Sine of
angle of inclination.
Dynamical Stability is amount of mechanical work necessary to deflect a
body in flotation from its normal position or tliat of equilibrium, and it is
equal to product of sum of vertical distances through which centre of grav-
ity of body ascends and centre of buoyancy descends, in moving from ver-
tical to inclined position by weight of body or displacement
To IDeterziiine ^Ceasure of Sta1:>ilit3r of* Hull of* a Vessel
or Floating Body.— ITigj. 1.
MMisure of stability of a floating body depends essentially upon horizontal dis-
tance, 6«, of meta-ceutre of body from centre
*^'8- '• / P of gravity of body ; and it is product of force
M /'.'.':-::j(||fc -^ of the water, or resistance to displacement of
I ■'~~-~-jL^ ^^ *'» acting upward, and distance of 6 «, or P x
... / l\ {-^^ G 8. If distanced M, represented by r, and
e "'""r~-|-- o \ »*! 7 f angle of rolling, c M r, by M<>, measure of sta-
B^7 — ""7 '!--.. — ; ^l'>vy-' bility, or S is determined by P r, sin. M® = S ;
W^ I el 'f ' '^'T"-'- **^^ *'**'® '"^ therefore greater, the greater the
/ Q r'-t' ' / 'i weight of body, the greater distance of mefa-
V r"*'* / cen<r« fh)m centre of gravity of body, and the
^— ---...._ J greater the angle of inclination of this or of
Assume figure to represent transverse section of hull of a vessel, 6 centre of
gravity of hull, w I water-line, and c centre of buoyancy or of displacement of im-
mersed hull in position of equilibrium. Conceive vessel to be heeled or inclined
over, so that «/ becomes water-line, and s centre of buoyancy; produce s M, and
point M is m^tc^^erUre of hull of vessel.
TntmverM mtla-eetUrt depends upon poeition of centre of boofucy, for it U that point wkere «
▼ertical line drawn from centre interaecte • line paesing throagh centre of graTity of null of Teaaa)
perpendicular to plane of keel.
Point of mMa-eentrt may be the aame, or it may differ slifrht^y for different anelee of heeliufr. Angle
of direction adopted to ascertain poeition of nuta-etntre should be greatest which, under ordinary cir-
enmetancee, ie or probable occurrence ; in different vessels this angle ranges from ao* to 6o*.
If mHa-et»tr€ is above centre of gravity, eqoillhriam (s Stable ) if It oolnddM with it, eqaiiibriam k
ifferent; and if it ie below it, eqaUibrinm is Unstable.
iiAVAL ABCHITECTUBE. 65 I
Comparative SLabUily of difl'erent hulls of vessels is proportionate to the distauce
of 6 M for same angles of heeling, or of distance G s. Oscillations of hull of a ves
sel may be resolved into a rolling about its longitudinal axis, pitching about its
transverse axis, and vertical pitching, consisting in rising and sinking below and
above position of equilibrium.
If transverse section of hull of a vessel is such that, when vessel heels, level of
centre of gravity is not altered, then its rolling will be about a permanent longi-
tudinal axis traversing its centre of gravity, and it will not be acuompunied by any
vertical oscillations or pitchings, and moment of its inertia will be constant while
it rolls. But if, when hull heels, level of its centre of gravity is altered, then axis
about which it rolls becomes an instantaneous one, and moment of its inertia will
vary as it rolls; and rolling uiust then necessarily be accompanied by vertical os-
cillations.
Such oscillations tend to strain a vessel and her spars, and it is desirable, therefore,
that transverse section of hull should be such that centre of its gravity should not
alter as it rolls, a condition which is always secured if all water-lines, as ti; ^ and ef.
are tiingents to a common sphere described about G; or, in other words, if point of
their intersections, o, wiih vertical plaue of keel, is always equidistant u'om centre
of gravity of hull.
To Cotnpxite Statical Stability;.
D c M sin. M = S. D representing displacement, M angle of inclination, and S
stability.
Illustration l— Assume a ship weighing 6000 tons is heeled to an angle of gO,
dist:incr c M = 3 feet,
Sin. 90 = 1564. Then 6000 x 3 X 1564 = 28152 foot-tons.
2— Weight of a floating body is 5515 lbs., distance between its centre of gravity
and meta-centre is n.32 feet, and angle M = 20^
Sin. M = .34202. Hence 5515 x 1132 x 34202 = 21 352.24/oo<-i6«.
Statical Surface Stability.
Moment of Statical surface stability at any angle is c zD. Assuming
centre of gravitv of vessel coincided with c; coefficient of a vessel's stability
at any angle of heel is expressed when the displacement is multiplied by
vertical height of the meta-^entre for given angle of heel above centre of
gravity, or U c M.
Approximately. Rule.— Divide moment of inertia of plane of flotation
for upright position, relatively to middk line bv volume of displacement;
and quotient multiplied by sine of angle of heel will give result.
Per Foot of Length of Vessel, | (B3 sin. M). B representing half breadth.
Dynamical Surface Stability.
Moment of Dynamical surface stability is expressed bv product of weight
of vessel or displacement and depression of centre of buoyancy during the
mclmation, that is, for angle M. j j &
Tto Compute Dynamical Stability of a Vessel.
Approximately. Rule.— Multiply displacement by height of meta-centre
above centre of gravity, and product by versed sine of angle of heel.
Or multiply statical stability for given angle by tangent of .5 angle of heel.
To Compute Slements of Stability of a Floating Body.
A^ __ c g
A *~*' Bin. li " *^' sin. M~^' *°** ®*°* *^ '" = <'• ^ representing area of
SSIfl!^ ««c«M)n; A' section immersed by careening of body, asfol;s horizontal
autance, er, Mween centres of buoyancy ; a horitonUd distance between centres of
^^iJ'XfiL^'^'^^ twm«r»ed and emerged by careening; g distance, c M. between
c^ire of bwyancy or of water displaced and meta-centre ; r distance, G M, bet%»een
centre of gramty and meta centre; c horizontal distance, G s, between centre of grav-
ity ana oflxne of displacement of it when careened ; e vertical distance between centres
qf^rw/Uy and buoyancy, all in feet ; and M angU of careening.
652 NAVAL ABCHITECTURE.
NoTB.~When centre of gravity, G, is belo^r tbat of displacement, c, then e Is -f-;
when it is above c it is — ; and when it coincides with c it is o; or e is — when
- < s; and a kxKiy will roll over when e sin. M = or >«.
Assamed elements of figure illustrated are A = 86, A' =: 21. 5, 6 = 21. 5, and c =: . 5.
The deduced arc < = 3.7, 0 = 3.87, ^=10.82, 0=14.9, and r^ 11.32. b repre-
senting breoiUlt at wattr-line or team in/eUy and P weight or dvg^lacement in lbs,
or tuns.
Then* = ^-X i4'9 = 3-7/««^ r = -^^-^=: 11.32 /««<, e^r—g^ g= ^'^
86 ^ .34202 .34202
= 10. 82 feetf c = . 342 02 X 1 1 . 32 = 3- 87 faet.
Of HuU qf a VesseL ( — ,^' -^-r ± e\ P, sin. M = S ; <Z cob. .5 M = d',
\io.7toi3*A /
— r-r = 9y — ^j(^ — «W±«; P (^^ + «6in."M) = S; and
10.7 to 13 (1 1.93) A *" sin. MVp / \^ /
P (» dr « sin. M) = S. d representing depUi of centre of gravity of displacement wi-
der voaier in equilibrium^ and d' depth when out of equUit/riuniy both in feet
Illustration i Displacement of a vessel Is looooopo lbs. ; breadth of beam, 50
feet; area of immersed section, 800 sq. feet; vertical distance from centre of grav
ity of bull up to centre of buoyancy or displacement, i.o feet, nnd horizontal dis-
tance a between centres of gravity of ureas immersed and emei^ed, when careened
to un angle of 9*^ 10' = 33.4 feet, immersed area being 50 sq. I'ueL
Sin. 90 10' = 1593. Then s = ^ x 33-4 = 20875 feet, 800 X 2.0875 := 50 X 33-4.
000
r = ^9_ ^ j-ggf g ^ 50^ = ,3. 1 feet, S = ( ^°' , ) -f 1.9 x
.1593 11.93X800 ^ '' ' \ii.93X8oo/^ ^ '^
loooooooX 1593 = 23905396 '^*-j and « = ( ■^— 2.0875) = \.Q feeL
^ .1593X10000000 /
2.— Assume a ship having a displacement of 5000 tons, nnd a height of me/a-c<^(re
of 3.25 feet, to be careened to 6° 12'. What is her statical stability?
Sin. 60 12'=. 1079. Then 5000 X 3.25 X .1079= 1753.37/oof-tofM.
3. — Assume a weight, W, of 50 tons to be placed upon her spar deck, having a
common centre of gravity of 15 feet above her load-line,
Then 5000 X 3 25 — 50 + 15 X . 1079 = 1747. 36/00/ f on*.
4. — Assume 100 tons of water ballast to be admitted to her tanks at a common
centre of gravity of 15 feet below her load-line.
Then 5000 x 3. 25 -f 100 x 15 X .1079= \^\i.'x^ fooiUms.
5.— Assume her masts, weighing 6 tons, to be cut down 20 feet,
Then ^ = — foot =/a/i of centre of gravity, and 5000 x (3- 25 H — ) X . 1079
= 1774.95 tons.
1?o Compute Klements or Po-^ver, etc., req.uire<l to
« Careen a Body or Vessel.
— ft5 / P
Sin. M (A — n sin. M) -fn sec. M — » — Z. -— 3/_ __ _ = in.
io.7toi3*AV 64.125 Ij A
W Z r := P c, and W Z = S. W representing weight or power exerted and I distance
at which weight or power acts to careet^ body, taken from centre of gravity of displace-
ment perpendicular to careening force, h vertical height from centre of gravity nfdiM-
plaeement to centre of weight or power to careen body when it is in equilibrimtn.
n horigontal distance from centre of vessel to centre of weight or power, L ZenptA of
vessel, m metacentre, and S cu tn preceding case, ail in feet.
* Unit for aection of a parallelofcnun la 10.7 ; of a Mmicircle la, aod of a triangl* taJB.
NAVAL AKCHITECTUEE. 653
Illustration. — A weight is placed upon deck of a vessel at a mean height of 3.87
feet from centre line of hull; height at which it is placed is xi.32, and other ele-
ments as in first case given.
Sec. 20° = . 342. ThenA = ii.32, » — 3.87, and / = .342 (n. 3 — 3.87 X •342) +
3.87 X 1.0642 — 3.7 = .342 X 10-I-4.12 — 3.7 = 3.84/ce<.
Assume W = 5515. Then 5515 x 3-84 = 21 iSy. 6 foot-lbs.
Or P (10 C0& M -f A sin. M) =1 S. 10 repreMenting distance of yaeighi frvm centre of
vcskL, and h height ofvo above water-line^ both infeeL
iLLUSTKATioff.— If a Weight of 30 tons placed at 20 feet from centre of hull or
deck, 10 feet above water-line, oareens it to an angle of 2° 9', what is its stability ?
cos. 2° 9' = .9993 ; sin. 2° 9' = .0375.
30 (20 X .9993 + 10 X .0375) = 30 X aa 361 = 610. 83 foot- tons.
Bottom and Iizizziersed Surface of Hull of Vessels.
To Conopxite Bottom and Side Surface of Hull.
Bottom and Side, Rule.— Multiply length of curve of amidship section,
taken from top of tonna^ or main deck b^nis upon one side to same point
upon other (omitting width of keel), by mean of len^^ths of keel and be-
tween perpendiculars in feet, multiply product by .85 or .9 (according to the
capacity of vessel), and product will give surface recjuired in sq. feet.
Example.— I<engths of a steamer are as follows: keel 201 feet, and between per-
pendiculars 210 feet, carved surface of amidship section 76 feet; what is surface?
Ck)efflcient 87. 210 -1- 201 -;- 2 = 205. 5, and 76 x 205. 5 x . 87 = 1 3 587 sq. feet.
Note.— Exact surface as measured was 13650 sq. feet
Bottom Surface, Rule. — Multiply length of hull at load-line by its
breadth, and this product by depth of immersion (omitting the depth of
keel) in feet; and this product multiplied bv from .07 to .08 (according to
capacity of vessel) will give surface requirea in sq. feet.
RxAMPLS. — Length upon load-line of a vessel is 310 feet, beam 40 feet, depth of
keel I foot, and draught of water 20 feet; what is bottom or wet surface?
Coefficient assumed .073. 3x0 x 40 X 20 — i x .073 = 17 199 sq. feet
Xo Compute Resistanoe to "Wet Surface of Hull.
C a v^ = R. C representing a coefficient of resistance^ a area of wet surface in sq.
feet, and v velocity of hull in feet per second.
Valn«BofC (•oo7> clean copjwr. I .014, iron plate.
' j.oi, smooth paint. | .019, iron plate, moderately foul.
Power required to propel one sq. foot of immersed amidship section at ^ is .073
that of smooth wet surface.
To Coini>ute EJlements of a Vessel.
Displaoexnent and it« Centre of Gravity.
Displacement of a vessel is volume of her body below water-line.
Centre of Gravity^ or Centre of Buoyancy of Displacement ^ is centre of
gravity of water displaced by hull of vessel.
For Duptacemenf, Rule.— Divide vessel, on half breadth plan, into a
number of equidistant sections, as one, two, or more frames, commencing
at !8 and running each side of it. Add together lengths of these lines in
both fore and aft bodies, except first and last, by Simpscm's rule for areas
(see page 344) ; multiply sum of products by one third distance between
sections, and product will give area of water-line Ijetween fore and aft>sections.
Then compute areas contained in sections forward and aft of sections taken, in-
cluding stem and rudder-post, rudder and stem, and add sum to area of body-see-
tioos already ascertained. ■*
* 7b ComptOa Artavf a WaUtAi.%t^ ue Mensp.' Atlon of SiirfacM, p«|{« 344.
31*
^54
NAVAL ARCHITECTURE.
Compute area of remaining water-lines in lilte manner Tabulate regnlts, ^nd
multiply them by Simpeon's rule jn like manner as for a water-line, and again by
consetutive number of water-lines, and sum of products between wAter-line and
product will give volume between load and lower water-line.
Add area of lower water line to area of upper surface of keel : multiply half sum
by distance between them, and product will give volume; then compute areas con-
tamed in sections forward and aft of sections taken as before directed.
If keel is not parallel to lower water-line, take average of distance between them.
Compute volume of keel, rudder-post and rudder below water-line; add to volume
already ascertained; multiply product by two, for full breadth, and product wiU
give volume required in cube feet, all dimensions being taken in feet
Ex AMPLE. -Assume
a vessel loo feet in
length by 20 feet in
extreme breadth, on
f load-line of 8 feet 9
inches immersion.
Figs. .2 and 3.
Distance between
sections, for purpose
of simplifying this
example, is taken
at 10 feet; usually
Ins. apart, and two or more Included in a section. Water-lines sTefaJJJt.'® ^ ^
ist Water-line.
4 5 ==
3 7-7 X
« 95 X
« 9-9 X
o 10 X
A 9.6 X
B 7-8 X
C 6.8 X
D 4
4
3
4
a
4
3
4
xo-?-3 =
Abaft section 4, rud-
der and post
Forward section D
and stem ........
5
30.8
19
39-6
20
38.4
15-6
27.2
4_
199.6
3j
665.3
25
20.7
7"
4
3
2
X
o
A
B
C
D
2d WcUer4ine.
2.7 =
6.9 X
8.7 X
9-5 X
9-6 X
9 X
7 X
5 X
2 =3 2
4
2
4
2
4
2
4
= 10.2
2.7
27.6
38
19.
36
14
20
176.9
io-h3 = 3i
589.7
Abaft section 4, rud-
der and post 13.2
Forward section D
and stem 9. i
612
4
3
2
X
o
A
B
C
D
3d Water-Une.
x-s =
5
6.6
8.7
8.9
7.6
7
3
X.3
X
X
X
X
X
X
X
ao
13-a
34-8
X7.8
30.4
«4
12
= 1.3
4 =
3 =
4 =
3 =
4 =
3 =
4 =
*44-9
xo-^3 = 3|
483
Abaft section 4, rud-
der and post j
Forward section D
and stem 5.^
495-4
4^ WcOer-line.
4
3
3
x
o
A
B
C
D
4-3
6.5
6.8
5
3.6
•9
•3
X
X
X
X
X
X
X
4
2
4
3
4
3
4
ZO'
Keel
Half breadth = . 35 x length of 98 feet =
Rudder-post and rudder ;
293*3
Abaft section 4, rod-
der and post 3.2
Forward section D
and stem g
a97-3 I
ist water-Une 7x1
2d
3d
4th
Keel
It
ResuUs.
711
612 X 4 = 2448 X I = 2448
495-4 X 3 = 990.8 X 3 = 198X.6
297- 3 X, 4 = "89.3 X 3 = 3567.6
24.8 24- 8 X 4 = 99.3
8096.4
5363.8
3
3)10727.6
DitpUuement, 3575.9 X a = 7i5<*8cM6e^
NAVAL ARCHITECTURB/ 655
To Compnte Centre of Oravity of Displacemexit.
Rule. — Divide sum of products obtAined as above, by consecutive water-
lines, by sum of products obtained in column of products by Simpson's mul-
tipliers, and quotient, multiplied by distance between water-lines, will give
depth of centre below load water-line.
IixusTKATitfN I. 8096.4, from above, -h 5363.8 = i. 5, which X 2 = 3 feet
Or, ** z=zd. n representing draught of vxxUr exclusive of any drag cf
* V ~ on/
ked^ a area of immersed surface of hull in sq. feet, and D disflaoement in cube feei.
2. — Assume draught of water 8 feet, displacement 7152 cube feet, and area of im-
mersed surface of hull iioo sq. feet. .
8 8
Then = —^yyi feet.
{, 7'52 \ 2X1-187
* V 1100X8/
To Compute Displaoement Approximately.
Coefficient of Dimlacement of a vessel is ratio that volume of displacement
bears to paraUelopipedon circumscribing immersed body.
V
= C. V representing volume of disj^acement in cube feet, L length at im-
\j D D
mersed toater-line, B extreme breadth, and D draught in depth of immernon, both
in feet.
Coefficient of Area of A midship Section in Plane of a WaterAmt is ratio
which their areas bear to that of circumscribing rectangle.
L representing length of water-line, and D distance between water-lineSy both in feet
Coefficients. (By S. M. Pook, Constructor U S. Navy.)
Rule. — Multiply length of vessel at load-line by breadth, and product by
depth (from load-line to under side of garboard-strake) in feet, and this
product by co^cient for vessel as follows : divide by 35 for salt water, 36
for fresh water, and quotient will give displacement in tons.
Amidship sections range (^rom .7 to .^ of their circumscribing square, and mean
of horizontal lines from . 55 to . 75 of their respective parallelograms. Hence, ranges
for vessels of least capacity to greatest are .7 X -55 = .385, and .9 x .75 = .675.
Merchant ship, very fbll 6 to . 7
" " medium 5810.62
River steamer, stem- wheel. . . 6 to .65
Sbipof the line 5 to 6
Naval steamer, first class 5 to .6
" 52 to 58
Merchant steamer, sharp 54 to . 58
Half clipper 52 to .56
Brigs, barks, etc 52 to . 56
River steamer, tug-boat, med'm . 52 to . 56
In steam launch Miranda, when making 16.2 knots per hour, with a displace
ment of 58 tons, her coefficient was 3.
Merchant steamer, medium. . . 52 to . 54
Clipper 5 to.54
Schooner, medium 48 to . 52
River steamer, tug-boat, sharp .45 to 5
" *' medium 45 to. 5
" *' sharp 42 to .45
Schooner, sharp. 46 to .5
Yacbts, sharp 4 to. 45
" very sharp 3 to .4
River steamers, very sharp. . . .36 to .42
To Compute Change of Trixu.
W /I T
-=r- X — = d'. D representing displacement at line of draught in tons, L length
at same lint in feet, and m longitudinal meta-centre.
iLHTBTRATioJr.—" ITarrior," at draught of 25. 5 feet, bas T,=r^8o feet, m = 475 feet,
and D = 8625 tona If, then, a weight of 20 tons was shifted fore and aft 100 feet,
20 X 100 380 « , ^ ^
—=2 X ^— = . 1856 feU = 9.29 in§.
?62$ 475
656
NAYAIi ABCHITECTUBB.
To Coinputo Common Centre of* Q-ra.yrity of Hull, Ar-
mament, Kngine, Boiler, eto., of a Vessel.
Rule. — Compute moments of the several weights, relativelj' to assigned
horizontal and vertical planes, by multiplying weight of each part by its
horizontal and vertical dutance from these planes.
Add together these moments, according to their position forward or aft, or
above or below these planes, and difference between these sums will give po-
sition forward or aft, above or below, according to which are greatest.
Divide results thus ascertained by total weight of vessel, and product will
give horizontal and vertical distances of centre of gravity from these planes.
Note.— To simplify computation in table, common centre of gravity of hull, ma-
chinery, etc., is taken, instead of centres of individual parts, as engine, boiler, pro-
peller, etc.
Illustration.— Vertical Plane at 0 and Horizantal at Load4ine.
Elbmsmts of a Stbam
FSIOATB.
Hull, bunkers, and ce-
ment in bottom
Engines, boilers, water,
and stores.
Coal
Battery and ammuni-
tion.
Masts, spars, sails, and
rigging
Anchors and cables. . . .
Boata
Water and ship's stores
Provisions and galley. .
Crew and effects
Officers' and mess stores
Total.
W«ight.
Tons.
1075
470
252
131-5
24
25
325
22
30
7-25
2C70
HOBIZONTAL.
Distances.
Forward. Abaft.
Feet.
1.6
16
62
27
40
40
I.S
17
Feet.
29
48
40
Moments.
Forward,
I 720
4032
8153
648
1000
880
360
510
17303
Abaft.
13630
156
290
14076
Vkktical.
Distances.
Above
Feet.
31
16
5
7
Below
Feet.
X
6.3
4
6
3
8
Momenta.
Above Bek^w
263
744
52
150
210
1419
1075
301 1
1008
150
66
_J8
5368
Moments forward Jg, 17303 — moments abaft, 14076 = 3227-5-2070 tons (toeight]
= 1.56 feet = distance of centre forward of gj.
Moments above load-line, 5368 — moments below, 1419 = 3949 -r- 2070 tons {weight)
= 1.91 fee.t = distance of centre below load-line. "
XoTR.— Rule, in Strength of Materials, to compute common centre of gravity,
page 819, would apply in this case.
To Compute I>eptli of Centre of Q-ravity or Bixoy-
arxoy Below oMeta-Centre.
= d. S representing statical stability^ D displacement in ton«, and sin. M
D sin. M
sine of angle of heel.
Illustration.— Elements of Fig. 2, page 654, are, statical stability at angle of
5.44O, 90 tons, and displacement 204.33 tons.
Sin. 5. 44° = .0999. Then
90
204-33X .0999
= 4.4i/«et
NAVAL ABCHITSCTITBE.
65;
To Ooxnpu.te Centre of Gt-ravltjr or Buoyaiicsr ^pproxi-
inately.
a , 9
— to — otmean draught ofhuU^ using larger coefficient for fbll-bodied vessela
5 20
To X)elineate Curve of Displacexx^exxt.
This curve is for purpose of ascertaining volume of water or tons weight,
displaced by immersed hull of a vessel at any given or required draught ; or
weight required to depress a hull to any given or required draught. From
residts o^ computation for displacement of vessel, proceed as follows, Fig. 4:
Fig. 4.
6-
keel
On a vertical scale of feet and ins.,
as A B, set off depths of keel and water-
lines, draw ordinates thereto represent-
ing displacement of keel, and at each
water-line, in tons.
Through points i, 2, 3, 4, and 5 d(
lineate curve A 5, which will represent
displacement at any given or required
draught.
Draw a horizontal scale correspond-
ing to weight due to displacement at
load-line, as A C. and subdivide it into Cons and decimals thereof, and a ver-
tical line let fall from any point, as a;, at a given draught, will indicate
weight of displacement at (fepth, on scale A C, and, contrariwise, a line raised
from any point, as z, on A C will give draught at that weight.
Illustbatiox. —Displacement uf hull (page 654) at load-line = 7151.8 cube feet,
which -r- 35 for salt water = 204.3 tons, hence AC reprcucntH tons, and is to be sub-
divided accordingly.
Assume launching draught to have been 4 feet, then a vertical let fall trom 4 will
indicate weight of hull in tons on A C.
Coi-fficients. {By C. JUackrow, M. I. N. A.)
DBMBimOIf OF ViaSBL.
Iron-Cluds,
Mail Steamera .
<
Uerchant, small |
Gunboats |
rroop Ships........ |
Swift Naval Steamers. . . . |
Fast SteamenB, R. N.
Coefflcient.
Length.
Breadth.
Mean
Draught.
Displace-
ment.
A midship
Section.
225
45
IS
.715
.932
325
59
24-75
.64
.81
350
35
21
.687
-85
385
42
22
.659
.88
368.27
42-5
18.71
.516
.812
220
27
8
.702
.912
90
*5
4
-637
v
"S
23
8
.536
z6o
31-3
12
.466
•745
350
49.12
23-5
.47
.674
340-5
46.13
15-75
"♦«
.68
337-3
50.38
22.75
-433
-787
270
4a
19
•497
.792
300
40.27
14
-4»4
.711
WatMT.
Itnee.
-755
•71
.84
.8
•63s
.742
.704
.6x6
.603
•7
.58a
.614
.628
.7x1
Curve of "Weiglit.
Xo Compute dumber of* Tons required to Depress a
Vessel One Inoli at any Drauglit of* AVater Parallel
to a Water-lixie.
Rule. — Divide area of plane by la, and again by 35 or 36, as may be
xeqaired for salt or fresh water.
Example. — Area of load water-line of a vessel is 1422 sq. feet; what is its ca*
psoity per inch in salt water ?
1422 -r- x2 = xxB-s, which -=- 35 = 3.38 tons.
6s8
NAVAL ARCHITEOTUBB.
'J?o Compute Centre of Ghravity of* Bottom Plating
of a Vessel..
LonffUudinal.
Rule. — Measure half girths of piatuig at equidistant sections, as at two
or more frames. Multiply these in accordance witii Simpson's role f«
areas and add products together.
Multiply each of these products in their order, by number representing
number at intervals of section forward and abaft of J8. Divide difference
of these moments by sum of products of half girths, previously obtained.
Multiply product by common distance between sections, and result will
give distance of centre of gravity from iS in a horizontal plane.
Illustration.— Assuni* half-girths aS in foUowiDg table, and distance between
sections lo feet
FORWARD.
Half-
Multi-
Prod-
Gtrtha.
plien.
uct.
Feet.
25
i.
25
23
4
92
21
2
42
»9
4
76
17
2
34
15
z
15
Malti-
Mo-
Sec-
pli«n.
menta.
tion.
No.
—
—
I ...
I
2
it
2 ...
3---
3
228
4...
4
136
5-*.
5
75
615
ABAPT.
H«ir-
Malti-
Prod-
MaUi-
Mo-
Oirtfat.
pHera.
net.
plien.
menta.
Feet.
23
4
92
I
2'
20
2
40
9
80
x8
4
72
3
2X6
16
2
3a
4
Z28
«4
z
"4
5
70
534
586
Sec-
tion.
No.
¥'"
^m . . • •
B. . . .
C . . .
D....
Moments forward, 615 — moments abaft, 586 = 29 ^ sum of product 534 = .054,
which X zo feet = .s4ffetfonoard of jgj.
Centre of X^ateral Resistance.
Centre of Lateral Resistance is centre of resistance of water, and as its po-
sit ion is changed with velocity of vessel, it is variable. It is genendly taken
at centre of immerseil vertical and longitudinal plane of vessel when npon
an even keeL
If vessel is constructed with a drag to her keel, the centre will be moved
proportionately abaft of longitudinal centre.
Yacht America had a drag to her keel of 2 feet, and centre of lateral re-
sistance of her hull was 8.08 feet abaft of centre of her length on load-line.
Centre of Sfibrt.
Centre of Effort is centre of pressure of wind upon sails of a vessel in a
vertical and longitudinal plane. Its position varito with area and location
of sails that may be spread, and it is usually taken and determined by tlM:
ordinary standing sails, sudi as can be carried with propriety in a moderatdy
fresh breeze.
In computing this position, the yards are assumed to be braced directly fore
and aft and the sails flat.
NoTi.— Centre of effort of sails, to produce greatest propelling efRsct, most accord
with capacity of vessel at her load-line, compared with fulness of her immersed
body at its extremitiea Thus, a vessel with a tall load line and sharp extremities
below, will sustain a higher centre of effort than one of dissimilar capacity and oo§*
ftractioR.
NAVAL ABCHITECTUBB.
659
To Compuite Xjooatipu pf Cez>tre of Sffbrt.
Rule. — Multiply area of each sail in square feet by height of its centre of
gravity above centre of lateral resistance in feet, divide sum of these prod-
ucts (moments) by total area of sails in square feet, and quotient will give
height of centre in feet.
2. Multiply area of each sail in square feet, centre of which is forward of
a vertical plane passing through centre of lateral resistance, by direct dis-
tance of its centre from that plane in feet, and add products together.
3. Proceed in like manner for sails that are abaft of this plane, add their
products together, and centre of effort will be on that side which has greatest
moment of sail.
ExAHPLK. — Assume elements of yacht America as rigged when in U. S. Service.
Sail.
Flying Jib
Jib
Foresail . .
Maiosail..
5383
Vertical moments 172575
Area of sails 5 383
sistance.
91 765 '\j 68 896
Height of
Cent, of Grav-
ity of ShUb.
Vertical
Moments.
Distance of Centra
ofGravity of bails.
Foreward. Abaft.
Mome
Foreward.
Feet.
28
26
34
35
18368
28262
49470
7647s
52
32
3
40
34 "2
34784
«72 575
68896
Abaft.
4365
87400
9*765
= 32.06 = height of centre above centre of kUerctl re-
MvnunU \
sistance.
5383
= 4.25 = distance of centre ahaft centre of lateral re-
Relative Fositioxxs of Centre' of Sffort and of X-iateral
Resiataiioe.
Square lUg,
4A
L(.75d' + d")
xo(d' + 0
= E.
Fore and Aft Riff.
io(d'-|-d")
rA = E,
and ^-^ = E'. L rqn'esenting length of load-line^ d distance of centre of buoyancy
of vessel beUno it, d' distance of centre of lateral resistance abaft centre of it, d" dis-
tance of centre of buoyancy before centre of it, E distance of centre of effort before
centre of lateral resistance, and E' distance of centre of effort above centre of lateral
resistance.
^^eta-Centre.
Meta-cewtre of a vessel's hull is determined by location of centre of grav-
ity or buwancy of immersed bottom of hull, for it is that point in transverse
section of hull, where a vertical line raised from its centre of gravity or
buoyancy intersects a line passing through centre of gravity of hull, as
Fig. I, page 650.
To Compute Heiglit of ^f eta-Centre.
By Moment cf Inertia, T) = ^* ^ representing moment of inertia qf area
of water-line or plane of flotation^ and D volume of displacement in cube, feet
NoTS. — Moment of Inertia of an area is sum of products of each element of that
area, by square of its distance flrom axis, about which moment of area is to be
computed.
To A.soertaixi Iifozxiezit of Inertia approxiraatelsr.
Rectangle =iCLB3- G = -L when L = 4B; C = — when L = 5B; andC =
12 50
SL when L = 6 B. With very fine lines and great proportionate length C = —
Ij emi 3 measured at load line.
66o
NAVAL AKCHITECTURE.
Volume
Illustbatiok.— As^me length of vesael 333 feet, breadth 43, draught x6, and
displacement 2700 tons. Length = 5.65 beams; hence C is talien at
of displacement =2700 x 35 = 92 500 cube foet
Then ^'X '33X433^
21
400
400 X 92 500
ia5i. Exact height of moment was 10.44 f^^
By Ordinaies, Rule. — Divide a half longitudinal section of load water-
line by ordinates peri)endicular to its length, of such a number that area
between any two may be taken as a parallelogram. Multiply sum of cubes
of ordinates by respective distances between them, and divide two thirds
of product by volume of immersion, in cube feet.
Illustration.— Take dimensions from Figs. 2 and 3, page 654.
4
3
2
k
Length.
. 5 ..
. 7.7..
. 9- 5 . . .
. 9.9* • '
.10 . . .
Cube.
. 125
. 456
. 857
• 970
.xooo
Len^tb.
B 7.8...
C 6.8..,
D 4 ...
Cube.
51460
2
102020
7151.8) 34306.6 = 4.77 fi.
Cube.
. 885
• 475
' 314
5146 X 10
If there are more ordinates, their coefficients must be taken in like manner, ae
X — 4 — 2 — 4 — 2 — 4 — X.
For operation of this method, see Simpson's rule for areas, page 343.
2 /* W^ rf X
Or, — / ^-j- — = M. y representing ordinates of haJf-breadth sections cU load-
3*-' IJ
line, d x increment of length, oftoadline section or differentiai ofx, and D displace-
ment of immersed section in cube feet.
By Areas.
— (a3 ^- 4 63 -f. 2 c3 -I- 4 d3 + €3) i. -f. F -I- A
3 3
D
= M. a, 6, c, d,
and e representing ordinates of isi or load toaier-line, P area of irregular section
between ist frame, and stem, and A area of like section between Uut frame and
stern-post y both in sq. feet, D displacement, in cube feet, and I distance between frames
or sections ofvtater-line, as may be taken, in feet
To Ascertain Areas ofT and. A*
—Fig. S.
— abxbc^
3
4 = F, and— dcX<fl'3-r-4^ A
3
Klements of Capacity and Speed of Several Types of
Steamers of R. N. {W. H. White.)
Claims.
Length.
LenKth
to
Breadth.
Displacement.
SpMd.
ObplMw-
ment.
to
Diaplace-
nwntf.
Ironclads.
Feet.
Tone.
Knots.
Recent types,
do. twin so.
300 to 330
280 to 320
5.25t05.7S
4-5 105
7500tO 9000
6oootO 9000
14 to 15
14 to IS
.9tox
.7 to .9
16 to 20
X5t0x9
Unarmorkd.
Swifl cruisers
Corvettes ....
Ships
Gun -vessels..
Gun boats ...
270 to 340
200 to 220
160
125 to 170
8oto 90
6. 5 to 6. 75
6
5.5 to 6.25
3 to 3. 25
3000 to 5500
1800 to 2000
850 to 050
420 to 800
200 to 250
15 to 16
12.75 to 13.25
IX
0.5 toix
8 to 9
x.3tOi.5
X tOl.2
X tOX.2
.8 to 1.4
.8tOi.i
20t0 24
X3 to 14
XOtOlI
7 to XX
5 to 7
Mkbohant.
Mail, large...
'< smaller.
Cargo, large..
'* smaller.
400 to 500
300 to 400
250 to 350
200 to 300
9' ton
8 toio
7. 5 to 10
7 to 9
7000 to 10 000
5000 to 7000
3000 to 6000
i5ooto 4000
14 to 15
13 tox4
XI to 15
9 to IX
•5 to .6
.4 to .5
3to -5
.2to .4
xotoxi
7 to 10
5to 0
3to 6
NAVAL AUCHITKCTUKE.
661
Xo Compute PoAver R,eq.uiired. in. a Steam Vessel, oapao-
ity of anotlier Vessel toeiiig given.
In vessels of similar models, — = V ; — j- = V ; —7- = C ; and — - = R;
V and V representing pi'oduct of volumes of given and required cylinders and revo-
lutions in cube feet, a and A area^ of immersed section of given and required
vessel in sq. feet a4 like revolutions and speed of given vessel, s and S speeds of given
and required vessel at revolutions of given vessel, both in feet per minute, r and r'
revolutions of given and required vessel per minute^ and C product of volume of com-
bined cylinder and revolutions for required vessel.
Illustration.— A steam vessel having an areaof amidship section of 675 sq. feet,
lias two cylinders of a combined capacity of 533.33 cube feet, and a speed of 10.5
knots per hour, with 15 revolutions of her engines. Required volume of steam
cylinders, with a stroke of 10 feet, for a section of 700 feet and a speed of 13 knots
with 14.5 revolutions
I' =■• 533- 33 X 1 5 — 8000 cube feet,
15X15745-2
8000X700 1. r * 133X8296.3
- — = 8296. 3 cube feet, — — J; =
15745.2 cube feel,
675
= 16 288. 1 ciibe feet.
and
16288.1
10.5-
= 561.66 cm6«
14-5 ' a X 14-5
feet, lofcicfc-t- 10 stroke of piston, 12 for ins,, and X 1728 ins. in a cube foot=z
— — — =8087.0 sq. ins. area ofecu:k cylinder = diameter of loi I ^ ins.
10 X 12
Approximate Rules to CoTupute Speed aud IIP o£ Steaxn
Vessels.
V3 of
1H»
= C
= 1/
Clip
— V ; and
V3dS
= IIP. Or,
'^
Clff V3A
- = V: and-— ^= IIP.
C representing coefficient of vessel, A area qf immersed amidship section in m.feet,
V velocity of vessel in knots per hour, and D displacement of vessel in tons.
NoTB. — When there exists rig. an unusual surface in freeboard,deck-hou8es, etc.,
or any element that eflects coefficient for class of vessel given, a corresponding ad-
ditloD to, or decrease of, foUowing units is to be made:
Rttnge of Coefficients as deduced from obsei'vation is cufoUoics:
SIDE- WHEEL.
Vbmil.
JBttamboat.
Medium line* .
Ftn« linet
Buamtr.
Medium fall Uum*
VId« Unc«t.
Sq.F,
43
150
136
675
T't.
73
465
300
3600
• Fall rigged.
K'to.
10
13
«9
10
15
V»A
IH»
470
570
540
650
650
V*D|
IH»
212
219
200
214
SIX
PPOPKLLER.
VCSSEL.
Sttamboat*
Mediam lines..
« <<
Fiu« lines
Steanur,
Medium full...
Torpedo boat.
45
150
550
390
2532
U7S
3600
27
t Bark rigged.
12
9
xo
13
20
v* a!v>d|
1K»
194
180
2x0
170
IH>
SOD
530
570
470
500
Coefficients €u Determined by Several Steamers of H. B. M. Service.
{C. Mackrow, M. I. N. A.)
Length.
Feet.
185
912
360
380
400
36a
400
Length
Areaof
Displace-
IR'
Beam.
Section at g{.
ment.
Sq. Feet.
Tons.
6.53
236
775
782
589
377
>554
1070
7-33
814
5898
2084
6.43
63a
3057
2046
6.52
1308
9487
3205
6.73
1 198
9152
5971
7 33
778
5600
3945
6867
6.73 I
n85
9071
3K
V»A ^
Speed.
I fP - ^•
Kuoto.
10.34
333
laSq
456
"•5
598
12.3
574
12.05
714
13-88
536
14. 06
548
>5-43
634
4-5
3-5 3 2-5
662 NAVAL ABCHITBCTURE.
^Approximate Rule for Speed, of* Sore^w Propellers.
(Molesuwrth.)
,o.V PN_ loiV . ?^_N. ^-„. and?^-P
"P"-^' T^-^' ~N~-*^' ^^-N' IT-''' *"'* N -*^
V and V representing velocities in knots and miles per hour^ P pitch of propeller in
feet, and N number of resolutions per minuU,
This does not include slip, which ranges from lo to 30 per cent
I*itolx of Sore-w- Propeller.
f*itch ranges with area of circle described by diameter of screw to that of
amidship section.
Area of screw circle to amidsbip ) | ^
section = i to ) 1
Tivo B.'ndi's.
Pitch to diameter of screw = I to | 8 | 1.02 | i.ii | 1.2 | 1.37 1 1.31 | 1.4 | 1.47
Four Blades. \ 1.08 j 1.38 | i 5 | 1.62 | 1.71 I.1.77 | 1.89 | 1.98
Length = 166 diameter
Slip or Side-^velieels.
Radial Blades. ~ - S. Feathering. '5 ^ ~^' = S. A representing
A A
length o/arc of immersed circumference of Modes, c length of chord of immersed arc^
and S slip, aU in feet.
A.rea of* Blades.
River Service. ''^^ — = A. Sea Service. '— - = A D representing diameter
of wheel in feet, and A area of each blade in square feet
Lengtii of Blades .7 in River service and 6 in Sea service.
Distances between Rculial Blades. 2.25 in River service and 3 feet in Sea service;
between Featliering blades, 4 to 6 feet.
Proportion of* Power Utilized in a Steaxn "Vesael.
p t „^^
Side Wlieel. r^— - = C. P representing gross Iff, « lost of
000002 59 d3r« ^ " " ' "^
effect by slip and oblique action of wheels, d diameter of wheds at centre of effecty
r revolutions per minute, and C coefficient for vessel
Illustration. — Iff of engines of a side-wbeel steamer is ti2o; slip of wheela
and loss by oblique action, 33.37 per cent. ; diameter of centre of effect of wheels is
29.5 feet, and number of revolutions 13.5 per minute; what is coefficient, and what
power applied to propel vessel f
NoTK. — Slip of wheels fVom their centre of effect in this case is 15.37 l*^^ cent,
and loss by oblique action 18 per cent Hence, representing total power by 100^
100 — (18 -j- 15.37) = 66.63 P^"" cent of power applied to wheels.
As assumed power that operates upon wheels in this case is taken at 86 x a per
eent of ))ower exerted by engines, 86.12 X 33-37 =228.74 per cent for sum of Ion
by wheels.
i,2o-(xi2oX 174^100) ^ 7981U = 65.63 coefficient
.00000259 X 295^ X 13.5* ««»6
Speed of vessel being 10 knots per hour = 17.05 feet per second, power applied
to pro{)el vessel at this speed = 65.63 X 17-05'=: 19076.13, and ff exerted =
19076.13 X 1705 X 60 _
— 59'- 3". Per cent.
^^ **^- ofPoww.
Friction of engines 1.5 lbs. upon 3848 sq. ina x 13-5 revolu-t
tious X 7oX2 ^ 33000 X 2 ) ^^^ , ,g g
Friction of load 6 per cent upon pressure of steam, less 2 lbs. ) g^ .
for iHction of engine, as above ) "*^45
Oblique action of wheels aoi.6 18
sup ot wheels 173.14 »5-37
-oibed by propulsion of vewe) ..,..f,.,,,., 591.36 5^8
Xiao 100
NAVAL ABCBITECTCBB.
663
P«r MDt.
of Power.
18.83
6.83
36.27
100
Bore'w Propeller. Friction of enginea 96.06)
Friction of load » §1. 48 J
*' of screw surface and resistance nf edges of blades 53. 44
Slip of propeller. 205. 55
Abflorbed by propulsion of vessel. 375-92
782.4s
NoTS.— From experiments of Mr Froude, he deduced that, as a rule, only 37 to
40 per cent, of whole power exerted was usefully employed.
With an auxiliary propeller, essential differences are in fViction of surfaces and
edges of blades of propeller and slip of propeller, being as 13 to 6. 83 in excess in first
case, and as 13.7 to 36.37 in second case, or $0 per cent less.
Reiistance o/BoUonu 0/ Hulls at a Speed qfone Knot per Hour,
Smooth wood or painted. 01 lb.
Smooth plank 016 "
Iron bottom, painted 0x4 **
CJopper. 007 lb
Moderately foul 019 **
Grass and small barnacles 06 "
Sailing.
Xlatio of Kffeotive JLrea of Sails and or Veseel^s Speed
under Sail to Velocity of* "Wind-
COUBSB.
5 points of wind.
3 " abaft beam . .
6 " of wind
Ratio of
EttmMv
Are*
ofSidli.
•59
.91
.68
Ratio of
to Wind.
Couaaa.
Ratio of
EffectiTO
Area
ofSaila.
Ratio of
Speed of
to Wind.
•33
.5
•5
Wind ab^m .........
.«3
I
.96
.6
" astern.........
•5
.66
" on quarter
Propulsion, and A.rea of Sails.
Plain saiU of a vessel are standing sails, excluding royals and gaff topsaOs.
Resistance of vessels of similar models but of different dimensions for equal
8peeds=D3
Hence -7 = f ^j . a and a' representing areiu of sails qfknotm and given ves-
teUj cmd D and D' tA«t> dUspUucaikKnlts in tons.
iLLUsnunoii.— Assome D and D' = 3400 and 1600.
Then (^2— 1 = V» 5* = «'3«> *»«**<» »'«* of sails a' = -^ — 763 per cenL
In Ve$telt of Dissimilar Models. — Plain saU area should be a multiple
of Di.
MMplesfor Different Classes of Vessels, R. M
SaiUng. Steamers.
Ships of Line 100 to zso Ships, iron-clad 6oto8o
Frigates ) Frigates )
Sloops. S X3ot0z6o Sloops [ 80 to 1 30
Brigs ) Brtgs )
Enfflish Yachts, designed for high speed, have multiples from 180 to 200,
mud when designed for ordinary speed from 130 to 180.
Wken Area o/SaU to Wti Surftue of Hull is <aJleen.— American yacht Sappho had a
ratio of 3.7 to I, and several English yachts nearly the same, while in some others
itwaabniatoi.
664
NAVAL ABCHITECTUKE.
I^ooation or IVIasts, etc. Load-line =z too.
Vrnmaim
Ship
Bark ,
Brig
Schooner ...
Sloop
Fore.
DbUnoe from Stem.
Main.
lo to 20
12 to 20
17 to 20
16 to 22
53*058
54 to 60
64 to 65
55 '" 61
36 to 42
Minen.
801090
81 1091
Fool of Sail.*
< HeU^tofCantn
I of Effecl aboT*
I Water-lfB« =
Brwulth.*
125 to 160
130 to 160
160 to 165
160 to 170
170 to 190
— I-
to 2
to 1.95
to 1.75
to t.75
1.25 to 1.75
1-5
1-5
1-5
>.5
* Meaaurad from Tack of Jib to Clevr <tf Spankar or Mainnll.
Rakeo/Mcuti.
ShipB. — Foremast o to .28 of length fVom hud, Mr. in ami Mizzen o to 25
Schooners. — Foremast .1 to .25, Mainmtist .63 to .77. Sloot)8.— .08 to .11.
A-rGB. of Sails.
Sails.
Jib
Foremast.
Mainmast.
3 Yard* upon
each Maat.
.08
•295
.417
4 Yarda apon
each Maat.
Sails.
3 Yards apon
each Maat.
4 Yarda apon
CHch Maat.
.08
295
•417
Mizzenroast. . . .
Spiuikcr or \
Driver. . . { * '
.127
.081
•«4
.068
Proportional Area of Sails upon each Mast under abate Divisions.
Sail.
Course.
Topsail
Topgallant sail ,
Royal
Spanker or Driver. . . . ,
Jib
Fore. 1
Main. 1
Mixcen.
Proporl
."5
.097
.162
.138
—
—
.389
•358
»o5
.09
.149
.127
.075
.063
.075
.063
.106
.089
.052
.045
•853
—
•045
—
.063
.033
—
.i—
—
——
.081
068
^—
.08
.08
•375
.
—
—
—
375
•417
.417
.208
.208^
I
■33
•303
•a»5
•15a
Balance of Sails. — Effect of jib is equal to that of all sails upon main-
mast, and sails upon mizzenmast balance those of foremast.
Areas of sails upon masts of a ship should be in following proportion :
Fore X. 414 I Main a | Mizzen i
When, therefore, main yard has a breadth of sail of 100 feet, fore yard
should have 70.71 feet, and mizzen 50 feet-, topgallant and royal yards and
sails being in same proportion.-
i^ngles of Keel for Different VeBselB.
Approximately. — j^ — = S. D repreuaUng displacement of vessel in Oti.,
M height ofmetat^mire above centre of gravity in feet, a angle of heel of vessel m cir-
cular mecuuref* and H height of centre ofegtect above centre of lateral t-esistance,
infeet.
Moment of sail should be equal to moment of atabilify at a defined awj/le
offieel.
Schooners, etc. .... 6° . 105
Yachts 60 to 90 .105 to .107
Circnlftr
Measure.
.07
.087
Angle.
Frigates, etc. 4^
Corvettes. 5^
Illustration. — Assume displacement 170 tons, height or meta-centre 6.75 foelt
H = 36 feet, and angle of heel 9^^ ; what should be area of sails ?
170 X 3240 = 380 800 lbs. 9° = . 107.
380800X6^75 X. 107 ^ ^8 ^^^
30
* 8ae rale, page 113.
NAyAL AECHITECTUKB.
665
Trikxnming of* Sails.
That a vessel's sail may have greatest effect to propel her forward, it should
be so set between plane of wind and that of her course, that tangent of angle
it makes with wind may be twice tangent of angle it makes with her course.
Or, tan. a = a tan. 6. a representing angle of sail with windj and b angle 0/ sail
and course of vessel.
Wind
AheMl.
.A.iigle8 of* Course axid.
AdrIm of Sail
with
Course,
3
35° 16'
Impulse
Wind
Abaft.
Sails Avitb. "Wind.
Angles of Sail
PoinU.
2
3
4
6
Angie
oT
Course.
112° 30'
123° 45'
135°
157° 30'
Tan-
gent.
2.166
2-737
3-562
7-5"
Half
Tan-
gent.
1.082
1.368
1. 781
3-754
with
Wind.
with
Course.
65° 13',' 47*^17.
69O 56' '
74° 17'
82° 25'
53° 49,
60O43'
75° i'
of Wind.
Let P 0, Fig. 6, represent direction by com-
pass and force of wind on sail, A B; fVom P
draw P C parallel to A B, from o draw o C per-
pendicular to A 6; o G is effective pressure
of wind on sail A B, and r C, perpendicular to
plane of vessel, is component of o C, which pro-
duces lateral motion, as heel and leeway, and
r o is component of 0 C, which propels vessel.
Isin.arrP; Pcos. aj = L; and Psin.a; = E.
I representir^ direct impact and P efftctive
pressure of wind on sail, L effective impact
producing leeway, and E effective impact which
propels vessel. »
Note.— The law as usually given is sin.'. This is manifestly incorrect, as it gives
results less than normal pressure for angles of small incidence. At an angle of in-
cidence of wind of 25°, the law of sin. is exact. Hence, although it may not be
exp.ct at all angles, it is sufficiently so for practical purposes.
Illustration i. — Assume wind 5 pqints ahead, and I = 100 lbs.
By preceding table angle of course with wind 56^ 15'; hence angle of sail a, with
wind 36° 12', as tan 36° 12' = 2 tan. 20° 3', and angle x 56° 15' — 36° 12' = 20° 3'.
Then, 100 X sin. 36° 12' = xoo X .5906 = 59.06; 59.06 X cos. 20° 3' = 59.06 X
-9394 = 55 48, and 59.06 X sin. 20° 3' = 59.06 x -3426 = 20 23 Ihs.
3. —Assume wind 4 points abaft, and I = 100 lbs.
Then, iooXsia2 740 17'= 100 X -96262 = 92.66; 02.66 X cob. 180° — 74° 17'-}- 45°
= 6o°43' = 92 66x.49 = 45 4i, and 92. 66 X sin. 60° 43' =92 66 X. 8722 = 80.82 i6».
To Compute Sailing IPower of a Vessel.
F/sin. w, sin. s = P.
7o Compute Careening Power of a Sailing Vessel,
Fy sin. yo, cob. « = P F represefniing area of sails in sq. feet, f force of wind in
lbs. per sq.faot, w angle of wind to sails, and s angle of sails to course of vessel.
To Compute A.ngle of Steady Keel.
Within a Range of%<>.
gPE
DM
= Bin. H. a representing area of plain sail in sq. feet, P pressure of wind
in lbs. per sq.faot, E height of centre of effect above mid-draught, in feet, D displace-
wsent ofhuUy in lbs. , and M height of meta-cenire in feet.
P assumed at i lb. per sq.faot, or that due to a brisk wind.
20
Illustbatios.— AsBame 0 = 15600, draught = 20, and £=62; hence 634-^=3
2
r, D = 6 800000, and M = 3.
Then
15600 X 1 X 72 _ 1 123200
6800000X3 20400000
= 05505 = 3°
zo
3K»
666
KAYAL ABCHITECTUlgUB.
Course and A-pparent Course of \Viiicl.
Apparent course of a wind against sails of a vessel is resultant of normal
course of wind and a course equal and directly opposite to that of vessel.
Illcstratiox. — If P, Fig. 7, repre-
sent direction by compaiffi and force of
wind, and a b direction and velocity of
vessel, firom P draw P c parallel and
equal to a h, join c a and it will repre-
sent direction and force of apparent
wind.
A C
Or, — r; = ratio of velocity oftxppareiii
C mT
aP
wind to UuU ofvettely — ^ z^ ratio of velocity oj wind to that of vessel.
c P
Resistance of Air, {Mr. FnnuU.)
Resistance, of wina to a vessel is estimated as equivalent to square of its
velocity.
In a caln), resistance of air to a steamer = one thirty-fourth part of resist-
ance of water, anU when a steamer's course is head-tc>, and combined veloc-
ity of vessel and wind = 15 knots, resistance is one ninth of that of the water.
Resistance of air to a sq fooi of surface at right angles to course of a ves-
sel is about .J3 lb., aixl whcL surface is mclined t) direction of wind, press-
ure varies as sine of angle 0I incidence.
Mean of angles of surface of a steamer exposed to wind may be taken at
45° ; hence their resistance is about .25 lb. per sq. foot when wind lias a ve-
locity of 10 knots per hour.
If sectional area of a steamer's hull above water is 750 sq. feet, resistance
to air at a speed of 10 knots in a calm would be 750 X .25 := 187.5 lbs., and
resistance to smoke-pipe, spars, and rigging (brig rigged) would be 201 lbs.
I-jee\vay-
Ant/le of Tjeeicay in gootl sailing vessels, close hauled, varies from 8° to
12°, and ill inferior vessels it is much greater.
Ardency is tendency of vessel to fly to the wind, a consequence of the
centre of effort being abaft centre of lateral resistance.
Slackness is tendency of vessel to fall off from the wind, a consequence of
the centre of eft'ort being forward centre of lateral resistance.
Remits of Experiments upon Resistance of Screw-propellers, at High Velocities
and Immersed at Varying D^Ots of Water.
Immcralon of
Screw.
Surface.
I foot
Resistance.
I
5
Immersion of
Screw.
Resistance.
a feet
3 "
7
75
Immersion of
Screw.
4 feet.
5 "
Reetstanos.
7-8
8
Slip ofPropeUer^ 15 per cent. ; of Sule-irheel {feathering bladeB)^ and tak-^
ing axes of blades as the centre of pressure, 23 per cent.
Tr"reelt>oard#
Measured fi'om Spar-deck stringer to surface 0/ water. Depth ofHotdfirom under-
side qfspar dedc to top of ceiling.
Hold.
Feet.
8
IP
Per Ft.
Ins.
«-5
9
Hold.
Feet.
12
X4
Per Ft.
Ins.
2.25
a-5
Hold.
Feet.
16
z8
Per Ft '
■I
Ins.
a- 75
3
Hold.
Feet.
20
23
Per Ft
Ins.
3- "5
3.25
Hold.
Feet.
24
26
Per Ft
Ins.
3-375
3-5
Hold. iPttr Fv
Feet. I las.
a8 I 3.625
5° 1^75
NAVAL ABCHITSCTUBB.
667
Plating Iron Knlls.
PA _,
d depth. Or, .osfy/d = T. / rqn^etenting distance betvoeen centra 0/ frames, and
d dqp*k ofiplaU, Mow load-line, all in feet, and T thickness of plate in ins.
, = T. D representir^ displacement in tons, L length of huU, b breadth^ and
INdasts and. Spars.
Lower masts at spar deck.
Bowsprit ^^ stem.
Topmasts " lower cap.
Topgallant masts " topmast cap.
Fore and ma in masts, when of pieces, x
Diameter for Dimensions.
Jib-boom at bowsprit cap.
Yards in middle.
Gaffs at inner end.
Main and S)^>anker booms at tJiHVail.
inch for each 3 to 3.25 feet of whole
- feet of whole length.
length. Mizzenmast .66 diameter of mainmast. Masts of one piece i inch for each
3.5 to 3.75 feet of whole length.
Bowsprit, depth, equal diameter of mainmast; width, diameter equal to foremast
Main and fore topmasts i iuch for each 3
Mizzen topmast i
Topgallant masts i
Royal masts. i
Topgallant poles i
Jib boom i
Fore and main yards i
Topsail yards. 875
Cross -jack, Topgallant, and)
Royal yards }
Main and 8piinker booms i 3-5
Gafls I " " " 3-5*04
SiuddiDg-sail yards and booma I " '' " 4.5104.75,
u
i(
((
(t
n
(i
t(
<t
l(
it
((
((
t(
1(
(I
((
C(
t(
i(
((
t(
<(
(I
((
t(
((
t(
t(
i(
cc
((
ic
it
to 3.25
3- 25 '' 3-33
3-25 " 3-33
3-66
2.87
2 ft. of length beyond bowsprit cap.
4
4
5
feet of whole length.
Rudder Head.
{Mgckrow. )
At>a
/ T A t>2
Pd = T: .iq6CD3=M; 3/ — __=rD; and =P. P representing press-
^ V • '96 C 2400
ure on rudder when hard over, in tons, d distance of geometrical centre of rudder from
axis of motion, in ins., T stress on head, and M moment of resistance of head, both in
t'ncA-totu, A immersed area of rudder xn sq. feet, v velocity of water passing i-udder
in knots per hour, and C coefficient = 3. 5 jter sq. inch for Iron, and . 125 for Oak.
iLLrsTRATioN. — Assumc iiroa of wooden 'rudder 24 sq. feet, distance of its geomet-
lical centre from centre of pintles 2 feet, and velocity of water 10 knots.
24 X 10
— = 1 ton. I X 2 X 12 =3= 24 istch-tons.
V.««
24
= 9.93 tfU.
2400 "V -196 X •125
ACemoranda.
Weights. — A man requires in a vessel a displacement ot 488 lbs. per month, for
baggage, stores, water, fUel, etc, in addition to his own weight, which is estimated
at 175 lbs. A man and his baggage alone averages 225 lbs.
A ship. 150 feet in length, 32 beam, and 22.83 in depth, or 664 tons, C. H. (0. M.),
bas stowed 2540 square and 484 round bales of cotton. Total weight of cargo
I 354 448 lbs. , equal to 4. 57 bales, weighing 1889 lb& , per ton of vessel.
A full built ship of 1625 tons, N. M., can carry 1800 tons' weight of cargo, or stow
4500 bales of pressed cotton.
Hull of iron steamboat John Stevens — length 245 feet, beam 31 feet, and hold
II feet; weight of iron 230440 lbs. And of one other— length 175 feet, beam 24
feet, and 8 feet deep; weignt of iron 159 190 lbs.
Weight of hull of a vessel with an iron frame and oak planking (composite), com-
pared with a hall entirely of wood, is as 8 to 15.
An iron hull weighs about 45 per cent, less than a wooden hull.
Iron ship, 254 feet in length, 42 beam, and 23. 5'hold, 1800 tons register, bas a stow-
age of 3200 tons cargo at a draught of 22 feet Weight of hull in service 1450 tons.
l,oss by Weight per Sq. Foot per Month ofMelaUing of a Vessel's Bottom in Service.
Copper .0061 lb. ; Muntz metal .0045 lb. ; Zinc .007 lb. ; and Iron .0204 lb.
Comparison between Iron and Steel pkUed Steamers— In a vessel of 5000 tons
displacemei^t, hull of steel-plated will weigh 330 tons less = 6.66 per eentwn less.
OPTICS.
MirFora, in Optics, aie either Pltme or SjAerical. A plane mimviit
plane reflecting gunac«^ and a spherical mirror 19 ons the Teflecting boi^
of which IB a [mition of aurtace of a aphere. It la concave or convei, «■
cording as inside or oulside of surface ia reflected from. Centre of it!
sphere ia termed Centre q/" cwmaare.
Focal — Point ia which 1 numlter of ra;^ meet, or would meet if preduoiL
/VincijNii Focal Diilnacn ia half raJiua
of cnrvature, and is generally termed lit
focrd Hiilan^. Line a i: ia tenned tit
= principal aril, and any nther riRht liiif
: throuKhcwhichmcetsIheniirrorisleriiiri
- a Secondary nxii. When the ioctdciil
rays are parallel to ttie principat arii, lit
reflected rays converge (o a point, F.
of the rays proceeding from any given poitl
r, and which are reflectcit ao aa to meet in u-
other point, on a lino passing Ihroufjh cenln
of sphere. Hence, their relation being mu-
tual, they are teniieil conjugate.
Coi^jaiiaU
■etbe/oci
is behind a mirror, and reflected rays diverge,)
lint, such focus ia termed Vitiaat, and a focus i
is termed RfoI.
OPTICS. 669
When a ray is diverted from vacuum into any medium, tlie ratio is greater
than unity, and is termed absolute index or index of refraction.
Mean Indices of Refraction,
Eye, vilreous humor i- 339
*' crystalliue lens, under i-379
" " '* central 1.4
Diamond 2.6
Gluss, flint 1.57
For indices of other substances, see page 584.
Heat increases refractive power of fluids and glass.
Glass, lead, 3 flint 2.03
" lend 2. sand 1 1.99
" " I, flint I 1.78
Ice 1. 31
Quartz 1.54
Critical Angle. — Its sine is reciprocal of index of refraction, the incident
ray being in the less refractive medium.
Thus, - . = sin, of angle.
' Index "^ ^
Visual Angle is measnre of length of image of a straight line on the retina.
Total Reflection is when rays are incident in the more refractive medium,
at an angle greater than the critical "angle.
Mirage. — An appearance as of water, over a sandy soil when highly heated
by the sun.
Caustic Curves or Lines are the luminous intersections from curve lines, as
shown on any reflective surface in a circular vessel.
1?o Compute Index or RefVaotioii.
Qin T
_. ' _^ = Index. I rqpresenting angle of incidence^ and R HuU of refradMn.
Sin. R
To Coxnpxite H.efVaction.
Concave-Convex and. Meniscus. — Effect of a concave-convex in refracting
light is same as that of a convex lens of same focal distance, and that of'a
meniscus is same as a concave lens of same focal distance.
2 R r
Meniscus y with parallel rays ^-— ; = F.
Magnifying Poioer. — In Telescopes the comparison is the ratio in which it
apparently increases length. In Mici'oscopes the comparison is between the
object as seen in the instrument and by the eye, at the least distance of
vision, which is assumed at 10 ins., and the magnifying power of a micro-
scope is equal to the distance at which an object can be most distinctly ex-
amined, divided by the focal length of the lens or sphere.
Linear power is number of times it is magnified in length, and Super-
ficialy number of times it is magnified in surface.
Magnifying power of microscofies varies, according to object and eye-
pr]as8, from 40 to 350 times tiie linear dimensions of object, or from 1600 to
X22 500 times its superficial dimensions.
Apparent Area. — As areas of like figures are as the squares of their linear
dimensions, the apparent area of an object varies as square of visual angle
subtended by its diameter.
The number expressing Magnification of Apparent Area is therefore
square of magnifying power as above described.
Illustbatioh. — If diameter of a sphere subtends i^^ as seen by the eye, and 100
a0 «eeo through a lelescope, the telescope is said to have a power of xo diameters.
670
OPTICS.
Xo Compute Slexnents of ^lirrors and Hieneies.
Or It'
li^irrors. Spherical Concave.* z= = D; =r: = l^
r — 2 I r — 2 I
Or L r d^
Spherical CmvexA — -,— =D; , , =1 Parabolic Concave. -7-r = P
'^ 2 Ii-|-r 2 L-|-r 10 A
UnequaUy Convex, t -r = F. Piano- Convex, g 2 B — . 66 f = F.
K -J- >■
Hyperbolic Concave \\ EUipf^c Concave.^ Spliere. . _ = F.
0 representing abject z:z x, r \'adiu8 of convexity^ I and L length or distance ofobijeci
from vertex nfcu^-ve, andfrmn external vei-tex, D dimension of object, d diameter of
base, Y focal distance, and h depth of mirror in like dimensions, I index of refraction^
and t tftickness of lens.
Illustration l— Before a concave mirror of 5 feet radius is set an object at 1.5
feet frona vertex of curve; what is r.itio of apparent dimenBion of image, and what
is length of and distance of object from external vertex ? Object = i.
— '^^- = 2. 5 f'^et, and -^^JH, = 3- 75 /«««•
5— 2X15 5 — 2Xi_j
2 If object is set at 4.5 feet f)rom vertex' of a like mirror, what is length of and
distance of inverted object ft'om internal vertex ?
— ?AL_ = ,.25 feet, and ^'^^^ = 5.625 feet.
2X45-5 2X4.5-5 ^ ^'^
3. — Before a convex mirror of 3.5 feet radius is set an object at 3 feet from ver-
tex of curve; what is length of and distance of object from external curve?
' ^ 3-5 _ .368 >rf, and ^^f^ ^i.iosfteL
2X3 + 3-5 2X3 + 35
4.— A parabolic reflector has a depth of 1.25 feet and a diameter of 2 feet; what
is its focal distance from vertex of internal curve ?
■=.^fe»t or 2.4 ins.
2«
16 X I 25
Uenses. Double Convex. t=F. When R = r = F;
m-ixK + r 2m — I
dF _ 'F _ S+F „ OF __ ^ SF _
F — J ' ¥ — 1 ' F ~" ' p_0~ ' S-l-F
Optical centres are in centres of lens. Hano - Convex and Ptano • Concow.
r
—7— = F. Optical centres are respectively centres of convex and concave sor-
R T
faces. Convex Concave (Meniscus) and Concavo- Convex. =F.
w — I xR— r
Optical Centres. Convex Concave. Delineate lens in half section, draw R fVom
its centre to circumference of lens (intersection of radii), draw r parallel thereto
and extending to its circumference, connect R and r at these external points of
contact with circumference and external curve, extend line to axis of lens, and point
of contact is centre required. Concavo- Convex^ Proceed in like manner, but in
this case r extends to, or delineates, the inner surface of the lens, •'vnd point of con-
tact with axis is centre required.
• D or \mage diMppean when / = .5 r. f W1i«n O it bepond F, It will be inrertod, m . ** = 1>*
aL — r
L r
•»"* 7dT r ~ '■ ^ When equAlly convex F = R. f When convex side to ezpoMd to pwmltel i»J«
•Dd when Mrallel rajra f»U upon plane aide, F as a R. | Rays of Ufrht, heat, or tound, Mflectod fron
.•?•..**' «J»yperbola, will diverge from ita concave lurfiMe, * and whw from the focua of as eUiPM»
wUlberaAraciedbyanrteceoftbeother. ^^
OPTICS. — PILB-DBIVING. 6^ I
WU» tiifett it htftmd/oeai ditUinc* (F), ite Image (D) will be inverted, u ^1= = D, and ^^ = /.
P r^e<en<»n^ magnifying povoer of lens, 8 J»m« ofwntMl sight, lo to 12 ins. for
far-stghted eyes and 6 to 8 for nearsigfiUed, ordinarUy 10 mm., V UmU of distinct
vuwn, O extreme disUmce ofoiijectfrom optical centre at distinct viHon, and m index
of reaction. ^
Illustration i.— If a double convex lens offline glass has radii of 6 and 6 25 ins
what is its focal distance ? Index of refraction = i. 57, see page 584. '
6 X 6.25
=== =5-37 tw-
1.57 — « X 6 + 6.25
2.— If a double concave lens has a focal distance of 2 ins., and object is 6 ins. from
vertex of curve, what is its dimension and what is its distance fh>m vertex of inner
curve ?
^ ^ 2 - .w .»rf 4X2
— -. — = 2 tiw., ana — ; — = i'.33 vns.
2 + 4 4 + 2
3.— If focal distance of a single microscope is 4 ins., what is its limit of distinct
vision, and what its magnifying power? 0 = 2.857 »»**.
2.857X4 . "0+4
4-2.857-'°*'"'^°^ -^ = 3.5 times.
Telescopes, Opera-glasses, etc.
D:o = F:/; o/^F = D, and ^ = i; M!L±Jl- = F+f f represent-
ing length of focal distance fi-om object lens.
Illustration— Principal focal distance of ocular lens of a telescope is .0 in. of
objective lens 90 ins. ; what is its magnifying power? '
90 -f- .9 = 100 times the oltject
PILE-DRIVING.
Effect of the impact of the ram of a pfle-driver is as the square root of
its velocity or heigat o£ its fall. Thus the theoretical velocity of fall is as
Vs g h or S Vh.
The impact or dynamic effect of the blow of a ram on a pile cannot be
determined with exactness, so long as it yields under the blow, as the yield-
ing cushions it and reduces its effect.
By my experiments in 1852 to determine the dynamic effect of a falling body, I
found it to be far greater than that given by the formula y/2 g h, and upon a late
repetition of them, under improved conditions of the instrument of registry, I find
it to be for one pound falling two feet, 52 pounda One pound falling 2 feet has a
velocity of xi.31 feet per second, but its dynamical effect or vis viva was 52 pounds,
or 4.6 times the velocity.
Observation and tests of the sustaining power of piles, at different locations and
under diflferent conditions, gave it as 2,13, and 3.7 to i times that deduced by the
formula 8 VA, which was but the net effect, or capf^city, of ram, less the friction of
its operation.
Wm. J. McAlpine in his operation on the foundations of the dry-dock in the Navy
Tard, Brooklyn, estimated the effect of a ram weighing 2240 lbs., falling 30 feet to n
reAisal, at 224000 lbs., or 2.28 times that given by the formula w 8 y/h.
EsBayists present a variety of formula, which differ in form. Some are com
paratively simple, while others embrace diameter, length, weight, and section; <
area, depth driven by last blow in feet or in inches, and Modulus of Elasticity of the
material of the pile, together with various factors for results.
When the losses of effect in the operation of a pile-driver are duly considered-.
viz., ftiction of ram in the guides of the leader, and of the hoisting line of ram in
the sheave and over drum (ascertained by experiment with a very heavy ram to
* + for tclaecopee kod — for qi)«r»-^liuMe, etc
672
PILE-DRIVING.
be equal to .2 foot of penetration: with a light ram it would be materially more),
the cushioning of it on head of a pile, however square it may be dressed oflr, the
want of vcrticality both of ram in falling and of plane of the pile to the blow and
consequent lateral vibration of it, the buckling of it In driving, the fVeqaent split-
ting of it on a boulder, and the condition of soil, whether dry, moist, or wet; if it
is imbedded or partially exposed to the air, or wholly immersed in wet soil and
water, and the integrity of the driving — they furnish the elements in determina
tion of a coefficient of safety.
Opposed to these effects is that of the subsidence of the soil around a pile that
has' been disturbed in driving, the effect of which, under favorable conditions of
soil, has approached to that of the resistance of the pile at its flnal blow.
The foUowinpr formula is constructed on the basis of a pile being driven
to a depression of one inch or less, as all estimates based upon a greater de-
pression are not only comparatively valueless, in consequence of the cush-
ioning of the ram, but if piles are not driven to such depression their utility
is decreased, and a greater number are rendered necessary to support the
weight to l)e imposed upon them, and in it I have omitted an element which
is universally given in others, that of the last depression of a pile as a divi-
sor, as I nut only fail to recognize its connection, but hold its introduction
erroneous.
To Coinpute Safe X^oad of* a l^ile X) riven to a Depres-
sion of* 1 Iiiclx- or l^ess.
4 W 8 y/h = L. W rqtresenting weight of ram, and L toad, both in lb*., and h
height of fall in feet.
From which result is to be deducted a factor of safety representing the faction
and losses of eff'ect.
Hence, the formula: - — ^ = L, or safe load in pounds.
For C, or coefficient of safety, in consideration of the several losses of effect re-
cited, and especially that of brooming uf the heads of a pile, It is assumed at from
3 to 6, according to the soil and the integrity of the driving.
Eliminating the numerator 4 and correspondingly reducing the 3 and 6, the for-
mula 18, -^ = L.
Illustration. — Assume an ordinary pile driven in firm soil by a ram of 3000 lb&
weight, falling 25 feet, with a flnal depression of .5 inch, and coefficient of 1.35;
what would be its safe load?
2000 X 8 ^25 2000 X 8 X 5 , ,.
z. — i — ^=£04 000 CM.
1-25 1.25
In practice, in the determining the capacity of a range of piles, it is proper
to reduce the result obtained by the fornmla, to meet incidental effects, as
negligence in driving, in the superintendence of it, and the frequent and un-
observed splitting or crushing of a pile on a stone or boulder.
A heavy ram and a low fall is most effective condition of operation of a
pile-driver, provided height is such that force of blow will not be expended
in merely overcoming friction of leader and inertia of pile, and at same time
not from such a height as to generate a velocity which will be essentially
expended in crushing fibres of head of pile.
When the soil is very soft or wet, concrete should be laid between the
heads of the piles to a depth of from 1.5 to 3 feet.
When the soil is of fine sand or light gravel, piles may be set two fiert
from their centres, but if it is saturated with moisture, a greater distance ia
necessary, otherwise small piles are liable to be disturbed by large.
(Continued on pa{fe 972.)
PILE-DRIVING. — PNEUMATICS. — AEROMBTEY. 6/3
File-fSixibiiig.
MUchelVa Screw Piles are constructed of a wrought-iron shaft of suitable
iliamet«r, usually from 3 to 8 ins., with 1.5 turns of a cast-iron thread of
from 1.5 to 3 feet diameter.
Hydraulic Process is effected by the direction of a stream of water under
pressure, within a tube or around the base of a pile, by which the sand or
earth is removed.
Pneumatic and Pkimm Process.— ¥ot illustration and details, see Trautr
wine's Engineer's Pocket-book, 647-8. New Edition.
Dr, Whewell deduced the following results :
1. A slight increase in hardness of a pile or in weight of a ram wiU con-
siderably increase distance a pile may be driven.
2. Resistance being great, the lighter a pile the faster it may be driven.
3. Distance driven varies as cube of the weight of ram.
Belative Resistance of FormcUions to Driving a Pile.
Coral 100 I Hard clay - . 60 I Light clay and sand. . . 35
Clay and gravel 83 | Clay and sand. 45 | River silt 25
PNEUMATICS.— AEROMETRY.
Motion of gases by operation of gravity is same as that for liquids.
Force or effect of wind increases as square of its velocity.
If a volume of air represented by i, and of 32°, is heated t degrees without
assuming a different tension, the volume becomes (1 -f- .002088 0 = V; and
if it requires a temperature in excess of t' 32^, it will then assume volume
(i -|- .002088 <' — 32°). All aeriform fluids follow this law of dilatation as
well as that of compression proportional to weight.
When air passes into a medium of less density, its velocity is determined
by difference of its densities. Under like conditions, a conduit will discharge
3a55 times more air than water.
To Compute tbe X>egree o£ Rarefkotion that may tte ef-
ieoted. in. a Vessel.
Let quantity of aur in vessel, tube, and pump be represented by i, and
proportion of capacity of pump to vessel and tube by .33; consequently, it
contains .25 ^f the air in united apparatus.
Upon the first stroke of piston this .25 will be expelled, and .75 of original
quantity will remain ; .25 of this will be expelled upon second stroke, whicfi
is ef]ual to .1875 of original quantity; and consequently there remains in
apparatus .5625 of original quantity. Proceeding in this manner, following
Table is deduceid :
No. of Sirokflt.
Air Expelled at each Stroke.
Air Remaining in Veaael.
z
.25 = .25
•75 = -75
4
3 _ 3
9_3X3
x6 4X4
»6 4X4
0
9 3X3
27_3X3X3
0
64 4X4X4
64 4X4X4
And so on, multiplying air expelled at preceding stroke by 3, and dividing
it by 4; and air remaining after each stroke is ascertained by nmltiplying
remaining after preceding stroke bv 3, and dividing it by 4.
674
PNEUMATICS. — AEROMBTBY.
IDistauoes a.t ^vliiolx "DiffereTit Sounds are A.u.di'ble.
Feet. Mile*.
A fUIl human voice speaking in open air, calm 460 .087
In an observable breeze, a powerful human voice with the) «
wind can be heard ) '^ ^° ^
Report of a musket x6 000 3.02
Drum 10 560 2
Music, strong brass band 15 840 3
Cannonading, very heavy 575 000 90
In Arctic Ocean, conversation has been maintained over water a distance
of 6696 feet.
In a conduit in Paris, the human voice has been heard 3300 feet
For an echo to be distinctly produced, there must be a distance of 55 feet.
Coefficients o/Effiux 0/ Discharge qf Air. {D^Aubuisson.)
Orifice in a thin plate 65 .751
Cylindrical ajutage 93 .958
Slight conical ajutage 94 1.09
To Conapixte Volniiae of Air IDi^oKarged. througli an Oper&«.
ixig into a Vacuvixxi, per Second.
a C V2 gh = Y in cube feet, a representing area, of opening in square feety C co-
effi/Hent ofeffiux, and y/i g h= 1347.4, ^ shoton at page 428.
Illustration. — Area of opening i foot square, and G = .707.
Then i x 707 X 1347-4 = 952.61 cube feet
Inversely y V -r- a = velocity in feet per second.'
"Velocity and I:*ressvire of Wind.
Pressure varies as square of velocity, or P oc V.
Va X .005 = P; \/2oo P =>V; «' X 0023 = P; and .0023 e* sin. a? = P.
V repre»!ntiim velocity in miles per Aof«r, v in feet per second, P pressure in lbs.
per sq.foot, and x angle of incidence ofvxind with plane of surface.
rrable deduced from a'bove Formulas.
Vel
ocity
Pressure
Honr.
per
Minnte.
on s
Sq. Foot.
Miles.
I
2
3
4
Feet.
88
176
264
352
Lbs.
.005
.02 )
•045}
.<!>8
5
6
440
528
• 125)
..8
8
10
704
880
32 )
•5
15
20
1320
1760
1.125
2
Character of the Wind.
Barely observable.
Just peroeptible.
Light breeze.
Gentle, pleasant
wind.
Fresh breeze.
Brisk blow.
Stiff breeze.
Velocity
Pressure
Hour. Minute.
on a
Sq. Foot.
Miles.
Feet.
Lbe.
25
30
35
320D
2640
3080
3»25
6.125)
40
45
3520
3960
8
iai25
50
60
4400
5280
12.5
18
80
7040
32
90
100
7920
8800
40^51
50 }••
Character of the
Wind.
Very brisk.
High wind.
Very high wind.
Gale.
StornL
Great storm.
Hurricane.
Tornado.
Illustration. — What is pressure per sq. foot, when wind has a velocity of x8
miles per hour? ,32 ^ .005 = 1.62 lbs.
To Compute Force of Wind upon, a Surfhoe.
»= a / a sin 2 a; \ „ ,, , ., ^ . , . - .
1 - . — ^— 1 = P V representing velocity of unna mfeet per seoondy a arem
oj surface in sq.feel, and z angle of incidence of wind.
At Mount Wasliiugtoii wind has been observed to have had a velocity of 150 miles
per hour= 112.5 lbs. per sq. foot.
Extreme pressure of wind at Greenwich Observatory for a period^ 20 years was
41 lbs. per sq. foot. ., ,f^
PITEIJMATICS. — AKBOMjETE Y. 67 5
Force of wind apon a surface, perpendicular to its direction, has been ob-
served as high as 57.75 lbs. per sq. foot ; velocity = 159 feet per second.
Dr. Button deduced that resistance of air varied as square of velocity
nearly, and to an inclined surface as 1.84 power of sine x cosine.
Figure of a plane makes no appreciable difference in resistance, but con-
vex surface of a hemisphere, with a surface double the base, has only half
the resistance.
At high velocities, experiments upon railways show that the resistance
becomes nearly a constant quantity.
Course of "Wind..
Dirtiumi* r^-vrrtl^-tnAa DirtlUcn in
Nortium Hemupitr*. ^ yoiones . 8t»itk«m HemitphM^
Wind has its direction nearly at
right angles to line between points of
liighest and lowest pressure of air, or
barometer readings, and its course is
with the point of lowest pressure at
its left, and its velocity is directly as
difference of the pressures.
In Northern Temperate zone, winds course around an area of low pressure
in reverse direction to course of hands of a watch, and they flow away from
a location of high pressure, and caase an apparent course of the winds in di^
rection of course of the hands.
To Compute Resistaiioe of* a Plane Surface to ^ir.
.0023 av^ = 'Pin lbs. a representing area of plane in sq.feet^ v velocity in direc
tion 0/ wind in /set per second^ -\- when it moves opposite^ and — when with the toind
When Barometer Pressure =yi Lbs,
{C. F. Martin, U. S. S. S.)
.004 a V» = P. V representing velocity of -wind in miUs per hour^ and a area of
pressure in sq.feet.
To Compute Hieiglit of a Column of l^eroury to induce
an J£filnx of Air tliroiigh. a given r^ozzle.
Barometer assumed at 2. 46 feet = 29. 52 ins. , and Temperature $2^.
pa
-g 5-^ = H, and 48.073 d* y/R = P. d representing diameter ofnoztle and H
height of column of mercury, both infect, and P volume of air in lbs. per me second,
Illustbation.— Assume d = . 19, and P = .7 lbs.
48.073' X.t9* ~ "'^'^ ^^^ *^°" ^ • '^' "^'^^ = •7-
To Compute Pressure or "WeigHt of Air under a given
Heiglit of Barometer and Temperature, I3iaoIiarged in
One Second.
30. 787 d'^ yj^ -^^ = pressure in lbs. Or, 48.073 d« ^B = lbs. b representing
height ofbaromfter in external air. B manometer or pressure of air in reservoir in
mercury, both in feet, and t temperature of air or gas in degrees.
Illcstkation. —Assume 6 = 2. 5 fett ; d = . 25 foot ; B = . x foot ; and t = x. oss^-
Hien 3a 787 X .0625 w . I X ''^"^•' = 1.924 X V'^465 = -9543 lbs.
6/6 PNEUMATICS. — A£BOM£TBY.
To Compute rreznperature for a given. Iuatitu.de and Sllei^
vatioxi.
82.8 COS. I -^ .001 981 E — .4 = t E representing elevation in feet
Illustration.— Assume 2 = 450; cos. =.707; and E=(Ss6 feet.
Then 82.8 x 707 — .001 981 X 656 — "^ = 58.54 — 1.299 — 4 = 58.54 — .899 =
57.641.
Xo Compute Volume of A.iv or O-as Discliarged through
au Opening and under a JPressure above that of ^jX^-
ternal ^ir.
d'
A ir. 1347. 4 C — Vb (6' -|- B) T = V in cube feet per second,
o
T = I ■+- .002 22 {t — 32°), and 6' = 2.5 — .00009 elevation.
Or, 621.28 d2 VB = V.
iLLrsTRATioN.— What would be volume of air that would flow through a nozzle
.246 foot in diara. from a reservoir under a pressure of .098 foot of mercury, into
air under a barometric pressure of 2.477 ^^^^-^ temperature of air 55.4°, location 45°
of latitude, and at an elevation of 650 feet above level of sea?
C = .7s; 6' = 2.5 — .00009X650 = 2.4415 (2.44); and ■ T r= 1.0502.
Then 1347.4 X 75 '-— — \/.o98 (2.44 + .098) X 1.0502 = 24.689 X y/.^Sij = 13.63
2.477
cube feet
. When Densities of External Air and that in Reservoir are ICqual,
1347.4 C -p \/B (6 -}- Bj T = V. b' representing height of mercury in reservoir.
Gas, ^J-^/t-zt — ^Trf — ^- P representing specific gravity of gas compared
with air, and L length of pipe or conduit in feet.
Illustration. — If a pipe .05 feet in diameter and 420 feet in length, communi-
cates with a gasometer charged with carburetted hydrogen (illuminating gas), under
a water pressure as indicated by a manometer of .1088 foot, what would be the dis-
cbarge per second?
d = .05 foot ; L = 420 feet ; and B = , . = .008 foot. Specific gravity of gas
13.0'
.5625.
4231
/ .cx)8 X -05* 4231 / 000 000 002 5000 . -
/ ^ =^^- . -T — ^—=. 013 71 cu6«/oot
V 420-1- 42 X. 05 -75 V 420 + 2.1
\/-5625 V 420 -1-42 X. 05
Resistance of Curves and A »^^«.'^Carves and angles increase resistance
to discharge of air or gas very materially. By experiment of D*Aubuisson
7 angles of 45*^ reduced discharge of gas one fourth.
To Compute Diameter of* X)isoharge-pipe or T>fozzle.
When Length and Diameter of Ptpe^ Volume^ and Presswe are given.
Illustration.— If a pipe 1000 feet in length, and .4 foot in diameter, leads to a
reservoir of air, under a mercurial manometric pressure of .t8 foot, what diameter
must be given to a nozzle to discharge 4 cube feet per second?
.. / 42X4^X45 . / 6.88128
Then 4 / ?_ - ?_ -'* _ . = * / = ^— — ^.000 405 3 =
V 42302 X 18X45 — ICXX5X4* V 32980.19 — 16000
.1418 /oo< = 1.703 ins.
Volumes of two gases flowing through equal orifices, and under equal pressures,
ure in inverse ratio of square roots of their respective densities.
* Specific gravity of mercnry compared with water*
BAn.WA.TS.
67;
To i:>efixie a
Fi|^i.
RAILWAYS.
Cvirve.— Fig. 1.
1719 c
a
{Molesumrth.)
or t tau. a; = R; R (cotan. x) = t;
1719 c
K
= a; R (cosec. a? — i) = d;
R (cosin. X) = *;' R (coversin. a;) = V;
5400— _^ ^mi (5400 — «) .000582 R = i
c repreienting any chord, t length of tangent, d distance of centre of curve from in-
terKcUon of tangents, s ha{f chord of curve, and I lengtli of curve, all in like dimensions
a tangential angle ofc in minutes, n number of chords in curve, and x half angle oj
intersection, fnU in formulas for number of chords and length of curve to be expressed
in minut€s.
Illustration. — Assume radius 900 and chord 400 feet; angle of iutersection =
12° 44' = 764 minutes, and x = 56* 15' 5".
Tangent of 56° 15' 5" = i. 496 73. Cotangent = .668 14.
1719 X 400 _ - . 1719 X 400 ^ , ,,_
, =R = 9oo/gg<; -^-^ — ^— = 764TOtnwte«; 900 X .66814=^ =
601.33 feet; 900 X 1.20269 — i =d= 182. 42 /ee<; 9ooX.555 55=« = soo/ee<;
900 X .16833 = V = i5i.5/««</ ^^^I^^^^^'^ = 2.645 '»»»«, and .000582 X 900 X
764
5400—3379 = xo58.6/ee&
Tangential Angles for Chorda of One Chain.
Radio* of
Cnrre.
TaDfrential
An«le.
Radios of
Carv«.
TangentlHl
Angle.
Radias of
Curve.
Tanf^ential
Angle.
Radius of
Curve.
Tonjrential
AuKle.
Chain*.
5
8
9
xo
12
5° «f ,
3° 34;87'
3° 11
20 51.9',
2° 23.25
Chain*.
15
20
25
30
35
'0 54-^'^
1° 25.95
1° 8.76'
57-3',
49.11
Chain*.
40
45
50
60
70
42. 9j'
38.2*
34-38'
28.65'
24.55'
I mile
1.25 mil's
1.5 miles
1-75 '*
2
21.48'
17.19'
12.28
10.74'
NoTB.— Angle for 2 chain chords is double angle for i chain chords. Angle for .5
chain chords is .5 the angle for i chain chords.
Carves of less than 20 chains radius should be set out in . 5 chain chords. Curves
of more than 1 mile radius may be set out in 2 chain chords.
Angles in above Table are in degrees, minutes, and decimals of minutes.
Sidiugs.
2 Vrf R — (.5 d)* = ?. R representing radium of
curve, I length of curve over points, and d distance
between tracks, _.
aU in feet. ^ , *^'«- 3-
\
T-arn-otit of XJneq.Ti.al Hadii^
^p;=y; »— y=*; a4-6=Z; r— y=A;
•/y(r+A) = a; R — «=rB; V«(R-|-B) = &.
R and r representing radii of the curves re-
spectively as to length, x distance between outer
rails of tracks and oUier symbols as shoum, aU
^feeL
aL*
678
BAILWATS.
Fig. 4.
Points and Orossings.
' ' R ' vsr. sin. a
^^ Xi 1} ail— 1 Ml a
_ serUing radius of curves^ 6 ffouffe o/roady a angle ofcrouimgy
^ -and X = R — G,aUin feet.
In horizontal curves, width required for clearance of
flange of wheel, and for width of rail at heel of switch,
render it necessary to make an allowance ii^ length of /,
as ascertained by formula.
For other diagrams and formulas, see Molesworth^s Pocket-
book, pp. 208-18, 2ist edition.
1710 c
To Compute Ta.iigexitial Aaigle ."^or Curves. — — — = 0. e
representing chord in feet, and a angle in minutes.
Illustration. — What is augle for a curve with a radius of 900 feet, and a chord
of 400 feet?
12^12<^ = 764 minutes.
900
1.56 1'
R
Curving of* Hails.
= V. I representing length of raU in feet^ v versed sine at centre, when
tUrved, in ins.
Illustration— What is curve for a rail 20 leet in length, with a radius of 900 feet?
i.5X2o«
900
=«666 ins.
Curves "by Offlsets in £2qual Cliorda.
Chorda Chord 2
= 3,0 qfaet
Illustration. — Assume chords 150, and ra-
T dius 900 feet.
22 500 _ 22 500 - _,
= i2.s feet; --5^: = 25 /erf.
2 X 900 900
To Compute /Versed Sines and Ordinates of Curves.
Fig. 6.
B — VR»-(.5C)» = i>i
(sO)'
4- w = D ; and
I.
R^
D
VR'' — »* — (R — r) = 0. D representing diameter of
\ eirelet and v versed sine of curve.
\ Illustration.— Assume radius 9cx>, and chord 400 feet
900 — a/Siocxx) — 40000 = 900 — 877.5 = aa.5yte<.
Relation of Base of Driving or Rigid "Wheels to Curve.
— ^ — . B. R representing minimum radius of curve, G gauffe of road, and B 6«we,
all in feet.
To Compute Slevation of Outer Rail.
For any Kadtua or Combination of Curve tvifk Straighi Line.
• 5 V y/G = c. V representing velocity of train in feet per second, G gauge <{^roa(L
and c Unglk of a chord, both in feet, the versed sine of which = eUvation m in$.
Va
On Curves.
i.as
^ G = E. E representing elevation of outer rail in ins
RAILWAYS.
679
Radii of* Ouirves set out in Tangcxxtial A^xxgles.
Angle for
Chord of
100 Feet.
Radio*
of
Curve.
Angle for
Chord of
100 Feet.
0 '
30
I
« 30
2
Feet.
5729.6
2864.8
1909.9
1432-4
0 '
2 30
3
3 30
4
Radio*
of
Curve.
Feet.
"45-9
954-9
818.5
716.2
Angle for
Chord of
100 Feet.
4 30
5
5 30
6
Radius
of
Curve.
Feet.
636.6
573
520.9
447-5
Angle for
Chord of
100 Feot.
O '
6 30
7
7 30
8
Radio*
of
Carve.
Feet.
440.7
409.3
382
358.1
NoTB.— If chords of leEss length are used, radius will be proportional thereto.
To Ascertain Radius of Curve in Inches for Scale, in Feet per Inch.
Divide radius of curve in feet by scale of feet per inch.
To Compute R,eq.\iired. "Weiglit of liail.
Rule. — Multiply extreme load upon one driving-wheel in lbs. by .005,
and product will give weight of rail in lbs. per yard.
Xo CJouupvite Radius of Curve aud Wlieel Sase.
o B 6 = R. —jr = B. B representing maximum rigid wJieel base of cars^ and Q
9G
gauge of way ^ both in feet.
Xo X>etermine Klevatiou of Outer Hail.
f^ any Badius or Construction of Curve with Straight. — Fig. 7.
Fig. 7. V .5 y/G — c. V representing speed of train in feet per sec-
ond, O gauge of rails in feet, and c length of chord, versed sine
V of which unit give at its centre the elevation required.
Thus, determine chord c, align it on inner
side of rail, and distance of rail from it at
centre of its length will give elevation re-
^\> quired, whatever the radius of rail.
N U iC 1.25 K
diameter ofwheelSy W vridth of gauge, P lateral play between flange and rail, and
R radius of curve, aU in feet, i -^ N raiio of inclination of tire, V velocity of train in
miles per hour^ and E elevation of outer rail in ins. {Molesworth.)
' "* ' = resistance due to curve, and W representing weight of body, both 'in
2 R
lbs. , C eoefficiet^ of friction of wheels upon rails = .ito .27, according to condition of
veather^ d distance of rails apart^ I length of rigid wheel base, and R radius of curve,
aU in feet (Morrison.)
iLLrsTRATioK.— Assume weight of locomotive 30 tons, radius of curve 1000 feet,
distance of rails apart 4 feet 8.75 ins., length of base 10 feet, and rails, dry, C = i.
30X2240X XX (4-73-1- 10) ^ j5,.
2 X xooo
To Compxite Resistance due to Gravity upon an In-
clination.
■ '^1° , = lbs. per ton of train.
gradient
Rise per ^lile, and K,esistanoe to Q-ravity, in l^bs. per
Ton-
Gradient of I Inch.
Rise in feet
R«sigtaace,.,
20
264
ZX9
25
211
89.6
30
35
151
64
40
132
$6
45
117
50
50
60
88
37.3
70
75
32
80 f 90
1
66 59
28 24.8
176
74-7
106
44.8
100
53
22.4
68o
KAILWAYS.
To Coxnpute X^oad 'wliicb. a Xjocoxxiotive -^vill Dra^tv -up
aix liicliiiatioxx.
T -H »• -f- *■' — W = L. T refrresenting tractive povoer of locomotive in lb$., r re-
sistance due to gravity, and r' resistance due to assumed velocity of- train in lbs. per
ton, W weight tf locomotive and tender, and L load locomotive can draw^ in tons, ex-
clusive of its own weight and tender.
Coefficients of Traction of Z,ocvmo^ut;«.— Railroads in good order, eUx, 4 to 6 IbB. ;
in ordinary condition, 8 lb&
In coupled engines adliesion is due to load upon wheels coupled to drivers.
To Compute Traction, £ietraotioii, and A^dliesive Fo'wer
of a I^ocoznotive or Train.
When upon a Level, a« P-=-D = T. a representing area of one cylinder in
sq. ins., s stroke of piston awl D diameter of driving-wheels, both in feet, P mean
pressure of steam in lbs. per sq. inch, and T traction, in lbs.
When upon an InclimUion. asP-r-D — rwh = T. r representing resistance
per ton, to weight of locomotive upon driving-wheels, in tons, h lieight of rise in feet
per 100 of road, and R = rwh=z retraction, in lbs.
Cwb-T- 100 = A. b representing base of inclination in feet per 100 of road.
Cw=:A. C = coefficient in lbs. per ton, and A adliesion, in lbs.
WJien Veipcity of a Train is considered.
When upon a Level, W (C + -/V) = R. When upon an TnclinaiUm^
W 0' A + C -|- V^) = K. V representing velocity of train in miles per hour.
Illustration.— A train weighing 300 tons is to be driven up a grade of 52.8 feet
per mile, with a velocity of 16 miles per hour; required the retractive power?
52.8 per mile =: i in 100 feet = r = 22.4 lbs. C = 5.
aoo (22.4 X I + 5 + y/^^) ~ 200 X 22.4 + 9 = 6280 lbs.
Velocity of Trains.
Miles per hour.
Resistance upon straight )
line per ton | )
Do., with sharp curves j >
and strong wind*. . . . ) | '^
10
Lto.
8.5
15
20
Lb*.
Lbs.
9.25
10.25
14
155
30
LU.
1325
20
40
SO
60
Lb*.
Lb*.
Lb*.
1725
23.5
«9
26
34
43-5
70
36.5
55
* Eqaal to 50 p«r cent. add«d to resisUnoe apon a ttnilght Ho*.
Friction of locomotive engines is about 9 per cent, or 2 lbs per ton of weight.
Case-hardening of wheel tires reduces their Ariction (Vom 14 to .08 part of load.
To Comp-ute ^^azimum ILioad that can l>e dra'^^n "by an
£^ngine, up tUe ^lazimnm Ghrade tliat it can .A^ttaiu,
Weight and O-rade being given. {Mag. McCldlan, U S. A.)
2 A 2 A 8 L
' . „ = L, and = — = 0. A representing adhuive weight of engine,
. 4242 6 -|- 8 4242 L w ^ 9 t
in lbs. , 6 grade in feet per mile, and L loaJ, in tons.
Note i.— When rails are out of order, and slippery, etc., for .a A, pat .143 A.
2. —With an engine of 4 drivers, put .6 as weight resting upon drivers; with 6
drivers the entire weight rests upon them.
Illustration.— An engine weighing 30 tons has 6 drivers; what are the moaBimtm
loads it can draw upon a level, and upon a grade of 250 feet, and what is its maxi
mum grade for that load?
.2X2240X30 '3440 _ ,^„^ , ,^, ,^^ „ i^^i .aXa24oX 30 _ 13440
•— — — 7— r =Tr— = 1505.4 lOn* tWJOW O WDCt ,-r = - - ^
424a-f-8 8.4242 ^ .4342X2504-8 zi4>05
.9X2240X30 — 8 X 1 17. 8 12497
117.8 tons up a grade of 2^0 feet.
= a5aiyis«t
4242X1 17- 8 49-97
Adhesion of a 4- wheeled locomotive, compared with one of 6 wheels, ip as 5 to 8
BAILWAYS.
68l
OPEKATION OP LOCOMOTIYEB. (O. CfhanuUy Am. Soc C. E.)
Adhesion of a locomotive is friction of its driviog-wlieels upon the rails-
rary ing with condition of the surface, and must exceed traction of the engine
upon them, otherwise the wheels will slip.
Improvements heretofore made in the construction of locomotives and
tracks have gradually increased the proportion which the adhesion bears to
the insistent weight upon the driving-wheels.
The first accurate experiments were those of Mr. Wood upon thQ early English
coal railways He deduced the adhesion to be as Ibilows:
Upon perfectly dry rails 14 of weight on drivera
" damp or muddy rails 08" ** " "
*' very greasy rails 04" " '* ♦*
In 1838, B. H. Latrobe indicated .13 as a safe working adhesion, while modern
Earo|)ean practice assumes about .2 of weight as maximum, and . 11 as a minimum,
except perhaps in some mountainous regions, subject to mista Thus, on the Soum-
mering line, adhesion is generally .16, and between Pontcdecimo and Bosalla, in
Italy, it never exceeds .12 in open cuttings, or .1 in tunuela
Extensive experiments made upon French railways, 1862-67, by Messrs. Vuille-
min, Guebhard, and Oieudonne gave following coefficients in actual working: dry
tofother^ extreme, .105 to 2; damp, .isa'to .139; wet, .078 to .164; light rain, .09;
extreme rain, . 109 to .2, mean, . 13 ; rain and Jog, .115 to . 14 ; heavy rain, 16.
Materially better results are obtained in United States, partly, perhaps, in con-
sequence of greater dryness of the weather, and certainly because of the American
method of construction and equalizing the weight between the drivers, and of mak-
ing the locomotive so flexible as to adapt itself to inequalities In the track.
Modem engines in America can safely be relied upon to operate up to an adhesion
equal to .222 in summer and .2 in winter, of weight upon the driving wheels.
From these data the following tables have been computed:
Ooeflioieiits of A.dhe8ioii upon X)rivins 'Wlie^tls per rPoxi.
CMditionofRKiU.
Bails very dry....
Rails very wet....
Ordinary working.
European
American
Practice.
Practice.
C.
I.hn.
C.
Lbs.
■3
670
•33
667
.27
600
•25
500
.2
450
.222
444
Condition of Rail*.
In misty weather .
In fh>8t and snow.
European
Practice.
C.
.015
.09
Lba.
350
200
American
PractiM.
C.
.2
.16
Lba.
400
333
Adhesion of Locomotivet, in Lbs. (.222 t« Summer and .2 in Winter).
Type of Locomotive.
American ,
Ten-wheeled ,
Mogul ,
Consolidation ,
Taok switching...,
4» 41
No. of Drivers.
4 wheels coupled. . .
6 ^* connected.
6
8
6
4
li
it
ti
44
4(
((
44
Weijrbt.
Locomotive. OnDriveta.
Lte.
64000
78000
88000
zoo 000
68000
48000
Lba.
42000
58000
72000
88000
68000
48000
Adhesion.
Summer. Winter.
Lbs.
Lba.
9350
8400
13000
Z1600
16000
14000
X9550
17600
15100
-13600
10650
9600
Tractive Power.
Traction of a locomotive is the horizontal resultant on the track of the
pressure of the steam, as applied in the cylinders.
D'PL-i-W=rT. D representing diameter of cylinder, L length of stroke, and Vt
dtatneter of driving wheels, all in ins, P mean pressure in cylinder, in Un. per iq.
inch, and T tractive force on rails, in lbs.
iLLUSTRATioy.-— Assume a locomotive, cylinders 18 ina in diam.. 22 ins. stroke,
wheels 68 ins. in diauL, and average steam pressure in cylinders 50 lbs. per sq. incb
Then 18 X z8 X 50 X 22 -7- 68 = 5241 lbs.
682
RAILWAYS.
Train. Resistances.
Usual fonnula for train resistances, on a level and straight line, is
[• B=^^pe\- ton of trainy BXkd \-6 = R per ton of train cUone. V repr^'
171 240
senting velocity in miles per hour, and 8 constant axle friction. {D. K. Clark.)
NoTB.*->To meet the nnfavorable conditions of quick curves, strong winds, and
imperfection of road, Mr. Clark estimates results as o})tained by above formula
should be increased 50 per cent.
Illustration. — At 20 miles per hour, the resistance would be:
' 20* -j- 171 -|- 8 = 10. 3 Ws. per ton of train.
This formula, however, is empirical. It gives results which are too large for
freight trains at moderate speeds, and too small for passenger trains at high spee^
Engineers are not agreed as to exact measure and value of each of the elements
of train resistances, hut following approximations are sufficient for practical use:
A naltfsis of Train Resistances.
Resistanee of traius to traction may be divided into four princi[)al ele-
ments : ist Grades ; 2d. Curves ; 3d. Wheel friction ; 4th. Atmosphere.
I St Grades. — Gradients generally oppose largest element of resistance
to trains. Their influence is entirely independent of speed, llie meas-
ure of this resistance is equal to weight of train niultiphed by rate of in-
cluuitioa or per cent of grade. Thus, a gradient of .5 per 100 feet (26.4
feet per mile) offers a resistance of 5X»''4o__. ^^ ^ jj^g^ p^j. ^j,^ ^^ ^^ ^^
per 2000 lbs., which is to be multiplied by weight in tons of entire train.
Following table shows resistance, dne to gravity alone, for the most usaal grades,
in lbs. per ton of train :
I St. Resistance due to Grades,
Rate per too feet
Lbs. per ton of 2340 lbs. . .
Rate per mile
Lba per ton of 3000 lbs. . .
Rate per 100 feet
Lbs. per ton of 3340 lbs. . .
Rate per mile
Lbs. per ton of 2000 lira. . .
I
.3
•3
•4
5
.6
■7
2.24
4.48
6.72
8.96
11.3
13-44
15.68
5
II
16
21
26
3a
37
2
4
6
8
10
13
»4
•9
I
I.I
1.3
«-3
1-4
i-S
2a 16
32.4
24.64
26.88
39.13
3136
33-6
47
53
58
63
68
74
79
18
20
22
24
36
38
30
.8
17.9a
4a
16
T.6
35-84
85
3a
2d. Curves. — Recent European formula is that given by Baron von Weber.
6504 -r- R — 55 = W R representing radius of curve in metres.
This formula assumes th^t resistance due to curve increases fester than radias
diminishes. It gives results varying from a rBsistance of .8 lb. per 2000 Ibe. per
degree for a curve of 1000 metres radius (3310 feet, or i^ 44') to a resistance of 1.67
lbs. per 2000 lbs. per degree for curves of 100 metres radius (331 feet, or ij^ ao').
Messrs. VuiUemin, Guebhard, and DieudonnS found curve- resistance to European
rolling-stock to be fh>m 8 to i lb. per 2000 lbs', per degree, on a gauge of 4 feet 8. 5
ins., while Mr. B. H. I>Atrobe, in 1844, found that with American cars resistance on
a curve of 400 feet radius did not exceed 56 lb. per 2000 lbs. per degree.
Resistance of stime curve varies with coning given tires of wheels, elevation of
outer rail, and speed of train running over it, but both reasoning and experiment
indicate that the general resistance of curves increases very nearly in direct pro-
portion to degree of curvature, or inversely to the radius.
Recent American experiments show that a safe allowance for cqrve resistance
may be estimated at .125 of a lb. \*bt 2000 lbs. for each foot in width of gauge.
Thus, for 3 feet gauge resistance would be .375 lb. per degree of curve; for standard
gauge of 4 feet 8.5 ina .589, say .60, and for 6 feet gauge 75 lb. per degrea
For standard gauge, when radius is given in feet, resistance due to this element Is:
•60 X 5730 -r- B = C in lbs. per ton of tram.
RAILWAYS. 683
This is somewhat reduced when curve coincides with that for which wheels are
coned (geoerally about 3,°U aud when train runs over it, at precise speed for which
outer rail is elevated, an allowance of .5 lb. per ton per degree is found to give good
results in practice.
2d. Resistance on Curves.
It follows from above estimate of curve resistance that, in order to have the Sftme
resistance on a curve as on a straight line, the gradient should be diminished by
.03 per 100 feet of each degree of curve. Thus a 2° curve requires an easing of the
grade by .09 per 100 feet, a 10° curve an easing of 3 per 100, etc.
This, however, need only be done upon the limitiim gradients, and when som of
grade and curve resistances exceeds resistance which has been assumed as limiting
the trains.
3d. Resistance due to Wfieel Friction,
Experimenters are not agreed whether friction of wheels increases simply with
weight which they carry, but also in some ratio with the speed. Originally as-
sumed as a constant at*8 lbs. per ton, improvemeuts in condition of track (steel
rails, etc.) and in construction and lubrication of rolling-stock have reduced it to
3.5 and 4 lbs. per ton for well-oiled train& I' ndei* ordinary circumstances, in sum-
mer, it will be safe to estimate it at 5 lbs. per ton on fli'st-class tracks, and 6 lbs.
per ton on fair tracks. It may run up to 7 or 8 lbs. per ton on bad tracks (iron
rails) in summer, and all these amounts should be increased fh>m 25 to 50 percent.
in cold climates in winter, to allow for inferior lubrication.
4th. Resistance due to A tmosphere.
Atmospheric resistar.ce to trains, complicated as it is by the wind which may be
prevailing, has not been accurately ascertained by experiment. It consists of—
ist Head resistance of first car of train, which is presumably equal to its exposed
area, in sq. feet, multiplied by air pressure due to speed.
2d. Head resistance of each subsequent car. This varies with distance they are
coupled apart, and so shield each other from end air pressure due to speed.
3d- Friction of air against sides of each car depending upon the speed. This is
generally so small that it may be neglected altogether.
4th. Effect due to prevailing wind, which modifies above three items of resistance.
A head wind retards the train, a rear wind aids it, while a side wind increases re-
sisUnce by pressing flanges of wheels against one rail, and, in consequence of curves,
a train may assume all Of these positions to same wind.
Recent experiments on Erie Railway seem to Indicate that in a dead calm re-
sistance of first car of a. freight train may be assumed at an exposed surface of 63
sq. feet,* multiplied by air pressiire due to speed, and that each subsequent car may
be assumed to offer a resistance of 20 per cent, of that of first car, while in a pas-
senger train first car may be assumed at an area of 90 sq. feet,t multiplied by air
pressure due to speed, and that each subsequent car adds an increment equal to 40
per cent that of first car, in consequence of greater distance they are coupled apart.
This resistance Is, of cotirse, entirely independent of cars being loaded dr empty.
In practice it has been found that an allowance of 1.5 to a lbs. per ton of weight of
a /reight train covers atmospheric resistance, except in very high wmdsi |
In consequence of complexity of elements above enninerated, exact fojfflulas can-
not probably be now given for train resistances, but following, if applied with judg-
ment (and modified to fit circumstances), will be fdund to give feirly accurate resuRs
in practice. They are for standard gauge, and in making them, curve resistance has
been assumed at .5 lb. per degree, wheel friction at 5 lbs., exposed end area of first
car at 90 sq. feet for passenger cars and 63 feet for freight cars, and mcreraent ft>r
sac<^e^ng cars at .4 for passenger trains and .2 for freight trains.
Fasseneer Train. W ^G + ^+ 5) + (« +^^) 9oP=R-
ITreisl&t Train. W (o-f — + 5) + (' "f-Y^j 63 P = R-
• ThU U !•« thsn itna of c»r, wliich jrenerally inea»are» «hont 71 "q- feet ; but part I« ■hi«ld«l bjr
tandM'. and Mria belsr eonrel, m whwlt, bolls, «tc., offer lew r*i»Unce Chan « flat pUne.
t Not ooin* end ana of paa^ngw cam Rrealcr than thut of freJRht cm, but Jo conaeqiieDca pf tha
prnj«etinr r^of the and foriMiri|oo4 io »«^Va of • copc»v» turfwe, wd w oppowa yrMt«r rwimiK*
Sbaa • fl«t plant*
684
BAILWASTB.
W rt^aenling voetght of train^ without engine, in tons (2000 Ibg.), G resistance of
gradient per ton (2000 lbs.; Bee table, page 683), C^ curve in degrees, n number of ears
in train. P pressure per sq. foot due to speedy to which an allowance must be made for
wind, if existing, R resistance of train, and 5, wheel friction, both in lbs.
Illustration i.— Assume a passenger train of 5 cars, weighing 136 tons (aooo lbs.),
ascending a grade .5 per 100 (26.4 feet per mile), with curves of 4°, at a speed of 60
miles per hour (for which the pressure is 18 lbs. per sq. foot), resistance will be:
136 (10+ a + 5) + ( I + — j (90 X 18) = 6524 I6»., of which 2312 lbs. are due to
gradey curve, and wheels, and 4212 lbs. to atmospheric resistanee.
2 Assume a fireight train of 31 cars, weighing 620 tons (2000 Iba), turning a cnrvt
of 3<), up a grade of 52.8 feet per mile (i foot per 100), at a speed of 21 miles per hour
(pressure 2 lbs. per sq. foot), resistance will be:
620 (20 -|- 1.5 -|- 5) -j- (i -f- —J (63 X 2) = 17 312 H>*., requiring a *• Consolidation "
engine to haul it, allowance being made for possible winds, etc.
i\BSume conversely, it is desired to know how many tons an American engine,
with an adhesion of 10650 lbs., will draw up a grade of .9 per 100 (47 feet per mile),
with curves of 4*^. assuming atmospheric resistance between 1.5 to 2 lbs. per ton of
train.
Resiistance firom grade .9 x 2000 -r- 100 z=z iBlbs.)
u u curve 4 -r- 2 = 2 " > 27 lbs.
»* " wheel friction 5, atmosphere 2 = 7" )
Hence, 10 650 -r- 27 = 395 tons, or about 20 cars, and in winter same engine will
haul 9600-^ 27 = 355 tons (2000 lbs.), or about 18 cars.
Following table approximates to best modern practice. For freight trains it gives
aggregate resistance, in Iba per ton (2000 lbs ), for various grades and curvea In
using it, it is sufficient to divide the adhesion in lbs. of locomotive used by number
found in table, in order to obtain number of tons of train that it will haul at or-
dinary speeds on gradient and curve selected. Of course, if grade has been equated
for curves, only number found in first column (for straight lines) is to be used in
computing tons of train on limiting gradient
Approximate FreigUt-train. Xleeiistaiioes.
Gauge 4 feet 8. 5 ins.
In Lbs. per 2000 lbs. at Ordinary Speeds.
Curve Resiatanee assumed at .5 lbs. per o. Wheel Friction at 5 Ws.^ Atmospheric JKe-
sistance at a lbs. per Ton.
U\ xs*
Gbadb.
•a
CUXYS.
Par
C«nt.
Per
Ulle.
I*
2*
Ibe.
3*
4*
lbs.
5'
6*
Ibt.
7'
8»
Iba.
9"
Ibe.
10"
Ibe.
IX'
12-
Ibe.
13"
ItM.
lb*.
lbs.
lbs.
Ibi.
Ibe.
Ihe.
Level.
Feet.
7
7-5
8
8.5
9
9-5
zo
X0.5
zx
"•5
za
12.5
13
«3S
.1
5
9
9-5
10
xas
zz
ZZ.5
za
12.5
«3
»3.5
X4
«4-5
15
«S5
.2
IZ
zx
"5
za
xa.5
»3
13-5
14
H-5
15
X5-S
r6
X6.5
»7
«7.5
•3
x6
13
^3-5
H
16.5
»5
iS'S
x6
Z6.5
»7
17-5
z8
'8.5
19
195
•4
21
15
15-5
x6
17
17-5
z8
18.5
»9
19-5
ao
20-5
2Z
21. 5
•5
26
17
17-5
x8
Z8.5
19
Z9.5
20
20. «;
21
21.5
72
2a. 5
23 23.5
.6
33
19
'9-5
ao
2a 5
2Z
2Z.5
22
22.5
23
23.5
"1
245
25 25.5
•7
37
az
2X.5
22
22.5 23
235 24
24.5
25
255
a6
26.5
27
27- 5
.8
42
23
23.5
^t
24.5 25
26.5 27
25-5
a6
26.5
27
27-5
a8
28.5
29
295
•9
47
25
25.5
26
27.5
28
28. s
29
29.5
30
30-5
31
3»-5
X
'^
27
27.5
28
2a5|29
29.5
30
30-5
31
3»-5
32
325
33
33-5
I.Z
29
29.5
30
30-5 31
315
32
32-5
33
33-5
34
34-5
35
35-5
1.2
63
3«
3»-5
32
32.5 33
33-5
34
34-5
35
35.5
36
36.5
37
375
>-3
68
33
33-5
31
34-3 35
355
3S
3<>-5
37 ! 37-5
38
38.5
39
39-5
'•4
74
35
35.5
36
365 37
37-5
3«
38.5
39 i 39-5 '40
40.5
41
4«-5
1-5
P
37 137-5
38
38.5 39
39-5
40
405
41 ' 41-5 1 42
42.5
43
43-5
1.6
85
39
39-5
40
40-5
41
41-5
42
425
43
43-5'
-44 1
44-5
45
45-5
Ibe.
\t
x8
ao
22
24
26
a8
30
32
34
36
38
40
42
44
46
TLLDSTBATunr.—AsBume a
«7hat weight will it haul up a
" Mogul
grade of
Ib«.
»4-5
16.5
ia.5
20.5
22.5
24- 5
26.5
28. 5
30.5
32 5
34-5
36.5
38.5
40-5
4a- 5
44-5
46.5
lbs.
" engine to have an adhesion of x6ooo .w». .
74 feet per mile, combined with a curve of 9<> f
16000-^ 39.5 = 405 tons (jooo lbs.).
BAILWATS.
685
Hence, To Compute Adhesion on a Given Grade and Curve, having Weight
of Train,
Rule.— Multiply tabular number by weight of train in tons (2000 lbs.)?
and product will give adhesion, in lbs.
ExAMPLB.— Assume preceding elements Then 39. 5 x 405 = 16 000 Ibt.
Nora.— A ^^CoDSolidalion" engine, by its superior adhesion (19550 lbs.) would
haul up a like grade and curve 495 tons.
IVlexnoretiida 011 Siiglish. Rail-virays.
Regulations {Board of Trade).
Cast-iron girders to have a breaking weight = 3 times permanent load, added to
6 times moving load.
Wrougbt-iron bridges not to be strained to more tban 5 tons per sq. inch.
Minimum distance of standing work from outer edge of rail at level of carriage
steps, 3.5 feet in England and 4 feet in Ireland.
Minimum distance between lines of railway, 6 feet.
Stations. — Minimam width of platform, 6 feet, and xa at important stationa
Minimum distance of columns fTom edge of platform, 6 feet. Steepest gradient for
sutions, X in 360. Ends of platforms to be ramped (not stepped). Signals and dis-
tant signals in both directiona
Carria0K«-— Minimum space per passenger no cube feet. Minimum area of elaSs
per passenger, 60 sq. in& Minimum width of seats, 15 ina Minimum breadth of
seat per passenger, 18 ina Minimum number of lamps per carriage, 3,
Requirements — Joints of rails to be fished. Chairs to be secured by imn splkei.
Fang bolts to be used at the Joints of flat-bottomed raila
CoMhmction. ^*'W' ^^'
Feet. In*. Fe«k Ink
Whith, single lino 18 34 6
doableline 30 38
top of ballast, single line 13 6 15 6
** *^ double line 34 6 39
Slope of cattings f^om centre, i in 3a Width of land beyond bottom of slope,
a to xa feet Ditch with slopes, i foot at bottom, i to i. Quick mound, 18 ina in
height Poet and rail-fence posts, 7 feet 6 ins. x 6 ina x 3- 5 ins., 9 feet apart, 3 feet
in ground. Intermediate posts, 5 leet 6 ina x 4 ins. x x. s ina , 3 feet apart Rail*
4of4Xi-5tna
Farliaznentarsr Regulations fbr Crossing Roads.
ti
Clear width of under bridge, or approach ....
Clear height of under bridge for a width of 12 ft.
u
u
M
(t
U
ti
a
it
it
it
ii
10
it
ii
at springing
Over bridge, height of parapets
Approaches, inclination
^ height of fencing
Tamplkii
Road.
Feet. Ins.
35 —
16 —
Z2 —
4 —
linjo
3 —
Pablie
Road.
Feet. Ini.
25 —
15 —
12 —
4 —
I in 20
3 —
OccuiniImmi
RmA.
Feet. Ine.
12 —
Z4 —
4 —
I in 16
3 —
In
Umifs of Deviation. — In towns, lo yards each side of centre line,
country, 100 yards, or 5 chains nearly.
Z«oe/.— In towns, 2 feet In country, 5 feet.
Gradient. — Gradients flatter than i in too, deviation 10 feet per mile
steeper. _ Do., steeper, 3 feet per mile.
Curve. — Curves upwards of .5 a mile radius, may be sharpened to .5 mile
rmdlua. Curves of less than .5 mile radius may not be sharpened.
3M
C86
BOADS, STBEBTS, AND PAYBMENTS.
BOADS, 6TBBETS, AND PAYEMBNTS.
Classiiioatioii of !Roads.
I. Earth. 2. Corduroy. 3. Plank. 4. Gravel. 5. Broken stone (Ma/v
adam). 6. St<ine sub-pavement with surface of broken stone (Telford).
7. Stone sub-pavement with surface of broken stone and gravel, or gravel
alone. 8. Kuoble stone bottom with sqrface of broken stone or gravel, or
both. 9. Concrete bottom with surface of broken stone or gravel, or bot^
d-rade of R-oads.
Limit of praeticable grade varies with character of road and friction of ve-
hicle. For best carriages on best roads, limit is i in 35, or 150 feet in a mile.
' Maximum grade of a turnpike road is i in 30 feet. An ascent is easier
for draught if taken in alternate ascents and levels, than in one continuous
rise, although the ascents may be steeper than in a uniform grade.
Ordinary angle of repose is z in 40 if roads are bad, and i in 30, to i in 20.
When roads have a greater grade than i in 35, time is lost in descending,
in order to avoid unsafe speed. Grade of a road should be less than its <m^
qfrepote. Minimum grade of a road to secure effective drainage should be
I in 3o. In France it is i in 125. ^
Inijonstruction of roads the advantage of a level iroad over that of an in-
clined one, in reduction of labor, is superior to cost of an increased length
of road in the avoiding of a hill.
Alpine roads over the Simplon Pass average i in 17 on Swiss side, x in bs
on Italian side, and in one instance i in 13.
In' deciding upon a grade, the motive power available of ascent and avoid-
able of waste of power in descending are to be first considered*
When traffic is heavier in one direction than the other, the grade in as-
cent of lighter traffic may be greatest
When axis of a road is upon side of a hill, and road is made in parts by
excavfition and by embankment, the side surface should be cut into steps,
in order to afford a secure footing to embankment, and in extreme cases,
sustaining walls should be erected.
Oonstrtaotion.
S2«tixnate of luabor in Coxistruotion of Roads, (if. AnediiL)
A day's work of 10 hours of an average laborer is estimated as follows:
In Cube Yards.
Work.
Picking and digging
Excavation and pitching)
6 to xa feet )
LoMding in barrows.
Wheeling in barrows per )
xoo feet J
Loading in cart&
Spreading and levelling. . .
Ordinary
Earth.
x8 to 33
8 to 19
33
3o to 33
x6 t0 48
44 to 88
Loose
Earth.
x6
8
Had.
7 tOx6
8
as
Clay and
Earth.
9
4
Graval.
Blaatlv
7 to XX
«'4
—
9.a
«9
—
34 to 38
—
17 to 37
30 to 80
^^
Time of pitching fh>m a shovel is one third of that of digging.
Ditches. — All ditches should lead to a natural water-coarse, and their
imum inclination should be i in 125.
Depressions and elevations in surfiice of a roadway Involve a material loss of
power. Thus, if elevation is 1 inch, under a wheel 4 feet in diameter, an inclined
Elane of i in 7 has to be surmounted, and, as a consequence, one seventh of w^abt
as to be raised x inch. *^
BOADS^ STREETS, AND PAVBMENTSr 687-
An unyieldiog foandation and surface are indispensable for a perfect roadway.
Eartb in embankment occupies an average of one tenth less space than in natural
bank, and rock about one third more.
Ruts. — Surface of a roadwaj should be maintained as intact as prac-
ticable, as the rutting of it not only tends to a rapid destruction of it, but
involves increased traction.
The general practice of rutting a road displays a degree of ignorancQ of
physical laws and mechanical effects that is as inexplicable as it is injurious
and expensive:
On compressible roadways, as earth, sand, etc., resistance of a wheel decreases as
breadth of tire increases.
Depressing of axles at their ends increases Mction. I^ong and pliant springs de-
crease effect of shock in passing over obstacles in a very great degree.
Transverse Section. — Best profile of section of roadway is held to be one
formed by two inclined planes meeting in centre of road aad slightly
romided off at point of junction.
Roods having, a rough surface or of broken stone should have a rise of
X in 24, equal to a rise on crown of 6 ins., and on a smooth surface, as a
block-stone or wood pavement, the rise may be reduced to i in 48.
On roads, when longitudinal inclination is great, the rise of transverse
section should be increased, in order that surface water may tliore really
run off to sides of roadway, instead of down its length, and consequently
gullying it.
Stone Breaking, A steanl stone-breaking machine will break a cube yard
of stone info cubes of 1.5 ins. side, at rate ol i to 1.5 ip per hoar.
IkCaoadaxni^eiS Roads.
In constniction of a Macadamized toad, the stones ( road metal ) used
should be hard and rough, and cubical in form, the longest diameter of which
exceed 2.5 ins., but when they are very hard this may be reduced to 1.25
and 1.5 ins.
The best stones are sach as are difficult of fratture, 9& basaltic and trapi
and especially when they are combined with hornblende. Flint and sili-
ceous stone are rendered' unfit for use by being too britUfl. L%ht gtanitat
are objectionable, in consequence of their being brittle and liable to disihte-
^ration ; dark granites, possessing hornblende, are less objectionable. Lime-
stones, sandstones, and slate are too weak and friable.
Dimensions of a hammer for breaking the stone should be, head 6 ins. in
length, weighing i lb., handle 18 ins. in rength ; and an average laborer can
break from 1.5 to 2 cube }^ds per day.
Stones broken up in this manner have a volume twice as great as in their
original form. 100 cube feet of rock will make 190 of 1.5 ins. dim^ion,
182 of 2 ins., «nd 170 of 2.5 ins.
A ton of hard metal has a volume of 1.185 cube yards.
Construction of a Roadway. — Excavate and level to a depth, of i foot^
then lay a " bottom *^ 12 ins. deep of brick or stone spalls or chips, clinker
or old concrete, etc., roll down to 9 ins, then add a layer of coarse gravel or
small ballast 5 ins. deep, roll down to 3 ins., and then metal in 2 equM layr
ers of 3 Ins., laid at an interval, enabling first layer to be fully consolidated
before second is laid on and rolled to a depth of 4 ins. ; a surface or '' blind'*
of .75 inch of sharp sand should be laid over last layer of metal and rolled
in with a free supply of water.
688
BOADS, STBESTS, AND FAVBMSNTS.
Prcpwrtion qf Oettert^ Fillers^ and Wheelers in different Soils.
<U a Run of 50 Yards. (Molestoorth. )
Whedert compufed
Loose earth, )
Sand, etc. )
Compact earth . . .
Marl
Gfltton.
I
I
Fillfln.
a
9
Wheelen.
3
2
Gettera.
Hard Clay
Compact \
gravel f '"•
Rock
I
I
3
FUlen.
1.25
2
I
Wb«el«n.
1-25
I
X
Telford Roads.
In construction of a Telford road, metalling is set upon a bottom course of
stones, set by hand, in the manner of an ordinar}' block stone pavement,
which course is composed of stones running progressively from 3 inches in
depth at sides of road to 4, 5, and 7 inches to centre, and set upon their
broadest edge, free from irregularities in their upper surface, and their in-
terstices filled with stone spalls or chips, firmly wedged in.
Centre portion of road to be metalled first to a depth of 4 ins., to which,
after being used for a brief peri6d, 2 ins. more are to be added, and entire
surface to be covered, " blinded," with clean gravel 1.5 ins. in depth.
Telford assigned a load not to exceed i ton upon each wheel of a vehicle,
with a tire 4 ins. in breadth.
Gl-ravel or Sarth, Roads.
. In construction of a gravel or earth road, selection should be made between
dean round gravel that will not pack, and sharp ^avel intermixed with
earth or clay, that will bind or compact when submitted to the pressure of
traffic or a roll.
Surface of an ordinary gravel roadwav should be excavated to a depth of
from 8 to la ins. for full width of road, the surface of excavation conforming
to that of road to be constructed.
The gravel should then be spread in layers, and each laver compacted by
the grfbdual pressure due to travel over it, or by a roller, tne weight of it in-
creasing with each layer. One of 6 tons will suffice for limit of weight.
If gravel is dry and wiU not readily pack, it should be wet, and mixed
with a binding material, or covered with a thin laver of it, as clay or loam.
In rolling, the sides of road should be first rolled, in order to arrest the
gravel, when the centre is being rolled, from spreading at the side.
To F&'form a mile of gravel or earth road, 30 feet in width between guttera,
material cast up from sides, there will be required 1640 hours* labor of men,
and ao of a double team.
Oordtiroy Roads.
A Corduroy road is one in which timber logs are laid transversdy to its plane.
Platik Roads.
A single plank road should not exceed 8 feet in width, as any greater width
involves an expenditure of material, without any equivalent advantage.
If a double track is required it should consist of two single and independ-
ent tracks, as with one wide track the wear would be mostly in the centre,
and consequently, wear would be restricted to one portion of its surface.
Materials.— SHeepen should be as long as practicable of attainment, in depth 3 or
4 ins. , according to requirements of the soil, and they should have a width of 3 ina.
R>r each foot of width of road.
Pine, oak, maple, or beech are best adapted for economy and wear.
Planks should be ft-om 3 to 3.5 ins. thick, and not less than 9 in& in width, or
more than 12 if of hard wood, or 15 if of soft.
A plank road will wear from 7 to 12 years, according to service, material,
and location, and its traction, compared with an ordinary Macadamized road,
is a>5 to 3 times less, and with a common country road in bad order 7 timea.
For other elements, see Earth-work, page 466.
BOAB6, STREETS, AND PAVEMENTS. 689
A.apb.alt.
Aspbalt pavements are made in two ways, either flrom a mixture of aspbaltum
with sand and a little powdered limestone, or fVom natural asphaltic limestone,
called sometimes ''rock asphalt," which contains from 6 to 12 per cent, of asphal-
tarn.
The asphalt pavements of America are principally made by the former, and those
of Europe by the latter method. The composition of one is of about 12.5 per cent.
r«flned aspbaltum, 2.5 residuum oil of petroleum or soft bitumen termed *' maltha,"
5 powdered limestone, and 80 sharp sand, by weight, mixed at about 3cx>°.
The rock asphalt pavement is made by powdering the natural asphaltic lime-
stone, heating the powder, and compressing it in place.
Asphaltic mastic, for floors, roofs, and sidewalks, is made from rock asphalt, by
adding aspbaltum to it as a flux and incorporating 60 per cent, more or less of sand
and gravel, according to the density needed and the temperature of the place, cel-
lar or walk, and whether exposed to the sun or not. The roadway needs a convex-
ity of at least . 15 of its breadth.
Artificial Atfhalt. — Heated sand, gravel, and powdered limestone, with gas tar or
coal tar, when mixed, possess some of the properties of asphalt mastic, but are
much inferior.
Bitwninoui Road may he made by breaking up asphaltic limestone, laying it 3
ins. thick, covering with coal tar and ramming. UseAil in country districts near
each deposits.
"^Tood Paveineiit.
CSose-grained and hard woods only are suitable, such as oak, dm, ash,
beech, and yellow pme, and they should be laid on a foundation of concrete.
Slook Stone Petvexxient.
Paving-blocks, as the Belgian, etc., where crest of street or area of pave-
ment does not exceed i inch in 7.5 feet, should taper slightly toward the
top, and the joints be well filled, " blinded," with gravel. The common
practice of tapering them downward is erroneous.
The foundation or bottoming of a stone pavement for street travel should
consist either of hydraulic concrete or rubble masonry in hydraulic mortar.
The practice in this country of setting the stones in sand alone is at variance
with endurance and ultimate economy, but when resorted to, there should be
a bed of 12 ins. of gravel, rammed in three layers, covered with an inch of
sand. Granite or Trap blocks should be 4 x 9 X 12 ins.
R.u.'b'ble Stone I*avexneiit.
Bowlders or Beach stone of irregular volumes and forms, set in a. bed of
sand, involves great resistance to vehicles and frequent repairs ; it is whol^
at variance wiw requirements of heavy traflfic or city use.
Ooiiorete Roads.
Concrete roads are constructed of broken stones (road metal) 4 volumes,
clean sharp sand 1.25 to .33 volumes, and hydraulic cement i volume. The
mass is laid down in a layer of 3 or 4 ins. in depth, and left to harden during
a period of 3 days, when a second and like layer is laid on and well rolled,
and then left to harden for a period of from 10 to 20 days, according to
temperature and moisture of the weather.
Roads. (MoUnoortk.)
Ordinary turnpike roads. — 30 feet wide, centre 6 ins. higher than sides ;
4 feet from centre, .5 inch below centre ; 9 feet from centre, 2 ins. below
centre; 15 feet from centre, 6 ins. below centre.
Foot-paths — 6 feet wide, inclined i inch towards road, of fine gravel, or
sifted qoarry chippings, 3 ins. thick.
CrM9-roaaa — 20 feet wide. Fo(^'paths — 5 feet
Side drains — ^3 feet below surface of road.
Road material — bottom layer gravel, burned clay or chalk, 8 ins. deep.
Top layer, broken granite not larger than 1.5 cube ins., 6 ins. deep.
(bgo
BOABSj STBEETS, ANP PAYEMSKTS*
!]Misoellaiieou.s ^otes.
MetaUxng should be from 6 ins. to x foot in depth, and in cubes of 1.5 to 1.75 iD&
One layer of material of a road should be spread and submitted to traffic or rolL
ing before next is laid down, and this process should be repeated in 2 or 3 layen
of 3 ins. each.
When new metal is laid on old, thd surface of the old should be loosened with a
pick. Patching is termed darning.
Sand and Gravel, Blinding, should not be spread over a new surface, as they tend
to arrest binding of metal. Mud should be scraped off of surface.
Hoggin is application of a binding of surface of a metal road, composed of loam,
fine grav0l, aud coarse sand.
Atetalled Roads should be swept wet
Soiling. — Steam rolls are most efftetive and economical, xooo sq. yards of metal-
ling will require 24 hours' rolling at 1.5 miles per hour. A roller of 15 tons' weight
will roll 1000 sq. yards of Telford or Macadam pavement in from 30 to 40 hours, at
a speed of 1.5 miles per hour^ equal .675 and .9 ton mile per sq. yard.
Sprinkling. — 60 cube feet of water with one cart will cover 850 sq. yarda 100
cube feet per day will cover looo sq. yards; ordinarily two sprinklings are necessary.
Oranite Pavement. — The wear of granite pavement of London Bridge was .22 aich
per year, and from an average of several streets in London, the wear per 100 vehicles
per foot of width per day is equal to one sixteenth of an inch per year.
Sweeping and Watering of granite pavement and Maeadam road, for equal areas
and under alike conditions in every respect, costs as i for former to 7 of latter.
By men, with cart, horse, and driver, costs 3.25 times more than by a machine,
one of which will sweep 16 000 sq. yards of street per iieriod of 6 hours.
Asphalt Pavement. — Average cost per sq. yard in Lohdon: foundatiM, 50 cents;
surface, $3.25; cost of maintenance per sq. yard per year, 40 cents. Wear varies
from .2 to 42 near curb, and .17 to .34 inch on general surface per year.
ITcuAm^.— Surface cleaning of stone or asphalt pavement by a Jet can be eff^ted
at fk-om I to 2 gallons per sq. yard.
Wood Pavement. — Wear of wood pavement in London, per xoo rehicl^s per day
per foot of width, .083 Inch per year.
Macadamized Roads. — Annual cost of maintenance of several such roads in
London was 62 oents per sq. yard.
Block Stone Pavement — Stones should be set With their tapered or least ends up-
wards, with surface Joints of i inch.
Fascines, when used, should bo in two layers, laid crosswise to each other and
picketed down.
BituminouH road may be made by breaking up asphalt, laying it 2 in& thick,
covering with c0.1l tar, and ramming it with a heavy beetle. To repair a bitnmi-
nous surface, dissolve one part of bitumen (mineral tar) in three of pitch oil or resin
oil, spread .625 of a lb. of solution over each sq. yard of road, sprinkle 2 lbs pow-
dered asphah (bituminous limestone) and then sand, aud sweep off the surplus.
Slipping. ~GTa.n\te safest when wet, and asphalt and wood when dry.
Gravelf alike to that of Roa Hook, ft'om its uniformity, will bear an admixture
of fVom .2 to .25 of ordinary gravel or coarse sand.
Annual cost of a Telford pavement 4.2 cents per sq. yard, including sprinkling,
repairs, and supervision.
Voids in a Cube Yard of Stone,
Broken to a gauge of a. 5 Ins. .... 10 cube feet
2 " 10.66 " "
"•5 '* "33 *
i(
Sbingie 9 eubeftet
Thames ballast. ... 4.5 " **
Fpr fhrther and full information, see Law and Clarke on Roads and Streets, New
York, 1867; Weale's Series. Tendon, 1861 and 1877; Roads, Streets, and ^vementa,
by Brev. M^.-Gen. Q. A. Gilmore, U. S. A., New York, 1876; Engineering Notes, by
F. Robertson, London and Now York, 187;^; and Gonstructton and Maintenance of
Roads, by Ed. P. North, C. E., see Transactions 4m. Socof C. K., voi Tiil.j May.187^
SEWKBS.
691
SEWEBS.
Sewen are the courses from a series of locations, and are classed as
Drains, Sewers, and Culverts.
Ih'abii are small courses, from one or more points leading to a sewer.
CtUverfs are courses that receive the discharge of sewers.
Greatest fall of rain is 2 ins. per hour = 54 308.6 galls, per acre.
Inclination of sewers should not be less than i foot in 240, and for
house or short lateral service it should be i inch in 5 feet.
Circular.
....^r
X representing
6*10.3.
55 V« 2/= *, and t> a = V.
D 2 1) , ^ ^
Egg. — = to, — = w , and D = r.
3 3
area of sewer -i- tuetted perimeter yf inclincUion of sewer
p«r mile, and v velocity of flow of contents in feet per
minute; a area ofjlmc, in sq.feet, V wdume of discharge.
in cube feet per minute ; D height of sewer, w and w
width at bottom and lop, and r radius of sides, in feet
For diameter of sewer exceeding 6 feet (r. Hawksley.)
D diameter of a circular sevoer of area required.
D-- = to'.
9
EUif^ie. — Top and bottom internal should be of equal diam-
eters. Diameter .66 depth of culvert; intersections of top
and bottom circles form centres for striking courses connect-
ing top and bottom circles.
Pipes or Small Sewers. — Height of 8eetion= i; diameter
of arch ^ .66 ; of invert = .33, and radius of siiles = i.
In culverts less than 6 feet internal depth, brickwork should be 9 ins. thick ;
when they are above 6 feet and less than 9 feet, it should be 14 ins. thick.
If diameter of top arch =. i, diameter of inverted arch = .5. and total'
depth ^ sum of the two diameters, or 1.5 : tlien radius of the arcs which are
tangential to the top. and mverted, will be 1.5.
From this any two of the elements can be deduced, one being known.
X>retinage or I^ands l^jr Pipes.
Soils.
Depth
ofPtpea.
DUtance \
apart. |
SoxLa.
Depth
of Pipea.
Distance
apart.
Coarse gravel sand ....
Light sand with gravel
Liirht loam
Ft. Ina.
4 6
4
3 6
3 2
Feet.
60
50
33
21
Ix>am with gravel . . .
Sandv loam
Ft. loa.
3 3
3 9
2 9
2 6
Feet.
27
40
21
Soft clav
Loam with clay
.Stiff clay
«5
I^iiiixu-axn ^Velocity and. Ghrade of Se-w^ers and Drains
in Cities. tWicksteed.)
Di«in.
Id*.
4
6
8
10
X3
Vel.
Mhiate.
Feet.
340
no
220
2ZO
X90
Grade,
xin
36
87
119
>75
Grade
Vd.
line.
Diatn.
Minute.
Feet.
Ina.
Feet.
146.7
'5
180
81.2
x8
180
60.7
24
180
44-4
30
180
3P2
36
180
Grade,
I in
Umde
jffle.
Diam.
Vel.
per
Minute.
Grade,
z in
Grade
jStfe.
Feet.
Ins.
Feet.
Feet.
244
21.6
42
180
686
7-7
294
18
48
180
784
6.8
392
13-5
54
180
882
6
490
10.8
60
180
980
5-4
588
9
A rea of SeiDers or Pipes. — An area of 20 acres, miles, etc., will not re-
quire ao times capacity of pipes for one acre, mile, etc., as the discharge from
the 19 acreSf etc., will not liuw into the main simultaneously with that from
one acre, etc. Ordinarily in this country an area of sewer or pipe that will
discharge a rainfall of i inch per hour (3630 cube feet per acre) is sufficient*
092
SfiWEBS.
^
Sewage.— The excreta per annum of 100 individuals of both sexea and
all ages is estimated at 7250 lbs. solid matter and 94 700 fluid, equal to 1020
lbs. per capita^ and in volume 16 cube feet, to which is to be added the
volume of water used for domestic purposes. A velocity of flow of from a.5
to 3 feet per second will discharge a sewer of its sewage matter and prevent
deposits. The minimum velocity should not be less than 1.3 feet per second.
Surilsice from -w-liioh Circular Se-^wers "witli proper Curves
■will discUarge tliat Proportion of "W^ater trona a 'Fall
or One IiioU iu X>epth. per XXour -^^liioh. >vould. reach
tUem, iiiclu.d.i£ig City I>raixxage. (John Roe.)
Inclination in Fbkt.
Nono. . . .
I in 480.
I in 240.
z in x6a
I in I20.
I in 8a.
I in 60..
DiAMKTER
OF Skwbbs in Fsbt.
3
2-5
3
4 1 S 1 6 1
Acret.
Acres.
Acre3.
Acres.
Acres.
Acres.
38.75
67.25
120
277
570
1020
48
75
135
308
■ 630
1117
50
87
155
355
735
1318
63
"3
203
460
950
2692
2180
78
143
257
590
1200
90
16s
295
570
1388
2486
125
182
318
730
1500
2675
Acres.
Acres.
1725
2850
«9a5
3025
2225
287s
3700
4225
3500
4500
5825
6625
4550
7125
Surface of a To-wn from* wliicli small Circular X>rain8
-will difitoliarge "Water ecLual ixi Volume to Two Inches
iix I>epth. per Hour. (John Roe.)
Inclination.
FbU of one in«
Acres.
.125
•25
•4375
•5
.6
I
1.3
«-5
1.8
3.1
IhAMRBK or
Draiv
r IN Ins.
3
4
5
6
7 8
Feet.
Feet.
Feet.
Feet.
Feet. Feet.
120
—
—
—
— -
—
20
I20
—
—
—
—
40
—
—
—
—
—
30
80
—
—
—
—
30
60
—
—
—
—
—
20
60
—
—
— >
—,.
— >
40
20
—
^■^
—
20
60
120
80
60
Inclination.
Fall of one in.
Acres.
2.1
2.5
4
5
5
7.8
9
xo
«7
75
5
3
8
DiAMrmt OF Drain in Iks.
9 I X2 IS I 18
Feet.
120
80
60
X2
»5
Feet.
Feet.
X20
—
80
—
60
340
—
ISO
_—
80
—
60
—
Fsst
340
X30
Dimensions, A.reas, and "Volume of »laterial per I^ineal
Foot of Kgg-shaped Se-wers of different Dimensions.
Intrenal Dimrksionb.
Depth.
Diam. of
Diam. of
Area.
Top Arch.
Feet.
Invert.
Feet.
Feet.
Sq. Feet.
2.25
1-5
•75
2-53
3
2
I
4-5
3.75
as
X.25
7.03
4 5
3
1-5
xo. 12
5-5
3-5
I-7S
13-78
6
4
2
x8
6.75
4-5
2.25
22.78
7-5
5
3-5
38.x 3
8.25
55
2.75
34-03
9
6
3
40.5
Cube Feet
2.81
356
4-31
5.06
5.8x
6.56
7-31
Area = product of mean diameter X height
Sewer Pipes should have a uniform thickness and be uniformly^ glaze^^
both internally and externally.
Fire-clay pipes should be thicker than those of stone-clay.
VoLUMR or Bbick-wokk.
4-5 In".
Ick.
*-l
9 Ins.
thick.
'sSc'r
Cube Feet.
Cube Feet.
9.56
xo.87
—
xa.75
—
14.35
—
15.75
19.69
a4-75
28.41
30.94
STABILITY. 693
STABILITY.
Stability, Strength, and Stiffness are necessary to permanence of a
structure, under all vai-iutions or distributions of load or stress to which
it may be subjected.
SUibUity of a Fixed Body — Is power of remainmg in equilibrio without
sensible deviation of position, notwithstanding load or stress to which it
may be submitted may have certain directions.
Stabilify of a Floating Body. — A body in a fluid floats, or is balanced,
when it displaces a volume of the fluid, wei<;ht of which is equal to weight
of body, and when centre of gravity of body and that of volume of fluid dis-
placed are in same vertical plane.
When a body in equilibrio is free to move, and is caused to deviate in a
small degree from its position of equilibrium, if it tends to return to its
original position, its equilibrium is termed Stable / if it does not tend to de-
viate further, or to recover its original position, its equilibrium is termed
Indifferent ; and when it tends to deviate further from its ori<^iiial position,
its equilibrium is Unstable,
A body m equilibi'io may be stable for one direction of stress, and unstable
for another.
^AfometU of Stabilify of a body or structure resting upon a plane is mo-
ment or couple of forces, which must be applied in a plane vertically inclined
to the body in addition to its weight, in order to remove centre of resistance
of body upon plane, or of the joint, to its extreme position consistent with
stability. The couple generally consists of the thrust of an adjoining struct-
ure, or an arch and pressure of water, or of a mass of earth against the
structure, toother with the equal and imralld, but not directly o[)posed, re-
sistance of ^ane of foundation or joint of structure to that lateral thrust.
It may differ according to position of axis of applied couple.
Coujjle. — Two forces of equal magnitude applied to same body or struct-
ure in parallel and opposite directions, but not in same line of action, consti-
tr.te a coaple.
NoTB. — For Statical and Dynamical Stability, see Naval Architecture, page 649.
To .A^scertain; Stability or a Body 0x1 a I^orizontal Plane.
— XTig..!.
Illustration. — Stability of a body, A, Fig. i, when a
thrust is applied as at o, to turn it on a, is ascertained by
multiplying its weight by distance a s, from fUlcrum a to
line of centre of gravity, c t.
Hence, if cubic^il block weighed 10 tons and its base is
6 feet, its moment would be 10 X — = 30 tons.
2
If upper part, abdc, was removed, remainder, aed^
would weigh but 5 tons, but its centre of gravity • would be -^ a « = 4 feet. Henoe
3
tifi moment would be 5 x 4 = 20 tons, although it is but half the weight
•To Compute ^Veiglit of a GJ-iven Sody to Sustain a
Ghiven 'X'liruet.
FA
!___ = W. F representing thrust in lbs. , h height of centre of gravity of body = c *,
and I distance offiUcrwm from centre ofgi'avity = a «.
IrxrsrrRATioy. — Assume figure to be extended to a height of 30 feet, and required
to bo capable of resisting the extreme pressure of wind.
694
STABILITY. — BEYBTUBNT WALLS.
Preesare estimated at 50 lbs. F = 6 x so X 50 = 6000 Iba at centre qf gravity of
surface of body.
Then
6<xx> X 10
= 200CX> lh».
NoTK I.— This result is to be increased proportionately with the factor of safety
due to character of its material and structure.
2. — If form of body has a cylindrical section, as a round tower, the thrust of wind
wonld be but one half of that of a plane surface.
When the Body is Tapered^ as Frustum of Pyramid or Cone, — Ascertain
centres of gravity of surface for pressure or thrust, and of body for its sta-
bility, and proceed as before.
ITo A.soertaiii Stai'bility oif* a Body on
aai Inoliixc^tioii.^IT'ig. 8.
iLLtiSTRATioN.— Stability of body, Fig. 2, when thrust
is applied at c, is ascertained by multiplyiog its weight
by distance a b from fulcrum, 6, to line of centre of
gravity, a fir.
If thrust was applied at o, stability would be ascer-
tained by distance s r fVom fulcrum r.
^lagles of* EqLiaili"brini» at -wliioli various SulDstances will
Repose, as deterxnined 133^ a OliiiLOineter.
Angle measured from a Horizontal Plane^ and faUiivg from a spout.
DegTMk
De^reeB.
Lime-dust 45
Dry- sand ,,... 40
Moist sand 41
Degrees.
Sand, less dry 39.6
Wheat 37
Com 37,
Common mold. . . 37
Common gravel. . 35 to 36
Stones or Coal. . . 43
Weiglit of a Cube I^oot of* I^aterials of Ifixxi'baiikxneuta,
"Walls, and Daxns.
Concrete in cement. . . 137
Stone masonry 130
Brick *• 112
Gravel 125
Loam 126
Sand
120
Clay.
Marl
120
100
Revetment TlTalls.
When a wall sustains a pressure of earth, sand, or any. loose material, it
is termed a Revetnaent wall, and when erected to arrest the fall or subsidence
of a natural bank of earth, it is termed a Face wall.
When eiirth or banking is level with top of wall, it is termed a Scarp re-
vetment, and when it is above it, or surcharged, a Counterscarp revetment
When face of wall is battered, it is termed Sloping, and when back is bat-
tered, Connt^r^oping.
Thrust of earth, etc., upon a wall is caused by a certain portion, in shape
of a wedge, tending to break away from the general mass. The pressure
thus caused is simuar to that of water, but weight of the material must be
r«duo«d by a particular ratio dependent upon angle of natural slope, which
varies from 45° to 60° (measured from vertical) in earth of mean density.
Or, natural slope of earth or like material lessens the thrust, as the cosine
of the slope.
Angle which line of rupture makes with vertical is .5 of angle which line
of natural slope, or angle of repose, makes with same vertical line. When
earth is level at top, its pressure may be ascertained by considering it as a
fluid, weight of a cube foot of which is equal to weight of a cube foot of the
earth, multiplied by square of tangent of .5 angle include4 between patnnl
slope and vertical
STABILITY. — ^REVETMENT WALLS. 695
Therefore squares of the tangents of .5 of 45° and .5 of 60® = .1716 and
•3333* which are the multipliers to be used in ordinary cases to reduce a
cube foot of material to a cube foot of equivalent tiuid, which will have
same effect as earth by its pressure upon a wall.
X^reseure of ICartb. agaiiist ftevetmeixt Walls.
Fig: 3. Let A B G D, Fig. 3, be vertical section of a revetment
wall, behind which is a bank of earth, A D/e ; let D 0
■^ represent angle of repose, line, of rupture^ or natural slope
which earth would assume but for resistance of wall.
In sandy or loose earth angle o D A is generally yP ;
in firmer earth it is 36°; and in some instances it is 45*^.
If upper surface of earth and wall which supports it are
both in one horizontal plane, then the resultant, I n, of
pressure of the bank, behind a vertical wall, is at a dis-
tance, D n, of one third A D.
line of Rupture behind a wall supporting a bank of vegetable earth is at
a distance A o from interior face, A D = .618 height of it.
When bank is of sand, A o = .677 h ; when of earth and small gravel =
.646 h ; and when of earth and large gravel = .618 A.
The prism, vertical section of which is A D o, has a tendency to descend
along inclined plane, o D, by its gravity \ but it is retained in its place bv
resistance of w^all, and by its cohesion to and friction upon face o D. Each
of these forcea may be resolved into one which will be perpendicular to o D,
and into another which will be parallel to o D. The- lines c », i I represent
components of the force of gravity, which is represented by vertical line c /,
drawn from centre of gravity, c, of prism. Lines nr,,lr represent compo-
nents of forces of cohesion aiid friction, which is represented b^* horizontal
line ft I. Force that gives the prism a tendency to descend is t /, and that
opposed to this is r /, together with effects of cohesion and friction.
Thus, ilz=:rl-\- cohesion + friction. Consequently, exact solution of prob-
lems of this nature most be in a great measure experimental.
It has been foand, however, and confirmed experimentally, that angle
formed witii vertical, by prism of earth that exerts greatest horizontal stress
against a wall, is half the angle which angle of repose or natural sioj)e of
"^arth makes with vertical.
AJI exu o r ail d a .
Natural slope of dry sand =39^, moist soil = 43<3, very fine sand = 21°, wet clay
=s 14O, and gravel = 35O.
In setting or founding of retaining walls, if earth upon which wall is to rest is
elayey or wet, coefficient of friction between wall and earth falls to .3; hence it is
necessary, in order to meet this, that the wall should be set to such a dc>|Hb in the
earth that the passive resistance of it on outer face of wall, combined with its fric-
tion on its bottom, may withstand the pressure or thrust on its inner face.
Moment of a Retaining Wall is its weight multiplied by distance of its centre of
gravity to vertical plane passing through outer edge of its base.
Mofnent of Pretmre of Earth against a retaining wall is pressure multiplied by
distance of Its centre of pressure to horizontal plane passing through base of wall.
Equilibrium of Retaining Wall is when respective moments of wall and earth are
eqaai.
SialnlUif of a Retaining WaU should be in excess of its equilibrium, according to
character of thrust upon it, and the line of its resistance should be within wall and
St a distance flrom vertical passing through centre of gravity of wall, at most . 44 of
distance of exterior axis of wall fh)m this line.
Confident ofStabUUy varies with character of earth, location, exposure to vibia-
iioos, floods, etc ; hence thickness of base of wall will vary from 1.4 to 2 6.
Backs of retaining walls should be laid rough, is crder to arrest lateral subsidenos
of the lllling.
696
STABILITY. — ^REVETMENT WALLS.
When flUing-ls composed of bowlders and gravel, the thickness of wall must bo
increased, and contrariwise; when of earth in layers and well rammed, it may b*
decreasecL
Courses of dry wall shoald be inclined inwards, in order to arrest the flow of
water of sabsidence iu filling from running out upon face of wall
Less the natural slope, greater the pressure on wall.
Sea walls should have an increased proportion of breadth, as the earth backing
is not only subjected to being flooded, but the walls have at times to sustain the
weight of heavy merchandise.
BuUrest. — An Increased and projecting width of wall on its flront, at intervals io
its length.
Counterfort— An increased and projecting width of wall at its back and at in-
tervals.
Coefficient of Friction of masonry on masonry .67, of masonry on dry clay .51,
and on wet clay .3.
Face of wall should not be battered to exceed i to 1.25 ins. in a foot of height, in
consequence of the facility afforded by a greater inclination to the permeation of
rain between the Joints of the courses.
Footing of a wall, projecting beyond its faces, is not included In its width.
Pressure.— Limit of pressure on masonry 12 500 to z6 500 lbs. per sq. foot wall
Thickneu of WaUt^ in Mortar^ Facet vertical For BaUtoayi or Like Strets.
Cut stone or Ranged rubble 35 | Brick or Dressed rubble 4
When laid dry, add one fourth.
Friction in vegetable earths is .5; pressure in sand .4.
When vegetable earths are well laid in courses, the thrust is rednced .5.
When bank is liable to be saturated with water, thickness of wall should be
doubled.
Centre of Pressure of earthwork, etc., coincides with centre of pressure of water,
and hence, when surfkce is a rectangle, it is at .33 of height Arom base.
The theory of required thickness of a retaining wall, as befbre stated, is, that tbe
lateral thrust of a bank of earth with a horizon^ surface is that due to me prism
or wedge-shaped volume, included between the vertical inner face of the wall and
a line bisecting the angle between the wall and the angle of repose of the material
To Compu.to Klemeixts of* Revetment 'Wa.Ua.^lFie- 4.
Let A D 0 represent angle of repose of material, against
a wall, ABC D. ADn = .5ADa Tan. ADll = .49'•
Tan. ADn, A — ,or — tan. ADn = V;
3 3
sin. DxDA . w*». . «-. «.
r— =Ao: tan. ADn=rp;
sin. 0 3
___^^___ — --tan.= ADn = P; - — tan.» ADii-=M;
CD a 3 3
Vfhz» wh3 w/t3 ^,tan.»ADw^_„>.
= m: —T— tan," A *)»»=£; tan.'ADn=S: h* — v—Pt
2*6 '3 'a
h tan. ADn^ /-'*^ =», aud ;* tan. ADn^ /2-^ = »'. h represenHng *«^ *if
V 3 " V 3 "
waU infeety V volume of section of prism of material A D n one foot in length in cube
feet^ W and to weights of a cube'jfbot of wall and of material, P, p, and p lateral
and moments of pressure of prisms of earth A D o and A D n upon *oott, ".*.'~ *!
inomenti of pressure and weight on and of wall, E and S equilibrium and^alnnpgoj
waUy all in lbs., and x and x , C Dfor weights of wall for equiUbrium and ttabuUjf,
Illustration.— A revetment wall, Fig 4, of 125 lbs. per cube foot and 4°^®®* *"
height, sustains a baLk of earth having a natural slope of 52 ^ 24', and a weigot or
89.25 lbs. per cube fout; what is pressure or thrust against it, eta f
STABILITY. — EEVETMENT WALLS. 69/
Tan.2 A Tin — .24a. Then .492 x 40 X.— = 3936 cube feet
«9:^52<4^ ^ ^^, ^ 35 „8.8 lbs. ^^^X^o- ^ ^^^,^ _^ ^^^ ^ ^^^
^^^^^ X .493' X ~ = 230384 lbs. 125 X 40 X ^^- -= 230400 rbs.
23 2 .
4oX.492.>/^^f5 = 9-6/e«<, and 40 x .492-^^^^^^ = »3-58/«e<.
ifV>r Rubble Walh in Mortar or Dry Rubble, add respectively to base as above
obtained, .14 and .42 part.
NoTB t. — When coefficient of Triction is known, use it for tan.^ A D »i.
S X C D fig. 5 = moment ofstabHity. (Molesioorth.)
2. — When either relative weights of equal volumes of wall and bank of earth or
their specific gravities are given, S and s may be taken for W afid w.
These equations involve simply the operation of a lever, the fulcrum being at
the outer edge of wall C. The moment of pressure of bank is product of lateral
pressure and i)erpendicular distance ft'om ftilcrum to line of direction of pi^ssure.
The moment of weight of wall is product of weight of wall and perpendicular
distance from fulcrum to vertical line drawn through centre of gravity of wall.
When Weights of Embankment and Wall are equdlper Cube Foot.
C for clay = . 336^ and for sand .267.
When WeighU areoi^to $, C for clay = . 3, and for sand .239.
When Wall has an Exterior Slope or Batter,— Fig. 5.
1^ «. ^,,0 ^ ^G 0 + E c'— 5-^ = M. M representing
I / mofmeni of weight of wall in lbs.
/ / iLLrSTRATiON.— Assume weight of wall 120 lbs. per
/ y ' cube foot, and C D and E C respectively 10 and 2. 5 feet,
,' y and all other elements as in preceding case.
"' „ 120X40 / — ; ■ 2.5^ ,.
Hence, X (10 + 2. 5 — 1 = 370000 to*.
(a;4-nA 1 = tan.« AD.n = S.
2 \ 3 / 3
Or. h^l 1 — tan.* AD n — n;i = «. x representing A ^ or CH. n ratio bf
V 3 3 W
difference of widths of base and top to height. In absence of tan.^ A D n put C, co-
efficient of material
C^ .0424 for vegetable or clayey earth, mixed with large gravel; .0464 if mixed
with snuUl gravel; .1528 for sand, and .166 for semi-fluid earths.
IixusTBATiov.— ABSame elements of preceding case, n = one fortieth, and tan.
A Dn =.492.
40 \/ J 2 + ^^^'- X .492^ — I = 12.6 feet
V 3 X 40 3 X 125 ^"^
Hence, thickness of wall at base =£12.64-1 (one fortieth of height) = 13.6 feet
NoTB-— If 91 = one twentieth, 40 */ — ^— s-f ^ ^^ X-492'— 2 = ii.63y«et
V 3 X 20* ' 3 X 125
HeDce, wall at ba8e = 11.63 4-9 (one twentieth of height) = 13.63/eet If C was
used, IS. 37 feet.
3 N
698
STABILITY. — BEYETMENT WALLS.
When Wall has an Inferior Slope or Batter, B E.—
Fig. 6.
wh' ^ „ oEr „
X tan.» =s P.
taHhfor equUibriwn;
w A3
M oftoaJU; and
hility.
--— X tan.a = M 0/
o 2
(dcxdc4-ce-^ =
X tan.2 0 En = M 0/ earth for ito
2
CoefficienU for Batter offoUowing Proportions.
Base = Height x Tab. number.
Weight of Etrtb to Wall.
Baitib of
Wall
Ai4
Clay.
to 5.
Saad.
Asx
Clay.
tox.
Sand.
I in 4
I " 5
I " 6
.083 ■
.122
.149
' .029
.065
.092
"5
•155
.i83
.054
.092
.1x8
Battbk of
Wall.
I in 8...
I " 12..
Vertical.
Weight of filarth tq, Wall.
As 4 to 5. n At I to X.
Clay.
.184
.221
•3
Sand.
.125
.x6
•239
Clay.
.2x8
.256
•336
Saad.
•»53
.267
Fig- 7.
To Compute I^ressure Ferpeudioular to Setc^ of Wall.
P » = — or — , and/« at right angle to back of vail,
whether vertical or inclined.
''^*",orLxt«n.AD«, or "><*'>< *"''^""..,
.
jL n o
, —7 7
g/f/
h
wx Ana
=/ ♦. L representing weight of triangle of em-
sm
hankmenit as kUn
L X A n X sec. m D o
ThJ8 is pressure Independent of friction between surfoces of wall and earth.
To iVsoertaixi and Compute .A^xxiouxit and Bfieot of Fric-
tion of Wall and Earth.— Fig. 8.
*'*fr ^- X *> Draw/ * by scale to computed pressure at right angle
"y f- yo tobackof wall, draw angle/* r = TO Do of natural slope
c* /,« , of earth with horizon, draw/r at right angle to/ ♦. make
rc=f », then cr will represent by scale effect of friction
against back of wall.
Assume friction to act at point ♦, then r « will give by
scale resultant of the two forces of pressure and friction,
equal to pressure in force and direction, which bears
against wall.
This resultant is also equal to/ « x sec. m D 0.
^ ^ ^, M>xA«xtan.»»iDo
= r#,or XsecmDo, or LxtaaADn
X sec. m D o.
To Asoertain Point of IMComent of Pressure of a "Wall.
FIf. 9. — Figr. 9.
^ p By its resisting lever I a^added to iU weight
Weight of wall as computed assumed as concentrated at its
centre of gravity • -
Draw a vertical line • 0 through its centre of gravity, and cob-
tinue line of pressure P * to f, take any distance r o bv scale rep-
resenting weight of wall, and r n, by same scale, for'amount of
pressure or thrust against wall, complete pamllelogram r o 11 it,
then diagonal ru will give resultant of pressure in aoiount sad
direction to overturn wall.
For stability this diagonal should fall inside of bate at a notet
oot less than one third of its breadth.
•m.
Vo
STABIUTT.— xBEVKTHSm' WALLS.
699
flg.Kv ^ r
Snroliargecl Zto-yetments.
o When the earth stands above a wall, as A B e,
y Fi^. 10. with its natural slope, Af, A B C is termed
a Surcharged Revetment,
If C r is line of rupture, A/r C is the part of earth
that prwses upon wall, which part must be taken into
the computation, with exception of portion A Be,
which rests upon wall; that is, the computation must
be for part Ce/r, whidi must be reduced by mnltiplj-
ing weight of a cube foot of it by square of tangent of
angle eCr = angle of lino of rupture, or half angle
e G o, which natural slope makes with vortical, and
then proceed as in previous cases for revetments.
. _. = Inreadtk or C D. W and w repre»enting weighU oftoaJU and
3 a W
embankment in Ibt. ptr cvbejbot^ and h' height of embankmenp^ asCe.
Illustration. — Height of a surcharged revetment^ BC, Fig. 10, is 13 feet, weight
130 lbs. per cube foot; what is its width or base to resist pressure of earth of a weight
of 100 Ibfl. per cube loot, and a height, G «, of 15 feet, angle of repose 45° ?
TaiL»(45«^a^ = .i7x6. Then .5 y/^^^^^^^'S Vo5i = 3.S2/iet
JPomt of Alomeiit of Pressure of a'Sur-
olxarsed 'Wall.— ITifi;. 11.
^f Draw a line, P «, paraUel to slope^ C r,' through centre
of gravity of sustained backing, B G r.
When, as in this cato, this section is that of a triangle,
point * will be at .33 height of wall.
When natural slope is 1.5 in length to i in height, as
With gravel or sand, to x .64= pressure P «.
In a surcharged revetment, as/B o, at its natural slope,
the maximum pressure is attained when the backing
reaches to r. When slope of maximum pressure, C n r,
intersects face of natural slope, B/ so that if backing is
raised to / or above it, there is theoretically no addi-
tional stress exerted at back of or against wall, but prac-
tically there is, fh>m effect of impact of vibration of a
passing train, proximity to percussive action, alike to that of 1^ trip-hammer, etc.
Wben backing rests on top of wall, as A B e. Fig. 10, small triangle of it is omitted
in computations. Direction of pressure against wall is same as when wall is not
To .A.eoertaixx
F«^ii.
,— o
surcbarged.
Fi^ x3
When Wall it set below Surface of Earth.— Y'lp;, 12.
1.4 tan. 45O
— y/^»t.(tan.45°-|y
2/V
»(L
e ' W
a refreuniing angle qf rtpote of earthy w and W totighU
of earth and wall per cube foot^f friction qftoall on bate
A B, and V weight ofioall.
lLLUSTRATiON.->If a wall of masonry. Fig. 12, 8 feet in thickness
and 13 in height, is to sustain earth level with its upper surfaee,
earth wieighing 100 lb& per cube foot, weight of wall 150 Iba per
cube foot =15600 lbs., and angle of repose of earth 30^; what
should be the depth of wall below surface of earth ?
Tan. 45 — 3o-r-2 = .5774, and /= .3.
*.. « s^ . . /'3'XiooX.S774''-^gX.3Xis6oo_ «g^ ^ 79360^5634.3
Tben 1.4 X .5774^ ~ = -8o84 X^ —
s=. ^<y97 feet
KoTK.— Gosfflcient of stability is assumed by French engineers for walls of fi)rti>
OcaiionB 1.4 ^ and if ground is clayey or wet/=.3.
^OO STABILITY. EUBANKUSNT WAL1£ AMD DAUS.
r
la CtoKHHitiiiB giMlilv of a Snrthargtd Wall, Fig. 13. mi
UuUdfirli,atinJi<auiiniigillaMraliim. (ifolcworM.)
r Unit of Surthoa Bt all
r any Heieht.
u iifiecliimt <U nHtnil q/'inn'
if, H, D^ a ODlKiiu if Oi maarial of vMCk pier it anutraeUd, due to ntpind
prcjHrc, and N Uc Rumier, Btnt. Ic;. 0/ wiUdi z= ^^^— .
..jiJ/mT' ' - ■ . -
Couttier/m-ta src Increased thicknetaca of a wall at i'> back, at inlerrals d
its length.
XCmbankment Walls anil l^ams.
Thrust of water upon Inner face of an Embankmeot wall or Dun is
borizoQtaL
When SotA Faca are VeMcal, Fig. 14-
Assume perpendicular eDibanknient or wall, A B C D, Fig. 14, to auBtiin
preaaure of water, B C ef.
Ffg, ,,. Let k i be t. vertical line pauing through 0, centre
of gravity of wall, e centre of pressure of waWr, dis-
tance Cc being = .33 B C. Draw cl perpendicular
ta B C ; then, biiicc section A C of wall is reclangular.
centre of gravity, 0, is in its geometrical centre, ind
, therefore l> 1=: .; D C. Now t U > is to be coniid-
*' end lu a Iwnl lever, fuk-rum of which is D, weight nE
wall acting in direction of centre of gravity, a, on arm
■D i. aiul preaaure of water on arm D ^ or a joice equal
~ ~ ' to that preseiu^ throating in directitm e L
Tbeu PxDl=Px— = Wx-— ,ocP = i5i^ — r TtpraenHng pramn
qfteater.
Noit — When this equailon hoMs, a will or embuikment will Jnsl be jp iln
point of oTerlumIng; but in order UiBl.tbey may have complete italiilitr, tliia
equalton eboulil give a mvch larger value to F than ita actual araaunl.
The fallowing formnlaa are for walla or embankmenta one fool in lenf^th ;
rttnHnff depth of vraier
equal, h breadth of woU
per fuhtfnnf in Im-
a wall or emhankment that will just suiUic
STABILITY. — EMBANKMBNT WALLS AND DAMS. 7OI
To Compute Equilibrium. A /— ^=6.
Illustration l— Height of a wall, B C, equal to depth of water, is 12 feet, and r«-
Bpective weights of water and wall are 62.5 lbs. and 120 lbs. per cube foot; required
breadth of wall, so that it may have complete stability to sustain the pressure of
water.
12 / ^^ = la X .4166 = 5 fttt^ breadth that tuill just sustain pressure 0/ the
water.
Therefore an addition should be made to this to give the wall complete stability,
say 2 feet; hence 5 -f 2 = 7, required width of wall.
2.— Width of a wall is 3 feet, and weight of a cube foot of it is 150 lbs. ; required
height of wall to resist pressure of fkresh water to the top.
V
02.5
To Compute tStalDility. A^/-^ = 6.
V 3W
Illustration. —Take elements of preceding case.
/2X62.5 „ ^ ^
12 /— = i2X.589 = 707/<«''
V 3 X 120 ^
Or, Divide i, 2, or 3, etc., according as the nature of the ground, the mate-
rial, and the character of the thrust of the water requires, by .05 weight of
material of wall, per cu^ie foot, extract the square root of quotient, and mul-
tiply result by extreme height of water.
EXAMTUL —What should be the tiiickness of a vertioal faced wall of masonry,
having a weight of 125 lbs. per cube foot, to sustain a head of water of 40 feet, and
to hare stability ?
Via -r-. 05 X las) 40 = ^^.32 X 40 = 22.63/e«<.
^r, h yj^^ = 40 V-3472 = 23.56/cffe.
When Dam has an Exterior Slope or Batter, a.<t A D.— Fiff. 15.
Fig. 15. A P__^j Assume prismoidal wall, A B C D, to sustain press-
ure of water, B C e/. ^
Draw A E perpendicular to D C ; A = B C, the top
breadth A B = E C = 6, and bottom breadth, D E,
of sloping part, A E D =r S.
Then weights of portions A C and A K D reipec-
'/"' 1 rjjjj^^^s^ tively for one foot in length are hbW and .5 W 8 A,
l> i"E"<r5rc~ "•' these weights acting at points n and i respectively.
To Compute ^lomeiit.
* 6 W X (3 -I- - j = moment for A C, and X — = nioment/or A E D.
W h / o Q^
Hence, f s -f- fc — '— | = mmnent of dam, S representing batter or base E D.
Illl^stbation.— Height of a dam, B C, Fig. 15, is 9 feet, base C £ 3, and K D 4 feet,*
what ia Its moment?
AC = 9X3Xi2oXU + |^) = 3240 X 5-5 = »7 820 lbs.
Hence, 1 7 820 + 5760 = 23 580 lbs. moment. Or, l?22l9 A ^ j'_ 1-^ = 54© x 43|
s 33 s8o lbs moment
3N*
702 STABUJTY.-^KMBANKMBNT WALLS AND DAMS.
To Compute KlementB of 'W'bII* or T>am» -witli an
Kicterior Batter.— Fie- lO.
When Width of Bailer U Oinm. J"—^ + -- - 3 = ft.
I[j.c9tli.TioN. -ABMina height of will 9 and b»tter 3 (Ml, ind W md b i» Mrf
To Compute WidtK uf Bane.
WhenWidlho/BaUeritGivin. Jl^ + j = B.
To Compute ^Vidtli of Batlar.
WAfnWU:iho/1^1ii>Givt»^ -J-^^--^ V = *
When Width of SollomiiGiren. ^38'-^^^ = *
To Determine Stability of •• Betalnine IVall op Dam *>r
Pi„ ,g^ protrBCtloii.-FiB. 18.
Aaauine A B C D, section ot s wall. On hnriinntil
Hne of centre of thrust or pressure, with 1 suitaMt
scale, lay off, from vardeal line ot centre of j.'isvily ■
ot wall, line 0 r = thniM u^aiiist wall, and on vertii:^
line at centre of icravitv of wall, at iU inleraeclion, ft
witlicentteof tlirii9t,lii fall H« = weight of wall.
Complete paralleltgram, anil if diagonal on or ils
riongation falls within C, the wall is slaWc. and
X distance from line ot ^moment of wall.
W r'prrjrnting almte meigkl of wall in On.
To Determine Centre nf OraTity of a -Wiill or Dnin.-
^If. le.
ByOrdinalu. 7 (* ^ + C D - ^^) = -, «.d ?^ (^;^^±^) = ■■
To Coinpule Bbbo of Dam.
What Height, Rale o/BiilUr. .mrf Wei^ of MaluiaU are 911™. Roi.i-
—MuUiuly square gf width of batter by .0166 weight of material pet culw
foot, add I, 3, or 3 times square of depth ot water, acciinling as resJSlaiK*
due to equilibrium is required, divide result by .05 weight ot mslenal pW
cube fbot, anil enlract square root of quotient.
EnHPta-ASBinne a dam 40 f™' m height, TOnslnicled of rauonry «t!''^JJ
STABILITY. — ^EMBANKMENT WALLS AND DAMS. 703
When Section of Dam is a Triangle^ Fi<j. 17. — As-
sume dam, A B C, to sustain a head of water, ef. .
KuLE.— Proceed as by ^ule for Fig. 14; multiply by
.OJ3 instead of .05.
ExAiiPLE.— As befiQre.
V(a -s- .033 X 125) 40 = '^/.48s X 40 = 27- 84 AeL
Or, Formula for S (C B), Ffg. 15. /—^ = ,8.28 feet
To Determine Section of a Vertical Wall which shall have Equal Resitt'
once of one having Section of a Triangle, (See J. C. TratUwine, Phila.^ 1872.)
To Coxxipute Tl]iiokiiess of I3ase of* a Wall or X>axn.—
Fi^, 18.
F'fr »*• Rule. — Divide i, 2, or 3 times square of depth of water
by .05 weight of material, add quotient to .5 batter on one
face, and square root of this sum, added to h^ batter on
other side, will give thickness.
'^3 Or, yj — m+ (~) + — = ^««. ft ond V representing
~ exterior and interior batters, and s, at before^ number of times
of resistance or square of depth.
ExAMRLE. — Assume a dam 40 feet in height, to batter 5 feet
on each side, constructed of masonry weighing izo lbs. per cube
foot, and to have twice the resistance due to its equilibrium; what should be
breadth of base, DC?
Higlx ^fasonry IDaxxis.
RubUe Ma8<Mir>% well laid in strong cement, will bear with safety a load
equivalent to weight of a column of it 160 feet in height Assuming such
masonry as twice weight of water, it is equivalent
to a pressure of aocxx) lbs. per sq. foot.
tiOg. B + '434 294 X ^ = ft. B representif^ width of
wall at top, and d depth at any desired point below topy
both in feet.
Ordinarily, B may be Utken at 18 feet, and iii cases
of extreme and exposed heights of dam at 20 and more,
and when 6 is determined. .9 of it is to be qb outer face
of wall, as A B, and . i on inner face.
_ Illustration. — Determine section of a dam, Fig. 19,
a£. 80 feet in height, at depths of lo^ 20, 40, 60, and 80 feet.
Log. B = 1. 3553.
«aS53 + '4343 ^ 5^ = ^^^ »a553 + -0543 = 2o-4» which X .9 = 18.36.
ti
»i
'•2553 + -4343X g- = log. i. 35534-. 1086 = 23. 11, which X..9 = aa8.
«'a5534- .4343 X 5^=5 log. X.2553 4- .3x72 = 39.68, which X .9 = 26.81.
** •
60
»aS53 + -4343X g^ = log. i.2553-f-.3257=:38.ii, which X .9 = 34•3•
8o
«a553 + -4343 X 33 = !<>«• "2553 + -4343 = 5oo7, which X .9 = 45.06.
704 STEAM.
STEAM.
Steam is generated by heating of water until it attains temperature
of ebullition or vaporization, and elevation of its temperature is sensible
to indications of a thermometer up to point of ebullition ; it is then
converted into steam by additional temperature, which cannot be in-
dicated by a thermometer, and is termed latent (See Heat, page 508.)
Pressure and density of steam, which is generated in tree contact with water,
rises with the temperature, and reciprocally its temperature rises with the press-
ure and density, and higher the temperature more rapid the pressure. There is
bat one and a corresponding pressure and density for each temperature, and steam
generated in tree contact with water is both at its maximum density and pressure
for its temperature, and in this condition it is termed saiurcUed^ from its being in-
capable of vaporizing more water unless its temperature is raised.
Saturated Steam is the normal condition of steam generated in ttee contact with
water, and same density and same pressure always exist in cot\jnnction with same
temperature. It therefore is both at its condensing and generating points; that
is, it is condensed if its temperature is reduced, and more water is evaporated if
its temperature is raised.
If, however, the whole of the water is evaporated, or a volume of saturated steam
is isolated from water, in a confined space, and an additional quantity of heat is
supplied to the steam, its condition of saturation is changed, the steam becomes
superheated^ and both temperature and pressure are increased, while its density is
not increased. Steam, when thus surcharged, approaches to condition of a gas.
With saturated steam, pressure does not rise directly with the (empentaro.
Steam, at its boiling-point, is equal to pressure of atmosphere, which is 14.733307
lbs. (page 427), at 60° upon a sq. inch.
In all computations concerning steam, it is necessary to have some or all of fol-
lowing elements, viz. :
Its Pressure, which is termed its tension or elastic force, and is expressed in lb&
per sq. inch. Its Temperature^ which is number of its degrees of heat indicated by
a thermometer. Its Density^ which is weight of a unit of its volame compared
with that of water. Its ReJative volume, which is space occupied by a given weight
or volume of it, compared with weight or volume of water that produced it
Under pressure of the atmosphere alone, temperature of water cannot be raised
above its boiling point.
Expansive force of steam of all fluids is same at their boiling-point
A cube inch of water, evaporated under ordinary atmospheric pressure, is convert-
ed into 1642* cube ins. of steam, or, in a unit of measure, very nearly 1 cube foot,
and it exerts a mechanical force equal to raising of 14.723307 x z44=:ai2ai563o8
lbs. z foot high.
A pressure of x lb. upon a sq. inch will support a column of mercnry at a tem-
perature of 60®, i-=- 4907769 (page 427) = 2.037 586 ins. in height; hence U will
raise a mercurial siphon gauge one half of this, or 1.018793 ins.
Velocity of steam, when flowing into a vacuum, is about 1550 feet per second wbra
at a pressure equal to the atmosphere ; when at 10 atmospheres velocity is increased
to but 1780 fbet; and when flowing into the air under a similar pressure it is about
650 feet per second, Increasiug to 1600 feet for a pressure of 30 atmoepherea
BoUing -points of Water, corresponding to diflerent heights of barometer, see
Heat, page 517.
Volume of a cube foot of water evaporated into steam at 2x2° is 1642 cube f)e«t;
hence i -7- 1642 = .000609013, which represents density or specific gravity of steam
at pressure of atmosphere.
Elasticity of vapor of aIcohol,at all temperatures, is about 2. 125 times that of steam.
Specific Oravity^ compared with air, is as weight of a cube foot of it compared
with equal volume of air. Thus, weight of a cube foot of steam at 2«2° and at
pressure of atnioRpherc is 266.124 grains; weight of a like volume of air at 32° 'S
565.096 grains, and at 62° 532.679 grains. Hence 266. 124 -r 532.679 = .499 59, «p««/*
gravity of steam compared with air at 32°, and with water it is .000609013.
* Pole's Formoia make* it 1712.
STBAH. 705
. Total Heat of* Saturated Steam. {BegnauU.)
From Water at 32°.
1081 .4 4* 'S^S '^ =■ ^^ ^^^ "^ representing initicU temperature ofwcUer.
.LLU8TRAT10N.— What is total heat of steam at 212*^?
108 1. 4 -f" •305 X 212 c= 1146.06.
As Specific heat of water is .9 greater at 212° than at 32 o, heDoe the 212° would
be 212.9, and 1146.33 tiie resuU.
Total Heat o/GrOseous Steam from Water of 2^° = 1074.6 + .475 T.
.A.l>sorptioii of* l^eatl
In Generation of x Lb. of Steam at 212° Jrom Water at 32°.
Sensible hoat, or heat to raise temperature of water Tharmal Units. Foot-liM.
ftora 32^10 212° 181.8X772 = 139655
Latent heat to produce steam 892.9
*' "to resist atmospheric pressure i^.y ]b&
persq. Inch 7'-4 _9|^4 • 3 X 77a =745X34
Total or constituent heat 1146 . i 884 789
In GenercUion of I Lb. of Steam at iy$ lbs. from Water at 32°.
Tbermal UniU. Foot-Ibi.
Sensibleheat as in preceding case from 32° to 370.8° 342-4 275333
Latent heat to produce steam 768.2 599050
" " to resist external pressure = 175 lbs 83.8 64694
Total heat from 32° 1194.4 933077
Mechanical Equivalent of Heat Contained in Steam.
I lb. water heated from 32° to 212° requires as much heat as would raise
180 lbs. 1°. Hence 181.8°
X lb. water at 212°, converted into steam at 212° (=:T4.7"lb& pressure),
absorbs as much heat as would raise 966.6 lbs. water 1°. Hence 964.3°
1146.1°
Mfckaniail Equivalent, or maximum theoretical duty uf quantity of heat in one
thermal nnit or one degree in i lb. of water, is 772 foot-lbs., which X 1146.1 units
of he€U=:8&4 jig.2 lbs. raised ifoot high.
Xo Compute Pressure of Steam
Above Perfect Vacuum.
When Height of Column of Mercury it mil Support is given. Rule. — Di-
vide height of column of mercury in ins. by 2.037 586, and quotient will give
pressure per sq. inch in lbs. '
ExAMPLK. —Height of a column of mercury is 203.7586 ins. ; what pressure per
aq. inch will it contain ?
903.7586-7- 2.037 5^6 = 100 Vbs.
To Compute "^Veiglit of* a Culye Foot of Steam.
Ruus. — Mtdtiply its density by 62.425.
ExAXFLB.. — Density of a volume of steam is .000609013; what is its weight?
.<xx> 609 013 X 6a. 425 = .038 016 825 Ufs:
Nora.— See table, page 708.
1 atmosphere or 14.723307 lbs. per sq. inch = 30 ins. of mercury.
To Co^npixte Temperature of Steam.
BuTJU. — Multiply 6th root of its force in ins. of mercury by 177.2, sub<
tract 100 from product, and remainder will give temperature in degrees.
ExAMPLK. — Wlien elastic force of steam is equal to a pressure of 64 ins. of mer*
cary, what Is its temperature?
KoTK.— To extract 6th root of a number, ascertain cube root of its square root
■^64 = 8, and ^B ^ 2. Hence, 2 x 177.2 — 100 = 254.4° t
Or, 7 ?^^ ' J 37X. 85 = <. p represeuHtut pressure in lbs. per sq. iacft.
6x993544— log- 1» _ x~ •»
706 STEAM.
To Compute "Voluzne of "Water ooxxtaixi«<i ifo. a given TTol-
vLxxxe of Steaxn*
Whm iU Dmmiy is ffiven, RuLE.^Multiply vdume of steam in cube
feet by its density, and product will give volume of water in cube feet.
ExAMPLB. — Density of a volume of 16420 cube feet of steam is .000609; ^^'^^ ^*
tbe weight of it in llw. ?
z6 420 X 'COO 609 = 10 = volume of toater^ which X 62. 425 = 624. 25 lb$.
To Cozxipu.te Pressvire of Steam in Ins. of IV^ieroixry, or
X^los. per Sq.. Iiicla.
When Temperature is ffiven, Kclb i. — Add 100 to temperature, divide
sum proportionally by 177.2 for temperature of 212°, and by 160 for tem-
peratures up to 445° ; or, 177.6 for sea-water, and J85.6 for see-water Mt>
urated with salt, and 6th power of quotient will giye pressure.
ExAMPLB.-~Temperature of steam is 254°; what is its pressure?
ICO -f- 254-^ 177.2 = 1.998, and 1.998* = 63.62 ins.
When Ins. of Mercury are given. 2. — Divide ins. of mercury by 2.037 5^6,
and quotient will give pressure.
When Pressure in Lbs. is given, 3. — Multiply pressure by 2.037 586.
To Compute Speoiflo Gravity of Steam oompcured 'writh
A.ir.
Rule. — Divide constant number 829.05 (1642 X .5049) by volume of
steam at temperature of pressure at which gravity is rec^uired.
ExAUPiJE.<-Pressure of steam is 60 lbs., and volume 437 ; what its specific gravity?
829.05 -J- 437 = r. 898.
To Compute Volume of a Cu"be Foot of "Water in Steana.
When Elaatic Force and Temperature of Steam are given. Rulb.— To
430.25 for temperature of 212°, and 33a for teiniiemturee up to 445°, add
temperature in de^ees ; multiply sum by 76.5, aud divide product by elastic
force of steam in ms. of mercury.
Note.— When force in ins. of mercury is not given, multiply pressure in lbs. per
sq. inch by 2.037 586.
Example.— Temperature of a cube foot of water evaporated into steam is 386^*
and elastic force is 427. 5 ins. ; what is its volume ?
Assume 369 for proportionate factor. 369 -\- 386 X 76. 5 -?- 497.5 = 13^1 cui(>€fidL
Or, for I lb. of steam, 2.519— .941 log. p =7 log. V in cubefset.
Assume p = 14.7 lbs. 2.519 — .941 log. 14.7 = 2.519 — 1.098= x. 421^ log. 96.34
cube fMt, which X 62. 425 = 164 JM.
Or, When Density is ^'ven.— Divide 1 by density, and quotient will giv^ vohune
in cube feet.
To Compute IDeusitsr or Speoifio 0>ravity of iBteaxxx.
When Volume is given. Rule. — Divide 1 by volume in cube feet.
Example.— Volume is 210; what is density?
I ^ 210 = .004 761. Or, for z lb. of pteam, .941 log. p ■» a. 519 =t log. D.
When Pressure is given. — Take temperature due to pressure, and proceed
as by rule to compute volume, which, when obtaiRed, proceeds as above.
To Coxxipute Volume of Steam reqiiirecl to raise a Ghiven
"Volume of Water to any Gl-iven Texxkperature.
Rule.— Multiply water to be heated by difference of temperatures between
it and that to which it is to be raised, for a dividend ; then to temperature
of eteam add 965.2^, from that aum take required temperature of water Ibr
divisor, and quotient will give volume of water.
6TBAM,
707
RxAMPLK.— Wbat volume of tsteain At ^la^ will ritta« loo cube feet of water at So^*
10 212°?
i — T — ' = '3-68 cube feet water; or, (13. 68 X 1642 — * 212) =;aa 450 of steam,
213-1-965.2 — 2X3
OCp Coisipvitd VoliiiTje of "Water, at any Oiven Temper-
ature, tliat must l>fl IVtixed -with. Steam to X^aide or Re^
duoe the M.ixtxtre to aiiy H.eqviired Temperature.
liuLR.>-^^roin required tempeiature subtract temperature of water ; then
ascertain how often remainder is contained in required temperature sub-
tracted from sum of sensible and latent heat uf the steam, and quotient will
give volume required.
Sam of Sensible and Latent Heats for a range of temperatures will be found under
Heat, pages 508 and 509.
KXAMPLB.— Temperature of condensing water of an engine is 80°, and required
temperature 100°; what is proportion of condensing water to that evaporated at a
pressure of 34 lbs. per sq. iucb ?
Sum of sensible and latent heats 930.120-1-257.60 = 1187.72O.
100 — 8o=:2a Then, 1187.72 — 100-7-20 = 54.386 to i.
When Temperature of Steam is given.
/-f-T
~Y. I representing latent heat,
t — w
T and t temperatures ofsiemn and required temperature, w temperature of condensing
VKUer, and V volume of condensing toater in cultefeet.
iLLDBTRATioir. — ^Temperature of steam in a cylinder is 257.6°, and other elements
same as in preceding example ; required volunie ot injection water? Latent heat
of steam at 230^5 = 930. 12°.
930. 120 + 2j7.i:J^^ io87_. 7_a ^ ^^^^ ^y^^
80
100
20
To Compvite Temperature of* Water in Condenser or
Reservoir odT a Steam-eii|?ine.
= t. Illustration. —Assume elements ds preceding.
loo*-
930. 12° 4- 257.6 -f- 54.39 X 80 _ 5539 _
54-39 -f' 55-39
To Compute Latent Heat of Saturated St'^atn.
X112.5 —•708 t^l. Illustration. — Assume temperature 257.6° as preceding.
1112.5 — .708X 257.6=930.12°.
To Compute Total Heat of* Saturated Steam.
'3<>S ^+1081.4 - H- iLLUBTRATiON.^Assume temperature as preceding.
.305 X 257" 6 "H J081.4 = 1160.
I£la«tio Force and Temperature of Vapors of A.loolxol*
fijther, Sulpliuret of Carbon, Feti oleum, and Tur*
pen tine.
Force in Tru. of Mercury.
o I loi.
P£TROLSUM
316 30
345 441
375 I 64
Oil OP
TCRPBNTINB.
*» 1
Int. 1
0
Ini.
0
Ini. 1
° 1
Ina.
Alcohol. |
Alcohol.
Ether.
Sulphurkt of
3«
L
140
13.9
34
6.8
Carbon.
50
.86
160
22.6
54
15.3
53-5
7-4
60
««3
IK
30
74
x6.8
72- 5
12.55
70
1.76
34-73
94
24.7
no
30
80
2-45
200
53
96
W4l
30,
212
126
90
3-4
21S
Ts
279.5
300
loo
n
220
120
39-47
347
606
120
240
III. 24
150
67.6
»7«
«3«»
10.6
264
166. X
819
3>5
357
370
47.78
69.4
7o8
6TB AM.
Saturated Steam.
Pi'essure, Temperature, Volumey and Density.
P&B880B>
*
S
I
B
11.
'•8
13
n«lty,
eight of
ibe Foot.
Pbksbubb
•
1
1^.
13
III
[ocli:
1 In
Mer-
; cury.
Ins.
r
jlc&b.
In
Mer-
cury.
1
If
r
Lb*.
0
1 °
Cub. ft.
Lb.
Lbe.
Ira.
0
0
Cub. ft.
Lb.
I
2.04
loa.z
1113.5
330.36
.003
58
118.08 ! 290.4
1170
7-24
.138
3
4.07
126.3
H19.7
172.08
.0058
59
120.12 , 291.6
Z170.4
7.12
.1403
3
6. II
141. 6
1124.6
117.52
.0085
60
122.16 1 292.7
Z170.7
7.01
.1425
4
8.14
1 53- 1
1 128. 1
89.62
.011 2
61
124.19
293.8
1171.1
6.9
-1447
5
10.18
162.3
1 130-9
72.66
.0138
62
126.23
394.8
"7'.4
6.81
.1469
6
12.22
170.2
"33-3
61.21
.0163
63
128.26
295.9
ZZ7Z.7
H
•'493'
7
14.25
176.9
"35-3
52.94
.0189
64
130.3
296.9
1172
6.6
.1516
8
16.29
182.9
"37-2
46.69
.0214
65
'32-34
298
1172.3] 6.49
.1538
9
18.32
188.3
I 138. 8
41.79
.0239
66
134-37
299
Z172.6 6.41
.'56
lO
20.36
'93-3
1140.3
37.84 .0264
1 67
'36.4
300
1172.9
6.32
.1583
ZI
22.39 ; *97-8
' "41-7
34.63 .0289
68
'38.44
30a 9
1173.2
6.23
.1605
za
2443
202
"43
31.88 .0314 j
69
140.48
30Z.9
"73-5
6.15
.1627
13
26.46
205.9
I 144. 2
29-57 -0338 1
70
142.52
302.9
"73-8
6.07
.1648
>4
28.51
209.0
"45-3
27.61 .0362 1
71
'44-55
303-9
304-8
"74'
5-99
.167
*4 7
29.92
212
1 146. 1
26.36 .03802
72
146.59
"74-3
5-9'
.1693
»5
30.54 213. 1
1 146. 4
25.85 .0387
73
148.62
305-7
1174.6
.1714
z6
32.57 216.3
1 147. 4
24.32 .041 I
74
150.66
306.6
"74-9
576
.'736
X7
34.61 219.6
"48.3
22.96 1.0435
75
152.69
307.5 1175 2
5.68
• '759
i8
36.65 j 222.4
"49-2
21.78 .0459
76
'54 73
308.4 ZZ7S.4
5.6Z
.1782
19
38.68 225.3
"50. 1
20.7
.0483
77
156.77
309.3
"757
5-54
.1804
20
40.72 228
1150.9
19.72
.0507
78
153.8
310.2
1176
5-48
.1826
3Z
42.75 230.6
"51-7
ii.84
.0531
79
160.84
31Z.1
1Z76.3
5-4'
.1848
23
44-79 1 233- »
1152.5
z8.os
-0555
80
162.87
3'2
"76.5
5-35
.1869
33
46.83:235.5
"53-2
17.26
.058
81
164.91
312.8
1176.8
5-29
.1891
84
48.86
237.8
"53-9
16.64 -0601
82
166.95
313.6
"77-'
5.23
.'9' 3
»5
50.9
240.1
"54-6
15.99 .0625
83
168.98
3'4-5
z 177.4
5- '7
.'935
36
52.93
242.3
"553
Z5.38 .065
b
171.02
3'5.3
Z177-6
5."
.'957
37
54-97
244.4
"55-8
Z4.86 .0673
85
'73-05
316.1
1177.9
5.05
.198
38
57.01 «
246.4
"56.4
14.37 -0696
86
175-09
316.9
1178.1
5
.200a
39
59-04
248.4
"57-1
139
.0719
87
'77- '3
317.8
1Z78.4
4-94
.2024
30
61.08
250.4
"57-8
13.46
.0743
88
179. 16
318.6
1 178.6
4-89
.2044
31
63. 11
252.3
"58.4
»3-o5
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89
181.2
3'9-4
Z178.9
4-84
.2067
33
65-15
254-1
"58.9
. 12.67
-0789
90
183.23
320.2
1179.1
4-79
.3089
33
67.19
255-9
"59-5
12. 31
.0812
91
185.27
321
"79-3
4-74
.31ZI
34
69.22
257.6
1160
11.97
•°?3 5
92
187.31
321.7
"79-5
4-69
.2133
35
71.26
259-3
1 160. 5
11.65
.0858
93
'89.34
322.5
Z179.8
464
.2155
36
73-29
260.9
iz6i
"•34
.0881
94
X9'-38
323.3
zz8o
4-6
.3176
K
75-33
262.0
iz6z.5
IZ.04
.0905
95
'934'
3a4-i
zi8a3
4-55
.2198
38
77-37
264.2
1 162
ia76
.0929
96
'95-45
324.8
Z180.5
4-5'
.2219
39
79-4
265.8
1162.5
10.51
.0952
97
197.49
325-6
1180.8
4.46
.2241
40
81.43
267.3
Z162.9
10.27
■0974
98
'99-52
326.3
1 181
4.4a
.2263
41
83.47
368.7
ZZ63.4
zao3
.0996
99
201.56
327.Z
1181.2
4-37
.3285
4a
85.5
270.2
1163.8
9.81
.102
100
203.59
327-9
Z181.4
4-33
.2307
43
87-54
271.6
Z164.2
9-59
.1042
ZOI
305.63
328.5
1181.6
4.29
.2329
44
89-58
273
1 164. 6
9.39 .1065
Z02
307.66
329. z
1181.8
4-25
.235*
45
9Z.61
274-4
Z165.Z
9.18
.1089
Z03
209.7
329.9
1182
^•"i
.2373
46
93-§5
275.8
Z165.5
2«
.111 1
Z04
2ZZ.74
330.6
Z182.2
4.18
.9393
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95-69
277.1
1165.9
8.82
•"33
Z05
213-77
331-3
1182.4
4- '4
.3414
48
97.72
278.4
1166.3
8.65
.Z156
Z06
215.81
33».9
ZZ82.6
4.1Z
.2435
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99.76
279.7
1166.7
8.48
"7 9
'*^
^'7-?4
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.a45«»
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Z01.8
281
1 167. 1
8.31
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zo8
219.88
333-3
ZZ83
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Z03.83
282.3
1167.5
8.17 .1224
Z09
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"83.3
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283.5
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8.04 .1246
110
223.95
334-6
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107.9
284.7
1168.3
7.88 .120 9
711
225.99
335.3
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3.93
•9543
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109.94
285.9
1 168. 6
7.74 .1291
ZZ2
228.03
336 ZZ83.9
%%>
.3586
55
III. 98
""IV
ZZ69
7.61 |.z3i4
7-48 .1336
"3
230.06
336.7 1184.1
56
1 14.01
288.2.
"69.3
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232. z
337.4 1184.3
3*83
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289.3
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1K5.8 1.7
:S
306
iBo
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-6uBt
I
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.107.8; ,.S9
.>oS.7 ' 1.54
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-749«
4<4.9
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i«0,7
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^a''
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£1
3:«*
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J7
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I
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■ -4J9!
Sm
6ia.j
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83^3
S33-6
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1148-1
Saturated Stean
1 from 33' to
SIS"
(CTo«W,)
■ ;
^.
!^^
f^.
r
sr:
Mmo-
S,.^!..
dk
/r*
3°
-i?i
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.615
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'g;.
160 9.63
16s .^8^3
4-731
MW
■M-8
ii
i*i*
s
sH
:E
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i!6oj
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ss
91
.1B1
■-97
50,8
593
18;
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.647
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rJi;
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OS
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18. J
7IO BTBAK.
GASEOUS STBAM.
When saturated steam is surcharged with heat, or superheated, it is termed
gaseous or steam-gas. The distinguishing feature of this condition of steam
is its uniformity of rate of expansion atove 330°, with the rise of its tem-
perature, alike to the expansion of permanent gasei.
Xo Compute 'Potal Meat of G^aseou« Bteaxn.
1074.6 + -475 < 3= H. t repraenting temp$r<Uure, and H Uttai hMt in degree*.
Hence, total heat at 21 3^, and at atmospheric pressure :=^ iz75<3°.
Specific gravity = .623.
T?o Compute Velocity of* Stean^.
Into a Vacuum, Rule. — To temperature of steam add constant 459, and
multiply square root of sum by 60.9 ; product will give velocity in feet per
second.
Into Atmosphere, j.6 y/k = V. V representing velocity eu above, and h height in
feet of a column ofeteam of given pressure and uniform density , weight of which is
equal to pressure xn %uiit of base.
Illustration.— Pressure of steam 100 lbs. per sq. inch, what is velocity of \\m
flow into tbeair?
Cube foot of water = 63. 5 Uw., density of steam at 100 lb& = 370 cnbefeet Ueoc#,
62. 5 : 100 : : 270 : 432 == volume at 100 lbs. pressure, and 4^2 X 144 = 63 30S feet sb=
height of a column of steam a( a pressure of 100 lbs. per sq. wA.
Then 3.6 -y/fia 208 = 898 feet
EXPANSION.
To Compute Point of Cutting; oflT to A.ttain I^imlt or
Expansion.
6-f/ 1< -i- P = point of cutting off. b representing mean back pressure for entire
stroke, in lbs.sP^r sq. in^, f friction of engine, P tnilial pressure of steam, all in ths
per sq. inch, and L length of stroke, in feet.
Illustration.— Assume stroke of piston 9 feet, pressure 30 lbs., mean back preas-
ure 3 lbs., and friction 3 Iba
3 + 2 X 9 -^ 30 = t'SfBet.
To Compute A.otua} {ifttio of fiSxpftnsion,
^ ■ =; R. c representing clearance or vofiime of space between valve seat asid
mean surface cf piston, at one or each end in feet of stroke, I length of stroke at point
qf cutting off, e^xcluding clearance in feet, and R aUual ratio of expansion.
Illustration.- Assume length of stroke 2 feet, clearance at each end 1.3 ina.,
aid point of cutting off i foot.
24-. 1
1.2 ins. =. I. Then — |— = 1.0 roWo.
i + .i
To Compute Pressure at any Point of Period of Ex-
pansion.
When Initicd Pressure is given. ? l-i-s=p. p representing pressure at period
of given portion qf stroke, both in lbs. persq. inch, and s any greaier portion qf stroke
Oian I.
When Final Pressure is given. P' x 1/ -5- « = p. P' rqtretenting final pressmre,
in lbs. per sq. inch, and U length of stroke, induding clearance, infiet
Illustration i.— Assume length of stroke 6 feet, clearance at each end 1.3 Iqbl,
pressure of steam 60 11)6. , point of cutting off one third ; what is pressure at 4 (bet r
i.aifM. ^. I /oot 60X 2 -h*-^ 4 +1 = 30.73 tea
ff.^What Is pressare tu above cylinder at s.8 feet, when final pressure is si Iba f
f aiX6 + .xHra.8 + .i^44.i7 {be.
STEAIC 711
rFo Coxnpiate Xilean or Total A-veratfe Pressure.
P(^'i-i-hyplogR— c) ^ ,^ ^^ ^ average pteMUre. T length of ttroke at
If
point 0/ cutting off, including clearance.
Illustbation. -^Assume elements of preceding cases: x -f- hyp. log. R= a. 065.
6o(..xX».o65-.i) ^ «5£i9 ^ ^,,365 Ibi.
6 6
To Compute Final Pressure.
Illustration.— ABsti me elements of preceding cases, steam cut off at 3 Te^t
6oX2-|-.i^6'f.i= 20.65 ^^•
To Compute ]Meaii Efl'ective Pressure.
r(r.+i.yMog,.«:;.)_,„(p._t)
Li
iLLuaTRATioN.— Assume elements or preceding cases, 6 = 2 Iba per sq. inch.
60(2.1 X 2063— .1) 254.19 ,
— i — ^ 3 = -^ — 8 = 4a 365 lbs.
1?o Compute Initial Pressure to Produoe et d^iven A.v«
erage Kfieotive or I^et Pressure.
r(i+hyp.log.R)-c '^'
Illustration. — Assume elements of case i.
6 + . I . . 42. 365 X 6 254. 19 . „
—^z=3.Q ratio. , ^ » — — -^^=z6olbt.
2-I-.X '' (2.1X2.065) — .! 4.2365
rVo Ooznpute Point of* Cutting oii^ fbr a O-iven Ratio of
Expansion.
L'-i-R — d. Or, L-I-C-7-R — c = «.
Illustration. — Assume elements of preceding cases : R = ; - == 2.9, and
2-|-.i ' 2.9
— .1 = 2 feet.
'Fo Compute Pressure in a Cylinder, at any Point of Ex-
pansion, or at Bind of Stroke.
Pr-i-(-f c = P, orP-;-R.
I1XU8TRAT10N. — Assume elements of preceding cases:
— r-— — = 60 ?**-i *nd — = 2a69 lb$.
2-J-.1 2.9
•X*o Compute Initial Pressure ibr a Required N'et Sfiiso-
tive Pressure fbr a O-iven Ratio of Kxpansion.
' Or, . -^ = P. W representing net-
a (/' I + hyp. log. K — f I r r^ hyp. log. R — c
^oarle infoot-lb$. =0 Lp' — 6, and a area of piston, in sq. ins.
iLi'USTKATioN. — Assume elements of preceding cases: area of piston = 100 sq.
ina. , back pressure 2 lbs., and net effective pressure = 42.365 lbs.
coo X 6 X 42. 365 — 2 =t 24 219 foot-lbs.
^4219 + 100X2X6 ^ 254^9 ^^j^^ 4g-3fl5X6 ^>S4<9^gp,^j.
,00 X2-«X 8.065—1 I06X4-2365 ' a.tXi.o65-.x 4.4365
^12 stbam;.
Points of* Sxpansion.
Relative points of expansion, including clearance 5 per cent., assuming
stroke of piston to he divided as follows, and initial pressure = i.
Point I .75 .6875 .625 .5625 .5 .4375 .37s .333 .25 .2 .125 .1
Ratio I 1. 31 1.43 1.55 1.71 1.9x2.15 2.43 2.74 3.5 4.46. 7.
H^. Log. of above Ratios.
.0 X.27 1.36 1.44 1.54 1.65 1.77 1.9 2 2.2s 2.43 2.79 2.9s
Receiver of Compound. JtJngin.es.
Volume — Into which the H». cylinder exhausts, should be from i to 1.5
times the volume of it, plus that of the clearance in it, when the cranks are
set at ano:les of 120° and 90°. When the cranks are opposite (180°) or very
nearly so, the volume may be proportionately decreased.
Pressure— In a Receiver should not exceed one half that of the boiler pres*
sure, and usually it is operated lower.
Receiver — Of a Triple compound engine need not have as great a vol-
ume, as the cranks are set at angles of 120° to each other.
If a receiver is insufficient in volume, the result is back pressure in the
IP cylinder. If otherwise, it has too great a volume, the result is that of a
material reduction of the pressure, when the exhaust port of the cylinder is
opened, a consequent loss of external work and of efficiency.
To Compute "Volume of a R,eoelver.
Single Compound.
AS— S 1.5
Cranks at 90°. —— = volume in cube feet A represevUing area of ff
cylinder, and S stroke of piston^ both in sq. ins.
Illustration.— Assume a compound engine having a H* cylinder of 28 ina,
cranks at 90^, and stroke of piston 36 ins. ; what should be volume of receiver?
3.1416
4 784 X .7854 X 54 t. ^ *
— ^^^8 = X728 =^9-^5 cube feet
Thriple Compound.
A^ — St
Cranks at 120° 5—— z^vdume in cube feet.
1728
Illustration. — Assume a triple compound engine having a IP cylinder of 28 Ins.,
cranks at 120°, and stroke of piston 36 ins. ; what should be volume of receiver?
3.1416
282x^^— 5— X36X1 o ^ ^ .
3 784 X 1.0472 X 36 ,. J. J
7^ " T^S = '7. ' Ctt6e/e.e.
{The Practical Engineer.)
The practice with some is to give the receiver an equal volume with that of the
cylinder fVom which it receives the steam.
Xo Compute !Mea.n. l?ressure of* Steam upoit a Piston
"by MjrperlDolio I^ogaritlims.
Rule. — Divide length of stroke of a piston, added to clearance in cylinder
at one end, by length of stroke at which steam is cut off, added to clearance
at that end, and quotient will express ratio or relative expansion of steam or
number.
Find in table, logarithm of number nearest to that of quotient, to which
add I. The sum is ratio of the gain.
Multiply ratio thus obtained by pressure of steam (including the atmos-
STEAM.
713
phere) as it enfers the cylinder^ divide product by relative expansion, and
quotient 'Will give mean pressure.
Note.— Hjrp. log. of any number not in table may be found by multiplying a
common log. by 2.302 585, usually by 2.3.
Proceed by referring to table pp. 331-334.
Example.— Assume steam to enter a cylinder at a pressure of 50 lbs. per sq. inch,
and to be cut ofl'at .25 length of stroke, stroke of piston being 10 feet; what wiil be
mean pressure?
Clearance assumed at 2 per cent. = .2 feet
10 -I- 2 = 10. 3 fea, stroke 10 -:- 4-F^ = 2- 38 feet Then 10. 2 -r- 2. 38 = 4. 20 rela-
tive expansion.
Hyp. log. 4.29 (p. 332) = 1.4563, which + i = 2.4563, and '-4563 X 50 ^ ^g^^ ^^
4.29
Relative Effect of steam during expansion is obtained from preceding rule.
Afeckantcai Effect of steam in a cylinder is product of mean pressure in
lbs., and distance through which it has [massed in feet
£2£Eeots of* ilSxpansiorL. {Essentially from. D. K. Clark.)
Back Pressure is force of the uncondensed Hteam in a cylinder, consequent
upon impracticability of obtaining a perfect vacuum, and is opposed to the
course of a piston. It varies from 2 to 5 lbs. per sq. inch.
It must be deducted flrom average pressure. Thus: assume pressure 60 lbs.,
stroke of piston as in preceding case, and back pressure 2 lbs.
At termination of..... I St, 2d, 3d, 4th, 5th, and 6th foot of stroke.
Pressure 60 30 20 15. 12 10 lbs. per inch.
Back pressure 22222 2 ** " "
Effective pressure "58 28 18 13 io 8 " *'
Total work done by expansion at termination of each foot or assumed
division of stroke of piston is represented by hyp. lo^. of ratio of expansion,
initial work ^ I.
Thus, for a stroke of 10 feet and a pressure of 10 lbs. :
At end of xst, 2d, 3d, 4th, 5th, 6ih, yih, 8th, 9th, and xotfa/bot.
8t«Mn Is «z|wnd«d \
into voU., hyp. V= .69 i.x 1.39 1.61 1.79 1,95 2.08 3.3 2.3
log. of which... )
Initial duty iitiiiii i i
Total duty.'. i 1.69 s.x 3.39 2.61 2.79 2.95 3.08 3.2 3.3
'"iilintS^bi'xoT} 1016.9 ai 33.9 26.1 37.9 29.5 30.8 32 IT
RMisUn^M for each I „ . #; a ,„,«,.,/;, a ««,
foot of stroke...}— =4 6 8 10 I3 14 16 18 30
Total effective I ^ 8x2.9 '5 i5-9 '6.1 159 '55 148 14
duty
13
Gain by expansion o 61.25 87.5 98.75 101.25 98.75 93.75 85 75 62.5
The same results would be produced if expansion was applied to a non-condens-
iog engine, exhausting into the atmosphere.
Again, assume total initial pressure in a non-condensing cylinder 75 lbs. per sq.
inch, expanded 5 times, or down to 15 Iba, and then exhausted against a back press-
ure of atmosphere and friction of 15 lbs.
At termination of. ist, 2d, 3d, 4th, and s^^ foot of stroke.
Total duty x 1.69 2.1 2.39 2.61
*• '* p^ormed... 75 X26.75 157.5 179-25 195.75 ^^^6*.
♦* backpressure.... x5 30 45 60 75 *» '*
" effective duly.... 60 96.75 112.5 119-25 120.75 " "
Gain by expansion o 61.25 87.5 ^8.75 101.25 per cent
From which it appears that the total duty performed by expanding steam 5 timet
its initial volume is full 2.5 times, or as 75 to 195.75.
30*
7*4
8TBAM.
Relative Kffeot of Kq^ual VolixxneB of Ste«ixi».
Relative toUU effect or work of steam is directly as its mean or average pressars
(A), and inversely as its filial pressure (B), or volume of steam condensed.
If former is divided by latter, quotieqt will give relative total effect qr work (G)
of a given volume of steam as udmitled and cut off at different points of stroke of
.piston, with a clearance of 3.125 per cent.
In following computations resistance of back pressure is omitted. If this press-
ure is uniform with all the ratios of expansion, it is a uniform pressure, to be de-
ducted from the total mean pressure in column (A).
Cat off at
Prw
(A)
lare,
(B)
Relative
Mean.
Fnal.
Effect.
I
I
X
I
•75
.969
.787
1.28
.6875
.946
.697
1-35
.625
■^
.636
1-45
•56*5
.576
1-54
•5
.857
.501
1. 71
Cat off at
375
■33
•35
.2
.125
.1
Preature.
(A)
Mean.
761
702
628
559
435
4i8-
Filial.
•394
•335
•273
.224
•15
•*3
(C)
Reiative
Effect.
1-93
3.Q9
23
a. 05
2.9
3-21
To Compute Total Effeotive WorU in One Strobe of Je*ii
ton, or a9 O-ivex). \>y au Iitdioator X>iasraixL.
u
a P (r I -}- hyp. log. R — c) = w, and a 6 L = to', to representing total work, and
to' bade pressure.
Note Pressure of atmosphere is to be included in computations of expansion;
it is therefore to be deducted from result obtuucd in non-condensing engines. In
condensing engines, the deduction due to imperfect vacuum must also be made,
usually 2. 5 lbs. per sq. inch.
Illustration. — Assume cylinder of a condensing engine 26. i ins. in diameter, a
stroke of 2 feet, pressure of steam 95 lbs. (80. 3 ■}- 14.7) per sq. inch, cut off at .5 stroke,
with an average back pressure of 2 lbs. per sq. inch, and a deacance of 5 per cent.
Area of piston,, deducting half area of rod =. 530 sq. ins. 2X5-7- 100 = . x dear-
ance, and 2-l-^i-5-i+-i = i-9 = ratio of expansion, and i -f hyp. log. 1.9 3= x.643.
Then 530 X 95 X 11 X 1.64a—-. 1 — 530X2X2 = 50 330X170*— «*«<>= 83777 »».
IixiNiTRAViQ».—>^ Assume cylinder of a non-condensing engine having an area of
3000 sq. ins., a stroke of 8 feet, steam at a pressure of 50 lbs. (35.3-1- 14-7), cut off mi
.25 of stroke, and clearunos .25 foot.
Ratio of expansion 3.66, back pressure 17 lbs., and i -{-byp. log. 3.66 = 9.397.
2000 X 50 (2.25 X 1 + hyp. log. 3.66 — .35) = looooo X 2.25 X 1 + 1.297 — .85 =
46057 5 fool-lbs.
2000 X J7 X 8 = 272 ooofhot-lbs. or negative effect, and 460 575 — 272 000 = 1 88 575
foot-tbs.
Total EflTeot of One I.-.b. of Expanded Bteazn.
If I lb. of water is converted into steam of atmospheric pressure = 14.7 lbs. per
sq. inch, or 2116-8 lbs. per sq. foot, it occupies a volume equal to 96.36 eubehet ;
and the effect of this volume under one atmo8|)here:^3ii6.8 lbs. x 96,^6 Jeet=z
55 799 foot-lbs. Equivalent quantity of beat exi>ended is i unit per 77a faat-Uft.^
= 55 799 -^ 772 =^ 72. 3 unitx. This is effect of i lb. of steam of a pressure of one at-
mosphere on a piston without expansion.
Gross effect thus attained on a piston by t \h of steam, fsnerated at pressaras
varying from 15 to joo lbs. persq. inch, varies trom 56000 to 62ooo/<n><-^«., equiv-
alent to trom 72 to 80 units of heat.
Effect of I lb. of steam, without expansion, as thus exemplified, fs reduced by
clearance according to proportion it bears to voltime of cylinder. If clearance is 5
per cent, of stroke, then 105 parts of steam are consumed in the work of a stroke
which is represented by 100 parts, and effect of a given weight of steam without ex-
pansion, admitted for full stroke, is reduced in ratio of 105 to loa Having deter-
tntned, by this ratio, effect of work by i lb. of steam without expansion, as reducfltd
by clearance, effect for various ratios of expansion may be deduced from that in
terms of relative operation of equal weighu of steam.
STEAM. 715
Volarae of i lb. of saturated Bteam of 100 lbs. per sq. Inch is 4.33 cube feat, and
pressure per sq. foot is 144X100= 14400 tbt.; theu total initial work = 14400X4.33
= 62 25'i foot-lbs. This amount is to be reduced for clearance assumed at 7 per cent
Then 62352 X 100 -?- Z07 = 58 273 fool-lbs. ^ which, divided by 77a (Joule's equiTa-
lent), = 75.5 units of heat.
Total or constituent heat of steam of 100 lbs. pressure per sq. inch, computed fk-om
a temperature of 212°, is 1001.4 units; and n-otn 102° (temperature of condenser
under a pressure of i lb.) the constituent heat is 1 11 1.4 units.
Equivalent, then, of net simple effect 75.5 units is 7.5 per cent, of total heat from
112®, or 6.7 per cent, from 102°.
When steam is cut olf at
I .75 .5 .33 .25 .3 .125 and . I of stroke,
comparative effects are as
t 1.26 1. 616 1.9s 214 3.27 2.51 and 2.6.
Total effects as given in table, page 718.
Effect of I lb. of steam, without deduction for back pressure or other effects, vanes
from about 60 000 foot lbs., without expansion, to about double that, or 120000 ^t-
Ibs.^ when expanded 3 times, cutting off at about 27 per cent, of stroke; and to
about ISO 000 foot-lbs. when expanded about 6 times, and cut off at about 10 per
cent, of stroke.
£^fiect of Clearance.
Clearance varies with length of stroke compared with diameter of cylinder,
with form of valve, as poppet, slide, etc.
With a diameter of cylinder of 48 ins., and a stroke of 10 feet, and poppet
valves, clearance is but 3 per cent, and with a diameter of 34 ins. and a
stroke of 4.5 feet and slide valves, it is 7 per cent.
iLLUsTaATioN OF EFFECT. — Assume steam admitted to a cylinder for .25 of its
stroke, with a clearance of 7 per cent
Mean pressure for i lb. = .637, and loss by clearance = 7 -f- 100 — .07, which, added
to .637, = .707, which is effect of a given volume of steam, if there was not any loss
by clearance, or a gain of it per cent
When steam is cut off at i .75 .5 .33 .25 .125 and .1 stroke.
Loss at 7 per cent clearance. . = 7 7.3 8.1 9.6 xi 15.3 ty percent
To Compute Net Vol time of Cylinder for G-iven Weight
of Steam, Hatio of Expansion and One Stroke.
RuLK. — Multiply volume of z lb. of steam, by given weight in lbs., by
ratio of expansion and by 100, and divide product by icx>, added to per cent,
of clearance.
RXAHPLB.— Pressare of steam 95 lbs., cut off at .5, weight .54 lbs., volume of i lb.
gteam 4.55, and wetght = .2198 lbs., stroke of piston 2 feet, and clearance 7 per cent
Ratio of expansion a -|- • 14 -^ iH-.i4 =: i. 88.
j:55X.54X«.88X«oo^46£:9g^ ci»6.^
ioo-f-7 107
To Compute Volume of Cylinder for diven BfTeot -witli
A Ghiven initial Pressure and Ratio of Expansion.
Rule. — Divide given effect or work by total effect of i lb. of steam of
like pressure and ratio of expansion, and quotient will give weight of steam,
from whidti compute volume of cylinder by preceding' rule.
EXAVPLB.— Assume given work at 50766 foot- lbs., and pressare and expansion aa
preceding.
Total work bv i lb., 100 Tbs. steam, cut off at .5, = by table 94 aoo^iMMba, and by
labia of maltipfierB for 95 lbs. = .998, which x 94 300 == g^ 019 Joot'lht.
Then ^^- :^ 54 lbs. weight of steam.
94013
]
7i6
STEAM.
Coixauniptioxi of Kxpauded Steam per IP of S^fibot per
Hour.
H* = 330cx), which x 60^ 1980000 foot -lbs. per hour, which — 1 lb.
steam, the quotient = weight of steam or water required per H* per hour.
Illustratiox.— Effect of i lb., 100 lbs. steam, without expausiou, with 7 per cent
of clearance = 58273 foot-lbs. ^ and = 34 lbs. tteam=z weight of steam con-
58 273
sumed for the effect per IP per hour.
When steam is expunded, the weight of it per "B? is less, as effect of i lb. of steam
is greater, and it may be ascertained by dividing 1 9800C0 by tbe respective effect,
or by dividing 34 Iba by quotient of total mean pressure by final pressure, as given
in table, page 718.
When steam is cut off at x .75 .5 .375 .33 .25 and .2 of stroke.
Volumesconsumedperl _^^ ,^ ^, ,« _ ,^^ ,^ ,^«ik,
H» per hour ..,\-^^ *^ 9 2> 18.5 17:6 16 14.9 a*.
Hence, assuming 10 lbs. steam are generated by combustion of i lb. coal per "BP
of total effect per hour,
The coal consumed per 1 _' , „ a« - - , «* w -a w a ,.«#»..
IP per hour T..J 3-4 ao9 «•« »*5 i-70 »-o 1.49 '"»•
SATURATED STEAM.
1*0 Compute E^iiergy and KfUciency of Saturated Steazv^.
| = R; 1 = ^; p^p'xa,or?or^=P; 33^ = C; | = D;
p-p'XaRS = X; i~-XD = H"; ^' = H'"; 15.5108 = *;
1 Y i'. * P". qp — aj*^^, X £980000 o * *
ft — X = A ; Rs = *^ } jv? °'X ' E — 0'*98ooooY = A;
X X
— = «; nlap—p' = x,»Qd = IH*; Rp— p'a = !»; PCX6o=jr;
2« .r «- 7 33000 1 ^ ^ ^3
^^000 1080000 ___
—■'■'— ,— 1= cube feet, -f— - - - i= cube feet water evaporated per hour per H?.
pa— pa 62.5 X .
V and V representing volumes of mass of steam entering cylinder and of it at
termination of stroke of piston; S and s volumes of t lb. steam when admitUd and
when at, termvnuUion of expansion ; C volume of cylinder per minute for each 1£P /
R and r ratios of expansion and effective cut-off ; F feed water per cube foot of vol-
ume of cylinder per stroke of piston^ and f per IH* per hom\ all in cube feet. D den-
sity or weight of i cube foot of steam at temperature of operation, in lbs. ; p mecut
pressure ; p' mean back pressure ; I initial pressure ; P mean effective pressure, or
energy per cube foot of volume of cylinder ; V' pressure per sq. inch or that equivalent
to hecU expended^ and P" pressure equivalent to expenditure of available heat, or en-
ergy, all in lbs. J Joule^s equivalent = t^h foot-lbs. ; Las per following table ; t and,
t' absolute temperatures of steam at initial pressure and of feed water in degrees ;
H D heat expended per cube foot of steam admitted ; H' heat expended per cube foot
of volume of cylinder, or pressure ec^ivaient to heat expended per aq.foot; W heal
r^ectedper cube foot of steam admitted; H'" he<U reacted per cube foot of volume
of cylinder ; A available heat per IH* per hour ; e energy per cube foot of volume of
cylinder to point of cutting off, or of steam admitted ; h and h' heat eapended and
rejected, and X energy exerted, all per lb. of steam and in foot-lbs. E effixiency ; x en-
ergy exerted per minute and per cube foot of steam admitted; a area of piston in
sq. \ns. ; I length of stroke of piston in feet, and ffeed water per IH* per hour^ in
cube feet
Illustrations. — Assume volume of cylinder and clearance (5 percent. = .6 inch)
X cube foot, steam (86.3 -{- 14.7) 100 lbs. per sq. inch, cut off at .5, mean pressure by
rule (page 711) 86 lb&, and back pressure 3 Iba
V=:i. v = 2. 8 = 4.33. «=8.3x. p = 86. 1>'=3. a=x44tii«.
<andf = 327.90 -I- 461.2° and 10004-461.2°. l:=»fseL « = i. L = i5774&
STEAM.
717
M-iri — i ratio.
33000
S6-3X144
4.33^-8.31 = .521 effective cut-off. 86 — 3 x 144 = 11952 Wt,
= 2.76 cuXtefeeL
= .231 Uu.
.231
3
or
198389
4-33 " » 2X433
772 X . 231 (789. 1° — 561. 2O) -f. 157 748 = 198 389 foot-lbs.
1 1 54 cube feet
= 99 195 foot-lbs.
198389
= 858 827 foot'Ws.
99195
= 68g Ibr.
■ 231 - - ,44
86 — 3 X 144 X 2 X 4-33 = «o3 $04 ft>ot lbs.
198 389 -i- .331 — 103 504 X .231 = 174 479 foot-lbs. 174 479 -r- 2 = 87 239 foot-lbs.
15. 5 X 100 X 144 X 4- 33 = 966 4s^ foot-lbs. 966 456 — 103 504 = 862 952 foot-lbs.
966456 . ,. 144X86 144X3 « 1980000 „ , jr s IK
■^—^2— = 111 600 lbs. ^-^-^ 7— ^5_^^=.jo7 E. -2 =i8so4673/oo<-Z6ai
2X4-33 III 600 .107
Or 1 980000 X zzz~: — '^ soA^n footdbs.
33904
103504
^ = .725!?.
33000
1080000 , 1. .r *
^ = .306 cube feet
62. 5 X 103 504
2X86 — 3 X i44 = 239O4/)0<-i6«. .1154X2,76x60 = 19.11 cube feet
I X 2 X 144 X 86 — 3 = 239O4^0t-to«.
103504
= ii952ybo<-/6*.
33000
= 2.761 cube feet.
2X4.33 '" ' 86X144 — 3X144
In illustration of connection of expenditure of available beat (A) and consumption
of fkiel, asBume coal to have a total heat of combustion of 10 000 000* foot-lbs.., cor-
responding to an equivalent evaporative power under i atmosphere at 212O of 13.4
liM. water and efficiency of furnace .5; then available heat of combustion of 1 lb.
ooal = 5 000 000 fbotlbs.
Hence, consumption of coal per lEP in an engine of like dimensions and opera-
tion with that here given would be 19 223 000 -i- 5000000 = 3.8444 Ihs.
Properties of Steazxi of Adaxixiiuzxi Density, {fitmkine.)
Per Cube Foot.
Twnp.
L 1
Temp.
L
Temp.
L
Temp.
L
0
1
0
0
0
32
'^S.
95
»999
158
9687
221
33»8o
4X
¥
104
L3571
167
11760
230
38700
50
1^'i
"3
3277
176
14200
239
248 *
44930
^
S55
123
4136
185
17010
51920
H8f
>3«
5178
.194
20280
257
59720
11
1171
140
6430
203
24020
266
68420
86
1538
'49
7921
212
28310
275
78050
Temp.
L
Temp.
L
0
0
284
88740
347
197700
293
100500
356
219000
302
113 400
3<>5
242000
3'»
127500
374
266600
320
143000
383
293100
^
150800
178000
392
321400
401
35" 600
L rtpresenHng UUent heat of eoaporaiion per cube foot of vapor in foot-lbs. of en-
ergy. To reduce tkit to umUs of heat divide by 772, or Joule^s equivalent.
SUPERHEATED STEAM.
The results attained by imparting to steam a temperature moderately in
excess of that due to the volume or density of saturated steam are :
1. An increaseof elasticity without a corresponding increase of water evaporated.
2. Arresting or reducing passage of water, in suspension, to cylinder (foaming), as
the heat contained in that water is wholly lost without affording any elastic effect
Both of these results, by increasing effect of the steam, economize AieL
Superheated steam should be treated as a gas.
The product of its pressure, p in lbs. per sq. foot, and volume r of z lb. of it in cube
feet, in the perfectly gaseous condition, is obtained by following formula:
42 140 T -J- i =5p r = 85.44 T. T temperature of steam +461. 2^^ and t 32°-!- 461-2^.
Illcstratiox.— Assume temperature of steam, 327. 90, superheated to 341.1^.
Then 42 140 x 461.20-f 341.10 -1. 32-1-461.20 = 68 549 foot-lbs.
Hence, as pressure of steam at 327.90= 100 lbs. per sq. inch, and at 341.1° iia
120 -T- 100 =: 1.2 to 1 = a gain qfonef{fth.
* Coal of ATBrago compoeltlnn, 14133 X 779 s* 10910676.
718
STBAH.
To Compute Synergy and Kfilcieiiioy of Superheated
Steaxu.
In foUowiog iiluBtratioDB elements are same as those in preceding cases for sata-
rated steam, with addition of the steam being superheated, so that
1 = 115 Mw., « = 338° + 461. 20=799.30 e' = 29oV46i-20 = 751.2°, 8 = 3.8, » = 7.4.
5-piS-Rap'S = X; 15.5108 = *;
ap — ap
E; A-X = A'i g^ = P;
— P".
h — X
= H'";
33000 -cube fed' ii?°-???-A-
RS"" * RS
Efficiency of saturated steam (p. 7 16) . 107, and, aa above, . 109 ; hence — = x.03 to i.
107
If, then, available beat of combustion of efficiency of furnace is assumed at 500000a
foot-lbs.^ as above, consumption of coal per X£P 18 1 83 486 -r- ji 000 000 =3. 637 lbs.
NorK.— For further illustrations Rankine's '' Steam-engine.'' lx>ndon, 1861, p. 436.
AVire-dra-wringf.
Wire drawing of steam is difference between pressure in boiler and pressure in
cylinder, and is occasioned as follows:
Resistance or friction in steain-pi|)e to passage of steam to steam-chest and piston.
Resistance of throttle-valve to {lassage of steam, when it is partly closed or of in-
sufficient area in pro|)ortion to steam pi )«.
Resistance from insufficient area of valves or ports.
Mr Clark, from his experimental investigation, declared, thiit resistance in a
steam pipe is inapprepiable, when its sectional area is not less than . i area of piston,
and its velocity not exceeding 600 feet per minute.
When velocity of a piston is flrom 200 to 240 feet per minute, area of steam may
be .04th of piston.
Sfieot or Kxpan^ion -witli Kqual Volumes, aud Kfieot of*
One Lb. of lOO Xjbs. Pressure per'fc^ci. Iiicli.
Cltarance aJt each End of Cylinder ^ including Volume of Steam Openings, 7 per cenL
of Stroke^ and 100 per cent, of Adminion = i.
Ratio
ofSs-
paasloo.
Point
of
ciitK>ir.
Tot*
Final.
L PBBaav
Mean.
BU.
Initial.
IniTlal
Vol ante
——
Initial
Initial
Maan
stroke
Preemre
PrMsara
Prewufe
e= I.
csi.
9 I.
?s I.
=s !•
I
I
I
Z
I
I.I
Z.18
1'
•847
■•?
1.004
1. 014
1.23
.8
.813
.98
1.02
1-3
•75
.769
.969
1.033
»-39
'7
.719
•953
1.049
1-45
.66
.69
.942
1.063
1-54
.635
.649
.925
Z.081
1.6
1.88
.6 .
•5
.625
•532
%'
J-09S
1.163
3.38
•4
.439
.787
1. 37 1
a. 4
•375
•417
.766
1.305
2.65
<33
•377
.796
»'377
2.9
•3
•345
.692
1-445
3-35
.25
.298
.637
'.57
4
.3
•2J
.567
1.764
4-5
.16
.act
.526
1.901
5
•14
.2
.488
::?si
55
.135
.183
•457
59
.11
.,69
•432
a.315
5l
.r
."59
•413
2.42X
6.6
.083
.15a
.398
3.5x3
7
:YA
.381
2.625
l^
.066
.348
2.874
8
<jo625
.135
•34a
2.934
AcTUAi. ErrscT.
Wefebt
P»f
Sq. Inch
par Foot
of Stroke
by 100 Lba.
Steam.
Volnoie
ofBtMra
of 100 Lbs.
for one
Btrok* par
Cube Foot.
By I I.b.
of 100 Lbs.
StMun.
of Steam
expended
pirH*
of Work
perHoor.
He»t
con-
rerted.
Lba,
Foot-lbk
Foot-lba.
Lba.
Unite.
.247
58273
100
34
§3.7
.333
63850
P:S
3x
.309
67836
39.9
28.3
87.9
.201
70246
9?
9x
•'9„
73513
96.9
26.9
95-2
.178
77343
95-3
35.6
100. X
•*?
79555
94.3
34.0
33^8
10&.9
.161
83055
9»-5
X07.O
•155
85125
2i'3
33-3
1x0.3
.131
94200
86
31
X23
.108
104466
78-7
^t
138*
.103
107050
76.6
18.5
.093
113 3BO
73.6
«7-7
M5-4
.085
1 16 855
69.3
16. 0
»5X-4
.074
124066
63.7
x6
X60.7
.063
132770
56.7
14.9
X7X.0
178,5
•055
138 130
52.6
X4-34
.049
142 180
48.8
1399
184.3
.045
'463*5
45-7
13-53
X89.5
.042
148940
43a
13.30
1308
X92.9
•039
»5i 370
^"•2
X96, X
•037
152955
39.8
13.98
«97-7
•035
155390
13.75
201. X
.033
1584x4
34.8
12. 5
305* a
'Oil
'$9433
34-«
XX.83
ao6.5
STBAU.
719
Itfixltipliercp fbr Actual T^elgbt and Sfieot for
Preatiure« than lOO ILjb6.
ActOAl
Effect.
otlxer
Proerar*
Malt
Sq. Inch.
Weight.
Um,
65
.666
70
•7«4
75
.763
80
.806
85
•855
Prauure
p*r
Sq. Inch.
Multipliers.
.„ , , . Actual
Weight. gjf^pt.
Lb*.
90
95
xoo
.901
•952
t
•995
•998
X
ItO
I20
1.09
I.I7
1.009
1. 01 1
Freunr«
Multiplier*.
p«r
Sq. Inch.
Weight.
Actual
Effect.
Lbe.
130
.1.28
X.015
140
1-37
I.022
X50
1.46
1.025
160
«.55
X.03X
170
1.64
1.033
•975
.981
.986
.988
.991
In this illastratioD, in connection with preceding table, no deductions are made
for a redaction of temperature of steam while expanding, or for loss by back
pressure.
When steam is Qut off at .0625, or one sixteentb, its expanbion is x6 times, but as
7 per cent of stroke is to be added to it (. 0625 -f. 07) =..1325 = 132. 5 per cent , or
nearly doable of 16^ or only a little over 7 times, as in 3d column of table on pre-
ceding page.
Column 7 is product of 58273 and ratio of total effect of equal weights of steam
when expanded, or average toUu pressure divided by average final pressure.
Thai, If staom ft cot off at .5, with a clearance-of 7 per cent, - ^ ^^-TL — =
.532 X 100 ir 53.2
X.6165, and 58 273 X x>6x65 = 94 900 Jbol-lbs.
Column 9 gives volume of steam consumed per H* per hour. Thus, afifiurae cyl-
inder to have an area of 293 sq. ins., a stroke of 2 feet, and pressure of steam 100 lbs.
without expansion.
292 X xoo X 2 = 58 4ooybo<-i6«., and 202 + 7 per cent of stroke for clearance t=
. 14 ; hence, 292 X 2. 14 -r- 144 r= 4.34 evbtfttl^ and weight of a cube foot of such steam
= .23 lbs., and 58400 : 4.34 x .23 :: 33000 : .564, which,x 60 minates^s 33.84, or 34
as per table.
The pressures are computed on premise that steam is maintained at a uniform
pressure during its admission to cylinder, and that expansion is operated correctly
to termination of stroke.
Column 10 is quotient of work in foot-lbs., divided by Joule's equivalent 772.
Thus, 94 200 -h- 772 = 1 22.
For percentage of constituent heat, converted from ioa° and 212^, assume
132 as iu last case:
Then 122 X 9 -J- roo r= 10.98 p<r cmi. for 102°, and 122 X 10 -^ 100 = 12. 2 per ctnL
for 21 2<*.
*' Wire-drawing" will cause a reduction of pressure during admission, and clear-
ance will vary from 3 to 8 per cent, according to design of valve, as poppet, long or
short slide.
In practice, wire-drawing of steam, and opening of exhaust befbre termination of
stroke, involve deviations f^om a normal condition, for which deductions must be
mnde, added to which there Is the back pressure, from insufficient condensation in
condensing engines, and fk-om pressure of air in non-condensing engines, and com-
pfessiott of exhaust steam at tcnnlnatiou of stroke.
1*0 Compute Q-aixx in. Feed "Water at Kis^ Temperatttr«.
T— <4-W — i0=H. T and t represi nting total heat in steam and Umptrature of
feed water, W and u> lemj^rature, of water Mourn oj^ and fed = heat lott ^y blowin§
offy and H tfAal heat required from fuel, all in degreet.
I LLUBTBATioN.— Assume Steam at 248^, fbed water loo^ in one case and t$cfl In
aoother, and density -^ , and toval beat at 248^ ==11570; what is gain ?
32
1157 — xoo + 348 — xoo = 1205° = total heal reqitired fivmJStA
((
(t
«
1x57 — 150+248—150=11050 =
H,« H-H'^.«>s-„o5^
H X20S *^
720
STSAM.
COMPOUND EXPANSION.
Compound Expansion is effected in two or more cylinders, and is prac*
tised in three forms.
ist. When steam in one cylinder is exhausted into a second, pistons of the
two moving in unison from opposite ends — ^that is, steam from top or for-
ward-end of first cylinder being exhausted into bottom or after-end of the
other, and contrariwise — this is iinown as the Woolf * engine.
2d. Steam from the ist cylinder is exhausted into an intermediate vessel,
or ** receiver,'' the pistons being connected at right angles to each other.
3d. Steam from receiver is exhausted into a 3d cylinder of like volume
with 2d, pistons of all being connected at angles usually of 120°.
The two latter types are those of the compound engine of the present tima
Expansion from Receiver. The receiver is filled with steam exhausted
from ist cylinder, which is then admitted to 2d, or 2d and 3d. in which it ia
cut off and expanded to termination of stroke.
Initial pressare in 2d, or 2d and 3d cylinders, is assumed to be equal to final press-
ure in iSt, and consequently the volume cut off in the one or the other cylinders
must be equal in volume to that or ist cylinder, for its full volume must be dis-
charged there(h)m.
Inasmuch as 3d cylinder is but a division of the sd, with addition of receiver,
this engine, in following illustrations, will, for simplification, be treated as having
but two cylinders.
In illustration, assume ist and 2d (flinders to have volumes as i to 2, with like
lengths of strolce, and tbat steam is cut off at .5 stroke, and equally expanded in
both cylinders, the ratio of expansion in each cylinder being thus equal to their
volumes.
Volume received into 2d cylinder would be equal to that exhausted from ist, as-
suming there would not be any diminution of pressure from loss of heat by inter-
mediate radiation^ etc. This is based upon assumption that expansion occars only
upon a moving piston; but in operation, expansion occure both in receiver and in
mtermediate passages, as nozzles and clearances; the 2d cylinder, therefore, receives
steam at a reduced pressure, increased volume, and reduction of ratio of expansion.
To meet this, and attain like effects, volume of 2d cylinder must be increased in
proportion to increased volume of steam and its ratio of expansion. Consequently,
there is no loss of effect aside firom increased volume and weight of parts by inter-
mediate expansion, provided primitive ratio of expansion is maintained by giving
relative increased volume to 2d cylinder.
Illustbation.— Assume cylinders having volumes as i and 3, initial steam of ist
cylinder to be 60 lbs. per sq. inch, stroke of piston 6 feet, cut off at one third, and
clearance 7 per cent
Final pressure, as per rule, page 711, = 22.62 lbs., and pressure as exhausted into
receiver, reduced one fourth, = 16.97 ]l)S., assuming there is no intermediate fall of
pressure. The steam, therefore, is expanded to 1.33 times volume of cylinder; a
like volume, therefore, must be given to 2d cylinder, to admit of this at a like press-
ure. If, therefore, the increased terminal volume of the steam in the ist cylinder
was augmented, including a clearance of 7 i)er cent, the effect would be as follows:
Volume admitted to 2d cylinder is equal to volume of ist added to its clearance,
or to .33 volume of 2d cylinder added to its clearance ; that is, to . 33 of 107 per cent. ,
or 35.66 per cent, consisting of clearance, and 35.66 — 7 = 28.66 per cent stroke of
2d cylinder. The steam exhausted into 2d cylinder thus Alls less than . 33 of its stroke
by 4.67 (33-33 — 28.66). As steam is expanded from volume of ist cylinder, plus its
clearance, to 2d cylinder, plus its clearance, ratio of expansion in 2d cylinder is equal
to ratio of volume of both cylinders, which is 3, and
too (i-eprexeniingJuU stroke) '{' 7 .. . 22.62 „ . ,
'-^ = 3, and final pressure = 7. 54 lbs. per sq. mch.
>
-*. J" -'^"^i*™* ^' AlWre, of New York, adoj>t«d this dedfrn of eoKlne In the steunbdate Htun
SekfvnLt At*, Oommtrte^ StnfUurt^ J\M Boy, aud Alat Bop.
ST£AM. 7^1
AoauntngTolnm* of receiver, or augmented terminal volome, ibr expanainn In ad
cyIlo4er, to have proportions of i, 1.25, 1.33, and 1.5 timea volume of ist cylindet
plus *ts clearance, the relations would be as follows:
Augmented terminal volumes) (times volume of
in ad cylinder } ' ''"S »'33 «'5 \ ist cylinder.
Sdo. do.
includiDg clear
anca
Final volumes in 2d cylfnder) (times volnmo of
added to clearance ( 3" 3-ai 3-2« 3-2i J ist cylinder.
Rrtio of expansion in 2d cyl'r. . 3 2.4 2.25 2
Intermediate reductions of) (ofterminalpross^
pressure.. J ** ** *5 -33 -^ ure in ist cyPr.
Equal to. o 4.53 5.65 xx. 31 lbs. per sq. inch.
Pressures in receiver and inl- )^ ^^ ,« . .^ ^ ,, ^. ^^ ^^
tialpr«8sure in 2d cylinder.. P»-^= '^'^ '^-^ "'31 do. do.
Final pressure in 2d cylinder .. . 7.54 7.54 7.54 7.54 da da
To Compute ICxpanaioxi in a Coxnpouud Ifinsfine.
RECEIVEK ENGINE.
Batio of Expansion. In iH cylinder ^ as per formula, {lage 710. In 2d cylinder.
— ^^ r = mtio. Of Intermediate Expansion = ratio, n representing ratio
of intermediate reduction of pressure between ist and 2d cylinder^ to final pressure in
%wt cyUnder, and r ratio ti/area of ist cylinder to that of 2d.
Illustration.— Assume » = 4, and r = 3
Then ^— ^ X 3 = a-as ratio, and — ^sa 1.33 raita.
4 4 — 1
TUal or Comtnned Ratio of Expansion, r R' = product of ratio of ist and 2d cyl-
inders by ratio of expansion in ist cylinder. As when r = 3, and R' = 2.653, then
9 653 X 3 = 7 959 to<«^ ratio.
Bence, Combined Ratio of Eaqaansion in both cylinders. r R'=:R''. R' rep*
nefm/tnp ratio of expansion in ist cylinder, and R" combined ratia
lLLCSrRATioif.~A8sume as preceding, and R' = 2.653.
Then ^^^ X 3 X a-653 = 5-969 oorndtned ratio.
X*o Ooznpute FlfTect fbr One Stroke and a O-iven Ratio
of li^jcpansion in ITirst Cylinder.
Without Intermediate Expansion, Rule. — Multiply actual ratio of ez-
Eansion in ist cylinder by ratio of both cylinders, and to hyp. lo^. of corn-
in^ ratio add i; multiply sum by period of admission to ist cylinder plus
cleanuioe,and term product A«
Divide ratio of both cylinders, less i, by ratio of expansion in ist cyl-
inder ; to quotient add i ; multiply sum by clearance, and term product B.
Subtract B from A, and term remainder C. Multiply area of ist cylinder
in so. ins. by total initial pressure in lbs. pf'r sq. inch, and by remainder C.
Proauct is net effect in foot-lbs. for one stroke.
With Iniermediate Expansion. Add effect thereof to result obtained above^
and by following formula:
Or, i' I + hyp. log. R"— c (« + -^) a P = B. arq^esentimg ana insq.im.,
p initial pressure in lbs. per <9. indi of tst cylinder, f length of admission or poim
^esMimg off plus dearance, c clearance infect, and E effect in foot-lbs.
3P
722
STBAM.
Iii«svBMioir.'»A8Baineareu orcyllttden x and 3 tq. Ids., length of stroke 6 feeL
pressure of steam 60 lbs. per sq. Inch, cut off at 2 feet, clearance 7 per cent, a&4
area of intermediate space, as receiver, one Ihtrd volume of ist cyllfider.
R" = ratio of expansion fn 2d cylinder ^ X 3 X a. 653 =r 5.969 hyp. log^
a. 653 X a. as + i X 3.4a — 3 — i-j-a.653 -|- x X 4a X i X 60 = 1.7865 + i X a.4« —
a-r-a.653-1-1 X .48X60 = 6.743 — .737X60 = 36a 36 yiK)t-Z6».
itt Cylinder,
Bfl^t on piston 60 lbs. X X Inch X a feet =x2o fooitJbt.
" of clearance 60 Ib&x 42 foot = as. a *^
Total initial effect = 60 X a X 4a =~i45.a foUlbt.
Then r45.2X t^- hyp. log. 2.653 or 1.976 5s= 286 91 /ooi-ttt
Less effect of clearance , ». sx a5.a_ J^
Net effect on piston above vacuum line = a6i. 71 jbot-lbM.
Less effect of back pressure 60-T-a.653sr2a.6x, whteh,x 3 «!• I _ ,e ^ *»
in& and 2 feet stroke |J___
Net effect on piston = ra6 05 >bo^-^&t.
2d Cylinder,
I45.a X I + hyp. log. a. as or x.8x =:a6a.8i/oof-f6t.
Effectof clearance 22.61 X3X*4a = 28.49 *' =t 234.32 ./bof-lftr
y>o.yf foot-tbs,
Tntermediate reduction of pressure, as given at page 721, =.25 X 22-61 =5.65 Iba
per sq. mch, which, x 3 sq. ins. and by 2 per foot of siroke,= 33.9/oo(-26«.
• Hence 360. 36 -f 33- 9 = 394- 26 foot-lbs.
Or, by sum of the three results, viz. :
ist cylinder. ... 126.05 ybot-/&«.
Intermediate expansion 33.9 *'■
2d cylinder.... 834.32 *^
394.27 Ji>ot-lb£
WOOLS' BiiGiNB. D. K dark.
Ratio of Expantion.—In xtt cylinder ttc per fbrmala, page 710. In 2d cylinder,
r -p- •\-x-i-i-\-x - nUio. r representing ratio of area of ist cylinder to that of ad,
I and I lef^th* of stroke and of stroke added to clearance^ in ins. orfeet^ and x ratU
oalue of intermediate ^heme.
iLLtJSTRATioN — Assums ? = 6 fut, T = 7 per cent. = . 42, r = 3, and x = . 333.
3Xg--- + .333
Then '4 = *-353» »'fl*M> ofeapanHon in 2d eyUndlT,
1+ 333
Total Actual Ratio ofBstpansUM. R' fr -^ -f- a j 1= ratio.
Illustration.— Assume preceding elements, R=: 3.653.
Then a. 653 (3 x r f- • 333) = 2.653 X 3 i37 = 8. 32a, total actual ratia
Combined Ariual Ratio of Expansion. R' f r 77 + *) -^ 1 -f * = ratto.
lu.otntATioit.-«iAinime preceding elemettts.
9653 (3 X ~- + 333 -^ t + 333) ^ j^ = 6.242, com(>tHM( 4ct«4< r^Wa
8TBAK.
723
To A.ttaixx Combined Xiatio of Sxpanaion and :Final
JPreasixre in. 2d Cylinder.
Assuming four cases as tpaken for Receiver £ngine with a clearance Off
7 per cent. The relations would be as follows:
I|it«riD«di4t« cpMcet ar« o .333
Volame of Mt cylinder o .357
Add to tbMe 1.07, tbe to1uoi« of i*t ) , __ . .„_
eyllBdor plua iU clmnmce, and. . . . C *' ~ *• 4a7
To Mune valoM of interinodiate apace '\
add ju tha volume of ad eylisder, I
•■d Uie aoioa tra the Anal voluipet | 3
by ezpaoeion In ad eylindor J
Ratioa oreznaa4o<i in adcyl*? ar««B»- ) . a^ . _ . ^.
tieoU of finalby initial volume*. . f *' ^^4 2. 352
•S
•535
1.605
3-357 3-535
9. 902
I
1.07
( part of volume of lat cylin-
1 der plm it* elMrtue*, or»
-1
total tnittal volnmea A»r eZ'
pMtion in ad evilnder 91
timea volnnie or latcyl'r
. .- ( tinea v^unM of «•( eyl-
4*°7 \ indar.
Intermediate fiille of preaanre are, io ) ^^
partaof final preaanre in lat cylinder )
•25
•333
for flnal pnMii
J anming Initial
] 63 lba.,an<t lli
I at 33.75 iba., t
o 5.94 7.9a
The initial preaaorea for ezpanaion in ) , __ fj:
ad cylinder are .\V. f » 75 -^
23-75 «7-8i «5'83
BmMtjinaS preumnt m a<f effFr are. . 8.47 7.57 7. 19
Combined Ratios in thete Four Catet*
ist ratio of expaasjoii. ... i to 3.653 Combined Rutio.
. . I to a.8o4=s S.653 X 2-8o4;;;«7.44.
X.909 ratioa of axpanaion.
of flnal pnenire ; or, aa-
1 preaanre at
nal premure
they are
XI. 87 ^pertf.inek.
(of final preaanre in tat eyl-
*5 \ ind«r,or
11.87 fff- ptr tq. in^.
6. 24 /&f. per tq. inch.
XSt
2d.
3<t
4tb.
2d
do.
do.
XSt
2d
do.
do.
do.
do.
«st
2d
do.
do.
da
do.
XSt
2d
do.
do.
do.
do.
. . . I to 2. 653
, . . j^lo 2.352 = 2.653 X 2.352 = 6.24.
...I to 2.6^3
. .. I to 2.202 = 2.653 X 2.202 = 5.84.
. .. I to 2.653
. . . I to 1.905 = 2.653 X X.905 = 5.05.
iDHial effeot of steam at 63 lbs. pressure, admUted to ist cylinder, for 2 feet, or ooa
third of stroke of piston, ana with a clearance of 7 per cent, or .43 feet, is as follows:
Effect 00 piston 63 x 2 feet x= 1 26/oo^/6«. ( Total initial
do. is clearance . . 63 x . 42 foot = 36. 46 = 63 x 242 = 1 52. 46/oo^^«. ( oflMt.
This sum is initial effect, on which effect by expansion is computed, while it is
0^46 foot-lbs. in excess of tbe initial effect on the piston.
The total effect, then, is computed as follows:
XSt case. 1 52. 46 x ( i + hyp. log. 7. 44) or 3. 0069 =s 458. 27 Net Eaat%.
Less effect of clearance 26. 46 431. 81 foot-lbs.
152-46 X (i + hyp. log. 6.24) or 2.831 = 43»-47
Lms effect of clearance..., 36.46 405.0X
152.46 X (1 + hyp. log. 5.84) or 2.7647 = 421-35
L^ effect of clearance 26.46 394.89
ad esse.
3d case.
4th case.
t(
it
152.46 X (1 + hyp. lojf. 5.05) or 2.6294 = 390. 20
Less effect of clearance 26.46 373.83
C(
The reductions of not effect in 2d, 3d, and 4th cases nre 6.2. 8.6, and 13.7 per cent
of effect in ist case.
To Compute S^ftect for One Stroke and a C3i-iven Corn-
bixied i^ctiial Ratio of Kxpattalon.
RuLB.-^To hyp. lo|^. of combined actual ratio of expansion (behind both
pistons) add i ; multiply sum by period of admission of steam to ist cylin-
der, added to clearance, and from pft)dact anbtract clearance. ^
Multiply area of ist cylinder in sq. ins. by initial pressure of steam in Iba.
per sa. mch and by above remainder. Product is net effect in foot-lbs. for
one soroke.
^24 STEAK,
EiiHPLt, — ABsnmadeiDflBlsoriBt lllnMntttoii
Hyp. log. 6.34+1 =".S3r;KbiCll,Xa-43=6,t
X6o = 38i8/i»l.»I.
Or,r(i + hyp.1og.R'l-C
I uiDia whoiher operaied In a nee
.18 apace bet»«iii ttia l»o cjlindei
VooirenglDBi Uie el!^ 13 greater,
f e elemaiils or llio elTo::! o( both (
' cleanuice lo tbe ptBImis of eacb engine, the
biy reducod, s> cempcred wlib tba mtloa «
INDICATOE.
:t perpendic-
ulars at eacb pmiiC Measure by scale of
pails (alike to Uiat of diagram) (he aclud
—1° mean prCBsure, as defined between the two
Q, lines at (op anil bottom of diagram, add the
~y results, divide eum by number ot polnla, and
- x* quotient will give mean piesaure in lbs. per
Eq. inch Dpon putim.
EuMPt,!.— PresBurea, ai above given, are :
iS + 35 + 35 + 3* + 3' + iS + tfi+io + 8+6 = a36,wblcb,-=-io, = aj,«»t
NoTt— If it Here preetloaWe to run an engine wilhout any load, and It BOmo-
ConcluB
protecting It from ce
beating of 11 prior
means Ibat may be
botUrthanltlsBei
oiiH on Actual Kjnoieiioy of Steam.
of hiebosl elHclcnoies ofatcam, aa uacd In an engine. masnB tar
ollngandcondeDBlnglu tbt^cyliuder must be employed. Super-
tbestmeana; and nem la Ihe aleiim-Jackel,
Incasesoriocom
hour le leaa thao Ibr
pan-loo. which lad
that of Blnglcoylinder condensing eaglnefi for like nliae of ei-
It ladednclbleJhim theH reaulis thnt the compound engine la mora afflolanl tbui
the Bioglecyllnder, and Ibal, of the iwo klnda of compound englnra, the reoaivar-
onglne IB more emcicnt than the Wootf.
Average oonsiimp
lnlongvoyageB,aSB
own by Mr. Bramweli, ranged from i.j io j.3 lbs. IDK-Oarit}
STEAM.
72s
To Compute Voluioae of* '^Vater Svaporated per JJ1>.
of Coal.
— ^rg — =i2 volume of vkxter^ in Ibi. V and v representing volume of steam and
relative volume ofwaier, in cuhefeet, W weight of cube foot ofwaJter, and F weight of
fuel consumed^ both in lbs. , and d dmsity of water ^ in degrees of saturation.
I].LiJ8HUTiON.~>Take case at foot of page.. V = 449887 cube feet, vs 838 cUbe
Jeet, W = 64.3, E = 1, and F = 4061 lbs.
449887-^838x64.3^3.,^ ,^,,
4061 X I
Gain in Fuel, and IniticU Pressure of Steam required^ token Acting Expan-
siveiy^ compared with Non-Expansion or Full Stroke,
Cntting
off.
Point of
Catting off.
Gain in
Fuel.
Cutting
off.
Point of
Cutting off.
Gain la
Fuel.
Cutting
off.
Point of
Cutting off.
Gain in
Fuel.
Stroke.
.75
.625
Per Cent.
22.4
3a
Lb«.
1.03
1.09
Stroke.
•5
•375
Per Cent.
49.6
Lbs.
1. 18
1.32
Stroke.
•25
•125
Per Cent.
58.8
67.6
LlM.
1.67
2.6
Illustration. —What muBtbe initial pressure of steam cut off at .5, to be equiv-
alent to 100 lb& per aq. inch at tall stroke?
zoo at full stroke = zoo, and zoo X x.z8 = zz8 lbs.
7o Compute G^ain. in Fuel.
RuLB. — Divide relative effect of steam b}^ namber of times the steam is
expanded, and divide i by quotient ; result is the initial pressure of steam
required to be expanded to produce a like effect to steam at full stroke.
Divide this pressure by number of times the steam is expanded, and sub-
tract quotient from i, remainder will give gain per cent, in fuel.
BxAXFLB.— When steam is cat off at .5, what is gain in fuel, and what mechanical
effect?
Relative effect, inclading clearance of 5 per cent.,= z.64; number of times of ex-
pansion = 2.
1. 64 -5- 2 = . 82, and z -T- . 82 = z. 22 tm'^to^ pressure.
1.22 ^ a =B. 61, and x -^ .6t = .^g per cent
Mechanical effects of steam at full and half strokes are 2 — z.64 = '36 difference.
Hence, z.64 ; .36 :: 50 (half volume of stoam used) : zo.07 per cent more fuel to
produce same effect at half stroke^ compared with steam atpiU stroke.
To Compute Consumption, of Fuel in a F-irnaoe.
When Dimensions of Qflinder^ Pressure of Steam^ Point of Culroffy HevO"
hitiftnsj and Evaporation per Lb. of Fuel per Minute are given.
Rule. — Compute volume of cylinder to point of cutting off steam, in-
doding clearance. Multiply result by number of cylinders, by twice number
cyf strides of piston, and by 60 (minutes) ; divide product by density of steam
at its pressure in cylinder, and quotient will give number of cube feet of
water expended in steam.
Multiply number of cube feet by 64.3 for salt water (62.435 for fresh),
divide product by evaporation per lb. of fuel consumed, and quotient will
give consumption in lbs. per hour.
ExAMPLB.-— Cylinder of a marine engine is ^5 ina in diameter by zo feet stroke
of piston; pressure of -steam hi steam-chest is Z5.3 lb& per sq. inch, out off at .5
stroke; number of revolutions 14.5, and evaporation estimated at ?{ 5 lbs. of salt
water per lb. of coal; what is consumption of coal per hour, when density of water
Is maintained at 2-32? (See Saturation, page 726.)
Volnme of steam at above pressure, compared with water (15.3 + '4: 7)* = 338*
Area of 95 ins. -f- 2. 5 per cent for clearance -r- Z44 = 50.45 cuite feet Point of cut-
ting off 5 feet>f 2.5 per cent = 5 t^% z.5 Ins., and 50.45 X 5 ^®t z.5 tn^ x Z4.5 x a
X 60 :^ 449 887 CM6f feet steam per hour.
3 P*
720
STJfiAM.
Hettoflv 449 887 -*- ^3'i ^ 53^- ^ cuhefut ybaiir^ whl(Sb, X 64.3 =« 34 SM RA , whict
— 8. 5 = 4061 Ibt. coal per Kimr.
Nora.— ElemeDts given are those of one engine of steamer AreHCy and consamp-
lion of clean fUel (selected) for a run of 12 days (one engine) was 3820 lbs. per hoar.
UfilizcUioti of Coal in a Marine Boiler,
Experiment gives from .55 to .8 per cent, of the heAt developed m the
combustion of coal, as utilized in the generation of steam. Ordinarily it
may be safely taken at .65.
SALINE SATURATION IN BOILEBS.
Average seo^water contains per xoo parts t
Chloride of sodium (com. salt) . . 2. 5 i Chloride of magnesium • 33. . * • =s 2.83
Sulphuret of magnesium 53; SalphuretoflTme 01.... = .54
Carbonate of lime and of magnesia .02
Saline matter 3.39
Water *.... 96.61
100
Hence, sea- water contains .0339th part oi its weight of solid matter in solatioa,
and is saturated when it contains 36.37 parta
Mean quantity of salts, or solid matter, in solution, is 3.39 per cent, three fourtbt
of which is common salt
Removal of Inarustation of dcale or fieditnent.
PattUoes, in proportion of .033 Weight of water. Mnlanes^ \u proportion of 1.6
lbs. per W ^t boiler. Oak, suspended in the water, and Mahogany or Oak gawdust,
and Tanfur^s and Slippery Elm bark, renewed fTeciuently, according (o volume of it,
and the evaporation of the water Muriate o/Ammontu and Carbonate o/Soda^ in
quantity to be determined by observation.
BLOWING OFF.
To Compute I^oaa of Keat toy Slo-wltig Off of Saturated
"Water fVom a Steam->l>oiler.
S^T Elf
^ = proportion of keat logt^ S — T X E = heat required fromjvdjbr
t
water evaporated in degrees^ and g_«i tf . > = 2om 9f heat per cent S repraeiUing
turn of sensible and latent heats of water evaporated, T temperature of feed water,
t difference in temperature qf water bloum off and UuU supplied to boiler, E volmmi
of waUr evaporated, proportionate to that blown off^ the latter being a constant quan-
tity, and represented by i.
Values of E at following degrees of sataratlon, and volames to be blown off:
I. as
«-5
^
1 ^
•3^1
> i
3«-
1-
Jk
1-
H
Si*
h
•as
4
1.65
.65
1-54
a
1
t
a. 75
«-7S
•35
9
'Z*
'25
1.33
•as
t.as
8
3
a
S
9
1.85
«S
1.18
a-5
1.5
66
a. as
a. as
Thus, when water in a boiler is maintained at a density of ~ , i volame of it if
evaporated, and an equal volume, or z, is to be blown off.
Hence 1 -f i — 1 = i =toAo of volume evaporated to tolumf hUnm off
ItxtBTRATioN I.— Polut of blowiug off is 2 (3a). pressuro of steam Is 15 3 lbs., men
Turial gauge, and density of feed water i (32); what is proportion of heat lostt
S=ii57«5 T=ioo« f=is.3 + i4.7=25o.40-iooP-isa4<i Rasi,
n^ "''^-'^^^-^^r-^^^a^j^rppormofhedtum
2. — Anume point of blowing off 1.75 (33); what wonld be loss of heat per cent in
preceding caaef
E = .75. ^^^ ; = 15.0 oer cent lott by blowing off.
»I57.8 — I0PX.7S+X5O-4
3.~AaBume elemejiu of preceding case. Wl^at is total heat required trsm tufl
for water evaporated ?
1157.8 — 100 X .75 = 793-35®'
To Cpnp&pute Voluroe oi* "W^ter 31o^^rzi Off to tli»t
Evaporated.
When Degree of SeUuration is Given. Rule.— divide 1 bv proportionate
volaoie of water evaporated to that lilown off, or value of £l as above, for
degree of saturation given, and quotient will give number of volumes blown
off to tiiat evaponted.
JU.USTB4X10M.— Degree of saturation in a nuirine boiler is ^^ ; what is volume
of water blown off?
E S3 1.35. Then x -4- 1.25 = .8 blown off.
Proportional Volumes 0/ Saline Af after in Sea-^iocUer,
Baltic X in 153
Blaclc Sea i '' 46
Red Sea ..x *' 13X
Atlantic, South. . x in 34
North..! " 23
Dead Sea i " 9.39
British Channel ... i 'in 28-
Mediterranean x '* 25
Atlantic, Equator.. x *' 35
When saline matter at temperature of its boiling-point is in proportion of xo per
cent , lime will be deposited, and at 39. 5 per cent salt
Temperature of water adds much to extent of saline depwltA
STEAM-ENGINE.
The range of proportions here given is to meet the requirements of
varifttions in speed, pressure, length of stroke, draught of wftter, etc.,
in the varied purposes of Marine, Biver, and Land practice.
For a R,anse of Pressxires of from 30 to 80 lb*. (AiiexroTi-
rial Oauere) po*" Sq.. IxxcU, Cnt Off at Half Stroke.
}*iglort-rod. Cylinder or Air-pump {Wrouffkt /ron), .1 to .14 of its diaui. ;
{Steel)f .08 diam. ; and (jCopper or Brass), .11 and .135.
Cbndenser {Jet), Volume, .35 to .6 of cylinder. {Surface.) Brass tulyes,
16 to 19 B W 6, .625 to .75 in diameter by from 5 to 10 feet in length, and
.75 to 1.25 ill pitch, condensing surfaces, .55 to .65 area of evaporating sur-
race of boiler with a natural draught; .7 to .8 with a blower, jet, or like
draught. Or, for a temperature of water of 60°, 1.5 to 3 sq. feet per IBP.
With a very eflBsctive and sufficient circulating pump, aress may \>& reduced to
.5 and .6.
EiTect of vertical tube surftice, compared to horizontal, is as 10 to 7.
Air-pump (Single acHr^ and direct connection). Volume from .15 to .3
steam (^Knder. Or, — ^— 2.75. For Double acting put 4 for a. 75. V and v
rmresenting volumes of condensing and condensed water per cubejbot, and n strokes
of piston per minute.
Foot and Delivery Valves, Area, .35 to .5 area of air-pump.
Delivery Valve {Out-board), With a Reservoir. Area from ,5 to .8 Foot
vahre.
NoTc— Velocity of water through these valves should not exceed x3 feet per
second.
728 STKAM-ENGINB.
Steam and Exhaust Valves, — (Poppets. = area for sieam, far
N r/' '»24CX)o '' '20000 "^
exhaust ; (Slide)^ for steam, and for exhaust, a representing
%rea ofsUam cylvnier in sq. itM., s stroke of piston in ins,, <md n nu'mX>er of revolu-
tions per minute.
It^edion Pipes, — One each Bottom and Suie to each condenser; area of
each equal to supply 70 times volume ^ft water evaporated when engine is
working at a maximum ; and in Marine and River engines the addition of
a BUge, which is property a branch of bottom pipe.
NoTK I.— Proportions given will admit of a sufficient volume of water when en-
gine is in operation in the Gulf Stream, where the water at times is at temperotare
of 84O, and volume required to give water of condensation a temperature of 100^ is
70 times that of volume evaporated.
2. Velocity of flow of water through cock or valve 20 feet per second fn river or at
shallow draught, and 30 feet in sea or deep draught service.
Feed Pump.* — {Single acting. Marine), Volume, .006 to .01 steam cylinder.
(River and Land), or when fresh water alone or a surface condenser is used,
xx)4 to .007.
NONtCONDKNSING.
li''or a Range of* IPressiires of fVom SO to IfSO lbs. (Aferca-
rial Ghauge) per Sq.. Incli, Cut Off at Kalf Stroke.
Piston-rod. — (Wrought Iron), Diam., .125 to .2 steam cylinder. (Steel)^
1. to 1.6 steam cylinder.
Steam and Exhaust Vaives, — Area is determined by rules ^ven for them
in a condensing engme, using for divisors 300Q0 and 22 750.
A decrease in volume of cylinder is not attended with a proportionate decrease
of their area, it being greater with less volume.
Feed-mtmp.* — (Single acting, Marine), Volume, .008 to .016 steam cylin-
der. (River and Land), or where fresh water alune is used, .005 to .01 1'.
Grexieral lElules.
Snsines.
Cylinder. Thickness,— ^Vertical), -^ = < ; (fforizontat), ^ ^ = / ; (Tf^
clined), divide by 2000 m a ratio inversely as sine of angle of inclination.
D representing diameter of cylinder, p extreme pressure in lbs per sq. inch that it
<ma^ be suJbijected to, and t thickness in ins.
Shafts, Gudgeons, Joumcds, etc. To resist Torsion. See rules, pp. 790, 796,
Coupling Bolts. — /- i'^^^* * representing number of bolts, D diameter
of shafty d' distance of centre of bolts from centre of shafly and d diameter of bolts,
ali in ins.
Cross-head, Wrought-iron, (Qlinder), - ^- = S, and ^y =: d, or ^s=.b.
a representinQ arta of cylinder in sq. ins., I length of cross-head between centres of its
journals xn feet, arid ^ product of square of depth d, and breadth, b, ofsajUon, both
in ins. (Air-pump), -^ = S, and as above for d and 6.
If section of either of them is cylindrical, for S put -y/S X 1.7.
Diam. of boss twice, and of end joumab same as that of piston-rod. Sec-
tion a( ends .5 that of centre.
• — ^j^M^^^^i^— ^— ^— ^^— ■ -^ . .
* See Formnlfls, page 736
STEAH-BN6INB. 729
Steanhpipe.^lU area should exceed that of steam-valve, proportionate to
its length and exposure to the air.
Connecting -ivd, — Lengthy 2.25 times stroke of piston when it is at all
practicable to afford the space ; when, however, it is imperative to reduce
this proportion, it may be twice the stroke.
Comparative friction of long and short connecting-rods is, for length of stroke of
piston, 12 per cent additional; twice, 3 per cent. ; and for thrice, 1.33.
Neck. — Diam. i to i.i that of piston-rod. Ctnire of body (l/onzontal),
1.25 ins. ; ( Verticat)y ,q6 inch per foot of length of rod.
With two c<>iii:e:tiog-rod8 or links, area of necks .65 to .75 area of attached
piston-rod.
Straps of Connecting-rods, Links^ etc, — (Strap), area at its least section
.65 neck of attached rod ; {Gib and Kejf), .3 diam. of neck, wiiith, 1.25 times,
(Slot) 1.35 times {Draft) of keys .6 to .8 inch per foot. Distance of Slot
from end of rod .5 diaiiu of pin.
Pins {Cranks, Beams, etc») . \/-q • 355 = <*• P representing pressure or thrust
of rod or beam, I lengUi 0/ journal in ins., and C,for Wrought iron = 640, Cast, 5601
Puddled steel, 600, and Cast, 120a
Length, 1.3 to 1.5 times their diam., and pressure should not exceeil 750
lbs. per sq. inch for propeller engine, and 1000 for side-wheel.
Qxinks {Wrougkt-iron), — Hub, compared with neck of shaft, 1.75 diam.,
and I depth, iuye, compared with pin, 2 diam., and 1.5 depth. Web, at pe-
riphery of hub, width, .7 width, and hi depth .5 depth of hub ; and at periph-
ery of eye, width, .8 width, and in depth, .6 depth of eye.
{Cast-iron,) Diameters of Hub and Eye respectively, twice diam. of neck
of shaft, and 2.25 times that of crank pin.
Radii for fillets of sides of web .5 width of web at end for which fillet is designed;
for fillets at back of web, .5 that at sides of their respective ends.
Beams, Open or Trussed, — Length from centres 1.8 to 2 stroke of piston,
and depth .5 length. If strapi)ed. Strap at its least dimensions .9 area of
piston-rod, its depth equal to .5 its breadth. End centre jownals each i, and
main centre journals 2.5 times area of piston or driving-rod.
This proportion for strap is when depth of beam is .5 length, as above; conse-
quently, when its depth is less, area of strap must be increased; and when dcjtth of
strap is greater or less than .5 width, its area is determined by product of its & (2^,
being same as if its depth was . 5 its width.
{Ccut-iron). Area 0/ Section 0/ Centre. - ' =A. p representing
extreme pressure upon pisUm in lbs. , d depth in ins., and I length in feet
Depth at centre .5 to .75 diam. of cylinder, and, when of uniform thick-
ness, a thickness of not loss than .1 of depth.
Vibration of End Centres.— I -^ 2 — >/(/ -^ 2)2 — («-,- 2)' = vibration at each
end ; s representing stroke of piston, in feet
Plumber BiocJcs {Shaft). — Binder d Wy C = depth, d representing (ham.
oftnats when tvoo to binder, I distance between bolts, b breadth of binder, all in ins.,
and Cfor wrought iron i, steel .85, and cast iron .2.
Hdding-down Bolts. P -r- 3 C = area at base of thread of each bolt. C for mild
steel for small and large bolts 6cxx) and 7000, for wi'ought iron 4500 and 6000, if but
two are used.
d fl
Binder {Brass). -- ^-^ = depth
730
STSAM-»N6m£.
Cbeib.— Angles of sides of plug trotn 7^ to 8^ f^om plane of ft
Putnps. — ^Velocity of water in pump opeiiiiigs should not exceed 500 feet
per liiinute.
Fiy-tvheels and 6ovemor$,^-Se6 Rules, pages 451 and 452.
'Water-'wrlieelfli.
Water-wheels (Amu). — Number from .75 to .8 diam. of wheel in feet
{Blatki) Wood. — For a distance of from 5 to 5.5 fleet between arms, thick-
ness from .09 to .1 inch for each foot of dlatn. of wheeL
Area of blades, compared with area of immersed amidship section uf a
vessel, depends upon dip of wheels, their distance apart, model and rig of
vessel.
In River service^ area of a sin.e:le line of blade surface varies from .3 to 4
that of immersed section ; In Bay or Sottnd service^ it varies from .15 to .2;
and in Sea set^ce^ it varies from .07 to .1.
NoTB.— A wroaght-iron blade .625 inch thick bent at a stress withstood by an
oalc blade 3.5 ius. thiclc.
Radial and, Featlierins.
Radial. — Loss of effect is sum of loss by oblique action of wheel blades
upon the water, their slip, and thrust and drag of arms and blades as they
enter and leave the water.
Loss by oblique action is computed by taking mean of square of sines of
angles of blades when folly immersed in the water.
Loss by oblique action of blades of wheel of steamer Arctic, when her wheels
were immersed 7 feet 9 ins. and 5 feet 9 ins., was 85.5 and 18.5 per cent., which
was the loss of useriil eftect of the portion of total power developed by engines,
which was applied to wheels.
Feathering. — Loss of effect is confined to thrust and drag of arms and
blades as they enter and leave the water.
Comparative Effects.— Irx two wheels of a like diameter (26 fbet, and 6 fbet immer-
sion), like number and depth of blades, etc., the losses are as follows
Radial 26.6 per cent. | Feathering 15.4 percent
Loss of effect by thrust and drag in a feathering wheel, having these elements
and included in the above given loss, is computed at 2 per cent.
Relative loss of effect of the two wheels is, approximately, for ordinary immer-
sions, 20 and 15 per cent from circumference of wheel
Centre of Pressure^ — -^ — -p- — d = c d and d' repretenting depths 0/ bmet
3 a— a *
below surface of water^ and e centre of pressure, all in like dinunsUmStfrotn bUtem
edge.
In the cases here given, centres of pressure are as follows:
Radial 6.4 ins. | Feathering 8.51ns.
Propellers.
Propellers (Screw). — Pitch should vary with area of circle described by
screw to area of midship section of vessel.
ARBA, TWO-BLADED,
Area of disk of propeller to mid- )
ship section being i to )
Ratio of pitch to the diameter of
propeller is z to
}
.8
1.02
4-5
I.IZ
1.2
3-5
1.27
1.31
a- 5
S.4 1*47
For Four-bladed screws, multiply ratio of pitch to dianu A0 given aborCi
^y ^•Z5' l^ngfh^ .166 diam.
STKiltf-ENGrNB.
731
iS!li9i.^^lip of a screw propeller is directly as its pitch, and economical
effect of a screw is inversely as its pitch , greater the pitch less the efl'ect.
An expanding pitch has less slip than a uniform pitch, and, consequently
is more effective.
To Compute Thrust of a Propeller.
UP ^ = T. 8 r^^aeiUing tpeed of vessel in knots per hour.
a
8LIDB VALYES.
AU Dimensions in Inches.
7o Ooxnpute X^ap required, on. Steam Knd, to Cut-off at
any given Part of* Stroke of* Piutbn.
Rule. — From length of stroke subtract length of stroke that is to be made
before steam is cut off; divide remainder by stroke, and extract square
root of quotient.
Multiply this root by half throw of valve, from product subtract half lead,
and remainder will give lap requirea.
EXAMPLK Having stroke of piston 60 ins., stroke of valve 16 ins., lap upon ex-
haust side .5 in =one thirty-second of valve stroke, lap upon steam side 3.35 ioa,
lead M ioa, steam to be cut off at five sixths stroke, what is tbe lap?
60 — T of 60 = 10. ^ /— = .408. 408 X — = 3-264, and 3.264 = 2.264 ins.
t> \ 00 3 3
To i^soertain Lap required on Steam Bud, to Cut-off
at -varioiiis Portions of Stroke.
Oistuice of piston fVom end of its stroke when steam is cut off,
in parts of length of its stroke.
Vaivs
vritkouA Lead.
Lap in parts of
stroke
"]
i
•354
6
323
i
3S6
A
i
A
\
i
iV
A
•a?
328
.204
•177
M4
102
iLUTRRATioii. —Take elements of preceding ca8&
Under \ is 204, and .304 X i6 = 3.264 t>« lap.
When Valve is to have Lead, — Subtract half proposed leiui from lap as-
certained by table, and remainder will give proper lap to give to valve.
If, then, as last case, valve was to have 2 m& lead, then 3.264 — 3 -r- 3 := 2. 364 t?if.
'Vo Ooznpute at -vrlxat Fart of Strolca anjr given X^ap on
Steam Side >vill Cut ofi*.
Rule.— To lap on steam side, as determined above, add lead ; divide sum
by half lenc^ of throw c^ valve. From a table of natural sines (pages 390*
403) find the arc, sine of which is equal to quotient; to this arc add 90°,
and from their sum subtract arc, cosine of which is equal to lap on steam
side, divided by half throw of valve. Find cosine of remaining arc, add i
to it, and multiply sum by half stroke, and product will give length of that
part of stroke that will be made by piston before steam is cut off.
ExAMPLB.— Take elements of preceding case.
Cos. (8ta.?;^^+'+9o<>-cos.^) + « x|=COSL(330,3'+goP-73^34')
s= 4«® 39', and COB. 48® 39'+ 1 X — = x.66 X 30= 49.8 ins.
3
To .Anoertain 3readtH of Porta.
Half throw of valve should be at least equal to lap on steam side, added to brsadtb
of port. If this breadth does not give required area of port, throw of valve must be
fnoTMUKd antU reqatred area is attained.
732
Port
STBAU-ENtilNB.
..
'",
>le>l>>>fa
±
A
X
A
±
.178
,091
:!is
!
i
.09
Dnlte<nCDlaiDD9oru
ctised ud Ihfl on« bvbluc
Undor odc alilh in lul
wiiglbotBlrolto = j.i8in
Rui.E.— To twice lap add twice width of a Bteam port iu ins., and Mini
wiil give stroke required.
F'X]>an4loD by ^p, wktb a elide valre operated by an eccentrli: iiloao. cannot bt
Bomewbal compeoBaled. Whan lap a increased^ throw of eccentric ebould also b»
When low eipansion 1b required, a cnt-off valve should be resorted to IL iddltim
To CompntB Distance ot s Finton ft-am Snd of i"
Cjtrolia, wlien X.ead produosH its Kftbot.
Rui.E. — Divide lead by wiiHh of steam pral, ijotli in ins., and term ItK
quotient sine : multiply its eorte«ponding vereed sine by h>l[ Hlroke, anil
pro-luct will give diaUnce of piston from end of its stroke, when steani isti-
mitted for return stroke and exhaustion ceases.
PLB— Simke orpleioD in ,s Ins., width of port a.
„....,™.x'i..,.,.
steam-e:n gine. 733
To Compute Distanoe of* a Piston iVozn IGxid of* its Stroke,
-^vliezx Steam is admitted, fbr its Return. Stroke.
Rule. — Divide width of steam port, and also that width, less the lead, by
.5 stroke of slide, and term quotients versed sines Jirst and second, Ascer-
Cain their corresponding arcs, and multiply versed sine of difference between
Jirst and second by .5 stroke, and product will give distance.
ExAMPLK. — Assame elements of preceding case, lap = .5 tncA, and stroke of
Elide 6 ins.
^^ and %^7~'^ = • 8333. and .667 and ver. sin. 80° 24' <v 70O 33' x — = . 3528 inch.
O -r- 20-7-2 2
To Compute X^ap and I^ead of I^ooomotive Valves.
To cut off at 33, . 25, and 125 of stroke of piston, lap ^ 289, . 25, and . 177 t, outside
lead = .07 t, and Inside lead = . 3 t. t representing stroke qfvcUvey all in tns.
HORSE-POWER
Harne-power is designated as Nominal, rndicated, and Actual,
Nominal^ is adopted and referred to by Manufacturers of steam-enginea,
in order to express capacity of an engine, elements thereof being confined
to dimensions of steam cylinder, and a conventional pressure of steam and
speed of piston.
Indicated, designates full capacity in the cylinder, as developed in opera-
tion, and without any de-ductions for friction.
A (^ualy refers to its actual power as developed by its operation, involving
elements of mean pressure upon piston, its velocity, and a just deduction for
friction of operation of the engine.
To Compute Korse-po^ver of* an £Cngine,
1)2 „ 1)3^
XS'omiual. — Non-condensinff, , and Condensmg, = ff. D repre-
Menting diameter of cylinder in ins., and v velocity of piston in feet per minute,
Noth-condensinff is based upon uniform steam-pressure of 60 lbs. per sq.
inch (steam-gauge), cut off at .5 stroke, deducting one sixth for friction and
losses, with a mean velocity of piston, ranging from 250 to 450 feet per
minute.
Condensing is based upon uniform steam-pressure of 30 lbs. per sq. inch
(steam - gauge), cut off at .5 stroke, deducting one fifth for friction and
losses, with a mean velocity of piston of 300 feet per. minute for an engine
of short stroke, and of 400 feet for one of long stroke.
, »r J • Al** — (/t-M4T7)2«r ^ ^
.A-otual. — Non-condensmg, ^l.-L-ju. =ff. A representing
" 33000
area of cylinder in sq. ins.y P mean effective pressure i^pon cyUnder piston^ inclusive
of atntosphere, ffriemon of engine in allits parts, addi^ to friction of load, both in
|to. per sq. inch, s stroke of piston in feet ^ and r number of revolutions per minute.
Sum of these resistances is IVom 12.5 to 20 per cent., accordmg to pressure oC
■team, being least with highest pressure.
* This viUue is best obtained by an Indicator; when one is not used, refer to rule
and table, pp. 710-12. In estimating value of P, add 14. 7 Iba , for atmospheric press.
are, to that Indicated by steam gauge or safety-valve. Clearance of piston at each
end of cylinder is included in tbts estimate.
t This value may be safely estimated in engines of magnitude at z.s to 2 lbs.- per
aq. inch, for Ariction of engine in all its parts, and friction of load may oe taken at 5
to 7.5 per cent of remaining pressure. Sum of these resistances in ordinary marine
engines is iVom 10 to 20 per cent , according to pressure of steam, exclusive of powev
required to deliver water of condensation at level of discharge or load-line of a ves*
8el. For pressure representing friction for different designs and capacities of en
sines as estimated by English authority, see pp. 473-5 and 662.
5Q
734 STBAM-ENGtNE.
Illustration,— Diameter of cylinder of a noD-ooDdensing engine is loins., stroki
of piston 4 feet, revolutions 45 per minute, and mean pressure of steam (steam
gauge) 60 [bs. per sq. inch.
A=78.54 gq. ins. f =60-^-14.7=74.7 lbs. /=a.5-f (6o4- 14 7—2.5) X. 075=7.92 ttt
Then 7854 X(6o-ht4.7-79«H"»4-7)XaX 4X45 = . . g ff
33000
NoTK t.— Power of a non-condensing engine is sensibly affiscted by chavActer of its
exhaust, as to whether it is into a heater, or through a contracted pipe, to afford a
blast to combustion.
2.— If an indicator is not used to determine pressure of steam in a cylinder, a
safe estimate of it, when acting expansively, is .9 of ftiU pressure, and when at full
stroke flrom .75 to ,8.
Condensing. ^HEIhll^m
33000
Power required to work the air-pump of an engine varies fh)m .7 to .9 lbs. per sq.
Inch upon cylinder piston.
Illustration. — Diameter of cylinder of a marine steam-engine is 60 in&, strolce
of piston 10 feet, revolutions 15 per minute, pressure of steam 50 lbs. yer sq. inch.
cat off at 25 Btrolce, and clearance a per cent
A = 2827. 4 *g. ins. P (per Ex. , page 713) = 28. 62 lbs. f= 1.5 + 28.62 — 1.5 X. 05
= 2.467 lbs.
Then '8'7.4 X .8j6- jjsgjO Xj° >05 ^ ^ ^
33000
From which is to be deducted In marine engines power necessary to discharge
water of condensation at level of load-line, which is determined by pressure due to
elevation of water, area of air-pump piston, and velocity of its discharge in feet per
second. *
Ap2*r __ J ^3000 S^
Indicated. = ff, and ^;—- — = A.
33000 • P««r
Britisli A^dzniraltsr l^vkle,^ Nominal. — — or^— ^=iff.
33000 6000
French. — {Force de Cheval.) 1.695 D' L r = H*. D and L in metert
.Illdstration.— Assume a diameter of cylinder of .254 meters, with a stroke of
piston of .3 meters and 250 revolution^ per minute.
1.695 X 254* X .3 X 250 = 8. 18 H>.
A Force de Cheval = 4500 kilometers per minute = 32 549 foot-lbs. = .987 57 ff.
One IP = 1.0139 Force de Oietaux.
Compound Indicated. A L r i^, i hyp. log. R"— M .000053 = ff-
L representing length of stroke in feet^ R" combined ratio of both cylinders, and b
back pressure.
Illustration. — Assume area of cylinder 3 sq. ins., stroke 6 feet, one stfoke of
piston, and steam 60 lbs. per sq. inch, cut offal .25.
A = 3 «^. ini., L = efset, n = i stroke, P i= 60 »#., R" = 5.969, d as 3 ift*
per sq. inch, and r = . 5, and 1 -f- **yp ^og R" = 1 -f- 1.7865.
Then 3 X 6 X 5 X f— g- X 1 + 1.7865 — 3) X .00005322 9 x laosa X 2.7865— J
X .000053 = .0132 IP, wnich, X 2 for t revolution, = .0264 IP per rewdmUon.
To Compute Volume of AVater required to "be Kvapo-
rated in aai JSngine.
Rule.— Multiply voliiine of steam expended in cylinder and 8tMtii'K*be8ta
by twice number of revolutions, and multiply product by density of steam
ftt given pressure.
* t For r«f«rtao* aea irt aad 3d roe(-pot« on prtvloiif (ag*.
1
STBiiM-SNQlNB. 735
BzAMpLi.— Wbal Tolume of water will m eagin* roquln* U) be evaporated per
revulution, diam. of cylinder being 70 ins., stroke of pislun 10 feet, and pressure of
sloam 34 lb& per eq. iucb, including Htntospbere, cut off at .5 of stroke ?
Area of cylinder = 3848, 5 im. ioXi»-!-as=6o in*., 6ox 3848- 5 = »39 9«o <^^^ *"*
Add, for clearance at one end, volume of nozzle, steam-chest, et£., 17 317 cube int.
Then 230010 + 17 317 -j- 1728 X 2 = 287.3 cube feet, which, x .001 336, density of
flteam at 34 lbs. presdure {9^ Noi« a), =^.3838 c^lteftet.
NoTB L^Thia refers to expenditure of steam alone; in practice, howeyer, a large
quantity of water '' foaming," differiog in diQ'Qrent c^ses, is carried into cylinder in
combination with the steam ; to which is to be added loss by leaks, gauges, etc.
3. — Volume of steam is readily computed by aid of table, pp. 708-0. Thus, den-
sity or weight of one cube foot of steatn at above pressure = .0835 lbs. Hence, as
62.5 Vbi, : X cube foot :: .0835 Ihi. : .001 336 cubefboL
To Compute "Voluxxie or Circulating "Water reqLuired by
'"^T* '^^ ~ = V T represetUing temperature qf sUam upon entering the con-
denser^ i, f^ and V lemperaturet of feed watery of water of condensation discharged,
and of circtUaiing water, all in degrees.
Illustration. — Assume exhaust steam at 8 lb& per sq. inch, temperatures of dis-
charge loo^, feed water i2o<^, and sea-water 75^
Temperature at 8 lb& pressure = 183O. "'4-t-'3 j^ 3—^^ _ ^^^^ times.
To Compute ^Volume of FIomt through an Ix^jeotion i*ipe.
Rule. — Multiply square root of product, of 64.33 ^^^ depth of centre of
opening into condenser, from surface of external water, added to height of a
column of water due to vacuum in condenser, all in feet, bv area of opening
in sq. ins. -j and .6 product, divided by 3.4 ({44 -r 60) will give volume in
cube feet per minute,
ExAMPLB.— Diameter of an ii^ection pipe is 5.375 ins., height of external water
above condenser 6.13 feet, and vacuum 24.45 ins. ; what is volume of dow per min.?
2^ J e Ids
Area of 5.375 in& = 32.69 1n&, c = .6. Vacuum -^^^ ^ = x3 lb& ; xa X 0.34
2.04
feet (sea- water) = 26. 88 feet, and 26. 88 -f 6. 13 = 33. i fset.
Then2^^ 33 X33.XX 22.69 X. 6^628^^
2.4 3.4 '^
To Coxnpute A-rea of an I»vJ option Pip9«
Rule. — Ascertain volume of water required by rule, page 706, in cube ins.
per second, mnltiply it by numb^ of volumes of water required for con-
densation, by rule, page 707, divide it bv velocity due to now in feet per
second, and again by 12, and quotient will give area in sq. ins.
EsLAMPUk—An engine having a cylinder 70 ins. diam., stroke of pisUm ro feet,
revolutions per minute 15, and steam 19.3 lbs., mercurial gauge cut off at .5; what
should be area of its injection pipe at its maximum operation?
Volume of cylinder 267.25 cube feet, cut off at . 5 = 133.625 ins.
Density of steam at 34 Iba (19.1 4- 14.7) = .001' 336. Velocity of flow of iidected
water (cfMnpated (hwa vacoum ana elevation of condensing water) 33 feet per second
Then 133.635 X 15 X 3 X 17*8 -5- 60 = 115 452 cube ins. steam per secondj and
115 453 X .ooi 336 ?= X54-34 cube ins. water per second.
Maximum volume of water required to condense steam is about 70 times volume
of that evaporated, which only occurs in the Gulf of Mexico; ordinary requirement
is about 40 times.
«54-a4 + «i-59 (= 7-5 PW cent, for leakage of valves, etc.) = 165.83, which, X TC
3 ti 6ot.i cube ins., and xx 608. x -r- 33 x 12 =: &9.3i iq. ins.
73^
STEAM-fiNG^INE.
Coefficient of velocity for flow under like conditions ::= .6; hence, 29.31 -r-. 6 =
48.85 iq. ins.
NoTK.— This is required capacity for one pipe. It is proper and customary that
there should be two pipes, to meet contingency of operation of one being arrested.
To Compute .A.rea. of &. Feed Pump. {Sea-tocUer.)
Rule. — Divide volume of water required in cube ins. by number of single
strokes of piston, both per minute, and divide quotient by stroke of pump, in
ins. ; multiply this quotient by 6 (for waste, leaks, "running up," etc.), and
product will give area of pump in sq. ins. /
ExAMPLK. — Assume volume to be 5 cube feet and revolutions of engine 15 per
minute, with a stroke of pump of 3.5 feet
5 X 1728
15
= 576, which -7- 3. 5 X 12 = 13.72, and 13.72X6 = 82.32 sq. int.
NoTB.— In fresh water, this proportion may be reduced one half
STEAM- INJECTOR. 'Wm. Sellers & Co., Incorporated,
Self-acting Injector, 1887, Class iV, Improved.
"Volume of Water l>ischarged per Hour.
No.
F
60
Cub. feet.
4-3
57
5-4
89
6.5
129
7-5
172
Pressure of Steam in Lbs.
90
Cub. feet.
67
107
»54
206
Tligltest admissib
120
180
Cub. feet.
75
121
176
234
' Cub. feet.
69
137
199
265
No.
Pressure of Steam in Lbs.
60
8.5
9-5
10-5
"•5
Cab. feet.
221
276
338
405
90
Cob. feet
265
332
407
446
120
tSo
Cab. feet.
301
376
460
55>
c temperature of water supply at 120 lbs. steam, 138^.
Cab. feet
340
425
520
623
Minimum capacity, 36^ to 40^ of maximum.
To Compute Size of* Ix\Ieotor re<iuirecl.
One H^ per hour will require from 15 to 40 lbs. of water per hour, accord-
ing to character of engine.
When the lbs. of coal burned per hour can be ascertained, divide them by
7.5, and quotient will give the volume of water in cube feet per hour.
When the area of grate-surface is known, multiply it by i.6 for IP.
In case of plain cylindrical boilers, divide the number of sq. feet of heat-
ing-surface by 10 for the IP. In case of flue boilers, divide by la, and with
multi-tubular boilers, by 15, for the nominal H*.
To Compute "Volume of* Injeotlori "Water required. x>er
IH? per liovir.
Operation. — Assame leinperatiire of water 80°, and of condensation xtxP. Vol-
ume of cylinder per IIP as per formula, pnge 716, and illustration, page 717, = 3.76
feet per minute.
Then, as per rule page 707,
1 146. 1 — 100
100— r 80
2.76 X 52-3X62.5
=:: 52. 3 cube ins. per cube foot ofstecun.
1728
= 5.22 U)8.y which, X 60, = 313.2 lbs.
To Compute Net "Volume of Feed. "^Vater required. x>ex*
in* per ilHLour.
Op£ration. —Assume elements of formula, page 716, and illustration, page 7x7.
Then. 1154 x 2.76 X 60 = 19.11 lbs.
Feed Pipes, — Vv z= diameter for small, and — Vu, for large puiaps.
d representing diameter qf plunger in ins., and o its velocity infaHper
STKAM:-£NGIN£.
737
Results of Operations of Steaxn-engixies. {D. K. Clark.)
OovDiitraie Ekodik.
8IN0LB.
Corliss, Saltaire
Pumping, CrossDess
" East London...
Snlzer, GorlisB valves. . ■ • .
Superheated, Hira
COMPOUND.
JEWer&Co {^^.[^kited
J*^w«>d {s^utsralir-.::::::
Donkin {j^teit".r?:
American, Woolf { t^'t^^^l^^f J"; ; ; ; ;
** j^'^^^lbSth?'."^^!!;;::;
NON-CONDENSING.
Marshall, Sons, ft Co
Davey, Paxman, ft Co
liOGomotive ''Great Britain"
it
((
ti
AeUal
Steam
Coal
Initial
Ratio of per
Prewura
Expao-
IH'ai
/£.
at
sion.
cut-off.
cnt-off.
Lbs.
Lba.
Lbt.
5-2
1451
2.5
34.5
6.07
14.27
2.2
46
3.62
12.92
'" "■
23-25
10
—
3-3
1°
4.132
"^
^~
60
1.85
1.852
14-45
14.85
i.6z
56
4.01
IO-94
1334
2.14
85. s
2.486
13.18
—
50-5
3.221
1387
—
—
2.31
actual
5.63
23.21
~
90
3.77
9.19
2a 71
—
90
4.8
16.87
.^
76
5
M-93
—
73
1-45
31-36
^
102
2.94
21.24
—
87
Steam
per IIF
per hour,
Lb*.
17
18
4
7
20.73
19.6
18.62
22.51
15-37
14.1
25-9
29.6
3"-36
21.24
Fraotioal Sfficieno^r of Steaxn-engines. Initial Volume = i.
CrUKDIHS.
« it
00NDEN8INO.
Single cylinder, jacketed. . .
Single cylinder
** " superheated
Ck>mpoand, Jacketed, Re-
ceiver....
* From boiler.
4^
6
4
4
6
SLg
GO
Lbe.
19.5
24
18.5
»9
Cylihdkbs.
Compound, jacketed, Woolf
Compound, Woolf.
NON-CONDENBINO.
Single cylinder,t jacketed.
Single cylinder, t
Ji3 .
C
&
ID
7
4
3
t 70 lbt. preMtire.
X 90 Iba. prsMure.
Standard Operation of a Portable Engine.
Grate 5.5
Heating surface 220
Coal per H* per hour. . . . 6.25 lb&
»» ** sq. foot of grate. 9
hour 50
sq. feet
t4 it
((
((
* M
s.
09
Lbe.
20.5
33
24
SI
Ibft
Water evaporated from )
and at 212° per hour. } • • • • 45o
" " per H* per hour 62.5
" " " sq. foot of I a „ u
grate J "*
<t
Ratio of heating surfitce of grate 40 to z.
MIXTURE OF AIR AND STEAM.
Water contains a portion of air or other uncondensable gaseous matter, and when
ft is converted into steam, this air is mixed with it, and when steam is condensed
It is left in a gaseous state. If means were not taken to remove this air or gaseoiii
matter fV'om condenser of a steam-engine, it would fill it and cylinder, and obstruct
their operation j but, notwithstanding the ordinavy means of removing il (hy air-
pump), a certain quantity of it always remains in condenser.
90 volumes of water absorb z volume of air.
3Q*
73«
STBAM-BNGINB.
s
It
g
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«
3 .-
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s
STE AM-KNQINK.— BOILEB. 7 39
BOIUBB.,
Its efficiency is determined by proportional quantity of heat of com-
bustion of fuel used, which it applies to the conversion of water into*
steam, or it may be determined by weight of water evaporated per lb.
of fuel.
Id foUowiDg reaalls and oomputatiooB, water ia held to be evaporated flrom atand-
ard temperature of 312°.
Proportion of surplus air, in operation of a furnace, in excess of that which is
chemically required for combustion of the fuel, is diminished as rate of combustion
is increased; and this diminution is one of the causes why the temperature in a
furnace is increased with rapidity of combustion.
When combustion is rapid, some air should be introduced in a furnace
above the grates, in order the better to consume the gases evolved.
Natural Draitght,
Grate (Coat) should have a surface area of i s^. foot for a combustion of
15 lbs. of coal per hour, length not to exceed 1.5 tunes width of furnace, and
set at an inclination toward bridge-wall of i to 1.5 ins. in every foot of length.
When, however, rate of combustion is not high, in oonsequence of low ve-
locity of draught of furnace, or fuel being insuflicient, this proportion of area
must be increased to one sq. foot for every la lbs. of fuel.
Width of bars the least practicable, spaces between them being from .5 to
.75 of an inch, according to fuel used. Anthracite requirin£f less space than
bituminous. Short grates are most economical in combustion, but generate
steam less rapidly than long.
Level of grate under a plain cylindrical boiler gires best effect with a fire
5 ins. deep, when grate is but 7.5 ins. from lowest point.
Depth, Cast-iron, .6 square root of length in ins.
{Wood), their area should be 1.25 to 1.4 that for coal.
Autonialic (Vicar's). — Its operation effects increased rapidity In firing
and more effective evaporation.
Ath-pit — Transverse area of it, for a combustion of 15 lbs. of coal per
hour, 2 to .25 area of grate surface for bituminous coal, and .25 to .3 for
anthracite. Or 15 to 20 ins. in depth for a width of furnace of 42 ins.
Furnace or Combustion Chamber. — (jDoal) Volume of it from 2.75 to 3 cube
feet per sq. foot of grate smrfiice. ( Wood) 4.6 to 5 cube feet.
The hif^her the rate of combustion the greater the volume, bituminous
coal requiring more than anthracite. Velocity of current of air entering
%n ash-pit may be estimated at 12 feet per second.
Volume of air and smoke (br each cube Foot of water converted into steam Is,
flrora coal, 1780 to 1950 cube feet, and for wood, 3900.
Rate of Combustion, •^ In lbs. of coal per sq. foot of grate per hour.
Cornish i^m^r«, slowest, 4 ; ordinary, 10. Stationary^ 12 to 16. Marine^
16 to 24. Quickest: complete combustion of dry coal, 20 to 23 ; of caking
coal, 24 to 27 ; Blast or Fan and Locomotivey 40 to 120.
Bridge-wall (CcUorimeter). — Cross-section of an area of 1.2 to 1.6 sq. ins.
for each lb. of bituminous coal consumed per hour, or from 18 to 24 sq. ins*
for each sq. foot of grate, for a combustion of 15 lbs. of coal per hour.
Temperature of a furnace is assumed to range from 1500° to 2000% and
volume of air required for combustion of i lb. of bituminous coal, together
with products of combustion, is 154.81 cube ftet, which, when exposed to
above temperatures, makes volume of heated air at bridge-w^all from 6oq to
750 cube feet for each lb. of coat constuned upon gtate.
740
STBAM-ENGINE. — BOILER.
Hence, at a velocity of draught of about 12 feet per second, area at bridge-
wall, required to admit of this volume being passed off in an hour, is 2 to 2.5
sq. his., and proportionately for increased velocity, but in practice it may be
X.2 to 1.6 ins.
When 9o lbs. of coal per hour are consumed upon a sq. foot of grate, 20 x 1.2 or
1.6 = 24 or 32 sq. ins. are required, and in a like proportion for other quantitiea
Or, When area of flues is determined upon, and area over bridge-wall is
required, it should be taken at from .7 to .8 area of lower flues for a natural
draught, and from .5 to .6 for a blast.
When one half of tubes were closed in a fire-tubular marine boiler, the evapora-
tion per lb. of coal was reduced but 1.5 per cent
Firing, — Coal of a depth up to 12 ins. is more efi^ective than at a less
depth. Admission of air above the grate increases evax}orative efiect^ but
diminishes the rapidity of it.
Air admitted at bridge-wall effects a better result than when admitted at
door, and when in small volumes, and in streams or currents, it arrests or pre-
vents smoke. It may be admitted by an area of 4 sq. ins. per sq. foot of grate.
Combustion is the most complete with firings or charges at intervals of
from 15 to 20 minutes.
With a fuel economizer (Green's) an increased evaporative effect of 9 per
cent, has been obtained.
When external flues of a Lancashire boiler were closed, evaporative power was
slightly increased, but evaporative efficiency was decreased; and when 25 per cenk
of like surface in setting of a plain cylindrical boiler was cut off. evaporation was
reduced but 1.5 per cent When temperature at base of chimney was 630*^, with a
fire 12 ina in depth, it was decreased to 556^^ with one 9 ina in depth, and to 539O
with one 6 in&
High wind increases evaporative effect of a furnace.
Stationary or Land» — Set at an inclination downward of .5 inch in 10 fe^
Smoke Preventing.— A test of C. Wye Williams's design of preventing smoke, at
Newcastle, 1857, as reported by Messrs. Longridge, Armstrong, and Richardson,
gave an increased evaporative effect with the '* practical prevention of smoke.'*
Hence it was concluded, ** That by an easy method of firing, combined with a due
admission of air in front of furnace, and a proper arrangement of grate, emission
of smoke may be effectually prevented in ordinary marine multi-tubular boilers,
with suitable coals. 2d. That prevention of smoke increases economic value of fuel
and evaporative power of boiler. 3d. That coals fV'om the Hartley district have an
evaporative power ftiUy equal to that of the best Welsh steam-coals."
Heating Surfaoes.
Marine {Sea-^ater), — Grate and heating surfaces should be increased
about x>7 over that for fresh water.
Relative Value of Heating Surfaces,
Horizontal beneath the flame =:.z
Tubes and flues =.56
Horizontal surfoce above the flame = t
Vertical = .5
I^inixxiUTxi Voluxnes of Fuel Consumed per Sq. Foot oiT
Cerate per Hour, for given Surface-ratios. (D.K.Clark,)
Dbsckiption of
BOILBR.
Stationary.
Aftarine ..•■••••••.
Portable
Locomotive (coal) .
(coke).
((
St
irface-ratios of 1
Heating; !
Surface to Grate.
10
15
20
30
40
SO
60
75
90
Lba.
Lba.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lba.
•7
1-7
3
6.8
Z2.I
Z8.9
26
—
—
•7
1.6
2.8
6.3
z.8
ZZ.3
175
24
—
—
.3
•4
.8-
3a
5
—
—
—
•3
•7
«.3
2-9
5-2
8.1
'i'7
18.3
a6.3
•4
z
Z.8
4
7
zz
z6
25
36
100
Lb*.
3a- S
44
At extreme consumption of fUel (120 lba) coke will withstand disturbing effect
^f a blast better than coal.
STB AM-EKGIKE. — BOILBB. 74 1
A scale of sediment one sixteenth of an inch thick will effect a loss of 14.7 per
<ent. of Aiel.
One sq. foot of ^re surface is held to be as effective as three of heating.
Relation of Gyrate, Heating Surface, and I^uel.
When Grate and Heating Surface are constant, greater the weight of fuel
consumed per hour, greater the voiurae of water evaporated ; but £e volume
is in a decreased proportion to fuel consumed.
In treating of relations of grate, surface, and fUel, D. K. Clark, in his valuable
treatise, submits, that in 1852 he investigated the question of evaporative perform-
ance of locomotive-boilers, using coke; and he deduced fl*om them, that, assuming
a constant eflQciency of ftiel, or proportion of water evaporated to fuel, evaporative
effect, or volume of water which a boiler evaporates per hour, decreases directly as
grate-area is increased; that is to say, larger the grate, less the evaporation of water,
at same rate of efficiency' of fuel, even with same heating surface.
3d. That evaporative effect incretue^ directly as square of heating surface, with
same area of grate and efficiency of fuel.
3d. Necessary heating surface increases directly as square root of effect — viz., for
four times effect, with same effloiency, twice heating surface only is required.
4th. Necessary heating surface increases directly as square root of grate, with same
efficiency; that is, for Instance, if grate is enlarged to four times its first area, twice
beating surface would be required, and would be sufficient, to evaporate same vol-
ume of water per hour with same efficiency of fuel.
Result of 40 experiments with a stationary boiler (fresh water), with an
evaporation of 9 lbs. water per lb. of fuel consumed, the coefficient .002 22
was deduced.
Hence, (—J .00222 = W. W representing volume of toater in cube feet^ and g
mnd h areas of grate and heating surfaces in sq. feet.
Illustration.— Assume a heating sur&ce of 90 feet, and a grate of 3; what will
be the evaporation?
Then 90-r- 3 x .002 22 = 1.998 cube feet.
NoTB.— A Galloway stationary boiler, with a ratio of grate area of 34.3 and a con-
sumption of 21.8 Iba coal per hour^ evaporated 2.9 cube feet of water per sq. foot of
grate. Hence the coefficient in this case would be .002 466.
To Conapiite .A^Teas of GH?ate and. Heating Surfaces,
"Volume of Water, and 'Weight of JFuel.
For a Temperature 0^281°, or Fi'essure of 50 lbs. per Sq. Inch.
To Compute "freight of Fuel.
When Water per Sq, Foot of Grate per Hour and Surface Ratio are Given.
g =:F, and a}R» = (E — C)F.
iLLUflTBAnoir. — Assume elements as preceding.
goo — .Qg X 50'
10
15, and .02 X 50' = ( 10) X 15 = sa
To Compute Ratio of Heating Surface to A.rea of Q rate,
and to Sfibct a Q-iven. Evaporation.
When Water and Fuel per Sq. Foot of Grate are Given. ^ —
*"'=R
X
W representing water evaporated per sq. foot of grate^ and F Jiiel consumed, both
in UfS. per hour. C and x specific constants for each type of boiler, and R (h-r-g)
ratio of heating surface to grate.
ILLDSTIU.TIOM.— Assume W = 200, G s 10, F = 15, and a; = .02.
/200— 10X15 . 200 — .02X50' J /(»3-33 — io)XiS
a/—- . ^ = 50; i_ = is; and ./5-^i-££ '^ ^ = 5a
V •<» «o V .02 ^
742 STEAM-ENGINE. — BOILEB.
Wkm ^fSdene^ of Fad and Fud eotuumed per 8q. Foot of Grate pef
ffour core gwen, •=- = E or e^jg^^Mincy ofjwl or weight of umter evaporated per Uk
"f^ y<i^=a
To Compute ITuel tliat may be oonsumed per Sq.. yoot
or Gt-rate per Hour, oorrespoudiris to a O-iveix ICflA—
cieiicy.
When Efficiency of Fuel^ that w, Weight of Water evaporcUed per Lb. qf
Fuel, and the Surface Rcitio, are given,
. C 4- = E. and ^ F.
Illustration. —Aasame elemente as preceding.
.o2X5o'H->oXi5 .02X50' .„^ 02X50' „,.
1 — ! ^ = 13.33, xoH =:i3.33,and ~ — szislbi.
15 15 13.33 — 10
Combtution qfCoai per sq. foot otgrB.io.'—NaturcU Draughty froni 20 to 25 ]bs. can
be consumed per hour —Steam-jet^ 30 lbs., and Exhaust-blast 65 to 80 lb&
From Results of Experimonts upon Marine Boilers, see Manual of D. E. Clark,
page 808 , he deduced the following formula, As applicable (o all surface ratios in
such boilers.
Newcastle 021 56 B» + 9.71 F, and for Wigan 01 R= -f jays F = W in Ufs.
And the general formolas he deduced fh>m ait the varioos experiments are as
followa
From and aJt ^i79
portable. 008 R«+8.6 F = W
Stationary... .o222R'-|-9.56 F = W
Marine oi6R« + io.25 F = W.
Locomotive, coal, 009 R* + 9-7 ^ = W.
Locomotive, coke 0178 R^ -f 7.94 F = W,
As the maximum evaporative power of fuel is a fixed quantity, the preceding
formulas are not fUUy applicable in minimum rates of its consumption and evi^K)-
rative quality.
With coal and coke the limits of evaporative efficiency may be taken respectively
at 12.5 and 12 lbs. water fh>m and at 212°.
Illustration 1. — Assume a marine flre-tubular boiler with a surfkce ratio of heat-
ing surface to grate of 30 and a consumption of coal of 15 lbs. per aq. foot of grate
per hour, what will be its evaporation per sq foot of grate?
016 X 3o«-|- 10.25 X IS = 168.15 '*«
2 Assume a like boiler, using flreah water, to have a ratio of heating sarfkce to
grate of 30 and an evaporation of 165 lbs. water per sq. foot of grate per hour, what
would be consumption of coal per sq. foot of grate per hour?
165— .016X30' ^,x.
=2 14.69 W«.
10.25
Tube Surface (Iron) per lb. of coal 1.58, per sq. foot of grate 32, and per I^ 4.2}
sq. feet.
Locomotive Boiler has fVom 60 to 90 sq. feet per fbot of grate, and coosamea 6$
Ibe. coal per sq. foot per hour.
Evaporative Capacitor oi* Tubes of Varying X^enstlx.
By Temperatures. {A J. Dutton, Eng. -in- Chief R. N,)
Diameter, external^ 2.75 ins. Length, 6 feet 8 ins. Combustion Chamber, 1644O
In Tubes.
2 ins. . .14260
3 " -..1405°
4 " ...1412°
5 infl...i3g8<'
8 ina. ..1410O
32 ins.. .11980
6 " ...1406O
14 " ...1368O
44 " ...1106O
-> " ...1400°
2r» " ...12950
56 " ...iois°
68 ins 9260
80 ** 887O
Connection . 7830
STKAU-JENaiNB. — BOILEB.
743
B.e0ult« of Op«v»tioii ol* Soil«rs Tiii<i«v "Vsivyitig Propor-
tions of Orate, A.refi, and Uenetb of Heating Surface,
X>rauglit of S^uroaoe* and. Rate of Coxnbnetion.
DiaCKIFTIOIV.
Fire- tabular,
Agricultural and Hoisting
Locomotive
Ecgliab.'
((
(i
Marine < ....
" ' ....
" 3.!!!
stationary 4.
(i
Area of
Grate.
Heating
Surface.
Grate to
Heating
Surface.
Coalper
Sq.F^t
of Orate
per Hour.
Evaporation of
Water from 213"
per eq. ft. per lb.
of grate, or Coal.
FCSL.
flq.Feet.
Sq.Feet.
Ratio.
Lbe.
Lbe.
Lbe.
4-7
158
1^
'3«
119
9-33
Welsh.
3-2
aao
69
12. 8
151
11.83
{fe''
9635
818
36.7
30.86
327
10.6
51
38
375
10.47
10.5
788
75
45
419
11.04
I<x6
1056
100
»57
1 401
ia4i
22
748
34
24.3
265
10.7
18
749
41.6
23.6
264
11.2
10.3
9«5
50
41-25
468
11.36
ia3
508
49-3
27.63
309.8
"•54
Lanc'r
ia8
151. 2
«4
28.87
205
7.39
Anth'e
31.S
945
30
«93-7
10.17
Welsh.
31-5
767
24.4
14
141.4
10. 1
(i
X New Castle.
2 and 4 Wigan.
* Eflbet of rednelng tbe tabe.«aH!Kces was tried b;
Date diagpnal rows, so that tbs tube sarfaee was
deep were as follows I
3 Experimented at New Yoriu
stopping one half the number of tubes in altera
tvoea 206.5 "l* f<B«t. The results with flres 13 ins.
Coal per sq. foot of grate per hour ,
Water from 212* per lb. of coal . . . ,
Smoke per hour, ^ery light
Tubes open.
. 35 lbs.
. 12.41 "
1 . 8.8 minutes.
Tubes half closed.
34 lbs.
12.23 "
8 minutes.
ICvaporati\re XCfieots of Soilers for Different Rates of
Cozulmstion, and Su.rfaoe Ratios. {D K. Clark.)
Water fi-om and at 312° per Hour,
SurfUoe Ratio 30.
Foelper
Sq. Foot
of^ Grate
per Hour.
Statiovabt.
Water
Masxmk.
Water
Fosi
W(
per
Sq.^KH.
per lb.
of Coal.
per
Sq. foot.
per lb.
of Coal.
per
Sq. foot.
JLbe.
Lbs.
Lbe.
LU.
Lba.
Lbs.
XO
116
IX.6
»>7
IJ.7
93
15
163
X0.9
168
IX.2
136
30
211
X0.6
219
10.9
179
30
307
ia3
322
xa7
265
«5
20
30
40
50
Lbs.
9-3
9
1.8
Surface Ratio GO.
per lb.
of Coal.
LoCOMOTtW.
Coal.
Water
Coke.
Water
per
Sq.Foot.
per lb.
of Coal.
per
Sq. foot.
per lb.
of Coal.
Lbs.
Lbs.
Lbs.
Lbs.
105
154
203
IO-5
X0.3
XO.X
95
«35
»75
9-5
1.7
299
XO
354
8S
X87
X9.S
»87.5
12.5
M9
9.9
168
XX.2
x«4
247
12.3
248
X2.5
X92
9.6
217
xa'9
203
342
11.4
348
XI.6
278
9-3
314
xa4
283
438
xa9
450
".3
364
9.x
4"
xa3
362
534
xa7
552
XX
450
9
508
xax
442
X0.9
X0.3
9-4
Sur
Water.
face
30
Rati
Fuel per
40
0 TO
Sq.Foot
50
•
(ofOrati
60
» per Ho
75
ar in Lbi
90
1.
xoo
LocoMomrK, coal . .
** " ..
" coke".
■ •
Persq foot.
" lb. coal.
*' sq. foot.
<< lb. coal.
Lba.
342
338
"•3
Lba.
439
XX
418
10.4
Lbs.
536
497
9-9
Lha.
633
xol7
576^
9.6
Lbs.
778
695
9-3
Lba.
927
ia3
815
9
Lbt.
xo&o
xa2
804
8.9
When a beater is used, and temperature of feed-water is raised above that ob-
taioed in a condensing engine, the proporiioQS of surC^^ ma^ be ooireeponuin^
vQcmced*
744
STSAM-ENGINB. — BOILER.
Hesx<s of Operation of varioixti Deelsnci of Soilexr, tiia«
d.er varying; Proportions of d-rate. Calorimeter, ^rea
and. Uengtli of ZleatinK Snrfiusey I^ranslit, Firing, and
Rate of Combustion.
Stationart.
Area
of
Gnte.
Heat.
iog
Sarface.
Grate
to
Heating
Soriaoe.
Lancashire double )
internal and ex- >
temal flued ' . . . )
tt (4 2
Galloway verticals
water-tubular', i
u i( a
Fairbaim' V.
Sq.Ft.
2<X5
21
21
3'-5
2a 5
2a z
14.3
Sq.Ft.
6l3
767
719
719
1017
607
377-5
Ratio.
39.8
36-5
23.8
34-3
49-5
30-3
36.8
French*
Cylindrical flueds. . .
Circuit of
HeatinfT
Surface.
1^
u
H 0
CoaTper
Su. Fbot
ofGrate
per Hour.
Water Evaporated
horn 312* per Sq. Foot
per lb. of of Grata
CoaL per Hour.
Feet.
0
Lba.
Lbe.
Lba.
79
5"
1535
8.3a
1354
80
505
21. 5
za88
3044
79
505
22.7
xo-77
3X3 4
80
630
18.3
zai7
1634
56
387
510
293
15-27
16.43
7-43
8.67
8.13
9.08
«3S
«33,
59*
Marine.
Horizontal fire- tub.'
ti t( 3
it it a
M tt
tt ft
ti ft
li ft
(C Wya WilUama)
it it
t( it
tt tt
M tt
tt tt
tt ft
At Pressure of Atmosphere,
3
3
za3
508
49-3
.—
—
27-5
za3
508
49-3
—
—
41.25
ia3
303
30
—
—
24
38! 5
749
3?
—
—
3X
749
36.3
—
^
3Z.X5
28.5
749
36.3
—
—
«9
15- 5
749
48.3
— '
600
37-4
23
749
34
—
600
Z7.27
4a
749
Z7.6
—
—
z6
za8
150
«3-9
8.5
—
za90
27.58
4-32
147
34
8.5
—
11.93 338?
IX. 36 469 1
Z2.33 368 9
zo 183 »
8.94 164 ">
IZ.13 335"
ia63 398
ZZ.7 [ 903 n
9.65 154 «3
a95 88 ^
7.34 40 M
' At Wigan, 1866-68, height of ohimneys zoo feet 3 Navy-
yard, Washington, U. S., chimney 61 feet. 4 At pressure of atmosphere, fires za insL
deep, at 40 lbs. pressure, evaporation was reduced 12 per cent 5 Bituminoue coal&
6 Antiirarite, at pressure of 6. 5 lbs. above atmosphere. 7 Fires 14 ins. deep, air ad-
mitted through furnace - doom 8 Ditto do., Jet blast 9 Half tubes closed ap.
>o Air through grate only. " Air through grate and door, no smoke. *' One open>
ing in door, temp. 635°, with two 63^^, with four 638^^, and with six 6oo<\ '3 Long
grates, air spaces (Ully open, no smoka M One fUmaoe, anthracite cool, 5 ins. deep.
iDrauglit.
Draught of Furnace, — Volume of gas varied directly as its absolute (em-
Eerature, and draught is best when absolute temperature of gas in chimney
; to that of external air as 25 to 12.
T-I-461.20
I Trial in France.
32O + 461.2O v
V, V, and V r^prenemiing abtohUe temperotwrtM at T
or temperature given^ and at 32^, in degrees and volume ofjumaee gat at tempera-
ture T in cube feet
Illustration.— Assume temperature of ftimace or T = zsoo^, and Z3 Ib& air per
lb. of IVieL
Z500 -t-4 1.2 _ g ^^ as 150 cube feet is volume of gasper U>. ofjiul at la
320-f"46i.2"
lbs. supply of air y 150 X 3- 98 = 597 cube feet
Vf V t
— =;■ SI C. W representing weight of fuel consumed inj^maoe per second in f&t.,
V volume t^air at 120 supplied per lb. of fuel in cuhefset^ t absolute temperature 0}
gas discharged bjf chimney in degrees^ a area of chimney in sq.fset, and C velocity qf
'"irent in diimney in feet per second.
STEAM-ENGINE. — ^BOILEB.
745
IixinsTRATioM. ^Assame W = . i6, v = 150, t = 1000 o, and ass.
.16x150X1000 34000
V
5X493-2°
3466
^9.73 feet
— .084 to .087 = D. D rqpraeiUing weight of a cube foot of gat discharged b§
dUmmey, in ibt, Iujobolatiov, ^^— x .086 = .0434 lb,
' xooo
— ( I + ^+ ^) = ^ ^ reprewntttinr a coegMent ofretiUanee andfiridioH of
uir through grate and fiUt^* f coefficUnt ofjriction of gas through flues and over
Booty surfaces A I length of flues and chimney ^ m hydraulic mean d^th,t and H height
^ chimney^ ailinfuL
Illubtration I.— Afeume C = 9.73, { = 60, and nt = .73, aU infeeL
P^(i + x3-^ ■ )=z?-'«Xi4 = 2o.6/eet ■ — j- = W.
64-33 V 1^ I 64.33 ««
a.— Assume preceding elementa 9-73 X 5 X 493-g° = . ,6 ».
150 X 1000
Hf Jl«i» H M 9IW5I*. y(H3jr-5-iH-G+:^=C
iLLnsTRATioN. — Assome precedi ng elementa V3a6x64.33-7-i4 = 9. 73 fed,
.192 x pressure in Iba per sq. foot= A«ad in ins. of water.
Temperature at base of smoke-pipe or chimney^ or termination of flues or
tub^ is estimated at 500° ; and baBe of chimney, or its ailorimetery should
have an area of 1.3 to 1.6 sq. ins. for every lb. of coal consumed per honr.
With tubes of small diameter, compared to their length, this proportion may
be reduced to x and 1.2 ins.
Admission of air behind a bridge-wall increases temperature of the gases,
but it must be at a point where their temperature is not below 800°.
I^oss of* PreasTire by iricw of Air in Pipes.
Length 3380 Feet^ or xooo Meters,
Velocity at EDtnnea of
LiamtUr «f Htm in Itu,
Fipo.
Foot Meter
4 1
6 1 8 1 10 1 x3 1
«4
per Second.
per Seeond.
Jjota of Preaeare In Lbi. per Sq. Inch.
3.38
X
"4
.076
•057
.057
.038
•038
6.56
a
•S^
•343
.25
.21
.172
•»53
9.84
3
I.183
.8
•593
•477
X
•343
13. X3
4
2.06
x-374
X.03
.84
.6
16.4
5
3.2 ^
3.x6
1.61
X.29
X.X
.923
X9.68
6
4.446
2.964
2.223
X.778
X.482
1.28
At Mount Cents Tunnel, the loss of pressure fVom 84 Iba per sq. inch, in a pipe
7.625 in& in diameter and i mile 15 yards in length, was but 3.5 per cent
Artificial Drauglit.
In production of draught in an ordinary marine boiler, from 20 to 33 per
cent, of total heat of combustion of fuel is expended.
Blast— By experiments of D. K. Clark and others it was deduced that tbe vacnura
in back connection is about .7 of blast pressure, and in the Aimace from .33 to .5
of that in back connection ; that rate of evaporation varies nearly as square root of
vacuum in back connection; that best proportions of chimney and passages thereto
are those which enable a given draught to be produced with greatest diameter of
blast- pipe; fbr the manifest reason, that the greater that diameter, the less tbe back-
pressure dfue to resistance of oriflce, and that these proportions are best at all rates
of expansion and speeds.
• Wbtch, In fnroMee coDtamioK from ao to 24 Ibe. co«l per m. foot of erete per boar, ie anigoed bf
Pcelet At 19. t Eetlmated by tame aothority et .oxs.
X Vor aifMreor dKslar flue !• .25 ita dlainetcr.
3»
74© STEAM-ENGINB*— DRAUGHT.— SAFETY VALVES.
Velocity of Drat^. Lodomotiife, 36.5 VH(T— Qst V. tl represenHn$
height ofdiimney or pipe in feet, T and t temperaturet of air at base and top of chim-
ney^ and V velocity in feet per second.
Sectional area of tubes within ferrules 2 grate.
*' " Of smoke-pipe , * 066 "
Area of blast-pipe (below base of smoke-pipe) 015 "
Volume of back connecttoD, < . 3 fget X Artea of gfate.
Height of smoke pipe 4 times its diameter.
i9t<airt^W<— Rings set above base of smoke-pipe, and shotild equally divide
the area; jets .06 to .1 inch in diameter, 3 ins. apart at centres.
A Steam-Jet, involving 50 per cent increased combustion of coal, produced
45 per cent, more evaporation' at nearly same evaporation per lb. of coaL
Fan Blowers. — See page 447.
Comparative Result of Experiments with a Steam -jet in a Matine Boiler^
with BUlmunom Cool, (NicoU and tynn^ Eng.)
Without Jet. With Jet.
Area of grate « « . . sq. feet 10.3 to. ^
Coal per sq. foot of grate per hour.... lbs 27.5 41.25
Water *' " " '* ....293.1 41937
" from 212° per lb. of coal " ......... it.9 11*36
Duration of smoke in an hour, ) ^,„„x«„
wyMgbt ;JmmBte8. x.i
Comparative ICffeot of Draught and filasts.
By late experiments in li^nglandy with boilers of two steamers, to deter-
mine relative effects of the different methods of combustioa, the results were,*
Natural draught i, Jet 1.25, and Blast z.6.
iriow or .A.ir. (HawksUy,)
In Cylindrical Pipes. 396^^=^, -|^ = A, 3x1^*^=0.
I^,and-X^^ = H>.
135 21200000
Tn Conduits of Various Sections, 7^^/%7 = ^i r^ • = *!
•^ V C « 633 006 a ^
, /a3h ^ Vah qh . V3Ct ,^ , w ». • ,.
796 . /TTT = ^' ~~zr = tz^i^^^ 2 = H». In which i «ch water is
'^ SJ G I 106 loo 07000000
taken as equivalent to a pressure of 5.2 lbs. per sq. inch for any passage.
V representing velocity in feet per sedond, h head of water in tfta., d diameter of
pWBy I length, and C perimeter, all in feet, a area of section in sq.feetf Q (Va) volume
ofair dischajrgedper second in cube feet, and IS horse-power.
^afet^r Valves.
Up to a pressure of 100 lbs. per sq. inch, area in sq. ins. equal product of
weight of water evaporated In lbs. per hour by .006.
Aet of Cmtffress (tT. A).— For boilers having flat or Atayed sffrfaces, 3d itia. for
every 500 sq. feet of effective beating iKirface; for cylindrical boilers, or cylindrical
flued, 24 sq. ina
Board of Trade, Eng.-^Tvro of .5 inch area per sq. foot of grata. Or, / — =r
diameter, <J representing area of grate in sq. int.
Locked 8afety-valve».^FAieci\vt heating surface^ less than 700 sq. feet, valve 2 in&
in diameter) leas than 1300, 3 ia& in diameter; less than 2000, 4 ins. in diameter;
less than 2500, 5 ins. in diameter; and above 2500, 6 ins. in diameter.
Or, (.05 6 -f- .005 S) ^j "^ =>= A^'^o of each cf two valves. 6 rqtresenUng jg. incht
r sq. foot of grate, and S sq. inch^per tq*fMtqfhecMn§ nnj/SMa
6TBAM-ENGINS. — FLUBS AND TUBES. 747
ItmsTRATiON.— Assume 6 = 50 sq. feet, 8=' 1600 sq. feet, and P = 80 Iba (m. g.)
Then, (.05 X 50 + . 005 X 1600) X Vxoo-i-80 =^ 3.5-1^8 X 11x8 = 11.73 »3- *»*•
Pipea.
AretM. .95 6 + 01 S ^/^r ■ ^ rqtreaefUing area of grate and S area qfh/eoA-
iug surface^ both in tq. /eet, and P pres9ure per mercuirial gauge in lbs.
(Copper), Thickness. Steam, . xas -| ^ ; Feed, .125 -f- —^ ; Blow (B«ttom
and Surface), .123 — ^ : Supply, i-\ ; Discharge, .i H j Feed, Suction,
9000 "^ ^' 200 SCO
d d
and Bilge discharge, 09 H , and Steam Blow - off, .05 H d representing
internal diam. of pipe, and p internal pressure per sq. inch in lbs.
Flanges. — Of brass, thickness 4 times that of pipe ; breadth, 2.35 times
diam. of bolt^ hcits^ diaiu. equal to and pitch 5 times thickness of iiauge.
For lower pressure or stress, pitch of bolts 6 tiroes.
B^ues and. Tubes.
Flues and Tubes, — Cross section, for 15 lbs. of coal consumed per hour,
an area of from .x8 to .2 area of grate, area being measurably inverse to
diameter, and directly increased with length. Thus, in Horizontal lobular
Boilers, area .18 to .3 area per sq. foot of grate, and in Vertical Tubular .33
to .25, area decreasing with their length, but not in proportion to reduction
of tem|)erature of the heated air, area at their termination being from .7
to .8 that of calorimeter or area immediately at bridge-wall.
Large flues absorb more heat than small, as both volame and intensity of heat is
greater with equal surfaces.
Tubes.— 8w face i sq. foot, if brass, and 1.33, if iron, for each lb. of coal
consumed per hour ; or 30 of brass and 27 of iron for each sq. foot of grate,
and 2.6 sq. feet of brass and 3.7 of iron per IH*.
Set in vertical rows, and spaces between them increased in width with
number of the rows.
Temperature of base of Chimney or Smoke-pipe, or termination of the
flues or tubes, is estimated at 500° ; and base of chimney, or its calorimeter,
with natural draught, should have an area of 1.33 sq. ins. for every lb. of
coal consumed per hour. With tubes of small diameter, compared to their
length, this proportion may be reduced to i and 1.2 ins.
When combustion in a furnace is very complete, the flues and tubes may
be shorter than when it is incomplete.
Evaporation.
I sq. foot of gnile surface, at a combustion of 15 lbs. coal per hour, will
evaporate 2.3 cube feet of salt water per hour.
A sq. foot of heating surface, at a like combustion of fuel, will evaporate
from 5 to 6.2 lbs. of salt water per hour ; and at a combustion of 40 lbs. coal
per hour (as upon Western rivers of U. S.), from 10 to 11 lbs. fresh water,
exclusive of that lost by being blown out from boilers.
13.8 to 17.2 sq. feet of surface will evaporate i cube foot of salt water per
hour, at a combustion of 15 lbs. coal per hour per sq. foot of grate.
Relative enraporating powers of Iron, Brass, and Copper are as i, i 32, and 1.56.
Nora— Boilers of Steamer Arctic, of N. Y., vertical tubular, having a surface of
33-5 to 1 of grate, consuming 13 Iba of coal per sq. foot of grate per hour, evapo-
rated 8.56 lbs. of salt water per lb. of ooal, locioding that lost by blowing out of
ffiti^rateq water.
74^ STSAM-£NGIN£. — ^SMOK.K-l'XPSS AND CHIMNEYS.
Water Surface.
At low evaporations, 3 sq. feet are required for each sq. foot of grate sui^
face, and at high evaporatiun 4 to 5 sq. feet.
Steam Hooni.
From 15 to 18 times volume ttiat there are cube feet of steam expended
for each single stroke of piston for 25 revolutions per minute, increasing
directly with their number. Or, .8 cube feet per ISP for a side-wheel ^igine,
and .65 for an ordinary and .55 for a fastr-running screw-propeller.
Space is required proportionate to volume of steam per stroke of piston
Thus, with like boilers, the space may be inversely as the pressures.
Steam-drums and steam-chimneys, by their height, add to the effect of
their volume, by furnishing space for water that is drawn up mechanically
by the current of steam, to gravitate before reaching the steam-pipe.
Grat^, — Area in sq. feet per lb. of coal per hour for following boilers.
Widths 1.5 diameter of furnace:
Ck)mi8h and Lancashire, slow
combustioQ • 2 sq. fbot
Marine, tubular 0510 066 ** *'
Portable, moderate forced . . 03 aq. foot.
Lo<;omoilve and like, strong
blast 01 •• •*
T^ichness of Tubes per B W G.
External diameter in ln& 3 3.35 3.5 3.75 3 3.35 3.5 3.75 4
Thicknessforpreasureof 50 lbs., number.. 13 is xi n ti zo 10 xo 9
" *» ♦» xoo *♦ " ..ix xo 99 98 88 7
Smoke-pipes and Cliixnixeys,
Area at their base should exceed that of extremity of flue or flues, to
which th^ are connected.
In Marine service smoke-pipe should be from .16 to .2 area of grate. In
Locomotive, it should be .1 to .083.
Intensity of their draught ia &9 square root of their height Hence, rela^
tive volumes of their draught ia determined by formula!
y/h . I a = votume in »q. feet k representing height of pipe or chimnty in feet, and
a its area in sq. feeL
When wood is consumed their area should be 1.6 times that of coal.
Chimneys (Masonry), — Diameter at their base shoald not be less than from
.1 to .11 of their height.
Batter or inclination of their external surface .35 inch to a foot, which is
about equal to i brick (.5 brick each side) in 25 feet.
Diameter of base should be determined by internal diameter at topi, and
necessary' batter due to height.
Thickness of walls should be determined by internal diameter at top ;
thus, for a diameter of 4 feet and less, thickness may be i brick, but for a
diameter in excess of that 1.5 bricks.
ArecL -^ = 0. C representing weight of coal consumed per hour ^ lbs,, and
V*
a area of ditto at top^ in sq. ins.
(Brick masonry.)— 2$ tons weight per sq. foot of brickwork in height is
safe if laid in hydraulic mortar.
Less the height of a smoke-pipe or chimney, the higher the temperatore at
its gases is required.
STBAM-KNGINE.— PUMPS. — PLATBS AND BOLTS. 749
VelocUiet of Ckrratt ofBeaied Air in a Chimn^ 100 Feet in Height,
In Feet per Second.
Air ftt BiM of ChimD«y.
Air
•t Bate
of Chimi
ley.
■ctamidAlr.
ISP'
asp*
390"
4S0*
F««t.
Feet.
Feet.
Feet.
loO
24
3?
33
35
K
S3
38
3»
34
50°
30
37
30
33
External Air.
60O
80°
ISO-
Feet.
18
«7
«So*
Feet.
26
«S
24
3SO*
Feet.
29
2C
2(
4SO-
Feet.
33
32
32
When Height of Chimney is legs than xoo feef, — Multiply velocity as ob-
tained for temperature by .1 square root of height of chhuney in feeL
Draught consequent upon a steam -jet in a smolie-pipe or chimney id
nearly equal to that of a moderate blast.
The most effective draught is when absolute temperature of heated air o^
gas is to that of external air as 25 to 12, or nearly equal to temperature 0'
melting lead.
In chimneys of gas retorts, ovens, and like furnaces, the draup:ht is more
intense for a like height of chinmey than in ordinary furnaces, in con-
sequence of the great nuiss of brick masonry, which, becoming heated, adds
to intensity of draught.
Chiinixes'-s. Lawrence Manufacturing Co.y Mass Octagonal
Height above ground 211 feet. Diameters 15, and 10 feet 1.5 Ids. Wall at base
as- 5. nod at top 11.5 ins. Shell at base 15 Ins., at top 3.75 ina
Foundation 22 feet deep.
EnglatuL ^Square. —Height 190 feet
** 300 **
Round. '* 313
It
.300
t«
Diameter at base so feet
" " 29 *»
»* ** 30 "
" »« ao "
Diameter at base usually i of height above groand.
Vacuum at base of chimney ranges from .375 to 43 ins. of water.
Ciroulating Puxnps.
Single-acting, — .6 volume of single-acting air-pump and .32 of double-
acting.
Dontbterocting. — .53 volume of double-acting air-pump^
Volume of Pump compared to Steam Cylinder or Cylindere,
Eoglne. Pamp Volume^
Expansive, i . 5 to 5 times. Single-acting ......... .08 to .045.
Compound do. 04510.035.
Expansive, 1.5 to 5 times.. Double-acting. 045 to .025.
Compound.. do 02510.02.
Fa/rf«.— Area such as to restrict the mean velocity of the flow to 450 feet
per minute.
PLATES AND BOLTS.
l^rouslit-iroii. — Tensile strength ranges from 455cx> to 70000 lbs.
per sq. inch for plates, and 60000 to 65000 lbs. for bolts, being increased
when sabjected to a moderate temperature.
English plates range from 45000 to 56000 lbs., and bolts from 55000 to
59 000 lbs.
D K. Chirk gives best quality of Yorkshire 56000 lbs, of StaflTordshire 44 800 Iba
Test or Plates. {U. S.) — All plates to be stamped at diagonal corners at
«bout four ins. Prom edge, and also in or near to their centre, with name of manu-
Ibcturer, bis location, and tensile stress they will bear.
Plates subjected to a tensile stress under 45000 lbs. per sq. inch, should contract
in area of section 12 per cent, 45000 and under 50000, 15, and 50000 and over, 25,
»t point of ruptura
750
STBAM-JBNGINE. — ^PLATBS.
Brands. (C No. i) Charcoal No. i.-^Platety will sastiiin a stren of 40000 lb& ptt
/4. inch; hard and unsulted for tluDging or bending.
(C No. I R H) BefieoUed, hard and durable, suited for furnaces, unsuited for oon«
tinued bending.
(C H No. I S) HheU, will sustain a stress of 50000 to ^4 000 lbs. in direction of fibre,
and 34000 to 44000 across it: hard and ausuited for flanging or even bending with
a short radius.
(C H No. I F) Flange^ will sustain a stress of 50000 to 54000 Iba, soft and suited
for flanging.
(C H No. X F B) Furnace and (C H No. i F F B) Flange Furnace. The first is
hard, but cl^)abIe of being flanged, the other is hard, and suited for flanging.
The especial brands are Sligo, Eureka, Pine, etc.
The best English plates known are the Yarkthire, as Lew Moor, Bowling, FamUy,
Monk Bridge J Cooper dt Co., etc. (See Steam-boiler*, W. H. Shock, U. S. N., x88a)
Bteel. — ^Tensile strength ranges from 75000 to 96000 lbs. Mr. Kirkaldy
gives 85966 lbs. as a mean.
Wn n used in construction of boiler-plates should bo mild in quality, containing
but about .25 to .33 per cent, of cart>on', for when it contains a greater proportion,
although of greater tensile strength, it is unsuited for boilers, fh)ni its hardness and
consequent shortness in its resistance to bending.
Crucible steel may be used, but that obtained by the Bessemer or Siemens- Martin
process is best adapted for boiler-plates. Its strength becomes impaired by the
processes of punching and shearing, rendering it proper thereafter to submit it to
annealing.
Steel rivets, when of a very mild character and uniformly heated to a bright red,
are superior to iron in their resistance to concussion and stresa
Copper. — Tensile strength is 33 000 Ibs^ being reduced when subjected
to a temperature exceeding 120°. At aia^ being 3a 000^ and at 550^ 35000 lbs.
"WrouKh-t-iron Sliell Plates.
Pressvire and. Xliickiiess. \(I. S. Law.)
Bated upon a Standard of One Sixth of Tensile Strength of Plates. Iron or Steel
RmuIU with a Tensil* Strength of 50000 Lbi.
Diameter* in Ins.
Thlck-
neee.
36
38
40
Inch.
Lbe.
Lbe.
Lba.
•as
116
110
104
•3125
•375
.5
145
174
232
137
165
220
156
208
4a
Lbs.
95
it8
142
190
46
48
54
60
66
7a
78
Lbe.
Lbe.
Lbs.
Lba.
LU.
Lbe.
Lbe.
9«
87
77
>
63
58
53
"3
X09
96
»7
79
I7
67
136
«3o
116
104
95
80
182
174
154
138
ia6
116
106
Lbs.
99
124
'49
198
I03
TJbs."
6i
71
81
9«
I2X
142
162
To which 20 per cent is to be added for double riveting and drilled holea
Iron plates .375 inch in thickness will bear, with stay bolts at 4, 5, and 6 Ina
apart fVom centres, respectively 170, 150, and 120 ItNa. per sq. inch.
Iron plates, as tested by Mr. Phillipa at Plymouth Dockyard, .4375 Indi in thick-
ness, with screw slay bolts 1.375 ina in diameter riveted over heads, 15.75 i^d 15.25
ins. fVom centre = 240 sq. ins. of surface for each bolt; bulged between bolts and
drew (Vom bolts at a pressure of 105 Iba per sq. inch of plate.
Iron plates .5 Inch in thickness, under like conditions with preceding case, l)ulged
and drew fTom bolts at a pressure of 140 lbs. per sq. inch of plate. Hence, it ap-
pears, resistances of plates are as squares of their thickness.
When nuts were applied to ends of bqlt through .4375 inch plate, its resistaaca is*
creased to 165 lbs. per sq. inch of plate.
84
90
96
Inch.
Lbs.
Lbe.
Lbs.
375
•4375
U
80
65
•5^
99
92
«7
.5625
III
X03
98
•75
148
138
130
•875
172
160
152
X
198
184
»74 .
X08
"4
120
ia6
13a
«35
X40
144
Lbe.
Lbe.
Lbe.
Lbe.
Lbe.
Lbe.
Lbs.
Lbe.
58
55
52
49
47
46
44
43
68
64
61
57
55
1?
69
5t
50
11
11
^
65
73
63
7»
1:
"5
\2
103
97
94
9«
88
8S
136
122
114
XIO
X06
X02
100
'54
146
138
130
126
122
118
"4
OylitxAj^iOBLl SHeUe^ {U.S. law.)
^To Compute Pressure for » <iHven Tliiokn»«s and
IDiaxueter, ox* Xlxiclcixess Ibr a. CMven i:*|:*es8ure aixd
IDiarueter,
For Pressure, RuLK.-^Multiply thickness of plate in ins. by one siztb
of tei^Ue strength of metal, and divide product by radiuls or half diameter
of shell in ins.
When rivet^'holes are drilled, and longitudinal courses are double riveted,
add one fifth to result as above attained.
ExAMPLx. —Assume baiter 8 feet in diara., and plates .5 inch tbick; what work-
ing pressure will it sustain, tensile strength of plates equal to a stress of 60000 Ib&r
8 X 12 5000
.5X6oooo-i-one8ixtb-i =- - = 104.16 Ibi.
3 40
For Thickness. Rule,— Multiply pressure by radius of shell, and dividi
product by one sixth of tensile strength of metsu.
ExAKPLS. ^Assume pressure, radius, and tensile strength M preeedlDg.
104.16 X96-r 2 __ 5000 _ ^^^
60000-r-one Sixtlj loooo
For Evaporation of Salt Water.— Add one sixth to thickness of plates and sac
tiooal area of stay bolts.
War Freiglit and. River Steamboats.
Standard. -^ 150 lbs. pressure for a boiler 42 ins. in diameter and platM
.25 inch thick.
For Pressure, Rule. — Multiply thickness of plate by 12 $00, and divide
re9iiU by r«4ius of boiler in ins.
ExAXPLK.— Assume a boiler 42 ins. In diameter, and plates ,25 inch in thickness;
what working pressure will it sustain ?
.25 X i» 600 -f- 42 •+• a = 150 J6».
JVoo/!— All boilers by U. S. I^aw to be tested to a hydrostatic pressure of 50 r^
cent above that of their working pressure.
Relative Alean. Strengftli of Riveted OT oiiits compared
to tliat of PlateB.
Allowances being mad^for Imperfections of Rivets, etc.
Plates^ 100; Triple, .72 to .75; Double or Square, .68 to .72; Double
with double abut straps, .7 to .75 ; Staggered, .65; Single, .56 to .6.
.Board of Trade^ Enghnd.
Coefficient or Factor of Safety. — When shells are of best material and
workmanship, rivet-holes drilled when plates are in place, abut 8tra])ped,
plates at least .625 inch in thickness and double riveted, with rivets com-
puted at a resistance not to exceed 75 per cent, over the single shear,* the
coefl^cient is taken at 5. Boilers must be tested by hydrostatic pressure to
twice that of working pressure.
Tepalle strengths of plat«s are taken, with fibre 47000 /lis. per sa. inch,
across it 40000 lbs., and when in superheaters from 30000 to 22400 lus.
*Z — -— ;j = P, and ^— = <. P representing pressure thai shell mil sus
1) 1/ 47 000 0 2
Unin per sq. inch in lbs., B least psr cent, of strength ofriwt or pluie (ufhicheoer it
least) at lap, D diam. of shell and t thickness of plate, both in tm., and C cot^gHcient
^safety-
• SbMuiBf or detrutlva ratbtanse of wroof ht iros is from 70 to 80 p«r cent, of it» tn^ailt atrwil^
752
STEAM-ENGIKB. — SHELLS. — ^PLATES.
iLLUSTRATiov. — Assome T = 50000 Z&f. tensile strength of plate, B = 7< fwr eewL.
D = xaotn«., C=5, and ^ = .5. What pressure will shell sustain, and what shoald
be thickness of plates for such pressure and diameter?
5ooooX.75_X^5Xi^6a.5 ».., and "0X62.5X5.^ ^^
X20X5 50000 X. 75X2
for all practicable deficiencies in drilling, punching, and riveting in trans-
verse courses, if existing, this coefficient is increased up to 6.75, and in lon-
gitudinal courses to 8.75, and when courses are not properly broken, an
addition is made to above of .4.
Diameter of rivets should not be less than thickness of plates.
at
:=C. =:P. and =rt
' d — '^J*"" 2C
MoUswortK
d rqoresenting diameter and t (hieknttt of
metai^ both in <«*., P towking pressure in lbs. per sq. inck^ and C as follows :
single riveted. Double riTelad.
Best Yorkshire plates ) ^«^ „,„.», ^f t^^^,,^ (€ = 6200 and 7800
one ninth of tensile
*' Staffordshire platea ... J """ "IV^* "'lu''"''"" V*=5ooo " 6200
Ordinary plates ) sirengm. (u — ^^^ a ^^^
Working stress not to exceed .2 tensile strength of joint or rivated plate.
Then for a pressure of no lbs., and a diameter of 42 ina, as given for a standard
C. S. ttoiler.
iioX 4a
Taking C as above for best single-riveted plate at 6200,
= -37« + **W-
2 X 6200
in thicknesSj or . 122 inch in eaceets 0/ U. S. Law for a plain cylindrical boiler ^ sniifiM
riveted.
IJoyd*a,
Thickness of shells to be computed from strength of longitudinal joints.
/JC
D
= P,
PD
CJ
= <, —5- = D, — = SB, and — j = «. t represenhng fhuac-
ness ofvlate, D diameUr ofskeUy p piteh and d diameter of rivets^ all tir ins. ; 3 per
cent, of strength of joint or rivets^ the least to he taken; C a constant ax per taUe;
P working pressure in lbs. per sq. inch ; n number and a area of rivet; xper cent,
of strength ofpkUe at joint compared vrith soUd plate, and xper cent, of strength of
rivets compared vrith soUd plate.
When plates are drilled, take .9 of 2;, and when rivets are in double shear,
put 1.75 a for a.
J O 1 M T.
T on f punched holes
"^P 1 drilled do
Double abut ^ punched holes
strap ( dribod do.
Constants.
Ibon Platsk
.5 inch
and
under.
»55
170
170
180
.75 inch
and
under.
165
180
180
190
AbOTA
.75incli.
170
190
190
200
•375 Inch
and
under.
200
215
Sm>b Platu.
•75 inch
and
Oader.
incn and
under.
2X5
230
230
250
AhOTA
.75iBch.
340
360
When plates, as in steam-chimneys, superheaters, etc., are exposed to direct ac-
tion of the flame, these constants are to be reduced .33.
Illustrations. — Assume pitch 4 ins., diam. of rivet 1.375 'ns., and thicknass of
plate I inch, both single and double riveted. Area 1.375 =: 1.48 sq. ins.
4 — '375 __ gjg ^^ ^g^ strength of joint compared to solidplate. - — ~- = .37
per cent, strength privet fo stttid plate when sinjfie riveted, and
».7SXi.48
4X1
= .647
per cent, when double riveted,
by 90 vrith drilled.
na
Rivets at Joint, — ^ X xoo with punched holes and
pt
8TBAM-EN6INB. — ^PLATES. — ^ABUT 8TBAPS, ETC. 753
nates.
To CoRfopute Tliiokness of* Plates fbr a Oiven Pressure
and Jr^itoh., aixd. Pressure and Pitolx fbr d-i-reu Thiolec-
zxess*
<a C /!» C /P P'
— 3-~P, /-r^=Pf and a/-^=^- * repraenting thickneu ofmetdCin
tixUgi^ths of an inthj p pitch ofilayt or diatanee apart at centra in \n». , P UHyrkif^
prtiturt in ttn. per tq. inckj tmd C a constant^ atJoUows :
For a Tensile Strength of Metal of 50000 IJbt. per Sq. Inch.
Screw Stay-hoUa toith Riveted Headi.^Plates up to .4375 indi in thickneu C =90,
Mid above that loa
Screw Stay-Mts wUh NtUs. —Plates up to .4375 inch in thickness G = no, and
tsbovethat laa
Screw Stay-bolts with Double Nuts and Wcuhen. — Up to 4.375 ins. in thickneu
C = 140, and above that i6a
When stay-bolts are not exposed to corrosion, these constants may be reduced 3.
Resistance of a flat surface decreases in a higher ratio than space between
stays. Hence, C must be decreased in proportion to increase of pitch above
that of ordinary boiler-plates.
iLLUsnunoir i.— Assume pressare no lbs. per sq. inch, and pitch of stays 5 ina }
what should be thickness of plate for screw-bolts and riveted heads?
0=95. Thenyi^=/-^ = S.38-^«««.
«
3. — Ateume thickness of metal 5 sixteenths inch thick, stay-bolts screwed and
riveted over its threads, and working pressure of steam 80 lbs. per sq. inch.
C=95. Then y5!^ = 5.45 in*. i»te*.
A-but Straps*
Doubte Abuts should be at least .625 thickness of plate covered. Single,
.125 thicker tbair plate covered, and IknAle, .625.
Stays.
Direct, — Tensile stress should not exceed 5000 lbs. per sq. inch for Iron,
and 7000 for Steel.
Diagonal or Oblique. — Ascertain area of direct stay required to sustain
the surface; multiply it b}* length of diagonal stay, and divide product by
length of a line drawn at a right angle to surface stayed, to end of diagonal
stay, and quotient will give area of stay increased to that which is required.
Stress upon an oblique stay is also equal to stress which a perpendicular
•tay supporting a like surface would sustain, divided by cosine of angle
which it forms with perpendicular to surface to be supported.
Illcstration. — AsBuroe pressure no lbs. per sq. inch, area of supported surface
f6 aq. ins., and angle of stay 45^^; whatl^ould be pressure or stress upon stay?
Cosine 45O = .707 II. Then no x 36 -r- .707 n = 5600 lbs.
754 »TOAJi'»«ttI««.'--GlilJiJ6lta.— FLUES, «TC.
Proportions of "Eyea oT Stajrs, Rods, eto.
DiusnsioMS
ITo. z* a sod a B z inch.
6= .9 "
•= .75 "
No. a. a and a = z '^
«- .75
M
Ko. 3. a and a s z *'
*= -75 ::
c=? .875"
No. I. No. 3.
FOBOBD AMD WbLDBD.
®
T— »
l(@
w
Wi
No. 3
Drilled wbou B,
When drilled flrom upset bar, dime^sioas mm» w for No. j. Pipy wb«ii of Meei
66 n^ck of rod.
Bt»y'TaQ\tB,-^Tr{mf j»re not to be 8ttbjecte4 to « greater stress than
60GO lbs. per sq. inch of section ; Steely 8000 lbs., both areas computs^ from
weakest part of rod, and when of steel they are not to be welded.
To Compute I>iaTnetpr and. I*itoli of Btay - t>olts, anci
R^ifieitanoe tUey M^iU @ui:*t9m-
Screwed. !^ = a, ^=p, ««1 (2^)' = P. Socket, t^^d
4 96
>/P
p, and
Cf)'
p. d rtpntmiHng dtameUr in ins.
Illustratton.— Assume pitch of stiiy bolts 6 ins , and working pressure zoo Iba
p«r sq. iiifib ; what should b« diaiP«t«rs of bolti, t»oth sorsw and socket f
6 X V'oo ^ g^y iJ^cJ^ SQrev>ed, apd ^^^^"^ = .63-f iwdi SockeL
70
C4l'<
= P,
95
O-irders. (Lloyd's.)
C(i»
= t, ^LiiLZ^ = a. LfTPrei^fin^
(L— p)DL
2en^A of girder, d its depths t its thickness git centre or sum of its thicknesses, D itr
distance apart from centre to centre, andppitdk of stays, tM in ins., and C a constam
as per following .*
One stay to each girder, C = 600a If two or three = 900a If four = zo 200^
Illustration. — Assume triple stayed girder, 24 ins. in length, 3 ina in depth, z
iQCh th>ck| and stayed ^i intervals of 6 ins. } what working pressure will it sus^^inf
r. T>.«« 0000 X 6' X I 3?4QOO • iw
C = 9ooa Then-* — ^; ^ v ^ — aaS-z n Z25 •*••
' (24 — 6)X6X24 2592
nues, Arclied or Circular iF'umaces. U, S. Law,
,3135 inch for each i(> ins. of 4iiimeter. Ri)gligh iron, being harder than
American, is better constructetl to resist compression, and conaequeptly 0
less thickness of inetal is required for like stress.
"XDr^*^» \/896^ ' ~~Tir-^'^'^^'^9Vr-^ Drepwentnv
tTBtern^l di(tm^ie^ <ifjtue or furnace, and t ihichuss qfpUtte, both in im., L lemgtM
f^ftue orfiimace between its ends or beiv^een its rings, infget, and P working preff-
ure in lbs. per sq, inch.
Illustration.— Assume diameter of flue 16 Ins., length 6 feet, and working pren
ma ofsteAm 8e Ibf- per sq iooh.
Then / — ?^^' = y/.oSsj = .29 inch. Furnace.— P not to exceed ?*^*
8TBAM-J&NOINB. — BIYBTING. 755
iLLiTSTRiTiair.^Assiinie diameter of a circular ftamaoe or width of a seraiclrcoUKv
one 48 ina , working pressure of steam 80 lb& , and length 6 feet
Then /?5l^|^i! = ^. 257 =; .507 tik* ihiekneu,
RTVETING.
Plates.— The strength of a joint is determined by ascertaining which
of the two, the plate or the rivets, has the least resistance ; the stress on the
first being tensile and the latter detrusive.
The tensile strength is to be taken from that of the article under consider-
ation, making due allowances for construction and location of the joint, and
the ccmsequent variation of stress, as with or across the fibre of the metal,
or exposed to high heat as in a superheater.
With or Across the Fibre, — From experiments of Mr. D. Kirkaldy and
others, the difference in strength of Iron plates is ascertained to be from 6.5
to 18 per cent., the average 10 per cent.
Steel Platet. — The relative strength of plates with or across the fibre, as
determined by Mr. Kirkaldy, for "Fagersta is 9 per cent., and for "Siemens"
it is without material difference.
Holes — The relative strength of plates when subjected to drilled or
punched holes, as determined by the experiments of Mr. Kirkaldy, is shown
to be 15 per cent.
In Riveted Joint exposed to a tensile stress, area of rivets should be equal
to area of section of plates through line of rivets, running a little in excess
up to .5625 inch diameter of rivet, and somewhat less beyond that, area be-
ing determined by relative shearing and tensile resistances of rivet and
plate.
Note. — For Riveting of Hulls of Vessels, see pp. 828-301
Essentially hy Nelson Foley.
Single Xjap Riveting. .
^^^^^— = bJbrplaU^ ^ = VJbrrivetSf ~Z^=Pt ptty=:etf and
'*^^ . -< = d. p representing pUcK^ t thtckness ofptaUy and d diameter oj rivets^
aU in tn»., a sectional area ofHatets in «f ins. « n number nj rtveto, and h and h per
cent, of plate between hales and of section of rivets to solid ptatCy I e. plate b^ore
being punched.
Illubtratiox . — Assume p = 3 ins.^ d = i ineh^ a = . 7854 inehj and f = 5 t'ndi
^""' = 66 per cent strength oflap^ _Z_ii = .533 per cent of rivet to tohdplate,
3 3X 5
— ^-j2 = 3 ins. . and ^'^^-^ X 5 = « »«<*• 3 X s X .523+ = -7854 o»w.
I — 66 1 — 66
When Shearing Strength of Rivet is not Equal to TensSe Strength of Plate,
— Then diameter of rivet must be increased in ratio of excess of strength of
plate over rivet
Or, ' '^ ■ _ < = d. T and S representing tensiU and shearing slrengthStiiriiiekmojf
I ^o S
6e tak^n at 5 and 4 for Iron and 7 and tfitr Steel
When ftill value of rivet aectioa is not allowed as by Lloyd's rules for drill^
holes, b' = b'x .9-
756
STEAH-BKGIKB. — BITXTIKa.
Pitches aa
batwaao JPit«h =
Ugaa Diam. of
ofHSlaa. RiTrtX
I Determined
batiraen f *=»» =
£d«a Uiam. of
ofllSla.. RivatX
by Diameter
batwaao JP'teh =
Edeea Diana, of
ofHolaa. WvetX
of Ri-vets.
betwaan P *<* =
Edgea Diam. erf
of Hdlaa. !"▼•* X
Par Cant.
50
5a
55
2
2.08
2.22
Par Cant.
58
60
62
2.38
2-5
2.63
Par Cent.
65
68
70
2.86
3- 13
3-33
Par Cant.
72
75
78
3 57
4
4-55
Opbration.— If distance between edges of holes, or p — d, = 65 per cent %T solic
t»laie, and diam. of rivet i inch, then 2.86 x x = 2.86 iru. pitch.
When PUUe and Rivets are 0/ equal strength in lUtimate tension, 6' = 6, = R
1. 27 B
Hence, -^ — ^ t=id. In illustration of B, assume p = 3, d = x. i , and t = .$.
1 — B
Then 3
. I.Q
I.I =: 1.9, and — -:
.633 ==bj or per cent. 0/ strength of pimched tc
•olid plate. Area i. x = .95, and
•95
3X.5
= .633 = 6', or per tent of section of rivet to
s(didpkite. Hence, B = .633.
iLLusTRATioif.— Assume as shown, B = .633.
Then ''^X- 33 ^ 5 _ , q^^ ©, i.i int. diam.
I— .633
Di
B
Or Strengtli
at Joint.
ameter or ]
Diam. = Thicknam
of Plata X
rlivets
B
Or Straogth
at Joint.
as Determix
Diam. sThieknaM
of Plata X
led Toy
B
Or Stranxth
at Joint.
Plate.
Diam. = Thielmaaa
of Plata X
Par Cant.
52
53
54
T = S.
X.38
'•44
'•5
.9 par cant.
ofSaction
of Rivet.
'•53
'•59
X.66
Par Cant.
55
56
57
T = S.
X.56
x.62
1.69
.9 mr cant.
ofSaction
of lUvat.
[:?
X.87
Par Cant.
S8
60
62
7 = 8.
X.76
1.91
2.08
.9Parcaati.
ofSaetioa
ofRirai.
'•95
2.xa
2.31
Opbration.— If thickness of plate = .5 inch and plate and rivet have equal resist
ance, or B = 62 per cent., then .5 x 2.08 = x.04 ins. diameter.
Double Uap Riveting.
Preceding formulas for single lap riveting apply to this, with substitution
of 2a for a and .64 for 1.27.
Illustration. —Assume p = 3 ins. , < = . 5 inefc, and 6' = . 589.
3X.5X.589
= .4418 area (if d,
.4418 X a
•64X.589y -_ „d
75
= .75 N and
= .5896'.
3X5
Diaxneter or Rivets as Determined by.Plate-
B
•r Strangth
•t Joint.
Par Cant.
68
69
70
Diam. = Thicknaas
of Plata X
T = 8.
'•35
1.42
X.48
.9 par cant.
OfSaction
of Rivet.
'•5
'•57
X.65
B
Or Strength
at Joint.
far Cent.
7'
72
73
Diam. = ThicknaM
of PlaUX
T = S.
x.56
X.64
1.72
.9 par cent.
ofSaction
of Rivat.
'•73
1.82
1. 91
B
Or Strangth
at Joint.
Par Cant.
74
75
76
Diam. =ThlrkinM
of PlaU X
TssS.
X.8x
1.91
.9 Mr cant.
ofSeeiloB
of RiTSi.
a
a.xa
2.25
Opiration. — Assume < = .5 inch and B = 70 per cent, tensile strength compared
to Bhearing being as 7 to 6. What should be diameter of the rivets?
•5 X 1.48 X •7* = .863 tscA. When rivets are in double shear, put x. 9 a for a.
STBAU-SNaiNK. — DUTY. — £VAPOBATIOS.
757
Triple Lap Rivetixifir*
Preceding formulas for single lap riveting apply to this, with substitution
*f 3 a for a and .42 for 1.27.
Illubtiution.— -Assame /> = 3 int., t . 5 inch, aud b' =: .883.
3-^i-l^^ = .44X5areao/d, li^^ x ■ 5 = • 74 f «• diam. . Ir^^.jsb,
and:^^:i^ = .883 6'.
3X.5 ^
I— .75
X>iameter of Rivets as Determined "by Plate.
B
>r Str«D(th
at Jolnu
Diain. =ThickueM
of Plat* X
P«r Cflot.
70
7« .
72
T = S.
•99
1.04
1.09
.0 Mr cent.
o/Sflctlon
of Rivet.
X.I
i-iS
1. 31
B
Or Straofcth
at Joint.
Per Cent.
73
74
75
Diam. = ThickucM
of Plate X
T = S.
X.2X
1.27
.9 per cent.
ofSectloo
of Rivet.
1.27
1-34
1.41
B
!Or Strengtb
at Joint
Diam. = ThickaM»
of Plate X
Per Cent.
76
77
78
T = 8.
1-34
1.42
1-5
.9 per ceai
ofSectloB
of Rivet.
X.67
Upbbation.— As shown by preceding tablea
Gheueral Formulas and IllviatratioxiB.
Bivets in Single Skear.
Rivets in Double Shear.
Rivets in Triple Shear,
1.27 B T
x(i — B)S
X.27 B T
1.75 (I --B)S
( = d,aDd
ptT
= 6'.
. , .a X.75 S _ ,
< = d,and— J5_^j,
1.27 BT , , .a2.5S .,
7 T>vQ « = d, and — -2__=: ft'.
2.5(1— B)S ^ ptT
ZigxHg rtivetinff. Strength of plate between holes diagonally is
equal to that horizontally between holes, when diagonal pitch =: .6 and nor-
tzonial = diameter of rivet + •4*
ThoBf. 6 p-\'. 4 p is. diagonal pitch.
"Dxity of* Steaxxi*enginea.
The conventional duty of an engine is the number of lbs. raised by it x
foot in height by a bushel of bituminous coal (112 lbs.).
Cm'nish Engine,^ A^veTSig9 duty, 70000000 lbs. ; the highest duty ranging
from 47000000 to loi 900000 lbs.
A condensing marine engine, working with steam at .75 lbs. (mercurial
gauge), cut off at .5 stroke, will require from 1.75 to 2 lbs. bituminous coal
per ff per hour.
Relative Cost of Steam-engixxes fbr Sq.iial Bjffeots.
In Lbs. of Coal per B? per Hour. jj^
A theoretically perftet engine 66
A Cornish condensing engine a. 38
A marine condensing engine x.75 to 3
Kvaporative Po-^ver of Soilers.
The Evaporative power of a boiler, in lbs. of water per lb. of fuel consumed,
is ascertained approximately by formula
1.833 ( Q I p) e=zlbs. 8 representing Mai heating surface in sq. fut^ F fuA
consumed in lbs. per hour, and e theoretical evaporative power ofthefktd.
Illustration. — Assame evaporative power of the tael at 15, consumption pef
boor 800 Iba, ood beating sarface x6oa
"^"^ ' '33 (,(i«,x^+8cc) ^ '5= •0.998 «»■
3S
758
BTBAM-ENGIKX. — WEIGHTS.
M^fidency ofUnUr. x.833 [-
x6oo
h
733-
y,i6oo X 2 -f- 800^
Tbe evaporative power of diSSerent fuels, fVom and at 3X2<^, is, for coals, fW>fn 14.3
to 16.8 lb&, the average of Newcastle being 15.3, for patent fuels 15.66, Lignite 13.5,
Coke 13.3, Peat 10:3, and Woods, when dry, 8.1. See A. E. SeaUm^ London^ 1883.
INTotes on. Horse-i^o^^^er.
A Lancashire boiler with a heating surface of 610 sq. feet and a grate-area of 35
will evaporate in ordinary operation 50 cube feet of water per hour; 3.12 sq. feet of
horizontal section per cube foot of water, and .5 sq. foot of grate-area per cube foot.
!N'ozxiiiial. Five Boilers. — Usually computed at 5.5 to 6 sq. feet of horizontal
section, 15 sq. feet of heating surface, and i sq. foot of grate-area.
Tbe IIP of such boilers will range from 3 to 4 times that of the nominal.
MttUitubular Boilers. — .75 sq. foot of grate-area and 2.5 ofheatiug surface.
"Weiglits of Steam-engiiies.
Side-wlxeels. — American Marine (Con lensii^f).
EMaixs.
Frame.
Vertical beam
Wood.*
(t
Wood.*
«<
Wood *
ct
Wood.*
((
Wood.*
Oscillatlne
Iron.
«(
Iron.
Inclined
Iron.
Water-
Cylindera.
Weight per
whaels. -
No.
Volume.
Cube Fodt.
Sbbtics.
Cabe Feet.
Lba.
Wood.
X
63
1 100
River.
Wood.
3
216
io4ot
Coast.
Wood.
X
430
1225
Coast
Wood.
3
253
1480$
Coast
Iron.
I
725
loSgt
Sea.
Iron.
2
540
850
Sea.
Iron.
2
1502
5508
Sea.
Iron.
2
535
xxoo
Sea.
Without frame.
t With frame 1109.
X Including boilers.
§ Single fraoM.
Bore-w FvoiieU&v»,— American Marine (Ctrndensing).
Enoimb.
Vertical direct, Jet Condens'g . .
*' *' Surfece Cond'g .
" *' Jet " .
II C( t(
Horizontal back-action
'* direct
Vertical compound. . , . ,
4(
i(
t«
4{
t4
•t
n
direct
be
Non-Condensing.
U (I <(
Cylindera.
Wbiobtc,
No.
Volnme.
Engine.
Boilers.
Per C. Ft.
Cylinder.
Cabe Fee t<
Lbt.
Lbe.
Lbs.
4
22040
X2IOO
8535
7280
12. s
5QOOO
48130
32000
12.5
35000
6650
33
120450
98000
6620
506
1 523 c6o
985600
4958
2
68
289 680
200800
7212
3
67
201000
200593
6009
3
4.8
24705
26373
10 641
2
24-3
94196
88050
7500
2
425 ^
1 022 400
840000
4380
X
3.6
30534
27301
X6066
X
35 „,
173028
100065
7 774
X
1.86
14 410
23481
19834
X
2.77
»4759
334x7
13431
Engligh Marine (Condensing).
DmatirnoK.
Trunk
Borizontal direct
Vertical direct
Oscillating
Vertical compound
Horizontal compound. .* .
Cylinders.
WsiOHVi.
Propeller
Boilers
Per
IH?
LU.
No.
Volume.
Engines.
and
Shafting.
and
Water.
Total.
Cube Ft.
Tons.
Tons.
Tons.
Tons.
3
230
121
47
257
425
465
3
382
223
85
303
611
338
2
393
165
48
144
357
781
2
440
117
43
135
29s
560
2
24
425
, -75
725
12.25
60
6
707
497
167
656
1320
368
2
52
55
X5
no
j8o
35i
3
?«
x^o
87
162
3x9
309
Sbb-
VtCB.
Sea.
Sea.
Sea.
Coast
Sea.
Sea.
Sea.
Coast
Sea.
Sea.
Coast
Sea.
River.
Coast
Per
Cabe Ft
Cylladei;
Tona.
«.8s
X.6
•9
•7
•Sa
X.87
3.44
a.ag
STEAM-XNGIKB.— WBIOBT OF BOIL£BS.
759
I^axid-ensines.— {•^'''■'C'^fi^'^'wtnjjr. )
MM«ntt.
VeittealY i8 lbs. X4 feet
beam l 30 ina. xs feel
Hor)»m% 14 tos. x a feet
22 ins. X 4 feet
it
Volant
of
CyVt.
7
a4«5
a. 2
10.6
Eftgifl«.
Spar-wheel
» *^ and
CoiluecthM8<
Lbe.
67200
105000
10914
56000
Lbe.
37800
137 »79
s«f0*ilm
BolleT%
Unh Vhoi
Complete.
Gralee,etc.
OfCyllhdOT.
lbe.
Lbi.
LW.
89600
96880
960ft
263879
79000
4*90
—
8200
gioo
—
30140
5600
fI?o Compute Weiglit of a Vertio*! Beam »nd 8ide-«inrlik»el
Jet Coiideiisins Knslne. {T. F. BowUmd^ A.8.C.E.}
Including cUl MeiaJb^ Boiler and A ttackmenfg^ Smoke-pipef Orateg, ttoH f1<»n,
and Iron in Wooden Wat6r-4theeUf oitiiUing Coat-bhnkers.
For a Presture per Mercurial Gauge of^o Oft. per 8q. itKh.
For twrface eondenter Odd 10 to 15 per cent •
Rule. — Multiply volume of cylinder in cube feet by Coefficieni in follow*
ing table corresponding to length of stroke, and product will give rough
weight in lbs. Fof finished weight deduct 6 per cent. .
Stfeke.
Feet.
5
6
CMfflcIent. ft ftttoke
2467
9340
Feet.
I
CMffident.
2213
2000
\ Stroke.
Feet.
9
10
Coeflclent.
1865
«730
Strok«.
Feet.
It
19
Coeflcleiit.
1619
«54fl
Example l— What are the rough and finished weights of a vertical beam engine,
cgrltoder 80 ios. in dtameter and 12 feet stroke ot piston?
Are» of 8a ins. rr 5026.56, which x 12 feet =± 419 cuJbefett^ and X 154^ for 12 fMt\
stroke = 647 774 Vbt. rough weight.
Then 647 774 x .06 = 38 866, and 647 774 — 38 866 a 608 908 lh». finished weight
\rKlOHtS Of ^OlLlfnA.
Wtiffhlt of Iron Boilers {indudintf Doors and PtcUe^^and exclusive ofStMik^
pipes and Grates) per 8q. Fi)ot of RetUing BUrfcboe,
SwrfoLce Mecuuredfrom Grates to Base of Smoke-pipe or Top o/Stsam CMmney.
BoiLsm. For a Workiltf Prtmur* tf tp Lbt.
Single return. Flue * tvater bottom. . . .
• a*. ••..4. <•<•••«. ••«.««<•... ^^* . . 4 .
Multi-flue '*'...... water bottom. . . .
t»
i(
((
«
((
((
u
«(
((
((
Horizontal return, Tubulart water bottom
{•••••••••••••••••••••a "■ • ■ • •
t( (( (( «
Vertical " *' f! .*.'..'.*.".*.!.*.'.".'!!..'.... wfttef bottom!!!!
Horizontal direct, Tubokir *......< '' '' ....
Wel«(ttt.
Lbe.
25.6 to 32.9
24 to 30
27 to 43
25 to 43
22-5 to 35
21 to 33
17.7 to 26.7
18.5 to 26.5
19.8 to 9318
17 to 21
23.5 l0 2A
18. 1 i(f it.6
16.3 to 17.3
24 to 20
Cylindrical, external ftimace,t 36 ins. in diam., .25 in^^h thick
" Fiae •' 1 36 to 42 •• .25 " *'
flToffMtttal direct, TabtOar Locottiottre. . . .
Vertittil CyMftder direct, Tabular. —
W«fctM of Cyttndrtcal FtfrftaCe and Shell Boilers, at! complete for Sea Sei^ice and
for a pressure of 60 lb& steam, 200 tlm pef IH*.
^ teeMd* tff Untbts eqiMre* Melt «y]fndrleftl. f Seeflon ofhrMaS «lfd efiell Mrtftre.
t yfuMflSMmt heftdf, .37$ Ifeeli tkAtkf ilae», .2$ bieb, maS mrftM eempafad to hel/dUuiietet «t»Mt
Noras.— 1. The range in the units of weight arises f^oni peculiaflttee of cottMrac-
t«4>iif eofieeqaent npon proportionate nnmber of ftirnaces. thloktiesees of netal, vol'
of shell compared wilA beating sarftM», character of staying etc
a. tf preasute is increased the above units must be proportionately increased.
760 STEAM-ENGINE. — ^BOILBB-POWEE, COMBUSTION.
Soiler-po'wer.
The power of a boiler is the volume or weight of steam alone (indepen-
dent of any water that it may hold in suspension) that it will generate at its
operating pressure in a unit of time.
Marine boilers of the ordinary type and proportions, with natural draught, burn-
ing anthracite coal, produce 3.5 to 5.5 IH* per sq. foot of grate per hour; with a
ft-ee burning or a seUii-biturainous coal, 5 to 7.5 IH*; and with a forced draught,
with 25 to 30 lb& best coal per sq. foot of grate per hour, 8 to zo IH^.
Marine engines, operating with a steam -pressure of 35 lbs. (m. g.),and with mod-
erate expansion, consume 30 Iba steam per Iff per hour, and with a high rate of
expansion, under a pressure of 70 lbs., 20 lbs. steam.
With a blast draught and consuming 30 to 40 lbs. of a fkir quality of coal per aq.
foot of grate per hour, 7 to 10 £P per hour can be attained.
In locomotive boilers, having fh>m 50 to 90 sq. feet of heating surface per sq. foot
of grate, and at a rate of combustion of flrom 45 to 125 lbs. of coke, an average evap-
oration of 9 Iba of water per lb. of coke has been attained at ordinary temperatures
and pressure.
G?o Coxxipu.te 'Volume of Aiv and Oas in a F-arnace.
When Volume at a Given Temperature is known. Rule. — ^Multiply given
volume by its absolute temperature, and divide product by the given abso-
lute temperature.
NoTB.— Absolute temperature is obtained by adding 461^ to given or acquired
temperature.
ExAMPLX.— Assume volume of air entering a Aimace at i cube foot, its tempera*
ture^<>, and temperature of furnace it^-^^y what would be the increase of volume?
I X 1623° -}- 461° 2084
600 -1-4610
= — - = 4 Hma.
521
Volume of Furnace Ghas per Xjb. of* Coal. {Rankine.)
T«npM»-
tor*.
32O
68
X04
213
57*
iUr Sapplied.
Tempera-
Air Sapplied.
uLbt.
18 Lbs.
24 Lb«.
fare.
13 Lbs.
xSLbe.
150
225
300
752°
3^
553
i6z
241
322
XZ12
'M
718
173
258
344
1472
882
20s
307
n
1832
697
X046
3»4
47*
2500
906
1357
34 Lbe.
738
957
XZ76
«39S
x8x3
Temperature of ordinary boiler nimaces ranges fVom 1500*=' to 2500°.
The opening of a Aimace door to clean the fire involves a loss of firom 4 to 7 per
cent, of fUel.
For other illustrations, see antt^ page 744-6.
Rate or Comlsustion.
The rate of combustion in a furnace is computed by the Iba of Aiel consumed per
iq. foot of grate per hour.
In general practice the rate for a natural draught is, for anthracite coal (W>m 7 to
z6 lbs., for bituminous, fhim xo to 25 lbs., and with artificial or forced draught as by
a blower, exhaust-blast, or steam-Jet, the rate may be increased trom 30 to no lbs.
The dimensions or size of coal must be reduced and the depth of the firt incr«aaed
directly, as the intensity of the draught is inereased.
Temperature of gases at base of chimney or pipe ^ould be 6o(^, and fkictUnal
resistance of surface of chimney is as square vf velocity of current of 1
Ordinarily fjrom 20 to 32 per cent of total heat of combustion is expended in the
Koduction of the chimney draught in a marine boiler, to whieh Is to be added the
3668 by incomplete combustion of the gaseous portion of the fUel and the dilation
"f the gases by an excess of air, making a total of fUUy 60 per cent ISteam-boiUn,
H. JSthocky U. S. N.f x88i.)
STKBNGTH OF MATERIALS. — ELASTICITY. 76I
STRENGTH OF MATERIALS.
Strength of a material is measured by its resistance to alteration of
form, when subjected to stress and to rupture, which is designated as
Crushing, DetrusiFe, Tensile, Torsion, and Transverse, although trans-
verse is a combination of tensile and crushing, aud detrusive is a form
of torsion at short lengths of application.
ELASTICITY AND STRENGTH.
Strength of a material is resistance which a body opposes to a per-
manent separation of its parts, and is ^measured by its resistance to
alteration of form, or to stress.
Cohesion is force with which component parts of a rigid body adhere to
each other.
Eiasticiiy is resistance which a body opposes to a change of form.
Elasticity and Strength^ according to manner in wbicbr a force is exerted
upon a boov, are distinguished as Citishinff Strength, or Resistance to Com-
pression; Detntsive Strength, or Resistance to Shearing; Tensile Strength,
or Absolute Resistance ; Torsional Strength, or Resistance to Torsion ; and
Transverse Strength, or Resistance to Flexure.
Limit of Stifftiess Is flexure, and limit of Resistance is fracture.
Neutral Axis, or Line of Equilibrium, is the line at which extension ter-
minates and compression begins.
Resilience, or toughness of bodies, is strength and flexibility combined ;
hence, any material or body which bears greatest load, and bends most at
time of fracture, is toughest
Stiffest bar or beam that can be cut out of a cylinder is that of which
depth is to breadth as square root of 3 to i ; strongest, as square root of 2 to
z ; and most resilient, that which lias breadth and depth equal.
Stress expresses condition of a material when it is loaded^ or extended in
excess of its elastic limit.
General law regarding deflection is, that it increases, caUeris paribus, di-
rectly as cube of tength of beam, bar, etc., and inversely as breadth and cube
of depth.
Resistance of Flexure of a body at its cross-section is- very nearly .9 of ita
tensQe resistance.
Coefficient of Ifilastioity.
Elasticity of any material subjected to a tensile or compressive force,
within its limits, is measured by a fraction of the length, per unit of force
per unit of 8ecti<»ial area, termed a con^ant, and coefficient of elasticity is
usually defined as the weight which would stretch a perfectly elastic bar of
uniform section to double its length.
Unit of force and area is usually taken at one ib. per sq. inch. E represenH-
ing denonUnaior oj" fraction.
Example. ^1f a bnr of iron is extended one 12000000th part of its length per llx
of stress per sq. inch of section, ^ ,
I3000000 E'
The bar wonld, therefore, be stretched to doable its normal length by a (brce ot
s 9 000 000 lbs. per sq. inch, if the material were perfectly elastia
3S*
762 STEBNGTH OP MATSBIAL8. — ELASTICITY.
The same method of expressing coefficient of elasticity is applied to re-
sistance to compression, f hat is, coefficient, in weight, is expressed by de-
nominator of fraction of its length by which a bar is compressed per imit of
weight per sq. inch of section.
Ultimate extension of east iron is 500th part of its length.
fiSxtexxsioii of*Ca8t*iron. Sar8,Avliexi suspeixded Vertically-
I Inch Square and 10 Feet in Length. Weight applied at one End.
Set.
Weight.
Extension.
Set.
Weight.
Elxtenston.
Set.
Weight.
E^ztension.
Lb*.
529
1058
Ins.
.0044
.0092
Ins.
.000015
Lbs.
2117
4234 ^
Ins.
.0190
•"397
Ins.
.000059
.00265
Lb*.
8468
J4820
Ins.
.0871
.1829
Ins.
•OP 855
.02555
^Woods.— MM. Chevaudier and Wertheim deduced that there was no
limit of elasticity in woods, there being a permanent set for every extension.
They, however, adopted a set of .00005 of length as limit of elasticity.
This is empirical.
MODULUS OP ELASTICITY.
Modulus or Confident of Mcuticity of any material Is measure of its
elastic reaction or force, and is height of a column of the material,
pressing on its base, which is to the weight causing a certain degree of
compression as length of material is to the diminution of its length.
It is computed by this analogy : As extension or diminution of length
of any given material is to its length in inches, so is the force that pro-
duced that extension or diminution to the modulus of its elasticity.
Or, 9 : P :: 2 : u^ = — . x repre$enUng length a substance x inch square and i/oot
in length would be extmded or diminished byjbroe P, and w weight of modulus in lbs.
To Compute "^WTeigHt of* Alodulua of Klastioity.
Rule. — As extension or compression of length of any material i inch
square, is to its length, so Is the weight that produced that extension or com-
pression, to nioduUis of elasticity in lbs.
ExAMPLK.— If a bar of cast iron, x inch sqaare and xo feet in length, \» extended
.008 inch, with a weight of 1000 lbs., what is the weight of its modulus of elasticity ?
.008 : I20 (10 X 12) :: looo j 15000000 Ws.
To Compute !Modulus of Klastioity.
WTien a Bar or Beam is Supported at Both Ends and Ijoaded in Centre.
Rule.— Blultlply weight or stress per sq. inch in lbs. by length of material
in ins., and divide product by modulus of weight.
Or, — _E, -g _M,
EM
:;:; W. I representing length in tiM., M modulus.
W umght in Ihs. per sq. inch, and E compression or ^eUnsion.
ExAMPLB 1.— If a wrought iron rod, 60 feet in length and .2 Inch In diameter, ti
subjected to a stress of 150 llis., what will it be extended?
Modulus of elasticity of iron wire is 38 230 500 lbs. (see following table), and
0fit.a2X.7854 = -3i4»6.
— i52_ = 477.46 Ua. per sq. inch, and 60 x 12 = 720 ins.
.31416
Then 477.46 x
_7?o_ ^ 3p77}± ^ .^„ ,8 inch.
28 230 500 28 230 500
3. — ^Take elements of preceding case under rule for weight of modnloa
x2oXxooo oj t. .008 X X5 000000 j.^
C: ss .008 iw^ = s= xooo fM.
15000000
f?9
STBBNGTH OF MATERIALS. COHESION.
763
l^odtxlns of EJlastioity and 'Weigplit ofVarioufc* ^laterials.
SUBaTAHCKS.
Ash
Beech
Brass, yellow
** wire
Copper, cast
Kim..
Fir, red
Glasa
Gun-metal
Hempen fibres....
Ice
Iron, cast
wrought. . . . .
wire
n
Height.
Feet.
4970000
4600000
2460000
4 112000
4800000
5680000
8330000
4440000
2790000
5000000
6000000
5750000
7550000
8377000
Weight.
Lbs.
1 656 670
1345000
8464300
14632720
18240300
1499500
2016 x>o
5 55O0OO
8 844 300
170000
2370000
17 068 500
25 020 000
28 230 500
SUBSTANCBS.
Height.
j Feet.
Larch 14 415 000
Lead, cast ' 146000
Lignum- vitse 1850000
Limestone 2 400000
Mahogany 6 570000
Marble, white 2 150000
Oak : 4 750000
Pine, pitch ; 8 700000
*' white 8970000
Steel, cast. 8530000
" wire 9000000
Stone, Portland . . . 1 672000
Tin, cast ; 1 053 000
Zinc ; 4 480000
Weight.
Lbft.
1074000
720000
1080400
3300000
207x000
2508000
I 7x0000
2430000
X 830000
26650000
28 689 000
I 718800
3510000
13440000
"^VeigUt a M:aterial 'will bear per Sqt. Incli, 'witliovit
I»ermaiieiit Alteration of its I^eiijStli.
Lbs.
Matbkial.
Metals.
Brass
Gun metal
Iron, cast
** wrought...
Lead
Steel
Lbs.
6700
xoooo
15 coo
17800
I 500
45000
M.;tkbiai..
Lbe.
stones^ etc.
Marble
4900
2000
1500
3540
liimestone*
Portland
Woods.
Ash
Matrkial.
Woods.
Beech
Kim
Fir, red....
Larch
Mahogany .
Oak"
2360
3240
4290
2060
3000
3960
* Taotile atreagtb 2800.
Coxxiparative Iriesilienoe of "Woods.
Asb X j Chestnut 73
Beech 86 Elm 54
Cedar 66 I Fir 4
Larch .84
Oak 63
Pitch Pine 57
Spruce 64
Teak 59
Yellow Pine... .64
MODULUS OF COHESION.
Xo Connpiite Tjextgth. of a Friaxzi of a ^laterial -wliichi -would
be Severed 'by its owxi "Weiglit -wlien Suspended.
RuLE.^Divide tensile resistance of material per sq. inch by weight of a
foot of it in length, and quotient will give length in feet
Illustration. —Assume tensile resistance of a wrought- iron rod to be 60000 lbs.
per sq. inchu Weight of i foot = 3.4 Ws.
Then 60000-7-3.4 =: X7 647.06 /eei.
Ijenffth in Feet required to Tear Amnder thefdUowing Substances:
Rawhid& 15 375 feet. | Hemp twine. . . 75 000 feet | Catgut . . . . 25 000 feet
Elasticity of Irory as compared with Glass is as .95 to i.
When Height is given. Rui.e. — Multiply weight of i foot in length and
X inch square of material by height of its modulus in feet, and product will
give weight.
To Compiite Height of ^dodvilus of Klaatlcity.
Rule. — Divide weight of modulus of elasticity of material by weight of
X foot oi it, and quotient will give height in feet.
Example. — Take elements of preceding case (page 762), weight of i foot being
3 Wm. i what is height of its modulus of elasticity ?
x5 000 000 -^ 3 s= 5 000 000 /e€t
764 STKBNGTH OP MATERIALS. — CRUSHING.
From a series of elaborate experiments by Mr. £. Hodgkinson, for the
Railway Structure Commission of England, he deduced following formulas
for extension and compression of Ccut Iron:
e ' e'
EzUtuion: 13934040 -= 290743200 -= = W.
c»
Compresnon : 12 931 560 -r — 522 979 200 -y^ = W. e and c repretenUng txtention
and compresiiony and I length in ins.
Illustration. --What weight will extend a bar of cast iron, 4 ins. square and 10
feet in length, to extent of .2 inch?
13934040X^-290743200^^^ = 23223.4 — 807.62 = 22415. 78, which X4tn*
= 89666.12 lb?.
CRUSHING STRENGTH.
Crushing Strength of any body is in proportion to area of its section^
and inversely as its height.
In tapered columns, it is determined by the least diameter.
When height of a column is not 5 times its side or diameter, crushing
strength is at its maximum.
Cust /ron.— Experiments upon bars give a mean crushing^ strength of
ICO 000 lbs. per s^. inch of section, and 5000 lbs. per sq. inch as just sufficient
to overcome elasticity of metal ; and when height exceeds 3 times diameter,
the iron fields by flexure. When it is 10 times, it is reduced as i to 1.75 ;
when it is 15 times, as i to 2 ; when it is 20 times, as i to 3 ; when it is 30
times, as I to 4 ; and when it is 40 times, as i to 6.
Experiments of IV^r. Hodgkinson have determined that an increase of
strength of about one eighth of destructive weight is obtained by enlargmg
diameter of a column m its middle.
In columns of same thickness, strength is inversely proportional to the
**^3 power of length nearly.
A hollow column, having a greater diameter at one end than the other,
has not any additional strength over that of an uniform cylinder.
Wrought Iron. — Experiments give a mean crushing stress of 47000 lbs.
per sq. inch, and it will yield to any extent with 27000 lbs. per sq. inch,
white cast iron will bear 80000 lbs. to produce same effect
Effects.— k wrought bar will bear a compression of yfy of its length, with-
out its utility being destroyed.
With cast iron, a pressure beyond 27000 lbs. per sq. inch is of little, if
any, use in practice.
Glass and hard Stones have a crushing strength from 7 to 9 times greater
than tensile ; hence an approximate value of their crushing strength may be
obtained from their tensile, and contrariwise.
Various experiments show that the capacity of stones, etc., to resist effects
of freezing is a fair exponent of that to resist compression.
Seasoning. — Seasoned woods have nearly twice crushing strength of un-
seasoned.
JBlastio I^imit ooinpared to Crusliiiig Resistance.
Wrought- iron Commerce 545
Bessemer steel 615
Cast steel - 473
Cast BteeL 69a
Fagersta steel { -'5
8TBBKGTH OF MATBBIAL6. — CBUSHINO.
765
Oraslilxis Strength, of various Il^aterialsy deduced ftaxa
Kzperimeiits of^MaJ. ^^^ade, Kodgkinson, Ca,pt. AleisSf
XJ« 6« A.«f Stevens Institute, and "by &• 1^« Vose*
flecftioed to a Uh\fbrM Meetsure of One Sq. Inch,
Cast Iron.
ftnmm un Uaxbbiau
Gan-metal, American.
«t
M
•4
mean.
liOW Mfxnr, Na i, Eoglisb.
" Naa,
Clyde, Na 3,
i4
Cntablng
WeighU
Lbs.
174803
85000
Z25000
100 000
62450
99330
106039
Fkovxn Avo MmbbiaIm
Clyde, average, English.
Stirling, mean of all, English ..
^ extreme, English . . . .
Extreme, English ]
Average (HodgkiDSon), English
Blaenavon Naa
CnitblBC
WdghC
LlM.
83000
i2«39S
134400
53760
153300
84340
Z09700
W^BOCGBT I BOH
American, extrem&
mean.
<l 127
•I %
730
500
040
English
t*
averaga
Xi 40
•I 37
900
40000
850
Various Mstals
AInminiom bronse, 95 oop. . . ,
Fine brass.... •••••••...
Cast copper.
Steel, cast
Fagersta
<t
129 990
164000
Z17000
Z05000
950000
154500
Steel, Bessemer. . . . .
** " soft.
" tempered....,
" Siemens
Tin, cast...
Lead
so 000
66200
335000
15500
7730
' Elastic Crushing Strength of Wrought Iron and Crucible Steel is equal to its ten
Bile, of Bessemer Steel, 50 per cent of its transverse strength.
Woona
Ash...
Beech.
Birch.
Box
Cedar, red
'* seasoned ;*.
Chestnut
Elm
*' seasoned
Hickory, white
LArch
Locust
6663
6963
3300
7900
10513
6000
6500
5350
6831
lOOOO
8925
3200
5SOO
9 "3
Mahogany, Spanish.
Maple
Oak, American white.
'^ Canadian white..
" *' live...
'' Englisii..
Pine, pitch....
" white....
" yellow. . .
Spruce, white.
Teak
Walnut
8to8
8100
lOOOO
7000
5Q82
6850
9500
6484
8947
5500
8000
6000
12 100
6645
Chestnut 900
Hemlock. 600
Pine, white 800
Crosawise of F^re,
Pine, Yellow- South... 1400
*' Oregon 1200
Northern 1000
((
Redwood 800
Spruce 700
White Oak 2000
Mmcreaae in Strengih of Cubes of Sandstone^ per 8g, Inch {under Bloch
of Wo<id\ aa Area of Surface is inci'eased. (OenH QiUmort^ U. S. A.)
Stohb.
T'ellow Berea sandstone . .
Inchxs.
Lbs.
6080
LU.
6990
9500
«.5
LlM.
8226
Lbt.
8955
10730^1x3000
2.25
Lb«.
9130
13500
«-75
Lbi.
9838
Z3200
Lb*.
10125
Lb*.
11730
7<5b
STRENGTH OF MA.TEBIAXS. — CBUBHINO.
Stones* Cements, eto. (Per Sq. Inch.)
Yiwjxam and Matbxial.
Basalt, Scotcb.
" Welsh .
BetOD, N. Y. S. Ck>DcretiDg Co. |
Brick, pressed |
(I
GIou(^ester, Mass. .
baril burned.
((
u
i(
((
(I
{
common
yellow-faced burned, Eug^
Stourbridge fire clay, ''
Staffordshire blue, "
stock, Kuglisb
Farcham. Knglish
red, English
Sydney, N.S .,..
Caen, France
Cement, Hydraulic, pure, £ng. |
rorllaod, sand i
sand 3
3 mos
I sand, 3 mos
9 mos
I sand, 9 mos. . . .
12 inch cubes, \
12 mos. [
I sand and gravel)
■ •
Roman
'' pure, Eng
Rosendale
Sbeppey, Eng
Concrete, lime i, gravel 3.... |
Freestone, Belleville, N. J
" Connecticut
" Dorchester, Mass
Little Falls, N.Y....
Glass, crown
Gneiss
Granite, Aberdeen, Eng
" Cornish, ♦'
" Dublin, •'
" Newry, *'
(C
((
(I
((
t(
i(
((
(1
i(
(I
it
t(
(i
((
It
((
(I
Cruskine
Weight.
Lba.
8300
16800
800
I 400
6222
10219
14 216*
3630
800
4000
1440
165P
7200
2250
S^oo
808
2228
1543
17000
32000
1280
600
3800
2464
5980
3330
FiapSEs Aivp Matbeial.
Granite, Patapsco, Md..
Portland, Eng.
Quincy, Uasa.
Greenstone, Irish
Limestone
t(
t(
(I
(t
It
compact, Eng.
Uaguesian, ''
Anglesea
Irish
It
t(
2650
i3oo
343
750
3270
1280
460
775
3522
3319
3069
2991
31000
19600
10760
6339
10 450
12850
Marble, Baltimore, Md j
East Chester, N. Y.f. . . .
Hastings, N. Y
Irish
Italian
** white
Lee, Mass
Montgomery Co., Pa.. . .
Statuary
Stoclcbridge, Mass.t
Symington, large
fine crystal
strat^ horizontal
Masonry, brick, common |
" •• in cement
Mortar, good
" lime and sand
ti
tt
ti
(t
it
tt
tt
tt
tt
It
<<
tc
It
It
It
tt
II
tt
tt
(t
it
Cnihini
Wrtlfrlii.
'' " beaten...
common
Oolite, Portland
Pottery- pipe, Chelsea
Sandstone, Aquia Creek §
Arbroath, Eng
Connecticut 0
Craigleth, Eng.
Derby grit "
Holyh'lHiaartz, Eng
Seneca IT
Yorkshire, Eng.
Slate, Irish. {
Terra Cotta
Whinstone, Scotch
t PoBt-offlce, Waih. J City Hall, New York,
Te«t«d by J. W. ReUIy, Ordnaac* Dapl.. UJ3.A. f SmithMnian Inititute.
5340
4570
15583
15000
18800
4000
9000
7800
3 '30
3600
14000
8057
18 061
i39'7
18941
17440
12634
9630
2270a
8950
3360
1038a
II 156
18248
10 124
500
800
760
240
460
595
120
3850
12000
5340
7850
II 789
5S25
3 '36
95540
1076a
5710
13890
23744
5000
8300
• Teated by anthor at Stavans Institata, N. J
§ Capitol, Treaaury Department^ and ^tent Office, WasjiinKton^ D. C,
I Crumwell, Conn. " " .......
Safe l^oad of* Hollcw, Oylindrioal, and Solid Ooluinus.
A.rolies, Chords, etc., of* Caat Iron.
IloUmo Columns. Per Sq. Inch. {F. W. Shields, M. I. C. E.)
Length.
Thick-
neM.
Load.
Lenicth.
Thick-
neaa.
20 to 24
diam's.
Inch.
•375
•5
Lb*.
2800
33^
20 to 24
diam's.
Inch.
.625
•75
Load.
Lenirth.
Thkk-
neia.
Load.
25 to 30
diam'&
Inch.
•375
•5
Lba.
2240
2800
Leof^.
25 to 30
diam's.
Tkiek-
neai
Inch.
.625
•75
Load
3360
39*
Solid Ooluznns, etc.— 3360 Ib& persq. inch. {BrymL)
.A.roUes>.~56ao IbA. per sq. incb.
SntBHOTB OF MATBBIALS. — CfttTSUlNG.
767
Ctoot^0 And I>o*tB.— J inch dldmeter waa not more than is didmMers in
length . 2 of breaking weight of metal. ^ uiamciere in
.625 inch diameter and not more than 25 diameters in length .5 of breaking weight
01 metal, and when more than 25 diameters in length from .i to .025 of brealcing
weight of metal {Baltimore Bridge Co.) as
"Wrouglit-iroii Cylinders and Rectangular Tubes.
LSNOTH.
CYUMDKKd.
10 feet
10
10
RsCTANGULilB TUBES.
10
S
«o
io
75
10
feet
((
10 *'
7.66"
IO '*
>
J
}intemal
dlaphng'4
ExtetDCl
Diameter.
Ins.
1-495
2.49
6.366
4-x
41
4-1
4-25
425
8.4
8.1
8.Z
8.1
8.1
Intern «1
Diameter.
X
X
X
X
X
X
X
X
X
X
Ina.
1.292
2.275
6.106
4X
41
4.1
425
425
425
8.1
8.x
8.1
8.x
Thicknesa.
Ins.
.1
.107
•13
•03
•03
.06
•134
•134
f.26
(.126
.06
.06
.0637
.0637
Area.
Sq. Ins.
•444
.804
2-547
.504
•504
1.02
2-395
2-395
6.89
2.07
2.07
3551
3-55'
Crashing Weight
per Sq. Inch.
Lba.
1466X
29779
35886
X0980
"514
1926X
21585
33203
29981
13276
13300
19732
33208
Strengtli per Sq. Incli of l^-Iiicli Cubes under Blocks
of ^Vood. {GenH GiUmore, U. A A.)
Sur/acei Worked to a Clear Bed.
Grakitb.
Staten Island bind .
Maine
Qnincy, dark
" light
Westchester Co. , N. Y
Millstone Point, Conn
New London, Conn
Richmond, Va.
•* " gray
Cape Ann, Mass {
Westerly, R. L, gray.
Fall River, Mass. , gray
Garrisons, Hudson Riverf gray. ,
Dulath, Minn., dark
Keene, N. H., bluish gray
Used In Central Park, N. Y., red
Jersey City, N. J., soap
Passaic Co., " gray
[^MKSTO!^.
Glen's Falls, N.Y
Lake Champlain, N. Y.
Cant^oharie, N. Y
Kingston, **
Garrisons, "
Marblehead, O. , white
Joliet, IlL, white
Ume Island, Mich., drab . . . . {
Bay, Wla , blaisb drab
22250
X5000
X7750
14750
18250
16 187
12500
21 250
14 100
12423
19500
"4 937
15937
13370
«7 75o
1287s
17500
20750
24040
II 475
25000
20700
*39oo
18500
12600
X6900
xSooo
25000
2x500
Limestone.
Bardstown, Ky., dark
Cooper Co., Mo., dark dttlb. ...
Erie Co., N.Y., blue
Caen, Franoe ,
Marblb.
East Chester, N. Y ,
Italian, common
Dorset, Vt
Mill Creek, 111., drab
North Bay, Wis. , drab
SANnSTONB.
Little Falls, N. Y. , brown
Beikrville, N. J., gray
Middletown, Conn., brown. . . . .
Haverstraw, N. Y., red. , . .
Medina, N. Y., pink
Berea, 0., drab {
Vermillion, 0. , drab
Fond du I^c, Wia, purple
Marqoelte, M icb. , "
Seneca, O., red brown
Cleveland, O., olive green
Albion, N. Y., brmm
Kasota, Minn. , pink
Fontenac, Minn., lipht haff. . ...
Craigleth, Edinburgh
Dorchester, N. B., freestone. . . .
Massillon, O. , yellow drab
Warrendtmrg, Xc, MoMb drab.
lbs.
16250
6650
12250
365c
13504
13062
7612
9687
20025
9850
XI 700
6950
4350
17725
7af3©
10390
8850
6250
7450
9687
6800
«3 5oo
X0700
6250
X2 000
?i5o
750
5000
768 STRENGTH OF MATSBIALS. CRUSHING.
To Coznpute Crusliing 'Weiglit of* Coliizxixi.s«
Deduced by Mr. L. D. B. Gordon from, Results of Experiments of various AtUhors
METALB.
Cast Iron. {Hodgldnson.)
SUid or UoUow.
Round, — ^ — 5-= W. Reotetngtilar, ^ ^^ = W,
1+'"- i+ —
400 5G0
For L, T, U, +, etc., put '^\- {Unwm).
900
""Wrouglit Iron. {Stoneif.)
SoUd or Hollow.
16 a x6 « __
Round, =- = W. Rectangular, = w
, r* , ra
2400 7000
steel. (Baker.)
Solid — Strong steeL
Round, —=zW. Rectangular, — = ^ = W.
goo 1000
Solid.— mid SteeL
30 a 30 a
Round, Za" — ^' Rectangular, ;:2"="*
1400 ' 2480
a representing area of section of metal in sq. ins., r ratio of length to leeut extemai
diameter or side, in like terms^ atid W crushing weight in tons.
iLtutsTRATioN.— What Is the crushing weight of a hollow cylindrical column M
cast iron, 10 ins. in diameter, 20 feet in length, and i inch in thickness?
20 X 12
a = area of 10 ins. — area of 10 — 1 x 2 = 28.28 ins. r = =34, and 24*
36X28.28 1018.08 ^ ^ ,^'°
= 576. Then, ^2 ■—=— =417.25 fotu = 934 640 26«.
.576 I + 1-44
400
Safe T^oads.— Cast Iron, one fifth. Wrought Iron or Steel, one fourth.
WOODS. (C. Shaler Smith.)
C * ^ C representing coefficient of material^ a area of sedion
', f yT^ in sq. ins. , I length, and d diameter or least side^ both in
I -|- I — I X .004 Wee terms, and W crushing weight in lbs.
CoefBcients.* For Crushing Stress per Sq. Inch of Section.
Hemlock 3100 I White Pine 3500 I Georgia' Pine. 5000
Spruce 3500 I Yellow Pine. 5000 | Oak, White. 6000
{Hodgkinson.)
Ash 9000 I Beech 7050 I Elm 7000
<^ Canadian 7000 | Cedar. 5100) ** rock ....toooo
Illustratiox. — ^Assume a Yellow-pine column 10 in& square and la tL in lengtlii
5000 X »o' tJOOOOO ,.
— — -. =- = 373373 *ft«-
/12 X i2\ = 1 4- 207.36 X .004
Safe Juoad.* One fifth. {J>epartment of Buildings, Oitiy qf New York.)
STTRENOTII 01" MATKE1AL8. — CB08HING.
769
To Compute Safe Xioad of Columns.
Ca«t Iron.
Hound or
Hectaiisular
Solid or Hollow.
) 80000 <
=w.
"Wrouglit Iron.
40000 a
= W
For Mild Steel put 48 000, and for Strong or Hard put 6000a
a representing area of gection in sq. ins.^ I length of column in ins. ^ r radim oj
Gyraiion =U~, I moment of Inertia (see p. 819), C coefficient, and W safe load in Ws.
Coefficients.
Cast Iron
Wrought Iron.
Steel, Mild....
0o. Strong..
Round.
Solid.
.000164
.000047
— .000022
— .000053
Iu.c0rRATioN.-~Wbat is the safe load for a Cylindrical and Hollow Cast-iron col
amn, 10 ina in external diameter, 8 ins. internal, and 20 feet in length f
Hollow.
.000272
.000059
— .000035
— .000087
Rkctakoular.
Solid.
.000189
.000049
— .000033
— .000096
Hollovr.
.000267
.000047
— .000081
— .000155
Area=28.28»g. in*. I = 5* -4* X .7854 = 289.8. r= /^ = 3.22.
V 28.28
80000X28.28 2 262 400
5x[x+(i^)x.cx)0 27] 5X[.+555oX.ooo27]
= i8z 100 lbs.
2. Assume a aolfd column of Strong Steel of like diameter and 15 feet in length.
Area = 78. 54 sq. ins. , and r = 2. 5.
78.54x60000 4712400 4712400
r~~ — = ■_ ■ — = — ^ — - — = 1 624 965
^x[.+(if^yX-.<»0053] 4X[.v,5.84X-.«x>053] ^X'*' &'■
For Relative Value ot various Woods and Comparison of Long and Short Col-
umns, see page 976. ~
Weiglit loorne -writli Safety "by Solid. Cast-iron Columns.
/» xooo Lbs.— {New Jersey Steel and Iron Co.)
Lenfftb.
2
..V
44
Ins.
I02
184
Feet.
Int.
5
12.4
6
9-4
36
88
164
I
7.2
30
76
146
—
24
66
J 30
9
—
20
56
"4
zo
—
18
4»
Z02
Z2
—
.18
80
»4
—
—
28
64
»6 .
—
—
—
52
x8
—
—
—
44
30
—
—
—
—
DiAMKTVK.
6 ' 7
8
9
10
II
12
»3
luB. Ins.
Ins.
560
Ins.-
728
Int.
916
884
Ins.
Ins.
Ins.
288 414
1126
1354
—
264 386
532
698
1082
1320
1570
242 360
502
660
850
1056
1282
1530
218 332
470
630
812
1016
Z240
i486
iqS I 306
180 282
440
596
774
974
1 196
1440
410
560
658
932
1152
1392
136 238
354
494
846
1056
1292
122
200
304
432
586
774
966
878
1 192
ZOO
170
262
378
520
686
1094
84
144
226
333
462
616
796
1000
72
Z24
196
292
410
552
720
912
»4
Ins.
Ins.
1798 I 2086
17541
1706
1656
1550
Z440
X332
1228
1130
2040
1992
1040
1828
1712
1596
Z482
1372
VoT Tnlies or Hollo-w Columns.
Subtract weight that may be borne by a column, of diameter of internal
diameter of tuue from external diameter, and remainder will give wei^^Iit
that may be borne. Thickness of metal should not be less than one twelfth
diameter of column.
ILLDSTRATTOR. — Required the safe load of a solid cast-iron column 6 ins. in diam-
eter und 20 feet in length.
UAder 6 and in a line with 20 is 72, which x 1000 = 72 000 lbs.
NoTX.— This is about one sixth of destruQtive weight
3T
J JO 6TRBNGTH OF MATJBBIAI^. — DEFLECTION.
DBFLBCTIOK.
X>efieotiozi ojf Sars, IB earns, GUrders, etc.
Experiments of Barlow upon deflection of wood battens detenniued,
that deflection of a beam from a transverse strain, varied directly «s cub<
of length and inversely as breadth and qube of depth, and that with
like beams and within limits of elasticity it was directly as the weight.
In bars, beams, etc., of an elastic material, and having great length com-
pared to their depth, deductions of Barlow will apply with sufficient accu-
racy for all practical purposes ; but in consequence of varied proportions of
depth to length, of varied character of materials, of irregular resistance of
beams constructed with scarphs, trusses, or riveted plates, and of unequal
deflection at initial and ultimate strains, it is impracticable to deduce any
exact laws regarding degrees of deflection of different and dissimilar figurei
and proportions.
From an experiment of Mr. Tredgeld it was shown that deflection of cast
ircMi is exactly proportionate to load uutii stress reaches a certain magnitude^
.when it becomes irregular.
In experiments of Hodgkinson, it was further shown that sets from de-
flections were very nearly as squares of deflections.
In a rectangular bar, beam, etc., position of neutral axis is in its centre,
and it is not sensibly altered by variations in amount of strain applied. In
bars, beams, etc., of east and wrought iron, position of neutral axis varies in
same beam, and is only fixed while elasticity of beam is perfect When a
bar, beam, etc., is bent so as to injure its elasticitv, neutral line, changes, and
continues to change during loading of beam, untQ its elasticity is destroyed.
When bars, beams, etc., are of same length, deflection of one, weight being
suspended from one end, compared with that of a beam Uniformlxi Loaded,
is as 8 to 3 ; and when bars, etc., are supported at both ends, deflection in like
case is as 5 to 8. Whence, if a bar, etc., is in first case supported in middle,
and ends permitted to deflect, and in second, ends supported, and middle
permitted to descend, deflection in the two cases is as 3 to 5.
Of three equal and similar bars or beams, one inclined npward, one down-
ward, at same an^le, and the other horizontal, that which nas its an^le up-
ward is weakest, the one which declines is strongest, and the one horiz<Hital
is a mean between the-two.
When a bar, beam, etc., is Uniformly Loadedf deflection is as weight, and
approximately as cube of length«or as square of length ; and element of de'
flection and strain upon beam, weight being the same, will be but half of that
when weight is suspended from one end.
Deflection of a bar, beam, etc.. Fixed at one End^ and Locuied at other,
compared to that of a beam of twice length. Supported at both Ends, and
Loaded in Muldle, strain being same, is as 2 to i ; and when length and
loads are same, deflection will be as 16 to i, for strain will be four times
greater on beam fixed at one end than on one supported at both ends ; there-
&re, all other things being same, element of deflection will be four times
greater ; also, as deflection is as element of deflection into square of length,
then, as lengths at which weights are borne in their cases are as i to 2, de*
flection is as i : 2^ x 4 = i to 16.
Deflection of a bar, beam, etc., having section of a triangle, and supported
at its ends, is .33 greater when edge of angle is up than when it is down.
In order to counteract deflection of a beam, etc., under stress of its load,
where a horizontal surface is required, it should be cambered on its upper
surface, equal to computed deflection.
6TBENGTH Oy MATSBIAJ.B. — DBFLJJCTION. 77 1
8qf€ D^cfioH,— One fortieth of an inch for each foot of span, with a
factor of safety for load of .33 of destructive weight = Y^m hut for ordinary
loads and purposes,
Caa Iron, Yihu to ttAjt •» »nd Wrought Iron, t At to ipfViy or y^j
after heam, etc., has hecoiue set.
When Length is uniform, with same we!<;ht, deflection is inversely as
breadth and square of depth into element of deflection^ which is inversely as
depth. Hence, other things being equal, deflection will vary inversely as
breadth and cube of depth.
lLLuaTBATio>.~-D6lleetioDB of two pine battens, of UDifurm breadth and depth, add
equally loaded, but of lengths of 3 aud 6 feet, were as i to 7.8.
Deflection of difierent bars, beams, etc., arising from their own weight,
having their several dimensions proportional, wiU be as square of either of
their like dimensions.
NoTK.— In construction of models on a scule intended to be executed in Aill di-
mensions, this result should be kept in view.
When a continuous girder, uniformly loaded, is supported at three points
by two equal spans, middle portion is deflected downwards over middle bear-
iiig, and it sustains by suspension the extreme portions, which also have a
bearing on outer bearings. Middle portion is, by deflection, convex up-
wards, and outer portions are concave upwards; and there is a point of
"contrary flexure, where curvature is reversed, being at junction of con-
vex and concave curves, at each side of middle bearing. This point is dis-
tant from middle bearing, on each side, one fourth of span. Of remaining
three fourths of each span, a half is borne by suspension by middle portion,
and a half is supported by abutment. Hence, distribution of load on bear-
ings is easily computed, as given above. Deflection of each span is to that
at an inde|)endent beam of same length of span as 2 to 5,
In a beam of three equal spans, deflection at middle of either of side spans
is to that of an independent beam as 13 to 25.
In a long continuous beam, supported at regular intervals, deflection of
each span is to that of an independent beam of one span as i to 5.
Cylinder. — If a bar or beam is cylindrical. Barlow gives the deflection 1.7
times that of a square beam, other things being equal ; D. K. Clark puts it
at 1.47.
Korxnulas tov X>eAeotloxi of Seams of Heotangular Sec-
tion, etc.
f'^^Loa.UdinMid^ -^ = D. Lo<uUa Uniformly. J^^^}^ = n
Both in , n.. ^ 2TOnW _
End,.) <t<«^<^P<n«L ^jj^3c = D.
SuppoHed at Both Ends,
Loaded in Middle, -Jl^--.-l). Loaded Uniformly. „ ^!\^, ^ = D.
m^ n^ W
Loaded at any one Point. . . .--^ =c D.
Supported (n Middle.
■? n W
End» Loaded Uniformly. — -^ ^ ^ ,-,-==3 0.
5 X 16 6 d3 c
{ representing length infeH^ b breadth^ and J depth, both in in*., W weight or stress
in lbs., m and n-dii^nces of weight between supports, C a constant, and I) dejlection
ffitnc
772 STEBNGTH OF MATERlALS.-^DEPLKCTION.
Deflect ion of* Beams or Sairs of l%ectan.gula.T*
tSection..
Xo Compute IDefleotion. of* a R.eotangular Beain ox* Sap.
Supported at Both Ends. Loaded in Middle,
CAST IRON.
13 W
Rectangular Beams. -^^ r-Ta = D. Cylindrical. For 36000 pat 34000.
36000 Ott^
I representing length in feet^ b and d in inches.
Illustration.— Assume a rectangular bar of cast iron, i inch square and loaded
nrith 224 lbs., 4.5 feet between its supports.
224 X 4. 53 ^ !^ ^ 67 incK
36 000 X I X 1 3 30 000
By actual experiment of Mr, Hodgkinson the deflection waa .561 inch.
WROUGHT IRON.
Rectangular Beams. r- - = D. Cylindrical. For 60000 put 4200a
60 000 o a3 ^
WOODS.
13 W
= D. I representing length in inciies, and W weight in tons.
bd3G
Mean <)fLa*lett-s, Barlow^ etc
c
Ash, Canadian 1476
" Eug 2722
Beech 2418
Blue Gum 2559
Elm 1227
Fir, Dantzic 2490
'* Riga 2920
Greenheart 1888
c
Iron-wood 4228
Larch 2100
Mahogany, Honduras 21 18
^^ Mexican. 3608
'^ Spanish.. 3360
Oak, Baltimore. 2761
'' Canadian 3445
" Eng 1848
c
Oak, French 2656
<^ white 2x14
Pitch pine 2968
Red " 2434
Rock-elm 2319
Spruce. 3300
" Amer 2669
Yellow pine 2084
Illustration. — What is the deflection of a floor beam of Yellow pine, 3 by 19 io&,
13 feet between its supports, under a uniformly distributed load of 3000 lb&?
8 6 (/J C ' 8 X 3 X 123 X 2084 86 427 848
8X3X i2''X 2084 X. 216 18668 415 ,
■ — := =1.25 tons.
5X2 985 984 14 929 920
* % for being uniformly distributed.
By a test of a like beam, the deflection waa .2Z3S'
13 "W
For Cylindrical Beams deduct one-third fi*om these constants, or 3t>i = D.
3.1404 c
For Torsional Defleotiou of* Iron Sliaft. (/>. K. Clark.)
W rl Vf r I
Cast Iron, ■ , = I). . Wrought Iron, ■ ,^ = D.
644 d4 ' o . ^^^^ ^4
W in tons and r radius or distance of applied power.
Deflection of* Continuous Oirders or Beams.
Beams of Uniform Dimensions^ Supported at Three or More Bearingu,
{D. K. Clark.)
I. Two Equal Spans or 3 Bearings.
Weight on ist and 3d hearings . 375 W I
'* " 2d bearing = i.25W/
2. Three Equal. Spans or 4 Bearinffs.
Weight on ist and 4th bearing = .4 W I
♦' " 2d "3d '' =1.1 W I
bearing = 1.25
3. Four Equal Spans or 5 Bearings.
Weight on xst and 5th bearings. 39 W I \ Weight on 2d and 4th bearing = 1.14 W i
Weight on 3d bearing = .93 W J.
STRENGTH OF MATEBIALS. — DBFLBCTION.
773
G?o Compnte Adaximuxxx i:4bad that may be 'borne by a
I{.ectai\su.lar 3eaxxi.
Deflection not to exceed Assiyned Limit of one hundred and tioentieth of cm
Inch far each Foot of Span.
Supported cU Both Ends. Loaded in Middle. -^
bd*
= W. 6 and d representing breadth and depth in ins.^ I length in feel, C wn-
stant^ and W weight or load in lb*.
Constants.
Oak, white 027
Ash, white 03
Pine, pitch 033
" yellow. 036
CTast Iron 0003
Wroaght Iron 0021
Hickory .0x8
Teak. 024
Oak, red 039
Hemlock .039
Pine, white.' 039
Chestnut, horse 051
Illustration. — What is maximum load that may bo borne by a beam of white
pine, 3 by 12 ins., 20 fbet between its supports, and loaded in Its middle?
G = .039.
Then
3 X 123 5,84
-=^- = - — ^ = 332.3 lbs,
20'-' X. 039 15.6 ^^ ^
WROUGHT IRON.
X>efleotioix of "^Troiagbt-iron Gars.
Supported at Both Ends. Wcigkt applied in Middle.
No.
FOBM.
t(
X. American.
2.' English...
3-
4-
II
((
I
((
1
•
1
n
1
a
3
Feet.
Id8.
Ins.
Z.83
I
I
2-75
2
2
a. 75
15
25
2-75
i-S
3
Weight and Deflection
by ActGal
Ob*9«rvation.
at one eizth
of Peel rue-
tivc Weight.
Lh«.
Ia«.
Lbd.
lUB.
600
.06
266
.027
4480
.08
1310
022
8960
.104
2128
.025
8960
.088
3800
•037
at ^,th of
an Incti for
each Foot of
Span.
Lb*.
148
1310
1873
2259
Ina.
•015
.022
.022
.022
3 a
I
n
s
1.29
1.25
.88
To Compute T>eflection. of, and "Weiglit tKat may be borne
by, a Reotangular Bar or Beam of 'Wroughit Iron.
W i» ^ W «3 _ 600006 d3 C D
l^'
= C.
= D.
« ^^^_^^
6oooobd^D " Coocobd^C
Illustration.— What weight will a beam 2 ina in breadth, 5 ins. in depth, and
15 feet between its supports, bear with safe deflection of y|^ of an inch for each
foot of space, or yAhi ^^ '^ length ?
C (h)m table = .88. D = y^^ of 15 = . la inch.
6ooooX2X5=*X.88x.i2 ,584000
.5' =-3377- = •"'•" '*••
D. R. Clark gives for Elastic deflection, 47000 for Rectangular bars, and 32000 for
Cylindrical.
NoTi.— Deflection of ^J^ to ^^ of the length may be allowed under special cir-
cumstances; but under orrinary loads the deflection should not exceed one fourth
of these, as y^\j^ to ^^.
Practice in U. S. is to uUow -1-^(^1^ after girder has taken its permanent set
In small bridges there is a slight increase in deflection from high speeds^ about
.z66 or . 144 of the normal deflection, with the same load moving at slow speed.
In large girders there Is no perceptible difference between the deflection at high
aad low npeedB.
3T*
774
8TREKQTH OF MATERIALS. — DEFLBCTIOK.
Deflection of \^t>onglit*iron Rolled Beatns«
Supported cU Both Ends. Weight applied in Middle.
W/3
70000 rf=» (4 a + 1.155 a')
--sC at RmluoMl Weight
D
and Deflection.
^
Flange*.
Weight tad Deflection
No.
Foui.
Width.
Mean
Thick-
Web.
Depth.
by Actual
Observation.
at one elxth
of DestractiTa
Weiffht.
0
I
Feet.
Int.
Inch.
Inch.
In*.
Lbi.
Ine.
Lbo.
Inch.
• 1.
10
3
.485
•5
7
Z2000
•4
3800
.127
1.05
2.
3-
it
it
20
20
4.6
5-7
.8
.643
•5
.6
985
"•75
16000
20000
«'«5
.85
6300
8000
•453
•34
^0
.98
Xo Compnte Deflection of*, and. AVeisl^t tbat aiay \>e 'borne
by, a 'Wrouglit-iron Rolled 3eam orUnifbfui and Syzxx—
metrical fSeotion*
Supported at Both Ends. Weight applied in Middle. (D. K. Clark.)
WZ»
=jD,
70000 d' (4 a 4* « • »5S <»') D
= W.
70000 jf* (4 a-|- "•'SS «')
I representing man infeet^ d reputed depths or depth less thieknest of lower flan fft
in ins.y a area of section of lower flange^ a' area of section qf web for reputed depih
off)eam, both in sq. ins.^ and W weight or stress in lbs.
iLLrsTRATiox.-^What 18 deflectioD of a wroaght-iron rolled beam of New Jersey
Steel and Iron To., lo 5 ins. in depth, flanges 5 by .5 inc., and width of web .47
inch, when loaded In itH middle with 8000 lbs., and supported over a span of 20 feet?
d =s> 10.5 — .5 .2 10 ins.y o = 5 X .5 = 2.5 »g. tiw., and a' = 10 X .47 — 4-7 *3- <W.
Then
8000 X 2o3
64 000 000 . .
— ^ = .50 inch.
"O7999 500
70000 X io»X(4X 2.5 -(-1. 155 X 4-7)
If weight is ouiforroly distributed, divide by 112 500 instead of 70000.
A like beam 6 ins. in depth, loaded with 2608 Iba, and supported over a span of
12 feet, gave by actual test a deflection of .3 inch, and by above formuU it is also
.3 ineh.
NoTB. — Deflection for such a beam, for a statical weight or stress of 17 100 lbs.,
unifrtmUy distributed, by rules of N. J. Steel and Iron Co., would be .54 inch, which,
with difftereoce iu weights, will make deflections alike.
Deflection of Wronglit-iron Riveted Beams.
Supported at Both Ends. Weight applied in Middle.
W /S
, — -3=r SB C at Redoced Weight and Deflection.
3__ + - j rfa D
No. FOBM.
Length.
Flangee.
Angles.
Web.
a
4
1
Weight and
by Aetna!
Observation.
Deflection
at one alztli
of DeatmctiTe
Weight.
C
Feet.
Ina.
Ins.
2.125X2
Inch.
Ine.
Lta.
loch.
Lbe.
Inch.
'1
7
45X
X.28
2.125X2
X.29
2X2
•35
1
7
4216
.1
406a
.096
.63
' T
11.66^
•5 1 X.3'25
4-5X 2X2
.25
12.5
77280
.46
ia88o
.075
1.96
A
1
•375
4-5X
X.3ia5
a X a
1
t(
•S.5 '
•5
7 X
•5
X.375
3X3
X.4375
•375
x6-5
"5584
.«75
19165
.148
3.86
STBBNOTB OF HATBBIALS. — DSFLSCTION.
775
To Compute IDefleotion of, and 'Weiglit tb.at may "be "borxxe
\>y, a Hive ted Beaxxi of* M^rouglit Iron.
W/3
168000
(^+t)
r=D.
d'Cf
168000 f^ -^Z^jd^C D
i3
W.
a, a', and a" representing areas of upper and Unoer flanges with their angle pieces^
and ofwebfnr its entire dq^lk, all in sq. ins.
NoTK. — If tliare are not any flanges, as in No. z, angle pieces alone are to be eomputed for flange
Illustration.— What weight will a riveted and flanged beam of following dimen-
sions sustain, at a distance between its supports of 25 feet, and at a safe deflection
of. 2 inch or j^jf of its length?
Topflange 6X-5^. | Web sins.
Bottomflauge 6X.5" | Depth 17 "
Angles 2.25 X 225 X. 5 ins.
a and a' each = 6 x .5 = 3 + 2.25-1-2.25— .5 x .5 X 2 = 7 sq. ins.
a" = . 5 X 17 = 8. 5 <9. ins. C, as per No. a,= .43, but inasmuch as flanges in this
are much heavier, assume .5.
168000
Then
C4^+^)
i7'X.2X.5
«5'
= 44303700^ ,,
15625
Strength of a Riveted beam compared to a Solid beam is as x to 1.5, while for
equal weights its deflection is 1.5 to i.
6.
7-
O
0
Tu."bvilar O-irders. "Wrouglit Iroxi«
Supported ai Both Ends. Weight apj
Ex-
ternal.
Ins.
3
24
24
35-75
12
Ho.
Smenou
•
X.
□
Thickness
.03 inch
3.
3-
top
bottom
.525 "
.372 " )
.244 "
sides .125 '*
" Thickness .75 "
thickness .0375"
0416"
.143 "
H
n
Dei
Inter-
nal.
Feet.
Ins.
Ins.
3-75
1.9
2.94
30
'5-5
22.95
30
16
23.28
45
24
34.25
»7
12
11.925
17
«7
9- 25
I 925
13-535
14-714
13.62
IS
d in Mi
Iddle.
1
•
g
t
2
Lbs.
"Ins.
Inch.
448
.1
.03
33*85
-56
•24
32538
X.IZ
•24
128850
1.85
.36
9 755
-6s
.136
2262
16800
.6a*
1.39*
.136
.136
o
I
^
Q
m
IS
C
288
473
224
362
62.8
47-9
119
* Destmetlve welgiit.
To Compute Deflection, of, and AVelgHt tliat may "bo
'bori»e bjr, a WrousUt^iron TiibYilar Gl-irder.
16 ft d* C D
= W.
W/»
= 0.
Illustkation. — What weight may be safely borne by a wrought-iron tube, alike
to Na 3 in preceding table, for a length of jo feet, and a deflection of .32 inch 7
16 X 16 X 243 X 224 X 24 _ 190 253 629 _
ao3 """ QTrwk '
30
27000
rUmged Rails,
Deflection of Iron and Steel Flanged Rails within their elastic limit, compared
with their transverse strength, is as 17 to ao, and with double-headed it is as n to a^
776
STBENGTH OF MATEBIALS. — DEFLECTION.
RAILS.
Supported at Both Ends. Weight applied in Middle.
Iron.
Na FoBM.
Head.
Bottom.
Weight
YaJd.
Feet.
Ills.
Ins.
Lbs.
' I
2.7s
2.25X1
2.25X1
60
a. "
3- "
4-5
5
2.3 Xi
2.3 Xi
2.3 Xi
2.3 Xi
55
82
^ T
2.75
3.5 X .8
2.25X1
60
= X
2.58
2.23X1
3-5 X .6
57
Ins.
4-5
4.5
5-4
4
3-5
Area.
Sq. Ins.
6.166
6.68
8.25
6.7
3-8S
Observed
Weight and
Dedection.
OeetmetlYW
Weight
and
Deflection.
Lbs.
»3440
II200
25760
II 200
II 300
Ins.
.034
.11
.2
•035
Lbs.
26680
24640
51520
26680
.097 20160
.065
.204
378
.065
.138
Steel.
No. FOKM .
Feet.
1
Ins.
Bottom.
•*•
• a. <
^^
Lbs.
Ins.
-r
5
—
—
78
7. "
Bessemer.
3.62
*""
—
86
^J.
5
2-5
,«-375X:|^
84
Web.
Dept
Centres
of
Heads.
h.
e
3
Ins.
Area.
Observed
Weight and
Deilection.
Deatmetlva
Weight
Deflection.
Inch.
Ins.
S.Ins.
Lbs.
In.
Lbs.
Inch.
•75
4-2
5-4
7.67
36086
•25
80192
•55
—
—
5-5
8.43
22400
.14
26680
.165
.65
3-37
4-5
8.24
27290
.24
27290
.24
70 Compute X)efleotioix of* I^oii^ble-headed. Rails 'witla.in
SlastiQ ILiimit. {D.K.Clark.)
Suppoi'ted at Both Ends. Weight applied at Middle,
IRON.
= D. a representing area of one head^ less portion per^.
W/8
57ooo(4ad'=+i.i55<d3)
taining to toeb^ d whole depth of rail, d' vertical distance between centres of heads,
t thicJmess of web, all in ins.^l length in feet, and W weight in lbs.
STEEL.
F^r 57 000 put 67 400.
iLLUSTRATiov.^Tftke oase No. 3 (Iron), in preceding table, with a weight of 36000
Iba ; what will be its deflection between bearings 5 feet aiiartf
0 = 1.911. •d' = 4.2. £{ = 5.4. { = .82.
26000X5* 3250000
Then
57 000 (4 X 1.9" X 4.2' + 1.155 X .82 X S-4') S7000X 284
= .a inch.
To Compute Deflection of Iron and Steel Rails of* XJix—
Bymmetrioal Section -witliin Slastio Limits.
«
Elastic Deflection of Steel Flanged Rails of Metropolitan Railway of London, aa
ftetermined by Mr. Kirkaldy, at a span of 5 feet, and loaded in middle', was .03 Incb
* ton. (See Manual ofD. K. Clar.k, pp. 667-670.)
6TKEN6TH OF MAT2:BIALS. — ^DBFLECTIOK.
m
CAST IRON.
Oefleotioxi of Reotangrular IBars and. Seams of* various
Seotions, etc., "by U, S. Ordnance Corps, Barlo->^»
Hoclglziuson, and Cubitt.
Supported at Both End*. Weight appKed in Middle.
FOBM.
z. American. ...
3.EDgli8lL ''
3. ** "
4- " I
5- " []
Length of Bear-
ing.
•
1
1
Feet.
Ins.
Ins.
1.66
2
2
A
Z
4
X
4
4-5
3
1
4-5
z
{'1
Weight and Deflection.
By Actual
Omervatlon.
Lbs.
5000
212
1008
1 120
2231
Ins.
.036
•33
•4
t4a
•51
At one sixth
of Bniftking
WeiKbt.
Lbs.
1666
80
5333
ai5
422
Ins.
.012
■ 12
2.1 ■
.27
.1
At ^th of
an men for
each foot of
span.
Lbs.
1805
22
3370
30
156
Ins.
.013
•033
1-33
.037
•037
^"^i II
I
C
3.8Z
4"
389
2.37
2-33
^o Compute 33efleotioxa of, and Weigrlit that msiy be
borne by, a H.eotangular Bair or Beam of Cast Iron.
Wi». _ Wis _ 104006^3 CD
= C.
= D.
W.
zo4oo6d*D "' 10400 &d*C /'
Illustration. — What weight will a beam 2 ins. in breadth, 5 ins. in depth, and
16 feet between its supports, bear with safe deflection of y-j^ of an inch for each
toot of span, or y^i^ of its length ?
C from table =:^ 3. 89. D — . y^ of 16 = . 133 ins.
10400 X 2 X 5* "x 389 )C.i33 _ I 345 162 „
i6i " "756" " ^^^^
gives C uniform for Rectangular bars of 2.69, and 1.85 for CylindrioaL
FLAKGED BBAMS. Cast Iron.
Supported at Both Endt. Weight applied in Middle.
To Compute Deflection of*, and "%Veiglit tliat may be
borne by* a ITlanged Beam of Cast Iron of LTniform
and Syxnmetrioal Section.
_ ^^' ^p 27000 da (40-fz.i55«''')D^^
37000 d' (4 a 4- 1. 155 a' 2) * l^
Illitstration.— What is deflection of a cast-iron beam (Hodgkinson's) 7.15 ins.,
flanges 2.6 x -86 ins. and 5 X z.6 in&, and width of web z inch, when loaded in its
middle with zi 200 lbs., over a span of 15 feet f
d = 7.z5— 1.6 = 5.55 int., 0= 5 X i.6±=: 8 tm., and «' = 7. zs — z.6 = 5.55 ini.
11200X15^ 37800000
Then
= .67 ivu.
27000X 5-55' (4 X 8+ Z.155 X 5.55') 27000 X 30.8 (32 + 35-57)
NoTX z. — ^The observed deflection of this beam was 1.28 ins., at one sixth of its de-
structive weight it was .3, and at j^ of an inch for each foot of span it wai
.135 inch.
3.— The mean ratio of elastic to destructive stress is 73 per cent.
Formulas for value of deflection signify that deflection varies Uirectly as weight.
aod as cube of length ; and inversely as breadth, cube of depth, and coefiBcient or
«ta8(iclty.
778
8TBENGTH OF MATERIALS. — ^DBFLKCTION.
Elastic Strength of Beams of Unsymmeiricai Section. — Elastic strength is
approximately dedacible from ultimate streogth, according to ordinary ratio
ox one to the other, ascertained experimentally. Elastic 'strength and de-
flection of a homogeneous beam of any section is same, whether in its nor-
mal position or turned upside down.
Comparative Strength, and X>eflectioii of Cast-irozi
Flax&sfed Seaxxie.
DMcriptioD of Beam.
Beam of equal flanges
** with only bottom flange.
" ** flanges as 1 to 2....
" *• " 1 104....
Comp.
Strength,
.58
.72
.63
•73
Description of Beam.
Beam with flanges as i to 4.5. .
'* *' " I to 5.5..
" " '• ito6 ..
♦• " " I to 6 73
Comp.
Streairtb.
.78
.83
.92
SHAFTS.
To Oozxip-ute Deflection and Distributed Weight for
X^imit of Deflection.
'\Vron.ghLt Iron.
DeJUction. Weight.
Round.
Square.
Bound.
Square,
Supported at Ends.
66400 d«
97 500 «*
39400 d«
58000 s*
Round -r-.
Wl»
Square.
jBSood*
ii6ooo<*
and
and
and
and
and
Fixed at End*.
Vf 19
133000 d*
= D.
D.
Snpported at End*.
664 d«
195000 s*
Cast Iron.
79000 d*
= D.
= D.
116000S*
Steel.
= D.
Wf«
' — 7 and
158000 d*
= D.
I*
975 «*
394 d«
580 «♦
788 d*
«6o»*
and
and
and
and
and
and
Fixed at Enda.
'330 d*
1950 «*
790 d*
1160 «♦
i«
= w
= w
S=W.
— Xrr-—^-
2320 6*
/«
= w.
232 000 «♦
d representing diameter and a Hde ofshajt, in ins., I length bettoeen centres 0/ bear-
ings, in feet, tmd W weight in lbs.
Deflection of a Cylindrical Shaft from its Weight alone,
-when Supported at Both Knds.
007 318 jrc~^' ' rtgpresenting length in feet, d diameter in ins., emd C cms-
stant, ranging from 475 to 550.
The greatest admissible deflection for any diameter is .001 67 ^= D.
d
A.dn>issible Distauoes bet-ween Seetrinfse. ^.9128 dC^L
Distance. 1
Pimm,
ef Shaft.
Wrooght
Iron.
Steel.
Diam.
of Shaft.
IM.
Feet.
Feet.
Im.
1
12.27
is.6i
5
9
15.46
15-84
6
3
17.7
18.19
7
4
19.48
20. 03
8
Distance.
Wronjcht
Iron.
Feet.
90.99
22.3
2348
«4-55
Steel.
Feet.
21.57
22.92
2413
35-23
Diam.
of Shaft.
Ins.
9
10
II
X2
Dbtanca.
Wrought
Iran.
Feet.
as- 53
96.44
97.3
98.1
StMl.
PMi.
97. x8
98.05
28.88
When Bids of Shaft are rigidly connected at Ends.
Barlow gives D = .66 of results obteined by above formula: but when d«fleetioi
of attached length is considerable, Navier gives I) ^ 25 of above.
8TBBNQTH OF MATE&IALS. — ^DEFLECTION. //Q
X>efleotioix of Miill and Vmotory Shafts.
= D. 2 representing length between supports in ins., W weight at middle
6wd*C
in ibs.t ^ diameter ofihaji in ins.^ and C as/oUows :
BesBemer steel 3800000 j Wroagbt iron....... 3500000
a?o Coxnpute X>efleotioix oi* a Csrlindrioal Sliaft.
RuLE.*-Divide square of three times length In feet by product of follow-
ing Qmtiants and square of diameter in Ins., and qaotient will give deflection.
Cast iroa, cylindrical 1500 | Wrought iron, cylindrical 1980
** " square 2560 1 " '* Square 3360
ExAMPLB.— Length of a cast-iron cylindrical shaft is 30 feet, and its diameter in
oontre 15 in& ; what is its deflection?
30X3 _ 8100 _
1500X15 337500
fiPRIKOB.
. Flexure of a spring is proportional to its load and to cube of its length*
Deflection of a Carriagt Spring*
A railway-carriage spring, consisting of 10 plates .3125 inch thick, and j
of .375 inchf length 2 leet 8 ins., wiJth 3 ins., and camber or spring 6 ins.,
deflected as follows, without any permanent set :
.5 ton 5 inch. 1 1.5 tona......... z.5 ina | 3 tons...* siaa
a " 1 " |d »' » " 14 •• 4"
Compression of an India-rubber Buffer ofs Tns. Stroke.
s ton 1.3 i&& I 2 toua 2 ins. | 5 tons.-. a. 75 Ina
i-Stona X.7S •' I3 " 2.375 " |to " 3
d-enerftl £>edudtidnB.
D^cHon depends essentially, upon form of Girder, Beam, etc
A continuous weight, equal to that a beam, etc., is suited to sustain, will
not cause deflection of it to increase unless it is subjected to considerable
changes of temperature.
Heaviest load on a railway girder should not exceed .x6 of that of de-
structive weight of girder when laid on at rest.
Semi-girders or Bcaffw.— Deflection of a beam, etc., fixed at one end and
loaded at other, is 32 times that of same beam supported at both ends and
loaded in middle.
Dtjtection consequent upon Velocity o/i^arf.— Deflection is very much in-
creased by instantaneous loading; by some authorities it is estimated to be
doubled.
Momentum of a railway train in deflecting girders, etc., is greater than
effect from dead weight of it, and deflection increases with velocity.
When motion is given to load on a beam, eto., point of greatest deflection
does not remain in centre of beam, eto., as beams broken by a travelling load
are always fractured at points beyond their centres, and often into several
pieces.
Heaviest running weight that a bridge is subjected to is that of a loco-
motive and tender, which is equal to 2 tons per hneal foot.
Gurders should not, under any oircumstiwicds, be deflected to e^tceed tom
Inch to a foot in length.
78o
STBEK6TH OP MATEBIALS. — ^DEPLECTION.
A carriage was moyed at a velodty of lo miles per hour ; deflection was
3 inch, and when at a velocity of 30 miles deflection was 1.5 ins.
In this case, 4150 lbs. would have been destructive weight of bars if ap-
plied in their middle, but 1778 lbs. would have broken them if passed over
them widi a velocity of 30 luilcs per hour.
Relative SHaatioity ox" various Alateriald* {TrunUmU.)
Ash 3.9 I Gtifitlron i | Pine, white 2.4 I Pine, pitch 3.9
Beech 3.1 1 Elm and Oak.. 2.9 | '' yellow... 2.6] Wrought Iron. .86
Cast Iron, — Permanent deflection is from .33 to .5 of its breaking weight,
and deflection should never exceed .125 of ultimate deflection, and it is not
permanently affected but by a stress approaching if^s destractive weight.
By oxperiments of V. S. Ordnance Corps (Report, 1852), set or permanent deflec-
tion was .38 of its breaking weight, ultimate deflecMun .133 ins. Deflection for
yj^ of span = .013, or . I of ultimate deflection.
By experiments of Mr. Hodgkinson (See Rep. of Comm^* on Railtoay Structures.
London, 1849), set for English iron bore a much greater proportion to its breaking
weight.
A beam, etc., will bend to .33 of its ultimate deflection with less than .33
of its breaking weight, if it is laid on gradually, atid but .16 if laid on
rapidly.
Chilled bars deflect more readily than unchilled.
Results or Sxperimexite on tlxe Sul::^eotioxi. of* Caat-irox&
Sars to ooxxtiuvied. Strains.
(Jiep. of Commas on Railway Structures^ Ix)ndon, 1849.)
Cast-iron bars .subjected to a regular depression, equal to deflection due to
a load of .33 of their statical breaking weight, bore 10 000 successive de-
{)ressions, and when broken by statical weighty ^ave as great a resistance as
ike bars subjected to a like deflection by staticieil weight.
Of two bars subjected to a deflection equal to that carried by half of their
statical breaking weight, one broke with 28 602 depressions, and the other
bore 30000, and did not appear weakened to resist statical pressure.
Hence, Cast-iron bars will not bear continual applications of .33 of their
breaking weight.
Mr. Tredgold, in his experiments upon Cost Iron, has shown that a load of 300
lbs., suspended from middle of a bar i inch square and 34 ins. between its sup-
ports, gaye a deflection of .16 of an inch, while elasticity of metal remained unim-
paired. Hence a bar x inch square and x foot in leogtb will sustain 850 lbs., and
retain its elasticity.
Wrought Iron, — All rectangular bars, having same bearing, length, and
loaded in their centre to full extent of their elastic power, will be so deflect-
ed that their deflection, being multiplied by their depth, product will be a
constant quantity, whatever may be their breadth or other dimensions, pro-
vided their lengths are same.
A bar of Wrought Iron, 2 ins. square and 9 feet in length between its sup-
ports, was subjected to 100 000 vibratory depressions, each equal to deflec-
tion due to a load of .55 of that which pormanently injured a similar bar,
and their depressions only produced a permanent set of J015 inch.
Greatest deflection which did not produce any permanent set was due to
rather more than .5 statical weight, which permanently injured It.
A wrought-iron box girder, 6x6 ins. and 9 feet in length, was subjected
to vibratory depressions, and a strain corresponding to 3762 lbs., repeated
''70 timetti did not produce any appreciable ^flect on the rivetSt
STBENGTH OP MATEBIALS. — ^DEFLECTION. 78 1
I>eflection of Solid rolled be^ms compared to Riveted beams i9 as i to. 1.5.
Wroughfc-iron Girders of ordinary construction are not safe when sub-
jected to violent impacts or disturbances, with a load equal to .33 of their
destructive weight.
Wood. — ^In consequence of wood not being subjected to weakening by the
effect of impact, a factor of safety of 5 for single pieces is held to oe suffi-
cient, but for structures, in consequence of loss of strength in its connections,
a factor of from 8 to 10 becomes necessary.
AVorUing Strength, or Factors of Safety.*
Elastic strength of materials is, in general terras, half of its ultimate de-
structive or breaking strength. If a working load of .5 elastic strength, or
.25 of ultimate strength, be accepted, equal range for fluctuation within
elastic limit is provided. But, as bodies of same material are not all uni'
form in strength, it is necessary to observe a lower limit than .35 where
material is exijosed to great or to sudden variations of load or stress.
Oast /»w».— Mr. Stoney recommends .25 of ultimate tensile strength, for
dead weights ; .16 for bridge guxlers ; and .125 for crane posts and machin-
ery. In compression, free from flexure, cast iron will bear 8 tons (17920
lbs.) per sq. inch ; for arches, 3 tons (6720 lbs.) per sq. inch ; for pillars,
supporting dead loads, .16 of ultimate strength; for piUars subject to
vibration from machmery, .125 ; and for pillars subject to shocks from
heavy-loaded wagons ancf like, .1, or even less, where strength is exerted in
resistance to flexure.
Wrought Iron. — For bars and plates, 5 tons (11 200 lbs.) per sq. inch of
net section is taken as safe working tensile stress ; for bar iron of extra
quality, 6 tons (13440 lbs.). In compression, where flexure is prevented,
4 tons (8960 lbs.) is safe limit ; in small sizes, 3 tons (6720 lbs.). For col-
umns subject to shocks, Mr. Stoney allows .16 of calculated breaking wei^t ;
with quiescent loads, .25. For machinery, .125 to .z is usually practised;
and for steam-boilers, .25 to .125.
Mr. Roebling claims that long experience has proved, beyond shadow of
a doubt, that good iron, exposed to a tensile strain not above .2 of its ulti-
mate strength, and not subject to strong vibration or torsion, may be de-
pended upon for a thousand years.
Sieel, — A committee of British Association recommended a maximum
working tensile stress of 9 tons (20 160 lbs.) per sq. inch. Mr. Stoney rec-
ommends, for mild steelf .25 of ultimate strength, or 8 tons (17020 lbs.) per
sq. inch. Limit for compression must be regulated very much by nature of
steel, and whether it be annealed or unanneided. Probably a limit of 9 tons
(20 160 lbs.) per sq. inch, same as limit for tension, would be safe max-
imum for general purposes. In absence of experience, Mr. Stoney further
recommends that, for steel pillars, an addition not exceeding 50 per cent,
should be made to safe load for wrought-iron pillars of same dimensions.
Wood, — One tenth of ultimate stress is aif accepted limit Piles have, in
some situations, borne permanently .2 of their ultimate compressive strength.
Foundations, — According to Professor Kankine, maximum pressure on
foundations in Arm earth is from 17 to 23 lbs. per sq. inch; and, on rock, it
should not exceed .125 of its crushing load.
Mcuonry, — Mr. Stoney asserts that working load on rubble masonry,
brick-work, or concrete rarely exceeds .16 of cru&hing weight of aggregate
mass ; and that this seems tobe a safe limit. In an arch, calculated pressure
should not exceed .05 of crushing pressure of stone.
* EMeBtUklly from Manaal of D. K. Clark, Londoa, 1877.
782
STRENGTH OF MATBBIALS. — ^DETBUSIVE.
Hopes, — For round, working load should not exceed .14 of ultimate strength.
and tor flat .11.
Dead Load. LhrtLoad.
Perfect material and workmanship 9 4
Dr. Rankine gives ( Good ordinary material J w!ltl .i o i
following fectors: I and workmanship... |JJ[™^- -♦ *^ * **J*°
A Dead Load is one that is laid on very gradually and remains fixed.
A Live Load is one that is laid on suddenly, as a loaded vehicle or train
passing swiftly over a bridge.
DBTBUSIVE OB SHBABIN6 STRENGTH.
Detrusive or Shearing Strength of any body is directly as its strength,
or thickness, or area of shearing surface.
H.e«i}lts of K:
Mbtau.
zperintieiits upon X>etmsive Strength of
Aletala -with, a Punob..
Diameter
of
Punch.
Brass
Cast iron..,.*.
Copper.........
Steel
** Bessemer.
Wrought Iron,
Ins.
Thieknflw
of
MeUl.
•5
.875
•5
z
a
Ins.
.04s
Power
ex«rted,
Lbs.
5448
•75
.615
1.06
Power regaired for a
Surface of Metal of Doe
8q. Inch.
Lbs.
37000
30000
30000
33300
90000
51800
99400
45000
43900
44300
f S)i3 O
-III
"^ S I
^•32
f» » g
In?
.08 3 983
.3 31950
.25 34720
{103600
184800
8s 870
297400
To Coxnpute Fewer to Piinoli Iron» Brass, or Copper.
Rule,— Multiply product of diameter of punch and thickness of metal by
150000 if for wrought iron, by 128000 if for brass, and bv 96000 if for
cast iron or copper, and product will give power requind, in Iba.
ExAMPLa.— What power is required to punch a hole .5 inch In diameter in a plate
ofbrass ,5inchtbiok? .5X.25Xi28ooo=t6ooolfr*.
Coznparisoix betvjreen. Detrusive aii<a Transverse
Strengths.
Assuming compression and abrasion of metal in application of a punch of
one mch m diameter to extend to .135 of an inch beyond diameter of punch,
comparative resistance of wrou«?ht iron to detrusive and transverse strain,
latter estimated at 600 lbs. per sq. inch, for a bar i foot in length, is as 3 to i»
Detrusive
Lbs.
Spruoe 470
Pine, white 490
WOODS.
Strength, of ^Woods,
Lbs.
Pine, pitch. . . 510 I Ash 650
Hemlock 540 | Chestnut 690
Per Sq, Inch.
Lbs. Lbs.
Oak 780
Locust 1180
To Oompute I^eiisth of Surface of Kesistanoe of "W^ood
to If orison tal Thrust.
RuLE;--Divide 4 times horizontal thrust in lbs. bv product of breadth of
wood m ins., and detrusive resistance per sq. inch in lbs. in direction of fibre,
and quotient will give length required.
«4?M"^^"*"^''* u".* of a lifter is 5600 lbs., breadth of tie beam, of pitch orOeorgta
pme, is 6 ina ; what should be len^h of beyond score for raOer?
Assume strength 510 as above. Then ^^5^ _> ''4oo _ ^
, 6 X 510 3060 '"'*
STSSNGTH OF MATERIALS. — DJSTSUSIYJE.
783
Sliearins*
"Wrouglit Iron.
Resistance to shearing of American is about 75 per cent., and of English
80 per cent., of its tensile strength.
Resistance to shearing of plates and bolts is not in a direct ratio. It ap-
proximates to that uf square of depth of former, and to square of diameter
of latter.
Results of* Kxperizxients -upon. Sliearing StrengtU of*
Various Aletals by I*arallel Cutters.
Wrought /rofi.— Thickness fh)m .5 to i inch, 50000 Iba per sq. inch.
Made by Inclined Cutters^ angle ^ 70.
Platm.
Brass..
Copfier.
Steel. . .
Wrought iron.
TkickoM*.
Power.
lua.
LU.
.05
540
.297
II 196
•24
14930
•5x
I
39 '50
44800
BoLn.
Brass..
Copper.
Steei...
Wrought iron.
{
IMam.
In*.
i.ii
•775
•775
.32
1.142
Power.
Lbe.
99700
II 310
28720
3093
35 4»o
K.e8ult or Experiments in Shearing, made at tJ. S. Ne^vy
Yard, 'Wasliington, on '^Vrougllt-iron Bolts.
Diam.
Inch.
-5
•75
Mlaimam.
Stnee.
Mazimam.
PerSq.Incb.
Diun.
Minimnm.
Street,
Mftziamm.
Lbe.
8900
18400
Lbe.
9400
19650
Lbe.
44 "49
39 553
Incb.
.875
I
Lbe.
25500
32900
Lbe.
27600
35800
PerSq.lBck.
Lbe!
4»5o:
40
501
708
Mean 41 033 lbs.
Result of* ICxp<eriznents on .87C Inoli Wrouslit-iron,
Bolts. (K Clark.)
Lbe.
Single shear 54 096
Doable ** 46904
Tone.
24.15
22.1
Lba.
Double Shear Of two .62S-inch plates
riveted together (one section) 45 696
Tensile strength 50 176 lbs.
Tom.
2a4
H.iveted Joints.
Elxperiments on strength of riveted joints showed that while the plates
were destroyed with a stress of 43 546 lbs., the rivets were strained by a
stress of 39088 lbs.
Oast Iron.
Resistance to shearing; is very nearly equal to its tensile strength. An
average of English being 24ooo*lbs. per sq. inch.
Steel.
Shearing strength of steel of all kinds (including Fagersta) is about 72 per
cent, of Its tensile strength.
^Treenails.
Oak treenails, i to 1.75 ins. in diameter, have an average shearing strength
of T.8 tons per sq. inch, and in order to fully develop their strength, the planks
into which they are driven should be 3 times their diameter.
'^^ood8,
When a beam or any piece of wood is let in (not mortised) at an inclina-
tion to another piece, so that thnist will bear in direction of fibres of beam
that is cnt, depth of cut at right angles to Jibres should not be more than .a
of length of piece, fibres of which, by their cohesion, resist thrust.
774
STRENGTH OF MAT£BIALB. — DEFLECTIOIT.
I>efieotlon ot Wfouglit-iron Rolled Sdatns*
Supported at Both Ends. Weight applied in Middle.
W/3
70000 rf* (4 a + 1.155 a')
- a C ai RedncMl Weight aad DeflecUon.
D
!
Fliuigea.
Weight and Deflection
No.
FOftM.
Width.
Mean
Thick-
new.
Web.
Depth.
by Actual
Observation.
at one tlxth
of Deelractive
Weight.
0
I
Feet.
Ins.
Inch.
Inch.
Ine.
Lbe.
Ine.
LU.
Inch.
• I.
10
3
.485
•5
7
12000
•4
3800
.127
1.05
2.
3-
20
20
4-6
5-7
.8
•643
•5
.6
985
"•75
16000
20000
«'«5
.85
6300
8000
•453
•34
•9a
98
To Comptite IDefleotion of^and Weislxt that may 1)6 Isorxie
V>y, a 'W rouglit-iron Rolled. Seana of XJuifbirui and Syxu—
txietrioal Heotion*
Supported at Both Ends. Weight applied in Middle. (D. K. CUark.)
W19
= D.
70000 d" (4 a-\-i. 155 a') D __
i»
= W.
70000 d* {4 a-f 1-155 <*')
I representing span in feet, d reputed depOi^ or depth less Mtcfenect of lower /Ian fft
in ins., a area, of section of lower flange, a' area of section qf web for reptded deptik
of (team, both in sq. ins., and W weight or stress in lbs.
iLLrsTRATiox.— What is deflection of a wroaght-iron rolled beam of New Jersey
Steel and Iron To., 10 5 ins. in depth, flanges 5 by .5 ins., and width of web .47
inch, when loaded in it8 middle with 8000 lbs., and supported over a span of 20 feet?
(2=a 10.5 — .5^2 10 i««., a=5 X .5 = 2.5 «g. in«.,and a' = 10 X .47 — 4-7 «9- ^ns.
Then
8000 Xao3
64000000 . .
.= —^ = .50 inch.
»o7999 5a>
70000 X «o* X (4 X 2.5 -f 1. 155 X 4-7)
If weight is uniformly distributed, divide by 112 500 instead of 7000a
A like beam 6 ins. in depth, loaded with 2608 lbs., and supported over a span of
I a feet, gave by actual test a deflection of .3 inch, and by above formula It is also
.3 ineh.
NoTB.— Deflection for such a beam, for a statical weight or stress of 17 100 lbs.,
unifornUy distributed, by rules of N. J. Steel and Iron Co., would be .54 inch, which,
with diSterence iu weights, will make deflections alike.
Deflection of "Wrouglit-iron Riveted IBeaxns.
Supported fit Both Ends. Weight applied in Middle.
W /3
-r^ —^ as C at Reduced Weight and Deflection.
•
Weight and Deflection |
No. FOBM.
Length.
Flange*.
Anglee.
Web.
1
by Actual
Obeerration.
at one sixth
of DeetractiTe
Weight.
Feet.
In*.
Ine.
2.125X2
Inch.
•
Int.
Lba.
Inch.
Lb*.
Inch.
■I
7 '
>
4-5X
X.28
2.125X2
X.29
2X2
•25
7
4216
.1
406a
.096
•I
ix.66^
•5
4-5X
•375
4-5X
X.3125
2X2
X.3«a5
a X a
■.25
<
".5
77380
.46
12880
.075
3. "
••.5
•S
7 X
X.375
3X3
•375
16.5
"5584
.«75
X9a65
.i4«
•5
X.437S
,
•
•63
1.96
3.86
STBByOTB OF UAT£BIALS. — DEFLECTION.
775
Ta Conapixte IDefleotion of, and Weiglxt tliat masr lae 'borne
1t>y, a liiveted Beazn of "Wrought Iron.
168000
(^+t)
= D.
d'Cf
168000 f— 5^ 1 Jda C D
i3
W.
a, a', and a" representing arecu of tipper and loioer flanges vrith tkeir angle pieces^
and ftfwehfnr its entire dqpik, aUinsq. ins.
NoT«.— If there are not any flange*, aa in No. x, angle pieces alone are to be oomputed for flange
Illcstratxon.— What weight will a riveted and flanged beam of following dimen-
sions sustain, at a distance between its supports of 25 feet, and at a safe deflection
of .2 inch or j^^j^ of its length?
Top flange 6X.5^'W. | Web sifu.
Bottom flange 6X.5 " | Depth 17 **
Angles 2- 25 X 2.25 X .5 tn«.
aanda'each = 6x.5 = 3H-8.25-f 2.25— .5X.5 X 2 = 7 sq. ins.
a" = . 5 X 17 = 8. 5 sq. ins. G, as per No. 2,= .43, but inasmuch as flanges in this
CUM are much heavier, asBumo .5.
168000 f^i^ + ?^^ i7»X .2 X.5
Then 5l2 4; =^3°3-722=,835.4'ft«.
25> 15625 ^^^
Strength of a Riveted beam compared to a Solid beam is as i to 1.5, while for
equal weights its deflection is 1.5 to i.
I'u'bu.lar GUrdera. Wrowglit Iron,
Supported at Both Ends. Weight applied in Middle.
Ho. Sionov
•
«. n Thickness
.03 inch
s. " "
top
3. " bottom
sides
4. " Thickness
.525 "
.372 " )
.244 " {
.125")
.75 "
5. ^j Thickness
.0375"
^0 "
04x6"
.«43 "
a
Feet.
3-75
30
30
45
"7
»7
»7
i
Dei
m
Inter-
nal.
Ina.
Ins.
1.9
2.94
15-5
22.95
16
23.28
24
34.25
12
11.925
9-25
I 9- 25
13.535
14.714
Ex-
ternal.
Ine.
3
24
24
35-75
12
13.6a
15
1
•
1
^
a
Lbe.
•Ine.
448
.1
33685
.56
32538
X.ll
128850
1.85
9755
.65
3262
.62*
16800
1-39*
•n u S
Inch.
.03
.24
•24
.36
.136
.136
.136
I
C
288
473
224
362
62.8
47-9
119
* DestmctWe welglit.
fPo Compute Deflection or, and '^^eiglit th.at znajr lae
borike bsr, a WrougUt^iron Tiibxilar Q-irder.
i6ftc|sCD _ Wl»
W.
= D.
/> iSbd^C
fLLuaniATiON.— What weight may be safely borne by a wrought-iron tube, alike
io No 3 in preceding table, for a length of 30 Ibet, and a deflection of .32 inch?
16 X 16 X 24S X 224 X .24 _ 190 253 629 _
305
27000
= 7046 lbs.
flanged Rails.
Deflection of Iron and Steel Flanged Rails within their elastic limit, compar«d
with their transverse strength, is as 17 to 20, and with double-headed it is as n to a^
776
STBEN6TH OP MATERIALS. — DEFLECTION,
RAILS.
Supported at BoGi Ends. Weight applied in Middle.
Iron.
Na FoBM.
5i
Head.
Bottom.
WelRbt
vS^d.
Feet.
Ins.
Ina.
Lba.
' X
2-75
2.25X1
2.25X1
60
a. "
3. "
4-5
5
2.3 Xi
2.3 Xi
2.3 XI
2.3 Xi
82
^ T
2-75
3-5 X .8
2.25X1
60
' J.
2.58
2.23X1
3.5 X .6
57
I o
Ins.
4-S
4.5
5-4
4
35
Area.
Sq. los.
6.166
6.68
8.25
6.7
5.85
Obserred
Weieht and
Deaection.
DMtrnetiTtt
WeiKht
and
Deflection.
Lbe.
13440
1 1 200
25760
II 200
ZI200
Ins.
•034
.11
.2
•035
.097
Lba.
26680
24640
51520
26680
30160
Ilsa.
.065
.204
•378
.065
.138
Steel.
No. FoBU.
Feet.
1
X
Ina.
-X
5
—
7- "
Beaaemer.
3.62
—
-1
5
2-5
Bottom.
Ins.
37
6.375X:g^
«
^
Lba.
78
86
84
Web.
Inch.
•75
.65
Depth.
Centres
of
Heada.
Ina.
4-2
3-37
S
o
Ina.
5-4
5-5
4-5
Area.
S.Ina.
7.67
8.43
8.24
Observed
Weirht and
Deflection.
Lba.
36086
22400
27290
In.
•25
•«4
.24
Deatmcttw
Weffcfat
and
Deflection.
Lba.
80192
26680
27290
Inch.
•55
.165
To Coxnpute Deflection of Doxilale-headed. Hails -witliii^
Slastio Xjiixiit. (/>. K. Clark.)
Suppoi'ted at Both Ends. Weight applied aJl Middle,
IRON.
= D. a representing area of one head^ leu portion per^
W^s
57 000 (4 ad'* +1.1 55 <d3)
taining to ttteb^ d whole depth of rail, d' vertical distance between centres of keadt^
t thicJmess ofweb^ all in tna., I length infeet^ and W weight in lbs.
STEEL.
For 57 000 put 67 400.
Illustration.— Take case No. 3 (Iron), in preceding table, with a weight of 36000
lbs. ; what will be its deflection between bearings 5 feet aimrt?
0 = 1.911. -d' = 4.2. (2 = 5.4. ^ = '82.
26000X5' 3250000 , .
= • ^- = . 3 xncn.
Then
57000 (4 X 1.9" X 4.2«+ 1.155 X .8-2 X 5-4^) 57000X284
To Compute Deflection of Iron and. Steel Rails of XJxi-
syxnmetrioal Section -witlxin Slastio Xjimita.
Elastic Deflection of Steel Flanged Rails of Metropolitan Railway of London, as
determined by Mr. Kirkaldy, at a span of 5 feet, and loaded in middlej was .03 incb
per ton. {See Manual ofD. K. Clar.k, pp. 667-67a)
STBKKGTH OF UA.TBBIAI.S. — ^DBFLBCTIOIf.
m
CASFT ntON.
Oefleotion of Reotangnlar Hara and Seams of -various
Seotions, etc., "by U. S. Ordiiazice Corps, BarloMr,
Xiodglzlusoii, and Oubitt.
Supported at Both Ends. Weight applied in Middle.
Weight and Deflection.
At^thof
FOBX.
I. American. ...
3.EDgli8b ''
3. " "
4- '• I
s- " O
k
1
M
•
1
n
1
3
Feet. Ins.
Int.
1.66
2
2
4
X
z
16
4
4
4-5
3
z
45
z
(2.5
I -5
By Actoal
ObeerTatloD.
Lbs.
5000
212
1008
1 120
2231
Ins.
•036
.32
•4
X.42
•5»
At one sixth |
of Braaliinj;
WetKht.
Lbs.
z666
80
5333
215
422
Ins.
.012
■ 12
2.1 '
.27
.1
an inch for
each foot of
span.
Lbs.
1805
22
3370
30
156
Ins.
.013
•033
1-33
•037
•037
5fl ^
1^1
^
• 5
I
c
3.8Z
4-zi
389
2-37
2-33
Vo Compute IDefleotion of*, and AVeight tliat may be
"borne 'by, a H>eotangular Bar or Beazxi of* Cast Iron.
= C.
= D.
-^ W.
zo40o6d3D "' lo^oobd^C /'
Illustration. — What weight will a beam 2 ins. in breadth, 5 ins. in depth, and
16 feet between its supports, bear with safe deflection of ^-j^^ of an inch for each
ftx>i of span, or j^fji ^^ '^ length ?
G from table =. 3. 89. D — . y^ of 16 = . 133 iiu.
10400 X 2 X 5* X 389 X.133 _ I 345 1<)2
16« ~ ~J556- - 343-5 lbs.
QariL gives C uniform for Rectangular bars of 2.69, and 1.85 for Cylindrical
FLAKGED BBAMS. Cast Iron.
Supported at Both Ends. Weight applied in Middle.
To Compute I>eflection of*, and "^Veiehit tliat may be
"borne "by, a Flanged Beam of* Cast Irozi of Uniform
and Symmetrical Section.
_ ^.^L ^p 2700od«Uo-H'i55a'')D^^
a7oood'(4 a+i.zssa^') ' P
iLLCBTRATioif.^What is deflcctlon of a cast-iron beam (Hodgkinson's) 7.15 ins.,
flanges 2.6 x 86 ins. and 5 X z.6 ins., and width of web z inch, when loaded in ita
middle with zz 200 Iba, over a span of zs feet ?
d = 7.15 — z.6 =5.55 ifUL, as= 5 X z.6 ±= 8 tn*., and a* = 7. 15 — z.6 = 5.55 inL
__ 1x200X15^ 37800000 . .
Then = ^' „, — 1 - = .67 in*
27000X555' (4 X 8 + Z.155 X 5-55') 27000 X 308 (32 + 35-57)
VoTB z.— The observed deflection of this beam was x.28 ins., at one sixth of its de-
structive weight it was .3, and at y|^ of an inch for each foot of span it was
.125 inch.
2.— The mean ratio of elastic to destructive stress is 73 per cent.
Formulas for value of deflection signify that deflection varies directly as weight,
and as cube of length ; and inversely as breadth, cube of depth, and coefficient or
•iaaticity.
788
STRENGTH OF MATERIALS. — ^TENSILE.
A.verage Xexxsile
Klastioitsr of* Steel Sara
LCom. qf Civil Engineerif z870>),
and Platei
DucBiPTioir.
Barg.
Crucible, hammered and rolled. . . .
Bessemer, " " . . . .
Fagcrsta, rolled
'^ uoannealed
hammered and rolled —
" *' annealed.
plateSf unannealed
'* annealed
" unannealed
«' annealed
tires
Krupp^s shaft
«
Siemens,
((
Elaiiicity per
Sq. loch.
LiM.
50557
43814
56560
34048
55 574
40858
30710
26940
32500
28780
40174
42 112
Elastic Exteo-
RaUoofElM-
sioii in PsrU of
tic to DMtmc-
Length.
tiv9 Strength.
Parta.
Percent.
I in 485
58.2
1 in 675
55
—
64.8
—
55.6
—
64.7
—
54
X in 980
59-2
I in 1020
565
— .
46.4
—
44-4
__
58.8
I in 185
Tensile strength of steel increases by reheating and rolling up to second
operation, but decreases after that.
Tensile Strexigtli of Various JVCaterials, dedtioed fvozxx
IiixperiiTieiits of* TJ. S. Ordnance Uepartment, ITair^
bairn, IrlodgkinsoUy Kirkaldy, and \>y tlie i^utlaor.
Power or Weight required to tear asunder One Sq. Jnchj in Lbs.
i(
((
tt
((
((
Ci
(t
<(
((
((
((
(/
(<
l(
((
((
((
Metals. Lb*.
Antimony, cast z 053
Bismuth, cast 3 248
Cast Iron, Greenwood 45 970
mean, Msyor Wade. . . 31 829
gun-metal, mean. .... 37 232
malleable, annealed . . 56 000
Eng., strong 29000
*^ weak 13400
*^«™««« ( 21280
gun-metal 23257
mean* 19484
Low Moor, No. 2 1 4 076
Clyde, No. i.. . . 16 125
" No. 3.... 23468
Stirling, mean.. 25764
Copper, wrought 34000
rolled 36000
cast 24250
bolt 36800
wire 61 200
Cold 20 384
Lead, ^Bst 1 800
pipe 2240
*' encased 3 759
rolled sheet 3320
Platinum wire 53000
Silver, cast 40000
Steel, cast, maximum 142000
" mean 88560
puddled, maximum 173817
Amer. Tool Co '79980
^i»^ ( 210000
wire <
( 300 ouo
plates, lengthwise 96 300
'' crosswise 93700
Chrome bar 180000
t(
ii
((
«{
Rni
((
((
(I
{(
((
(i
Mktals. Lba.
Steel, Pittsburgh, moan 94 450
" Bessemer, rolled. j ^6650
' ( 135000
hammered 152 900
Eng., cast 134000
" plates, mean.... 93500
plates 86800
puddled plates 62 720
crucible 91 570
homogeneous. 96 280
blistered, bars 104000
Fagersta bars 80600
'* plates 98560
Whitworth's. ( !^^^
X 152000
Siemens's plates. . I ^^
Knipp'B shaft 93 243
Tin, cast 5000
'' Banca , a 100
Wire rope, \)er lb. w't per fathom 4480
u i( galvanized steel, ** 6720
Wrought Iron, boiler plates. . . J J5 500
rivets 65000
bolts, mean '60 500
*' inferior 30000
hammered 54 000
Shalt 44 750
wire 73 600
No. 9 xooooo
No. 20. 120000
diam. .0069 inch 301 168
galv'ized .058 ** 64 960
Eqg. , heavy foiling. 33 600
plates, lengtbw'e 53 800
'* crosswise 48800
u
i(
i(
((
((
((
(C
((
t(
((
(t
({
(I
<(
It
((
(<
By Comm's on application of Iron to Railway Structare.
STRENGTH OF MATEBIALS. — ^TENSILE.
789
MbTALS. Lbs.
WroQghi Iron, EDg., mean 51 000
" Eng., Low Moor 57 600
'* '' Lancashire 48800
" " Thames 65920
" " armor plates .... 40000
" " bar j 31300
( 56000
" •' ** charcoal 63000
" " rivet, scrap 51 760
*' Russian, bar, best 59 500
*' " " ...49000
" Swedish, " best 72000
" '' " 48900
Zinc. . . .' 3 500
" sheet '. I 7000
( 16000
Allots or Cowpositions.
Alloy, Ckip. 60, Iron 2, Zinc 35, Tin 2 . 85 120
'* Tin 10, Antimony 1 11 000
Alaminium, Cop. 9a 71 600
" maximum 96320
Bell- metal 3 670
Brass, cast 18000
" wire 49000
Bronze, Phosphor, extreme 50915
" " . mean 34464
" ordinary 23500
'* Cop. 10, Tin 1 33 000
" " 9, " 1 38080
" 8, " 1 36000
" *• 2, Zinc 1 29000
Gnn-metal, ordinary...... 18000
" mean 33 600
** bars 42 040
Speculum metal 7 000
Yellow metal 48 700
Woods.
Ash, white 14000
*' American 9500
** English 16000
Bamboo 6 300
Bay 14000
Beech, English 11 500
Birch 15000
** Amer., black 7000
Box, African 23000
Bullet 19000
Cedar, Lebanon 11 400
*' West Indian 7500
" American u 600
Chestnut. 12 500
'* horse. loooo
Cypress , 6000
Deal, Christiana 12 400
Ebony 27000
Elm { ^«»
( 13000
Gum, blue 18000
** Alabama 15860
Hackmatack 12 000
Hickory 11 000
Holly x6 000
Uince ( '7350
**^ (33000
Woods. Lbs.
Larch | 4200
( 9500
Lignum vitae n 800
Locust i ^^°°°
{ 20500
Mahogany, Honduras 21 000
Spanish { ^«»
( 12000
Oak, Pa. , seasoned bo ^la
^ »■ ) 25 22e
" white 16 500
'* live, Ala 16 380
" red 10250
" African 9500
" English i 4500
u T^ . , 1 7571
" Dantzic 4200
Pear 9 860
Pine, Va 19000
" Riga 14000
" yellow. X3000
*' white ii8co
'^ 13000
Poon ,3 300
Poplar 7 000
Redwood, Cal 10833
Spruce, white i '^^90
( 12400
Sycamore i 9600
( 13000
Teak, India 15000
" African 21 000
Walnut, Eng 7 800
" black 16633
" Mich 17580
Willow 13000
Yew 8000
Across Fibre.
Oak 2 300
I'ine 550
MfSCELLANECUS.
Basalt, Scotch 1469
Beton, N. Y. Stone Con'g Co. . . . ( 3oo
(500
Blue stone 77
Brick, extreme 750
*' inferior. i '°°
\ 290
Cement, Portland, 7 days { 4oo
" *' pure, I mo. 393
*' '* sand 2, 320 days.. 713
" " "J " .. 948
" " pure, " .. 1152
'* *' sand I, in w^ater )
1 mo. I *°'
" " " 1 " ly'r.. 319
" '* " 3. I year 310
" " 5,1 " .... 214
" " " 7,1 " .... 163
" Hydraulic, 284
" Rosedale, Ulst. Co. , 7 days 104
" " sand 1, 30 " X02
«• " 91008. { 560
790
ST££NOTH OF MATERIALS. — TOBSION.
MlSCELIJLNBOUS. Lb».
Cement, Roman, in water 7 days . 90
" ♦' " I mo... 115
" " " I year . 286
" " sand 1, 42 days. . 284
" " " 2, " .. 199
" " " 3, » .. 160
Flax..... 35000
Glass, crown 2 546
Glue 4000
Granite 578
Gutta Percba 3 500
Hemp rope { J^^
Ivory 1 000
Leather belting. 330
Limestone | ^sJo
Marble, statuary 3 200
*' Italian 5200
Marble, white 9 000
" Irish 17600
MlSCKLLANBOUa IJm.
Mortar, i year { ^^
" hydraulic | ^^^
" ordinary 35
Oxhide ....' 6300
Rope, Manila 9000
*■* tarred hemp 15000
Sandstone 150
'* fine green ij6o
Arbroath { ^563
" Caithness { ^ J^
» Portland I ^^
" Craigleth 453
Silk fibre 52 000
Slate {,1^
Whalebone 7 000
TORSIONAL STRENGTH.
SHAFTS AND GUDGEONS.
Shafts are divided into Shafts and Spindles, according to their mag-
nitude, and are subjected to Torsion and Lateral Stress Combined, or to
Lateral Stress alone.
A Ouclffeon is the metal journal or Arbor upon which a wooden shaft
revolves.
Lateral Stiffness and *S<rtfn^<A.— Shafts of equal length have laXeral stiff-
ness as their breadth and cube of their depth, and have lateral strength as
their breadth and square of their depths.
Shafts of different lengths have lateral stiffness diroctly as their breadth
and cube of their depth, and inversely as cube of theur length ; and have
lateral strength directly as their breadth and as square of their depth, and
inversely as their length.
Hollow Shafts having equal lengths and equal quantities of material have
lateral stiffness as sc^uare of their diameter, and have lateral strength as their
diameters. Hence, in hollow shafts, one having twice the diameter of an-
other wiU have four times the stiffness, and but double the strength ; and
when having equal lengths, bv an increase in diameter they Increase in stiff-
ness in a greater proportion than in strength.
When a solid shaft is subjected to torsional stress, its centre is a neutral
axis, about which both intensitp^ and leverage of resistance increase as radius
or side ; and the two in combmation, or moment of resistance per sq. inch,
increase as square of radius or side.
Round Shaft, — Radius of ring of resistance is radius of gyration of sec-
tion, being alike to that of a circular plate revolving on its axis, viz., .7071
radius. The ultimate moment of resistance then is expressed by product
of sectional area of shaft, by ultimate shearing resistance per sq. inch of
material by radius, and by .7071.
Or, .7854 da r S X .7071 = .278 d» S = R W. (D. K. dark.)
d represerUing diameter of shaft omd r radius, S ulHmate shearing streu ofmoU-
rial in lbs. per sq. inch, R radtus through which streu is applied, in ins., and W
moment of load or destritctive stress, in Ws.
ence.
.278 d* S
= W;
RW
.278 d'
= S; and
V"^
X 1.534=*
8TREKGTH OF MATERIALS. — TORSION. 79 1
Rinind Jhajt. — Strength, compared to a square oi! equal sectional area,
is about as I to .85. Diameter of a round section, compared to side of
square sectioti of equal resistance, is as i to .96.
Square Shaft, — Moment of torsional resistance of a square shaft exceeds
that of a round of same sectional area, in consequence of projection of cor-
ners of square ; but inasmuch as material is less disposed to resist torsional
stress, the resistance of a square shaft, compared to a round one of like area
of section, is as i to 1.18, and of like side and diameter, as 1.08 to i.
H.nco.Si2i^!i!i = w. aoUowHo^ Shaft.. :2Zi<!?l^£!l5 = w.
When Section is comparatively T%in, ''^^ = W. * representing tide^
d, and d' extemcU and internal diameters, and t thickness of metal in ins.
Torsional Atwle of a bar, etc^ under equal stress, will vary as its length.
Hence, torsional strength of bars of like diameters is inversely as their
lengths.
Stress upon a shc^ft/rom a weight upon it is proportional to product of Vie parts
€>ftkafl nuUtiplied into each other. Thus, if a shaft is 10 feet In length, and a weight
upon centre of gravity of the stress is at a point 2 feet from one end, the parts 2
and 8, multiplied together, are equal to 16; but if weight or stress were applied in
middle of the shaft, parts 5 and 5, mqltiplied together, would produce 25.
When load upon a shaft is uniformly distributed over any part of it, it is consid-
ered as united in middle of that (lart; and if load is not uniformly distributed, it is
considered as united at its centre of gravity.
Deflection of a shaft produced by a load which is uniformly distributed over its
length is same as when .625 of load is applied at middle of its length.
- Resistance of body of a shaft to lateral stress is as its breadth and square
of its depch ; hence diameter wiU be as product of length of it^ and length
of it on ome side (fa given pointy less square of that length*
iLLrsTRATioN. — Length of a shaft between centres of its Journals is 10 feet; what
should be relative cubes of its diameters when load is applied at 1, 2, and 5 f^t
from one ebd? and what when load is uniformly distributed over length of it?
IXl^ — £»= d3; and when uniformly distributed, d3 -i- 2 = d'.
10 X i = io— i2 = 9 = cu6c qf diameter at i foot; 10 X 2 = 20 — 2^ = i6=zcube /
qf diameter at sfeet ; 10 x 5 = 50 — 5' = 25 = cube of diameter at sfeet.
. When a load is uniformly distributed, stress is greatest at middle of length, and
is equal to half of it ; 25 -f- 2 :i= 1 2. 5 = cuJbe of diameter at 5 feet.
Torsional Strength of any square bar or beam is as cube of its side, and
of a cylinder as cube of its diameter. Hollow cylinders or shafts have great-
er torsional strength than solid ones containing same volume of material.
To Coxnpxxte Diameter of. a Solid. SHaft of Cast or
l?^rovig;lit Iron to Resist ILjateral Stress alone.
When Stress is in or near Middle, Rule. — Multiply weight by length of
shaft in feet; divide product by 500 for cast iron and '560 for wrought iron,
and cube root of quotient will give diameter in ins.
ExAXPLK.^-Weight of a water-wheel upon a cast-iron shaft is 50000 lbs., its length
30 feet, and centre of stress of wheel 7 feet from one end ; what should \ye diameter
of its body ?
3/ /5ooooXjo\ _ ^^^^ ^.^^ ifweigM was in middle of its length.
Hence diameter aft 7 feet from one end will be, as by preceding Rale, 30 x 7 —
7« = x6i = relative cube of diameter at 7 feet ; 30 X 15 — is'' = ««5 = relative cube
i»f4iamettr at 15 feet^ or at middle of its length.
Then, as ^a^s : 14.43 *.: -^161 : 12.89 iiu., diameter ofshafl at 7 feet from one end.
792 STBENGTH OF MATERIALS. — TOBSION.
For Bronze, 420 ; Cast steel, 1000 to 1500 ; and Paddled steel, 500.
When Stress is unifornUy laid along Length of ShcLfl. Rule. — Divide
cube root of product of weight and length by 9.3 ftx Cast iron and 10.6
for Wrought iron, aud quotient will give diameter in ins.
Example.— Apply rule to prccediDg case. — — = 12.31 ins.
9-3
For Bronze, 8.5 ; Cast steel, 18.6 to 27.9 ; and Puddled steel, 9.3.
When Diameter fw Stress applied in Middle is given. Rule. — Take cube
root of .625 of cubie of diameter, and this root will give diameter requued.
ExAJiPLE. — Diameter of a shaft when stress is uniformly applied along its length
is 14.4a ina \ what should be its diameter, stress l>cing applied in middle?
i^.62S X 14-423 = i/.625X 3000 = 12.33 to*. ~~
To Compute Diameter or a Solid Slia^t of Cast Iron to
Resist its AVeigh.t alone.
Rule. — Multiply cube of its length by .007, and square root of product
will give diameter in ins.
Example.— Length of a shaft is 30 feet; what should be its diameter in body?
V(3o» X .007) = V»89 = 13.75 ins
HOLLOW SHAFTS.
To Compute Diameter of* a Hollo'pe Sliaf^ of Cast Iron
to Sustain its I^oad. in A.ddition to its "Weigbt.
When Stress is in or near Middle, Rule. — Divide continued praduct of
.012 times cube of length, and number of times weight of shaft in lbs., by
S(iuare of internal diameter added to i, and twice square root of quotient
added to internal diameter will give whole diameter in ins.
Example. —Weight of a water-wheel upon a hollow shaft 30 feet in length is 2.5
times its own weight, and internal diameter is 9 ins. ; what should be whoie diam-
eter of shaft?
To Compute Diameter of a H.ound or Square Slistft to
licuist Combined Stress of Torsion and Weigbt.
Rule. — Multiply extreme of pressure upon crank-pin, or at pitch-line of
pinion, or at centre of ellect upon the blades of a water-wheel, etc., that a
sliafl may at any time be subjected to ; by length of crank or radius of
wheel, etc., in ft*et *, divide the proiiuct by (^efficient in following Table, and
cube root of (quotient wUl give diameter of shaft or its journal in ins.
0'.^/ = '^
ExAMPLK.— What should be diameter for journal of a wrongbt-iron water-wheel
shaft, extreme pressure upon crauk-pin being 59 400 lbs., and crank 5 feet in length?
When T\to Shafts are used, as in Steam-vessels, etc., foiih One Engine.
Rule. — Divide throe times cube of diameter for one shaft by four, and
cube root of quotient will give diameter of shaft in ins.
0.^^ = ^
RxAMPLa.— Area of journal of a shaft is 113 ins.; what should be diameter, two
shaOs being used ?
Diameter for area of 113 = 19. Then ^ = 1396, and Vx^gG = 1019 '
STBEKGTH OF MATXBIAX8. — TOBSION.
793.
torsional Strengtii of* VcM-ioup - IMEdtals. ^
(Mqj. Wm. Wade, U. S. Ordnance Corps, 1851, Steel Committee [England, 1B68], and
Stevens Institute, /V. J., 1878.)
Rediiced to a Uniform Measure of One Inch in Diameter or Side.
Stress applied at One Foot from Axis of Body and at Face of Axis.
I Torsional
Computed Strength
Bamb ako Mbtals.
TonaUe
Strangtb.
De«truc
Rt
35 Ids.
Cast Iron.
Lb«.
Lbs.
^^ Area i sq. inch )
45000
520
Area2.97 8q. ins. )
^5v Diam. ) I^east . , .
§3 =1.9} Mean...
^^ ins. ) Greatest.
■■ Side X inch : . . . >
■1 Area x sq. inch )
9000
31 829
45000
(t
3800
1550
2145
2840
350
Wrought Iron.
„afc, Diam. ( Least . . .
gH = 1.9 > Mean —
^^ ins. (Greatest.
Area 2.83 sq. in&
38027
56300
74592
1250
1375
1500
Bbonzi.
^^ Diam.= ( Least
1.9 ins. (Greatest.
Area 2.83 sq. ins.
X7698
56786
500
650
Ckfvt Stbbl.
*- (( Diam.c= (I^asi....
X.9 ins. (Greatest.
Area 2.83 sq. iD&
41 000
128000
2600
7760
BSSSBMKK STKRL.
tt Diam. = 1.382 ins. ^
AreaI.sBq. ins.)
36960
1568
at
12 Ins.
Lbs.
xo8a
7904
3664
4462
5907
728
2600
2860
3120
1040
135a
5408
161 40
326X
d9
= T.
492
330
530
65
85
•!
728
376;
416 1
452.
152
X97
788
2353
1236
O /is
Coefflci«nt^^^=::W.
7
Ids.
100
45
130
125
120
30
38
160
475
iL
10
Int.
95
90
40
35
«25
120
X20
"5
"5
no
28
26
36
34
»S5
470
550
465
K
' is
In*.
85
30
"5
1 10
105
10
1m.
8b
25
ixo
105
100
245 340 835
230 1 225
Xo Coxnpvite X>iameter oT Shafl^B or Oak and Fine.
Multiply diameter ascertained for Cast Iron as follows: Oak by 1.83,
Yellow Pine by 1.7 16.
IMetals and. "Woods.
Ultimate Tornonai Strejigth. — Of Cast Iron may be taken as equal to its
tranAverse strength for American and .9 for En<;Ush, or as .a6 of its tensile
strength for American and .23 for Kn^lish. Of Wrouf^ht Iron, as .7 to .8 of
its transverse strength for American and .7 to i for English, and of Steel, as
.73 of its tensile strength.
JClasfic Torsional Strength. — Of Cast Iron may be taken as equal to its
transverse strength, of Wrought Iron 40 per cent, of its ultimate torsional
strength, of Steel 44 per cent, of its tensile strength, and 45 per cent of its
ultimate torsional strength.
Bessemer Steel. — Has a torsional strength of 6670 lbs. per sq. inch at a ra-
dius of one foot, being somewhat less than ihat of Cast Iron, Fagersta has 50
r cent, of its ultimate transverse strength, and Siemens 44.5 per cent, of
U ultimate tensile. _.
794 BTBKITGTH OF HATBBIALS. — T0B8I0K.
NoTB.— Exampltt b«re given are deduced ftrpm iDstencea of sQcceatftil practice;
wbert diameter bas been less, fkacture bas almost universally taken place, strev
being increased beyond ordinary limit-
2.— Wben sbafls of less diameter tban 12 ins. are required. Coefficients bere given
may be sligbtly reduced or increased, according to quality of tbe metal and diame-
ter of sbaft; but wben tbey exceed tbis diameter, CS>efficientz may not be increaaed,
as strengtb of a shad decreases very materially as its diameter incr^SSea.
Order of shafts, with reference to degree of torsional stress to which they
may be subjected, is as follows :
z. Fly-wbeel. | 2. Water- wheel | 3. Secondary shaft. | 4. Tertiary, etc
Hence, diameters of their journals may be reduced in this order.
To Compute IDiameter of a "^VroviBlit^iron. Oeixtte Sltctf^
for conueotiiig X>vo Kiigpiiies at a Riglit A-nsle.
Conditions of such a sbaft are as follows :
Greatest stress that it is subjected to is when leading engine is at .75 of
its stroke, and following engine .25 of its stroke ; heqce, position of each
crank is as sin. 22,° jo' x 2 ;= .7074 of length of crank or radius of power.
Consequently, 3 / - "-^-^ — = d. P representing extreme pressure on piston.
NoTR.~In computing P it is necessary to take very extreme pressure that piston
may be subjected to, bowever sbort tbe period of time. Average presspre does not
meet requirement of case.
iLLUSTaATiox. -^Extreme pressure upon each piston of two engines connected at
a rigbt angle wiis m 502 lbs., and stroke of pistons 10 feet; what should have been
diameter of centre sbaft? and what of each wheel or driving shaft?
For ordinary mill purposes, driving shafts should be as cube root of .75 cube of
centre shaft.
Thus 3yi!^i?!2<3 = , 6.79 <«.
To CoiDpute Toraioxial Btrensth o£ Hollo^w Sliafta aud
Gy-lixxdema.
RuLE.--From fourth power of exterior diameter subtract fourth power of
quotient
ExAifPLR.— What torsional stress may be borne by a hollow cast-iron shaft, hav*
ing diameters of 3 and 2 in&, power being applied at one foot fh>m its axis?
C = 13a 3« — 2* X 130 = 8450, which -^- 3 X I = -*^- = 2816.6 lbs,
3
To Coiapute Torsional StrenstU of Round And Sq.viar«
SUaits.
Rule.— Multiply Coefficient in preceding Table by cube of side or of
diameter of shaft, etc., and divide product by distance from axis at which
stress is applied in feet ; quotient will give resistance in lbs.
iLLCRTRATioN.— What torsloual stress may be borne by a cast-iron shaft of beat
material, a ina in diameter, power applied at 2 feet (Tom its axis.
C from table = ,30. iSoXj* ^ 1040 ^ ^ ^^
a a
For steamers, when Trova heeling of vessel or roughness of sea the stress may ba
tonfined to one wheel alone, diameter of Journal of iu abaft should be eoual to
hat of centre shaft ^
8TBENGTH OF MATJSBIALS. — TOBBION. 795
GTTDGSONS.
rro CoixkputA I>iAniet6r of a tSingle Q^udgeoti of Cast
Iroii, to Support a given "WeiKlit or Stress.
Rule.— Divide square root of weight in lbs. by 25 for Cast iroD, and a6
for Wrought iron, and quotient will give diameter in ins.
ExAMPLK.— Weight upon r gudgeon of a ca8t*iron water-wheel shaft it 62 500 iba ;
what should be its diameter t
as 85
7o Compute I>iameter or T-wo GI-udfl;eotis oi* Cast Iron,
to Support a gi-ven Stress or 'Weigh.t.
Rule.— Proceed as for two shafts, {«ge 79a.
'X*o Compute XJltimate torsional Strength, of Round and
Square Shafts* {D. K. Clark.)
Cast Iron. Mound, —^ — = W; 1.534 3/-^ = di^and ^-g^x=S.
Square. ^^ = W, and 1.36 3/—- = t. HoUaw, ■ ■ ^^-^ ^ = W
S rtpre^nting uUimate sharing strength, and W mometU of load, both in 26f., s tide
qfiquare sh^, and R radius of stress, b^tk in ins.
Illustration. — What is ultimate torsional strength of a round cast-iron shall
4 in& in diameter, stress applied at 5 feet from its axis ?
«.i- .278 X 4* X 20000 -.
Assume S = 20000 lbs. Then — ^ — ^-^ = 5930 Vbt.
5 X 12
By experiments of Msjor Wade, ordinary fbnndry iron has a torsional strength
of 7725 lbs., or 644 lbs. per sq. inch at radius of one foot.
772 K X a'
Thus, take preceding illustration. Then ^^ ^ ^ = 8240 Vbs.
5 X ta
*Wroueh.t Iron. Bpund, —4 = W- Square, -^^ — = W.
When Torsional Strength per sq. inch for radius of i Jnch is ascertained,
substitute C for .278, wi, .2224, or .32.
Stress which will give a bar a (>ermanent set of .5*^ is about .7 of that
which will break it, and this proportion is quite uniform, even when strength
of material may vary essentially.
Wrought Iron, com^uired with Cast Iron, has equal strength under a stress
which does not produce a permanent set, but this set commences under a less
force in wroiignt iron than cast, and progresses more rapidly thereafter.
Strongest bar of wrought iron acquired a permanent set under a less strain
than a cast-iron bar of lowest erade.
Strongest bars give longest Sractures.
£214.^ 1 D^.^j «»<^'^ rsr When S is not known, substitnte for
Hteel. Hound. ^^— = w, g ^a,-. ^3 per cent of tensile strength.
Torsional Strength of Cast Steel is from 2 to 3 times that of Cast Iron.
• Followmg rules are purposed to apply in all instances to diameters of
joamals of shafts, or to diameter or side of bearings of beams, etc, where
lenfilh <^ journal or distance npon which strain bears does not greatly ex-
ceed diameter of journal or side of beam, etc. ; hence, when length or distance
is greatly increased, diameter or side must be correspondingly increased.
Coefficientt for torsional breaking stress of Iron, Bronise. and Steel, as de-
termined by Major Wade, are: Wrought Iron, 640; Cast Iron, 560: Bronze,
460 ; Cast Steel, i iso to i68a Puddled Steel does not differ essentially from
that of caat iron.
796
BTBKNQTH OF MATEKIALS.tHTOBSION.
Formulas for Minimum and Maximum Diam. of Wrovghi-iron Shafts.
(X E. Seatony London, 1883, and Board 0/ Trade, Eng.)
Compound Engines, y - -' -— S = diameUr. V and d representing diam-
eter of law and high pressure cylinders, and 6 hal^f stroke, aU in ins., p pressure of
sUam in boiler, in lbs. per sq. inch, and C a coefficient, atfbUows :
Ancle
Crwik. ! ^"°^-
Shaft*.
Pro-
peller.
90O
(2468
\
4000
2880
5400
Ansle
f
Crank.
Of I
Shafta.
^'"•'•!,^r.
lOC-
(2279
I4000
2659
5400
Crank.
1 10^
ShiAa.
Cnnk.
1 4000
Pro-
peller.
2487
54<»
Aosle
Ciaak.
180^
Cnnk.
Pro-
peller.
{20l6
4000
»352
5400
if-^
C = diameter. A. E. Seaton, London, 1883.
Side'Wfuel Engines, Sea Sertriee. — One cylinder erank journal, G = 8o; outboard
too; Two cylinder crank journal 50; outboard 65; and centre shaft 58.
Propeller Engines. -^Onn cylinder crank journal 150; Tunnel 130; Two cylinder
comiwund crank 130; Tunnel no; Two cranks, crank 100; Tunnel 85; Three cranks,
crank 90; and Tunnel 78.
River Service. — C may be reduced one fifth.
iLLrHTRATiox.— With a compound propeller engine, steam cylinders 20 and 40
Ins. in diameter, by 40 ins. stroke, operating under a pressure of 80 lbs. steam
(mercurial gauge), what should be the diameter of the shafts of wrought iron?
{/^
20' X 80 + 40* X 15
4000
X40
=</
56000
4000
X 40 = 8.24 ins. crank shaft;
and 3/?—°^ X 40 = 7.46 ins. propeller ^aft
Journals or 6hai\;s, etc.
Journals or bearings of shafts should be proportioned with reference to
pressure or load tu be sustaine<i by the journal. Simplest measure of bear-
ing ca))acity of a journal is product- of its length bv its diameter, in sq. ins. ;
and axial area or section thus obtained, multiplied by a coefficient of pressure
per sq. inch, will ghe bearing cajyacity.
8ir William Fairbairn and Mr. Box give instances of weights on bearings of
shafts, etc., from which following deductions are made, showing pressure per sq.
inch of axial section of journal :
Crank pins, 687 to 1150 lbs. per sq. inch.
Link bearings, 456 to 690 lbs. per sq. inch.
Frossuro on bearings, as a general rule, should not exceed 750 Iba per sq. inch of
axial area.
Length of Journals should bo i. xa to x.5 times diameter.
Journals of Locomotives or Like Axles are usually made twice diameter, and to
sustain a pressure of 300 lbs. per sq. inch of axial area, or xo sq. ins. per ton of load.
Solid. Cyliudrioal Couplixxgs or Sleeves.
<^4- V5-5<*=i^; 3<i=L; .8d=2; .35(1+. 12 = ]:. d representing diameter,
and L length ofdeeve, I length of lap or scarf of shaft, k breadth of key, its dqM be-
ing ha^fits biieadth, and D diameter of conning or sleeve, att in ins.
ITlauged Oouplixigs.
<*4-V3.5d = T>; 3d4-i=F; .3<i + .4=<; d^-i^L; Z-r-4=«. D repre-
senting diameter ofbmlt/ of coupling, F diameter qf flanges, I thickness ofbotkfiangee,
I, length of each coupling, .? projection of end of one shaft and retrocession of other
from centre <ifcoupUng, and d diameter of shaft, aU in ins.
Supports for Sliafts. (Molesworth.)
5 ^d^ = L. L represetUing dista$»ce of supports apart, infest
STSBM6TH OF HA-TSSUlIA — ^TOBSIOK.-
797
^
/Xi w
To RetUt Lateral Stress, l/'-c*^ ^- ^ repretenting weight or pressure
%t cerOte cf length in lbs., and D diameter or side, if square, in ins. '
Value o^C— Wrought Iron, 560; Cast Iron, 500; Cast Steel, zooo to 1500; Bronze,
(2o; and Wood, 4a When Weight is distributed put 2 C.
Values cf G for Shafting of Vdricus Metals^ as observed by different
AiUhoritieSj and deduced from FommloH of Navier, — -r^ = 0.
VUvmate Besistanee.
MXTAI.
Wrought Iron.
American, Pembc,Me.
** Ulster....
" inean..w.
English, re&ned
Swedish ,
4t
61673
61 815
66436
49148
54585
61909
Mktal.
Cast Iron.
American, mean I
«« 18 trials
English, mean. . |
36846
38300
42831
44957
22132
38217
MCTAL.
Stbel. ■
American, Conn..
" Spindle
«* Nash. I. Co.
English, Shear. . . .
Bessemer <
82926
102131
95213
III 19X
73060
79663
16 WR ^
Mill and Faotory Sliafter. (J. B. Francis.)
Cylindrical. Square
Mean value of T.
d»T
x6R
= W
Coat Iron { J*^ Wroughtlron. . . . | J9
33 000
65000
" mean 35000
Eng. 30000
4(
41
Steel.
(i
«(
1000
.000
mean.,.. 50000 1 *' mean.
'* Eng 45000 i
( 76'
( 'IIK
000
000
86000
Bessemer 78000
Illushbation. — Whafc is the ultimate or destructive weights that may lie borne
by a Round Cast-iron shaft 2 ins in diameter, and by a Square shaft 1.75 ins. sido,
stress applied at 25 ins fh>m axis ? Aissume T = 36 00a
Round Square.
3.1416 X 2» X 36000 _ /i.75*X 36000 \ . '
16X25 ^^ V 25
Their lengths should be reduced, and diameter increased, in following cases :
, I St At high velocities, to admit of increased diameter of journals, thereby
rendering them less liable to heating?. 2d. As they approach extremity of a
line of shafting. 3d. Attachment of intermediate pulleys or gearing.
3) -rry/2— X819 i{&«.
Prime Movers of Power. Transmitters of Power,
^;^^*^3y!«^ = d,and.otnd» = Iff. ^J^^ ^ d, tm^i .02 n d^ ^l^.
Steel, l/^^J^ = <^. and .016 n d» = Iff. 3/3'asIH* ^ ^ ^^^^j ^^^ ^ ^„^ j^
Ca^
Tron ^^^^^ = *>and.oo6nd» = Tff. 3/?^i^^ = d, and .012 nd« = IH».
IH* representing horse-power transmuted, n numl}er ofrevohUiens, and d diameter
of shaft in ins.
Illustration i.— What should be diameter of a wroaght-iron shaft, to simply
traosmit 128 ff at 100 revolutions per minute r
/50X 128
V 100 V i°o
9. —What W will a steel shaft of 4 ins. diameter transmit at 100 revolutions per
(Dioutef
.032 X 100 X 4 ' = 204.8 horses.
3X*
TSAKSTSRSB STRKNGTH.
TVansverse or Lateral Strenffth of any Bar, Beam, Bod, etc.» U ux propor
tion to product of its breadth (ind sauare of its depth; in like-sided l^r&
beams, etc., It is as cube of aide, and ia cylinders as cube of diameter os
section.
When One End it Fixed and the Other Projecting, strength ia inversely m.
distance of weight from section acted upon ; and stress upon any section ii
directly as distance of weight from that section.
When Both Ends are Supported only, strength is 4 times greater for an
equal length, when weight is applied in mid^e between supports, than if one
end only is fixed.
When Both Ends are Fixed, strength is 6 times greater for an equal length,
when weight is applied in middle, than if one end only is fixed.
When Ends Rest merely upon Two Suppotis, compared to one When Ends or*
FHxedf strength of any bar, beam, etc, to support a weight in centre of ft, is
as 2 to 3.
When Weight or Stress is Uniformly Distributed, weight or stress that can
be supported, compared with that when weight or stress 19 applied at one end
or in middle between supports, is as 2 to i.
In Metals, less dimension of side of a beam, etc., or diameter of a cylinder,
greater its proportionate transverse strength, in consequence of their having
a greater proportion of chilled or hanimere^l surface, compared tc their de-
ments of strength, resulting from dimensions alone.
Strength of a Cylinder, compared to a Square of like diameter or sidea, is
as 5.5 to 8. Strength of a HoUow Cylinder to that of a Solid Cylinder, ot
same area of section. Is about as 1.65 to i, depending essentially upoc the
proportionate thickness of metal compared to diameter.
Strength of an Equilateral Trian(/ular Beam, Fixed at One End and
fjoaded at the Other, having an edge up, compared to a Square of the same
area, is as 22 to 27 ; and strength of one, having an edge doum, compared to
one with an edge up, is as 10 to 7.
NoTK^In Barlow and other authors the comparison In this case Is made whan
the beam, etc., restet) upoa supports. Hence the stress is contmriwise.
Strongest rectangukr bar or beam that can be cut out of a cylinder is one
of which the squares of breadth and depth of it, and diameter of the cylinder,
are as i, 2, and 3 respectively.
Cast Irou.
Mean transverse strength of American, as 4etermined by Major Wade, U
681 lbs. per sq. inch, suspended from a bar fixed at one end and loaded at
the other ; and mean of English, as determined by Fairbaim, Barlow, and
others, is 500 lbs.
Experiments upon bars of cast iron, x, 2, and 3 ins. square, give a reanlt
of transverse strength of 447, 348, and 338 lbs. respectively ; being in the
ratio of I, .78, and .756.
■^i^ood.8.
Beams of wood, when laid with their annular layers vertical, are stronger
than when they are laid horizontal, in the proportion of 8 to 7.
Relative Stiffness of* iMlaterials to Resist a rTraixsverse
Stress.
089 I Cast Iron. ... 1 | Oak 095 I Wrought Iron i. 3
073 I Ww. 0731 White pioe,., .1 " | Yellowpin^. .98;
STBBNGTB OF UATBBIALS. — TRAKBVXBSX.
799
Strength of a Rectangular Beam in an Inclined pontion, to resist a vertical
stress, is to its strengthln a liurizontal ]H)sition, as square of radius to square
of cosine of elevation ; ttiat is, as square of length of beam to square of dis-
tance between its points of support, measured upon a horizontal plane.
Woods.
tntimaU Resiitance.
Caiifornia Red Tine.
California Spruce. . .
Canadian Red Fine..
Cedar
4500
5000
5000
5000
Cbestnat
Georgia Pine...
Hemlock
Northern fine.
LbB.
5000
7000
3500
6000
Oregon Piue.
Spruce
White Oak...
White I'ine. .
Lb«.
6500
^000
6000
4000
rrransverse Strengtii or Various JVIaterials.
(U. S. Ordnance Departmenty Hodgkinton, Fairhaxm^ Kirkaldj/, by the Author ^ and
Digest of Pkyncol TesU. )
Bower reduced to uniform Measure of One Inch Square, and One Pool in Length;
Weighl suspended from one End.
Safe Stress*
Woons {Continued).
Gum, blue 136
Hackmatack tos
Hemlock « 100
Hiokorjr sto
r^rch, Russian 118
Lignumvft«9 i6>
Locust 295
Mahogany 112
Maple 20s
Oak, white 150
live. 160
African 207
Rnglish 130
French 160
Metals.
Brass 260
Cast Iron, mean (MaJ. Wade) 681
ordinary 373
extreme, West P't F'dry 980
gun -metal,* " " 740
Kng , I.0W Moor, ooli blast. 472
'* Ronkey, " 581
" Ystalyfera, *♦ 770
" mean, 65 kinds 500
^' 15 kinds, cold blast 641
planed bar. 518
Copper. 244
sSteel, hammered, mean 1500
cast, soft 1540
*' bard 4200
hematite, hammered 1620
Krupp*s shaft 2096
Kagersta, hammered 1 200
Wrought Iron, mean 6cx>
English 475
Swedisht 665
(C
i(
tt
ti
n
4<
«(
i(
((
ti
it
t(
It
41
^^
u
tt
(t
it
tt
(t
tt
tt
Canada. 146
Spanish 105
Fine, white 123
pitch 137
yellow 130
Georgia 200
Poon 184
Spruce, Canada ta)
" black 87
Sycamore 125
Tamarack 100
Teak 165
Walnut 112
Woods.
Ash 220
** English t6o
" Canada. lao
Balsam, Canada 87
Beech 130
" white 112
Birch 137 ! Brick, common, mean
Cedar, white. 160
*' Cuba, mean. 84
Chestnut 160
Elm 125
" Canada, red. 170
Fir, Baltic, mean 13
isaiuc, mean 13^
Canada, yellow { ^J
*' " red 120
9reenheart, Guiana 160
Stonxs, Bricks, stc.
20
*' pressed, " 40
Cement, mean T5
" " Portland i '®"'
I 37- 5
hydraulic, Porlliiud. . 5
Roman 2
It
It
ti
tt
tt
tt
Puzznolana.
Portland, i year
Concrete, Eng., flre-brick beam,)
cement )
t
3"
• This WM with a lmsll« itrMictk of 97000 lU.
t With 840 n«. tfa* fUflMiioo WM 1 iaeh, aad th« 4a«tkUy of Uia m«Ul dmtsofmA.
Boo HtRltNViTH UK MATKKIALS.-
-TBANSVEESE.
TV % S.-*»'
X ^ V
, ^ kI
*N»
"^-'is
*.?<.
•«M<^
«ll.
3-4
«3
I0.8
'9
24
10.7
1-3
4-3
42-5
18
26
25
• ••••••
iNteMn
22
II to 15
IZ
.... 9a
Stobsb, Bricks, xtc
Marble, Adelaide 4.5
" Italian, white u.S
Mortar, lime, 60 dajTE 2.$
X iirae, T sand 3
1 " 2 " 1.7s
I " 4 " i.aS
Oolite, English, Portland 21.3
Paving, Scotch, Caithness 68
Ireland, Valentia. 68. 5
Welsh 157
English, Yorkshire, blue., zo.4
*' Arbroath ty
Slate 8z
" Bangor. '..... 90
" English, Llangollen 43
Stones, English, Bath. 5.3
Kentish, Rag 35.8
Yoiicsh ire, landing 23. 5
4i
((
{(
14
U
Caen
12.5
«^v
•WM<««IW Strength of Woods, compared with their Breaking Weighty
is as jfcUows :
♦ --k^
•*^'
Fvr Cent.
.. 29
.. 25
•• 32
.. 38
Per Cent.
Norway Spruce.... 30
Oak, Dantzic 36
'' English 33
Pitch Pine 24
Percent.
Red Pina 39
RigaFir 3S
Teak 33
Yellow Pine 30
,^^4V*»* i» Strength, of several "Wciods "by Seasoning.
Per Cent.
^^ ,^.44,7 I Beech 61.9 I Elm 12.3 | Oak. ..-,.26.1 | White pine.... 9
Concretes, Cements, etc.
Matsbials.
vxvNCKBTES (English).
<>c^^k'k beam, Portl'd cement
^^ sand 3 parts, lime i part
CKMBNTS (English).
^{^ c)i^ and chalk
•MUoid I
^•«*i»i>«y
Breaking
Weight.
Matkbialb.
Bnainc
Weight:
LbB.
31
•7
BRICKS (English).
Best stock
Lb*.
11.8
Fire-brick
14
10.7
5-8
2-5
New brick
5-4
37-5
10.2
5
Old brick
Stock brick, well bnrned.
" inferior, burned. : .
|^«*»n8verse Strengtlx of Varions ITigures of Cast Iroxi.
4(^cect to Uniform Measure of Sectional Area of One Inch Square and One Foot in
Length. Fixed at one End ; Weight, suspended from the other.
Brenkins
Woigki:
Form of Bar or Beam.
Square
♦
Square, diagonal vertical. . .
Cylinder
3W cylinder; greater)
meter twice that of [
»r )
Breaking
Weight.
Lba.
673
568
573
794
Form of Bar or Beam.
I
CI
Rectangular prism.
2X.5 ins. in depth.. .
3X.33 " in depth...
4X.25 '^ in depth...
▲ Equilateral triangle, an
edge up
▼ Equilateral triangle, an
edge down
2 ins. in depth X 2 X )
.268 inch in width.. ]
2 ins. in depth X 2 X )
.868 inch in width..)
I
Lbs.
1456
2393
2652
560
958
ao68
I 555
STBBKGTH OF MATERIALS. — TBAN6VER8E.
80k
Solid and HoUoiiv Csrlinders of various :MaterialBo
One Foot in Length. Fixed cU one End ; Weight suspended from Oie other.
Matbkiau.
WOODS.
Ash
(t
Fir*
White pino. .
ti
u
External
Dmm.
Ins.
2
2
2
Z
3
Internal
Diam.
Breaking
Weight.
Matcruls.
Inch.
X
Lbs.
685
604
772
610
HKTAL.
Cast iroD, cold)
blast (
STONE-WARE.
Rolled pipe of )
fine clay )
External
Diam.
Interna)
Diam.
Breakiiift
Weijcbt.
Ids.
Ins.
Lbs.
3
—
12000
2.87
X.928
19c
* An inch^sqaare batten, from same plank as this specimen, broke at 139 Ibt.
f^oxrxxiulae ibr Xraxis-verse Stress of* fLeotaiigixlar Sars»
SeaxxiB, Cylinders, etc.
Fixed at One End, Loaded at (he Other,
Bars. Beams, etc. = S: =;W: =^l\ - — = 6: / — — d:
IW
Bars, Beams, etc.
JlW
and Cylinder 3 / — - = b and d.
fixed at Both Ends, Loaded in Middle,
6S bd'
IW enbd'
w
=«;.
JJL-h
6iid''- *
. /2-5-r = d\ and Cylinder 3 /— — = b and d.
V 0 o O Y 0 o
Fixed at Both Ends. Loaded at any Othet' Point than in Middle,
2*»»W
Bars, Beams, etc. ^^^^-, =S; ^__^ =W; ^^^775 = i;
2 mn
VTs?-ft- = ^' and Cylinder 3^
3S6da
2 m n W . , _
— —J— = 6 and d.
3 St
3 Sid
,=&i
Supported at Both Ends. Loaded in Middle,
Bars, Beams, etc.
IW
= S;
I
= W;
4Sbd^
W
4 6d=»
^ /—rr-r= d ; and Cylinder 3 /— - = 6 and d.
V 4 o ^ V 4 ^ .
= li
IW
4Sd'
= fr.
8uj}ported at Both Emh. leaded at awf Other Point than in Middle.
m n \\ .. ^Ibd^ _. vi nW . mnW
/
m n
= W;
S6d2
= «;
Bars, Beams, etc. , - -— = S :
' lb d^
fmnW _ j«ij . /mnW
— ^ = d; and Cylinder 3/ . ~ & and d.
S/d'
= 6;
In Square Beams, etc., for b and d put ^^ = -VgT" = * In Cylinders, for
& d' pot d* as abova
jrA«n «w.9A« M uniformly distributed, same formulas will apply, W r<7>rc-
setUing only half required or given loeight,
S representing stress in a Bar, Ream, or Cylinder, one foot in length, and one inch
square, side, or in diameter ; and W weight, in lbs. ; b breadth, and d depth, in ins.;
I length, m distance of toeight from one end, and nfrom the other, all in feet
Briok-worli-
A brick arch, having a rise of 2 feet, and a span of 15 feet 9 ins., and 2
feet in width, with a depth at its crown of 4 ins., bore 358400 lbs. Lp^id along
itib centre.
802 STBENGTH OF MATERIALS. — TEANSYBBBS.
Coelfioient or B^aotor of Safety.
CoeffieieiU or factor of safety of different materials must be taken in view
of importance of stnicturef or instrument, probable or required period of du>
ration of it, and if it is to bear a quiescent, vibratory, gradiutl, or percussive
stress, and to meet these varied conditions, it will range from .125 to .3 of
the maximum or ultimate strength here given or ascertained.
To Compute Transverse Strength, of a Rectangular Bar
or Geaixi.
When a Bar or Beam is Fixed at One End, and Loaded at the Other.
Rule. — Multiply Coefficient of material in preceding Tables, or, as luay be
ascertained, by breadth and square of depth in ins., and divide product by-
length in feet.
Note. —When a beam, etc., is loaded uniformly tbroaghont ita length, result must
be doubled.
ExAMPLK. — What weight will a cast-iron bar, 3 ins. square and projecting 30 ina
in length, bear without permanent injury ?
Assume strength of material at 660, and its elasticity at one fifth or .3 of its
strength.
_. ^^ 660 X .2 X 2 X 2» 1056 ,.
Then = — ^ = 422. 4 to*.
V 2.5 2.5
f^ Dimensions of a Beam or Bar are Required to Support a Given Weight
at its End, Rui.k. — Divide product of weight and length in feet by Confi-
dent of material, and quotient will give product of breadth and square of
depth.
ExAMPLK. — What is the depth of a wrought- iron beam, 2 ina broad, necessary to
support 576 II0S. suspended at 30 ins. fh>m fixed endt
Assume strength of iron at 15a
Then ^^-^2^=g6, and /^=2.tg ins. depth.
When a Beam or Bar is Fixed at Both Ends, and Loaded in the Middle,
RuLR. — Multiply Coe^ieni of material by 6 times breadth and square of
depth in ins., and divide product by length in feet
NoTK.— When beam is loaded uniformly throughout its length, result most be
doubled.
ExAMPLK.— What weight will a bar of cast iron, 3 ina square and 5 feet in length,
support in middle, without permanent injury?
Assume strength of material as in a previous case at .2 of 660-
Then 66oX.2X2X6X2^^6336^^^ ^
5 5
If Dimensions of a Beam or Bar are Bequired to Support a Given Weight
in Middle, bcttoeen Fixed Ends, Rule. — Divide product of weight and
length in feet by 6 times Coefficient of material, and quotient will give prod-
uct of breadth and square of depth.
Example.— What dimensions will a square cast-iron bar, 5 feet in length, require
to support without permanent injury a stress of 2160 Iba ?
Assume strength of material at .2 of 660 or 132, as preceding.
Then '' ° ■ } = ^ — = 13.64, vffdeh, divided hvifor assumed. hreadlh =s 6.89,
13a X 6 79a J T> . ^ ^ -1
and V6.8a=: a.6x ins. dqi>tk.
When Breadth or Depth is Bequired. Rule. — Divide product obtained
by preceding rules by square of depth, and quotient is breadth; or by
breadth, and square root of quotient is depth.
^.XAMPLK.— If 128 is the product, and depth is 8; then ia8-^8* = 3,6reaMk
128 -i- 2 = 64, and V'64 = 8, depth.
STRENGTH OF MATEBIAL6. — TRANSVEBSE. 803
When Weight is not in Middle between Ends, Rule. — ^Multiply Coefficient
of material by 3 times length in feet, and breadth and square of depth in
ins., and divide product by twice product of distances of weight, or stress
from either end.
EzAXPLB.— What weight will a cast-iron bar, fixed at both ends, e ina square and
5 feet in length, bear without permanent iujury, a feet Irom one end J
Assume strength of material at .2 of 660 or 133, as preceding.
mh^ «32X3XSX2X2» 15840 „
Then — — = — ; = -=—^- = 1320 iw.
2X(2X3) >2
When a Beam or Bar is Sunported at Both Ends^ and Loaded in Middle.
Rule. — Multiply Coejficient of material by 4 times breadth and square of
depth in ins., and divide product by length in feet.
Note. — When beam is loaded uniformly throughout its length, result must be
doubled.
ExAMFLK. — What weight will a cast-iron bar, 5 feet between the supports, and a
Jna square, bear in middle, without permanent ipjury?
Assume strength of iron at 133, as preceding.
Then 132 X 2 X 4 X a' = 4224-7-5 = 844.8 lbs.
If Dimensions are Required to Support a Given Weight. Rule. — Divide
product of weight and length in feet by 4 times Coefficient of material, and
quotient will give product of breadth, aind scjuare of depth.
When Weight is not in Middle between Sitjworts. Kulk. — Multiply Coef-
fidenl of material by length in feet, and breaath and square of depth "in ins.,
and divide product by product of distances of weight, or stress u-om either
support
ExAXPLK. — What weight will a cast-iron bar, a ins. square and 5 feet in length,
aupport without permanent ii\jury, at a distance of 2 feet fVom one end, or support f
Assume strength of iron at 13a. as preceding.
2X(5 — 2) 6
To Compute PresHure upon. Snds or upon Supports.
Rule i. — Divide product of weight and its distance from nearest end or
support, by whole length, and quotient will give pressure upon end or sup-
port farthest from weight.
a. — Divide product of weight and its distance from farthest end, or sup-
port, by whole length, and quotient will give pressure upon end or support
nearest weight.
ExANPUL^What is pressure upon supports in case of preceding example?
= 352 Ihs. upon support farthest from the weight; — 528 lbs. upon
support nearest to weigfU.
When a Bar or Beam, Fixed or Stmported at Both EndSy bears Two
Weights at Unequal Distances from Ends.
mW , Iw . , ,^ . nw , I' W * «, ^
-= — -}- -7- = pressure at w end^ and — — 4. — -— •■= pressure at W end.
L I4 L L
IK and n representing distances of greatest and least weights from, their nearest
end, W and w greatest and least weights^ L whole length, I distance from least weight
to farthest end, and V distance of greatest weight from farthest end.
iLLUSTRATioif. — ^A beam 10 feet in length, having both ends flxeU in a wall, bears
two weights— viz., one of 1000 lbs., at 4 feet from one of its ends, and the other of
3000 lbs, at 4 feet from the other end; what is pressure upon each end?
4 X 2000 . 6 X 1000 ,1 A 4 X 1000 , 6 X aooo . ,. . _.
VO. 4- -ii — ,400 lbs. atw: — 1600 Iht. at W.
10 xo xo xo
8CH STEENGTH OP MATEBIAIiS. TBANSVBBSA.
/
When Plane of Bar or Beam Pi^ojectB OtHiquely Upward or Downward,
When Fixed at One End and Loaded at the Other. Rule. — Multiply Ooi
efficient of material by breadth and square of depth in ins., and divide product
by product of length in feet and cosine of angle of elevation or depression.
NoTK— When beam is loaded uniformly along its length, Yesult must be doubled.
ExAVPLB. — What is weight an ash beam, 5 feet in length, 3 ina square, and pro-
jecting upward at an angle of 7*^ 15', will bear without permanent injury?
Assume breaking weight of ash at 160, and its elasticity at .25 of its strength, a&i
cosine of 70 15' = .993.
TK^^ 160X. 25X3X3* 1080 ,,
Then — - — -- =: — - = 217.74 los.
5X.993 4-96
To Compute Transverse Strengtla of an. lCq,xiilateral Tri
angle or T Seani.
RuLK. — Proceed as for a rectangular beam, taking following proportioaf
of Coefficient of material :
Fixed at One or i Equilateral triangle, edge op 6 X d» X 2 C
J^nfh l^, \ Equilateral triangle, edge down 6 X d« X .34 "
isoin Jijnas. ( f beam, flange up b%d^x.^^'
Sunnortfid at ( Equilateral triangle, edge up 6 X d« x .34 '*
au^riea at, 1 Rqajiateral triangle, edge down ft x d=^ X • 2 "
DOtn HMOS, ( J beam, flange up : 6xd=X-42"
To Compute Transverse Strength, of a Solid Cylinder
RuLK. — Proceed as for a rectangular beam, and take .6 of Coefficient or
of product.
A mean of z8 results with cold blast gun-metal, gave a coefficient for 740 lbs.
W/ien Fixed at One End^ and Loaded at the Other, RuLB. — Multiply
weit^ht to be supported in lbs. by length of cylinder in feet , divide product
by .6 of boefficient of material, and cube root of quotient will give diameter.
Note.— When cylinder is loaded uniformly throughout its length, cube root of
half quotient will give diameter
Ex AMPLR. —What should be diameter of a cast-iron cylindrical beam of gun -metal,
8 ins. in length, to break at 15 000 lbs. ?
, /150OOX 8-r-I2 _ /lOOOO _ .
I ^ = I = 2.8ain«.
V 6X740 V 444
When Fixed at Both Ends, and Loaded in Middle, Rule. — ^Multiply
weight to be supported in lbs. by length of cylinder between supports in
feet ; divide product by .6 of Coefficient of material, and cube root of one
sixth of quotient will give diameter.
NoTK.— When cylinder is loaded uniformly alCDg its length, cube root of half the
quotient will give diameter.
Example. — What is the diameter of a cast-iron cylinder of gun-metal, 2 feet be>
tween supports, that will break at 35964 Iba ¥
35 964 X a
.6X 740
Mean results of cylinder and square bars gave 444 and 740 Iba Hence, strength
of a cylinder compared to a square is as 444 to 740 or .6 to i.
Then 4X33X444 ^ ^y ^ j2 lbs.
= 163, and ? /^ = 3 <»M.
X
To Compute Diameter of* a Solid Cylinder to Support
a given 'Weisl^t.
When Supported at Both Ends, and Loaded in Middk, Rule.— Multiply
weight to be supported in lbs. by length of cylinder between supports in
feet ; divide product by .6 of Coefficient of material, and cube root of one
fourth of quotient will give diameter.
STESNGTH OF HATJBBIALS. — TBANSVEESE. 805
NOR.'-WheD cylinder is kntded uniformly along its length, evbe toot of hAlf the
potient will give diameter.
ExAMPLs.— Wiiat is diameter of a cast-iron gun-metal cylinder, i foot between Its
lapports, that will break at 4&000 lbs. f
48000 X I o ^ * A08
^^— = 108, and 3 / — =3 1«*
.6X740 V 4
Heotangular, (i>. K. Clark.)
{t) Loaded at Middle. 2-y^ = W. (q) Loaded at One End. l~.zs^
Cylindrioal.
(3) Loaded oLMiddU. 5Ji^ = w. (4) Loaded at One End. iiZi^^W.
W representing vUimaJte stress in tons.
Above Coefficients are for iron of a tensile strength of 7 tons per sq. inch.
(0 (2) (3) (4) (1) (2) (3) (4)
Hence, for 8 tons put 9.3 3.3 6.3 x.6
9 ** X0.4 2.6 7.x X.8
XI " X2.7 3.3 8.6 3.3
10 " 1 1. 5 2.9 7.9 3
8.r
For IS tons put 13.8 3.4 9.4 3.4
13 ** 14.5 3.6 10.3 3.6
14
it
16
4
IX 3.8
«s
u
17.3
4-3
IX.8 3
!I?o Ooxapixte JDeetxructive "Weisb-t, or l^oads tliat xnay "be
l>oriie 'by ^Vroue^t-iroix Rolled Beams and Ghirders,
or Riveted Xixbes of* various IT'ig^iires and Sectioxis.
Supported at Both Ends, Load applied in Middle.
When Section of Beam or Girder is that of any of the Figures infoUofw-
ing Table, Rule. — Divide product of area of section, depth, and Coej^ient
lor girder, etc, from following Table, by length between supports in feet,
and quotient will give deatractive weight in lbs.
NoTB.— The Coefficients given are based upon experiments with English iron.
Solid Beams.
IzJiUSTRATioir. — What load will destroy a wrought iron grpoved beam of following
dimensions, 10 feet in length between supports, and loaded in its middle?
Flanges, 5.7 x -6 inch; Web, .6 inch; Depth, 11.75 ins. ; Area, 13.34 sq. ins.
AflBume Coefficient 463^ ds for like case (xx) in following table, page 806.
'3-34 X 11.75X4638 726983
= = 7a 090.3 UfS.
xo 10 ^
Ultimate stress for such a beam by experiment was estimated at 97 997 lb&
Formulas of Various Authors give foUowing Results:
D. K. Clark. ■ "r'-'SSS^; _ ^ ^ representing area of section of lower
.0 *
JUmge^ a' area of section of web, less onejlange^ d depth of beam, less average depth
ilfoneflangefoil m ins., I length in feet, and W ultimate deslructine weight in tons.
This formula is based upon the assumption that the beam has lateral support
11.75 — .6(4X^7^-6H-»i55Xxi.75 — -^X.e) 238-69 _ ,0 „v:,v ^
-__ = =E 39. 78, which x 2340
^ _ .0 X xo O
.s 89 X07 lbs.
If OLBSWOETH. ^-^^— = W. C = 7616 Ibs. , and for hd» put 6 d' — 3 6' d'».
5 = 5.7 • ft' = S-7— •6-^a =2.55 : d = ii.75 : d' = 11.75— ^6 X 2=10.55 '
and 5.7 X 11.7s" — 2 X 2.55 X icss'-'^ 786.94 — 567.63 = 219.31.
-_. 4X7616X210.31 6781060 ^ „ „ ,.
Then, - — — ^-^ = — ^- = 56 508.8 lbs.
' loX 12 120 ^ ^
b and d representing exterior and b' and d' interior dimensions, and I Imgth aU in ins.
Fairbaim's formula would give a result less than half of the first, and Hodgkir
son^s alike to that of Molesworth.
• V
8o6
PLATS AND BOX GIBDEBS.
Steel Plate Grirders-
Steel Box G-iTd.eTm,
Safe Loads in Tons of 2000 lbs. Uniformly DisfribtOed,
Tensile Strength^ 15000 lbs.
Plate.
Carnegie Steel Co.
Sox.
30X.6 Ins. 33X.6 Ixis.
Web Plate.
Flanges, 1 2 X . 375 in*- AngUs, s x . s
X 3-5 »»»*•
. J
Load. |
|28
.added
plates.
Centre
tre of 1
i|2
Feet.
Ton*.
Tons.
20
9367
4.62
21
89.2a
4.38
22
85.15
4.19
23
81.46
4
24
78.07
3?3
25
74-94
3.68
26
72.06
3-54
^l
69.4
342
28
66.91
329
29
64.6
3- 17
30
62.45
3.07
31
60.44
:m
32
58.55
33
56.77
2.79
34
55"
2.7
3?
52.04
2.50
38
49.3
2.42
40
46.83
2.31
nil
III
Q-go
Si
Feet.
20
21
22
23
24
25
26
2
29
30
31
32
33
34
36
38
40
Load.
^
Tons.
105.82
ioa78
96.2
2.01
8.18
84.65
81.3.
78.3
75-58
72.98
70-55
68.26
66.14
64.13
62.24
58.79
55.7
52.9
Ik
Tons.
5.08
4.85
4.62
4.42
4.23
4.06
3.9'
376
3-63
3-5
3.39
3.29
3.1
3.0
2-99
2.83
2.67
2.55
30X.3 Ins. 33X.6 Ins.
"Web Plates.
FUmges^ 16 X . 375 Flanges, 20 X • 437J
ins. ins.
Angles, 3.5 x 3-5 X .5 *»«•
si's
^1
Feet.
20
ai
22
23
24
25
a6
27
28
29
30
31
32
33
34
36
38
40
o .
^^5
liOAD.
Tons.
1 13.6
107.24
102.37
97.02
93.83
90.08
8^ 6a
83.4»
8a 12
77-05
75.07
72.65
7a 38
68.24
66.23
62.56
59.26
56.31
Tods.
6.61
6.3
6
5-75
5.52
5-3
5.09
4-9
73
57
41
27
»3
02
9
%
1 . .
Load.
Distance
Centre to Cen-
tre of Bearfoga
With
Weight of
Girder.
?co
Feet.
Tons.
Tons.
20
150.2
9.17
21
143- 1
8.75
22
>36.5
8.33
23
i3a6
7.96
24
135.2
7.64
25
12a I
7.33
26
"5-5
7.06
27
XII. 2
6.8
28
107.3
6.54
29
103.6
6.3a
30
xoaa
6.1
3«
96.9
592
32
93-9
573
33
2J
5.56
34
88.4
5-39
36
83-4
509
38
79 4-82
40
75-1
4-58
3ex.6 Ins. 48X.6aO Ins.
Web.
Flanges, 12 X -375
ins. Angles, 5 X
3.5X.5«»».
ao
ai
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
"8.35
1X2. 7
107.57
102.9
98.61
94.66
91,03
87.65
84-53
81.61
78.89
76.34
7396
71.72
69.61
65-75
62.28
59-14
5.54
5.28
5- 04
4.82
4-63
4-44
4.27
4.11
3-q6
3.82
3-7
3-58
3.46
3-36
3.27
307
2.91
2-77
FUmges, 14 X 625
ins. Angles, 6 X
6 X .625 ins.
ao
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
176.01
167.63
160.02
153.06
146.68
14a 82
135-3
130.3
125.73
121.38
"7-35
"3.56
III. ox
106.67
103.55
97.78
2.64
8
ti
7-74
7-37
7-03
6.73
6.44
6.18
5.95
5-73
5.52
5.34
5.17
)8
4-7
4-55
4.3
4.07
387
4.98
4. 8 J
Sex.a Ins. 4aX.G ins.
"Webs.
Flanges, 24 X .5625 Flanges, 30 x .6875
ins. Angles, 5 X
3.SX.5«*u>
ins. Angles, 4 X
3.5 X .5 *ns.
ao
21
23
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
213.3
203.3
194. 1
185-5
177.0
17a 8
164.3
158. 1
152.4
147.2
142.3
"37
133
129.
125
1x8.6
1Z2.4
X06.7
I a. 22
11.65
IX. la
X0.64
io.a
9.78
I
8.43
8.15
88
65
42
a
81
44
12
30
21
22
23
24
25
36
27
28
29
30
3>
32
33
36
38
40
329.2
313.5
274-3
263-3
2532
2438
235.2
227
2x9.5
212.3
205.7
'99-5
3.6
2.9
173-2
164-5
;i
18.29
1.7.41
16.63
15.9
15. 24
14-63
14.07
'355
13.06
X3.6x
13. x8
11.79
XX- 43
XO.08
"0-7S
10.15
9.63
9.X4
Bdcklino.— To arrest the bockling of these girders, strips of plate, termed Fltttrt, are let vertical
on the outer sides onlv of a web plate, together with other ▼ertieal angles, termed Biiftiiur; both of
which are riveted to the web plate, and both of these •dditiou an Ml at itttarvala, deps^deot Qpo« th«
length of the girder and the character of its stress.
STBEN6TH OF HATEBIALS. — TBANSYEB8E.
807
X^olled Steel Seameu
SiqfR Load for One Foot^ Uniformly Distributed and Supported Sideunge.
Carnegie Steel Co., Pittsburg, Pa.
[nd«z.
Depth.
B77
3
B23
4
B 21
5
B 19
6
B17
7
Bzs
8
B.3
9
Bii
10
B 9
13
B 8
za
B 7
15
B s
15
B 4
IS
B80
18
B 3
30
B 3
30
B I
M
DMicnaUon.
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Light
Heavy
Standard
Width.
Flaage.
Ina.
3.423
2.521
2.33
tw
2.66
»47
294
4S«
575
33
t^
3.66
4.087
4.271
4
4446
4.772
4-33
4-805
t^
5- 086
5
S.366
5.612
5.25
5-55^
5-746
5.5
6.096
6.293
6
6.479
6.774
6.4
6.095
6.259
6
6.325
6.399
6.25
7.063
7.284
7
7.07
7-254
7
W«b.
Ins.
.263
.361
•17
.363
•4*
.19
•357
.504
.21
•352
•475
•23
•353
.458
•25
•357
•541
.37
.406
•732
.29
•455
•749
•31
•436
.576
.822
.46
^^56
•41
.686
.882
is^
1. 184
.8x
•555
.7x9
.46
•575
.649
•5
.663
.884
.6
.57
•754
-5
Area.
BflCttOB.
I Weight
Sq.Ine.
1.91
2.21
1.63
2-5
3-09
3.31
4-34
3.87
4^34
5.07
3-0i
S-«5
5.88
6.03
7-5
S-33
7-35
10.39
6.31
8.83
11.76
7-37
10.39
9.36
13.24
16.18
11.84
13.24
16.18
13.48
19.12
23. 06
17.67
25
29.41
23.81
»7-65
20.59
'5-93
20.59
33. 06
19.08
25
29.41
23-73
25
29.41
33.33
Foot.
LU.
6-5
7-5
S-S
8.5
IO-5
7-5
13.35
14-75
9-75
14-75
"7-25
13.35
»7S
30
15
SO. 5
18
25
35
3X
30
40
25
35
31- :
45
55
40
45
55
42
65
75
60
85
100
80
60
70
55
70
65
85
100
80
85
too
80
Teoeile Strength
per Sq. Inch.
13500 16000
Lbs.
15000
10 300
13800
36500
29800
34900
45400
50500
40300
66600
73800
60500
93300
100400
86300
136300
143600
1x8 500
X70300
' 207000
157300
223600
264500
203500
317000
299700
396800
445800
373500
506400
567800
490800
706700
768000
676600
908600
Z000600
883900
779600
853000
736700
X 016600
1 057 400
974700
X 257 200
1379800
X 222 100
X 505 900
X 653 300
1449900
Lbs.
19 100
20700
17600
33900
38 100
31 800
58x00
64600
51600
86300
93x00
77500
XX9400
128600
XX0400
x6i6oo
182500
X5X700
3x7000
365000
30I 300
386300
338500
260500
405800
383700
507900
570600
478 100
648200
726800
628300
904600
983000
866100
1 163000
I 280700
I X3I 300
997700
X09I 900
943000
X 301 200
X 353 500
1247600
X 609 300
X 766 100
1 564 300
1927600
21x5900
X 855 900
Index refen to lUuBtration in Catalogue.
For safe load of Iron deduct 25 per cent
For permanent stress, absolately (Vee fVoni vibration, a greater strain would be
allowable, and, contrariwise, If the stress is vibrative or mainly that of a live load,
the loads here given should be relutively redOced.
8o8
STRKNGTH OF MATKBIALS. — TBANSVERSB.
A difltorenoe ot 35 per cent to ettber directtan sbonld be made, according to char-
acter of load to be supported or stress to be borne.
Elastic Transverse Strength of Wrought-iron Bars is about 45 per cent, of their
transverae strength, of Solid rolled beams, 50 per cent. ; and of double • headed
rails, 46 per cent, of their transverse strength; of Fagersta Steel, 56 per cent, of
its transverse strength; of double- beaded Steel rails, 47 per cent ; of Beasemer
Steel, 37.5 to 48 per cent. ; and of Steel flanged, 68 per cent
Transverse strength of Solid Cast-iron Beams or Girders is aboat 50 per cent, of
ultimate strength.
NoTR.— Actual breaking weight of a xa 5 ins. beam of New Jersey Steel and Iron
Co., weight 35 lbs. per foot, for a length of span of 20 feet, is 60000 lbs.
Rolled Steel X>eok Seazns.
Safe Load for One Foot, Uniformly DistritnUed, Supported Sidewise.
Add to Web
for each
lb. increate.
Ids.
049
042
037
033
029
026
Depth.
Web.
Flange.
Area.
Int.
Ins.
Int.
Sq. Int.
6
2.8
4.38
41
6
4-3
4-53
5
7
31
487
|-3
7
5-4,
51
6.9
8
31
5
5-9
8
4-7
5. 16
7.2
9
4-4
4-94
It
9
S'Z
5-«>7
8.8
xo
3.8
5.2s
8
10
6.3
5-5
10.5
"•5
42
5»7
95
"•5
5-5
5-3
10.9
I.mu1ii.
Weight.
Tensile
perSq
Btrencth
. Inch.
12000
x6uuu
Lbs.
Lbs.
Lba.
14. 1
48800
65 100
17.16
57600
76800
18. zx
77300
X03000
23.46
93400
124600
2ai5
97400
X29800
24.48
112600
X 50x00
26
141800
X89X00
30
156400
908500
27.23
169600
226x00
35-7
205600
274100
32.2
221000
294700
37
244800
326500
Steel Sull> A.Tigle8.
5
6
6
6
7
7
8
9
10
xo
.31
2-5
2.94
—
10
.31
3
3.62
—
12.3
.38
3
5.00
—
13-75
.50
3
—
17.2
.34
3
4.71
—
16
•44
3
5- §7
—
18.25
•41
3-5
5.66
—
19.23
•44
3-5
6.41
—
21.8
.48
3-5
7.8
—
26.5
.63
3-5
9.41
—
32
32500
43300
45300
52800
60400
69600
60400
70400
80500
92800
76700
93600
X02300
124800
115 700
158800
154200
2x1700
172500
230000
Operation, of Tallies.
To Cozxipixte Depth, of a Beaxxx to Support a TJxiiforxnly
distributed Load.
Rule. — Multiply load in lbs. by length of span in feet, and take from
table the beam, load of which is nearest and in excess of product obtained.
Illustration. — What should be depth of a steel beam to sustain with safety a
UDiformly distributed load of 30000 lbs., over a span of 15 feet?
30000 X 15 = 450000, which is load for a beavy beam 12 ins. in depth.
Weight of beam should be added to load.
Inversely.-^U the load is required, divide load in table by span of beam in fee4,
and subtract weight of beam.
"Po CoxKipute Deflection of Like Beaxxis.
Rdle. — Divide square of span in feet by 70 times depth of beam in ins.
Illustration. — Assume beam as preceding.
>5"
*'^5
70X12.25 857.5
=5.962 ins.
STBBKatB OP MATBB1AL8. — TBANSVSltSB. 6oQ
Compsurative Strexig^tli and I3eii«otion o^ Cast-iron
Flanged Beams.
DncximoN or Bsam.
Comp.
StfeDfi^ha
DBRCKimoR or Bbam.
Conp.
StrMifftht
Beam of equal flanges
.58
.73
Beam with flanges as i to 4. 5 . . .
'* withflaiige8a8it0 5.5...
t
* ' with only bottom flange. .
" with flanges as 1 to 2.. 1.
•63
" with flanges as I to 6
X
** with flanges as i to 4. .'. .
•73
" with flanges as i to 6. 73 . .
'9*
Rolled 'Wroue*hit-lron Seams— Snglislx,
8qfc Stress for a
Span of XO FtA, {D, K. Clark.)
1
Ultimftto
' Safe^lnM
Dqith.
Brwidtb
of FlangM.
ThieknaM. Weight p«r
Lineal Foot.
Strength.
Londed
Unlfortnly
Web.
Flaiigw.
In Middle.
DUtriboled.
Ilia.
In*.
Inch.
Inch.
Lbs.
Lbe.
Lbe.
3
a
.1875
.3187
5-5
3800
9x0
x86o
3
3
.25
•3"5
10
5600
3.125
X.635
.1875
.3x87
§•5
2490
830
4
3
■25
.3«2S
8
5490
1830
4
3
35
•375
12
8510
3830
4-75
3
.25
.3125
8
6940
3310
5
3
.3125
•4375
»3
«3440
4480
6420
5
4-5
•375
• 5
23
'9?Z°
5-5
3
.375
•4375
10
X1880
3960
6
S
•4375
.5625
30
23830
7940
6.35
3
.3"5
.4375
XX
13440
4440
6.35
3.35
.3"5
•375
x8
X3000
4330
5820
6.35
335
.3"5
.4002
X2.5
X7470
7
3.35
.281
•375
14
14790
4930
7
3.35
•3125
•4375
14
17020
5670
7
3.62s
.3125
•4375
»9
33300
7760
7
3-^5
•3«25
•5
'9
35980
30830
8660
8
«.375
•3125
•4375
15
6940
8
a- 5
•375
•375
«5
21 280
7090
8
4
•37S
•5
3X
34 5a>
XI 500
8
5
•375
•5625
39
44800
itm
8
5x25
4375
.5625
29
47040
9.25
3-75
•4375
•5
24
41560
13850
9-5
4*5
•375
.6875
30
59360
19750
18660
xo
4-5
4375
•5625
32
56000
xo
4.75
4375
.5625
32
58240 •
19410
xo
4-75
75
.625
36
76160
35390
X3
5
5625
•817s
43
X00800
33«oo
X3
6
5625
.9375
•875
56
136 640
45530
«4
5-5
5625
60
150 020
50000
■4
6
5635
8»75
60
153360
50750
x6
5625
75
.8175
63
188160
(
53730
'^^^ro-ach.t-iron Reotangular Grirders or Tubes. (Siffd.)
Sufportsd fU Both Ends. Loaded in Middle.
A d C
— - — == W. A representing area of section in sq. int., d dqpM in ifu., I lenglh be-
tween supports infui^ and W destructive weight in lbs.
iLLUsriuTioK.— What is the destructive weight of a rectangular girder, 35.75 ins.
ID depth by 34 in breadth, metal .75 inch thick, and length between supports 45 fbetr
Assume C or ooefBoient =: 37 00, as per cause (x8) in preoediog table, page 806,
imd area = 87.375 ins.
Then «y-37SX3S.75Xyoo^xx5S7528^ 68339 ^
45 45 ^ ^^y
W { I w
By experiment it was 257 080 lbs. By Inversion ^j-r = A, and -— ■= A
HoDGKiMBOM's formula would give a result of 259373 lbs., and Molmwobts'c
8lO ST&ENGTH OF MATBBIALS. — TBAKSVBBSBi
.. ^ XJiieq.ually ILioaded Beoxna, etc.
i" W
■ = to. 2 representing length between suppwtt, and m and n dixtancet from
points of support^ aU in like denominatum^ and W and w destructive and safe voeights^
also in like denomination.
To Coxnp^ute l^estruotive AVeiglit and A.rea of Sottozn
l>late.
AdC «♦ Wl ^ ^ Wwin . ,
— V ^ » Cd ~ * ^^ . = A. A r^^itenting area ofplaie in sq.
uu., d and I d^rih and length, m and n diskunees of load at other points than in
middlet aU infeet^ and W weight in lbs.
NoTB.~-^ufflcl6at metal staoald be provided in sides to resist tranBverse and
■hMuriog stress, and in: upper flange to resist crushing.
Illustration — What area of wrought iron is necessary in bottom plate of a rec-
tangular tubular girder, 3 fbet in depth, supported at both ends, and loaded in middle
with 130000 lbs. f
C, ascertoined tqr experiment for destructive stress, 180000 lbs. , and area 7. x sq. tns.
Z30000 X 30 .
—5 rr — = 7. 22 sq. ins.
180000X3 ' *
"Wroueh-t-iron Oylindrioal Seams or Tubes.
= W iLLusTRATioir.— What is destructive weight of a cylindrical ttib«,
19.4 in, in diameter, . 131 Inch in thickness, and 10 feet between its supports?
Area of metal s= 5.05 sq. ins., and G = 2856, as in the 19th case of table, page 806.
Then S-°SX.».4Xrf56^ 3 ^
10
^tAd' tS
D. K. GlaAk. ' J = ^> ^ representing diameter^ i thickness of metal, and
I length, aU in ins., S tensUe strength qfmetat per sq. inch, and W weight, both in lbs,
». « 3.14 X 1 2.4«X. 131X45000 2846x43 „
S = 45000 26<. ^ ' ^2 ^ ^^ — = ^-^— ^ = a37«7-9^
^' toXia xao ^' ' y
Molssworth'S formula gives a result of 23286.x lbs.
"WroTiglit^iroii Ejlliptioal Seaxns or Tubes.
A.d*C
— ^^TsVf. Illu8Tra.tiok.~ Assume diameter of tube 9.75 and 15 in&, metal
.X43 inch in thiokneflfl^ and distance between supports 10 feet
A =s 1^ 56 «9. im. 0 •= 3147, as per case (20) in preceding table, page 806.
ThOB 5-56X.5X3.47^»fe452J^^ a^
10 10
'J^K.Oi*AWL ''^^^ ^ — ' — £::W. b anddr^artsentingcoi/^vgaile ondtrmU'
verse diameter, I length between siwpportM, t thickness of meial, aU in ins., 8 tensile
strength of metal pmsq. inch, and W destructisie weight, both in lbs.
8 = 44«»».. '•57(9-75'+.5')X.M3X440°o^^^6^^^
^ 10 X 12 120
NoTK.~B. Baker, in his work on Strength of Beams, etc., I^ondon, 1870, page a6,
shows that ordinary method of computing transverse strength of a hollow shaft 1^
difference of diameter alone is erroneous, in consequence of Joes »f resistanoe to
flexure in a hollow beam.
Grirders aixcL Seaxn.8 of TJnsyxninetrical Section.
4Sd
2— . = W. Srepresmting tensile resistance of metal, and W destruUive weight,
both in lbs., d distance between centres of compression and extension, or crushina and
-taMOc resislances, in ins. , and I length between st^pmis, in feet.
NoTB.~To ascertain d, see Rale, page 8x9,
STBBNOTH OF MATBSIAL&. — TBANSVSBSS. 8lf
ILLU8TRATI027.— Dimensions of a rolled wrought- Iron girder, xi feei in lengUi li»
tween its supports, is as follows :
Top flange 2.5 X i inch. 1 Bottom flange 4X38 inch.
Web. 325 '* I Depth 7 ina
What is its destructive weight?
d = 5.23 ins S assumed at 45000 iba Then - — 45000 x 5- «« _ g^g ^^^
n X 12
Strength of Riveted Beams or Qirders, compared with Solid, is less, and deflec-
tion is greater
'WYouslit-lron. Ixiolined 3 earns, etc. ■
L W
-y. =10 ii and I representtng Ungtht or indvMlion^ and horixonUd /tne, in lihf
denominations^ and W and w dettruetive and safe toeights on horiamtcU line cmd ui*
dination^ also in like denominaUont.
JPlate Grirders.
A d C
-= W A rqnresenttng section in sq. tfu., d depth in int.^ aand I Umf^ te<
T .
^ tween supports in fiet.
iLLDSTRATioir What load will destroy a wrought- iron plate girder or beam of
following dimensions, 10 feet in length between its supiwrts?
Width of web 375 inch.
Deplhof web 23.5 in&
Depth of beam ..14.35 **
Top flange 4.5 X 375 inch
Bottom flange 4-5 X -375 "
Angle pieces a X-3i25'*
Area of Section = 13 <g. ins.
Aasame coefficient of 5180 as per case (14) in preceding Table, page 80&
Then ii2<i±fSil5;5»2525?5=95.j55„J6t
MoLBSwoRTH. r-j = 5- L rtpresenivng load equaUy distributed, and S stress on
o a
centre, both in tons, and d effective depth of girder in feet.
By actual ex{)erimeni L = 48 tons for 16.5 feet 1)etween supports; hence,
10: x6 51:48 79.2 fotu = 39.6 when supported in middle, and 14.25 ins. = X.1875./ML
Then ag^^io _ 396 _ ^g ^^iSch x 2240 = 03 363.3 Ua.
8x1.1875 9.5 •» yjJ :»
D. K. Clabk. _ifLjLiil55^ = W. d representing depth of girder or beam
.6 (
letM depth of lower flange in ins., a and a' areas of sections oj bottom flange and of
«oe6, ai its reputed depths both in sq. ins.^ and I length between supports inject
({=1425— .375=3x3.87517111 a S3, and a s 5 49. tut.
Then '3-875(4X3±j-x55_X5) ^ £4^ ^ ^, ,^5 ^hj^h X 2240 = 9ao75.« ibi.
.6 X xo o
Mr Clark assumes, however, that for girders of like ooastruction the destructive
should be taken at two thirds of that deduced by the formula.
IOwden or Beams without Upper and Lower Flanges.
ILU78TRATI0H. — Assume angles 2.125 X 28 above, 2.125 x 3 below, web
.25, depth 7 Ins., and length between supports 7 feet
Area of section = 6.35 sq. in«., and C z=. 3840, as per case (15) In preceding TaUe^
page 806.
Then?-3SX7X384o^»72688^
7 7
•^ + .a5a'Xs<l
Approximate. ^ 1 = W* a representing area of sections ofupptt
mnd lower angles, a' area of section of web for toted depth, both in sq. ins.,d dq^ <^
^rder in in$.,and W load or stress in lbs.
8l2 STRENGTH OF MATBKIALS. — TBANBYEBfiS.
« = 4.6 »q. int,^ and a'= 7 x -95 = 1.75 «g. tni.
Tlien -^ ^ =51:--:= 13.687, which x 2340= 30658.8 Ibt.
7 7
mON AND 8TBBL RATLa.
Symznetrical Seotiou.
To Compute Transverse Streujetli. {D. K, CUurk.)
•nd 7 — ^ ^ = S. ^repruenHngtim
HU itrenglh in lbs. or torn per sq. tndk, a area o/one head or flange exdusive 0/ cen-
tred portion eomporing loeb, in sq. ins.^ cC depth or distance between centres of heads,
d depth of rcUl, t thicleneu of ioe5, 1 distance between supports^ all in ins.^ ani W
weight in lbs. or tons, alike to S.
Illustration l— What is destructive weight of a wrought-iron double-headed
rail, 5.4 ios. deep, having a web of .8 Ids., an area of head of i.o sq. in&, distance
between centres of its heads 4.3 in&, and between its supports 5 feet?
S assumed at 50000 lbs.
Then
50000 f 4 X J.9 X ^^ + »• 155 X .8 X 5-4')
_ 50000 X (24.8a -f- 36.93)
5X12 ~ 60 "
43i25aa
3.— What is destructive weight of a Bessemer steel double-headed rail, 5.4 ioa
deep, having a web of .75 inch, an area of head of 2 sq. ina, and distance between
beads 4.3 ins. ?
S assumed at 80000 lbs.
80000 (4 X 2 X ^+ 1.155 X .75 X 54') 8o««v«*«
Then !^^ ^ / ^80 ooox 51.39^^3 ^^^
5X12 60
NoTB.— Tnuuvenc •tnofcth of BewtiMr Baili lacreMct rery generally, in direct proportion witk
IIm proportion of Carbon in it.
XJusytnmetrioRl Section.
' = W. d" representing vertical distance betvueen centres of tension
w ft
and compression, h height of neutral axis above base of section, and I length between
supports, all in ins., and A. sum of products, obtained 09 multiplying areas of strips
of reduced section under tensile Hreu, by their mean distances, ra^ectivebf, that ii,
Uu distanott of their centres of gravity, fi-om the neutral axis, in ins.
Bovrstring Grirder.
To Compute Diameter of a V^roiiglit-iron Tie-rod of an
A-rohed. or BoA^strine d-irder of Cast Iron.
/ r = <t W representing weight distributed over heam in lbs., I length
V45ooXfc -r »
between piers or tupporte in feet, and h height between centre of area ofseetian qf
girder and centre of rod in ins.
Illustration. —Required diameter of tie-rod for an arched girder, 25 feet be-
tween its piers, and 30 ins. between centres of its area and of rod, to safely support
a uniformly distributed load of 25 000 lbs. f
/25000X25 7625 000 . ^
- /— ~ — - = , /— ^ = V4-62 = a. IS »fW.
V 45<»X30 V 135000 ^' ^
If two rods aw used Then */— = i- 5? »nf 5= diameter of each rod.
STBENGTU OF MATBSl^ALS. — XJE(ANSV£BS£. SlJ
CAST IBON»
Transverse Strenstli of* GMrdera axid Seama.
{ptimxdfrum EajperimieniU pf BarUno, Hodgkinton, Hvghett Bramah, Cubitt,
Tredgoldy and o^r*.)
Bediueed to a Vnififrm Meature of One Foot in Length.
Supported ai Both Endi. Strest or Weight tqtpUed in Middle.
DMtracttT« W«i|sht
Difttane*.
SSCXIOH*
1 1
+
D
J.
T
±
T
X
H
I
±
FIjuikm.
Int.
4 X2
1.52 X .78
i-S X .5
i-S X .5
1-5 X .5
«S X .5
1-53 Xx
2 X .51
_
W»b.
Im.
I
z
3
z
z
Z.56
•5
•5
.5
•5
•5
«t
aaSX .53
23-9 X3-I2
Z.76X .4
z.7^X .26
1.78 X .55
X-07X .3
2.1 X -57
«-54X .32
6.5 X .5t
2.5 X 1.5
3-75X1.4
{:
3
425
3.29
.29
} -3
.32
•34
I.2S
Depth.
Ink
Z
z
3
3
4
4.07
3
3
4
3.04
a.oa
2.52
2.83
5x3
36.1
5*3
5-13
5- 13
5«3
8.18
Fe«(. Im.
I
4 6
13 6
4 6
5
4 6
3 «
3 «
3 I
3 «
4
4
5
4 6
20
4 6
4 6
4 6
4 6
iz
ArM.
Sq.Iu.
I
I
9
3
4
Z2
2.35
2
a
2.6
t.59
4.98
4
2.28
183-5
2.82
2.87
3.02
5.4X
15
FwDto-
taact.
Lb>.
2240
500
5080
5100
Z0300
6720
6666
5208
4536
7104
33"
4004
2569
4x43
2988
9503
403 3x«
6678
7368
8270
2ZCXI9
3S62d*
ofOneFooilAtf
Lbt. i
a 240 2240
2250 j 2250
63 580 I 2540
2550
2896
700
3x36
2676
233X
5475
2553
30x9
X963
1650
X320
3656
1220
2077
2250
2402
3406
3x93
22950
463^0
33600
30 coo
X6I45
14 062
22420
10267
x6oi6
X0276
207x5
Z4940
42763
8066240
30512
33200
372x5
94540
39« 853
A<2G
* Stirling Iron.
Hence, ^=y^ = W. A rq»retenting area of section, d dqpih in int. , { length infset,
and W detlruetive weight in lbs.
NoTB. — When lengths are less than those instanced, breaking weight will be in-
Ij in consequence of increased stability of girder.
8 14 STKENGTH OP MATERIALS. — tBANSVERSE.
To Compute Transverse Streiigtli or Destrtiotive Stress
of Cast-iron. See^ns or GhircLers, of* various BH^nres.
Supported at Both Bnds. Weight applied in Middle.
When Section of Beam or Girder is alike to any of Examples given in
preceding Table. Rule i.* — Divide product of area of section and deptb
in ins., and Qt^^dent for girder, etc., from preceding Table, by length be-
tween supports in feet, and quotient will give breaking weight in lbs.
' ExAMPLK.— Dimensions of a beam, having top and bottom flanges in proportion
of I to 6, give an area of section of 25.6 sq. ins., a depth of 15.5 ins., and a length
between its supports of 18 feet; what is its destructive weight?
NoTK.— In consequence of increased area of metal over case No. ax ia Table, Coef-
ficient of 3402 is reduced to 330a
- Dimensions.— Top flange, 3 x .75 ins. ; bottom, 18 X -75 0= 13.5 sq. ins. ; web,
15.5 X .7 a' = io.8 sq. ins. , and d' = 15.5 — .75= 14.75 ins.
j^^^ 25-6 X 15.5X3300 ^ i30|440 ^ ^^ ^^g g ^
10 18
D. K. Clark. — — — r^^i — -' = W. a representing area of bottom flange, a'
oftoeb at depth d* of beam, less depth of bottom fUmge in sq. ins., I length between
supports inject, and W destructive weight in tofu.
Then ^ ^^ ^^ ^ ^ ^^ = — — ~ = 31.71, which X 2240 = 71 030.4 lbs.
Hodgkinsom's formula would give a result of 53491.2 lbs., and Molbsworth's
54248.3 »«.
Rule 2. — From product of breadth and square of depth in ins. of rec-
tangular solid, the dimensions of which are the depth and greatest breadth of
btam in its centre, subtract product of breadths and square of deptlis of
that part of the beam which is required to make it a rectangular solid, and
then determine its resistance by rule for the particular case as to its being
supported or fixed, etc.
This rule is applicable only in case referred to, vie., when area of section is great
compared With area of extnyne dimensions.
Mr. Baker, in case of a hollow cylindrical shaft, where thickness of metal is but
one eighth of extreme diameter, computes result at but .4 of that of a solid beam.
This is in consequence of resistance to flexure in hollow beam being more than
proportionally greater than in solid.
Example.— Take 7th case Arom preceding Table, page 813, for length of one foot
Coefficient for cold-blast iron = 500.
Then 1.53 X 4.07"— x. 52 X a. 51 « X 4 X 500 = (aS- 17 — 9.58) X 2000 = 31 i8o lbs.
Result as by experiment, 30000 lbs.
NoTB L — These rules are applicable to all cases where flange of beam is as shown
in Table, and beam rests upon two supports, or contrariwise, as to position of flange,
when beam is fixed at one end only.
a. — When case under consideration is alike in its general character to one in
Table, but differs in some one or more points, an increase or decrease of metal is ob-
tained by an increase or reduction of the Coefficient, according as the diflferences may
affect resistance of beam.
^— The Co^cients here given are based altogether upon experiments with Eng-
lish iron.
• Utility of thMC roles in preferenr« to thoM of Hodgkincon, Fairbairu, Tr»dfco)d, Hugbw, nnd
Barlow is manifest, as in one case the Co«ffiHent of th« metal is considered, and in the other cases the
metal Is assumed to be of a nniform Tshie or strength.
Onlj Tsriable element not embraced in this rule is that consequent upon any pecollality of fora of
MeUoB ; as, for Insiaaee, in that of a Hodgkinson, or like beam, where area of one flange ip-eatly as-
eeeds the rest ef section, and this flanf^e is other than below, when beam rests upon two supports or is
fixed at both ends, or than above, when beam is fixed at onu or both ends.
This deficiency is met to som^ extent by the three cases in table, where proportion of flangw aro i to
•f X to 3, and r to 6.5.
i For thick castings put 7, and pat Co^feunt same as tensile strength of metal in tons par aq. ineh.
STSSNGTH OF MATERIALS. — TSAKSVBBSB. gl5
9*l*zi«ed Hollow or A^nnnlaf Beams of Symnaet'lo^l
Beotions. {D. K.€la»'k.)
When Depth is Great Ocmpared with Thickness of Flanges,-^¥igs. i, 2, and 3.
X. 2. 3' <txS(4aH-ii55aT^^y a representing area o/ane
II I^I flange, a' area of web or ribs, both in sq. ins., d depth of
I II beam,ltssd^of<meflange,anAldistWMebett»eein9up'
I^B LmJI pvrts, both in ins.y S tensile strength of metai, and W
weight between supports, both in lbs.
When Depth of Flanges ia Great Compared with Depth of Beam,—¥lgs»
4 and 5.
4- 5-
II
d'»
S(4a-^ + i.i55<(l«)
- — J = W. a representing area of one flange less
thickness qfweb, in ag. ins., t thickness of web, d' reputed depth or
distance between centres of flanges, and d deptfi of beam, all in ins.
When Section of Circular or Elliptic Beam is Small Compared with Diam-
eter,— Figs. 6, 7, and 8.
O"'^" o '0
I
-=w.
b and d representing mean breadth and d^pth.
Illustration i.— Assume Figs, i, 2, and 3, 20 ins. In depth, width of flanges on
top and bottom ribs 5 ins., thickness of flanges and webs i inch, and of sides of
Fig. 3 .5 inch; length between supports 10 feet, and S 20000 lbs. ; what would be
breaking weight of each ?
-. 20-1 X 20000 (4X54-»'55X 18) ^ 38oo?M20 + 2?iZ?) = „9 168.4 »*•
10 X 12 '**
2.— Assume Flga 4 and 5, 6 ms. in depth, area of flanges 3 Ins., widths of webs i
inch, and length and S as in preceding case.
^2
10 X 12 '2°
^-Assume Fig. 6 10 ins. in diameter, Fig. 7, 7. 5 ^ns. in depth and 12 ins. in width,
and Fig 8, 12 ins in depth and 7.5 ina in width, and thickness of all metal x inch.
Then Fiir 6 3MX lo'X « X 20000^6280000^ ^^^^^^^ ,j,^ ^hich is .4 of
inen, rig. D 10X12 "o
that of solid cylinder.
dS? to difference between it and section of beam under computation, will be suf-
flcientiy accurate. See Illustration, page 814.
If greater accuracy is required, see page 810, or D. K. Clark's Manual, pp. 5i3-»7-
N<yrB.— To compute loaatton of neutral axis of beams of unsymmetrlcal section,
te« also D. K. Clark, pp. 5i4'«S-
5Sk?P ti'SSilliVm^rlyoSrSJhtb TdU^^Sr. H. -r». tU .tr.«g»h « low « .4 «/
that ofMUd cjlindw, ia oopm^imbm of k>M «f rMteUaeo to flozura.
8l6 STBSN6TH OP MA7BSIAL8. — TBAKSYBBSB.
Oeneral fnorznnlas for X^estnioti-ve MTeli^lxt of Soli4
JBeama of S3rxx&zxieti.-ioal Section.
Supported at Both Ends. WeigM applied in Middle,
Une ofNeutrca Axis runs through centre of gravity of section.
aodrS «. . / W „ ,
J = W, and ^^^^ = S. In square beams for ad pat dK a and d ftp
resenting area and depth of section, r radius of gyration {hal/daOh o/tea» = il
I length of beam between iU supporU in ins., W destrueUve weight in tons or lbs.,
and S tensile strength of material m Wee tons or Vbs. per sq. inch.
Illustration.— Assume dimensions of cast-iron beams, Figs, x, a, 3, 4, and 5 as
Ibllows, via. : t and 2, 5 x 5 *&& ; 3i a-S X 10; 4, 5.64 diameter; and 5, 7.25 x a-'sq,
or equal areas; distance between sapporU 60 ina. and tensile strenffth of iron =
26 000 Iba
♦ *■ 'm ^9
Areu of each 25 sq. ina Radius of gyration, No. i, .5775; a, .4083; 3, .5775; 4,
_ a X 25 X 10 X -5775 X 26000 ^
«• ^ ' = 125 las tbi.
, •Xa5X707*X.4o83Xa6ooo ^ „
■• ~ 6r =62545 »fc
_ •X5*tX.5775X 26000 . ^^
3* ^ — =Oa56aat.
4. For formula for square beams substitute "^^ = W
Then m »S X 564 X 26000 -854 hd'Q
"*•"*• g^ =oiioo»».; andfi>r5. / a^*^** ^W.
•7854 X 4-39 X 7.25* X 26000
6i = 78 53a »«.
• SSf/^r°*°^*'r f ^^?} ®^"** ^ * transverse strength tor Cast iron of 550 fbf
a tensile strength of 26000 Iba, and of Wrought iron of 600 Iba for a like str^
of 50000 Iba (as per table, page 788).
O a ^ jk. +
4C bd^
— J — = W. 0 representing coefficient of strength of metal in lbs., b and A
breadth and dtpth in ins. , I length in feet, and W destructive weight in tons.
^ — R — 4-7 = 6a'. ^ondr representing external and internal raditu.
7- 5 = 6d« h' and dT representing interior breadlh and depth,
tt «f 2
a .38R3 = 6d2 5. ~ = ^' ^ representing d^th or height.
'5^ ^.<'! + » 6'tf'* = W. b and d representing breadth and death ofe^bvt <m/I
vesical rib, and b' and d' breadth and ^^^^hSrS^rx^!tJSSal to (SS^ rii
Values of C 550 for a tensile strength of Caa Iron of 26000 Iba. ner an innh o»<f
^for ^ike strength of Wrought Iron of sooo^ba, and>o^ ^' ^^ '^
• Dlagoosl oraqom. t In aaqM. tom ^a.xA
STBEN6TH OP MATERIALS* — TBANSVEBSB. 817
Flaxxsed Beams of* XJnssrxxxnaetrioal Beotion* (Z>. K. Clark.)
"Ezj 35 o c^^
^-^ = W. S repramiing total tentiU strength of KCtion in U». per sq. inch, d
nertieal duitanoe between centres of tension and compression in ins., I length in ins.,
' and W weight in lbs.
iLLFSTRjiTioN. — If the aectional area of a beam of cast iron is 5.9 sq. ins., the
depth or distance between centres of tension and compression 5.6 in&, distance be-
tween 8U)>port8 5.5 feet, and tensile strength of metal 30000 lbs. per sq. inch.
Then 4 X 5-9 X 30000 X 5-6 ^ 3.964 800 ^ ^^
5-5 X 12 66
STEEL.
Xo Compute Q^raiiaverse StrengtH of Steel Bars.
Supported at Both Ends. Weight applied in Middle.
i.iSS S bd'
— i-T = W. S representing tensile strength in Ibs.^ I length between support*
in ins. J and W weight in lbs.
Illustration.— What is ultimate destrnctive stress of a bar of Cracible steel,
9 I0& square, and 3 feet between supports? 8=190000 IbB.
TK«« I- 155X90000X2* 831600
Then 1- = . = 34 650 Ibt,
2 X 12 24
To Compute Seotioix of* Louver Flange of* a Q-irder or
Cylindrical Shaft of Cast Iron to Sustain a Safe Load
in its lifiddle. (Baker.)
/ d W
—3^— = M. I representing distance between supports in feet, d d^th of girder, etc. ,
in ins., W xoHght in tons, C coefficient, and M moment of weight around support.
iLLrSTRATioN.— What should be section of a girder, 12 ins deep, to sustain a safe
load of 10 tons in its middle, between supports 16 feet apart?
Stress assumed 2 tons per sq. inch, and Factor of safety 4. — =480= M.
4
And -T— = = 0. S representing stress assumed in tons, and a area of section of
flange in sq. ins. _. 480
* Then — =z2osq.%ns.
12X2
IT'or R,ectang;ular, I>iagonal« or Circixlar Beam or Sliaft.
♦
10.8 ^^ 8.4
Gheneral Formulas fbr Computation of* Destructive
^Veiglit of* a Beam or a-irder of* any form of* Cross
Section and of* any IVlaterial. (B. Baker,)
Load applied at Middle.
S M (i + QO
~^ = W. S representing tensile strength of material per sq. inch in tons,
If moment of resistance of section sc product of elective depth of girder or beam, and
effective area of flange portion of section, in sq. tns.,Q resistance due to flexure, I dis-
tance between supports in feet, and Q' = Q x thickness of web of section, both in ins.
Average Values of Sfor Various MaterialB.
torn.
CMt Iron 7
V^roogbt Iron • • ai
Total.
Steel 40 to 50
Pi»tes 35
3Z
ti
Tom.
Oak .'9.5104.5
Pine a "3.5
8l8 STRENGTH OF MATERIALS. — TBANSYEBSB.
Svbstituting Values of S and Q in a General Equation.
Sacnoir.
CMt Iron.
Wrought
Iron.
Steel.
Oak.
Pfa*.
■
W=.875-^
d«6
=1.75 —
=3 to 5 -j-
d«6
=.1410.25-^
= .II tO.2— =—
♦
W==.75-j-
(23
=2.635104.25 —
d'
=.1 t0.l6-r-
— .08 to. 14 —
•
<Z3
W=.562Sy
=X.I25 ^
_2t0 3.25y
— .08 to, 14 —
=:.o6tO.II —
d representing depth of a rectangular bar^ tide of a square, or diameter of a rounds
b breadth of a vertietU bar, all in ins., and I distance between supports in feet
DMoment of Resistance.
Moment of Resistance of a cross section is the static force resisting an ex-
ternal force of tension or compression, and it is equal to moment of Inertia,
divided by distance of centre of effect of the area of fibres which are respec-
tively^the most extended or compressed from the neufnU axis of the section.
Xo Coxupnte ACoxuent of ftesistaiioe.
-T = M. I representing moment of inertia, and d distance of centre oj effect of
area offJbres of extension or compression.
Work of fiesistanoe.
Under a Quiescent Load. — Intensity of Elastic resistance increases uni-
formly with total space through which action of stress operates ; hence, it
may be defined by a triangular section.
Consequently, . 5 s L = R. s representing spa^e passed through, L load, and R re-
sistance.
To Compute Adoment of fiesistance.
— ^- and —r- = R Q a coefficient = one siaUk of destructive weighty I moment
of inertia, h height of neutral axis from base of section, R moTnent of resistance, and
M modulus of rupture.
Note.— Neutral axis, for all practical purposes, is at centre of gravity of anp
section.
For Radius of GyrcUion, see Centre of Gyration, page 609.
For other rule for computation of Moment of Resistance, see Strength of Beama^
B. Baker, London, 1870.
M!oxiaent of* Inertia.
Moment of Tnertia is resistance of a beam to bending, and moment of any
transverse section is equal to sum of products of each particle of its area into
square of their distance from neutral axis of section.
, A B Illustration.— If transverse section of a beam. A B C D, Fig. i, is
8 X 20 ins., its neutral axis will be at middle of its depth, o r; divide
A B, o r, into any number of equal spaces, as shown, then each s|iace
will be 2 X 2r7=4 sq. ins., and the distances of the centre of each
square ftova neutral axis will be as follows "
•
•
.
•
•
•
•
•
•
.
•
•
•
•
•
•
I, I.
2,2.
3. 3-
2X2X4X1*= i6
2X2X4X3^=144
2X2X4X5' = 40o
4,4. 2X2X4X7'= 784
5, 5- 2 X 2 X 4 X 9'= 1296
2640 X 2 for low>
p er half = 5280 = moment.
Note.— If the area of the figure in illustration had been more minutely divided,
the result 'Would have ^proximated more nearly to the above result.
For Moment of Inertia of a Revolving Body, see Centre of Gyration, page 609.
STfiSNGTH OP MATfiBIALS. — THANSVBRSE. "819
To Compute AComent of Ixxeirtia of a Solid Seaxxi.— iri^. 9.
2.^ bd*
12
= M.
IU.U8T&ATI0N.— Take elements of preceding case.
Then
8X20S 64000
12
12
= 5333-33 moment.
Or, . 3 f > n» fr = M. t representing breadth of vertical divinonSy n number ofhori-
tontal divisiom from plane o/netUrut axis, b IrreatUk^ and d dqtUi o/beam.
iLLUSTRATioy.— Take elements of preceding case.
« = 2, n = 5, and fc = 8.
Then .3Xa»X5'X8 = 2400 X 2 for lower half=. 4800 = moment
5- Beams of Various Figures. — Figs. 3, 4, 5.
t ■ 6(j3_6'd'» ^ 6rf3 — 26'd'» „
k!.»ft'» 1 ■>**> 3- -7Z » 4 and 5. = M
*
r
.12 12
_ b' and d' representing respectively breadth less
V </t»dlme«« ofweby and depth less Viickness of flanges.
^
.7854 r4 = M.
•
.7854C<3=pM.
6d3
•e-*-*
' !!-=«■
o
.7854(r*— r'*) = M.
♦
12
♦•r#
.iir« = M.
r representing radius^ t transverse and c conjugate diameters, and s side.
To Compute Common Centre of G^ravity and. Vertical
Distance 'bet'>v-een Centres of Crusliine; and 1?enaile
Stress of a G-irder or 3eam.
Rule. — Multiply surface of section of each part or Hp^xre composing
whole, by distance oi its centre from centre of one of tho two extreme parts
or figures, as • ; divide sum of their products by sum of surfaces of sec-
tion, and result will give distance of common centre of gravity from centres
of each extreme part or figure. ~
EzAMPLB.— Take annexed figure.
2-5 X 1X0 =^2.5 Xo = .0
■h.»
8
Above
•335 X
(^ + jj = .335 X 3-3' = '076
38 X4X (-|--}-5 62 + ^) = i.52 X 6.31 =9.591
4.34s 10.667
Dividing 10.667 ^7 4-34S = 2.455 = <li«tonc« qf common cemtrefrom centre of upper
part.
X.52 Xo =1.52 Xo = .0
BeUno •
325 X 5.62 X (^ + ^) =1-826x3 = 5.478
a.5 X f~-|-5.6a + '-|-]=a.5 X6.31si5.775
5.846 21.253
Dividing 21.225 by 5.8465=3.631 =s distance of common centre from centre ofUnoer
part
HeDc«, 3.631 + ^ = 3.821 = distance of common centre from bottom^ and. 3.631 -f
2
1.65a s 6.983 3s distance between centres qfgrcnoitjf.
820 STB£KGTH of MATSBIAL8. — TBAJTSVBBSJi.
8.
h^
r*
I
To Cozxipixte TO'entral A.xis of*a Seaxxi of XJn-s^rmzxietrioal
Bectioxx.— Figs. 3, -^^ a, 6, r^ 8, and. &. (Z>. iC. CterA;.)
Operation. — Divide section as reduced into its simple elements, and
assume a datum-line from which moments of elements are to be computed.
Multiply area of each element by distance of its own centre of gravity from
datum-line, to ascertain its moment. Divide sum of these moments by to-
tal reduced area ; and quotient is distance of centre of gravity of redbiced
section, or of neutral axis of whole section, from datum-lue.
Illustration.— Ftg. 8 annexed is la in& deep, i2 ins. wide, and i inch thick.
Extend web, c d, to the lower surface at d* and d", leaving 5.5 in&
of web, a d' and d" 6, on each side. Reduce this width in the ratio
of 1.73 to I, or to (s-s-r- i.73=r) 3.2 ins., and set oflf d' a' and d" b*
each equal to 3. 2 ins. Then reduced flange, a' 6', is (3. 2 X 2 = 6. 4 4-
I =) 7.4 ins. wide, and reduced section consists of two rectangles,
a' b' and c d. Assume any datum-line, as «/, at upper end of sec-
tioD, and bisect deptlis of rectangles, or take intersections of their
diagonals at g and o, for their centres of gravity. Distances of Uieee
^_ 1 from datum-line are 5.5 and 11.5 ins. respectively, and areas of the
9,'d,'d*hf b rectangles are xi X x = zi sq. ina, and 7.4 x z =7.4 sq. in&
Then, <;d=:ii x 5.5= 60.5
a'y= 7.4Xii-5=« ^5-1
x8.4 x45.6rr7.91 inf.
Showing that centre of gravity of reduced section, being neutral axis of wbola
section, is 7.91 ins. below upper edge, in line ii. Centre of gravity of entire section
at • , it may be added, is 8.65 ins. below upper edge, or .74 inch lower than that of
reduced section.
Neutral axes of other sections, Figs. 3 to 7, found by same process, are marked on
the figures. Section of a flange rail. No. 7, which is very various in breadth, may be
treated in two ways; either by preparatorily averaging projections of head and
flange into rectangular forms, or, by taking it as it is, and dividing ii into a con-
siderable number of strips parallel to base, for each of which the moment, with re-
spect to assumed datum-line, is to be ascertained. First mode of treatment is ap-
proximate; second is more nearly exact
To Coznpvite Ultimate Stren^li of Hoxnogren.oo'as Beams
of XJnsy-xnixietrioal Seotion. '
Operation. — Resuming section, Fig. 9, for which neutral axis has been
ascertained,
To Comptde Tentile Resistance,
Divide portion below neutral axis t t, Fig. 9, with reduced width of
flange, a' b\ into parallel strips, say .5 inch deep, as shown,
and multiply area of each etrip by its mefin distance from
neutral axis for proportional quantity of resistance at
strip. Divide sum of products, amounting in this case
to 31.3, by extreme depth below neutral axis =4.09 ins.,
„ and multiply quotient by 1.73 S (ultimate tensile resist-
y I I ance at lower surface). The final product is total tensile
w V resistance of section ; or,
31-3X1.73 _ g ^^ tcnsiOt retittance.
4.09
S rqtresentif^ tdtimate temiU strength of material per sq. inch.
Again, multiply area of each strip by square of its mean distance from neu-
tral axis, and divide sum of these new products, amounting to 104.6^ by
sum of first products. The quotient is distance of resultant centre of tensiie
stress, <f , from neutral axis. Or, resultant centre is,
= 3.34 ins. below neutral oasis,
31-3
This process is that of ascertaining centre of gravity of all the tensile re6isv*nc6A
— t
d'
BTBENGTH OF MATSfilALS* — T&ANBY£BS£.
821
By a slmilAr process for upper portion in compression, sum of first products is
Ascertained to be same as for lower portion = 31.3.
But maximam compressive stress at upper portion is greater than maximum
tensile stress at lower portion, in ratio of tbeir distances firom neutral axis, or as
1.73 8x^^ = 3-34 S, and ^^ — ^^ — = 13.24 S total compressive resistance,
which is same as total tensile resistance, in conformity with general law of equal-
ity of tensile and compressive stress in a section.
Sum of products of areas of stress, divided by squares of their distances irespec-
tively from neutral axis, is 164.9, ^^^ resultant centre c, Fig. 9, Is ^^-^ = 5.27
31-3
int. above neutrai axis.
8am of distances of centres of stress or of resistance ft-om neutral axis, 3.34 4-
5.27 ::= 8.61 in*. =: distance apart of these centres as represented by central line, c' d .
Abbretfiated Computation.— -Ab upper part of section is a rectangle, its resultant
centre = | of height, or 7.91 X # = 5.37 ins. above neutral axia Average resist-
ance is half maximum stress, viz., that at upper portion, which is 3.34 S per sq.
inch.
Area of rectangle therefore =: 7.91 x i = 7.91 sq. ins., and 7-9' X334 _. j^^^^ g
2
compreuive resistance, as before determined.
Uomentof tensile resistance = 13.21 X 8.61 ins.= 113.76 S,also = — , or ^-t— =»
4 '
W. S representing total resistance of section in lbs., d vertical distance apart of
centres of tension and compression^ arid I length between supports, all in ins.
Strength of Beam Inverted. — When inverted, maximum tensional resistance of
beam at its lower surface c. Fig. 8, is 1.73 S.
Area of rectangle i i 0=7.91 sq. Ins., and ^-^ — LZL- -i 6.79 S totai tensile re-
sistance, or about one half of beam in its normal position.
Non.— For other rule for eompatation of caotre of gravity, see Strength of Beanu, etc. B. Baker,
I^ndoB, xS/a
Ooxnparative Qualities of* "Various ^letals.
IdnAM.
! Least. . . .
Greatest.
Mean. . . .
Wrought Iron ^ ^'^^^
Cast Steel.
BroiMse . . •
Greatest.
liOast. . . .
Greatest.
L<ea8t. • • •
Greatest.
Doniity.
6.9
7-4
7.225
7.704
7.858
7.729
8.953
7.978
8-953
Comprei
■Ion.
Sq. Ids.
84529
174 120
144^x6
40000
127 720
198944
391 985
TentiU.
Major Wade.
Tentil*
to Com-
preuioD
Hftrd.
ness.
4-57
S94
ITaotors of* Safet^^.
Girders^ Beams, etc., of cast iron should not be subjected to a greater stress
Ihan one sixth of their destructive weight, and they should not be subjected
to an impulsive stress greater than one eighth.
The following are submitted by English Board of Trade, Commission-
ers, etc
SniUOTDBB.
Cast Iron.
Girders... ..<•..
Colamna
tanks.. .
Macblaery......
Stms.
Dead
t«
<i
Live
Shock
Factor.
3 t06
4
8
10
Stkccturb.
Wrought Iron.
Girders
Bridges. ....
Stsel.
Brtdgea....
stress.
Dead
Live
Mixed
Mixed
Factor.
822 8T&£N6TH OF liATBAIALS. — TSANSVBBSE.
Grirders, Beams, Xjintels, eto.
Transverse or Lateral Strength of any Girder^ Beam, Breast-summer^
Lintel, etc., is in proportion to product of its. breadth and square of its
depth, and area of its cross-section.
Best form of section for Cast-iron girders or beams, etc, is deduced
from experiments of Mr. E. Hodgkinson, and such as have this forpi of
section T are known as Hodgkinson^s.
Rule deduced from his experiments directs, that area of bottom Jktnge
shmdd he 6 times that of top flange — flanges connected i>y a thin ver-
tical web, sufficiently rigid, however, to give the requisite lateral stiff-
ness, tapering both upward and downward from the neutral axis ; and
in order to set aside risk of an imperfect casting, by any great dispro-
portion between web and flanges, it should be tapered so as to connect
with them, with a thickness corresponding to that of flange.
As both Cast and Wrought iron resist compression or crushing with a
greater force than extension, it follows that the flange of a girder or beam
of either of these metals, which is sutnected to a crushing strain, according
as the girder or beam is suppoHed at both ends, orflxed at one end, should be
of less area than the other flange, 'which is subjected to extension or a ten-
sile stress.
When girders are subjected to impulses, and sustain vibrating loads, as in
bridges, etc., best proportion between top and bottom flange is as i to 4 ; as
a general rule, they should be as narrow and deep as practicable, and should
never be deflected to more than .002 of their length.
In Public Halls, Churches, and Buildings where weight of people alone
are to be provided for, an estimate of 175 lbs. per sq. foot of floor surface
is suflicient to provide for w^eight of flooring and load upon it. In comput-
ing other weight to be, provided for it should be that which may at any time
bear upon any portion of their floors ; usual allowance, however, is for a
weight of 280 lbs. per sq. foot of floor surface for stores and factories.
In all uses, such as in buildings and bridges, where the structure is ex-
posed to sudden impulses, the load or stress to be sustained should not ex-
ceed from .2 to .16 of breaking weight of material employed; but when load
is uniform or stress quiescent, it may be increased to .3 and .25 of breaking
weight.
An open-web girder or. beam, etc., is to be estimated in its resistance on
the same principle as if it had a solid web. In cast metals, allowance is to
be made ror loss of strength due to unequal contraction in cooling of web
and flanges.-
In Cast Iron, the mean resistances to Crushing and Extension are, for
American as 4.55 to i, and for English as 5.6 to 7 to i ; and in Wrought Iron
are, for American as 1.5 to i, and for English as 1.3 to i ; hence the mass of
metal below neutral axis will be greatest in these proportions when stress is
intermediate between ends or supports of girders, etc.
Wooden Girders or Beains, when sawed in two or more pieces, and slips
are set between them, and whole bolted together, are made stiffer hj the
operation, and are rendered less liable to decay.
Girders cast with a face up are stronger than when cast on a side, in the
proportion of i to ,96, and they are strongest also when cast with bottom
flange up.
Most economical construction of a Girder or Beam, with reference to at-
taining greatest strength with least material, is as follows: The outline of
8TSSNOTH OF MATBBIALS. — TBANSVBBSB. 823
tapi bottom, and sides should be a curve of vaiioos fbrmsv according as
breadth or depth throughout is equal, and as girder or beam is loaded only
at one end, or in middle, or uniformly throughout
Breaking Weights of Similar Beams are to each other as Squares ofiheis
Uke Linear Dimensions,
By Board of Trade regulations in England, iron may be strained to 5 tons
per sq. inch in tension and compression, and by regulation of the Pouts et
Chaussdes, France, 3.81 tons.
Bivets .75 and x inch in diameter, and set 3 ins. from centre in top ol
girder, and 4 ins. at bottom.
Character of fracture, as to whether it is crystalline or fibrous, depends
upon character of blows ; thus, sharp blows wUl render it crystalline, and
slow will not disturb its fibrous structure.
For spans exceeding 40 feet^ wrought iron ia held to be preferable to
cast iron.
Biveting, when well executed, is not liable to be affected by impact or
velocity of load.
A Coupled Girder or Beam is one composed of two, fastened together, and
set one over the other.
n?rujssecl Seazns or G^irders.
Wrought and Cast Iron possess diflTerent powers of resistance to tcDsion and com-
pression; and wlien a beam is so constructed that these two materials act in uni-
son with each other at ttress du« to load required to be ttome, their combination will
effect an essential economy of material, tn consequence of the difficulty of ac^ust-
fbg a tension- rod to the stress required to be borne, it is held to be impracticable to
conetruct a perfect truss l>eam.
Fairbalm declares that it is better for tension of truss rod to be low than high,
whtob position is fblly supported by fbUowing elements of the two metals *
Wrought Iron has great tensile strength, and, having great ductility, it undergoes
much elongation when acted upon by a tensile force. On the contrary, Cast Iron
has gre«t rnrehing strength, and, having but little ductility, it undergoes but little
elongation when acted upon by a tensile stress; and, when these metals are re
leas^ (Vom the action of a high tensile stress, the set of one differs widely fYt)m
that of the other, that of wrooghi iron being the greatest.
Under same increase of temperature, expansion of brought is considerably great-
er than (bftt of cast iron; x.8i* tons per sq. inch is required to produce in wrought
iron same extension as in cast iron by i ton.
FairlNlim, in his experiments upon Englirii metals, deduced that within limits
of stress of 13440 lbs. per sq. inch for cast iron, and 30340 lbs. per sq. inch for
wrought iron, tensile foroe applied to wrought iron must be 2.25 times tensile force
applied to cast iron, to produce equal elongations.
Relative tensile strengths of oast amd wrought iron being as i to x.35, and theii
resistance lo extension as x to 2.95, therefore, where no initial tension is applied to
a truss-rod, cast iron most be ruptured before wrought iron is sensibly extended.
Resistance of cast iron in a trussed beam or girder Is not wholly that of tensils
strength, but it is a combination of both tensile and crushing strength^ cm* a trans-
verse strength ; hence, in estimating resistance of a trussed beam or girder, trans-
verse strength of it is to be used in connection with tensile strength of truss.
Meaui transverse strength of a cast- iron bar, one inch square and one foot in
length, supported at both ends, stress applied in the middle, vnthoul set, is aboui
900 Iba ; and as mean tensile strength of wrought iron, also udthout set^ is about
20000 1d& per sq. inch, ratio between sections of beams and of truss should be in
mtlo of transverse strength per sq. inch of beam and of tensile strength of truss.
Girders under consideration aro those alone in which truss is attached to beam
Kt its lower flange, in which case it presents following conditions:
* EkogiUioii of GMt and wioq^t Iroa bdqc 5500 and zoooo,line» wooo H- SSOO^
824 BTKBNGTU OF MATKBlALd. — T&AKSVEBSB.
X. When fnui rmuparaUel to lower JUmge. a. Whm truu runt of cm indUnoHtm
5o lower flange^ being dqnreaed betow itt centre. 3. fl^en beem it arched v^UMurd^
and truss runs as a choid to curve.
Consequently, in all these cases section of beam is tbat of an open one with a
cast-iron upper flange and web, and a wrougbt-iron lower flange, increased in its re-
sistance over a wbolly cast-iron beam in proportion to the increased tensile strength
of wrought iron over cast iron for equal sections of metals.
From various experiments made upon trussed beams, it is shown :
I. That their rigidity far exceeds that of simple beams; In some cases ft was fh)m
?r to 8 times greater, s. That when truss resists rupture, upper flange of beam be-
ng broken by compression, there is a great gain in strength. 3. That their strength
is greatly increased by upper flange being made larger than lower ona 4. That
their strength is greater than that of a wrought-iron tubular beam containing same
area of metoi
Comparative Value of "^Vrouglit-iron Sars, HolloTV
O-irders, or 1*111368 of* Various ir<ig>xireis {Engliik),
Circular tul)es, riveted •• z
Flanged beams. ... • ••»••• 1.3
Elliptic tubes, riveted. •..•••• 1.3
Rectangular tubes, riveted 1.5
Circular, uniform thickness •••• z.7
Plate beams..... ..•...•• • 1.7
Elliptic, uniform thickness ••• x.8
Rectangular, uniform thicknesa a
General Deductions from Exper-imenis of Stephenson, Fairbmrn^ OUntl,
Hughes, etc.
Fairbairn shows in his experiments that with a stress of aboot xa 330 Iba per sq.
inch on cast iron, and 38000 Iba on wrought iron, the sets and elongationa are
nearly equal to each other.
A cast-iron beam may be bent to .3 of its breaking weight if load is laid on grad-
ually; and 16 of it, if laid on at once, will produce same effect, if weight of beam
is small compared with weight laid on. Hence, beams of cast iron should be made
capable of bearing more than 6 times greatest weight which will be laid upon them.
In beams of cast or wrought iron, if fixed or supported at both ends, flanges
should be in proportion to relative resistances of material to crushing or extension.
Breaking weights in similar beams are to each other as squares of their like linear
dimensions; that is, breaking weights of beams are computed by multi|4ying to-
gether area of their section, depth, and a Constant^ determined flrom experimenta on
beams of the particular form under investigation, and dividing product by distance
between supporta
Cast and wrought-iron beams, having similar resistances, have weights nearly as
a.44 to X.
A box beam or girder, constructed of plates of wrought-lron, compared to a single
rib and flanged beam X o^ equal weights, has a resistance as xoo to 93.
Resistance of beams or girders, where depth is greater than their breadth, when
supported at top, is much increased. In some cases the difference is fhlly one third.
When a beam is of equal thickness throughout its length, its curve of equilibrium,
to enable it to support a uniform stress with equal resistance in every part,
should be an ElUpse^ and if beam is an open one, its curve of equilibrium, for a nni-
form load, should be that of a FarabolcL Hence, when middle portion is not wholly
removed, its curve should be a compound of an ellipse and a parabola, approaching
nearer to the latter as the middle part is decreased.
Girders of cast iron, up to a span of 40 feet, involve a less cost than of wrought
iron.
C^ist-fron beams and girders should not be loaded to exceed .3, or sutjected to a
greater stress than . 166 of their destructive weight ; and when the stress is attended
with concussion and vibration, this proportion must be increased.
S^nplo cast-iron girders may be made 50 feet in length, and best form Is that of
Hodgkinson ; when subjected to a fixed load, flanges should be as i to 6, and when
to a concussion, etc., as x to 4.
Forms of girders for spaces exceeding limit of those of simple cast Iron are vari-
ous; principal ones adopted are those of straight or arched oast-iron girders in
separate pieoes, and bolted together— Trussed, Bowstring, and wrought-iron Sox
and Tabular.
STBXKGTH OF HATSBIALS. — TSANSVBBSB.
825
Straight or Ardied Girder^ formed of separate castingS) la entirely dependent
apoa bolls of connection for its strength.
TruMed or Bowstring Girder is made of one or more castings to a single piece,
and its strength depends, other than upon the depth or area of it, upon the proper
adyustment of the tension, or the initial strain, upon the wrought- iron truss.
Box or Tubular Girder is made of wrought iron, and is beat constructed with
cast-iron tops, in order to resist compression: this form of girder m l>est adapted to
aflbrd lateral stiflhess.
When a ffirder has four or more supports, its condition as regards a stress
upon its middle is essentially that of a beam fixed at both ends.
The following results of the resistances of materials will show how they
should be distributed in order to obtain viaximum of strength with mimmum
of dimensions :
Cast Iron,
(t
English..
Granite
Limestone
To Tension,
21000
32000
13000
23000
578
670
2800
To Crushing.
90300
140 500
5800D
Z16000
15000
4000
9000
Oak, white, mean.
♦♦ English " .
Wrought iron
English
It
To Tension.
IIOOO
6500
45000
59000
(31000
53000
t6ooo
To CriMh'ff.
7500
3100
47000
83000
4POOO
65000
4000
Yellow pine
The best iron has greatest tensile strength, and least compressive or crushing.
Conditions oi^ H'arxus and Dimensions of £fc S^^iinmeti^ioa]
Seam or Oirder*
When Fixed at One Mid, and Loaded at the Other.
1. When Depth is uniform throughout entire Length, section at eyery point
must be in proportion to product of length, breadth, and square of depth, and
as square of depth is in every point the same, breadth must vary directly as
length ; consequently, each side of beam must be a vertical plane, tapering
gradually to end.
2. When Breadth is umform throughout entire Length, depth must vary
as square root of Length ; hence upper or h>wer aides, or both, must be deter-
mined by a parabolic curve.
3. When Section at every point is similar, that w, a Circle, an Ellipse, a
Square, or a Rectaiigle,'8idR8 of which hear a fixed Pistportion to each other,
the section at every point being a regular figure, for a circle, the diameter
at every point must be as cube root of length; and for an ellipse or a rec-
tangle, breadth and depth must vary as cul^ root of length.
Illustration. — A rectangular beam as above, 6 ins. wide and i foot in depth at
its extreme end, and a feet in length, is capable of bearine 6480 Iba ; whai abooM
be its dimension at 3 feet? i^^ _ ^^87, dnd ^3 = 1.4^
Then 1.587 . 1.442 :: i : 9086, and 6 and 12 x .9^86 = 5.452 and ia9.
Hence 5.45a X 10.9'^ ^^ l>i52! = ..A
3 4
When Fixed at One End, and Loaded unifomdy throiighon: its Length,
I. When Depth is umform throughout its entire Length, breadth must in-
crease as the sqiutre of length.
3. When Breadth is uniform throughout its entire Length, depth will vary
disectly as length.
3. When Section at every point is nmHar, as ct Circle', Ellipse, Square, and
Bectctngie, section at every point being a r^ular figure, cube of depth must
be in ratio of square of length.
826 STBBNGTH OF MATEBI1.LS. — TBANSYSXaS,
iLLvntuTios.—Take preceding cue.
Then 4' : 3' :: 12* : 973, and ^979 s 9.9 til dt^^
When Supported at Both Ends.
1. When Loaded in the Bliddle, Ooeficieni w Factor of Safety of the beam,
or |iroduct of breadth and sqnare of depth, must be in proportion to distance
from nearest support ; consequently, whether the lines forming the beam are
straight or curved, they meet in the centre, and of course the two halves are
alike.
3. When Depth is Uniform throughonty breadth must be in ratio of length.
3. When Breadth is Uniform throughout, depth will vary as square root
of leiij^h.
4. When Section at every point is similar^ as a Circle, Ellipse, Square, and
Rectangle, section at every point being a regular figure, cuue of depth will
be SLA square of distance from supported end.
When. Supported at Both Ends, and Loaded uniformly throughout its
Length.
z. When Depth is Uniform, breadth will be as product of length of beam
and length of it on one side of given point, less square of length on one side
of given point.
2. When Breadth is Uniform, depth will be as square root of product of
length of beam and length of it on one side of given point, less square of
length on one side of given point.
3. When Section at every point is similar, as a drcle, EXUpse^ Square^ and
Rectangle, section at every point being a regular figure, cube uf depth will
be as product of length of beam and length of it on one side of given point,
less square of length on one side of given point.
Tniliptioal-sided Seams.
To Determine Side or Cvirve of* an Klliptioal-sided Beaxn..
/— ^ =3 d L represenHmg load in lbs., I length in feet,.C eoefficienty and b
breadth in ins.
Illfstratiom.— What should be depth iu centre of abeam of white pine, 10 fcei
m length between its sapiMrts, and 5 ins. in breadth, to support a load of zoooo lbs.?
A8SumeC=:ioa Then ^ / — -— = ^/ zstoins.
Hence, outline of beam is that of a semi-ellipse, ha\'iog 10 feet for its transverse
diameter, and 9 ina for its semi-coi^Jugate.
Note.— Weight of 6ir()er, Beam, etc., should In all cases be added to stress or loai.
lilisoellaneouM lUvistrations.
I.— What should be side of a rectangular white oak beam, 2 ina in width, and 6
feec. between its supports, to sustain a load of 360 Iba ?
Assume stress at .3 of breaking weight of 150 lbs. = 3a
V4XaX39 Va40
9. - -What should be breadth and depth of such a beam if squarsi'
V 4X30 V >20
3.— What should be diameter of a cylinder?
360 X 6 . , /lao .
^^-— — = xao,and3/ — = 3.1 ina
.6X30 V 4
8TSSN6TH OF MATERIALS. — ^TBANSVEBSB. 82/
STEEL.
To Coizipute Transverse Strength, of Steel Bars.
Supported at Both Ends. Weight applied in Middle.
'''^^ = W. S repreientif^ tensile strength in lbs. ^ I length between supports
in ins.i and W weight in lbs.
Illustration. — What is ultimate destructive stress of a bar of Crucible steel,
2 ins. sqaare, and 2 feet between supports ? S = 90000 lbs.
__ 1.155X90000X2* 831600 , ,.
Then — ^2Jl^ Ci — = -2. ~ 34650 lbs.
2 X 12 24
ElaHic Transverse Strength is 50 per cent, of its ultimate strength.
JJardeinnff iu oil increases its strength from 12 to 56 per cent. Thus,
Soft steel, 131 520 lbs. ; soft steel, cooled in water, 90 160 lbs. ; soft steeli
cooled in oil, 215 120 lbs.
Krupp's is about .45 of its tensile breaking weight, .24 of its compressive
or crushing strength, .38 of its transverse, and .39 of its torsional.
Friction of a steel shaft compared to one of wrought iron is as .625 to i.
Capacity of steel to resist a transverse stress is much less than to resist
torsion.
Relative diameters of steel and wronglit-iron shafts, to resist equal trans-
verse stress, are as .98 to i, and weight of such a proportion of steel shaft
compared with one of wrought iron will be about 4 per cent, less, and friction
of bearing wiU be 6 per cent. leas.
CYLINDERS, FLUBS, AND TUBES.
Hollow Cylinders. Cast Iron.
To Compute lillements'or XIollo'^v Cylinders viritLin
l^imits or IQlastio Btrengtli. (D.K. Clark.)
P P
S X hyp. log. R = P. r^ — - = a — = hyp. log. R. S representing
nyp. log, A B
elastic tensile strength of metal in lbs. per «g. inchj R ratio 0/ external diamettr to tn-
d' r'
temal^ = -r = — , and P internal pressure in Uts. per sq. inch, d and d' representing
internal and external diameter^ and r and r' internal and external racist, all in ins.
NoTB.— Hyperbolic Logarithm of « number is equal to product of it* common lopirltbm and 3.3036
Illustration i. — Diameters of a hydroetailc cyHoder 5.^ by 13.125 ins. ; what
pressure within its elastic strength will it sustain per sq. inch?
Aflsome S = loooo Ws. Hyp. log. R='? "^ x 2.3026 = log. 2.5 X 3.3036 =: .oa.
5-3
Then 10 000 X -92 = 9200 lbs. per sq. inch.
Noes.— For Bunting Strength take maximum itrength of metal.
3 — A water-pipe .75 inch thick has an internal diameter of 10 Ins., what i^ its
bursting pressure r
S = 30000 lbs. fiyp. toflr.— -^^^^=.1398.
Then 30000 X • 1398 = 4x94 lbs.
3. — If it were required of a hydrostatic praes to sustain a pressure of 589050 lbs.
upon a ram of « ins. in diameter, what would be pressure on ram, and what should
be thickness of metal, assuming it equal to an elastic tensile stress of 15000 lbs.
per aq. inch f
Area of 5 ins. = X9-635. ^° = 30000 = pressure per sq. inch on rasik,
19.035
Then ^°°°°asa, which =hyp. log. 11 = 739, Md 7.39 X s = 3695 sT«Bfemal 4i
15000
umeler. 36.95 — 5 = 31.95, which -r- 3 = 15.975 *»•*• thickness of metal
S28 STBBKGTH OF MATBBIAL9. — TBAKSVB&SS.
'^^rouglxt Iron, and Steel*
2 P ^ 2 P
S=P.
= &
4- 1 = (P + hyp. log. S)
B, + hVP.log. — — i
Illustration i.— If diameters of a wroagbt iron cylinder are 5 and 15 ins., and
altimate or destructive strength of metal is 4ocxx> lbs. per sq. inch, what is its break-
ioig pressure? »5 ♦r » ^ r.^
— = 3- SyP- log. 2 = .477 1? X 2.3026 = 1.0986.
5
Then
3 + 1.0986 — 1
X 40000 = 61 972 Vbt. per »g. inch = 61 972 X 5 -?- 15 — 5 =
30 986. 2 Ubi. per sq. inch of tection of metal.
2.— A steam-boiler 6 fi^i in internal diameter, of wrougbt-iron fyiates .375 fncb
thick and double riveted longitudinally, burst at a joint by a pressure of 300 Iba pel
6q. inch; what was resistance of joint per sq. inch of its section?
72 -f- -375X2
72
Then
= Z.0104. ffyP' log. 1. 0104 = .010345.
2 X 900 600
1.0104 -|-. 0x0 345 — I .020745
= 29 405 lbs. per sq. inch of section of joint
SHIF AlfD BOILEB PLATES.
(Seepages 751-^57 for Boiler Ritfeting.)
tntimate Tensile Strength of X^iveted and. 'Welded
Joints of Wronglit-iron Plates. (D K.Clark.)
Entire Plate = loa
J01NT8.
Plate.
•375
50
40
Scarf- welded
Lap-welded
Single hand riveted
♦' " snap-) j ^^
headed ] ' 5°
«« "by machine! 40
'• *• counter-)
sunk head . . . } ' *^
102
66
60
56
52
52
■4375
106
69
SO
52
54
50 J
Aver-
Z04
62
SO
53
49
49
^ Joints,
Double rit'd, snap- \
headed )
*' " counter- ^
sunk and snap- [
headed )
" ^* with single)
welt, counters'k S
and snap-headed)
Plate.
Avar.
.5
•375
72
•4375
70
•«••
S9
67
53
69
73
65
52
6S
60
59
Strength of Riveted Joints per Sq. Inch of Single Plate, ( Wm. Fairbaim.}
Single Lapped. — Machine riveted. Pitch 3 times, 25 000 lbs.
Hand riveted. Pitch 3 times, 24000 lbs.
Rivets " staggered," and equidistant from centres, 30 500 lbs.
Abut Joints. — Hand riveted. Rivets not "staggered,'* and equidistant
from centres, single cqver or strap, 30000 lbs.
Rivets " square,*' single cover or strap, 42 000 lbs. ; doable covub Of
straps, 55 000 lbs.
Comparative Strength, of H.iveted Joixsitfl.
Entire Plate .375 ins. thick = zoa
Double riveted, double strap, or fish- ) „
plated joint j '^^
Double riveted lap Joint 72
Double riveted, single strap, or fish- ) ^
plated joint J 05
Single riveted lap joint 60
For all joints of plates over . 5 inch, other than double welded, these proporiioiM
are too high.
A closer pitch of rivets should be adopted in single than in double riveted abnte
etc.
STRENGTH OF MATEBIALS. — TBANSYSBSB.
829
X>iTxieiisionB of* liivetSy Pitcl^^ I^ap, eto.
Plsto.
Diwn.
Leneth
from Head.
Pitch,
Lap.
fhickiMM.
of Rivet.
SingU.
DoubU.
Staggerad.
Inch.
Ids.
Ina.
Ins.
Ins.
Ins
Ins.
.25
•5
1.125
i.S
1.5625
2.75
2.4375
•3"5
.625
1-375
1.625
2
3-4375
3 ^
•375
'P ]
1.625
'•75
2.4375
4-125
3.625
•5
.8125
2.25
2.125
2.625
4 4375
3-9375
.5625
•9375
a. 75
2-375
3
5- 1875
4-5625
.625
z
3
2.625
3-25
5-5
• 4.8125
•Z5
1.12$
3-25
3
3.625
6.1875
5.4375
.875
1.25
4
3-375
4 „
6.875
6.0625
1
1.5
4-5
4-375
4 875
8.25
7-25
Straps. —Single, .125 thicker tbun the plate; Double, each 625 of thickness of
>late.
To Compute X>iaxxiet«r of* Rivet.
Ordinarily^ Ti.25-|-.i875 = (L t repretenting tkicknes* ofplaU^ and d diameter
}f rivet
Pitch of* R.ivet0. (Nelson Foley.)
PlatML
Single
Staggered.
MetAl between the
. Holes.
52 to 62 per cent.
68 to 75 " "
Diam.
of RiveU.
l.4*<>«-3
1.4 to 2. J
Plates.
Square.
Triple. .
Metal between tb6
Holes.
70 to 78 per cent
761080 "
ii
Diam.
of Rivet*.
.99 to 1.7
.77 to I
I*roportionB of* Single Rivet "Wrought-iron tTointa.
(French.)
Thidraesa
Diameter
Pitch of
Width of
Thickness
Diameter
Pitch of 1
Width of
of Plau.
of RiveU.
~ Rivets.
Lap.
of Plate.
of Rivets. Rivets.'
Lap.
■il'a
Inch.
Mil's
Inch.
Mil's
Ins.
Mil's
Int.
Mil's
Inch.
Mil's
Ins.
Mil's; Ins. !m{1's Ins.
3
.»8
8
.3>5
27
1.06
30
1.18
10
•394
20
.787
.827
56 2.2 58 2.28
4
-i5«
10
•394
32
1.26
34
^H
11
-433
21
57 2.24! 60
2.36
5
.197
12
.472
37
1.46
40
1.58
12
.472
22
.866
58
2.fi8 Co
2.36
6
.236
14
-551
43
1.69
44
1.73
13
.512
23
.906
60
si< 36 62
2-44
7
.276
16
.63
48
1.89
50
1.97
"4
•55«
24
•945
62
2.44 64 2.52
8
-3«5
17
■^
51
2.01
51
2.13
«5
•59»
25
-984
63
2.48
66
2.6
9
.354
»9
54
2.13
56
2.2
16
.63
26
1.024
65
2.56
68
2.68
IDouTale-Riveted and Doulale-S trapped Plate- Joints.
(Mr. Brunei. )
Plates, 20 ins. in width, .5 inch thick, Abut jointed, with a Strap or Fish-plate on
each side, 10 ins. in width. Holes punched
20 .6875 inch rivets, 4 ins. pitch, set ''square," tensile 8ti-engUi.77 per cent
,8 .75 " " " " "Staggered," " *' . 78.6 "
24.75 " ^i 5 'i '< "square," " "• 84 "
To Compnte IP and Economy of* a Steazn-Boiler.
Steam at 70 lbs. m. g., and Evaporation ofyt lbs. of Water per Hour from 212°.
(T+32<^)-FxW ^^^ (Tjh_320)-FxW^^
«-f32°)-2l20X3O (*-2120)XC
T representing total heat fr&ni the water at 32° at pressure of steam, t total heat from
the ufoter at 70 lbs., and F temperature of feed water, all in degrees, W weight of
water evaporated, C weight of fuel consumed, and E evaporaiUm, all in lbs. per hour.
iLLCsTRATioy.— Assume steam at 98 lbs., water at 135°, evaporation 10505 lbs.,
and consnmption of fuel 1105 Iba per hour.
xi84.i°4- 32°- 1^ X 10 505 ^ ^ 1 ,84. lO-f 32°- 135° X TO 505 ^ ,^64 Ws
37y^ ' (ii77.90-2i20)Xiio5 ^atex.
(«i77-9°+ 32°) — 212° X 30
4A
830 STBBNGTH OF MATERIALS. — ^TRANSYSBSS,
Hulls of* ATessels.
U.S. and
Plato.
British
Lloyd*.
iDCh.
Inch.
•3»as
.625
•375
.625
•4375
.625
•5
•75
•5625
.75
.625
:^s
.6875
•75
.875
.8125
.875
875
I
•9375
X
1
K
Diameter
of Rivets.
LiTMrpooI
Admiralty,
Eng.
Millwall,
EoK.
Pitch
of Rivets.
Length of Rtrala.
CooDtur- Snap-
sank, headed.
Ins.
Ins.
lacb.
IBS.
Ins.
Ins.-
•5
.5
.625
1-75
Z.I25
x-5
.625
.625
.625
2
i-a5
Z.625
.625
•75
.625
2.Z25
1375
1-75
•75
•75
•75
2.25
15
a
•75
•875
•25
2^437
1.6875
2.1875
.8125
.875
.875
a. 56
19375
2.1875
2.375
•^5
•875
.875
2.812
2.625
.875
z
•?75
3-125
2375
2.75
2.875
•9375
I
.875
3375
2-5
I
Z-I25
z
3^625
2.625
3
1.0625
1.125
z
3.875
2.75
3125
1.125
1. 125
z
4-125
2.875
325
Lap of Joint or Course should be .5 pitch of rivets added to .3 diam. of rivet.
NoTB — Lloyd^s requires a spacing of 4.5 diameter. Liverpool Registry, 4. Ad-
miralty, 4.5 to 5 in edges and abuts of bottom and bulkhead plates, and 5 to 6 in
other water-tight work. Bureau Veritas, 4 diameters for single riveting, and 4.5
for double.
STEEL PLATES.
Steel Plates, according to M. Barba, .354 inch thick are equal to wrought
iron .AJ2 inch thick, or as 3 to 4 ; consequently, when iron rivets are used,
their diameter should be in proportion to an iron plate.
It is ascertained also that they are best united by iron rivets.
A steel plate .3125 inch thick requires an iron rivet .5625 inch in diam-
eter, and 1.375 ^^^ apart.
Bridge I'lates and Rivets.
Plates .25 to .5 inch thick. Rivets .75 to i inch diameter, and 3 ins. apart
from centres in upper flange or girder, and 4 ins. in lower
Bivet Heads.
i-/<T7\ tMiptoideUf Fig. i. — D diameter, R radius of head = D, r radius of
a flange 3= .4 D, c d^^ at centre=.s D.
Segmentaly Fig. 2. — D diameter, e depth at centre = .625 /^35s.**
D, R radius of head = ,75 D, o depf Jk below head = . Z25 D. "
Countersunk, — Head 1.59 3, angle 60°. Countersink .45 diam. ot plate.
Cheesehead or heads, section of which is a parallelogram. Head .45 D^
diameter 1.5 D.
Rivets.
Shearing strength of a Lown oor rivet =s 40 320 d^ or 18 (x* in tons.
d representing diameter of rivet n ins.
IV) -txnoranda.
PnnchlDg holes for riveting weakens plates, varying fh>m zo to 20 per oenk, ac-
eording to their temper, hardest losing most
Countersunk riveting does not impair strength of Joint, as compared with ex
temal head.
Diagonal abut Joints are stronger than M|uare.
Shearing strength of rivets should not exceed that of plates.
Maximum strength of Joint is attained at 90 to zoo per cent of net aectfon of plate.
Shearing strength of Eqglisb wrought Iron is taken at 80 per cent of Its teosili
strength.
STRENGTH OF HATBBIALS. — ^TKAKSYEBSE.
^31
LEAD TJfU.
Xiesistauoe of Xjead. Fipe to luternal f^ressvire.
(iCirXM2<2y, Jardine, ojuI i^atr&atm.)
Dtem.
Thkk.
Inch.
Wcigbt
LU.
BtmtiBg
Pr«M«».
DUm.
Thick.
I1«M.
Weight
Foot.
Bonting
PreMQVv.
DUm.
Thick,
new.
Inch.
Weight
iBCh.
Lb*.
Id*.
Ineb.
Lbs.
Lb*.
Int.
Lbs.
•5
.2
2-3
"579
1.25
.21
5-3
683
2
.21
9.2
.625
.3
2.6
"349
1-5
.24
71
734
2
.2
.^
•75
.22
3.«
1191
1-5
.2
—
528
3
•25
—
I
.3
4««
91 *
IS
.2
—
626
a
•25
—
Bunti '
Pl«Mur«.
I . I H I 11
Lbs.
498
448
364
374
Tensile strength of metal = 2240 lbs. per sq. inch.
To Compnte Tliickixees of* a IL«ead fipe -wlien IDiameter
and. Pressure in XjI>s. per fdq.. Inch, is given.
Rule. — Multiply pressure in lbs. |>er sq. inch by internal diameter of pipe
In ins., and divide product by twice tensile resistance of metal in lbs. per sq.
inch.
iLLrsTBATioir.^Diameter of a lead pipe is 3 fna, and pressure to which it is to
be submitted is 370 lbs. per sq. inch ; what ehouUt be thiulcuess of metal f
17^X3 ^ if lo^.^
0240 X 3 4480
Difference in Weight between Pipes of *' Common," "Middling," and "Strong"
(8 12 per cent
To Oompnte Weiglit of I^ead IPipe.
0> _ d' 3. 86 = W. D and d rtpreimUng extemcU and inUmat diamtten in ins. ,
and W weigM of a lineal /boi in Ibi.
To Cosnpate ^MCajtimunx or Gurstins Pressure tbat iia*3r
be lyorne \>y a Uead Pipe.
Rule. — Multiply tenoile resistance of metal in lbs. per sq. inch by twice
thickness of pipe, and divide product by internal diameter, both in ins.
Illustration.— What is bursting pressure of a lead pipe 3 ins. in diameter and
.5 inch thiclc?
"*°=, 746.6 »*.
3340 X -5X2
3 3
Assume a column of water 34 feet in height to weigh 15 lbs. per sq. inch; what
head of water woatd such a pipe sustain at point of rupture?
15 '• 34 •• 746<6 : 1693.3/eei
Resistance of GJ-lass GJ-lobes and. Cylinders to InternsUl
Pressure and Collapse. {Flint GUiu.)
Burtting Preuure.
OLOREa
CTUNDBR.
DUoMttr.
Tbirkn«M.
Per Sq. Inch.
Piameter.
Length.
Thicknew.
Inch.
.079
own Glass).
Per Sq. Inch
laa.
4
5
Inch.
.034
.033
Lbe.
84
90
Int.
4
E
Ina.
7
lliptioal (Ol
Lb4.
383
6
.059
IS*'
4.1 1 7 \ ,999 \
109
CoUapting Pntture.
5
i
.0x4
.035
.059
393
1000*
900*
3
4
4
«4
7
«4
.014
.034
.064
85
303
397
\
832 STSEKGTH OF MATEBIiLLS. — TBAKSVSBSB*
^langaneee Sronze.
Manganese Bronze, No. 2, has a Tensile strength of 72000 to 78600 Iba,
\ier sq. inch, its elastic limit is from 35000 to 50000 lbs., its ultimate elm-
gation IS to 23 per cent., and its hardness alike to thstt of mild steeL
T^-ansverse Strength. — Destructive stress of a bar i inch square, supported
at both enda at a distance of i foot = 4200 lbs., bending to a right angle be-
fore breaking, and requiring 1700 lbs. to give it a permanent seL
HEM0RA17DA.
Cast Iron.
Beams cast horizontally are stronger than when cast vertically.
Relative strength of columns of like material and of equal weights is*.
Cylindrical, 100 « Square^ 93; Cruciform, 98*, Triangulartiio. {ffodgtdnson,')
If strength of a cylindrical column is 100^ one of a square, a side of which
is equal to diameter'of the cylinder, is as 150.
Repetitum cf Stress. — A piece submitted to transverse stress broke at
1956th strain, with a stress .75 of that of its original ultimate resistance.
Resistance to Bursting of TMck QffUnders, — Mean resistance to bursting,
of chambers of cast-iron guns is as follows {Bfajor Rodman, U.S.A.') :
Thickness of metal = x calibre, length = 3 calibres, 52 217 Ibt. per sq. inch.
Thickness of metal = .5 calibre, length = 3 calibres, 49 zoo lbs. per sq. inch.
The tensile strength of the iron being. x8 820 U)S.
Diam. of cylinder 2 ins., length 12 ina, metal 2 ina, 80229 lbs. per sq. inch.
Diam. of cylinder 3 ina, length 12 ina, metal 3 in&, 93702 lbs. per sq. inch.
Tensile strength of iron being 26 866 Uis.
Sudden Applications of Stress. — Loss of strength by sudden application
of load was, oy experiment, 18.6 per cent in excess of load appliod gradually,
and its elongation 20 per cent, greater.
Lotif Ternperaiwe. — ^Tensile strength at 23^ nnder sudden application of
load, was reduced 3.6 per cent., and elongation z8 per cent
"Wrou-gh-t Iron.
Increased Hammering gives 20 per cent greater strength with decreased
elongation.
Hardening. — Water increases strength more than oil or tar. A bar .87
inch in diameter, forged and hardened in water, attained a tensile strength
of 73 448 lbs. (ifr. Kirkaidy.)
Case Hardening. — Loss of tensile strength 4950 lbs. per sq. inch.
Cold Rolling added 18.5 per cent to tensile strength, and when plates
were reduced .33 in thickness, strength was nearly doubled, with but .x per
cent elongation. Specific graivity was reduced.
Fibre. — Plates are about 12 per cent, stronger with fibre than across it
A ngles, Tees, etc., have from 2200 to 4500 lbs. less tensile streogth than
rectangular bars.
Galvanizing does not perceptibly affect strength.
Welding. — Strength as affected by welding varies by experiment from a.6
to 43.8 per cent, less, average being 19.4.
Elcutic Strength is about .45 of its tensile breaking weight, .15 of its com-
pressive or crushing strength, i^nd .5 of its transverse strength.
Effect 0^ Screw Threads. — i inch bolts lose by dies 6. 11 per cent, and by
chasing 28 per cent
Steel.
Sled can be hardened in water at a temperature of 310**.
8TBBNGTH OF HATBBI4X8.— rTBANSYBilSS.
833
WOODS.
rro Coxnptxte TransTrerse Btrengtli of* JUarge Timber*
J)e8linictive Stress.
F%xed at One End, and Loaded at the Other, '-^—^ — = W.
O ^j |. JJ
Fixed at Both Ends, and Loaded in Middle, - — ^ = W.
♦ Siqtported at Both Ends, and Loaded in Middle, ^^^ = W.
Fixed at Both Ends, and Loaded at any other point than) -45 8 5 <!»_■--.
the Middle. } I "
Suppojted at Both Ends, and Loaded at any other point \ -38 fed' I __ ^
than the Middle, j m n '
* Hence, — ^-^, = S, and — = ,.2 8.
h, d, and I representing breadth^ depth, and length to or between supports, dU in
ins., S mean of tensile and crustiing strengths of material at two thirds of its Valve,
as determined by experimeiUs, W ultimate weight or stress in lbs., and m and n dis-
tances oftoeudfrom nearest supports in ins.
When a beam is uniformly loaded, the stress is twice that if applied in its middle
or at one end.
Values of 1.S S.
Hence, for other coefficients, as .3, 1.8, etc., the values will bo proportional
Wood*.
Ash, white.
** Canadian
'* English.
Beech
Birch
Cedar
*' Cuban
Chestnut
Cypress , .
Eun, English ,
" Rock, Canada. ,
Fir, DantEic ,
Greenheart ,
Gum, blue ,
Hackmatack
Iron wood ,
Larch
1.38
3.38
2-4
2.46
a- 55
2-5
1.6
1.6
»-53
.8s
Z.12
2.63
2.5
3.81
2
1.36
364
1.77
Woods.
Locust ,
Mahogany, Honduras.
Oak, Pa. ,
" Va !..,
" white ,
" English ,
*' Dantzic. ,
" French ,
Pine, Va. ,
pitch ,
white
" yellow
•' " Canada..
Redwood, Cal
Spruce
Teak
Waluut, black
i.a s
3-7
2-3
2
2-3
2.5
1-7
1-35
2.44
3
2.2
2.71
3-87
1.8
X.I
1.2 '
3J7
1.25
iLLnsTRATiON I.— What is destructive stress of a beam of English oak, 2 ins.
square, and 6 feet between its supports?
1.2 flrom table = 1.7, and S = .66 of 5700 (mean of tensile and crushing strength)
= 3762 tbs.
6X12 72
By experiment of Mr. Tiaslett it was 688 lbs.
2.— Wh.'it is destructive stress of a beam of yellow pine, 3 ins. by 12, and 14 fiBet
between its supports?
X. 2 from table = 3. 87, and S= .66 of 10 200 (mean of tensile and crushing strengtlnj
s's6733 tbs.
3^87X_3X i2» X 6732 ^ 111254^27 ^ „
14 X 12 168 ^^
If the twain was fixed at both ends then 3.87 would be 5.8.
Or, as 1.2 : x.8 :: 3.87 : 5.8.
4A*
834
BTBBNQTH 07 HATXBIAL8.— TBANSVKB6B.
mom
o m o m O
o r^ o r>. o
000 mm 0
m Q »rt
O Q m
o t>
I 00 CMO
• rN,or».or^or>.oi^_
00 m«o o 00 m m 0 00 mpe
i-i « cn ■♦ m t^oo o « ■♦ r^ pv 2
M M M M M M
>ii8j§iiij§iiy§i
N m ON m ■-• ONOo oo
»« « ci en ^
\o tvoo o M ro m
M « N »o ♦ mvo 00 o* M « ^
Q . mo m Q
m o m O m
8&S
mvo >♦
m O >n o
m « ' ""
ro M moo 0\ 0 0«B m c^ t^ ct
r^ f»vo •♦00 00 mvo '♦■oo oo r*i m
M ^ t>. O ■♦oo en ov m « o> b«.vo m
•^Nooeo 8 0 NOOmSo n<»o5 ctOA
m r^ o « \o O ■♦00 m o\ m m
MMfiwMfom^m
0 0 0 0^
m »»« « w moo
M e« '♦xooo o
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O Q 0 0 O O O O
t^O m^t>.i*j« m
m t* o ♦oo moo m
MMWNMcnm^
iv8§.§.>8 8vg3.^>8 8^^3..8 8>8
4 w «o ♦ m O »^oo wOvOfnoomoo^
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♦ mo.0 «NO osmf^wvo o
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JmmroQ mmmo m\f> m Q roinroQ
. M m M N ♦ ov r>.oo M (^NO oo n 0\ ov m
►« « m ♦vo 00 M
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• nOMQNOMQMOetQMOMQ
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^ MHC«^mt<«ovM mvo o\ « moo
M H H H C4 et M
i8888888888888888
2 ** ♦ OvvO mvo Ov ♦ M 0 « ♦ OvvO mvo
" w « m ■♦o 00 o « ♦vo O'^tt \n
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m
STBBNGTH OF MATERIALS. — ^TBANSYEBSS. S3 5
Floor SeaxxiB of* "Wood-
Condition of stress borne by a Floor beam is that of a beam supported at
both ends and uniformly loaded.
1?o Cocupute Cetpaoity of* Floor Geaxns, d-irders, etc.
Supported at Both Ends.
Rule. — Divide product of breadth and square of depth, in ins., and Coeffi-
cient for material, by length in feet, and result will give weight in lbs.
Or, — ^ = W. When Fixed at Both Ends. ^'^^''^ ^ w.
BxAMPLK.— The dimensions of a white-pine floor timber are 4 by 12 ins., and its
length between aopports 15 feet; what weight will it sustain in its centre?
C, as per preceding table = 112. 5. Then ^-^^- — ^}?:1 -. _L_2? — ^330 jbj.
When Uniformly Loaded, Multiply the result by 2.
Xo Compute IDeptli of* a Floor Seaxn or GMrder.
Sujyported at Both Ends.
When Length between Supports and Breadth are Given. Rule. — Divide
Croduct of length in feet, and weight to be borne in lbs., by product of
readth in ins., and Coefficient for material, and square root of quotient will
^ve depth in ins., for distance between centres of one foot
When the ComputatUm is made Independent of the Preceding Table,
J~T^^^- When Fixed at Both Ends. Jl^^d.
V 4 oC V " "^
C as may be assumed or ascertained.
When Distance befween Centres of Beams is greater or less than one Foot,
Rule. — Divide product of square uf depth of the beam, when distance 6e-
tween centres is onefoot^ and distance given, by 12, and square root of quotient
will give depth of beam.
ExAMPLB. —Assume beam in preceding case to be set 15 ins. from centres of ad-
Joining beams; what should be its depth ?
/122 X 15 /3160
To Compute Breadth, of* a F'loor Beam or Gl-irder.
1
Supported at Both Ends.
When Length and Depth are given. Rule. — Divide product of length in
feet, au<l weight to be borne in lbs., by product of square of depth in ins.,
and Coefficient for material, and quotient will give breadth in ins.
Or, i-^ = 6. When Fixed at Both Ends. '^ ^ = b.
'd'C • 1.5 da C
When Uniformly Loaded, multiply the result by 2.
Example.— Take elements of a preceding case, page 834.
15 X 4330 64800
.... .... ., ... sg' I .... =4. YtlC..
la'* X 112.5 1O200
When Distance between Centres of Beams is greater or less than One Foot,
RvLK, — Divide product of breadth for a beam, when distance between centres
it omfootf and distance given, by X2, and result will ^ve breadth.
836
STRENGTH OF MATBJEIALS. — TBANSYEBSS.
' ExAMPLS.— Assame beam, ag in preceding case, to be set 15 ins. firom centre of
adjoining beams; what should be its breadth ?
12 12
WhenWdght is Suspended or Stress home at any other point than the Middle,
See Formulas, page 801.
Header and Trimixier Beams.
Conditions of stress borne, or to be provided for by them are as follows :
Header supports .5 of weight of and upon tail beams inserted into or at-
tached to it, and stress upon it is due directly to its length, weight of and
that upon tail beams it supports, alike to a girder loaded at different points.
Tiimmer beams support, in addition to that borne by them directly as
floor beams, each .5 weight on headers.
KoTK. — In consequeDce of efTect of mortising (when stirrups or bridles are not
used), a reduction of fkilly one inch should be made in computing the capacity of
depth of headers and trimmers.
rro Compute Breadtlx of a Itleader Beam.
When [Tntfarmhf Loaded, Rule. — Compute weight to be borne in lbs. by
tail beams, divide it by two (one half only being supported by header), mul-
tiply result by length of beam ip feet, and divide product by product of
twice CoeJkierU of material and square of depth, and result will give breadth
in ins.
Or, — TT 7F = ^' W r^pregenting weight in lbs. per sq. foot
2 C (I
Example. —What should be breadth of a Georgia pine header, 13 ins. in depth,
10 feet in length, supporting tail beams 12 feet in length, bearing 200 lbs. per sq.
fbotof area?
C, as per preceding table, 1x2.5, and depth = 13 ^ i = 12 mi
la X 10 X 200 -r- 2 X 10 120000
2X112.5X122 32400
= 3.7m«.
To Conapu-te th.e Capacity of* a PUoor XJnirornaly loaded
'^rlieix one of ita Sides rests upon a Header Beam.
1. Determine the capacity of a trimmer and header beam at the point
of their coimection. Assume the less, as tliis limit of their capacitv to sus-
tain a load, and twice tliis capacity will represent that of one half of the
floor at the points of connectibn of the header and trimmers, the other half
resting on the walL
2. Compute area of floor in square feet, first by its length from wall of
building to face of header beam, and its width from the centre of the spaces
between the trimmers and the beams beyond ; thep add that determined by
the width of the trimmer and the centre of the space between it and the
beams, and the length of it by the widtli of the opening between the face of
the header and the wall, as hatch or stairway, and this combined area will
be that which rests upon the header and trimmer.
3. Divide the capacity of the header and trimmers as obtained, by the half
area of the floor resting thereon, less the area reauired or allotted for passage
way (but not considered by the Department of Baildings), and the quotient
wifl give the capacity of the floor in lbs. per square foot, from which is to
be deducted the weight |)er square foot of the beams, flooring, ceiling, etc
8TBBN6TH OF H&TBBIAIiS.-- TB1.!NSVEBBB.
837'
Xo Comp'ate IDeptli or a Header 3eani.
KuLE. — See rule for depth of a floor beam, page 835, with the exception
that a header, alike to a trimmer, is assumed to be always uniformly loaded.
/
46C
= d.
To Compute Breadth of a Triinmer Beaxxx.
With One Header and One Set of Tail Beams. RuLE.-^Proceed as for
oomputation of dimension of a beam loaded at any other point than middle.
m
Untformiy Loaded. H + c'x — K** cX W = L, product of area, ofjloor and load
per sq.foot, and L -. — = breadtk.
I
H representing length of header, c dUlanee between centres of beams, m and n,
lengths of tail beams and width of hatch or stairway, c* twm of half distance ofc,
added to half of an assumed width of trimmer, and I length of trimmer^ cUl in feet,
W load per sq. foot on floor, and C coefficient in lbs., b breadth of one sq. inch of the
material, and d depth of beam in ins.
ExAMt'LM.— What should be breadth of a trimmer or carriage beam of Georgia
pine, 23 feet in length, 15 ins. in depth, sustaining a header 10 feet in length, with
tail beams 19 feet, distance between centres one foot, and designed for a load of 270
lbs. per sq. foot of floor?
Assume C = 275, as assigned by the Department of Buildings, N. Y.,m and nr= 19
and 4 feet, d = 15 — 1 = 14, and c' = .75.
10 + . 75 X 2 X 4-75 + 4 X 273 = 15 828.75 and ^ 111 = 6-75 ins.
I X 196X275-^23
NoTK I. —Depth of trimmer beams is usually determined by depth of floor beams;
where not, proceed to determine it as for a header.
a. — ^When a trimmer beam is mortised to receive headers, it is proper to deduct
X inch from its depth, as in preceding illustrations. When bridle or stirru)) irons
are used to suspend headers, a deduction of the thickness of the iron only is neces-
sary, usually .5 inch.
With Two Headers and One Set of Tail Beams.^Yig. i.
Operation. — Proceed for each weight or load as for a beam, when weights
are sustained or stress borne at other point than the middle.
ah ^
= W and w. a representing area of floor in sq. feet, L load per sq.foot, and
W and w weights or loads at points of rest on trimmers.
KoTK.— Halfleid and some other authors give complex and extended formulas,
to deduce the dimensio'^s of a Girder or Beam, under a like stress.
Upon consideration, bowcvor, it will be readily recognized that a beam loaded at
more than one point is simply two or more beams of proportionate width, as the
case may be, loaded at different points, and connected together.
Fig. I.
^ /..
KB
B
■^_. W.M«^ ..^
_n
1
w W
12 X to — 5X300 18000
Illustration. — • What should be breadth of a
trimmer beam of Yellow pine 25 feet in length, it
ins. in depth, sustaining two headers 12 feet in
length, set at 15 feet from one Wall and 5 feet from
the other, to support with safety 300 lbs. per sq.
foot of floor? •^ ^
1 = 2$, w = i5, n = io, r = 2o, » = 5, 0=125,
and d = 1 1 — i = 10 for loss by mortising.
12 X 5 X 300 »8ooo
= =4500 lbs. at W, and
4 4 ^-^
=.4500 lbs. atw.
838
STRENGTH OF MATERIALS. — TBANSVBBSB.
Then '3X10X4500^675000^^ ^g ^^ ^^ 5X20X4500^450000^,
25 Xio'X «25 3" 500
in#., and 3. 16 ~|- 1-44 = 36 ins. combined breadth.
25 X 10' X 125 312500
44
Fig. 2.
(
■m
With Two Headers and Two Sets of Tail Btams.-^F\g. 2.
Opekation. — Proceetl as directed for Fig. i.
Illustration. — What should be breadth of a
trimmer beam of Yellow or Georgia pine, 25 feet in
length, 13 iDS. in depth, sustaining two headers 12
feet in length, one set at 15 feet from one wall
and the other at 5 feet from the other, to support
with safety 300 lb& per sq. foot of floor?
1 = 25, m = i5, n = io, * = s, r = 2o, C =
-r---
-n
W
Iff
Z12. 5, and <2=i2 — i=sii for lost by morUting.
15 X 12 X 300 54000
4 "~ 4
Then'5X'°X'3 5oo
= i3 5ool6«. atW.
12 X 5 X 300 18000
= 4500 Vbs. at Iff.
2025000
25 X 11" X 112.5"" 340312
20X5X4500 450000
3= 5.94 im, breaiihfor load on header at isfeet
— 1.33 ins. breadth for load on header at 5 feet, and
25 X II* X 112.5 340312
5.94 -^ X.32 = 7- 26 ins. combined breadth,
WUh Three Headers and Two Sets of Tail Beams* — Fig. 3.
Fig. s- Operation. — Proceed as directed for Fig. 1.
Illustration.— What should be breadth of a trim-
mer beam of Yellow pine, 20 feet in length, 13 ins. in
depth, sustaining 3 headers 15 feet in length, set at 3,
7, and 13 feet from one wall, to sustain a load of 300
lbs.
p^"^*
....
...(-..
_
^"
I JVf
—
m —
n - — ^
m
w'
1
^o-
\ ^
per sq. foot of floor?
i = 20, TO = 13, n = 7,
= 12 ins., and C= 125.
7, 0 = 3, <i=:=Z3 — X
to' to
W
15 X 7 — 3 X 200 12 OOP
Then 7-^ 'l><i25o ^477_75o^^ .
20X122x125 360000
3X 17 X3000 153000
15X7X200 21000 „ ^ ,„
— — — = ■ = 5250 Ws. at W;
4 _4
= 3ooo»«. at to; and -'^-^-^-~A^ *°°. ^joooHw. at iff'.
7 X 13 X 3000
20 X 12* X 125
273000
and
20 X 12= X 125
bined breadth.
=s.43%ns.
360000
Hence, i.33-H.76 4--43 = 2'5a *»*.
= .76 ins.;
360000
Stirruips or Bridles.
Stirrups are resorted to in flooring designed for heavy loads, in order to
avoid the weakening of the trimmers by mortising.
Average wrought iron will sustain from 40 000 to 50 000 lbs. per sq. inch.
Hence 45 000 lbs. as a mean, which -4- 5 for a factor of safety, = 9000 lbs.
A stirrup supports one half weight of header, and being doubled (looped),
the stress on it is but .5-^3=: .25 of load on header.
To Coznpvite IDixxiensiouis o£ Stirrups or Bridles.
W
= area. Hence
area
■=: width.
2 X C thickness
Illustration. — What should be area and width of .75 inch wronght-iron stirrup
irons for a weight on a header beam of 240 000 lbs. ?
240 000 -f- 2
€ = 9000
2X9000
120000 , ,, . .6.66 __ . .,../'
— =6.66 sq. ins., and — = 8.8 ins, z=zwidth,
18000 .75
6TBENGTH OF MATXSIALS. — TRANSYSSSX. 839
GUrder.
Condition of stress borne by a Girder is that of a beam fixed or supported
at both ends, as the case may be, supitorting weight borne by all beams
resting thereon, at the points at which tliey rest.
To Compute X>ixxiensions of a Oirder.
RuLK,— Multiply len^h iii feet by weight to be borne in lbs., divide
product by twice* the CoeJficietU, and quotient will give product of breadth
and square of depth in ins.
ExAXPLK.— It is required to determine dimensions of a Yellow-pine girder, 15 feet
between its supports, to sustain ends of two lengths of beams, at distances of 5 feet,
each resting upon it and ndjoining wall, 15 feet in length, having a superincumbent
weight, including that of beams, of aoo lbs. per sq. foot.
Condition of stress upon such a girder is that of a number of beams, 15 feet in
length, supported at their ends, hihI sustaining a uniform fitress along tlieir length,
i>r ?()o \\v*. u|K>n each superficial foot of their supporting area.
Coefficient =. 137. 5.
15 X 15 X 200 -¥■ a (for half support on the uall) — 22 500 Un.
IS X 22 ^OO /1227 2
Then -^ = 1227.2 = 6 and d^. Assume 6 = 12 in»., then / — ^=10.1
2X1375 V 12
in». the depth.
'Vo Compute O-reateat X^oad upon a Oirder, aitd Uixueii-
sions tliereof.— FiK. 1.
]Vhen a Beam is Lotuhd at T100 Points.
Flfr I < ^ » ^ ^ ^ffgct of weight at 1,
'S^^p^^^^
r s
--- = effect of weight at 2,
if
m
1 ^ _ (W u-\-ws) = the two effeU*
W w *
if 1, and — (w r -\- \\ m) =z two effects at 2.
Then, for weight and dimensions, same formulas will apply.
Illustration.— Assume weight of 8000 lbs. at 3 feet fi-om one end of a white pine
beam 10 inches in depth und 12 feei in length between its bearings, and anotlior
weight of 3000 lbs. at 5 feet from other end. 0= 112.5.
8000 X 3 X 12 — 3 = 2t6ooo effect of weight at location i, and 3000 X 5 X 12 — 5
B 105 000 effect of weight at location 2. Hence i, being greatest, = W, and 2 = w.
Then, ^^ x 8000= 18000 at W, and 5-^ X3ooo = 875o at w; and
^ (8000 X 9 + 3000 X s) = 21 750 = ^'a' «#^c/ at W, and — (3000 x 7 + 8000 x i
ta 12
:= 18 750 = total effect at w.
Hence, to asoertain total elTect and dimensioni.
_2X75oX3X.2..^ ^,. breadth,
12 X io« X 1 12.5 ^ ^"^
rm/!ca/i(m.— Breadth at W. i8oooX3Xg _ ^ ^^^ ^^^ ^^ — 18000
12 X 10^ X iia.5
= 3750 and ^^° X 3 X 9 _ ,„^ as 3. 6 4-. 75 = 4-35 »«*•
^^^ 12X102X112.5 '^ ^ ' '
* Fwr bdBK oBlfenaly 1(m4«4.
840
STBSN6TH OF MATERIALS. — TBANSYEB8B.
JBeazxx I^oaded Uxxifbrznly aud at Several f oints.
To Determine EqucU Weight at Centre Fig. 2.
Fig. a.
Illustration. — What shoald be
breadth of a beam of Georgia pine,
20 feet in len{;tb, 15 ins. in depth,
uniformly loaded with 4000 Ibe.,
and sastaining 3 headers or con-
centrated loads of 6000 lbs., at re-
spective distances of 4 and 9 feet
firom one end and 7000 lbs. at 6
feet fVom the other end ?
TO = 9, n=z:ii, r=r6, 0 = 4, « — 20=1*14, ^=15-^1 = 14, L = 4ooo, and
0 = 800-7-4 = 200. — J— z=w; -y- = W; --=10'; and -7 — i-2 = toad tn
I
centre uniformly distributed.
4X 16x6000
20
•= 19 200)
9X II X6000
2 — = 29700;
20
6 X 14 X 7000
20
29 400 lbs.
Then — {6000X 11 + 7000 X 6) + 6000 ^^ — i=-2-X 108 coo -f- 13200 = 61 800 /!>«.
20 20 20
omitting uniformly distributed load
4000
= 2000 lbs. concentrated at centre of A B.
Then to obtain total effect at W, 10 : 9':: 2000 : iBoo=: effect of load. Hence,
92< _.i X 1800^ ^^.^^ ^^^^ ^ 61 800 = 707x0 lbs., and 7-'7ioX9Xii
20 ^ ' ' ' ' 20 X 142 X aoo
= 8.93 ins. breadth ofhetm.
Operation deduced by Graphic Delineation of Greatest Stress without uni-
form Lomd,
Fig. 3. <- ^ >
A
Momenta of weights =
w'or W mn
and
Vf su
I > I ' I
19200, 29700, and 29400, and
let fall perpendiculars i, 2, and 3
proportionate thereto.
Connect 10', W. and «o with
A B, and sum of distances of in-
tersections of these lines upon perpendiculars, from z, 2, and 3, respectively, will
give stress upon A B at these points.
Whence, greatest stress at greatest load will be ascertained to be 61 800 lb&
When Loaded at Three Points, '!^ ^wn-^w s)-^v>^'^ = Greatest Stress,
as in rig, 2. i ^ ' ' ' 4
Illustration.— Take elements of above case, omitting uniformly distributed load.
-2.(6oooX II X70ooX6)4-6ooo-i^-^=~ X 108000+13200 = 61800 /6«.
ao
W«»
20 20
Deflection, oi* GMrdera and Seams.
^ Cbd^ „,. ,/W«» ^ ^,/C6dSD , -
D; -^^=W; ^^^ = d; and^-^— =1. Z rg»re«««.
Cbds
ing length in feet, b and d breadth and depth, and D deflection in ins.
Values of C for Various Woods, {Haifidd,)
Ash 4000
Chestnut 2550
Hemlock 2800
Hickory 3850
Pine, Geoi^ia.
'' pitch...
« white. . . ,
" red
- SQoo
. 3836
. 2900
4959
Larch 2093
Oak, white 3100
"• English, mean. . 2686
Spruce 3500
Illustration. — ^What would be deflection of a floor beam of white pine, xo feet
in length, 4 ins. in breadth, and 8 in depth, with 4000 lbs. loaded in its middle?
_ 4000X10* 4000000 - . .
C = 290a ~ ~ — r^ = = .674 xneh.
^^ 2900X4X8= 5939200 '^
• Load luifonnljr dUtribntod.
STBEN6TH OF MATERIALS. TBANSVBBSE. 84I
When Weight is Uhiforrnhf Distributed,
I^SWZ. £^» = w; 3P^M1J> = 1, and 3/^'^'''' = ^
Cbd* ' .625i» ' V •625W ' V C&
Hence, Deflection in preceding illustratioD would oe 674 x •625 = .421 ins.
Illustration. — What should be length of a white-pine beam 3 by 10 Ins., to sup*
port 6000 lbs. nniformly distributed, with a deflection of 2 in& ? C = 290a
V -625 X 6000 V 3750
A fair allowance for deflection of floor beams, etc., is .03 inch per foot of length;
.04 inch may be safely resorted to.
"Weiglits of* inioors and. of ILioad.8.
DtoelUngs, — Weight of ordinary floor plank of white pine or spruce, 3 lbs.
per sq. foot, and of Georgia pine, 4.5 lbs.
Plastering, Lathing, and Furring will average 9 lbs. per sq. foot.
Clay Blocks (Flat Arch) 5.25 X 7.25 ins. in depth and i foot in length,
ai lbs. = 80 lbs. per cube foot of volume.
Floors of dwellings will average 5 lbs. per sq. foot for white pine or spruce,
and on iron girders will average from 17 to 20 lbs. per sq. foot
Weight of men, women, and children over 5 years of age, 105.5 ^bs., and
one third of each will occupy an average area of 12 x 16 ins. = 192 sq. ins.
=? 78.5 lbs. per sq. foot.
Of men alone 15 x 20 ins. =: 300 sq. ins. =48 in 100 sq. feet
Bridges, etc, — Weight of a body of men, as of infantry closely packed, =
138 lbs. each, and they will occupy an area of 20 x 15 iiis. = 300 sq. ins. =
66.34 lbs. per sq. foot of floor of bridge, and as a live or walking load, 80 lbs.
per sq. foot.
Weight of a dense and stationary crowd of men, 120 lbs. per sq. foot
Bridging of Floor Beams increases their resistance to deflection in a very
essential degree, depending upon the rigidity and frequency of the bridges.
\^eigli.t on Floors, etc., in. addition to Weiglit oCStmct-
lire, per Sq.. Foot.
Ball rooms 85 lbs.
Brick or stone walls 115 to 150 ''
Churches and Theatres. . . 80 "
Dwellings 40 "
Factories. aoo to 400 "
Grain.... i zoo "
Roel^, wind and snow. ... 30 to 35 lb&
Slate roofs 45 "
Snow, per inch . 5 lb.
Street bridges 80 lbs.
Warehouses 250 to 500 '*
Wind 50 "
Sicarfei*
Relative resistance of scarfs in Oak and Pine, 2 ins. square, and 4 feet in
length, by experiments of Col. Beaufoy.
Scarf 13 ins, in Length and 13 ins, from End, or 1 inch from Fulcrum,
Vertical, — no lbs. gave away in scarf.
Horizontal, large end uppermost and towards fulcrum, — loi lbs. fHstenings
drew through small end of scarf ; small end uppermost, etc., 87 lbs. gave
away in thick part of scarf.
Factors of Safety.
Statical or Dead Load at .2 of destructive stress, but for ordinary pur-«
poses it may be increased to .25, and in some cases with good materials to .3.
1am Load at .1 to .125 of destructive stress.
See also page 802.
' B
94^
SUSPENSION BBIDGB.
SUSPENSION BRIDGE.
To Coxnpute Klexxient*.
C L Q a* „
-—or ^^ — = 8;
8« 2 t»
vm*
(5 0)
3 = »i
sy(5jv;=-s
— :=^ tan. angle 0]
2 X
L
n — I
= S';
iy(.5C)='+-^t,» = J; ^ = co<.'-;
C
L-^2
«V(Vt+'='>'"^'=''
CI,
2 t>
8
M^r+'='"
= X, aad
L-=-2 xcoa «
Bin. c
V(2t')*+(C-^2)«
= Stress at • . C representing chord or span, a hcdf chord^ and v versed sine of
chord or curve of deJUiUion, in feet, L distrUntUd load inalunve of suspended ttriict-
ure Q load per UneaL foot, and S stress at centre, all in tons, x distaw;e ofanymnnt
from centre of curve, and h height of chain at x above centre of it, both m/e< «
stress on chain at any point, as x,from centre of span, « stress on anytenn^n-roO,
and t Hress at aJbutvientSy aU in tons, n number of tensim-rods, o angle qf tangent
of chain with horizon at any point, asx,r angle of chain with vp-tu>at at abtUmtnUy
I length of chain, in feet, and z angle of direction of chain.
Assume C = 300 feet, L = 1000 tons, v = 2$ feet, x = 100 feet^ n = 30, r = 71° 34',
and a =12° 32'.
Then,
3g°X'^=^,Soo«mg = S;
8X25
1500 ;y7^^y+ X = 1536.56 tow =t:«;
tan.^o; 2 -^(5 X 300)' + -j25' = 305-5/«'=^;
25 X 100' - . -
(.5X300^'
4X11.11 - ,
sc .2233 = 12° 3a — =
2X100
300 X 1000
8X1500
= 25 = «;
121^ = .3333 = yi'' 34'— = <»^ <^^^ »• J
306
1500
zooo
//i2<15y_^,_,^23, ^,^_^. and
30—1
2X25
= 34.48 ton« = »';
.3162 = 18026'.
V(2X25)2 + (300-=-2)«
For a deflection of .125 of span, horizontal stress is equal to total load.
To Construct curve, see Geometry, page 230.
To Compute Ratio -wliich. Stress on Chains or Cal>les at
eitlier Foint ofSxispension Bears to wh.ole Suspended.
"Weiglit of Strnotvire and ILioad.
- — . - z= R. R representing ratio.
2 X sin. » ^ "
Illustration.— Assume elements of preceding case.
= I. s8 ratio. By a preceding formula ft would be i. 536.
2 X .3162
Stress on Back Stays, — The cables being led over rollers, baving: free mo-
tion, tension npon them is same, whether angle i is same as that erf r or not
Stress on Piers. — When angles r and i are alike, stress on piers wDl be
vertical, but when angle of i is greater or less than r, stress wiU be oblique.
To Compute Hoi:^zontal Stress and "Vertical Pre88-a.re
on I*iers,
Scos. e;=;=Si», ScoahtsSo, Ssio. « = Pt\ andSsio. n=Pa SiondSo
representing stress, and P i and P o pressure, inioard and outward.
Note.— Span of New York and Brooklyn Bridge 1595.5 feet, deflection zaS feet»
angle of deflection at piers from horizontal 15O 10'.
TBACTION.
843
TBACTION.
Hesults of SjxperixnezLtB oxi 'Praotion. of Itoads
and. r*avexxien.ts. {M. Morin.)
ist. Traction is directly proportional to load, and inversely proportional
to diameter of wheel.
ad. Upon a paved or Macadamized road resistance is independent of
width of tire, when it exceeds from 3 to 4 ins.
3d. At a walking pace traction is same, under same circumstances, for
carriages with or without springs.
4th. Upon hard Macadamized, and upon paved roads, traction increases
with velocity : increments of traction being directly proportional to incre-
ments of velocity above velocity of 3.28 feet per second, or about 2.25 miles
per hour. The equal increment of traction thus due to each equal increment
of velocity is less as road is more smooth, and carriage less rigid or better
hong.
5th. Up(Hi soft roads of earth, sand, or turf, or roads thickly gravelled)
traction is independent of velocity.
6th. Upon a well-made and compact pavement of dressed stones, traction
at a walking pace is not more than .75 of that upon best Macadamized
roads under similar circumstances ; at a trotting pace it is equal to it.
7th. Destruction of a road is in all cases greater as diameters of wheels
are less, and it is greater in carriages without springs than with them.
Experiments made with the carriage of a siege train on a solid gravel
road and (m a good sand road gave following deductions :
I. That at a walk traction on a good sand road is less than that on a good
firm gravel road.
3. That at high speeds traction on a good sand road increases very rapidly
with velocity.
Thus, a vehicle without springs, on a good sand road, gave a traction 2.64t
times greater than with a similar vehicle on same road with springs.
Results ^^th, a Dynamometer.
Wagon and Load 2240 lbs.*
Relat'e nam-l
BOADWAT.
On railway, 8 lbs
On best stone tracks, 12.5 lbs.
Good plank road, 32 to 50 lb&
Stone block pavement, 79. 5 **
Macadamized road, 65 Ibe. . . .
b«r of boi
forlik«eff6ct.
X
1.56
4 to 6.25
4.06
8.12
Roadway.
Telford road, 46 lbs
Broken stone or conte, 46 lbs.
Gravel or earth, 140-147 Iba {
Common earth road, 200 lbs. .
Rebt'a nam>
b«r of borMS
for like Affect.
5-75
5-75
>7-5
18.37
as
NoTX. — By recent experiments of M. Dapuit, he dedaced that traction is inverselv
proportional to square root of diameter of wheel.
Relation of force or draught to weight of vehicle and load over 6 different con-
ttmctions of road, gave for different speeds as follows:
Walk. Trot. . ^ . ' Walk. Trot
Stage coach, 5 tons. . 1.3 x ( Carriage, seats only, on springs.. 1.29 x
lieBistanoe to 1?raotion. 0x1 Common R,oads,
On Macadamized or Uniform Surfaces. (M. DupuU.)
z. Resistance is directly proportional to pressure.
a. It is independent of width of tire.
3. It is inversely as sauare root of diameter of wbeeL
4. It is independent of speed.
^— ^~ ~^^'™— 0
• gu TVeo/tM <m Boathf 8tr««t$, and PavMMnU, hf Brt*. Mc^.-6«n'l ^. A. GUlmort, U. B. A,
t Talford Mtimated it at 3.5.
844
TBACnON.
On Paved and Rough Roads,
Resistance increases with speed, and is diminished hy an enlargement of
tire up to a moderate limit.
Traction on Various Roads. — Traction of a wheeled vehicle is to its weight
upon various roads as follows :
Per Ton.
Stone track, best 12.5 to 15
'♦ " 38 to 39
♦* pavemoDt. 14
Asphalted 22
Plank 22
Block stone )
pavement....) ^
to 36
to 28
to 45
to 35
Per zoo Ibe.
.55 to .58
1.25 to 1.3
•5 to 1-5
I to X.25
.98 to 2
1.4 to Z.6
Per Ten.
Telford road. ... 46 to 78
Macadamized... 4610 90
"'' loose 67 to Z12
Gravel......... 134 to 180
Sandy ^., 14010313
Earth 2cx> to 290
Per ISO lbs.
2. z to 3.5
3 to 4
3 to 5
6 to 8
6.3 to 14
9 to 13
Hence, a horse that can draw 140 Iba at a walk, can draw upon a gravel road
6-fB
z40-=-
X 100 = 2000 lbs.
Resistance on Common Roads or Fields.
{Bedford EzperimenUy 1874.*)
Oravillbd Road.
{Hard and dry^ rising i in 430.)
2 horse wagon without springs.
2 ♦♦ •' With "
z " cart without ''
Abablb Fikld.
{Hard and dry, rising i in locxx)
a horse wagon without springs.
a " ** with
z ** cart without
Mazl-
mum
Draft.
AT«rHr«
H»d«-
AT«r«iw
Dr«ft.
Speed
l£ar.
Teloped
Lb*.
Lta.
MUm.
W.
320
*59
a.5
Z.06
400
251
2.6
'•a
300
133
2.47
z8o
49-4
2.65
•35
zooo
700
a. 35
A.3tf
6.7
Z200
997
2.53
ZOOO
7ZO
2-35
4-45
400
2Z3
2.6z
z.4a
Draft per Tod
00 Level.
43.50r.oz93
44.5 " .02
34.7 " .ozs
28 '* .OZ35
axo
»94
2ZO
or
099
0625
Wofk
per(P
Ho%a.
IF.
•53
.87
•44
•35
a. 18
3-35
Z.23
Z.48
Fore wheels of wagons were 39 ina, and hind 57 ina in diam. ; tires varying fTooa
2.35 to 4 ina ; and wheels of cart were 54 ina in diam., and tires 3.5 and 4 ins.
Springs reduced resistance on road 20 per cent, but did not lessen it m the field.
From these data it appears, that on a hard road, resistance is only from 25 to . 16
of resistance in field. Lowest resistance is that of cart on road = 28 Iba per ton ;
due, no doubt, to absence of small wheels alike to those of the wagons.
Assuming average power without springs to be .6 H* on road, aa average for a
day^s woric, it represeuta .6 X 33000 = 19800 foot-lbs. per minute for power of a
horse on such a road.
Resistance of a smooth and welMaid granite track (tramway), alike to those id
London and on Commercial Road, in (Tom Z2.5 to Z3 lbs per ton.
Omnibus. t ( Weight 5758 Ibt.)
Average Speed per Hoar. Per Ton.
Granite pavement (courses 3 to 4 ina ) 2. 87 milea Z7.41. Iba
Asphalt roadway 3.56 " ^-^i
Wood pavement 3.34 '* 4Z.6
Macadam road, gravelly 3.45 '' 44-48
granite, new 3.51 " zoz,o9
ti
ii
(t
t(
Tout
44.75 Iba
69-75 "
106.88 "
ti
tc
ii4.3«
359-8
Note.— The resistance nqtad for an asphalt roadway is apparently incoDaisteni
with that for a granite pavement, for when it is properly constructed it is least
resistant of all pavements.
* Bh r*port in Enffi»t*rittg, Juif ro, Z874, pojf* 23.
t A^poK 8tc. ArU, Limde», 1879.
TKACTIOK. S4S
Wagon • (Sir Jckn MaeneU. )
Weight 2342 lbs. Speed 2.5 MiUi per Hour.
RMisUnce.
Per Ton. Total.
Well-made stone pavement 31.2 lbs 33 lb&
Road made with 6 in& of broken hard stone, on a foundation) «, ^ ^
of stones in pavement, or upon a bottom of concrete f ^^ ^
Old flint road, or a road made with a thick coating of broken I ^ ^ ^ «(
stone, on earth ) ^
Road nutde with a tbi<;k coating of gravel, on earth. 140 ** 147 "
Stage Coach.. (Sir Jofin Macneil.)
Weight 3192 lbs. Gradients 1 to 20 to doa
Speed. Metftlled Road.
At 6 miles per hour 62 lbs. per ton.
«t g it u ^^^ ^^ ...,,,....,...,, 73 *• "
«' 10 " '* .!..,! !!*.!!!.!!!!!!!!.!!!.!.!! 79 ** *'
Man. — It waa foand that, from ■oma anezplained caaM, tt\e net frictlonal reiittAnre at •QUtl apeeda
varied conaidarabiv, according to gradient, reaiatanoea being a maziniom for ateepeat gradient, and a
mlDiRinm for gradienta of t in 30 to i in 40 ; for theae they Are leaa than i In 600. Mom of action of
the boraea on the carriage may have been an inllueotial eleioeat. (J), K. Clark.)
To Compute Resist&uioe to "Praotion on Various Roads.
[Sir John Macneil.)
OH ▲ LEVEL.
Rule. — Divide weight of vehicle and load in lbs. by its unit in following
table, and to quotient add .025 of load ; add sum to product of velocity of
vehicle in feet per second, and Coefficient in following table for the particular
TtMid, and renult will give power required in lbs.
Or. — - - - -4- u> .025 4- C t> = T. W and w representing weights ofveliicle and load.
unit • -' ■ * w n, %
Coefficients Jor Traction of Various Vehicles.
Stagecoach 100
Heavy wagon 93
4 horse wagon without springs 55
2 horse wagon without springs 54
2 " " with " 42
1 ♦' cart without " 36
Coefficients for Roads of Various Construction.
Pavement 2
Broken stone, dry and clean 5
" " covered with dust.... 8
" *♦ muddy 10
Macadamized road 4.3
Gravel, clean 13
*' . muddy 32
Stone tramway 1.2
Sand and Gravel 12.1
iLLtTSTKATiON.— What is the traction or resistance of a stage coach weighing 2200
lbs., with a load of 1600 lbs., when driven at a velocity of 9 feet per second over a
dry and clean broken stone road?
2200 -|- 1600
100
+ 1600 X .025 + 5 X 9 = 123 H«.
7o Compute I'o'^ver neoe8sar3rto Sustain a Veliicle upon
AH Inclined H.oad, and also its Pressure tliereon, oniit>--
ting £fieatr or ITriotioxi.
AT AN INCLINATION.
W : A C :: o : B C, and W : A C :: p : A B.
Or, r « : « o :: A B : B C: W : e 0 :: I : h; whence,
Affiume A B of such a length that vertical rlsQ
B C =: I foot; then,
j^ = -- ^ -=W«iii A=o,aDd^^ = -^'^AJL^ = WcoB.A=|K
^^ VaB»4-i ^^ V^AB^^+i
r^
846 TRACTION.
Or, -7- = P; — ;— = 0; or, —3:^^ = P, and —3^:^:=:::: = 0. W ranresentina
Vfeighct ofvehicU and load o, and P power or force n/toettary to sustain load on road,
p pressure qfload on surface^ all in Ibs.j h height of plane, I inclined length of road
or plangy and I' horizontal lengthy ail in feet
Illustration. — Wbat is power required to sustain a carriage and its load, weigh-
ing 3800 lb&, upon a road, inclination of which is i in 35, and wbat la its pressure
upon road?
Sin. A ^ :o98 56. Cos. A =r .999 59. I = 35*0x4.
Then 3800 x .028 56=108.53 U>s.z=: power, and 3800 X .999 59=3798.44 lln. pressure-
To Compute litesistaxioe of* a X^oad 011 an. Inclined Road.
Rule. — Ascertain the tractive power required, and add to it the power
necessary to sustain load upon inclination, if load is to ascend, and subtract
it if to descend.
Example i.— In preceding example tractive power required is 123 lbs., and sus-
taining power for that inclination 108.53; beuce 123 + 108.53 = 331.53 lbs,
3. — If this load was to be drawn down a like elevation.
Then 123 -^ 108.53 = 14.47 ^''
7o Compute Po'^ver necessary to Alove and Sustain a
Veliiole eitlier A^scending or II>e8cending an li^levation,
and at a fciven Velocity, omitting Rfieot of ITriotion.
f — j^ + — \ COS. L T (W + w) sin. L. -f re = B. I. representing angle of
elevation for a stage wagon and a stage coach, and t units as preceding; upper sign
taken when vehicle descends the planCy and lower when it cucends.
Illustration.— Assume a stage coach to weigh 2060 lbs., added to which is a
load of 1 100 lbs., running at a speed of 9 feet per second over a broken stone road
covered with dust, and having an inclination of t in 30; what is power necessary
to move and sustain it up the inclination, and what down it ?
0 = 9, 0 = 8, sin. of L_ = sin. of i<^ 54'-|- T^ .0333, and cos. L. =3 .9995.
_, /2o6o-4-noo , iioo\ , — : ,
\ i^ "^ ~i^) ^ -9995+ (2060+ iioo) X .0333 + 8 X 9 = 5907 +
Z05.23 -|- 72 = 236.3 lbs. up inclination.
. . /2060 + 1 100 , 1 100\ , ; : .
\ 1^ ^ ~4o / ^ '^^^ + 8X9 — (2060 + iioo) X .0333 = 59.07 + 7«
•^ 105. 33 = 25. 84 Ws. down indination.
Tractive and Statical Resistance ofli^levations. {GiUmore.)
T
-- = flr'. T rqfn-esenUng traction in lbs per ton^ W vKight of load in Ibt..
and g^ grade of road.
Illustration. — Assume traction as per preceding table, page 844, 200, and weight
of vehicle 3 tons; wbat should be least grade of road?
200X2 I
=0897 = — +•
2 II
4480' — 200 X 2
Showing that, for a road upon which traction is 300 lbs. per ton, the grade should
not exceed one in height to one eleventh fall of base; hence, generally, the proper
grade of any description of road will be equal to force necessary to draw load upon
like road when level.
Practically, greatest grade of a Telford or Macadam ize<l road in good condition
= .05, and a horse can attain at a walk a required height upon this grade, without
more fatigue and in nearly same time that he would require to attain a like height
over a longer road with a grade of .033, that he could ascend at a trot.
For passenger traffic, grades should not exceed .033.
v:
TBACTIOH.
847
R*si«t«ziO« of* Oravitjr »t Different Inolinations of
O-raule. For a Load of 100 Lbs.
Grad«.
R
Grade.
Lbt.
1 in 5
19. 6z
I in 35
X in zo
9-95
I in 30
z in 15
6.65
X in3s
X m 20
4.99
z in 40
R
Lta.
4
3-33
2.85
2.5
Grade.
R •
Lb*.
1 10 45
2.22
I in 50
I in 55
z in6o
2
1.82
Z.67
Grade.
R
Lbe.
I in 70
I in 80
1.43
1.25
z m 90
z.zz
I in 100
z
Indination Of Roadt.^¥o^et of dradght at dilTerent inclinations and velocities
la as follows {Sir John MacneU) :
Inclination.
Angle.
Feet
per Mile.
z in 20
X in a6
X in 30
X in 40
X in 60
205a'
aO„'
1^55'
ZO26'
57.5'
264
903.4
176
Z32
88
Traction at Speed
• of per
Frictional Resistance per
Hour of
Ton at Speeds of per Hour oi
6 Miles.
8 Miles.
10 Miles.
6 Miles.
8 Miles.
10 Miles.
268
296
3x8
76
96
1X2
2Z3
2x9 .
225
63
68
7a
«65
X96
2O0
41
63
66
z6o
166
X72
56
6x
65
zzz
X20
128
72
78
8x
G-rade.
Grade of a road should be reduced to least of practicable attainment, and
aa a general rule should be as low as i in 33, and steepest grade that is ad-
missible on a broken stone road is i in 20.
The condition of traction Is /-f-siu. a L, which should not exceed F, and sin. a
p
should not exceed j f or/ f representing coefficient of friction, a angle ofin-
dinaiion^ L load, and P power in lbs.
Illustration.— In case, page 846, weight or load = 2060 -f- "00=3x60 lbs., Co-
efficient of friction for such a road = .042 pet xoo lbs., and sin. x° 54' = .033 x6.
Then .042 -|- .033 16 x 3160 = 237. 5 lbs.
Traction of a Vehicle compared to ite Weight on Diffei^ent Roads*
{F. Robertson, F. R. A. S.)
Stone pavement x in 68 I Flint foundation x in 34
Macadamized road z ** 49 | Gravel road z '' 15
Sandy road x in 7.
Assuming a horse to have a tractive force of X40 Iba continuously and steadily at
a walk, be can draw at a walk on a gravel road 15 x x 40= 2x00 lbs.
!F*rictioii of R^oads.
Friction of Roads. — According tp Babbage and others, a wagon and load
weighing 1000 lbs. requires a traction as follows :
Of Load.
Loose sand 25
fresh earth 125
Common side roads x
or Load.
Macadamized 033
Dry. high road 025
Well paved road 0x4
Railroad ( ^^SS
I 0059
Sled, bard snow, iron shod 033 of load.
Coefficients of Friction in Proportion to Load.
Gravelled road. { '^^S
067
Per 100 lbs. Per Ton.
Ontvel nmd, new 083 186
Oooimon road, bad order. . .07 Z57
Band road 063 Z4z
Broken stone, rutted 053 z 17
** " fair order... .028 63
*• " pertlBct order .0x5 34
tlAoadamized, new. ....... .045 zoz
*' 033 74
" gravelly 03 4^
^jirth, f ood ord^r. 0*$ ^6
Far zoo lbs.
Wood pavement 0Z9
Asphalt roadway oza
Stone pavement ozs
Granite '' 008
Stone '' very smooth .006
Plank road ot
««"»»y {-^
Stone track 05
P«rTon
4a
27
34
18
13
92
8
«3
zzs
848
TBACnON.
To Ooxnpxate Frlotlonal Reeistaxioe to TFraotlon of a
Stage Coaoli on a NLetalled Roa<l in. Grood Coxxdition.
30 -f 4 V -f- y/io o = R. V representing speed in miles per hour^ and R Jridionai
resistance to traction per ton.
NoTE.~Formula is applicable to wagons at low speeda
Canal, Slacfe^water, and. River,
On a canal and water, resistance to traction varies as square of velocity,
from that of 2 feet per second to that of 11. 5 feet.
When velocity is less than .33 miles per hour, resistance varies in a less
degree.
In towingf velocity is ordinarily i to 8.5 miles per hour.
Resistance of a boat in a canal depends very much upon the comparative
areas of transverse sections of it and boat, it being reduced as difference
increases.
In a mixed navigation of canal and slack-wat-er, 3 horses or strong mules
will tow a full-built, rough-bottomed canal boMi with an immersed sectional
area of 94.5 sq. feet, and a displacement of 240 tons, 1.75 to 2 miles per hour
for periods of 12 hours.
With a section of but 24.5 sq. feet, or a displacement of 65 tons, an aver-
age si)eed of 2.5 miles is attained for a like period.
By the observations of Mr. J. F. Smith, Engineer of the Schaylkill Navigation
Co., a canal boat, with un immersed section alike to that above given, can be towed
for 10 hours per day as follows:
Per Hour.
By I hone or
mule.
By 2 hones or
malea.
By 3 horaee or
moles.
By 4 hones or
males.
By 8 horses or
mules.
I mile.
X.5 miles.
1.75 miles.
Z.875 miles.
2.5 milea
Assuming then, the tractive power of a horse as given in table, page 437, the above
elements determine results as follows:
TrsctioD
Tractive Power
divided by Load.
Horses.
Miles.
I
250-
-240
1-5
165X2-
r 240
1-875
140X3-
r-240
132X3-
■-240
3
125X3-
r240
a- 5
100X3-
^ 65
in Lbs. per Ton.
in Lbs. per Sq. Foot of
immersed SecUon.
Z.04
2.65
1.38
3-49
X.7S
4-44
2.65
4.19
1.56
3.98
4.61
12.24
z
3
3
3
3 (iigbV); !;!!'.;!
Upon a canal of less section and depth, a displacement of Z05 tons, with v:n im-
mersed section of 43 sq. feet, a speed of 2 miles with 2 horses was readily obtained,
which would give a traction of 2.38 lbs. per ton, and of 5. 72 lbs. per sq. foot of im-
mersed section.
Alaximuzxz Powex* of a Horse on a Canal. (MoUtworfk.)
33-545678 9
Miles per hour 2.5
Duration of work in
hours
10
•IS
6.5
ZZ.5 8 5.9 4.5 2.9 2 z.5 X.X35 .9
Load drawn in tons '. . 520 243 Z53 zo2 52 30 19 13 9
Street Railroads or Trazn^vays. (OtnH QiUmcTt.^)
Upon a level road, and at a speed of 5 miles per hour, the power required to dran
a car and its load is firom -^^ to -m^ of total weight, varying with condition of
rails and dryness or moisture of their surface.
* TreatiM on Roads. Streets, and Pavemento. D. Van Nostrand, 18761 K. T.
TBACTION. — WATEJB.
T*o Compute ReBistaxice of* a Car,
849
T V ti ft' ^^ it.
TX6=/; = c; =r; and /+c4-r = R. T representing toeighi
<« Um$. /friction tn Ite., « speed tn miie< ji«r ibour, a area qfjront or section of ear
Ml sq.fiutf c coneuttiony r resistance of atmosphere, and R total resistance, all in lbs.
iLLnsTRATiov.— Assume a car and load of 8960 lbs., with an area of section of 56
sq. feet, and a speed of 5 miles per hour.
Then -5^ = 4 tons; 4X6 = 24 lbs. friction ; 1^=6.66 lbs. concussion:
2240 ^ -^ ' 3
5 5- = 3. 5 Ibt. retistance of air ; and 24 + 6.66 + 3. 5 = 34. 16 Ths.
400
In average condition of a road, the resistance of a car may be taken at -j^, which,
in preceding case, would be 74.66 lb& On a descending grade, therefore, of i in
74 66, the application of a brake would not be required.
WATER.
Fresh Water. Constitution of it by weight and measure is
By Weight. By MeMON. { By Weifcbt. By MaMUV.
Oxygen... 88.9 i | Hydrogen., ii.i 2
Cube inch of distilled water at its maximum density of 39.1°, barom-
eter at 30 ins., weighs 252.879 grains, and it is 772.708 times heavier
than atmospheric air.
Cube foot (at 39.1^) weighs 998.8 ounces, or 62.425 lbs.
Note. — Yor facility of computation, weight of a cube foot of water ia
asually taken at 1000 ounces and 62.5 lbs.
At a temperature of 32° it weighs 62.418 lbs., at 62° (standard tem-
perature) 62.355 lbs., and at 212° 59.64 lbs. Below 39.1° its density
decreases, at first very slow, but progressing rapidly to point of conge-
lation, weight of a cube foot of ice being but 57.5 lbs.
Its weight as compared with sea-water is nearly as 39 to 40.
It expands .085 53 its volume in freezing. From 40° to 12° it ex-
pands .00236 its volume, and from 40^ to 212° it expands .0467—
times = .000 27 1 5 for each degree, giving an increase in volume of i
cube foot in 21.41 feet
Volumes, Heielit, and. Pressure or Pure >Vater.
Cnb« Ids. FMt.
At 32° 27.684 = 2.307 \ 1 Lb.
** 39-1° «7.68 = 2.3067 f_. Pressure
•* 62° 27.712 = 2.3093 i" per
•« 212° 28.978 = 2.4148 ) sq. inch.
At 62° 1 Ton = 35.923 cube feet
" " I Lb. =27.71 " ina.
" 39.1° I Tonneau = 35.3156 " feet.
" " 1 Kilogr. = 0353 " "
H^gfU of a Column of Water at 62° or 62.355 Ibt.
I lb. per sq. inch = 2. 3093 feet, and at pressure of atmosphere = 33.947 feet =
«X347 meCen.
loe and Snoi^.
Cube foot of Ice at 32° weighs 57.5 lbs., and i lb. has a ydume of
30^067 cube ins.
Volume of water at 32**, compared with ice at 32®, is as i to 1.085 53, ««-
ponsion being 8.553 per cent
Cube foot of new fallen snow weighs 5.2 lbs., and it has 12 times bulk of
water.
850
WATBB.
if^ainfkll.
Annuai Fall at different Places,
LocAnoH.
Alabama
Albany
Algiers
Alleghany
Antigua
Archangel
Aiibarn
B<ahamas
Bi Jtimore
Barbadoes
B^th, Me
Belfast
Biskra
Bombay
Bordeaux
Boston
Brussels
Buflalo
Burlington, Vt
Calcutta
Cape St. Francois. .
CajieTown
Cbarloston
Cherbourg
Cologne
Copenhagen
Cracow
Demerara
" 1849
DDver (EngL)
Dublin
DumfVies
East Hampton . . . .
Edinburgh |
Fairfield
Ins.
30-17
4«-35
7-75
46.66
45
14-52
30-17
42.19
39-9
55-87
3458
39-46
.2
no
29.7
39-23
29
27.27
32
81
150
23-31
54
39-7
24
23
13-33
91.2
132.21
37-52
30.87
36.92
3852
24-5
29
3293
LocATtoir.
Ft. Crawford, Wis..
Ft Gibson, Ark
Ft. Snelling, Iowa.
Fortr. Monroe, Va..
Florence
Frankfort, Oder...
^' Main...
Geneva
Gibraltar.
.i
Glasgow
Gordon Castle, Sc
Granada |
Great Britain
Greenock
Halifax
Hanover
Havana
Hongkong » .
Hudson
India.
Jamaica
Jerusalem
Kefy West
Khassaya, India. . .
Lewistbn
Liverpool
London , .
Louisiana
Madeira
Manchester
Marseilles. . .
Int.
2954
30.64
30.32
52.53
35-9
21.3
16.4
32.6
47.29
21.3
31
293
105
126
32
61.8
33
22.4
52
81.35
J9-32
130
34-31
65
34-39
610
23-15
3412
25.2
5J.85
22
36.14
43
18.2
Locmow.
Michigan
Mississippi
Mobile, 1842
Naples
Newburg.
New York
Ohio
Palermo
Fari&....,
Philadelphia
Plymouth (Kngl.)..
Port Philip
Poughkeepsie
Providence.
Rochester.
Rome
Santa Fe.
Savannah
Schenectady
Siberia
Sierra Leone
Sitka
St. Bernard .....<.
St, Domingo
St. Petersburg
State of N.Y
Sydney
I^mania
Trieste
Ultra MuUay, India
Utica
Venice
Vera Cruz
Vienna
Washington
West Point
33-5
45
54-94
41.8
40.5
36
36
23.8
23. z
49
44
29.16
32.06
36.74
29
39
74.8
55
47-77
7-75
84
85-79
48
120
17.6
33-79
49
35
46.4
263.21
39-3
34-1
62
r9.6
34- 6«
48.7
Average rainfall in England for a number of years was, South and East, 34 ins.;
West aud hilly, 43.02 to 50 Ins., and percolation of it was estimated at 30 per ceut.
Mean volume of water in a cube foot of air in England is 3.789 gnxins. .
Globe, mean depth 36 ins.
Cape of Good Hope in 1846 T in 3 hours. 6.2
At Khasdaya, in 6 rainy months 550 ins. ; in i day, 25. 5
JEvaporation. — Mean daily evaporation, in India .^ inch; greatest .56; in Eng-
land .08. At Dijon, when mean depth of rainftill was 26-9 ins. in 7 years, evapora-
tion was for a like period 26.1 ins., and in Lancashire, Eng., when full was 45.96
ins., evaporation was 25.65.
Voluirie of R,ainfall.
Bainfall, depth in ins. , X 2 323 200 = cube feet per sq. mile.
X 17. 378 74 =: tniiliont of gallons per sq. mila
X 3630 = cube feet per acre.
X 27 154-3 =& gaUoQs per acre.
Mineral Waters are divided into 5 groups, viz. :
1. Carbonated, containing pure Carbonic acid — as, Seltzer, Germany; Spa, Bel-
gium ; Pyrmont, Westphalia; Seidlitz, Bohemia; and Sweet Springs, Virginia.
2. Sulphurous, containing Sulphuretted hydrogen— as, Harrowg<Ue and Chelten-
ham, England; Aix-la-Chapelle, Prussia; Blue Lick, Ky. ; Sulphur Springs, Va,, etc
3. AlKaliqe, coatalning Carbonate of soda— these are rare, as, Vichy, Emg.
t(
l(
11
ti
(t
t»
i(
(I
((
WATEB.
851
4. Chalybeole, oontaining Carbonate of iroB-^as, Hampsteod, Tunbrldge, Chelten-
ham, and Brighton, England; Spa, Belgium; Ballston and Saratoga, N. Y. ; and
Bedford, Penn. *
5. Saline, containing salts — as, Epsom, Cheltenham, and Bath, England; Baden-
Baden aud Seltzer, Germany; Kissingen, Bavaria; Plombiiiree, France; Seidlitz,
Bohemia - Lucca, Italy ; Yellow Springs, Ohio; Warm Springs, N. C. ; Congress
Springs, N. Y. ; and Grenville, Ky.
Brief Rules for Qualitative Analysis of Mineral Waters,
First point to be determined, in examination of a mineral water, is to which of
above classes does water in question belong.
1. If water reddens blue litmus paper before boiling, but not afterwards, and blue
color of reddened paper is restored upon warming, it is Carbonated.
2. If it possesses a nauseous odor, and gives a black precipitate, with acetate of
lead, it is Sulphurous.
3. If, after addition of a few drops of hydrochloric acid, it gives a blue precipitate,
with yellow or red prussiate of potash, WHt«r is a Chalybeate.
4. If it restores blue color to litmus paper after boiling, it is Alkaline.
5. If it possesses neither of above properties in a marked degree, and leaves a
Wge residue upon evaporation, it is a Saline water.
River or canal water contains .05 1 ^ u ^i ^ ^ ».*.
Spring or well water " .07 j °* *** '"'"™* "^ 8"^"" """*"■•
R,e*ageiit8«
When water is pure it will not become turbid, or prodace a precipitate
with any of following Re-agents:
Baryta Water^ if a preripitiite or opaqueness appear. Carbonic Acid is present.
Chloride of Barium indicates Sulphates, Nitrate of Silver^ Chlorides, and Oxalate
of Ammonia, Lime salts. Sulphide of Hydrogen, slightly acid, Antimony, Arsenic,
Tin^ Copper, Gold, Platinum, Mercury, Silver, Lead^ Bismuth, and Cadmium; Sul-
phide of Ammonium, solution alkaloid by ammonia. Nickel, Cobalt, Manganese,
Iron, Zinc, Alumina, and Chromium. Chloride of Mercury or Gold and Sulphate of
Zinc, organic matter.
ITilter I3eds.
Fine sand, 2 feet 6 ins. ; Coarse sand, 6 ins. ; Clean shells, 6 ina , and Clean gravel
2 feet, will filter 700 gallons water in 24 hours per square foot, by gravitation.
Sea Water. Composition of it per volume :
Chloride of Sodium (common salt).. 3.51
Sulphurct of Magnesium 53
Chloride of '* 33
02
Carbonate of Lime )
" of Magnesia )
Sulphate of Lime 01
Water. 96.6
By analysis o£ Dr. Murray, at specific gravity of 1.0291, it contains
Muriate of Soda a^aoi I Muriate of Magnesia 42.08
Sulphate of Soda 33- 16 | Muriate of Lime 7.84
Or, I part contains .030 309 parts of salt x= ^ part of its weight
Mean volume of solid matter in solution is 3.4 per cent., .75 of which is
common salt.
Soiling Points at Different Degrees, of Saturation.
Sftit, by Weight,
in 100 ParU.
3-03 = A
6.06 = A
"•"-A
Boilinf?
Point.
2x3. 2^^
214. 4«
216.7^
Salt, by WelRbt,
in 100 Parta.
'5- 15 = /if
i8.i8 = A
21.22 = ^
24.25= A
Boiling
Point.
217.9"^
2x9°
220.2^
221.4^
Salt, by Weijfht,
in 100 Parts.
«7-28 = A
30.31 =J4
33.34 = H
♦36.37 =H
Boiling
Point.
222.5^
223.7^
234.9^
3360
852 WATER. — WAVES OP THE SEA.
De]^o«ita at Difierent IDefirrees of Saturation and Vein
peratvire.
When 1000 Parts are reduced by Evaporation,
Yolam* of Water.
Boiling Point.
Salt in xoo ParU.
Natura of DepodL
1000
"99
X02
2X4°
217O
228O
3
xo
29.5
None.
Sulphate of Lima
Common Salt
It contains from 4 to 5.3 ounces ol salt in a gallon of water.
SaUne ConterUt of Water /rom tetteraL Localities.
Baltic...... ^.6
Black Sea 21.6
Arctic 28.3
South Atlantic 41 a
North Atlantic . . . . , 43.6
Dead Sea. 385
British Channel.... 35.5
Mediterranean 39.4
Equator 39-42
There are 62 volume? "f carbonic acid in xooo of sea- water.
Cube foot "* 62^ weighs 64 lbs. Its weiglit compared with fresh water
being very nearly as 40 to 39.
Height of a Column of Water at 60° or 64.3x25 lbs.
At 62°, X Ton = 35 cube feet x Lb. per sq. inch = 2.239 ^^^y ^°^ ^^ pressure of
atmosphere = 32.966 feet = xao48 metera
■WeiglitB.
A ton of Aresh water is taken at 36, and one of salt at 35 cube feet
WAVES OP THE SEA.
Arnott estimated extreme height of the waves of an ocean, at a distance
ftom land sufficiently great to be freed from any inflaence of it upon their
culmination, to be 20 feeL
French Exploring Expedition computed waves of the Pacific to be 22. feet
in height
By observations of Mr. Douglass in 1853, he deduced that when waves had
heights of
8 feet, there were 35 in number in one mile, and 8 per minnta
x5 " " sand 6 " " 5 "
20 " " 3 " " 4 "
J. Scott Russell divides waves into 2 classes — viz. :
Waves of Translation, or of ist order ; of Oscillation, or of 2d order.
"^^aves of the B^irst Order.
1. Velocity not affected by intensity of the generating impulse.
2. Motion of the particles always forward in same direction as wave, and
same at bottom as at surface.
3. Character of wave, a prolate cycloid, in long waves, approaching a true
cycloid. When height is more than one third cl length, the wave breaks.
JATavett of the Seooncl Order.
1. Ordinary sea waves are waves of second order, but become waves of the
first Older as they enter shallow water.
2. Power of destruction directly proportional to height of wave, and great-
est when crest breaks.
3. A wave of 10 feet in height and 32 feet in length would only agitate
the water 6 ins. at 10 feet below surface ; a wave of like hei^t ana 100 feet
in length would only disturb the water 18 ins. at same depth.
Average force of waves of Atlantic Ocean during summer months, as de«
termined by Thomas Stevenson^ was 611 lbs. per sq. foot; and for winter
months ao86 lbs. During a heavy gale a force of 6983 ll». was observed.
Wi.ySS OS* TBB SEA.
8S3
Jl Scott Russell deduced tbat a wave 30 feet in height exerts a force of i
Con per sq. foot, and that, in an exposed position in deep water, 1.75 tons
may be exerted upon a yertieal surface.
At Cassis, France, when the water is deep outside, blocks of 15 cube me-
ters were found insufficient to resist the action of waves.
Breakwaters with vertical walls, or faces of an angle less than i to i, will
rdiect waves without breaking them. Waves of oscillation have no effect
on small stones at 22 feet below the surface, or on stones from 1.5 to 3 feet,
12 feet below surface.
A roller 20 feet high will exert a force of about i ton per sq. foot.
Greatest force observed at Skerryvore, 3 tons per sq. foot ; at Bell Rock,
1.5 tons per sq. foot.
Waves of the second order, when reflected, will produce no effect at a depth
of 12 feet below surface.
Action of waves is most destructive at low^water line.
Waves of first order are nearly as powerful at a great depth as at sui&oe
To' Compute Velocity,
When I is less Gian d. .55 y/l or 1.818 y/l = V.
When I exceeds 1000 d. V32.17 <i= V, and When Height of Wave becojnes a sen-
sible Proportion to Depths yj z^- ^7 (' + 3 ~i) = ^•
Xo Ooxnp-ute Keiglit of AVaves in Reservoirs, etc.
I. sv'L -|- (2- 5 — V^^) = ^^9^ »»> f^^f- L representing length of Reservoir ^ Pundf
etc, ccpoMd to direction of windy in miles.
Tidal Waves.
Wave produced by action of sun and moon is termed Free Tide Wave,
Semi-diurnal tide wave is this, and has a period of 12 hours 24 -|- minutes.
Professor Airy declared that when length of a wave was not greater than
depth of the water, its velocity depended only upon its length, and was pro-
portionate to square root of its length.
When length of a wave is not less than 1000 times depth of water, velocity of it
depends only upon depth, and is proiiortionate to square root of it; velocity being
same that a body &Uing free would acquire by falling through a height equal to half
depth of water.
For intermediate proportions, velocity can be obtained by a general equation.
Under no circumstances does an unbroken wave exceed 30 or 40 feet iu height
A wave breaks when its height above general level of water is equal to general
depth of it
Diurnal and other tidal waves, so far as they are fVee, may be all considered ag
ruDDing with the same velocity, but the column of the length of wave must be
doubled for diurnal wave.
XjmgCti of Wave.
Depth of WaUr.
F««t.
I
FMt.
xo
FMt. FMt.
lOQ 1000
FMt.
10 000
FMt.
100 000
-
Velocity per SMond.
Faet.
FMt.
Faet
FMt.
FMt
FMt.
FMt.
I
a. 26
5-34
5-67
—
—
—
10
3.d6
7«5
z6.88
17.9a
»7-93
—
100
— .
7»5
22. 6a
53- 19
fS-S^
56.71
aooo
«.
32.6a
7»-54
168.83
179.31
lOOOO
-«•
—
—
71-54
aa6.94
533-9
40
854 WHfiSL GJEASma
WHEEL GEARINa
Pitch Line of a wheel is circle upon which pitch is measured, and it
is circumference by wiilch diameter, or velocity of wheel, is measured.
Pitch is arc of circle of pitch line, is determined by number of teeth
in wheel, and necessarily an aliquot part of pitch Una
True or Chordial Pitch, or that by which dimensions of tooth of a
wheel are alone determined, is a straight line drawn from centres of
two contiguous teeth upon pitch line.
Line of Centres is line between centres of two wheels.
Radius of a wheel is semi - diameter bounded by periphery of the
teeth. Pitch Jtadivs is semi-diameter bounded by pitch line.
Length of a Tooth is distance from its base to its extremity.
Breadth of a Tooth is length of face of wheel.
Depth of a Tooth is thiclt ness from face to face at pitch line.
Face #/ a Tooth, or Addendum, is that part of its side which extends
from its pitch line to its top or Addendum line.
Flank of a Tooth is that part of its side which extends from pitch
line to line of space at base of and between adjacent teeth ; its length,
as well as that of face of tooth, is measured in direction of radius of
wheel, and is a little greater than face of tooth, to admit of clearance
between end of tooth and periphery of rim of wheel or rack.
Cog Wheel is general term for a wheel having a number of cogs or teeth set in or
upon, or radiating from, its circumference.
Mortice Wheel is a wheel constructed for reception of teeth or cogs, which ar9
fitted into recesses er sockets upoja fac^ of the whe«L
PliUe Wheels are wheels without arms.
Rack is a series of teeth set in a plane.
Sector is a wheel which reciprocates without forming a full revolution.
Spur Wheel is a wheel having its teeth perpendicular to its axia
Bevel Wheel is a wheel having its teeth at an angle with its axia
Croum Wheel is a wheel having its teeth at a right angle with its axia
. Mitre Wheel is a wheel having its ieeth at an angle of 450 with its axia
Face Wheel is a wheel having its t6eth set upon one of its sides.
Annular or Internal Wheel is a wheel having its teeth convergent to its centre.
Spur Gear. — Wheels which act upon each other in same plane.
Bevel Gear —Wheels which act upon each other at an angle.
Inside Gear or IHn Gearing. — Form of acting surfaces of teeth for a pitcb-cirGle
in inside gearing is exactly same with those suited for same pitch-circle in outside
gearing, but relative position of teeth, spaces, and flanks are reversed, and adden-
dum-circle is of less radius than pitch-circle.
A Train is a series of wheels in connection with each other, and consists of a
series of axles, each having on it two wheels, one is driven by a wheel on a preced-
ing axis and other drives a wheel on following axia
Idle Wh^el.—A wheel revolving upon an axis, which receives motion ftrom a pro.
ceding wheel and gives motion tQ a following wheel, used only to affect direction of
motion.
Trundle, Lantern, or WaMower is when teeth of a piniob are constructed of round
bars or solid cylinders set into two disks. Trundle with less than eight staves can-
not be operated uniformly by a wheel with any number of teeth.
Spur, Driver, or Leader is (erm for ft wbeej tbat impels another: one impelled ia
Pinion, Driven, or FoUotuer. -
Teeth of wheels shoald be as enuUl and nnmerouB as is consistent with
strength.
When a Pinion is driven by a wheel, number of teeth in pinion should not
be less than 8.
When a Wheel is driven by a pinion^ number of teeth in pinion should not
be less than lo.
When 2 wheels act upon one aootber, greater is termed Whul and lesser Pi$non.
When the tooth of a wheel is made of a material different from that of wheel it is
termed a Cog; in a pinion it is termed a Leaf, in a trundle a Stave, and on a disfc
a Pin.
Material of which co^ are made is about one fourth strength of cast iron.
Hence, product of their bd^ should be 4 times that of iron teeth.
Number of teeth in a wheel should always be prime to number of pinion ;
that is, number of teeth in wheel should not be divisible by number of teeth
in pinion without a remainder. This is in order to prevent the same teeth
^coming together so often and uniformhf as to cause an irregular w€Ar of their
faces. An odd tooth introduced into a wheel is termed a Hunting tooth or Cog.
The least number of teeth thai it is practicable to give to a wheel is regu-
lated by necessity of having at least one pair always in action, in order to
provide for the contingency of a tooth breaking; and least number that can
be employed in pinions having teeth of following classes is : Involute, 25 ;
Epicycloidal, 12 ; Staves or Pins, 6.
Velocity Ratio in a Train of Wkeels.^-To attain it with least number of
teeth, it should, in each elementary combination, approximate as near as
practicable to 3.59. A convenient practical rule is a range from 3 to 6.
IlxusraATiON. I 6 36 216 1396 velocity ratio.
z 2 3 4 elementary combinaiion.
To increase or diminish velocity in a given proportion, and with least
quantity of wheel-work, number of teeth in each pinion should be to number
of teeth in its wheel as i : 3.59. Even to save space and expense, ratio
should never exceed i : 6. {Buchanan.)
To Compute Pltoli.
RuLS.-^ Divide circumference at pitch-line by number of teeth.
ExAMPLS.— A wheel 40 ins. in diameter requires 75 teeth; what is its pitch f
3.1416 X 4o-i-75 = 16755 ins.
To Compixte True or Clxordial Pitch.
RuiJt. — Divide 180° by number of teeth, ascertain sine of quotient, and
multiply it by diameter of wheel.
EzAMPLB. — Number of teeth 18*75, and diameter 40 ins. ; what is true pitch?
i8o-f- 75 = 2° 24', and Bin. of 2° 24' = .041 88, which X 40 = 16752 ins.
To Cozxipute Diameter.
Rt7LE. — Multiply number of teeth by pitch, and divide product by 3.1416.
Example. —Number of teeth in a wheel is 75, and pitch 1.6755 ins. ; what is di.
' meter of it? ^g ^ 1.6755 -r- 3. 1416 = 40 ins.
When the True Pitch is given, Ruul— Multiply number of teeth in wheel
by true pitch, and again by .3184.
. EzAXPLB.— Take elements of preceding case.
75 X 1.675a X .3184 =» 40 ins.
Or, Divide 180° by number of teeth, and multiply cosecant of quotient by
pitch.
i8o-i- 75 = aio 24', and coa 2^ 24' = 23.88, which X 1.675a = 40 *^
856 WHEEL 6EABIN6.
To Compute Nxaca.\>eir of Teetlu
Rule. — Divide circumference by pitch.
To Coxupute r^umber of Teeth in a Pixxion or ITollO'^^ev
to b.ave a given Velocity.
Rule. — Multiply velocity of driver by its number of teeth, and divide
product by velocity of driven.
EXAMPLK I.— Velocity of a driver is 16 revolutions, number of its teeth 54, and
velocity of pinion is 48 ; what is number of its teeth ?
16X54-5-48=18 teeth.
3.— A wheel having 75 teeth is making 16 revolutions per minute; what is num-
ber of teeth required in pinion to make 24 revolutions in same time?
16 X 75 -j- 24 = 50 ^«**-
To Compute Proportional Radius of a "Wlieel'or Pinion.
Rule.— Multiply length of line of centres by number of teeth in wheel,
for wheel, and in pinion, for pinion, and divide by number of teeth in both
wheel and pinion.
ExAMPLK.— Line of centres of a wheel and pinion is 36 in&, and number of teeth
in wheel is 60, and In pinion x8; what are their radii?
|^^ = 27.69 in*. to*«J. ^^ = 8.z int. pinion.
60+18 ' ^ 6o-|-x8
To Compute IDiameter of a Pinion.
When Diameter of Wheel find Number of Teeth in Wheel cmd Pinion cere
given. Rule. — Multiply diameter of wheel by number of teeth in pinion,
and divide product by number of teeth in wheel
EzAXPLB.— Diameter of a wheel is 25 in&, number of its teeth 210, and number
of teeth in pinion 30; what is diameter of pinion?
25 X 30-7- 210 = 3.57 ins.
To Compute dumber of Teeth required in a Train ot
TViieels to produce a g;iven Velooitjr.
Rule. — Multiply number of teeth in driver by its number of revolutions,
and divide product by number of revoluticms of each pinion, for each driver
and pinion.
ExAMPi,!.— If a driver in a train of three wheels has 90 teeth, and makes 2 revo-
lutions, and velocities required are 2, xo, and x8, what are number of teeth in each
of other two?
xo : 90 :: 2 : x8 =: teeth in ad wheel. x8 : 90 :: 2 : xo = teeth in yi wheel
To Compute Velocity of a Pinion.
Rule. — Divide diameter, circumference, or number of teeth in driver, as
case may be, by diameter, etc., of pinion.
When there are a Series or Train of Wheels and Pinionit. Rule. — Divide
continued product of diameter, circumference, or number of teeth in wheels
by continued product of diameter, etc., of pinions.
Example i —Tf a wheel of 32 teeth drives a pinion of 10, npoD axis of which there
Is one of 30 teeth, driving a pinion of 8, what are revolutions of last?
— X ^ = ^ = la revolutions.
10 8 80
2. — Diameters of a train of wheels are 6, 9, 9, xo, and 12 ina ; of pinions, 6, 6, 6, 6,
and 6 ins. ; and number of revolutions of driving shaft or prime mover is xo; what
are revolutions of last pinion ?
1><_9_X_9X 10 Xj2^Xjo_ 583200 _^^^^^
6X6X6X6X6 l^^^*'*^"**^
WHESL OBABINO.
857
To Compute Proportion that 'Velocities of* 'Wh^ls iu
a Xraiu slxould 'bear to oue another.
Rule. — Subtract less velocity from greater, aud divide remainder by one
less than number of wheels in train ; quotient is number, rising in arithmet-
ical progression from less to greater velocity.
EXAMPLK.-— What should be velocities of 3 wheels to produce 18 revolutioos, the
driver making 3?
__ — = 7.5 = number to be added to velocity of driver = 7. 5 + 3 = 10. 5, and
'o^S + 7-5 = >8 revolutiong. Hence 3, 10. 5, and 18 are velocities of three toheeh.
I»itoh of TVlieels.
^o Ooxnpute Diameter of a Wheel for a given Pitoli,
or :Pitoh fbr a given Diameter.
From 8 to 192 Teeth.
No. of
Diame-
No. of
Diama-
TMth.
ter.
Teeth.
tor.
8
2.61
45
14.33
9
2.93
46
14.65
10
3'24
47
14.97
II
3-55
48
15.29
12
3-86
49
15.61
13
4.18
SO
15.93
14
4.49
51
16.24
15
4.81
52
16.56
16
5-12
53
16.88
17
5-44
54
17.2
18
5-76
55
17.52
19
6.07
56
17,8
90
6-39
57
18.15
21
6.71
58
18.47
22
703
59
18.79
23
7.34
60
I9.II
24
7.66
61
1942
ss
7.98
62
19.74
26
8.3
63
20.06
27
8.61
64
20.38
28
8.93
6S
20.7
29
9-25
66
21.02
30
9-57
67
21.33
31
9.88
68
21.65 1
32
10.2
69
21.97 1
33
10.52
70
22.29 ;
34
10.84
71
22.61
35
II. 16
72
22.92
36
11.47
73
23.24
37
11.79
74
23.56
38
12. II
75
23.88
39
12-43
76
24.2
40
I2.t4
77
24.52
41
13-06
78
24.83
42
13.38
79
2515
43
137
80
2547
44
14.02
81
25.79
No. of
Diame-
1 No. of
Diame-
Teeth.
ter.
Teeth.
ter.
82
26.11
1 "9
37.88
83
26.43
1 120
38.2
84
26.74
121
38.52
85.
27.06
122
38.84
86
27.38
123
39.16
87
27.7
124
39-47
88
28.02
125
39-79
89
28.33
126
40.11
90
28.65
127
40.43
91
28.97
128
40.75
92
29.29
129
41.07
93
29.61
130
41.38
94
29^3
»3i
41.7
95
30.24
132
42.02
96
30-56
133
42.34
97
30.88
134
42.66
98
31.2
135
42.98
99
31.52
136
4329
100
31.84
137
43.61
1 lOI
32.15
138
43-93
102
3247
«39
44-25
103
32.79
140
44-57
104
3311
141
44.88
105
33.43
142
45.2
106
33-74
143
45.52
107
34.06
144
4584
108
34.38
145
46.16
109
34.7
146
46.48
no
35.02
147
46.79
III
35-34
148
47.11
112
3565
149
47-43
"3
35-97
150
47-75
1 "4
36.29
151
48.07
"5
36.61
152
48.39
116
36.93
153
48.7
117
37.25
' 154
49-02
118
37.56
155 '
49-34
No. of
I'eeth.
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
»75
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
Pitch In this table is true pitch, as before described.
1?o Compute Cirouxnferenoe of a "Wheel*
Bulk. — Multiply number of teetb by their pitch.
4C*
Diame-
ter.
49.66
49-98
50.3
50.61
50.93
51-25
51.57
51.89
52.21
52.52
52.84
53- »6
53-48
53.8
54-12
54-43
54-75
55-07
55-39
55-71
56.02
56.34
56.66
56.98
57-23
57-62
57-93
58.25
5857
58.89
59-21
59-53
5984
60.16
60.48
60.81
61.13
858 WHBBL GEABING.
Xo ^onapute Revolvitloixa of* a '\Vb.eel or Pinion.
RuLU. — Multiply diameter or circumference of wheel or number of its
teeth in Ins., as case may be, by number of its revolutions, and divide prod-
uct by diameter, circumference, or number of teeth in pinion.
ExAXPLK.— A pinion 10 ins. in diameter is driven by a wheel a foet in diameter,
making 46 revolutions per minate; what is number of revolutions of pinion t
2 X 12 X 46 -t- 10 = 1Z0.4 revoltUums.
To Compute dumber oi* GTeetli. of a "^^heel for a gi-vewk
IDiameter and Pitoli.
Rule. — Divide diameter by pitch, and opposite to quotient in preceding
table is given number of teeth.
EiAMPLB.-^Diam. of wheel is 40 ins., and pitch 1.675; what is number of its teeth?
40 -r- 1.675 = 23.88, and opposite thereto in table is 75 =3 number 0/ teeth.
To Compute Diameter of a "Wlieel for a given I*itclx and
JS'vimber of ITeetli.
Rule. — Multiply diameter in precetling table for number of teeth by
pitch, and product will give diameter at pitch circle.
Example.— What is diameter of a wheel to contain 48 teeth of 2.5 Ins. pitch?
1 5. 29 X 2. 5 = 38. 225 »'♦»*•
To Compute Pitoli of a "^Vlieei fbr a giveii Dian&eter and
Number of Teetli. '
Rule. — Divide diameter of wheel by diameter in table for number of
teeth, and quotient will give pitch.
ExAMPLB.— What is pitch of a wheel when diameter of it is 50.94 ina, and num-
ber of its teeth 80? ^^^^ ^ 25.^7 _, ^ ,,„.
G-eneral Illustratioia,8.
z.— A wheel 96 ins. in diameter, making 42 revolutions per minute, is to drive 0
shaft 75 revolutions per minute; what should he diameter of pinion?
96 X 42-^75 = 53" 76 »«*
2.— If a pinion is to make 20 revolutions per minate, required diameter of an-
other to muke 58 revolutions in same time.
58 -7- 20 = 2.9 = ratio of their diameters. Hence, if one to make 20 revolutions is
given a diameter of 30 ins., other wilt be 30-7-2.9 = 10.345 *'^'-
3.— Required diameter of e pinion to make 12.5 revolutions in same time as one
of 32 ins. diameter making 26. .
32 X 26-1-12.5 = 66.56 iriM.
4.— A shaft, having 22 revolutions per minate, is to drive another shaft at rate
of 15, distance between two shafts upon line of centres is 45 in& ; what should be
diameter of wheels ?
Then, ist. 22 -f 15 : 22 :: 45 : 26.75 stru. in radius of pinion.
2d. 22 4-15 ' '5 ''- 45 ' i8.24 = tn«. in radius of spur.
5.~A driving shaa, having 16 revolutions per minute, is to drive a shaft 81 revo-
lutions per miuut«, motion to be communicated by two geared wheels and two pul-
leys, with an intermediate shaft; driviag wheel is to contain 54 teeth, and driving
pulley upon driven shaft is to be 25 ins in diameter; required number of teeth in
driven wheel, and diameter of driven pulley.
Let driven wheel have a velocity of V16 x 81 = 36, a mean proportional between
extreme velocities 16 and 81.
Then, ist 36 : 16 :: 54 : 24 = teeth in driven tohe^
2d. 81 : 36 : : 25 : II. II = ins. diameter of driven pulley.
6.— If, as in preceding case, whole number of revolutions of driving shaft, num-
l>er of teeth in its wheel, and diameters of pulleys are given, what are revolutiona
of shafts?
Then, ist 18 : 16 :: 54 : 4S ^rewkUions of intermediate thafL
34. 15 : 48 :: 45 : ^^rwokUions of driven «^ft.
WBBBI. GBABINa— T££TH OS WUtiBLS.
859
Q?eetli of "^^Hieels.
Kpiosroloidal. — In order that teeth of wheels and pinions should work
evenly and without unnecessary rubbing friction, the face (J'l-am pitch litte
to top) of the outline should be determined by an epicycloidal curve (see
page 228), and that of the dank {from pitch line to base) by an hypocycloidal
(see also page 228).
When generating circle is equal to half diameter of pitch circle, hypocy-
cloidal described by it is a strai;;ht diametrical line, and consequently out-
line of a flank is a right line, and radial to centre of wheel
If a like generating circle is used to describe face of a tooth of other wheel
or pinion respectively, the wheel and pinion will operate evenly.
Illustration.— Determmo all elements of wheel
—viz., Pitch circle, Number of teeth, Pitch, Length,
Face, and Flauk.
Cut a template A to pitch circle c c of wheel, and
secure it temporarily to a board.
Having determined depth of tooth, set it off on
pitch line, as a o, Fig. i, and above it apply a sec-
ond template, a; radius of wheel is equal to half
radius of pinion; insert into, or attach exactly at its edge, a tracer ., roll template
a along A, and tracer will describe un epicycloidal curve, a r, and by inverting a
describe o r, and faces of a tooth are delineated.
To describe flanks, define pitch line c c, Fig. 2, and arc n n,
drawn at base of teeth or board A (as in Fig. 1), secure a strip
of wood, u;, equal in length to radius of wheel, and locate
centre of it, a;, draw radii x a and z o, and they will define
flanks, which should be filleted, as shown at s s. Define arc
X2, and length of tooth is determined.
Proceed m like manner conversely for teeth of pinion, and
wheel and pinion thus constructed will operate truly.
In construction of the teeth of a wheel or pinion in
the pattern-shop, it is customary to construct the wheel
or pinion complete, out to face of wheel at base of teeth,
and then to insert the teeth in rou^h, approximately
shaped blocks, by a dovetail at their base, fitting into face of wheel, and then
the outline of a tooth is described thereon ; the block is then removed, fin-
ished as a tooth, replaced, fastened, and filleted.
Involxite.
Teeth of two wheels will work truly together when their face is that of an
involute (see page 229), and that two such wheels should work truly, the
circles from which the involute lines for each wheel are generated must be
concentric with the wheels, with diameters in same ratio as those of the wheels.
Assume A c. B c, Fig. 3. pitch radii of two wheels designed
tc work togetner, through c, draw a right line, e t, and with
perpendiculars e c, i c, describe arcs no^rg, and involutes
n CO and res define a face of each of the teeth.
To describe teeth of a pair of
wheels of which Ac, Be, Fig. 4,
are pitch radii, draw c t, c e, per-
pendicular to radials B t and A «,
and they are to be taken as the
radials of the involute arcs from
which the faces of the teeth are
to be defined ; then fillet flanks at
base, as before described, Fig. 2.
Tovolnte teeth will work with truth, even at varying
distances apart of the centres of the wheels, and any wheels of a like pitch will work
in anion, however varied their diametera
86o
WHSiEL OBABING. — TSJSTH OF WHBiBLS.
— 4
Ciroixlar teeth are defined as follows :
Assume A A, Fig. 5, pitch-line^ b b line of baae
of teeCh, and t i face-line. Set off on pitch-line
divisions both of pitch and depth of teeth, then
with a radius of 1.25 pitch descril)e arcs as o s
upon pitch line for faces of teeth, then draw ra-
dial lines ov^rtt^ to centre of wheel for flanks,
strike arc it Ui define length of tooth, and fillet
flanks at base as before described.
proportions of Teetli.
In computing dimensions of a toothy it is to
be considered as a beam fixed at one end,
weight suspended from other, or face of beam ,•
and it is essential to consider the element of velocity, as its stress in opera<
tion, at high velocity with irregular acti(m, is increased thereby.
Dimensions of a tooth should be much greater than is necessary to resist
direct stress upon it, as but one tooth is proportioned to bear whole stresv
upon wheel, although two or more are actually in contact at all times ; but
this requirement is in consequence of the great wear to which a tooth is sub-
jected, shocks it is liable to from lost motion, when so worn as to reduce its
depth and uniformity of bearing, and risk of the loss of a tooth from a defect
A tooth running at a low velocity may be mat^ially reduced in its dimen-
sions, compared with one running at a high velocity and with a like stress.
Result of operations with toothed wheels, for a long period of time, has
determined that a cast-iron (Eng.) tooth with a pitch of 3 ins. and a breadth
of 7.5 ins. will transmit, at a velocity of 6.66 feet per second, power of 59.16
horses.
Xo Conoipute IDizxiensions of* a Tooth, to Resist a gi-ven
Stress.
Rule. — Multiply extreme pressure at pitchrline of wheel by length of
tooth in decimal of a foot, divide product by Coefficient of material of tooth,
and quotient will give product of breadth and square of depth.
SI
Or,
b d^. S repreitnting stress in lbs., and I length in feet
The Coefficient of cast iron for this or like purposes may be taken at from 50 to 70.
Pitch A B = 1.
Length co = . 75.
Working longtn c c = .7.
Clearance e to o r= .05.
Depth r» = . 45.
Space* ©=.55.
Play «i»— r« = .i.
Face B c = .35.
Nor. — It \» Deoessary fint to detsnnine pitch, in
order to obtain either length or depth of a tooth.
Example. — Pressure at pitch-line of a cAst-
iron wheel (at a velocity of 6.66 feet per sec-
ond) is 4886 lbs. ; what should be dinensions
of teeth, pitch being 3 ins. f
3 X 75 = 2- 25 length of tooth, which -s- 12 = . 1875 = length in decimal of afoot
Coefficient of material is taken at 6a
4886 X.I 875
60
= 15. 27. If length = 2. 25, pitch = 3, and depth = j. 35 in».
PUches of Equivalent Strength for Cast Iron and Wood.— Iron i. Hard wood x.a&
Then ^^^ = 8.39 ins. breadth.
1.35=^ ^^
When Product ofbd^is obtained, and it is required to ascertain elthef
dimension, yj—r- = d^ptt, and -— - = breajdih.
WBBKL GBAXINO. — TBKTH OF WUEBtS.
86 1
T^ Coznpnte IDeptlk of a Tooth.
I. Wken 8tru$ is given. Rule.— Extract square root of stress, and mul-
tiply it by .02 for cast iron, and .027 for hard wood.
a. When IP ig given. Rule. — Extract square root of quotient of ff di-
vided by velocity in feet per second, and multiply it by .466 for cast iron,
and .637 for hard wood.
ExM.TtFut.—W to be transmitted by a tooth oiT cast iron is 60, and velocity of it
at its pitch-line is 6.66 feet per second ; what should be depth of tooth ?
60
V 6-66
X .466 = 1.398 ins.
To Compute H? of a Tooth.
Rule. — ^Multiply pressure at pitch-line by its velocity in feet per minute^
and divide product by 33cxx>.
EXAVPLB.— What is ]^ of a tooth of dimensions and at velocity given in preced-
ing example.
4886 X 6.66 X 60" -7-33000 = 59.16 horses.
To Oompute Stress that may be borne by a Tooth.
Rule. — ^Multiply Coefficient of material of tooth to resist a transverse
fftnun, as estimated for this character of stress, by breadth and square of its
depth, and divide product by extreme length of it in decimal of a foot.
•ExAMPLB. — Dimensions of a cast-iron tooth in a wheel are 1.38 ins. in depth, 2.x
in& in length, and 7.5 in& in breadth; what is the stress it will bear?
6oX7.5Xi.38»^^3j^jj,
Coefficient assumed at 6a
2.1-:- 12
Following deductions by the rules of (''Terent authors for like elements are sub-
mitted for a cast-iron tooth:
Pitch 3 ins. I Depth.... x.j8 tna. | Braa(!th... 7.5 itu. \ Length.... s.i ins.
Actual Powsb in Sthem Exibrd
at m MA>etty </4oo/Mf ptr min., 4886 Ibi.
/H
By Above Bute /— x .446
" Fairbaim .025 y/W.
•• Imperial Journal ^ I — p . .
V 1576
Depth of
Tooth.
Ins.
1. 398*
1.76
Actual Powbr in Sivkss Exkrtid
<rt a vdoeitjf 0/ ^00 feH jitr min., 4886 Ibt:
I W
By Bankine , / .
V 1500
-Tredgold i-^
" Buchanan
V-
556 H
Depth of
Tooth.
X.8
2.25
2.24
H rqpretentinff horsepower (60), W Hress in 26«., and v velocity in feet per second.
Depth, Pitch, and Breadth. (M. Morin.)
Cast iron .o28-/W=:d .057^^ = ?.
Hard wood 038 -/W = d. .079 v'W= P.
W rqpresetUing weight or stress upon tooth in Vbs.^ d depth of toothy and P pitch
in ins.
When velocity of pitch -circle does not exceed 5 feet per second bzs^d^
when it exceeds 5 feet 6 = 5 c^, and if wheels are exposed to wet 6 = 6 d.
b represetUing breadth.
iLLrsTEATioN. — Assomc pressurc at pitch-line of a cast-iron wheel upon a tootb
equal 6000 Iba, and velocity 5 feet per second.
Then .028 ^^6000= 2. 17 ins. Depth, and .057 v'6ooo = 4.4x ins. Pitch.
NoTB. — For farther niaatratioM of Fornmtlon of Teeth, Berel Gefirliifr, Wiilis'i Odontoftrapi..
SteToe, Tmodlee, etc., see Motely's Engineeriog, Shelton'a MechkDic's Gaide, Fiurbaim's M^wattn
and IbebiiMrjr ofCoaatroction, etc.
09
• ThU depthi with • hrwdth of 7.5 in*., is .z of nltimato atrtDfth of vrmf ttMBg th of Aneikaa
CMt Iroo.
^C>2 TESTH OF WHEELS. — WINDING ENGINES.
FROPOBTIONS OF WHEELS. ^
With six flat A rms and RU)8 upon one ride of them^ at *■■■( ; or a Weh
in centre, as ■■j^*
JHm. — Depth, measured from base of teeth, .45 to .5 of pitch of teeth, hav-
ing a web upon its inner surface .4 of pitch in depth and .25 to .3 of it in
width.
NoTS.~-When.f3uw of wheel is mortised, depth of rim shoald be 1.5 times pitch,
and breadth of it 1.5 times breadth of tooth or cog.
IltA. — When eye is proportionate to stress upon wheel, hub should be
twice diameter of eye. In other cases depth aroimd eye should be .75 to .8
• of pitch.
Arm. — Depth .4 to .45 of pitch. Breadth at rim 1.5 times pitch, increas-
ing .5 inch- per foot of length toward hub.
Rib upon one edge of arm, or Web in its centre, should be from .35 to .3
pitch in width, and .4 to .45 of it in depth.
When section of an arm differs from those above given, as with one with
a plane section, as ■■■■■, or with a double rib, as laaJt i^ dimensions
should.be proportioned to form of section.
In a wheel of greater relative diameter, length of hub and breadth of arms,
or of the rib or web, according as plane of arm is in that of wheel, or con-
trariwise, should be made to exceed breadth of face of wheel (at the hub)
in order to give it resistance to lateral strain.
Number of arms in wheels should be as follows*.
z. 5 to 3. 25 feet in diameter. ......... 4 I 5 to 8. 5 feet in diameter 6
3.25 ''5 " *' 5 1 8.5 "16 " " 8
16 to 24 feet in diameter 10
With light wheels, number of arms should be increased, in order better to
sustain rigidity of rim.
Mortise Wheels. — Their rim or face should be .9 pitch of tooth, and twice
depth of rim of a solid wheel.
WINDING ENGINEa
With Winding Engines, for drawing coals, etc., out of a Pit, wher« it
is required to give a certain number of revolutions, it is necessary to
have given diameter of Drum and thickness of rope, which is flat made,
and contrariwise.
To Compute IDiaxneter of* a IDruxn.
Where Flat Ropes art used, and are wound One part over the other, Rulk;
—Divide depth of pit in ins. by product of number of revolutions and 3.1416L
and from quotient subtract product of thickness of rope and number of rev-
olutions ; remainder is diameter in ins.
Example.— If an engine makes 20 revolutions, depth of pit being 600 feet and
rope I inch, what sbouid be diameter of drum ? '
600 X J2 7300
— ^ — I X 20 = ^— r 20 = 94.59 xns,
30X3.14IO 62.832 yr-^Pir
To Compute I>iaxueter of Roll.
Rule. — To area of drum add area or edge surface of rope ; then asceitain
by inspection in table of areas, or by calculation, diameter that fives thia
area, and it is the diameter of RolL ^^
WINDING ENGINES. — WINDMILLS. 863
ExixnjL — What )8 diameter of roll in preceding example?
Area of 94.50 = 7027.2-4- (&rea of 7200 x 1)^=7200 =14097-31 &D<i ■>/'4^^7'^~*~
.7854 = 151.85 int.
Or, Radius of drum is increased number of revolutions multiplied by thickness
of rope ; as ^^^ + 20X 1 = 67. 295 ins.
To Compute Nixmbeir of R.evolu.tious.
RVLE.^-To area of driim add area of edge surface of rope ; flrom diameter
of the circle having that area subtract diameter of drum, and divide re-
mainder by twice thickness oi rope ; quotient will give number of revolutions.
Example.— I<ength of a rope is 2600 ins., its thickness i inch, :jid diameter of
dram 20 ina ; what is number of revolutions?
Area of ao-f area of rope =314. 16-^2600=2914.16, diameter of which is 6a9i,
. 60.91 — 20 , ,.
and — = 20.45 revoltUunu.
1X2
Or, subtract diameter of drum from' diameler of rolU and divide remainder by
twice thickness of ro]Yc; as6a9i — 2o = 4a9i, and 40.91-7-1 x 2 — 2o.45rei7o/u^ton<.
Xo CompTite Point of l^eetlns of* A.8oeiidiiie and IDe-
soeiidiiig Suokets Avlien two or more are iised.
To Compute Point of Meeting of Buckets. Rulk. — Divide sum of length
of turns of rope by 2, and to quotient add length of last turn ; divide sitin
by 2, multiply quotient by half number of revolutions, and product will
give distance from centre of drum at which buckets will meet,
NoTK I.— Meetings will always be below half depth of pit
2. --At half number of revolutions buckets will meet
ExAMPLK.— Diameter of a drum is 9 feet, thickness of rope 1 inch, and revolu-
tions 20; what is depth of pit, and at what distance nrom toQ will buckets meet?
■8.544-3B.48 , -r — zn — .30 71499X10 - ,
a ^-^ 4- 38.48 -S- 2 X - = ^ ^^ =35 995 X 10 = 359.95/ee<.
To ComptUe this Depth. Ritle. — To diameter of drum add thickness of
rope in feet, and ascertain its circumference ; to diameter of drum add quo«
tient of product of twice thickness of rope and number of revolutions less i,
divided oy 12 for a diameter, and circumference of this diameter is length
of last turn, also in feet ; add these two lengths together, multiply their sum
by half number of revolutions, and product will give depth of pit
9 + thickness of rope =:9-f.,2^ofx=9. 083, which x 3- 1416 = 28. 54 feet = length
ofp^ twm. 9.0833 ■\ • — ^~' X 3-1416 = 38.48 /«et = ltri9th ofUut turn.
Then 28.54+38.48 X — = 67.02 X lo = 67o.2/e6^, depth qfpit
WINDMILLS.
Drimn^ 8hc{ft of a vertical windmill should be set at an elevating angle
with horizon when set upon low ground, and at a depressing angle when set
upon elevated ground. Range of these angles is from 3^ to 15°. A velocity
of wind of 10 feet per second is not generally sufficient to drive a loaded
mill, and if velocity exceeds 35 feet per second the force is generally too
great for ordinary structures.
Angle of Sails should be from 18^ to 30® at their least radius, and from
7^ to 17° at their greatest radius, mean angle being from 15^ to 17° to plane
of motion of sails. Length of a whip (arm) is divKled into 7 puts, saiu ex-
tending over 6 parts.
864 Wind-mills.
Whip in parts of its length : Breadth .055, at top ^16 ; Depth .025, at top
.0125; Width of sail .33, at axis .2. Distance of sail from axis .014 of
length of whip, and cross-bars 16 to 18 ins. from centres.
To Compute A.nglea of Sa^ia*
18 d'
930 i— = angle of sail with plane of its motion at any part of it d repn^
wenUng distance qfpart ofsaUfrom its aaas^ and r extreme radius ofsaily both in feet
Illustration.— Assame r = 14, and length of sail la feet, £{ = .5 of is or three
sixths of sail = .5 X 18 + (14 — 12) = 2 = 8 feet.
18 X 8*
Then 23° ^— = 23 — 5. 88° = 17. 12O.
Hence, angle of sail with axis = 90° — 17. la** = 73.88°.
If radius of sails is divided into 6 eqnal parts, angles at each of these parts will
be as follows:
Dbtanoe from /.ids.
X a 3 4 S 6
Angle of sail with axis 67.5O 69O 71.5O 75O 79.5O 85°
" " with plane of motion 22.5° 21° 18.5° 15* x<xs® 5°
To Compute Klemeuts of Windmills.
3.16 » 11.5 » A t>s .^^
r'sm. a; ' r ' -^# » 1080000 •
ffX 1080000 . /R«-fr« . .. _,_.- - . .
=^- = A; ^ ' — =.r^. V representing velocUif of unnd per see-
ondy r' radius of centre of percussion of sails, and R and r outer and inner radii of
sails, cUl in feet, x mean angle of saU to plane ofmoUoUy n wumber ofreooluiiont oj
ariM per minuU, a v angular velocity, A area tfsaUs in sq.feet, and W horse-power.
Illustration.— If a windmill has 4 arms of 28 feet, with a mean angle (a;) of 16°,
with an area of sail of 150 sq. feet each, having an inner radius of 4 (bst, and is op-
erated by wind at a velocity of 40 feet per second; what are its elements?
_. 11.5X40 /28*'-f-4* , ,_. 3.16x40
Then — ^—^- = n =83; ./ ^^-^=sr'=z 20 feet; -^l_ai_=n = 82.95;
20 "'' V 2 aox.27564 ^""
4Xi5oX64ooo_ _ 3555 X io8oooo_ ^ ^
X>ed.u.ctioii8 fVom 'Velocities -varying fVoxxi 4 to O ITeet per
Second. {Mr. SmecUon.)
1. Velocity of windmill sails, so as to produce a maximum effect, is near-
ly as velocity of wind, their shape and position being same.
2. Load at maximum is nearly, but somewhat less than, as square of ve-
locity of wind, shape and position of sails being same.
3. Effects of same sails, at a maximum, are nearly, but somewhat less
than, as cubes of velocity of wind.
4. I^ad of same sails, at maximum, is nearly as squares, and their effect
as cubes of their number of turns in a given time.
5. In sails where figure and position are similar, and velocity of wind the
same, number of revolutions in a given time will be reciprocally as radius or
length of sail.
6. Load, at a maximum, which sails of a similar figure and position will
overcome at a given distance from centre of motion, will be as cube of radius.
7. Effects of sails of similar figure and position are as si^uare of radius.
8. Velocity of extremities of Dutch sails, as well as of enlarged sails, in
all their usual positions when unloaded, or even loaded to a maximum, ia
"tnsiderably greater than that of wind.
WINDMILLS. — ^WOOD ADTD TIUBBB.
865
Rentilt» of* Experiments on BJfieot of* 'Windmill Sails.
When a vertical windmill is employed to grind com, the millstone usu-
ally makes 5 revolutions to i of the saiL
1. When velocity of wind is 19 feet per second, sails make from 11 to 12
revolutions in a minute, and a mill will grind from 880 to 990 lbs. in an
hour, or about 22 440 lbs. in 24 hours.
2. When velocity of wind is 30 feet per second, a mill will carry aU sail,
and make 22 revolutions in a minute, grinding 19^ lbs. of flour in an hour;
or 47 616 lbs. in 24 hours.
Reairdts of Operation of* 'Windmills. (A. M. Woo^, M. S.)
Vdocity of Wind 15 to 20 Miles per Hour.
BevohUioni of Wheel and OaUons of WaUr raised per Minute.
nation
of Mm.
AVTVininnn
of
WhMl.
asFMt.
er nlMd to
50 Feet.
an ElcTatu
ICO Fe«t.
>nof
200 Feot.
Power
doTeloped.
Cost per Hoar.
Actual.* Per IP.
Feet.
No.
Gallons.
Gallons.
Gallons.
Gallons.
IF
CenU.
CenU..
8.5
701075
6.16
3.02
—
—
.04
.60
>5
10
601065
19.18
9-5.6
4-75
—
.12
.70
5.8
»4
SO to 55
97.68
22.57
XI. 25
5
.28
1.63
5-?
18
40 to 45
52.16
24.42
ia.2i
.61
2.83
4.6
20
35*040
124.95
63 -75
3'-25
'5-94
.78
3- 56
4-5
25
30 to 35
212.38
106.96
49-73
36.74
«-34
4.26
3-«
• Inel
odiog InterMt at 5 per
oeBt.p«r ai
umm.
WOOD AND TIMBER.
Selection of Standhig Trees. — Wood grown in a moist soil is lighter,
and decays sooner, than that grown in dry, sandy soil.
Best Timber is that grown in a dark soil, intermixed with gravel.
Poplar, Cypress, Willow, and all others which grow best in a wet soil,
are exceptions.
Hardest and densest woods, and least subject to decay, grow in warm
climates ; but they are more liable to split and warp in seasoning.
Trees grown upon plains or in centre of forests are less dense than
those from edge of a forest, from side of a hill, or from open ground.
Trees (in U. S.) should be selected in latter part of July or first part
of August; for at this season leaves of sound, healthy trees are fresh
and green, while those of unsound are beginning to turn yellow. A
sound, healthy tree is recognized by its top branches being well leaved,
bark even and of a uniform color. A rounded top, few leaves, some of
them turned yellow, a rougher bark than common, covered with parasitic
plants, and with streaks or spots upon it, indicate a tree upon the -de-
cline. Decay of branches, and separation of bark from the wood, are
infallible indications that the wood is impaired.
Green timber contains 37 to 48 per cent, of liquids. By exposure to
air in seasoning one year, it loses from 17 to 25 per cent., and when
seasoned it retains from 10 to 15 per cent.
According to M. Leplav, green wood contains about 45 per cent of its
weight of moisture. In Cfentral Europe, wood cut in winter holds, at end of
following summer, fully 40 jMjr cent, of water, and when kept dry for sev'
eral years retains from 15 to 20 per cent, of water.
Felling Timber. — Most suitable time for felling timber is in midwinter and
In midsummer. Recent experiments indicate latter season and month of July
4D
i^
866 WOOD AND TIMBEB.
A tree should be allowed to attain full maturitr before being felled. Oak
matures at 75 to 100 years and upwards, according to circumstances ; Ash,
Larch, and Elm at 75 ; and Spruce and Fir at 80. Age and rate of growth
of a tree are indicated by number and width of the rings of annual increase
which are exhibited in a cross-section of ita body.
A tree should be cut as near to the ground as practicably as the lower
part furnishes best timber.
Dressing Timber. — As soon as a tree is felled, it should he stripped of its
bark, raised from the ground, reduced to its require<l di.ucusious, and its
sap-wood renmved.
ImpecUon of Timber. — Quality of wood is in some degree indicated by its
color, which should be nearly uniform, and a little deeper towards its cen-
tre, and free from sudden transitions of color. White spots indicate decay.
Sap-wood is known by its white color ; it is next tu the bark, and soon rots.
Dereots of* Timber.
Witid-ahakes are serious defects, being circular cracks separating the con-
centric layers of wood from each other.
Splits, Cfiecks^ and Criicks^ extending toward centre, if deep and stronely
marked, render tinibiT unfit for use, unless purpose for which it is intended
will admit of its being split through them.
Brash is when woo<l is porous, of a reddish color, and breaks short, with-
out splinters. It is generally consequent u{H>n decline of tree fiom age.
Belled is that which has been killed before being felled, or which has died
from other causes. It is objectionable.
Knotty is that containing many knots, tliough sound ; usually of stinted
growth.
TtoiHed is when grain of it winds spirally ; it is unfit for long pieces.
Dry-rot is indicated by yellow stams. Elm and Beech are soon afifected,
if left with the bark on.
Large or decayed knots injuriously affect strength of timber.
Heart-shake. — Si)lit or cleft in centre of tree, dividing it into segmen^
Star-shake, — Several splits radiating from centre of timber.
Cup-shake, — Curved splits separating the rings wholly or in part.
Rind-gaU. — Curved swelling, usuaUy caused by growth of layers over spot
where a branch has been removed.
Upset. — Fibres injured by crushing.
Foxiness. — Yellow or red tinge, indicating incipient decay.
Do€Uin€S9,^A, speckled stain.
Seasoiiins and FreBerviixs Timber.
Seasonmg is extraction or dissipation of the vegetable juices and moisture
or soliditication of the albumen. When wood is exposed to currents of air
at a high temperature, the moisture evaporates too rapidly, and it cracks ;
and when temperature is high and sap remains, it ferments, and dry-rof
ensues.
Wood requires time in which to season, very much in proporti(H3 to density
of its fibres.
Water Seasoning is total immersion of timber in water, for purpose of
dissolving the sap, and when thus seasoned it is less liable to warp ana crack,
but is rendered more brittle.
WOOD AND TIHBEB. 86/
For purpose of teasontng, it should be piled under shelter and kept dry ;
should have a free circulation of air, without being exposed to strong cur>
rent«. Bottom pieces should be placed upon skids, which should be free
from decay, raised not less than 2 feet from ground ; a space of an inch
should inten'ene between pieces of same horizontal layers, and slats or piling-
strips placed between each layer, one near each end of pile, and others at
short distances, in order to keep the timber from winding. These strips
should be one over the other, and in large piles should not be less than i inch
thick. Light timber may be piled in upper portion of shelter, heavy timber
upon ground floor. Each pile should contain but one description oi timber,
and they shoidd be at least 2.5 feet apart.
It should be replied at intcr\'als, and all pieces indicating decay should be
removed, to prevent their affecting those wnich are still sound.
It requires from 2 to 8 years to be seasoned thoroughly, according to its
dimensions, and it should be worked as 9oon as it is thoroughly dry, for it
deterionrtes after that time.
Gradual seasoning is most favorable to strength and durability of timber.
Various methods have been proposed for hastening the process, as 8teamiiig^
which has been applied with success; and results of experiments of various
pnxjesses of saturating it with a solution of Cofrosive suldimtUe and Anti-
tepUc ^uids are very satisfactory. Such process hardens and seasons wood,
at the same tlmye that it secures it from dry<rot and from attacks of woru)s.
Woods are densest and strongest at the roots and at their centres. Their
strength decreasing with the decrease of their density.
Oak timber loses onB fifth of its weight in seasoning, and about one third
in becoming perfectly dry.
Pitch pine, from the presence of pitch, requires time in excess of that due
to the densitv of its fibre.
Mah(^any should be seasoned slowly, Pine quickly. "VHiitewood should
not be dried artificially, as the effect of heat is to twist it
Salt water renders wood harder, heavier, and more durable than fresh.
Condition of timber, as to its soundness or decay, is readily recognized
when struck with a quick blow.
Timber that has been for a long time immersed in water, when brought
into the air and dried, becomes brashy and useless.
When trees are barked in the spring, they should not be felled until the
foUagft is dead.
Timber cannot be seasoned by either smoking or charring ; but when it
is exposed to worms or to the production of fungi^ it is proper to smoke or
char it, and it may be partially seasoned by being boiled or steamed.
Timber houses are best provided with blinds which keep out rain and
snow, but which can be turned to admit air in fine weather, and the houses
should be kept entirely free from any pieces of decayed wood.
Kiln-drj^ng is suited only for boards and pieces of small dimensions, as it
is apt to cause cracks and to impair the strength, unless performed very
slowlv.
Chairing, Pfiinting^ or covering the surface is highly imirious to any hut
seasoned wood, as it efleotunlly prevents drying of the inner part of the
wood, in consequence of which fermentation and decay soon take place.
Timber is subject to Common or Dry-rot, former occasioned by alternate
exposure to inojsturc and dryness, and as pro;;ress of it is from the exterior
covering of the surface, if seasoned, with paint, tar, etc., is a preservative
u
868 WOOD AKD TIMBSB.
Common-rci is the conseqaence of its being piled in badly-ventilated sheds.
Outward indications are yellow spots upon ends of pieces, and a yellowish
dust in the checks and cracks, particularly where the pieces rest upon pil-
ing-strips.
Dry or Sap-rot is inherent in timber, and it is the putrefaction of the veg-
etable albumen. Sap wood contains a large proportion of fermentable ele-
ments.
Insects attack wood for the sugar or gum contained in it, andyVifi^ subsist
upon the albumen of wood ; hence, to arrest dr^'-rot, the albumen must be
either extracted or solUlilied.
Most effective method of preserving timber is that of expelling or ex-
hausting its fluids, solidifying its albumen, and introducing an antiseptic
liquid.
Strength of impregnated timber is not reduced, and its resilience is improved.
In desiccating timber by expelling its fluids by heat and air, its strength
is increased fully 15 per cent.
The saturation of wood with creosote, tar, antiseptics, etc, preserves it
from the attack of worms. Jarrow wood, from Australia, is not subjected
to their attack.
In a perfectly dry atmosphere durability of woods is almost unlimited.
Rafters of roofs are knovm to have existed 1000 years, and piles submerged
in fresh water have been found perfectly sound &» years from period of
their being driven.
Resistance of woods to extension is greater than that of compression.
Impregnation of* 'Wood-
Several of the successful processes are as follows :
Kyan^ 1833. — Saturated with corrosive sublimate. Solution z lb. of chlo-
ride of mercury to 4 gallons of water.
Burnett {Sir Wm.)^ 1838. — Impregnation with chloride of zinc by sub-
mitting the wood endwise to a pressure of 150 lbs. per sq. inch. SoluticHi,
I lb. of the chloride to 4 gallons of water.
Boucheri, — Impregnation by submitting the wood endwise to a pressure
of about 15 lbs. per sq. inch. Solution, i lb. of sulphate of copper to ia.5
gallons of water.
BetheL — Impregnation by submitting the wood endwise to a pressure of
150 to 200 lbs. per sq. inch, with oil of creosote mixed with bituminoos
matter.
Robbins^ 1865. — Aqueous vapor dissipated by the wood being heated in a
chamber, the albumen solidified, then submitted to vapor of coal tar, resin,
or bituminous oils, which, being at a temperature not less than 325°, readily
takes the place of the vapor expelled by a temperature of 212*^.
H(iyford^ 1 87-. — Aqueous vapor dissipated by the wood being heated in a
chamber to a temperature of from 250*^ to 270^, the albumoa solidified, then
air introduced to assist the splitting of the outer surfaces. When vapor is
dissipated, dead oils are introduced under a pressure of 75 lbs. per sq. inch.
PlankSj Deals^ and Battens. — When cut from Northern pine {Pinus St/lve^
stria) are termed yellow or red deal, and when cut from spruce {Abiesj aUfo,
etc.) they are termed white deal.
Desiccated wood, when exposed to air under ordinarv circumstances, ab-
sorbs 5 per cent, of water in the first three days ; and will continue to al^orh
it until it reaches from 14 to 16 per cent, the amount varying according
to condition of the atmosphere.
WOOD XSt> TIUBBB.
869
X>Tirabilit3r of Various "Woods.
jRteeet 2 feet in Lengthy 1.5 int. Square, driven 38.5 ins. into the JSarth.
Coodition
Wood.
Acacia
Asb, Amer
Cedar, Va
*^ Lebanon.
Elm, Eng
*' Can
Fir
Larch
Oak, Can
" Memel .
** Dantaic
" Chestnut
Pine, pitch. .
" yellow
" white.
Teak
After 3.5 Years*
Good
Much decayed.
Very good
Good
Much decayed.
attacked
Surface only attacked. . . . .
Very much decayed
^( (( II
It
it
u
Very good
Surface only attacked. « . ,
Attacked
Very much decayed
Very good.. . .,
Jfififeot of Oreosotiixg.
RetuUt of Eseperiments wWi Various Woods {E. R. Andrewsy
After 5 Years.
( Externally decayed, rest per
( fectly sound.
Decayed.
Sound as when driven.
Tolerable.
Entirely decayed.
Decayed.
Much decayed.
{Attacked in part only, rest fair
condition.
Very rotten.
it
tt
{Some moderately, most very
much, decayed.
{Attacked in part only, rest fair
condition.
Much decayed.
Very rotten.
Somewhat soft, but good.
Wood.
Oak [^^eia
I creosoted . . ,
Cotton-wood Y^^-
Water
absorbed.
Per cent.
•2543
.026x
.2
.0
•714
.347
Wood.
Hard pine.... {^„,ii;;
Gum,bl«k..{2;^-^;
B'""."""*- {created..
Water
absorbed.
Per cent.
.16
.0
z
•"5
•43
.124
Sesquoia Gigantea of California, dried, .4722; creosoted, .0.
Fluids will pass with the grain of wood with great facility, but will not
enter it except to a very limited extent when applied externally.
.A.bsorptiozi of f^reservingf Solution "by different Woods
for a I^eriod of T T>a.yH, Average Lbs. per Cttbe FooL
Black Oak. 3.6 | Hemlock 2.6 I Rock Oak 3.9
Chestnut. 3 | Red Oak 3.9 | White Oak 3.1
Proportion of "^^ater in various "Woods.
Pine (Pinus Sylvestris L.) 39. 7
Red Beech {Fagus sybfcUica) 39.7
Red Pine [IHnus picea dur) 45. 3
Spruce {Abies, cUba, nigra, rttfrra, )
excelsa) ) ^5
Sycamore {Acer pseudo-pUUamu) . . 27
White Oak {Quercus alba) 36. 2
White Pine {Finus abies dur) 37. 1
White Poplar {Populus alba) 50.6
Willow {SaUs caprea) 26
X)iinensions of Timber \>y Seasoning.
Woods. Ins. Ins.
Pitch Pine, South 18.375 to 18.25
Spruce 8.5 to 8.375
White Pine, American.. 12 to 11.875
Yellow Pino, North. . . , . x8 to 17. 875
Alder {Bettda cUnus) 41.6
Ash {Fraxintu excelsior) 28.7
Beech {Fagtu sylvaiica) 33
Birch {Betula alba) : 30.8
Elm {Ulmus campestris) 44.5
Horse-chestnut (^<cu^tMAtj>poca<t.) 38.2
Larch ( Pintu larix) 48.6
Mountain Ash {Sorbus aucuparia). . 28.3
Oak {iluercus robur) 34. 7
m
I>ecrease
Woods. Ins. Ins.
Cedar, Canada 14 to 13.25
Elm XX to 10.75
Oak, English X2 to 11.625
Pitch Pine, North. . . lox 10 to 9. 75X9- 75
Weight of a beam of English oak, when wet, was reduced by seasoning
ftook 972.35 to 630.5 lbs.
^40
870
WOOD AND TIMBEB.
^Weiglit or ei CiiDe Woot of Oak and Yello-w Pine.
AOB.
Green. . .
1 Year.
2 Years.
White Oak, Va.
Round. Square.
64.7
53-6
46
67.7
53-5
49.9
Yellow Fiae, Va.
Round. Square.
47.8
39-8
34-3
39-2
34- a
33-5
LiveOdL
78^7
66.7
In England, Timber sawed into boards is classed as follows :
6.5 to 7 ins. in width, Battens f 8.5 to 10 ins., Deals; and 11 to 12 ina^
Planks. {See also paye 62.) ^
Distillation. — From a single cord of pitch pine distilled by chemical ap-
paratus, following substances and in quantities stated have been obtained :
Charcoal 50 bushels.
Illuminating Gas. . . .about 1000 cu. feet.
IllumiDating Oil and Tar. . . 50 gallons.
Pitch or Resin 1.5 barrels.
Pyroligneous Acid 100 gallona
Spirits of Turpentine - ao "
Tar I barrel
Wood Spirit 5 gallons.
Streiigtli of TixnlDer.
Results of experiments have satisfactorily proved: That deflection was
sensibly proportional to load ; That extension and compression were nearly
the same, though former being the greats ; That, to produce equal deflection,
load, when placed in the centre, was to a load uniformly distributed, as .638
to I ; That deflection under equal loads is inversely as breadths and cubes
of the depths, and directly as cubes of the spans. {M. Morin.)
It has also been shown, that densitv of wood varies very little with its age.
That caefficient of elasticity diminishes after a certain age, and that it de-
pends also on the dryness and the exposure of the ground where the wood
is grown. Woods from a northerly exposure, on dry ground, have a high
coefficient^ while those from swamiM or low moist ground have a low one.
That tensile strength is influenced by age and ex|wsure. The coefficieiU
of elasticity of a tree cut down in full vigor, or before it arrives at this
condition, does not present any sensible difference. That there is no limit
of elasticity in wood, there being a ])ermanent set for every extension.
Average Result of Experiments on Tensile Strength of Wood in Various
Positions per Sq. Inch. {MM. Ckevandier and Werlheim.)
With the fibre, 6900 lbs. Radially, 683 lbs., and Tangentially, 723 lbs.
To Cotnpute "Volume of an Irregular Socl;sr.
By " Simpsons Rule."
Operation.— Take a right line in the Qgure for a base line, as A B, divide the fig-
ure into any number of equal parts, and compute the areas of their plane sections
as I, 2, 3, etc. , at the points of division, by rules applicable to area of a plane. Then,
operate these areas as if they were the ordinates of a plane curve or figure of same
length as the figure, and result will give volume required.
Illustration.
-Assume a figure having areas as follows, and A B = 24 feet
Sections, i Areas, 3 feet Multiplier, x Products,
a
3
4
5
5
7
9
XX
4
3
4
X
3
ao
36
and 84 X a4-t-4-»-3 = 168 cubefosL
HISCBLI.ANEOUS MIXTURES. 8/1
MISCELLANEOUS MIXTURES,
Cexnents.
Much depends upon manner in which a cement is applied as upon the
cement itself, as best cement will prove worthless if improperly applied.
Following rules must be rigorously adhered to to attain success :
1. Bring cement into intimate contact with surfaces to be united. This is best
done by heating pieces to be joined in cases where cement is melted by beat, as
with resin, shellac, marine glue, etc. Where eoiutions are used, cement must be
well rubbed into surfaces, either with a- brush (as in case of porcelain or glass),
or by rubbing the two surfaces together (as in making a glue joint between pieces
of wood).
2. As little cement as practicable should be allowed to remain between the united
surfaces To secure this, cement should be as liquid as practicable (thoroughly
melted if used with heat), and surfbces should be pressed closely into contact until
cement has hardened.
3. Time should be allowed for cement to dry or harden, and this is particularly
the case in oil cements, such as copal varnish, boiled oil, white lead, etc. When
two sorftices, each . 5 inch across, are joined by means of a layer of white lead
placed between them, 6 months may elapse before cement in middle of joint be-
comes hard. At the end of a month the joint will be weak and easily separated: at
end of 2 or 3 years it may be so firm that the material will part anywhere else tnan
at joint Hence, when article is to bo used immediately, the ouly safe cements
are those which are liquelied by heat and which become hard when cold. A joiut
made with marine glue is firm an hour after it has been made. Next to cements
that are liquefied by heat are those which consist of substances dissolved in water
or alcohol. A glue Joint sets firmly in 24 hours; a joint made with shellac varnish
becomes dry in 2 or 3 days. Oil cements, which do not dry by evaporation, but
harden by oxidation (boiled oil, white lead, red lead, etc.) are slowest of all.
Stone.— Rcs'm, Yellow Wax, and Venetian Red, each i oz. ; melt and mix. -
Aqviarium.
Litharge, fine white dry Sand, and Plaster of Paris, each z gill; finely pulverized
Resin, .33 gill.
Mix tborooKbly and make into a paat* with bc4led Unwed oil to which drier has been added. Best
weU, and let stand 4 or 5 hoan before naine it. After it ha* stood fur 15 hours, however, it loses iU
atreoKth. Olaai eeinented into a frame with this cement will resist percolation for either salt or fresh
A.dtieaive for Fractures of* all Kinds.
White Lead ground with Linseed-oil V^arnish, and kept from contact with the air.
Requires a few weeks to harden.
Stone or Iron.
Compound equal parts of Sulphur and Pitch.
Brass to Olass.
Electrical.— Res\n, 5 ozs. ; Beeswax, i oz. ; Red Ochre or Venetian Red, in pow-
der, I oz. Dry earth thoroughly on a stove at above 212° Melt Wax and Resin
together and stir in powder by degreea Stir until cold, lest earthy matter settle
to bottom.
Used for fastening bniM-work to glass tubes, flasks, etc.
Chinese Waterproof.
Schioliao.'^To 3 parts of Fresh Beaten Blood add 4 parts of Slaked Lime and a
little Alum; a thin, pasty mass is produced, which can be used immediately.
Materials which are to be made specially waterproof are painted twice, or at most three time*.
IVooden public bnildinn of China are painted with tchw4i«o, which irives them an unpleasant red-
dish appearance, but adda to their durability. Pasteboard treated with it receives appearance and
•trength of wood.
Clxina.
Curd of milk, dried and powdered, 10 ozs. ; Quicklime, i oz. ; Camphor, 2 drachma
Mix, and keep air-tight. When need, a portion is to be nixed with a little water Into a paste.
Cisterns and 'Wat#r»-caslcs.
Melted Glae, 8 parts; Linseed oil, boiled into a varnish with Litharge, 4 part&
This cement hardeot in aboot 48 honrs, and renders the joints of weoden cisterns and casks air «b4
wAter tight.
8/2
MISCELLANEOUS MIXTUBES.
Clotb. or I^eatlxer.
ShellM, X part; Pitch, a parts; India Rubber, a parts; and Gatta Percha, lo
parts; cut small; Linseed oil, 2 parts; melted together und mixed.
£Cartb.en and Ghlass "Ware.
Heat article to be mended a little^above 212°, then apply a thin coating of gum
Shellac u|K>n both surfaces of broken vessel
Or, dissolve gum Shellac in alcohol, apply solution, and bind the parts firmly to-
gether until cement is dry.
Or, dilute white of egg with its bulk of water and beat up tborongbly. Mix to
consistence of tbin paste with powdered Quicklime.
Um immedUtely.
XCntozxiologistB*.
Thick Mastic Varnish and Isinglass size, equal parta
Q-ixtta Perolia*
Melt together, in an iron pan, 2 parts Common Pitch and i part Gutta Percha.
Stir well toflwther until thorouKfaly ineorpomted, and then poor liquid Into cold wat«r. MTben cold
it is black, soud, and elastic ; but it aoflana with beat, aud at km* la a thin fluid, it may be aaed aa »
•oft paste, or in liquid state, and answers an excellent purpose In cementing metal, glaMj poroelatn,
■ivory, etc. It may be used instead of putty for glasing.
Olass.
SoreVs.—Vxx commercial Zinc White with half its bulk of fine Sand, add a sola-
tion of Chloride of Zinc of 1.26 spec, grav., and mix thoroughly in a mortar.
Apply immediately, as it hardens very quickly.
Holes in Castiiiss.
Sulphar in powder, i part; Sal-ammoniac, 2 parts; powdered Iron tumiogs, 80
parts. Make into a thick paste.
Make only aa required for immediate ose.
Hydraialio iPaint.
Hydraulic cement mixed with oil forms an incombustible and waterproof paint
for roofs of buildings, outhouses, walls, etc.
Iron "WavB.
Sulphar, a parts; fine Black-lead, x part Heat sulphur in an iron pan until
it meits, then add the lead; stir well, and remove. When cool, break into pieces
as required. Place upon opening of the ware to be mended, and solder with an
iron.
Kerosene !L«amps, etc.
Resin, 3 parts; Caustic Soda, i; Water, 5, mixed with half its weight of Plaster
of Faria
It sets firmly in about three quarters of an honr. Is of irreat adbesiTe power, not permeable to kero-
sene, a low conductor of beat, and but superficially attacked by hot water.
Xjeatlier to Iron, Steel, or O-lass.
X.— Glue, z quart, dissolved in Cider Vinegar; Venice Turpentine, x oz. ; boil very
gently or simmer for 12 hours.
Or, Glue and Isinglass equal parts, soak in water 10 hours, boil and add tannin
until mixture becomes ''ropy;" apply warm.
Remove surface of leather where it is to be applied.
a. — Steep leather in an infusion of Nutgall, spread a layer of hot Glue on 8ar>
fiice of metal, and apply flesh side of leather under pressure.
Xjeatlier Selting;.
Common Glue and Isinglass, equal parts, soaked for 10 hours in enough water to
cover them. Bring gradually to a boiling heat and add pure Tannin until whole be-
comes ropy or appears alike to white of egg&
Clean and rub sur&ces to be joined, apply warm, and clamp firmly. '
^loldins and rreznporar3r A-dliesion.
SoJl^Velt Yellow Beeswax with its weight of Turpentine, and color with finely
powdered Venetian red.
WImb cold it has the hardness of MMp, bat it Malbr wrfteDed and molded with the floftn.
ICISCELLANEOUB MIXTUSSS. 8/3
l^altha, or Ghreek IMastio*
Lime and Sand mixed in manner of mortar, and made into a proper consistency
with milk or size without water.
Plaster of Paris, in a saturated solution of Alum, baked in an oven^ and reduced
to powder. Mixed with water, and color if required.
IMetal to GMaaa.
GopctI Varnish, 15 parts; Drying Oil, 5 ; Turpentine, 3. Melt in a water hath and
add 10 of Slaked Lime.
IMending Sliells, etc.
Gum Arabic, 5 parts; Rock Candy, 2; and White Lead, enough to color.
Xjarge Ol^jects.
WolUuton's TrAi<«.— Beeswax, i oz. ; Kesin, 4 ozs, ; powdered Plaster of Paris, 5
oz. Melt together. 1
Warm the edges of the object and apply warm.
By means of thlB cement a piece of wood may be fiwtened to achnck. which will hold when cool ; and
when work !■ finished it may be removed by a smart stroke with tool. Any traces of cement may be
vtmoTed by Bcnuine.
IMCar'ble Workers and. Ooppersmitlis.
White of egg, mixed with flnely-sifled Quicklime, will unite objects which are
not submitted to moisture.
Foroelain.
Add Plaster of Paris to a strong solution of Alum till mixture is of consistency
of cream.
It seta readily, and is salted for cases in which large rather than small surfaces are to be united.
Rust Joint.
(Quick ifiSetttn^ir.)— Sal-ammoniac in powder, z lb. ; Flour of Sulphur, a lbs. ; Iron
borings, 80 lbs. Made to a paste with water.
(Slow iSrettm^.)— Sal-ammoniac, 2 lbs. ; Sulphur, i lb. ; Iron borings, 300 lbs.
The latter cement is best if joint is not required for immediate use.
SteaxTL Boilers, Steam-pipes, etc.
Finely powdered Litharge, 2 parts; very fine Sand, z; and Quicklime slaked by
exposure to air, i.
This mixture may be kept for any leOKth of time without injuring. In using it, a portion is mixed
Into paste with Unseed oil, boiled or crude. Apply quickly, as it soon becomes hard.
Soft— Red or White Lead in oil, 4 parts; Iron borings, 2 to 3 parts.
JTard— Iron borings and salt water, and a small quantity of Sal-ammoniac with
firesh water.
rrransparent— d-lass.
India-rubber, i part in 64 of chloroform ; gum Mastic in powder, 16 to 24 parts.
Digest for two days, with frequent shaking.
Or, pulverized Glass, 10 parts; powdered Fluor-spar, 20; soluble Silicate of Soda,
60. BoUi glass and fluor-spar must be in finest practicable condition, which is best
done by shaking each in fine powder, with water, allowing coarser particles to de-
posit, and then by pouring off* remainder, which holds finest particles in suspension.
The mixture must be made very rapidly, by quick stirring, and applied Immediately.
TJiiitins Xjeatlier and HVIetal.
Wash metal with hot Gelatine; steep leather in an infusion of Nutgalls, hot,
and bring the two together.
"Waterproof UMastio.
Red Lead, i part; ground Lime, 4 parts; sharp Sand and boiled Oil, 5 parts.
Or, Red Lead, x part; Whiting, 5; and sharp Sand and boiled Oil, 10.
Wood to Iron.
Litharge and Glycerine. — ^Finely powdered Oxide of Lead (litharge) and Concen-
trated Glycerine.
The compoeitlon is insoluble in most acids, is unaffected by action of moderate heat, sets rapidly,
■ad acquires an extraordinary hardness.
7V«m«r'«.— Melt i lb. of Resin, and add .25 lb. of Pitch.
While boiling add Brick dust to give required consistency. In winter it may be
necessary to add a little Tallow.
g^4 MISCELLANEOUS MIXTUEBS.
GLUES.
!&£arine.
Disflolve India Rubber, 4 parts, in 34 parts of Coal-tar Naphtha; add powdered
Shellac, 64 parts.
While mixture is hot pour it upon metal plates in aheeta. When required for
use, heat it, and apply with a brush.
Or, India Rubber^ x part; Coal Tar, 12 parts; heat gently, mix, and add powdered
Shellac, 20 parts. Cool. When used, heat to about 250°
Or, Glue, 12 parts; Water, sufflciMit to dissolre; add Yellow Resin, 3 parts; and,
when melted, add Turpentine, 4 parts.
Strong Glue. — Add Powdered Chalk to common Glue.
Mix thoroughly.
Afuoilage.
Curd of Skim Milk (carefully freed lh>m Cream or Oil), washed thoroughly, and
dissolved to saturation in a cold concentrated solution of Borax.
Thia madUge ke0p« well, and, w regards adfaeslTe power, far raqMuM ^m Arabic.
Or, Oxide of Lead, 4 lbs. ; Lamp-black, 2 lb& ; Sulphur, 5 ozs. ; and India Rubber
dissolved in Turpentine, 10 lbs.
Boll together until they are thoroughly combined.
Pre$ervation of Mucilage.— A small quantity of Oil of Cloves poured into a bottle
containing Gum Mucilage prevents it from becoming sour.
To Resist !N£oisture.
Glue, 5 parts; Resin, 4 parts; Red Ochre, 2 parts; mixed with least practicable
quantity of water.
Or, Glue, 4 parts; Boiled Oil, i part, by weight, Oxide of Iron, i part
Or, Glue, i lb., melted in 2 quarts of skimmed Milk.
Pafclim eut.
Parchment Shavings, x lb. ; Water, 6 quarts.
Boil nntil dlMolred, th«o itrain and evaporate alowly to pioper camlataace.
Rion, or Japanese.
Rice Flour; Water, sufficient quantity.
Mix together cold, then Ixrfl, etlrrlDg It during the tliaa.
I^iquid.
Glue, Water, and Vinegar, each 2 parts. Dissolve in a water-bath, then add Al.
cohol, I part
Or, Cologne or strong Glue, 2.2 Iba ; Water, i quart; dissolve over a gentle heat;
add Nitric Acid 36^^, 7 ozs., in small quantities.
RemoTe from over fire, and cool.
Or, White Glue, 16 ozs. ; White Lead, dry, 4 oz& ; Rain Water, 2 pinta Add Al-
cohol, 4 ozs., and continue heat for a few minute&
Klastio and Street.-" Stamps or Rolls.
Elastic.— DiBBoWe good Glue in water by a water-bath. Evaporate to a thick con-
sistence, and add equal weight of Glycerine to Glue; submit to heat until all water
is evaporated, and pour into molds or on platea
Sioeet^-SubstHute Sugar for the Glycerine.
Xo A-dlxere Sxigravings or Xjitliographs upoix "^^ood.
Sandarach, 250 parts; Mastic in tears, 64 parts; Resin, 125 parts; Venice Tor
pentine, 250 parts; and Alcohol, xooo parts by measure.
BROWNING, OR BRONZING, LIQUIB.
Sulphate of Copper, x oz. ; Sweet Spirit of Nitre, x oz. ; Water, x pint
Mis. Let etand a few dayt before aee.
MISCELLANEOUS MIXTURBB. g^J
Gun 33arrei».
Tfncture of Mariate of Iron, i oz. ; Nitric Ether, i oz. • Sulphate of Copper, a
Acmples; rain water, i pint If the prooess is to be hurried, add 2 or 3^raius or
OxymariaCe of Meroury.
Wbmi bami b finUbed, let it remain • short time in lime-water, to neutralize any acid which may
have penetrated , then rub it well with an iron wire acrHtch-brwb.
Afler Browning. — Shellac, i oz. ; Dragon's-blood, .25 oz. , rectified Spirit, i qt.
Dissolve (tnd filter.
Or, Nitrio Acid, spec. grav. 1.2; Nitric Ether, Alcohol, and Muriate of Iron, each i
part Mix, then add Sulphate of Copper 3 parts, dissolved in Water xo parta
LACQUERS.
Small Arms, or Waterproof Paper.
Beeswax, 13 lbs.-. Spirits Turpentine, 13 gallons; Boiled Linseed Oil, i gallon.
All ingredienta should be pure and of beet quality. Heat them together in a copper or earthen tM'
■el over a gentle fire, in a water-bath, until they are well mixed.
I5riglit Iron. Worlc.
LinseedOil, boiled, 80. 5 parts; Litharge, 5.5 parts; White Lead, in oil, 11.35 parts;
Resin, pulverized, 2.75 parts.
Add litbarice to ol| ; eimmer over a alow fire 3 honn ; itnUn, and add rMln and white lead ; keep it
fently warmed, and etir until resin is disatilvwl.
Or, Amber, 6 parts; Turi>entine. 6 parts; Resin, i part; Asphaltum, i part; and
Drying Oil, 3 parts; heat and mix well.
Or, Shellac, z lb. ; Asphaltum, 6 lbs. ; apd Turpentine, i gallon.
Iron and. Steel.
Clear Mastic, 10 parts; Camphor, 5 parts: Sandarae, 15 parts; and Elimi Gum,
5 parta Dissolve in Alcohol, filter, and apply cold.
13rass.
Shellac, 8 ozs. ; Sandarac, 3 oz& ; Annatto, 2 oz& ; and Dragon's-blood Resin, .25
oz. ; and Alcohol, i gallon.
Or, Shellac, 8 oza ; and Alcohol, i gallon. Heat article slightly, and apply lacquer
with a soft brush.
■^Tood, Iron, or ViTalle, and rendering Olotli, Paper, etc.,
"Waterproof.
Heat 120 lbs. Oil Varnish in one vessel, 33 Iba Quicklime in 32 lbs. water in an-
other. Soon as lime eflTervosces. add 55 Iba melted Indii^ Rubber. Stir mixture,
and pour into vessel oC hot Varnish. Stir, strain, and cool.
When used, thin with Varnish and apply, preferably hot
To Clean Soiled Kngravings.
Ozone Bleach, x part; Water, lo; well mixed.
Indelilsle, fbr ^arising Uiiien* etc.
z.— nJuice of Sloes, i pint; Gum, .5 oz.
This requires no " preparation " or mordant, and Is very durable.
2 — ^Nitrate of Silver, i part^ Water, 6 parts. Gum, 1 part; Dissolve.
3. — Lunar Caustic, 3 parts; Sap Green and Gum Arabic, each i part ; dissolve with
distilled water.
'■'^ Preparation.^^ — Soda, x oz. ; Water, i pint; Sap Green, 5 drachm. Dissolve,
and wet article to be marked, then dry and apply the ink.
Perpetualy for Tomb-Hones, Marble, <<c.— Pitch, n parts; Lamp-black, i part;
Turpentine sufficient. Warm and mix.
Copying /nX^— Add x oz. Sugar to a pint of ordinary Ink-
SOLDERING.
Base for Soldering.
Strips of Zinc in diluted Muriatic, Nitric, or Sulphuric Acid, until ns much is de-
composed as acid will eflTeot. Add Mercury, let it stand for a day; pour off the
Water, and bottle the Mercury.
WbeQ rM|uirt<|, rub snrface to b« soldered with a cloth dipped in the Mercury,
8/6 MISC£LLANBOUS KIXTUSB8.
YAKNISHES.
"^Vat erp roof.
Flour of Sulphur, i lb. ; Linseed Oil, z gall. ; boil tbem until they are thoroughly
combined.
Good for waterproof textile fkbric&
Karness.
India Rubber, .5 lb. ; Spirits of Turpentine, x gall. ; dissolve into a Jelly ; then mix
hot Linseed Oil, equal parts with the mass, and incorporate them well over a slow fira
17'astenine I^eather on "Pop Rollers.
Gum Arabic, a.75 oz&, and a like volume of Isinglass, dissolved in Water.
To Preserve Q-lass from the Sun.
Reduce a quantity of Gum Tragacanth to fine powder, and dissolve it for 34 hours
in white of egg well beat up.
"^Tater-oolor IDra^^vines.
Canada Balsam, i part; Oil of Turpentine, 2 pftrt&
Mix and size drawing before applying.
Oladeots of Katural Kistorsr, SKells, ITisli, etc.
Mucilage of Gum Tragacanth and of Gum Arabic, each i ox.
Mix, and add spirit with Corrosive Sublimate, to precipitate the more stringy por-
tion of the Gum.
Iron and Steel.
Mercury, 120 parts; Tin, 10 parts; Green Vitriol, 20 parts; Hydrochloric Acid of
X.3 sp. gr., IS parts, and pure Water, 120 parts.
Blaokl>oards.
Shellac Varnish, 5 gallons; Lampblack, 5 ozs. ; fine Emery, 3 ozs. ; thin with
Alcobfd, and lay in 3 coats.
Black.
Heat, to boiling, Linseed Oil Varnish, 10 parts, with Burnt Umber, a parts, and
powdered Asphaltum, x part
When copied, dilute with Spirits of Turpentine as may be required.
Balloon.
Melt India Rubber in small pieces with its weight of boiled Linseed OIL
Thin with Oil of Turpentine.
Transfer.
Alcohol, 5 0x8. ; pure Venice Turpentine, 4 ozs. ; Mastic, i ox.
To render Canvas "Waterproof and Flial>le.
Yellow Soap, i lb , boiled in 6 pints of Water, add, while hot, to ixa Iba of oil Psaintt
Waterproof Bags.
Pitch, 8 parts. Wax and Tallow, each i part
To Clean VarnisH.
Mix a lye of Potash or Soda, with a little powdered Chalk.
STAINING.
"W^ood and Ivory,
Tdlow.—DWate Nitric Acid will produce it on wood.
Red.— An infusion of Brazil Wood in Stale Urine, in the proportion of x lb. to a
gallon, for wood, to be laid on when boiling hot, also Alum water before it driea
Or, a solution of Dragou^s-blood in Spirits of Wine.
Btacik.— Strong solution of Nitric Acid.
B2«e.— For Ivory: soak it in a solution of Verdigris in Nitric Acid, which will turn
it green; then dip it into a solution of Pearlash boiling hot
Purpfe...^Soak Ivory in a solution of Sal-ammoniac into four times its weight of
Nitrous Acid.
ifoftoyany. —Brwil, Madder, and Logwooa, aiewlved in water and put on lioi,
MISCELLANBOUS MIXTUBBS. 8/7
BOBCELLANEOUS.
Slacking fbr Hamess.
Beeswax, .5 lb. ; Ivory Black, 2 ozs. ; Spirits of Tarpentine, i oz. ; Pmssian Blue
ground in oit, z oz. ; Copal Varnish, .25 oz.
Melt wax and stir it into other ingredients before mixture is quite cold; make it
into balls. Bub a little upon a brush, and apply it upon harness, then polish lightly
with silk.
rFo Olestii Srass Ornaments.
Brass ornaments that have not been gilt or lackered may be cleaned, and a very
brilliant color given to them, by washing them in Alum boiled in strong Lye, in the
proportion of an ounce to a pint, and afterwards rubbing thiem with strong Tripoli.
rro Harden Drills, Cliisels, etc.
Temper them in Mercury.
To Clean Coral.
Brush with equal parts Spirits of Salts and cold water.
Or, dip in a hot solution of Potash or Chloride of Lime. If much discolored, let
it remain in solution for a few hours.
Slaclcing, "^vitliont Folisbiing.
Molasses, 4 oz& ; Lamp-black, .5 oz. ; Yeast, a table-spoonful; Eggs, 2; Olive Oil,
a teaspoonftil; Turpentine, a teaspoonAiL Mix well
To be applied with a iponge, without bruahlng.
J>u.bl>ing.
Resin, 2 Iba ; Tallow, i lb. ; Train-oil, z gaUoo.
Anti-fViotion Gl-rease.
Tallow, 100 lbs. ; Palm-oil, 70 lbs. Boiled together, and when cooled to 80° strain
through a sieve, and mix with 28 lbs. of Soda, and 1.5 gallons of Water.
For Winter, take 25 lbs. more oil in place of the Tallow.
Or, Black Lead, i part; Lard, 4 parts.
To Attacli Hair Felt to Boilers.
Red Lead, i lb. ; White Lead, 3 lbs. ; and Whiting, 8 lbs. Mixed with boiled Lin-
seed Oil to consistency of paint.
Ir'astils fbr Fuxnisating.
Gum Arabic, a ozs. ; Charcoal Powder, 5 ozs. ; Cascarilla Bark, powdered, .75 oz. ;
Saltpetre, .25 drachm. Mix tc^ether with water, and make into shape.
Ifor "Writing -upon Zino Labels.— Horticultural.
Dissolve 100 grains of Chloride of Platinum in a pint of water; add a little Mu-
cilage and Lamp-black.
Or, Sal-ammoniac, i dr. ; Verdigris, x dr. ; Lamp-black, .5 dr. ; Water, 10 drs. Mix.
To Remove old Ironmold.
Remoisten part stained with ink, remove this by use of Muriatic Acid diluted by
5 or 6 times its weight of water, when old and new stain will be removed.
To Cut India Hubber.
Keep blade of knife wet with water or a strong solution of Potash.
.A.dliesive fbr Rubber Selts.
Coat driving surface with Boiled Oil or Cold Tatlow, and then apply powdered
Chalk.
T^iard.
jo parts of finest Rape-oil, and z part of Caoutchouc, cut small Apply heat until
it is nearly all dissolved.
To Preserve Leatlier Ij el ting or Home,
Apply warm Castor Oil. For hose, force it through iL
To Oil X^eatlxer Selting.
Apply a solution of India Rubber and Linseed OIL
a£
8^8 MISCSLLANEOUS MIJtTUBJSS.
I>res8ins for Zjentlner Selts.
I. ^Beef Tallow, i part, and Castor Oil, 2 parts. Apply warm.
2.— Beef Tallow, 3 lbs. *, Beeswax, i lb. Heaiea and applied warm to botL sides
Files.
Lay dull flies in diluted Sulphuric Acid until they are bitten deep enoogb.
To Remove Oil fVom I^eatlxer.
Apply Aqua-ammonia.
To Clean Faint.
Wash with a Solution of Pearlash in water. If greasy, dse QuicUima
Or, Extract of Litherium diluted with from 200 to 300 parts of water.
To Remove Faint.
Mix Soft Soap, 2 ozs., and Potash, 4 ozs., in boiling Water, with Quicklime, .5 Ih
Apply hot, and let remain for i day.
Or, Extract of Litherium, thinly brushed over the surface 2 or 3 times.
To Clean I^arble.
Chalk, powdered, and Pumice-stone, each i part; Soda, a parta Mix with water.
Wash the spots, then clean and wash off with Soap and Water.
Paste fbr Cleaning; ^letals.
Oxalic Acid, i part; Rottenstone, 6 parts. Mix with equal parts of Train Oil and
Spirits of Turpentine.
"Watclxmalser's Oil, -wlxieli never Corrodes or Thickens.
Place coils of thin Sheet Lead in a bottle with Olive Oil Expose it to the sun for
a few weeks, and pour off the clear oil
Durable Paste.
Make common Flour paste rather thick (by mixing some Tlour with a little cold
water until it is of uniform consistency, and then stir it well while bot7tnp water is
beiug added to it); add a little Brown Sugar and Corrosive Sublimate, which will
prevent fermentation, and a few drops of Oil of Lavender, which will prevent it be-
coming moldy. When dried, dissolve in water.
It will keep for two or three yenr* In « covered veoMl.
To XCxtraot G-rease from Stone or !N£arl>le.
Soft Soap, I part ; Fuller's Earth, 2 parts ; Potash, 1 part. Mix with boiling water.
Lay it upon the spots, and let it stand for a few hours.
Stains.
To JB^fftoM.— Stains of Iodine are removed by rectified Spirit; Ink stains by Ox-
alic or Superoxalate of Potash; Ironmolds by same; but if obstinate, moisten them
with Ink, then remove them in the usual way.
Red spot* upon black cloth, ttom acids, are removed by Spirits of Hartshorn, or
other solutions of Ammonia.
Stains of Marking-ink, or Nitrate of SUDer.—Wet sta^n with fresh solution ol
Chloride of Lime, and, after 10 or 15 minutes, if marks have become white, dip the
part in solution of Ammonia or of Hyposulphite of Soda. In a few minutes wash
with clean water.
Or, stretch the stained linen over a basin of hot water, and wot mark with Tinc-
ture of Iodine.
Preservative Paste for Otgects of IN'at'ural History.
White Arsenic, i lb. ; Powdered Hellebore, 2 lbs.
To Preserve Bottoms of Iron Steaxn-l>oilers.
Red Lead, 75 parts; Venetian Red, 17 parts; Whiting, 6.5 parts; and Litharge,
1.5 parts by weight.
To Preserve Sails.
Slacked Lime, 2 bushels. Draw off the lime-water, and mix it with 120 gaUons
water, and with Blue Vitriol, .25 lb.
MISCELLANEOUB OPBEATIONS AND ILLUSTRATIONS. 8/9
'Wh.ite'waah..
For oatside exposure, slack Lime, .5 bushel, iu a barrel; add common Salt, i lU;
Sulphate of Zinc, .5 lb. ; and Sweet Milk, i gallon.
To Preserve 'WTood^vorlc.
Boiled Oil and finely powdered Charcoal, each i part; mix to the cousistence of
paint Apply 2 or 3 ooatSL
Thii composition ii well adapted for cask*, water-aponta, ate.
To Polieli AVood.
Rub surface with Pumice Stone and water until the rising of the grain is removed
Then, with powdered Tripoli and boiled Linseed Oil, polish to a bright surface.
Paiut for Wind.o"vv Grlass.
Chrome Green, .95 oz.; Sugar of Lead, t lb. ; ground fine, in sufficient Linseed Oil
to moisten it Mix to the consistency of cream, and apply with a soft brash.
The fflaaa ■hoold be well cleansed before the paint is applied. The above quantity is sufficient for
abont 200 feet of glass.
To IVIalce I>raixi Tiles Porous.
Mix sawdust with the clay before burning.
MISCELLANEOUS OPERATIONS AND ILLUSTRATIONS.
I. — It is required to lay out a tract of land in form of a square, to be en-
closed with a post and rail fence, 5 rails high, and each rod of fence to con-
tain 10 rails. What must be side of this square to contain just as many
acres as there are rails in fence ?
Opbration. I mile = 330 rocb. Then 320 x 320 -f- 160, sq. rods in an cure = 640
acres; and 320 X 4 tides and X 10 rails =; 12 800 rails per mile.
Theo, as 640 acres t 12 800 rails : : 12 800 acres : 256 000 raUs, which mil enclcse
356000 acres, and v^256ooo x 6^.5701 = number of yards in side of a sq. acre, and
-T- 1760, yards in a mUe =. 30 miles.
2.<^How many fifteens can be counted with four fives?
OPERATION. ^^AX^Xi^^^^.
1X2X3 6 ^
3. — What are the chances in favor of throwing one point with three dice?
Opbration. — Assume a bet to be upon the ace. Then there will be 6x6x6 = 216
different ways which the dice may present themselves, that is, with and vxithout an ace.
Then, if the ace side of the die ts excluded, there will be 5 sides left, and 5X5X5
s= Z25 ivays without the ace.
Th/srefore, there will remain only 216 — 125 =3 91 ways in which there cotdd be an
9ce. The chance, then, in favor of the ace is as 91 to 125 ; that is, out of 216 throws,
the probability is that it will come up 91 times, and lose 125 times.
4. — The hour and minute hand of a clock are exactly together at la;
when are they next together ?
OraiATiOK.— As tiie minute hand runs xi times faster than the hour hand, then,
as II : 60 :: I : 5 min. 27j'j sec. = time past 1 0^ clock.
5. — Assume a cube inch of glass to weigh 1.49 ounces troy, the same of
sea-water .59, and of brandy .53. A gallon of this liquor in a glass bottle,
which weighs 3.84 lbs., is thrown into sea-water. It is proposed to deter^
mine if it will sink, and, if so, how much force will just buoy it up?
Opsration. 3.84 X 12 -f- 1.49 = 30.92 cube ins. of glass in botUe.
231 cube ins. in a gallon X '53 = 122.43 ounces of brandy.
Then, bottle and brandy weigh 3.84X 12 + 122.43 = 168.51 ounces, and contaiD
S61.92 cube ins., which x -59 = i54-53 ounces, weight of an equal bulk of sea-water
And, 168.51 — 154.53 = 13-98 ounces, weight necessary to support it in the water
880 MISCBLLANEOUS OPBSATIONS AND ILLUSTBATIONS.
6. — A fountain has 4 supply cocks, A, 6, C, and D, and under it is a cis*
tern, which can be filled by the cock A in 6 hours, by B in 8 hours, by C in
10 hours, and by D in 12 nours ; now, the cistern lias 4 holes, designated E,
F, 6, and H, and it can be emptied through E in 6 hours, F in 5 hours, G in
4 hours, and U in 3 hours. Suppose the cistern to be full of water, and that
all the cocks and holes were opened together, in what time would the cistern
be emptied?
Ofkr^tioh.— Assume the cistern to hold 190 gallona
hn.
If 6
5
hn. gall. bn. gsU.
If 6 : Z30 :: X : 20 <jrf A
8 : 120 :: I : 15 at B.
so : X90 :: X : la a< G.
IS : X90 :: X : 10 at D.
■Bun in in x hourj 57 gaUont.
8>U.
hn.
CiOL
I20
:: X :
ao
atE.
xao
24
at F.
xao
. . A <
: 30
at 6.
Z20
•• T
: 40
at H.
4
3
Bun out in 1 hour^ 114 gaUcns,
57
Bun out in I hour more than run in, 57 galiont.
Then, as 57 ffaUom : x hour:: xao gaUom : 2. 105+ howrt.
7. — A cistern, containing 60 gallons of water, has 3 cocks for discharging
it ; one will empty it in i hour, a second in a hours, and a third in 3 hoars ;
in what time will it be emptied if they are all opened together?
Opkration.— xst, .5 would run oat in x boar by the ad cock, and .333 by the 3d;
consequently, by the 3 would the reservoir be emptied in x hour. .5 -)- .333 -|- x =
{^-f- f + f > ^ng reduced to a common denominator^ the turn 0/ these 3 = J^ ; whence
the proportion, xz : 60 :: 6 : 32^^ minutes.
8. — A reservoir has 2 cocks, through which it is supplied ; by one of them
it will fill in 40 minutes, and by the other in 50 minutes ; it has also a dis-
charging cock, by which, when full, it may be emptied in 25 minutes. If
the 3 cocks are left open, in what time woiud the cistern be filled, assuming
the velocity of the water to be uniform ?
Operation.— The least common multiple of 40, 50, and 25, is aoa
Then, the zst cock will fill it 5 times in aoo minutes, and the ad, 4 times in aoo
minutes, or both^ 9 times in aoo minutes; and, as the discharge cock will empty it
8 times in aoo minutes^ hence 9 — 8 = x, or once in aoo mumtes=z^a hours.
9. — The time of the day is between 4 and 5, and the hour and minnte
hands are exactly together; what is the time?
Opxration. — Difference of speed of the hands is as x to xa=:xx.
4 hours X 60= 240, which -i- zx = ax min. 49.09 mc, loAicA istobe added to 4 Aoura
la — Out of a pipe of wine containing 84 gallons, 10 were drawn off, and
the vessel refilled with water, after which 10 gallons of the mixture were
drawn off, and then 10 more of water were poured in, and so on for a third
and fourth time. It is required to compute how much pure wine remained
in the vessel, supposing the two fluids to have been thoroughly mixed.
Opsration. 84 — 10 = 74, quantity after the isl dra/ught
Then, 84 : 10 : : 74 : 8.8095, and 74 — 8. 8095 = 65. 1905, quantity after ad drau^U.
84 : 10 : : 65. 1905 : 7. 7608, and 65. 1905 — 7. 7608 = 57. 4297, quantity etfier 3d drctught^
84 : 10 : : 57. 4297 : 6. 8367, and 57. 4297 — 6. 8367 = 5a 593, ^^umtity after 4th drauffht,
= result requiroi.
II. — ^A reservoir having a capacity of 10 000 cube feet, has an influx of
750 and a discharge of 1000 cube feet per day. In what time will it b»
emptied? ^ xoooo ^
Operation. = 40 daya
xooo — 750 ^
Cfonirariwise : The discharge being xooo and the inflax xaso cube feet per hone
In what time will it be filled?
_ zoooo »
Operation. = 40 hours = x day i6 hours,
1250 — xooo ^ '
MISCELLANEOUS OPEBATIONS AND ILLUSTSATIONS. 88 1
12. — A son asked his father how old he was. His fiither answered him
thus : If you take away 5 from my years, and divide the remainder by 8,
the quotient will be one third of your age ; but if you add 2 to your a^e, and
multiply the whole by 3, and then subtract 7 from the product, you will have
"Jie number of years of my age. What were the ages of father and son ?
Opebation.— Assume &iber's age 37.
Then 37 — 5 = 32, and 32 -;- 8 = 4, and 4 X 3 = 12, «)n'» atf«. Again: i2-l-2 = x4,
and 14X3 = 42, and 42 — 7 =: 35. Therefore 37 — 35 = 2, error too lilUe.
Again: Assume fktber^ age 45; then 45 ~ 5 = 40, and 40 -^ 8 = 5. Therefore
5 X 3 = 15, wn'« o^. Again: i5 + 2 = i7,andi7X 3 = 51. and 51 — 7 = 44. Tbere-
fore 45 — 44 =: I, error too little.
Hence (45 sup. x 2 error) — ■ (37 sup. x i error) = 90 — 37 = 53, and 2 — 1 = 1.
Ck>n8oquently, 53 uJiUher^s age. Then 53 — 5 = 48, and 48 -J- 8 = 6 = . 333 0/ son^s
age^ and 6 X 3 = 18 years^ son^s age,
13. — Two companions have a puree! of guineas. Said A to B, if you will
give me one of your guineas I shall have as many as you have left. B re-
plied, if you will give me one of your guineas I shall have twice as many as
you will have left. How many guineas had each of them ?
Opxration.— Assume B had 6.
Then A would have had 4, for 6 — 1 = 4 4- 1 = 5. Again : 4 (A's parcel) — i =. 3,
and 64-1 = 7, and 9x2 = 6. Therefore 7 — 6 = 1, error too Utile.
Again : Assume B had 8.
Then A would have 6, for 8 — i = 6 + 1 = 7< Again : 6 (A's parcel) — 1 =r 5, and
8 + 1 = g, and 5 x 2 = low Therefore 10 — 9 = 1, error too great.
Hence 8 X 1 = 8, and 6x 1=6. Then 84-6 = 14, and 1 + i = 2. Whence, di-
▼idiog products by sum of errors, x4 -7-2 = 7 = B's parcel, and 7 — 1 = 54-1=6
for A when he had received i o/B\ also 5 — 1 X2 = 74-'=8 = B'8 parcel when he
had received i 0/ A.
14. — If a traveller leaves New York at 8 o'clock in the morning, and walks
towards New London at the rate of 3 miles per hour, without intermission;
and another traveller starts from New London at 4 o'clock in the vening,
and walks towards New York at the rate of 4 miles per hour continuously ;
assuming distance between the two cities to be 130 miles, whereabouts upon
the road will they meet ?
Oprkation. —From 8 to 4 o'clock is 8 hours; therefore, 8 x 3 = 24 miles, per-
formed hy A b^/mre B tet out from New Lomdon ; and, consequently, 130 — 24 = 106
are the miles to he travelled between them after that.
Hence, as (3 4- 4) 7 : 3 : : 106 • *^ = 45^ more miles travelled by A at the meeting i
consequently, 24 -f- 45^ = 69^ miles from. New York is place of their me^ng.
15. — If from a cask of wine a tenth part is drawn out and then it is filled
with water ; after which a tenth part of the mixture is drawn out , again
is filled, and again a tenth part of the mixture is drawn out: now, assume
the fluids to mix uniformly at each time the cask is replenished, what frac-
tional part of wine will remain after the process of drawing out and replen-
ishing has been repeated four times?
Opkration.— Since . i of the wine is drawn out at first drawing, there must remain
9. After cask is filled with water, .1 of whole being drawn out, there wiU remain
9 of mixture; but .9 of this mixture is wine; therefore, after second drawing, there
o*
wUl remain .gof.g of wine, or -^ ; and after third drawing, there utill remain .9
of .9 of.g of wine, or ^.
Hence, the part of wine remaining Is expressed by the ratio .9, raised to a pawei
tapomnt of which is number of timet cask htu been draxonfrom.
Therefore, ^odumoZ part of wine is ■ — = .6561.
882 MISCBLLAXEOUS OPERATIONS AND ILLU6TBATIONS.
i6.— Tnere is a fish, the head of which is 9 ins. long, the tail as long as
the head and half the body, and the body as long as both the bead and tait
Required the length of the fish.
Opkratiox.— Assume body to be 24 ins. in length. Then 24 -7-24-9 = 21, lengtM
of taiL
Hence 21 -f 9 = 30, length of body, which is 6 ins. too great
Again : assume the body to be 26 ins. in length. Then 26-f- 2 + 9 = 22, length of
taiL Hence 22 -{- 9 = 31, length of body, whicb is 5 ins. too great.
Therefore, by DotUtle Position, divide difference of products (see rule^ page 99)
by diffei-ence of errors (the errors being alike), 26 x 6 — 24 X 5 = 36 = difference of
products^ and 6 — 5 = 1= difference of errors.
Consequently, 36 -r- 1 = 36, length of body, and 36 -f- s -f- 9 = 27, length of tail, and
36 4- 37 4~ 9 = 72 ifu. , length required.
17. — A hare, 50 leaps before a greyhound, take.s 4 leaps to the greyhound's
3, but 2 leaps of the hound are equal to 3 of the hare's. How many leaps
must the greyhound take before he can catch the hare ?
Oprkation. — As 2 leaps of the greyhound equal 3 of the hare, it follows that 6 of
the greyhound equal 9 of the hare.
While the greyhound takes 6 leaps, the hare takes 8; therefore, while the haro
takes 8, the greyhound g^tins upon her i.
Hence, to gain 50 leaps, she mnst take 50 X 8 = 400 leaps ; but, tohUe hare takes
400 leaps, greyhound takes 300, since number of leaps taken try them are ai4to 2.
18. — If a basket and 1000 eggs were laid in a right line 6 feet apart, and
10 men (designated from A to J) were to start from basket and to run alter-
nately, collect the eggs singly, and place them in basket as collected, and
each man to collect but 10 eggs in his turn, how many yards wtnild each
man run over, and what would be entire distance run over ?
Operation. — A's course would be 6 x 2 feet {first term) + lo x 6 X 2 feet {last
term) = 132 = sum, of first and last terms of progression.
Then 132 -=- 2 X 10 = 660 feet = number of times X half sum of extremes = turn of
all the terms, or the distance run by A in his first turn.
B'b course would be Fi x 6 x 2 = 1 32 feet {first term) -f 30 X 6X2 = 940 feet (last
term) = 372 = sum of first and last terms.
Then 372 -^ 2 x lo := i860 = sum of all the times, or Ws first turn.
A's last course would be 901 x 6 x 2 =#10 812 /«c« /or thefirtt term, and 910x6x2
= 10 g2o feet for the last term of his last turn.
Then 10 812 + 10 920 -?- 2 X 10 = 108 660 = sum of the terms, or distance run.
B's last course would be 911 x 6 x 2 = 10^-^2 feet for the first term, and 920X6X2
r= II 0^0 feet for the last term of his last turn.
Then 10 032 -|- 11 040 -?- 2 x 10 = 109 860 = sum of the terms or distance run.
Therefbre, if A's first and last runs = 660 and 108 660 /r«^ and the number of
terms 10, then, by Progression, the sum of all the terms = sa66oo feet.
And if B's first and last runs =: i860 and iog96o feet, and the number of terms 10,
then the sum of all the terms = 558 6oo/««<.
Consequently, 558 600 — 546 600 = 12 000 = common difference of runs, which, be-
ing added to each man's run — sum of all runs, or entire distance run over.
A's run,^466oo = 182 200 yds.
B's " 558600 = 186200 "
C's " 570600=190200 '*
D's " 582600 = 194200 "
E's " 594600 = 198200 "
F's run, 606600 = 202 200 yds.
G'8 " 618600 = 206200 ♦'
H's " 630600 = 210200 "
I's " 642600 = 214200 "
J's " 654600 = 218200 "
6 006 000 ^e<, wh ich -f- 5280 = 1 1 37. 5 miZ«t.
i9> — If, in a pair of scales, a body weighs 90 lbs. in one scale, and but 4c
lbs. in the other, what is the true weight?
V(4oX9o) = 6o»J.
MISCELLANEOUS OPEBATIONS AND ILLUSTBATIONS. 883
do.-— If a steamboat, mnning uniformly at the rate of 15 miles per hour
through the water, were to run for i hour with a current of 5 miles per hour,
then to return against that current, what length of time would she require
to reach the place from whence she started ?
Opemation. 15 -f- 5 = 20 mileSy the distance run durinff the hour.
Then 15 — 5 = 10 miles is her effective velocity per hour when returning^ and
20-^ 10 = 2 hoto's^ Uie time qfreturning^ and 2 -f i = 3 hours, or the whole time oc-
cupied.
Or, Let d represent distance in one direction^ t and t' greaier and lets times of run-
ning in hours, and c current or tide.
t-\-t'
2 t) X C d
Then, - — -;= velocity of boat throu^fh the toater, and -7 = c.
' X ' t
21. — Flood-tide wave in a given river runs 20 miles per hour, current of
it is 3 miles per liour. Assume the air to be quiescent, and a floating body
set free at commencement of flow of the tide ; how long will it drift in one
direction, the tide flowing for 6 hours from each point of river V
Operation. — Let x be the time required; 20a; = distance the tide has run up, to-
gether with the distance which the floating body has moved; 3X = whole distance
which the body has floated
Then 2ox^3X:=::6X20f or the length in tHilei of a tide.
20
X = — — - X 6 = 7 hours, 3 minutes^ 31- 7^5 seamds.
22. — A steamboat, running at the rate of 10 miles per hour through the
water, descends a river, the velocity of which is 4 miles per hour, and re-
turns in 10 hours ; how far did she proceed ?
X X
OPERATiOM.^Let 09 = distance required, - ,-- = time of going. = time of
104-4 *o — 4
X X
returning. Then, — (----=10; 6a>-f-i4* = 84o; 2005 = 840; 840-^20=42 mite*.
14 6
23. — From Caldwell's to Newburgh (Hudson River) is 18 miles ; the cur-
rent of the river is such as to accelerate a boat descenciing, or retard one
ascending, 1.5 miles i>er hour. Suppose two buats, running uniformly at the
rate of 15 mdes per hour through the water, were to start one from each
place at the same time, where will they meet V
Operation.— Let a;:^the distance fVom N. to the place of meeting; Us distance
from C, then, wilt be 18 — x.
Speed of descending boat, 1 5 -|- x . 5 = 1 6. 5 miles per hour ; of ascending boat, 15 —
1.5 = 13.5 mtte«j70rAour. ~-r--=ztimeof boat descending to point of meeting.
= time of boat ascending to point of meeting.
X 18 — X
These times are of course equal ; therefore, -j— = . Then, 13. 5s = 297 —
10.5 13.5
x6. 5X, and 13. 5X 4- 16. 5X = 297, or 30X = 297.
Hence x = — = 9.9 mUes, the distance from Newburgh.
30
24. — There is an island 73 miles in circumference; 3 men start together
to walk around it and in the same direction : A walks 5 miles per hour, B 8,
and C 10 ; when will they all come aside of each other again ?
Operation.— It is evident that A and C will be together every round gone by A ;
bence it remains to ascertain when A and B will be in conjunction at an even round,
as 3 miles are gained every day by B. Therefore, as 3 : 1 :: 7^ : 24.33-I-; ^"'1 *«
the coDjanction is a fractional number, it is necessary to ascertam what number of
a multiplier will make the division a whole number.
73-4- 24.33-I- s 3, {^ number of days required in which A wiU go round $ timei^
B 8, and C xo times.
884 HISGSLLANBOUS OPBBATIONS AND ILLUSTBATIONa
25. — Assume a cow, at age of a years, to bring forth a cow-calf, and then
to continue yearly to do the same, and every one of her produce to bring
forth a cow-calf at age of 2 years, and yearly afterward in like manner ;
how many would spring from the cow and her produce in 40 years ?
Opkration.— The increase in ist year would be o, in 2d year i, in 3d i, in 4th 3,
in 5th 3, in 6th 5, and so on to 40 years or terms, €04^ term being = mm of the two
preceding ones. The last term, then, will be 165580x41, fVom which is to be sub-
tracted X for the parent cow, and the remainder, X65 580x40, wUl represent increcue
required.
26. — The interior dimensions of a box are required to be in the propor-
tions of 2, 3, and 5, and to contain a volume of 1000 cube ins. ; what should
be the dimensions r
^ - /IOOOX23 - _ /xoooXs* , . , /ioooX5' , .
Operation.— 3/- = 6.43; 3/ ^- = 9.65: and 3/ i^^ = i6in«.
VaXsXS 'V2X3X5 ^ ^' V2X3X5
And what for a box of one half the volume, or 500 cube ins., and retaining
same proportionate dimensions ?
. ^o
Operation. — 2 X 3 X 5 = 30, and — = X5.
15 X 9-65'
Then
,3/ii>^' = ,.; 3/:
7.66; and
V^
x5 X i6»
= la tnt.
30 V 30 V 30
27. — The chances of events or games being equal, what are the odds for
or against the following results?
Odds.
Five XCvents.
Against. In favor.
31 to I
4 33 to 1
All the 5 X out of 5
4 out of 5 2 out of 5
5 to 3 in &vor of the 5 events result-
ing 3 and 3.
G?lxree Kvexxts.
Four Kvezits.
Odds.
15 to X
2.2 to X
Af^ainst.
In favor.
Odds.
7 to X
Even
Against.
In favor.
I out of 3
( 2 or all out
I of3
All the 4 I out of 4
3 out of 4 2 out of 4
5 to 3 against 2 events only, or that
the 4 events do not result 2 and a.
T-wo Bvexits.
Odds.
3tox
Even
Against.
Both events
only out
2
(i on
I of;
In ftiTor.
X out of a
( X only out
I of 2
AH the 3
[ 2 or all out
I of3
3 to I in favor of the 3 events result-
ing 2 and I.
28. — Required the chances or probabilities in events or games, when the
chances or probabilities of the results, or the players, are equal.
Even that the events result x and x.
Events
or
Games.
2X
ao
17
x6
15
X4
13
X2
That a
named erent
occurs a
majority or
more of
times.
Even
1.33 ^ I
Even
X.55 to X
Even
x^ to I
Even
X.5 to I
Even
X.6 to X
Against a
named event
Against each
occarring
an exact
event occur-
ring an equal
miyority of
times.
number
of times.
5 to X
^.M
—
4.66 to X
4.5 '0 »
—
—
4.4 to X
4.4 to I
—
—
4.1 to I
4 to X
^—
—
3.8 to X
3.7 to X
—
-~'
3-44 to X
Events
or
Games.
Tliat a
named event
occurs a
majority or
more of
Umee.
Against a
««»»<«( event
occurring
an exact
majority of
times.
XI
Even
3-4 ^0»
xo
I
X.7 to X
Even
3tOx
X.75 to X
Even
2 to I
Even
^^^ *»
I
5
2.7 to X
2.2 to X
4
3
2
2.2 to X
Even
3 to I
x.66tox
Agaiuat each
event occur-
ring an equal
number of
timea.
3.06 to I
2.66 to x
2.2 to X
1.66 to I
Even.
29. — The chances of consecutive events or results are as follows ;
jii. — 2047 to I. I la — 1023 to I. I 9. — 5ixtOi. I 8. — 255 to I. I 7. — 127101. I 6. — 63101.
Hence it will be observed that the chances increase with the number of eventa
very nearly in a duplicate ratio.
Illustration.— The chances of xx consecutive events compared with 10, are as
9047 to 1023, or 2 to X.
MISCELLANEOUS OPEBATIONS AND ILLUSTBATIONS. 885
30. — Required the chances or probabilities of events or results in a given
number of times.
The numercUor of a firaction expresses the chance or probability either for the re-
sult or event to occur or fail, and the denominator all the chances ^r probabilities
both for it to occur or fail.
Thus, in a given number of events or games, if the chances are even, the proba-
bility of any particular result is as — ■, — = — ; — ~ ; —7— , etc., being i out of
i-f-i 2 2 + 2 3 + 3
3, 3 out of 4, etc., or even.
If the number of events or games are 3, then the probability of any par-
ticular result, as 2 and i, or i and 2, is determined as follows :
Number of permutations of 3 events are i x 2 X 3 = 6, which represents number
of times that number of events can occur, 2 and i, or i and 2, to. which is to be
added the 2 times or chances they can occur all in one way or the reverse thereto.
Hence, —7—^ = ^ = — ^ = — , or 3 to i in fevor of result; and probability ot
♦2-1-6 4 4-3 1' ^ , F J
one party naming or winning two precise events or results, as winning 2 out of 3,
is determined as follows: Number of permutations and chances, as before shown,
are 8. Hence, number of his chances being 3, ? = 4 = 77^— = — , or 3 to 5 in
3 + 5 8 8 — 3 5
fiivor of result; and probability of one party naming or winning all, or 3 events
or results, is determined as follows: Number of permutations and chances being
also, as before shown, 8. Hence, as there is but one chance of such a result,
— ^ = 4- = TT^ = — , or I to 7 in favor of result.
1 + 7 8 8 — 1 7' '
If number of events, etc., are 4, then probability of any particular result,
as 2 and 2, or of winning 2 or more of them, is determined as follows :
Number of permutations and chances of 4 events are 16. Hence, as number of
chances of such a result are 11, —. — = -? = -2 = — , or as 11 to 5 in favor
S + ii 16 16 — II 5
of the result, and that the results do not occur precisely 2 and 2. The number of
chances of such a result being 10, ^-J — = -f- = 5 = — , or 5 to 3 against it.
6 + 10 8 8 — 5 3
If number of events, etc., are 5, then probability of any particular result,
as 3 and 2, is determined as follows :
Number of permutations and chances being 32, and number of chances of such
a result being 20, — ~ — = ^ = -r^ — = ^ = — ,ora85t03in favor of the
12 + 20 16 10 — 10 0 3
result; and that it may occur precisely 3 out of 5, the number of chances are
«o __'o_5_ 5 =5.^ or II to 5 against it
jo-f-22 32 x6 16 — 5 XX
31. — ^What is the dilatation of the iron in a railway track per mile, be-
tween the temperatures of —20° and +130°?
Opbbation. 20° + i3o<^ = 150°. The dilatation of wrought iron (as per table,
page 519) is, from 32^' to 312** = iSaP = .001 357 5 times its length.
Hence, as x8o : 150 :; .cox 357 5 : .001 047 9 = °"'Q47 9 ^f ^^^ ^f^^^ jjj ^ ^j|gj _.
33. — A steamer having an immersed amidship section of 125 sq. feet, has
a speed of 15 miles per hour with 300 H*. What power would be required
for one of like model, having a section of 150 sq. feet for a speed of 20 miles?
As power required for like models is as cube of speeds.
Then i^S — f.a relative Meetions. and — r— *= 2.37 relative poweri
135 '5' =^3375 ^'
Besot, 1 : 1.9 :: 8.37 : 3.844 iime9 W>
886
MARINE 8T«:AM£BS ANP SNGIinCS.
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MAKINE STEAUERS AND BNGINKS.
887
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C
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so ^0 00 « O -
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to 8 avo tn^ t<«i t I I 101 |Rc*R.8
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g -s
=* 3 S
02 ~ s;
M)
■ rt ti SS • ^ « OD SPfl —
a
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SQ
9
888
MAKIKE, BIVBB,
er
Coxxi pound Guid.
Lengths and HuU^ in fed cmd teniht ; DnxugJU^ PropeUer^ and Side Whede
Sur/aoeSt in sq.fset; WeigMs and Displacements, in Tons (/a34o At.;
DimnBioMS
AND
Capacitibs.
Tons.
Service
Length on deck . . .
" bet. perp"™
" tonnage . . .
Beam, do
Hold, do.
Decks
{• • • •
• • • •
Draught, load
Displacement do. . .
Imm'd Sec-n at do.
Freeboard
Cylinders, W
" Int
" L. P. . . . .
Stroke of piston...
Steam pressure. . . .
Revolutions
Boilers
Grate surface
Heating do
Condensing do
Propeller, diam. . . .
Pitch
Side wheels, diam..
Breadth
Coal, weight
Consumption. . . .
Combustion
Cargo
Passengers
Crew
IH>
Speed
Rig
Speed in, Knots per Kotxr.
City of
Paris
and
New
York.
1.
Steol
PandF
527.6
525
527.6
63.2
32
4
5581
10499
as
2 of 45
2" 71
2"lX3
150
86.5
9
X293
50625
33000
3300
Blut
1372
395
1917s
20
Bark'Ds
Colombia.
8.
StMl.
PandF
474
463
4635
SS-6
3S8
4
3737
7363
24
10000
ao:
« it
14.7
of 41
66
2 " zox
66
150
74
9
X320
35 000
2 0f x8
3a
Natural
X096
X3000
20
3-ia Scli'r
Naim-
■hire.
8.
StMl.
RefriK'tor
350.5
350
35a 6
47-7
24.3
2
2438
3720
34-3
7880
1058
4
37
44
71
48
z6o
70
3
30p
6963
303a
«6.5
18.5
X366
3000
Natural
5360
SO
48
2000
xx.s
Brig
Br«m«r-
havflD.
4.
StMl.
PetroUam
350
340
339-6
42.6
37.3
3
a 179
3393
3X.3
6600
870
5
as
40
66
4a
x6o
63
3
X54
4800
3383
X7.6
X7.6
821
Nataral
4000
^S
1550
10
3-in Seh'r
Tyne-
•idoY.
Simon
Duiaoia
aadMa-
na((va.
6.
Iron,
FandP
26a5
360
360
33-7
IS- a
3
693
1390
174
3560
530
38.5
46
75
4a
160
74
3
3X6
6618
3450
z6
3Z
130
2400
Natural
1080
1389
as
3400
X5.X
3-mSeh
6.
StMl.
Fruit
184
174.8
x7Sa
37.8
«9
3
S14
7x7
16.3
X463
404
\i
36
40
33
160
90
z
63
30I0
ZO
14s
Electric
and
nolk.
143
1005
Natural
936
16
30
670
13.5
Sch'r
7.
Iron.
Flailing
III. 9
X06.9
107.4
30.S
IX.5
k
xx.s
330
«3S
13.75
30
3a
23
ISO
X34
X
800
390
I
I
Natural
X3
388
ia35
Dandy
DSoL
8.
Iron.
FandP
388.75
377- a
375
48
24
3
3oai
3Z
6760
934
*3
3a
Sa
84
54
x6o
76
3
X0500
6400
18
23
1000
5000
NaadB
4000
50
3500
»4.5
4-inSck
R.eniarl^s. No. 1. J. & G. Thomson, Glasgow, Scotland; Area of Immersed
Horizontal Section at Load-line, 16 500 O foot = coefficient .5. No. S. Laird
Bros., Birkenhead, Eng. No. 8. R. & W. Hawthorn, Ledie it Co., New-
No. 4. RusseD
castle, Eng. ; Hull 3375 tons. Engines 180, and Boilers X56.
& Co. and 6. Stewart ft Co. , Greenock, Eng. ; Hull 1950 tons, Engines and Boilers
330. >Xo. 6. Tyne Steam Shipping Co., Newcastle, England; Engines 135
tons, Boilers 220, and Water 60, "Well- deck." No. 6. Grangemoath Dock-
yard Co. k Hudson & Gorbett, Glasgow, Scotland; Hull 391 tons, Engines 53, Boilers
40, and Water 27; Area of Load-line 3850 nfect, and of Sails .231a Na 7.
Earless Co., Hull, Eng. ^No. 8. The Wm. Cramp k Sons S. and E. B. Co., Phil-
Wa, Pena No. f and 10. Delaware River L & B. and E. Co., Chester
AKD INLAND STKAUSBS.
889
and. IiVeislit.
Xiriple Sxpaxxsion*
in feet cauX ins.; Engines, in ins.; Pressure, in lbs. ; RevoltUions, per minute ;
Fuel, in lbs. per Hour; P Passengers and F Freight.
Speed in. AdCiles pex> Hour.
8miU
lUaa.
Paritan.
Tnaearo-
ra.
Racina.
Jofan F.
Smith.
New
York.
Ata-
Unto.
Suaque
hauna.
9.
10.
11.
IS.
18.
14.
16.
1«.
Iron.
steal.
Steel.
Iron.
Iron.
Iron.
Iron.
Iron.
PandF
PandF
F
FandP
PandF
P
Yacht
Yacht
343-5
—
306.7
330
130
3x5
240
166.5
326
40a
396.7
389.3
— •
X22
^ —
228.5
150
33a- 5
403-5
203.5
X22
30X
223.9
164
4a6
52
40
35
4a
4a 2
a6.33
32
as
18.x
23
—
9
XI
15-2
»3
a
X
a
X
1
X
3
I
1335
3075
1937
80a
X42.39
X092
284
117
3416
4593
2669
X04X
X35.60
«553
568
233
»3-7
13
16
—
5-3
6-33
X2
9-3
3"5
4775
3570
—
X55
xooo
XO42
310
511
643
634
2x8
83
235
246
138
8.5
7
9-7
—
3
6
4-75
4-5
45
75
li
a8
X4
—
30
"7
— —
—
aia
•^
^—
^—
38
86
xxo
6x
SO
26
75
60
42
54
9aiuix4
t*
36
x8
xa
30
22
t
xxo
x6o
1x0
"5
50
XX5
x6o
24
90
xoo
30
X28
X64
4
8
3
a
I
3
a
I
480
850
i6a
90
—
230
X46
65
Z3 000
36000
5574
4000
1258
5360
4534
2z8o
i5ooo<
Jet
—
624
5700
3226
1470
15
—
14
10.5
6.4
—
^
8
»4
—
»7-5
«6.5
9
—
—
—
—
35
—
—
—
3a x6
—
—
—
«4
—
—
—
X2.5
—
—
aoo
300
230
xxo
15
50
170
50
I75^H•
X.9 p. H?
3340
X400
4
3.5 p. BP
—
—
ffataral
Nateral
Natural
Nataral
Nataral
Blaat
Blaat
Blast
600
900
3140
310
—
—
—
«6S
1 300
—
—
ISO
2100
x8
—
—
aoo
o^
—
8
50
45
—
3000
7500
1800
750
300
3700
1950
925
«9
31
16
«4-5
13
»3
1745
18
Sch'r
—
Sch'r
Snh'r
—
—
3-m Sch'r
Sch'r
Robert
E. Ue.
17.
Wood
PandF
315
306
315.8
48.5
9.3
I
1479
2 of 40.5
10
148
21
.?8
3360
39
17
Nfltural
1425
300
150
21
Mary-
land.
18.
Steel.
Fandl
332
316.4
42
20.4
2
1892
2419
16
4690
650
8
33
35
56
160
85
2
152
4656
13.3
16
300
Natural
3100
8
'9
I200
13.5
Sch'r
Penn., and W. and A. Fletcher Co., Hoboken, N. J. No. 11. Globe Iron
Works, Cleveland, Ohio; Hull 1240 tons, Engines 200, and Boilers 70 tons.
Xo. IS. Cha& F. Elmes, Chicago, 111., and Burger k Burger, Wis. ; Freight and
Cabin on deck ; Hull 350 tons, Engines 40, Boilers 36, and Water 23.— ^ No.
IS. Pusey & Jones Co., Wilmington, Del No. 14. W. & A. Fletcher Co.,
Hoboken, K. J. ; Water-wheel blades, 13 of 45 in& ^No. 16. Same builders
as No. 8. ^No. 16. The Harlan & Hollingworth Co., Wilmington, Del. ; Hull
136 toss, Engines 20, and Boilers 25.
No. 17. Jas. Howard k Co., Jef-
fersonviUe and American Foundry, New Albany, Ind. ; Water • wheel blades, 23
of 35 Ins. Na 18. Detroit Dry Dock Co., Detroit, Mich. *, Hqll 1250 tons,
Engines 140, and Boilers 70.
4F
890
STEAM-VESSELS. FERRT AND TOWING.
IFerry Passenger and Team, and To-w-Tjoats-
Single, Compound, and Triple Expansion,
Length and Hull, in feet and tenths; Draught, l*ropeller, and Side Wheels, in feet
and ins. ; Engines, in ins. ; Pressure, in lbs.; Revolutions, per minute ; Surfaces,
in sq. feet ; Wei^ts and Displacements, in Tons of 2240 tbs. ; Fuel, in tbs. per
Hour; P Passengers and T Teams.
Speed in Aliles per Hour.
DlMKHSIONS
AND
Capacitibs.
Tons.
Montank
and
WhiUball.
Ferry.
1.
Iron.
PandT
209
195
196
37-4
65
14.1
839
1088
"880
a»5
7-5
in
Jotin G.
McCul-
lou^h.
Ferry.
20.5
8.66
5
Natural
loio
3500
4130
470
104
5«
29.5
X2
2.
Steel.
TwdP
915
'98.5
198.5
45
62
»4-5
X
1008
i3»o
II
»340
450
7-75
3S
50
36
IQD
I30
9
140
a of
Berf^n.
F^rry.
8.
steal.
Paii4T
203
2CX>
220.4
37
63
16.6
I
734
J117
9.5
560
235
6.9
18.5
27
4a
24
160
169
3
81
3463
3 of
8
8.91
4
SeiTice
Leugtb OQ deck
'• bet. perp're. .
" tonnage
Beam do.
" over guards. . .
Hold, tonnage
Decks
{• « • •
• ■ • •
Draught, load
Displacement do
ImmersedSec'n at do.
Freeboard
Cylinders, H*
Int
LP 50
Stroke of Piston so
Steam Pressure 50
Revolutions 33
Boilers i
Grate surface 168
Heating do. 1380
Condensing do jat
Propeller, diam. . . {
Pitch
Blades
Side-wheel diam
" width...
Coal, weight
Consumption
Combustion Natural Natural
IBP
Team space 3500 4530
Passenger do 4130 5200
Weight, Hull
Engine
Boilers
Water
Speed 12 12 14.6
Remarks. No. 1. Side wheel, T. S. Marvel k Co., Newburgh, and Quintard
Iron Works, N. V.; Double ends. No. 2, Ncafie and I^vy, Penn Works,
Pbila., Pa. ; Propeller at each end. No. S. Hull same as 1, and Ilelamater
Iron Works, N. Y. ; Propeller at each end ; Weights : of Hull as launched ; Knginea. not
including steering and ventilating; donkey pum))s, piping and chimney; augmented
surface, 7524 Gfo«t. \os. 4. and 5. The Harlan and Hollingsworth Co., Wil-
mington, Pel, Propeller nnd Side-wheel. No. 6. Neafie and Levy, Phila. ;
one Wrecking pump, 16 and 20X 18 ins., three 8-inch suctions on each side, caiNicity
f'oo tons water per hour; one fire pump, eight 2.5-inch streams ; Electric search-
igbts, 6000 candle power, several of 2000 candle arc-lfgbts. No. 7. The
Puscy k Jones Co., Wilmington, Del. — No. 8. Hull same as Nos. 1 and 8, and
engines W. k A. Fletcher Co., Hoboken. N. .1. ; Propeller at each end: No. 8 and
these* designed bv r.oi v a Steveqs, Hoboken. N. J.
IS
1580
Natural
1007
3448
4330
321
177
48.5
«5
In-
trepid.
Maine.
Ferry,
Inter-
natiop-
al.
Meteor.
Pat-
•raon*
and
M»t«.
4.
$.
6.
1.
sEcl.
Iron.
Iron.
IroB.
Iron.
Towtofr
TandP
'Howiatr- Tawiiife.
PaadT
118
189.3
140
95
933
XIO
'75
129.6
87.66
2x7
"4
174
X30
9»-5
33.5
36.5
26
18.5
40
—
63.5
—
— .
63
II. 6
1J.3
x6.9
8.6
16.6
I
I
I
x
3
108.0
317.8
545-7
400
55-6
850.3
300
95.6
—
9-5
7.3
12
8
xo.6
303
678.5
530
150
750
164
206
260
4
5*6.5
5-5
— -
6.9
33
46
16
>6
3 of 20
—
••—
24
—
— .
40
^
41
32
2 of 36
36
130
30
cB
38
100
32
160
100
X25
90
»4
—
100
X20
X
z
2
z
3
71-5
76
80
45-5
91
3503
2»59
3400
1318
333«
1105
Jet
IIOO
553
3224
9-5
—
9-5 •
8
2 of
■—
—
—
8.6
14^16
-^
—
»4
XX
4
—
4
4
4
—
20.5
—
-»—
—
_
8,6
-.—
.^
-_
60
40
370
z6
13
-—
—
—
430
—
Natural
Natural
Natural
Nataral
Natural
—
650
800
380
X350
—
3420
—
—
3760
450
2896
—
4750
—
—
-~'
50
^80
13
13
26
vxo
20.5
39-75
—
3X
80
17.6
39.6
—
—
40
»3-5
13
15
13
M-5
MABlNlfi BTJfiAM VB8SfiL8 AUTD BNOINBS. 89!
"Wood. Propelleris.
HzRRnHOFFt R N., Vertical Dibkot Eitginb (Compound).— Length on deck, 46
feet; over aUf^B/eei; beam, g feet; hald^sfeet.
DUpiacement at load-line, 7.44 torn. Area of tection at Umd-Une, 2x7.8 iq.feet
Area of wetted iurface, 365. 5 iq. feet. Coefficient offineneu, . 396.
cytMder.— 8 and 14 ins. in diam. by 9 ine. stroke of pistoa
Conden$er, External.— Surface.
Propeller.—^ blades, 3 feet in diam. by 4 feet z inch pitch.
Blower, 42 ins. in diam.
BvUer ^vertical coil). Heating surface, 174 sq. feet. QrcUe», 12.5 sq. feet.
Preature of Steam, 53 lbs. per sq. inch. Revolutions, 333 per minute. IIP, 68.4.
Speed, xai8 knots per hoar. With 129 lbs. and 466 revolutions, 14.26 knots. IWt
169.5. Weight of Engines, Boiler, and Water, 5300 lt)&
Hbrrbshoff, Vbrtical Dirbct Engine {Compound). — Length over all, 96 feet;
beam, 1 1 feeL Displacement, 27 tons.
Cylinder.— 13 and 22 ins. in diam. by 12 nns. stroke of piston.
Surface Condentimg.
Pressure, 130 lbs. per sq. inch.
Revolutions, 460 per minute. Speed, 20 knots per hour. IW, 425.
Propeller, 3 bladea Pitch, 5 feeL
Hbrrbshoff, R. I. N.— Vertical Direct Enuixe {Compound).— Length over aU,
60 feet ; beam, Tftet; hold, 5. 5 feet. Displacement at load-draught of yz inx., 7 Urns
(2240 lbs.).
Cylinders. — 8 and 14 ins. in diam. by 9 ins. stroke of piston. Surface condenser.
Pressure of Steam.— 140 lbs. per sq. inch, cut off at .5.
RevolmUons, 600 per minate. Speed, 19.875 knots per hoar.
Cable or K,ope To"%ving.
''NrrrRA."— Horizontal Direct Engines {Condensing).— Leimth of boat, i^B fset;
beam, 24. 5 feet ; hold, 7. 5 feet.
Immersed section, 74.4 sq.feet. Displacement, 200 tons at load line of ^ysfseL
Immersed section, 263. 7 Sq. jeet Displacement, 949 tons. Tow. —3 barges.
Cylinders. — 2 of 14.18 in& in diam. by 23.625 ins. stroke of piston.
IH*, net effective, loa Speed, 7.73 miles per hour.
Propellers.— Tyf in, 4 feet 2 ins. in diam.
/SXreM.— Gable, 7485 lbs. Per ton of displacement, 6.5 Iba ; per sq. foot of Im.
menied section, 22 Ibe.
PueL-Per mile and ton of displacement (1149), -^7^ ^^^■
To-wiiig. "Wood. Side "Wheels,
*'Wx. H. Webb.'*— Harbor an'd Coast.— Vertical Beam Engines {Condensing).
-^Length upon deck, 1 85. 5 fe^t ; beam, 3a 25 fe^ ; hold, to. 8 feet.
Immersed Section at load-line, 194 sq.fDeL Displacement 498.35 tons, at load-
draught of y. as feet.
Cylinders. — 2, of 44 ina. in diam. by 10 feet stroke of piston ; yolume, 211 cube feet
Condensers. — Jet, 2, volume 105 cube feet. Airpumj».—2, volume 45 cube feet.
WeUer-uiheeli.— Disan., 30 feet. Blades (diTided), 21; breadth of do., 4.6 feet;
depth of do., 2.33 feet Dip at load-line, 3.75 feet.
Boilers.— 2 (return flue). Heating surface, 3280 sq. feet. Orates, 147.5 sq- feet
8nuke-pipe.—kTes^ 11.6 sq. feet, and 35 feet in height above the grate leveL
Preuure ^ Steam.— 2s lbs. per sq. inch, cut off at .5 stroke. Revolutions, zi pel
minute. IIP, 1500.
/\i^.~AntbracHe or Bitnminoua. Consumption, 1680 lbs. per hour.
Speed.— 20 miles per hour.
H'eiyA<«.— Engines, Wheels, Frame, and Boilers, 310579 lb&
892 BIVSB 6TBAHB0ATS, sms AND 6TBBN WHBBL.
"Wood. Side "Wlieele.
Passexigrer.
" Mart Powell," Hudson Ritbp.— Vertical Beam Engine {Condensing).— Lenfj^
on water-line^ 2'^ feet; over all, ig^feet ; 6eam, 34 feet 3 tiw. ; over all, 6^ feet; Ao&t,
gfeeL Deck to promenade dedc, 10 feet.
Immerged section (U load-line of 6 feet^ soo tq. feet Displacemisnt, 800 tons at
mean load-araught of 6 feet-.
Area of transverse head surface ofkuU a^Hfve water, 2000 sq. feet
Cylinder— 72 ins. in diam. by 12 feet stroke of piston*, volume, 338 cube feet
Clearance at each end, 12.5 cube feet.
Steam and Exhanut Valves, 14.75 ins. in diam. Air-pump, 40 ins. in diam. by 5
feet 2 ins. stroke of piston. Condenser. — Jet^ 128 cube feet Crank-piny 8.75 iD& in
diam. x 10.75 ins.
Beam, 22.5 feet in length; centre, 9.75 in diam.
Water-wheels — Diam. 31 feet; blades (divided), 26; breadth of do., 10 feet 6 in& ;
width, I foot 6 Ins. ; immersion, 3 feet 6 ins. 5^/ia/ls.— Journal, 15.625 ins. by 17 ina
Boilers.— 2 (flue and return tubular), of steel, u feet fVont by 26 feet in length;
shell, 10 feet in diam. and 16 feet i inch in length. Furnaces, 2 in each, of 4 feet
10 IBS. by 8 feet in length. Healing Surface, 2660 sq. feeC; and Superheating, 340
sq. feet in each. Grates, 152 sq. feet. Flues, 10 in each, transverse area, n feet
7 ins. I*ubes, 80 in each, 4.5 ins. in diam., 6 feet 6 ins. in length, and 8 feet 7 ins.
in transverse area.
Steam Chimneys, 8 feet in diam. X 12 feet in height. Smoke-pipe, 4 feet 6 ins. in
diam. and 68 feet in height fk'om grates.
Combustion, Blast. Blowers, 4 feet in diam. and 3 feet in width. Revolutions, 78
per minute. Fuel (anthracite), 6280 lbs. per hour, or 40 lbs. per sq. foot of grate
per hour. Per sq. foot of heating surface, 2.25 lbs.
Speed, 23.65 miles per hour.
Pressure of Steam, 28 lbs. per sq. inch, cut off at .47 stroke; terminal pressure,
16.4 lbs. ; throttle, .625 open. Vacwwn, 25 ins. BevolMitMns^ 32.75 P^i* minute.
Temperatures.— Reservoir, 120°. Feed water ^ 120°. Chimney, 740°. EP.— Total,
1900. IBP, 1560. Net, 14501
EvaporalMn.— Water per lb. oTcoal, from 120°, 7 lbs.; per lb. of comhnstible,
fl-om 120°, 8.2 lbs. ^eam per total BP per hour, 21. i lbs. Coal per do. do., 3.14 Iba
Weights. Engine. — Frame, keelson, out - board wheel - f^mes donkey engine,
and boiler, blower engines and blowers, all complete, 360000 lbs. Botters.— Iron
return flue. 120000 lbs. Steel return tubular, 116 000 lbs. Water, 128000 lbs.
Capacity.— 21000 passengers and their baggage.
Memoranda.— 1h\B vessel was originally but 266 feet in length, and when length-
ened the cylinder of 62 in& in diam. was removed and replaced with one of 72 ins.
Engine designed throughout for original cylinder and a pressure of trota 50 to 55
lbs., cutting ofl'at .625 of stroke, with throttle wide open.
Engines and Boilers built by Fletcher, Harrison, k Co., New York, 1861 and 1875.
Iron. Stern. W heels.
Passenger eind iF'reigUt.
Horizontal Engines {Non-emidensing). — Length upon deck, no feet; beam, 14
feet {deck prqjecting over, 4 feet) ; hold, 3. sf^'
Immersed section at load-Hne, 10.25 sq. feet DispUteement at load-draught of x. i
feet, 33 Urns.
Cylinders.— Two, of 10 ins. in diam. by 3 feet stroke of piston; volame of piston
space, 1.6 cube feet
WheeL—msLva. 13 feet. Blades, 13; breadth of do., 8.5 feet; depth of do., 8 ins.
Revolutions, 33 per minute. Boiler.--One (horizontal tubular). Tubes, xoo of a
ins. in diam.
Fuel.— BliuminoMS coal. Consumption, 4480 lbs. in 24 hours.
HulL-Plates, keel, No. 3; bilges, No. 4; bottom, Na 5; sidoB, N06. 6 and 7.
Frames, 2.5 X .5 ins., and 30 in& apart firom centrea
BIVER STEAMBOATS, STEBN WHEELS.— -OIL LAUNCH. 893
"Wood. Stem "^riieels.
Passenger and I^eok F'reigh.t.
"MoHTANA.*'— HoRizoNTAi. Enoinbs (Non-condensifig) — Length vpon deck {over
alt)y 248 Jiet ; al waUr-line, 345 feet ; beom^ 48 feet 8 ins. {over aU, 50 feet 4 int.);
hold, 6 feet; draught of water ai load-line, 5.5 feet.
Immersed seetion at load-line^ 344 sq. feet Displaeement ai mean light draught
ofaa inf., 594 tons (aooo lbs.)
Cylinders.— Two, 18 ins. in diam. by 7 feet stroke of piston.
ValveSy 4.5 and 5 ins. In diam. Piston-rod, 4 ins. Steam-pipe, 4.5 ina Oormeet*
ing-rodf 30 feet in length.
Waier-wheel, 19 feet in diam. by 35 feet face; blades, 3 feet in depth. Shaft,
xa25 in& in diam.
Boaers.—Yoxxr (horizontal tubular), 4a ins. in diam. by 26 feet in length. Two
floes in each, 15 in& in diam. Heating surface, effective, 1023, total 1431 sq. feet
Furnace, 6.5 X 17 feet Orales, 4.16 X 17 fe«t; surface, 70.8 sq. feet Smoke-pipes.
—Two, 3 feet in diam. by 55 feet 3 ins. in height Exhaust or Blower draught
Calorimeter.— Ot Bridge, 15.27; of Flues, 0.82; and of Chimneys, 14.14 sq. feet
Areas of grate, compared to calorimeter of flues, 7.2; to ditto, of chimneys, 5; and
of bridge, 4.6 sq. feet
Steam-room^ 562; and water space, 294 cube feet
Hull.— Frames, 4X6 ins. and 15 ins. apart at centrea Intermediate do., 4x6
ins., and running for 7.5 feet each side of keelson. Flanking. —BotXom, oak, 4 ina ;
side do., 2.5 to 4 ina Deck beams, pine, 3X6 ina Deck plank, 2.5 ins. Keelson^
oak ; side do. , eight each side, one each 7, 8. 75, and 9 ina , and five 6. 75 ins. Wales,
one each side, 9 and 7 ina by 3, and one 10 X 2.5 ina Deck posts, 3.5 X 3 ina and 4
feet apart D^ beams, 5.5 X 3 ina Knuckles, oak, 6 x 12 ins. Bulkheads, one
longitudinal and one athwartsbip at shear of stem. Sheathing of wrought Iron,
.o6as to .135 inch fh>m Just below light to load-line.
Hog iVctf.— White pine, 8.5 and xz Ina square. Chains, z.5 ina in diam.
Weif^. — Boilera 29 264 ; water, x8 351 ; and boilers, chimneys, grates, and wat^^r,
55 672 Iba Hull, oak, 520 560; Pine, 91 437 ; Bolts, spikes, etc, 8000, and Deck and
guarda 76000 Iba ; Hull alone, 310 tona
Weight of hull compared to one of iron as 8 to 5, efltectlog a difilnrence of abonk
sootona
•'PiTTSBCBOH."— HoEizoNTAL Enoinu {Non-condensing). — Length on deoky 35a
feci; beam, 39 feet; hold, 6 feet; draught ofwaUr al load-line, afeeL
Immersed section at load-Une, 75 sq.feeL Displacement at load-draught of a>%e^
380 tons (2000 Iba).
^Kndcr*.— Two, ax Ina in diam. by 7 feet stroke of piston.
WaUr-wheeL—ai feet In diam. by 28 feet fece.
BoOers.— 3 (horizontal tubular), 47 Ina In diam. by 28 feet in length. Two flra
in each.
Oil Kngine Zjaiancli.
Slements or Snsine and Dimensions of X^aunolu
Consumption .9 pint ordinary Mineral Oil per Iff per Hour.
TfP^
w
No.
6
No.
■ X
5
4
a
3
LMIDch.
Leofth. I Breadth.
Feet
4
5
6
FceU
16
az
27
* I>«V«io|>«i bjr Brake
Welghtf
Lbe.
896
1568
Type.
No.
3
2
I
H?»
No.
5
10
IS
Laoncfa.
LcbkUi.
Feet
30
40
45
Bfcadth.
Feet.
7
7
7-5
Weigktl
Lba.
1848
2688
3136
4F*
t Of «agf^« withoot «0«
894 BIVBB STSAMBOATS.— ^AILINGt YfiSSKLSa.
Passenf^ev »n4 7)^ol^ ^peisht.
"PiTTflBUROH."— HojiizoNTAL E9GINB9 {Non-condensitig). — Length on deeky asa
' fset; beam, sgfeet; hold, 6 feet; draught ofwcUer at load-line, 2 feet.
Immersed tection ai load-Une, 75 nq.feet DispUuxment at load-draught ofa/M^
380 tofM (2000 IbB.).
(;^{tfider«.— Two, ai ins. in diam. by 7 feet stroke of piston.
Watcr-tvJiccl. — 21 feet in diam. by 28 feet face.
Boilers.— 2 (horizontal tubular), 47 ins. in diam. by a8 fe«t in length. Two fires
in each.
Iron. Stem Wheels.
Horizontal Engines {Non-condenstng). — Length upon deck, no feet; beam^ 14
feet {deck pnyectimg over, 4 feet) ; hold, 3. 5 fett.
Immersed section at load-line, 10.25 ^qfeet. Displacement at load-draught ofi.x
feet, 33 tons.
Cylinders.— Tvro, of 10 ins. in diam. by 3 foet stroke of piston; volame of piston
space, 1.6 cube feet
Wheel— Di&m. 13 feet. Blades, 13; breadth of do., 8.5 feet; depth of do., 8 in«.
BevoluHons, 33 per minate. Boiler. -^i^e (horizont^ tubule). ^6m, 100 of a
ins. in diam.
J*u«;.— Bituminous coal. Consumptiomy 4480 lbs. in 34 hours,
HuU.— folates, keel, No. 3; bilges. No. 4; bottom, No. 5; sides, Noe. 6 and 7.
Frames, a.$ x .5 ins., and ao ins. apart trofa centrea
Steel.
"CHATTAHOOCffEK."— IsrcuNED ^xGiNEs {Honcondensing).— Length on deck^ 157
feet; beam^ 3h$f^^i *<>W, s/eirf.
Im^nersed section at load-line, 153 »q. feet. Freight eapaoity^ 400 tons <aooo lbs.).
Cylinders. — Two, 15 ins. in diam. by 5 fset stroke; volume of piston space, xa.a6
cube feeftk
Wheel.— Ons, 18 feet in diam. ; blades, 2 feet in depth.
Boilers. — ^Three (cylindrical flued). Diam. 42 ins. ; length, 22 feet; 2 flues' of xo
ins. in each. Heating surface, 690 sq. feet. Orates, 48 sq. feet
Pressure of Steam, 160 lbs. per sq. inch, cut off at . 375. Revolutions, 22 per min.
Consumption of Fuel, 12 tons (2000 lbs.) in 24 hours. Mating of HuUy .1875 to
.25 inch. Light draught, ax m&
Iron Propellers.
Vbbtical Dirbct Engines {Non-eondensing). — Length on deck, jofeet; beam, 10^5
feet; draught, 12 ins.
PropeUers, 2. — 2 blades, 16. ins. in diam., set 11 ins. below water-Una
BoUer (tubular coil). Revolutions, 4B0 per minute.
Speed, ia49 miles per hour.
Water led to propellers through tunnels in bottom at sidea
"Louise."— Vertical Tandem Engines (CompouTid) Length, 60 feet ; beam^ la
feet; hold, /^.^sfeet.
Displacement at load-draught of a. s feet, 8 tons.
Cylinders, 5 and 10 ina in diam. by 8 tna stroke of pistop.
Surface Condenser.— BoUer (vertical tubular), 4 feet in diam. by 8.5 in length.
Iron. Sailiiifs "Vessels.
^passenger and. y>'eight«
English. — Ship — Length upon deck, xjZfeet ; do. at mean load-line of tg. 16 feet,, tjy
feet; keel, lyt feet; beam, 32.88 /«e^; depth of hold, 2i.75/e«<; keel (mean), ^.jsf'oeL
Immersed section at load-line, 387 sq. feet. Displacement at load-draught of ig. 16
feet, 1385 tons; at deep load-draught of 20 feet, 1495 tons; and, in proportion to its
circumscribing parallelopipedon, . 524.
Load-line. —Area at load-draught, 4557 sq. feet Angle of entrance, 57° ; of clear
Hn^, 64O Area in proportion to its circumscribing parallelogram, .784.
YACBTS.-r-OUTTBBS. — PILOT SOXT. 805
Cenire of Oravity^ 6.416 feet below mean load-line. Centre of Displacement (grav-
ity of), 6.25 feet below loadltfie; aod 4.33 feet before middle of length of load line.
Immersed Surface. —Bottom^ 7370 sq. feet. Keei,^ 1130 sq. feet. Sails^ 13 282 sq. fbet.
Mcta-centre^ 6.66 feet above centre of gravity of displacement. Centre of Slffbrt
before centre of displacement, 3. 5 feet ; height of do. above mean load-line, 55. sfoet.
Steam Lauhch ''Hbrbbsboff."— Vkbtical Engine {Compound).— Lenffth^ ^2 fi^
1 inch; beam, S.jsfset.
Displacement at mtan load-draught o/(to rabbet of keel) 19 ins., 8939 Iht.
W€iffids.—lSLvXL and Machinery, 6555 lbs. Coal, 1120 Iba
Yaclits. "Wood.
*" America/' ^BOOV^K.—Lengtk over all, o/i feet ; iqwn deck, gifi^t ; cU load-Ktte^
90. 5 fuet ; beam, 22. $feet ; at load-line, 22 /eei ; depth of hold, 9. 25 feet. He^t at
tide Jrom under side ofgarboard stroke, 1 1 feet. Sheer, forward, 3 feel ; q/l, i. 5 feU,
Immersed section at load-line, 131. 8 *a.feeL Displaecmtnt at load-droMght ofB. 5
^feet, from vndir side ofgarboard stroke and of n feet ajt^ 191 ton*; andy in pro-
'portion to Volume of circumscribing parcUlelopipedon, .375.
Displacement at 4 feet {from garboard strake), 43 tons ; at s J^ 66 tons ; at6
feet, 93 tons ; at 7 feet, 127 tons ; and aJt Sfeet, 167 tons.
Centre o/6rart<y.— Longitudinally, 1.75 feet aft of centre of length upon load-
line. Sectional, 2.58 feet below load-line. Of Fore body, 14.35 feet forward; and
of After body, 19 feet aft. Meta-centre, 6. 72 feet above centre of gravity.
Centre of Effort, 31 17 t<Bet from load line. Centre of Lateral Resistance, 6.33 feet
abaft of centre of gravity. Area of Load-line, 1280 sq. feet. Mean girths ^im-
mersed section to loadline, 25 feet.
Load-draught. '-Vorvrax^ 4.91 feet; aft, ii 5 feet. Rake of Stem, 17 feet
Spars. —Mainmast, 81 feet m length by 23 ins. tn diam. Foremast, 7^.5 feet in
leDgth by 34 ins. in diam. Main boom, 58 feet in length. Main gaff, 28 feet. Ik>rs
gaff, 24 feet Rake^ 3.7 Ina per foot. Drag ofKeel^ 3 feet. Tons, 170.56.
*'JrMA," SuyoT.— Length Jbr tannage, ^2.25 feet; an toaler-Hne, 70 feet 7 int.;
beam^ igfeet 8 ins.; hold, tfeet 8 ins. Tons, O. M. 83.4; N. M. 43.98.
Load-draught, 6.2s feet.
Hails.— Mainsail, hotst, 40.75 feet, foot 54.25, and gaff 37. 66; Jib, hoist, 49.75 fec^
foot 39. 5, and stay 63. 5. Qaff topsail, hoists 24. 5 feet.
.^rAu. —MainsaiU 2333 sq. feet Jib, 986, and Topsail, 454.
Cutters,
''Tara '' (English) ^how.— Length on load-line, 66 fest; beamy 11.$ feet
Immersed section at load-line, 11.5 sq. feet. Displacement, 75 tons.
Spars.— M€ut, deek to honnds, 42 feet Boom, 58 feet. Gaff, 39 feet BowmrU
ontaide of stem, 30 feet MaH to stem, 26 feet Tnpmast, foot to hoondi, 35 feet
BaUoon topsail yard, 46 feet Ca;in)as, area, 3450 sq. feet Tons, C. H., 90.
BaUaxL —At Keel, 38. 5 tone. HuU, i. 5 tons.
*' Mischief" (EngUtk), Sloop. — Length on load-line, 61 fset; beam, ig.gfeet.
Immersed section at load-UnCy 60 sq. feet Displacement, 55 tons.
Pilot Soat.
•' Wm. H. Asmnwall," Scboosnn.— Length of keel, 74 feet; upon deck, 80 yifrt;
beam, igffet ; hold, 7.6 feet. Draught of water, 6 feet forward ; aft, g.5feeL
Keel, 22 ins. in depth. False keel. 12 ins. in depth at centre.
Spars.— Mainmast, 77 feet in length. Forenuut, 76 feet Jfotn boomj 46 feet
Main gaffy 31 feet F^e gaff, 30 feet
7Vm«.-~N. M.,46.^.
886
MAKINB 6TBAMEBS ANP BNGINSS.
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HABINB STEAMERS AND ENGINES.
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JELSMEXTS OF MACHINBS AND SNGINSS.
ELEMENTS OF MACHINES AND SNGINEa
BLOWING ENGINES.
Fumaca^^ThtJO. Fineries. — Two, {England.)
240 Tons Forge Pig Iron per Week.
SCngizie {tMa-condeoBiaf^-^CyUnder, 20 ms, in diam. by 6 feetstrokeof piatoa
Boilers.— Six. (plain cylindrical), 36 ins. in diam. and 28 fe^* in length. GrMet,
100 aq. feet
Blowing Ciff*nders.^TwQ, 63 in& In diam. by 8 foot stroke of pifiton. Presture,
ft. 17 lb& per sq. inch. BevoluiiofUf 23 per minute.
Pipes, 3 feet in diam.= 168 area of cylinder.
Tuyeres. — Each I'timace, 3 of 3 ins. in diam. ; 1 of 3.25 ins. ; and x, 3 of 3 ina
Each Finery, 6 of 1.33 ins. ; and 1, 4 of 1. 125 in&
Temperature of BUut, 600°. Ore, 40 to 45 per cent of iron.
Furnacet* — Eight, diam. 16 to tS/eet. Dowlms iron Works {England}.
1300 Tom Forge Iron per Week; discharging 44000 Ctdfe Fei-t of Air per
MintUe.
Siificin.6 (non-condensing).— C^tnder, 55 ins. in diam. by 13 feet stroke of piston.
Pressure o/Sleam.-^6o lb& peraq. inch, out oSsX .33 the stroke of piston. V43ilves,
I30 ins. in area.
Boilers.— FAght (cylindrical flued, internal fiirnace), 7 feet in diam. and 42 feet in
length; one flue 4 feet in diam. Grates, 288 sq. feet
Fly Wheel. — Diam., 32 feet; weight, 25 ton&
Blowing Cylinder, 144 ins. in diam. by 12 feet stroke of piston.
RevolMtions, ao per minute. Bleat, 3.25 lbs. per sq. incb. Discharge pipe, dtenL
5 feet, and 420 feet in length, rofvex.— Exhaust, 56 sq. feet; Delivery, 16 aq. fbet
Furnaces. — Lackenby {England),
800 Tons Iron per W^eek,
Sn^ne (horieoMal, compound condensing). -~ 32 •»d6o ins. in diam. by 4.$
feet stroke of piston.
Blowing Cylinders.— Ttm, 80 ins. In diam. by 4.5 fk»et £itroke of iiistoB. Pmmrey
4.5 lbs. per sq. inch. Revolutions, 24 per minute.
Pipe, 30 ins. in diam. ; volume, 12.25 ^imoB that of bkming cylinders.
H*. — Engine, 290 lbs. ; Blowing cylinders, 258; efficiency, 89 per cent
Totvet.— Area of admission, . 16 of area of piston ; of exit^ . 125.
Volume. — 190000 cube feet of air are supplied per ton of iroa.
BloAver and Extiausting VBXk.
The Huyett <t Smith Manufacturing Co., Detroit, Mick.
Blower.
Grate
Surface.
Outlet
Diam.
Pulleys.
No.
Sq.Ft.
S^, IM.
[n«.
I
4
15
2
9
ro
30
3
^ .
14
50
4
4
^8
75
5
1
7
26
»25
6
56
280
7
9
Face
Pulleys.
Reviola>
tions
at 3 01.
Air at
3«
H?at
30*.
flevolv-
tivm
at 6 oz.
Air at
60s.
IP at
60B.
Ina.
PcrMla.
OoteFt
No.
FwMtai.
0«k«Ft
No.
I
5500
930
■38
7SOO
»330
I.t
'•5
3500
1870
.76
5000
2670
3.16
2-5
27CX}
3120
1.27
4000
4440
363
325
2000
4680
1.91
30Q0
6670
5-5
425
1500
7830
3-2 ,
2300
II 100
^l
5-25
1300
10900
4-47
1600
15600
13.8
6.25
1000
17500
7*5
1400
24900
ao.4
* 40 feet would have afforded economy in f««L
\tawuaMp. X015.)
BI.BMSNTS OF MACHINES AND JSNaiNSS.
899
COTTON FACTORIES. (BngKih.)
For driving 23060 Hand-mule SjnndUs, with Preparafion^ and 260 Loomt^
with common Sizir^.
Bngixie (condeDSiDg). — Cylinder, 37 ins. in diam. by 7 feet stroke of piston;
▼olame of piston space, 53.6 cube feet
Preitsure o/iSteam.— (Indicated average) 16.73 ^^ P^^ <^* ^^^^- SevolutumSf 17
per minute.
faction of Engine and SfAo/ttn^. — (indicated) 4.75 lbs. per sq. inch of piston.
IH*, 135. Total power = i. Available, deducting fViction == ■717.
305 hand- mule spindles, with preparation^
or 230 self-acting " *'
or 104 throstle " "
or Z0.5 looms, with common sizing.
Including preparation :
I throstle spindle = 3 hand-mule, or 2.25 self-acting spindlea
X self-acting spindle = j. 2 hand-mule spindlea
NoTSs.— Each IH* will drive
DREDGING MACHINES.
Dredginff 20 Feet from Water-line, or 180 Tons of Mud or Silt per Hour
II Feet from Water4ine,
Length upon deck, 123 feet; beam, 26fxt. Breadth over aU, 41 feet.
Immersed section at load-line^ 60 sq.feet. Displacement, 141 tons, at load-draught
of 2. Bj feet.
ICngiiie (non-condensing).~C^2t'mier«, two, 12.125 ins. In diam. by 4 feet stroke
of piston.
Boilers. — ^Two (cylindrical flue), diam. 40.5 ins., and length, 90 feet 3 ins.; two
flues, 14.625 ins. in diam. Heating surface, 617 sq. feet. Grates, 37 sq. feet
Pressure of Steam, 25 lbs. per sq. inch; throttle .25 open, cut off at .5 the stroke
of piston. BevtAutions, 42 per minute.
Buckets.— Two sets of la, 2.5 feet in length by 15 ind. at top and 2 feet deep; vol-
ume, 6.35 cube feet. Chain Links, 8 ins. in length by .5 inch diam.
Scaiws or Caimds.—¥o\xT, of 40 tons cf^xictty each.
STEAM HOPPER DREDGER. {Wm, SimoM %• Co,)
Iron.
"Neptuwr" {English).— Length, lyyfeet; breadth, 32 feet.
Dredge from 6 Ins. to 25 Feel. Capacity of Hopper, 500 to 600 Tons.
Kngiiaes — Two (compound), 375 IP, for ^^vAgKtig and propulsion, and one for
raising bucket-ftume and anchor-post&
A like designed dredger ot 1000 tons' capacity has dredged 25000 tons silt per
week and transported it 4 miles.
Dredging 1000 Tons of Mud or Silt per Hour, 5 to 35 FVef mi Depth,
Capacity of Hopper, 1000 Tons.
Mngines.— Two (comiKtnnd), ]P 1000. Speed.— ^ knots per hoar.
Steaxxi IDredsine Crane, {EngUth.)
Lift, 30 Feet per Hour.
V
h
Urn.
araSo
34640
9i
IS
Tons.
as
3
Um.
II20
1^
Tooa.
25
»68o I 37.5
Tone.
20
3«
ii -6
too
^^%
M*» E
C. Y<to.
ao
»5
^"5
Is
s i
a
•9
0
Lb*.
18000
33480
Tona.
5
7
Lba.
3^40
3360
Tons.
50
60
TODI.
40
54
A -6
c.yd#
30
40
goo BLBMBNTS OF MACHINBS AND BNGHTEB.
BSleotrio X«aiixi.oli« Steel*
"Hilda," "Mart," "Flo," and "Thbo."— icw^, 4o/«rf; Beam, 6.5; Hold,
3.x. — Load-draughty ^o passengers, 1.66 feet. Motor, ]^ 3.5. Revolutions, 700 per
minute. Speed, 6 miles per hour.
Awuimulators, under the seats, and when fblly charged, capacity for 8 hours at
fkill speed. Charging is effected at landings at termination of route.
BttUders.^J. B. Seath k Co., Glai^ow, Scotland.
Hopper Drkdgbr ^' Belfast No. 3. " Iron and SmL.— -Length aver aUy i^feet,
on deck, 189; between perpendiculars and for tonnage, 185; Beam, 2!^.$ feet; Hold,
14.1 feet; Tonnage, Gross, 760 tons; Net, 372; Mean drat^ght, g. 5 feet, loaded, 12.5.
Displacement, x86o tons. Immersed Section, 490 OfeeL Freeboard, 2.7$ feet
Dredging Capacity, 1000 tons per hoar.
Cylinders. Two of 20 ins. in diam. and two of 38. 5 ins. Stroke of piston 30 ina
Pressure of Steam, 90 lbs. per Qinch. Revolutions per minute, 80. B? 850.
Boilers, two. Orate surface, 81 Qfeet. Heating surface 2130, and Condensing 1x5a
Propeller, 9 feet in diameter, f^uel, capacity 50 tons. Crew, 13.
Weight, Hull, 500 tona Speed, 8.5 knots per hour.
Builders.— Wm. Simons & Co., Renfrew, Scotland.
(t '
Hbrcules." Panama Canal.— Length on deck, 100 feet; beams, 40, 60, and 45
feet ; depth o/hold, 12 feet. Slot, 315 feet in length by 6 feet 7 ins. in vndth.
Ways.— Two, one 40 feet and one 60 feet, by 5 feet in width.
Buckets. — 38; volume, 1.33 cul)e yardR Spuds, 2 feet in diam. and 60 in length.
Engines Two of 100 H* each, and two of 40 H* each.
^ot^rx.— Three (horizontal tubular), 16 feet in length.
Elevator and Discharge. -^iiaxlmum, 24 cube yards per minute.
Crane. (TVood.)
HulL— Length on deck, iix>fset ; beam, 44 feet ; load-draught, 4.$ feet
Radius of crane, 46 feet; height, 70 feet; counter-balawx, 70 tons.
Boiler.— HeaUng surface, 500 sq. feet. Pressure of Steam, 80 lbs. per eq. indi
IIP, 150.
iVope«er».— Two, 4.25 feet in diam. Bpe^, 5 miles per hour.
Engine to operate crane. Cylinder. — 10 m& in diam. by 12 ins. stroke of piston.
FLOUR MILLS.
30 BameU of Fkfur per How.
"Water-'wlieels, Overshot- s, diam. 18 feet by 14.5 feet face. Buckets, 15
ins. in depth. Water.— Head, 2.5 feet Opening, 2.5 ins. by 14 feet in length ovei
each wheel.
5 Barrels of Flour per Hour, and Elevatinff 400 Bushels of Grain 36 Feet,
"^Vater-'wlieel, Overshot— Di&m. 22 feet by 8 feet fiice. Buckets, 5a of i
foot in depth. Water.— Head, from centre of opening, 25 ina Opening, 1.75 in&
oy 80 ins. in length.
Revolutions, 3. 5 per minute. Stones, three of 4. 5 feet ; revolutiooB, xsa
T%ree Run of Stones, Diameter 4 Feet.
'^Vater-vT'lieel, Overshot^Diam. 19 feet by 8 feet fooe. Buckets, 14 ins. in
d^th.
Or,
6teaxxx-exiBine (non-condensing).— Cy{tiul«r, 13 ins. in diam.by 4 feet stroka
Boiler (eylindrical flued)— Diam. $ feet by 30 in length; two flues 90 ins. in diani.
ELEMENTS OF MACHINES AND ENGINES.
901
HOISTING ENGINES.
Wor File IDriving, Hoistins, Miinine, eto»
Co., New Yorlc.
IP
do.
4
6
10
»5
30
as
SlNULK CYUNDBRS.
DOUBLK CYUKDERS
Cylinder.
Cspacity.
Coat, with
Boiler.*
tf
Cylinder.
Capacity.
Ins.
Lba.
$
Ko.
Ins.
Lba.
5X5
xooo
600
8
5X8
2000
6X8
1250
675
12
6X8
2500
7X 10
x8oo
825
20
7 X 10
3500
8X 10
2800
1050
30
8X 10
6000
9X 13
4000
1275
40
9X 12
8000
10 X 12
5000
»375
50
10 X 12
9000
Coat, with
Boiler.*
£BgilM.
10"
30
Dmoit
Ina.
12 X-24
14X26
* Complete.
Details and. Operation.
Boiler.
DimeB-
aiona.
Ina.
32X75
40X84
Tubes.
No.
48 of 2 in.
80 of 2 in.
Ram.
Leaders.
HoUt.
Lift.
Ram.
Blows
Mmute.
No.
25
29
Pilea
per 10
Hoars.
Lba.
»953
2700
Feet.
40
75
Feet
8 tUi2
8 to 12
No.
50
100
$
950
1050
1350
1550
2000
2350
Fnel
per
Hoar.
Lba.
70
80
* Weight complete, 8500 lba.
Iblinit^g Gngrines and Boilers. (Variov* Cap€U:itiet.)
Engine^ Boiler^ eta, as given for Pile Driving, page 90a.
Operation. — 250 to 300 tons of coal in 10 hoars. Fud^ 40 lbs. coal per hoar.
Water, 20 .gallons per hour.
Weight ofEngint and Boiler j 4500 lbs.
Tlie HaiicooLc Inspirator. For a Lift of Water oj 25 Feet.
Mo.
Diair
Steam-pipe.
leter.
Soctlon.
Diaehar|;e
at Preasare
of 60 Lbs.
Ins.
Ina.
G'lU.perh'r.
10
•375
.5
X20
12.5
.5
•75
220
X5
•5
•75
300
30
•75
X
540
25
X
'.»5
900
No.
30
35
40
45
50
Diameter.
Steam-pipe.
Ina.
125
1.25
1-5
x-5
2
Saction.
'•5
1-5
3
3
2.5
Discharge
at Pressure
of 60 Lbs.
G'lls.perh'r.
1260
1740
2230
2820
3480
Temperature of feed water at ao feet lift, 100° ; and on 3 feet lift, 145O.
HYDROSTATIC PRESS. (Cotton.)
30 Bales of Cotton per Hour,
Kngine (non-condensing).— Ci^hncfer, 10 ins. in diam. by 3 feet stroke of piston.
Pressure of Steamy 50 lbs. per sq. inch, full stroke. Bewlutions. 45 to 60 per
minnte.
Fresses.— Two, with 13-inch rams; stroke, 4.5 feet
iVmpg.— Two, diam. 2 ina ; stroke, 6 in&
For 83 BcJes per Hour,
Kngine ^non condensing).— CyZinder, 14 in& in diam. by 4 feet stroke of piston.
Boilers. —Three (plain cylindrical), 30 ins. In diam. and 26 feet in length. Grates,
33 sq. feet. I^rssure ofSteam^ 40 lbs. ver sq. inch. Revolutions, 60 iwr minute.
iVewe*.— Four, geared 6 to i, with two screws, each of 7.5 ins. In diam. by 1.625
Ui pitch.
^^^ (wrought iron).— Journal, 8.5 ina ^y Wheel, 16 feet in diam. ; weight,
902 £L£M£]!4TS OF MACHINES AND ENGINES.
LOCOMOTIVE.
*' Expuuxknt" [Compound^-^Cylmders^ one each, la and 26 in& in diam., and
•ne 26 ins. by 2 feet stroke of piston.
BoiUsr. —Heating mr/acey 1083.5 sq. feet Grate, 17.1 sq. feet. Pressure of Steam,
150 lbs. per sq. inch, cut off at .35. Speedy 50 miles per hour. Weight. — Empty,
34.75 tons.
Street liailroad or Traxxi-wasr ICxxfi^ne.
Cylinder, 7 ins. in diam. by 11 in& stroke of piston.
Boiler, 78 tubes 1.75 ins. in diam. by 4 feet in length. Healing turface, 160 sq.
feet. Grate, 4.25 sq. feet Wheels, 3.33 feet in diam. Base, 4.5 feet Gauge,- 4
teet 8.5 ins.
Co<<.— Average per mile in England, 2.52 pence sterling = 4. 48 centa
PILB-DEIVING.
Driving One Pile.
Kngine (non-condensing) Cylinder, 6 ins. in diam. by i foot stroke of piston.
Boiler (vertical tubular;.— 32 ins. in diam., and 6.166 feet in height Grates, 3.7
•q. feet Furnace, 20 ins. in height Tubes, 35, 2 ins. in diam., 4.5 feet in length.
Revolutions, 150 per minute. Drum, la ins. in diam., geared 4 to x. Leader, 40
feet in height Mam. — 9000 lbs., 2 blows per mi uute. /lice^, 30 lb& coal per hour.
Driving Two Piles.
Kngixxe (non-condensing).— (7^£tnder«, two, 6 in& in diam. by x8 in& stroke of
piston.
Boiler (horizontal tubular). — iSJiell, diam. 3 feet, and 6 feet in length. Furnace
end 3.75 feet in width, 3.5 feet in length, and 6 feel in height
Pressure of Steam, 60 lbs. per sq. inch. Revolutions, 60 to 80 per minute.
Frame, 8.5 feet in width by 26 feet in length. Leaders, 3 fbet in width by 34 feet
in height Bams.—1yio, 1000 Iba each, 5 blows per minute.
PUMPING ENGINES.
Corliss Stkam- engine Co., Providence, R. /.—Vertical -Beam Ekginb {Com-
pound).— Cylinders.— 18 and 36 ins. in diam. by 6 feet stroke of piston.
Pumps.— YovLT plunger, 19 ins. in diam. by 3 feet stroke of piston. Displacement
per revolution of engine, 84.96 cube feet
Boilers.— Three, vertical fire tubular. Grate.— g^ sq. feet Heating surface, 1680
sq. feet Pressure of Steam, 125 Iba per sq. inch, cut off at .23 feet Revolutions^
36 per minute. IIP 313. F/y-w/<€«f.— 25 feet in diam., weight 62 ooolft*.
/W2.— Cumberland coal, 486 Iba per hour, inclusive of kindling and raising staam.
Ash and Clinkers, 9.4 per cent Duty for one week, 113 271 000 foot-lbs.
Water delivered, 17 621 gallons ))er minute, against head of 180 feet
Duty, average for 1883, per 100 Iba anthracite coal, 106 048 ooo.^t-<&f.
For Mevating 200 oc» Gallons of Water ptr How.
Lynn, Jlfo«s.— Enoine (Compound).— Cylinders, 17.5 and 36 ina in diam. by 7 feet
stroke of piston; volume of piston spare, 61.2 cube feet Air Pump (doable act-
ing), 11.25 ^^^- >° diam. by 49.5 ins. stroke of piston.
Pump Plunger, 18. 5 ins. in diam. by 7 feet stroke.
Boilers.— Tvro (return flued), horizontal tubvilar; diam. of shell, 5 fteet; drum, 3
feet ; tubes, 3 ins. Length of shell, 16 feet Grates, 27. 5 sq. feet
Pressure of Steam. 90.5 Iba ; average in high-pressure cylinder, 86 lbs., cat off at
t foot, or to an average of 44.5 lbs. ; average in low-pressure cylinder, 27 Iba, cut
off at 6 ina, or to an avemge of 10.8 lbs.
Revcifdions, 18.3 per minate. Fly Wheel. — Weight, 24000 Iba
JSvaporation qf Water, 4644 Iba per hoar. Loss of action by I\nnp, 4 per cent
Consumption of Coal — Lackawanna, 291 lbs. per hour.
I>vly, 205773 gallons of water per hoar, under a load and fHctional resistanue of
73-41 ">a per square inch, equal to 103 923 217 foot-lbs. for each xoo Iba of ooaL
XLSMJBNTS OF HAOilNESy MILLS, BTC.
903
** GaskiU" at Saraiiyga, N. F,
Sngine {Horizontal Compound). Cylinders. —High pressure, 2 of 21 ins. diam.
Low pressure, 2 of 42 ins. ditun., aU 3 feet stroke of piston. Pumps. — ^Two of 20 ins.
diam. by 3 feet stroke of piston.
Fly Wheel, 12.33 ^^^ '° diam. ; weight, i2cxw lbs.
Boilers (horizontal tubular). — Two of 5. 5 fleet in diam. by 18 fbet in length. Heat-
ing twrfiut, 2957 sq. feet. Grates, 51 sq. feet of grate; to heating surftice, i to 58,
and to transverse section of tubes^ i to 7. Ckimneys, 75 feet
Pressure q/^Veam.— Mean of 20 hours, 74.25 lbs. per sq. inch. RtvolutiffM, 17.87
per minute. Iff.— -High pressure tylmders, 109. 2 ; low-pressure, 76 65. Total, 185,8.
Puel. — Anthracite, 6.9 lbs. per sq. foot of grate per hour. Evapwati<m, per sq.
fixH of heating surface per hour, 1.175 lbs. ; per lb. of coal, 9.25 lbs. ; per cent, of
uon-combustible, 3.2.
Duty, 112 899993 foot-lbs. per 100 lbs. coaL Heating surfaee per lEP, 14.9.
Steam per sq. foot of surface per hour, z. 19 lbs. ; per sq. foot of surface per lb. ot
coal per hour from 212*^, 11.28 lbs.
Sriosson's Caloric. For an Elevation of^ Feei.
COST
Dixnen-
•loiu.
Ins.
5
6
8
13
12^
occupied.
Floor. Helghl.
Valume
Hour.
Iiu.
34X18
39X20
48X21
54X27}
48X53^
Ina.
48
51
63
63
65
Gall.
150
300
350
800
1600
Kp^
Foel
Sactlon
and
per Hoor.
Ww
Die-
Nut
ckargv*
Anthr.
Oaa.
Gaa.
Ina.
Lba.
Cub. ft.
$
•75
15
150
•75
»-s
18
900
I
3-3
as
235
i-S
6
—
—
a
la
—
—
Coal.
Daap W«ll Panp.
Extra.
Pipe* per Foot.
^"^ Plain
3IO
250
330
450
10
15
ast
.64
.80
.93
Gal van
.86
"•»5
1.35
* Over 90 feet, ga centa.
t Duplex.
TncludiiiK engine and pump, oil-oan and wrench, complete in all but suction and
discbarge-pii»o.
SUGAR MILLS.
Expressing 40 coo lbs. Cane-juice per day, or for a Crop of 5000 Boxes qf
450 Vbs, each in four Months^ Grinding,
Kngine (non-condensing).— Cyh'n<i«r, 18 in& in diam. by 4 feet stroke of pistcoi.
Bailer (cylindrical flued).— 64 ina in diam. and 36 feet in length; two return fluea,
oo ins. in diam. Heating surface, 660 sq. feet Grates, 30 sq. feet.
Pressure of Steam, 60 lbs. per sq. inch, cut oflT at . 5 the stroke of piston. Revolu
tions, 40 per minute.
Rolls. — One set of 3, 28 ins. in diam. by 6 feet in length; geared i to 14. Shc{fUt
xz and 12 ins. iu diam. Spur Wheel, 20 feet in diam. by 1 foot in width. !r/y
Wheels 18 feet in diam. ; weight, 17 400 lb&
Weights. -^EngSne, 61 460 Iba ; Sugar Mill, 65730 )b& ; Spur Wheel and Connect
ing Machinery to Mill, 28 680 lbs. ; Boiler, 18 530 lbs. ; Appendages, 6730 lb& Total,
181 120 lbs.
BTONK AND ORE BREAKBRS.
(Se«p 957.)
No.
A
I
3
3
4
Re-
•elver.
Ina.
4X10
5X10
7X10
5X15
7XZ5
D'b).
Feet.
1.66
275
2
2-33
233
•y-
Face.
V'loclty
per
Minute.
^ si
Ins.
Feet.
H».
6
250
4
6
t8o
5
V
X
6
9
9
x8o
9
Weight.
LUa.
4000
6700
8000
9 100
10490
No.
Re-
ceiver.
Ina.
9X15
11X15
:«3Xi5
15X20
18X24
Pal
D'm.
ley.
Face.
Ina
Weight.
Feet.
Feet.
H*.
Lba.
3.5 9
2.33 ' 6
250
x8o
9
9
13360
ziSoo
2 33 1 8 180
9
Z1760
3 5 ; 10 1 150
12
32600
6
12
135
za
37500
NoTx.-^Amonnt of product denends on distance Jaws are ael apart, and speed.
Product given in Table is due when Jaws are set z.5 ins. open at bottom, and ma-
chine is run at ita proper speed and diligently fM. It will also rar>' somewhat witll
character of stone. Hard stone or ore will crush faster than sandstone.
A cube yard of stone Is about one and one third tons.
904
ELSMENTS OF MACQINSS.— CHIMNEYS.
STEAM FIRE-ENGINE.
A-ZKioalzeag, IN". U. let Class*
Steam Cylinder.— Two of 7.625 ina in diam. by 8 ina stroke of plaiOB.
Water Cylinder. — ^Twoof 4.5 ins. in diam.
Boiler (vertical tubalar). — HeaJting surface^ 175 SQ- feet. Grates, 4.75 sq feei
Pressure of Steam. — 100 lbs. per sq. inch. Revolutions, 200 per minute.
Discharges. — Two gates of 2.5 Ins., through hose, one of 1.25 in& and two of i inek
Projection.— Uorlzonia], 1.25 ins. stream, 311 feet; two i inch streams, 256 feet
Vertical, 1.25 ins. stream, 200 leet. Water Pressure.— With 1.125 ina nozzle, 200 Iba
Time of Raising Steam.— From cold water, 25 lbs., 4 mln. 45 sea
Weights. — ^Engine complete, 6000 Iba ; water, 300 Iba
SAW -MILL.
T\do Verticiil Saios, 34 Ins. Stroke, Lathes, etc
Bxksine (non-condensing). Cylinder.— 10 ina in diam. by 4 feet stroke of pistoo.
.Bot'^rf.— Three (plain cylindrical), 30 ins. in diam. by 20 feet in length.
Pressure of Steam. — 90 Iba per sq. inch. Revolutions, 35 per minute.
NoTS.— This engine has cut, of yellow-pine timber, 30 feet by 18 ina in i minuta
STONE SAWING.
Kmerson Stone Sa-w Co. (Diamond Stone Saw, Pittsburgh, Penn.).—
to H*, 150 sq. feet of Berea sandstone, inclusive of both sides of cut, in z boar.
CHIMNEYS.
Lawrence, Afcus, Octagonal, 222 Feet above Ground, and 19 Feet behm.
Foundation, 35 Feet square and 0/ Concrete 7 Feet deep, {Hiram F. Mills.)
Shaft.— 224 fe®^ ^° height, 20 feet at base, and n. 5 at top; 7i ins. thick at base
and 8 at top. Core. — 2 feet thick for 27 feet, and i foot for 154.
ITorizontal Flues.— 7.$ feet square, and VerticcU flue or cylinder of 8.5 feet, 234
high, with walls 20 ins. thick for 20 feet, 16 ft>r 17 feet, 12 for 52 feet, and 8 for 145 feet
Purpose. — For 700 sq. feet grate surface. Weight— 2250 tona Bricks, 550 cool
New York Steam Heating Co. Quadrilateral, 220 Feet above Ground
and I Foot bekw. (Chas. E. Emery, Ph.D.)
Shaft.— 220 feet in height, and 27 feet 10 ina by 8 feet 4 ina in the clear insidei
Foundation.—i foot below high water. Copod^i^.— Boilers of 16000 W.
Cost of* Steam -SSngrines and. Soilers ooxnplete, and of
Operation per Day of* lO Hours, inolnsive of ILtabor^
li^uel, and Repairs. (Cheu. E. Emery, Ph.D.)
II-P.
6.25
12.5
29
XI2
276
5$«
EDgine.
Portable Verticals . u.
HorizonUI ( ^ 8
Single Condensing. . .
M
M
Water Erap-
oratod per
Coal per
Labor.
pile*
and Re-
pairs.
Coat
of
IH?p«r
Hour.
Lb. of
Coal.
IIP.
Day.
Cod.«
LU.
LlM.
Lbs.
Lb*.
1
$
$
42
7-5
56
394
1-75
•33
•73
38
7-5
51
1308
1-75
'i^
»-33
32
8
40
2.25
.60
2.43
23
8.8
26.1
3300
3-75
1. 17
14.58
aa.2
8.8
25.2
7831
425
a.xa
22.2
8.8
25.2
15663
6
4.0a
a9.x6
• 1 4.43 per tea (soio IbO* incladipf cartagt.
Total
Coat of
Opermfn,
iocloding
Coal.
$
3.86
3-56
5-45
XX.66
33.97
4»-5«
ORAPHtC OPBRATION.
905
GRAPHIC OPERATION.
6olu.ti(>iL8 of Questions "by a Grrapliic Operation,
I. If a man walks 5 miles in i hour, how far will he walk in 4 hours?
Operation. —Draw borizontal line, divide it iuto equal parts,
as I, 2, 3, and 4, representing hours. From each of these
points let fall vertical lines A C, i z, etc., and divide A C into
miles, as 5, 10, 15, and 20, and fh>m these points draw equi-
distant lines parallel to the borizontal.
Hence, the horizontal lines represent time or hours, and
the vertical, distance or miles.
Therefore, as any inclined line in diagram represents both
time and distance, course of man walking 5 miles in an hour
is represented by diagonal A e; and if he walks for 4 hours,
continue the time to 4, and read off ft-om vertical line A G the distance = 20 miles,
3. How far will a man walk in 2 hours at rate of 10 miles in i hour ?
His coarse is shown by the line A o, representing 20 miles.
J. If two men start from a point at the same time, one walking at the
rate of 5 miles in an hour and the other at 10 miles, how far apart will they
be at the end of 3 hours?
Their courses being shown by the lines A r and A 0, the distance r 0 represents
the difference of their distances, xo cx> 20 = 10 mUes.
4. How long have they been walking?
Their courses are now shown by the lines A o and A 4, the distance 3 4 representa
the difference of their times, or 3 fv 4 = 3 hours.
5. When they are 10 miles apart, how long have they been walking?
Their courses are again shown by the lines A r and A 0, the distance r o repre-
sents the difference of their distances of 10 miles, and A 2, 2 hours.
6. If a man walks a given distance at rate of 3.5 miles per hour, and then
rans part of distance back at rate of 7 miles, and walks remainder of dis-
tance in 5 minutes, occupying 25 minutes of time in all, how far did he run?
A a e t er C Operation.— Dn,w horizontal line, as AG,
representing whole time of 25 minutes; set
off point e representing a convenient fV-actibn
of an hour (as 10 minutes), and a i equal to
corresponding fhiction of 3.5 miles (or .5833);
draw diagonal A n, produced indefinitely to O,
*i jt , . nf' / > and it will represent the rate of 3.5 miles per
^ ^ ' ^ hour.
Set off G r equal to 5 minutes, upon same
a * "•• ®^*^® ^ ^^'^^ of A C; let foil vertical r «, and
^ ' ^ draw diagonal C u at same angle of inclination
as that of A n; then firom point u draw diagonal u 0, inclined at such a rate as to
represent 7 miles per hour; thus, if i n represents rate of 3.5 miles, s 0, being one
half of the distance, will represent 7 miles.
The whole distance between the two points is thus determined by G x, and dis-
tance ran by u «, measured by scale of miles employed.
Verification.— The distances A e and A t are respectively 10 minutes =r. 166 of an
hour, and .5833 mile = .166 of 3.5 miles. Hence, C aj = .875 mile, and t«*=.5833
mile. Consequently, the man walked AO = .875 mile = 15 minutes, ran Ott =
5833 mile = 5 minutes, and walked u G = .2916 mile.
7. If a second man were to set out from C at same time the man referred
to in preceding question started from A, and to walk to A and return to C,
at a uniform rate of speed and occupying same time of 25 minutes, at which
points and times will ne meet the first man ?
Operaiion.—AB A G represents whole time, and Cx distance between the two
points, V i and t x will represent course of second man walking at a uniform rate,
and he will meet the first man, on bis outward course, at a distance fVom his start-
^g- point of A, represented by A o, and at the time A a; and on his return course
JA distance Av^xm, and at the time A c.
4G»
7^
/
5
/
V
go6
MISCfiliiANSOUfL
UIBCEIuImATSVOXJB. .
No., Diatn«t©r, euid Nuinteer of t^hot. {American Standard.^
CoiTipresaed. JBuoliL Sliot.
No.
3
2
Balls, .38 Inch, 85 No. per lb. ; .44 Inch, 50 So. jnrr lb.
Diam. '
Shot 1
per Lb.
No.
Dfcim.
Shot
per Lb.
No.
DUun.
iMk.
•25
.27
No.
284
flgt
a
0
lotih.
•3
•B2
No.
>73
J 40
00
000
Inch.
•34
.36
8hot
per Lb.
■ ■«
No.
"5
98
CkiiUedL iSliot.
No.
DUm.
Inch.
12
.05
IJ
.06
10
Trap
10
.07
9
ITrap
Shot
per Or.
No.
No.
2385
9
1380
8
I J 30
8
8t>8
7
716
7
Diaui.
Shot
perQt.
No.
Inch.
.08
Trap
Trap
.M.
Mo.
585
495
409
345
299
6
I'
3
2
Warn.
Inofa.
.IX
.12
•13
.14
Shot
periOs.
No.
223
172
136
109
86 :
No.
DUm.
Shot
per Ob.
Inoh.
Mo.
I
.16
73
U
•»7
6,
Bll
.18
52
«»B
.19
1
43
Z>rop Sliot.
No.
Extra Fine Post
Fine Dust
Dufit
la
11
10
10
Diam.
Inch.
.015
•03
.04
.05
.06
Trap
.07
Pelleto
per Os.
No.
84021
10784
(♦565
a. 326
1346
1056
848
No.
9
9
8
I 8
i 7
I 7
6
Diam.
PeHeU
per Oe.
-No."
■Dfaun.
Inch.
No.
Inch.
Trap
688
5
.12
.08
568
4
•13
Trap
472
3
•»4
Trap
B99
338
2
I
■.M
.1
291
B
••«7
.11
s»i8
BB
.a«
iPtoDete
perOs.
No.
z66
132
xq6
86
7«
59
50
No.
Diam.
BBB
Inch.
.19
T
.2
HT
.2iK
F
.22
FF .
.23
PolMc
perOa.
No.
42
36
3«
27
24
The senile of the T^e Roy «tAndard (adopted by the Sportsman^s Canvontiou) com-
mences with .24 inch for TT shot, and reduces .01 inch for each size to .05 inch for
No. 12. The number of peftlets per oz. being the actual number in perfect shot
The number of pellets by this standard is neaidy ideniical with that of ihe Amer-
ican Standard.
Tatham'fi scale is same as I..e Roy's, but number of pellets isdeduced mathemat-
tcally, by com.puting them fVom the speciflc gravity of Ihe lead.
DT>aints, IMameter and O-rade of, to IMsoliarge Rainfall.
Diam.
Grade
one in.
Acres.
Diam.
Grade
one In. ,
Int.
Ins.
'
4
30
•S
40
JIO
.6
20
S
80
60
•5
.6
7
20
60
6
'iO
60
X
X
8
1
lao
80
Acres.
•1.2
1-5
x.s
i-S
x-S
1.8
Diam.
Ins.
9
x^
Grade
oneiin.
60
xao
80
12P
80
Acres.
Diam.
Gnido
one in.
Acna.
Ins.
S.I
80
5.8
2.x
n .
240
7«
«-S
ixao
7«
a'TS
80
9
4-5
60
zo
5-3
iS
240
10
British and Aletrio M.c9aBUiree« CovMinevciial XBkiixii-vialenti
OcT. (<?• Johrutont Stonet, F. JR. S.)
Yard
'Foot
Inch.
■MURmtUtt.
.... 9x4.4
....30*-8
.... 25.4
Wti^. Orutnfiua.
Pound 453-6
Oonoe ^8.35
Grain 0648
To/vum. CiA» Gnili'a
Gallon 4554
Quart XX36
Oonoe 9&4
HSMOBANDA. §0^
MEMORANDA.
Pliysioal and Mieoliatiical Sllements. Cozistructiozis,
and. Results.
Belting. Double. — 600 IP (to be transmitted) -?- velocity of belt in feet per
minute, or 191 W-r- number of revolutions per minate-i- diameter of pulley in feet
r= width in ins. Mackine BeUs.~ isoo to 2000 ^•i-^loclty of belt in feet per
minute = width in in& {Edward Sawyer.)
Slast I*ipe of a Xjooomotive. Best height is from 6 to 8 diameters
of pipe, and best effect when expauded to full diam. of pipe at 2 diameters ft-om base.
Boiler Ftivetiiis. A riveting gang (2 riveters and i boy) will drive in shell,
furnace, etc., a mean of 12.5 rivets per hour
Briols or Compressed Fiael is composed of coal dust agglomerated
by pitchy matter, compressed in molds, and subjected to a high temperature in an
oven, in order to expel the moisture or volatile portion of the pitch and any fire-
damp that may exist in the cells of the coal.
Bridge, Highest At Garabil, France, 413 feet from floor to surface of water,
and 1800 feet in length.
Bronze, M:a.lleal3le. P. Dronier, In Paris, makes alloys of copper and
Un malleable by adding from .5 per cent, to 2 per cent, quicksilver.
Buildlxie 13epartznent, Reqiiirexnenta of. (New York.)
Fumaae Flues of Dwelling Houses hereafter constructed at least 84nch walls on
each side. The inner 4 ins. of which, Arom bottom of flue to a point two feet above
2d story floor, built of fire brick laid with fire-clay mortar; and least dimensions of
fumaco' flue 8 ins. square, or 4 ins. wide and 16 ins. long, inside measure; and when
furnace flues are located in the usual stacks, side of flue inside of house to which it
belongs may be 4 ins. thick. If preferred, furnnce flues may be made of fireclay
pipe of proper size, built in the walls, with an air space^of i inch between them,
and 4 in& of brick wall on outside.
Boiler Flues to be lined with fire-brick at least 25 feet in height from bottom,
and in no case walls of said flues to be less than 8 ins. thick.
All flues not built for furnar>es or boilers must be altered to conform to the above
requirements before they are used as such.
Steam Pipes not to be laid within two inches of any timber or woodwork, unless
it is protected by a metiti shield, and then the distance not to exceed one inch. All
floors, ceilings, and partitions to be protected from beat by a metal tube one inch
in diameter in e.xcess of the pipe, and the intervening space filled with mineral
wool, asbestos, or other incombURtible material.
Horizontal, and Hot-Air Pipes In stud partitions to be double, with an interven-
ing space between them of at lea.st half an inch, and a space of tliree inches around
a pipe: the inner face of the i)artition to be lined with tin plate and the outer faces
with iron lath or slate. Hot-air pipes not to be permitted in any stud partition un-
less it shall be at least eight feet distant in a horizontal line from the furnace To
shield the effect of their heat in wood or stud partitions, to have a double metal
collar, with two inches of air space between them and holes for ventilation, or to be
enclosed iu brick masonry at least four inches in thiokness.
Cement. Iron to Stone.— Fxne Iron filings, 20 parts. Plaster of Paris, 60, and
Sal Ammoniac, i ; mixed fluid with vinegar, and applied forthwith.
Ckiimney Drauarlxt. W — to fc = D. W and w representing weights of a
cube foot of air <U eztemeu and internal temperatures, h height of chimney or pipe in
feet, and D value of draught. See Weight of Air, page 521.
Chinese or India Ink Improves with age, should be kept in dry air,
and in rubbing it down the movement should be In a right line and with very little
pressure.
909
MEMOBAKDA.
Coal, Efifeotlve Value of*. Theoretical quantity of heat per W is
2564 units per hour, and average quantity of heat in a lb. of coal that is utilized
in the generation of steam in a boiler is 8500 units; hence, theoretical quantity
of coal required per W per hour = |^ =
8500
3 Iba'j after the water has been heated
into atmospheric steam, being theoretically nearly 7.5 per cent, of total heat re-
quired to change 30 lbs. water at 60° into steam of 60 lbs. effective pressura
The total beat developed by the combustion of coal^ when utilized evaporatively.
ranges Arom .55 to .8, but in practice it does not exceed 65 per cent
Coast and Bay Service. A velocity of current of 2.5 feet per second
will scour and transport silt, and 5 to 6.5 feet sand. For river scour the velocities
are very much les&
Cold, O-reatest. —220^, produced by a bath of Carbon, Bisulphide, and
liquid Nitrous Acid.
Corrosion, of* Iron and Steel,
as a mean, tally one third greater.
The corrosion of steel over iron is,
Cost of* Family of* ^eolianics in France ranges flrom $220
to $600 per annum, of which clothing costs 16 parts, food 6x, rent 15, and mis-
cellaneous 8.
Crnshins Resistance of* Sriok. A pressed brick of Philadelphia
clay withstood a pressure of 5cx>ooo lbs. for a period of 5 minutes.
Kavtbxvork. Shovelling. — Horizontal, 12 feet. Vertical, 6 Itet When
thrown horizontal, 12 to 20 feet, i stage is required, and fh)m 20 to 30, a Stages.
When vertical, 6 to 10 feet, i stage is required.
WkeeUarrow. —Proper distance up to 200 feet
Nxkxxxbev
of* X^oads and
One Laborer.
Voluxne of* HSartli
(C. Hersckell, C. E.)
Diatance.
Trip*.
Volame.
Distance.
Tripe.
Volume.
DistauM.
Feet.
Tript.
Feet.
No.
Cub. Yds.
Feet.
No.
Cob. Yds.
No.
20
120
23-5
150
96
13-3
350
88
50
no
16.9
200
94
12.8
400
86
70
100
14.4
250
92
12.4
450
^
100
98
13.8
300
90
X2
500
83
per "Day,
VoIuiiml
Cub. Yds.
11.6
zx.a
X0.9
JO. 5
Volume of a barrow load, 2.5 cube feet
Portable Railroad and Hand Car«.— For a distance of 550 feet^ 60 cube yards can
be transported per day.
Horse Cart. — Volume of* £artli transported
One Laborer.
per X>a3r.
Diatance.
Tripe.
Volume.
Distance.
Trips.
Volume
Distance.
Tripi.
Feet.
300
500
No.
86
67
Cub. Yds.
13.6
Feet.
1000
1500
No.
43
31
Cnb^Yds.
8.6
6.4
Feet.
2000
2500
No.
25
21
VoluD*.
Cob. YdiT.
5
4.3
Volume of each load, 8 cube feet
Ox Cart is lees in cost at expense of time.
Bleotrio J^isht, Candle Po-wer of*. Maaeim Ineandacent Laimp.^.
Current with 30 Faure cells, 74 volts, z.8i Amperes, 16 standard candlea Wi^ 59
like cells, 124 volts, and 3.2 Ampdres, 333 candles. (Paget HiUs^ LL. D.)
The elavated electric lights at Ia)S Angeles, Cal., are distinctly visible at sea for •
distance of 80 miles.
S^ngine and Sugar ^lill, Weights of*. Enoins (noneondentdv)'
—Cylinder. — 30 ins. in diam. by 5 feet stroke of piston. Boilers (cylindrical flue).—*
70 ins. in diam. by 40 feet in length. Weights. — Engine, 105000 lbs. : Boiltrty com*
plete, 75 000 lbs. ; Sugar-mill, 40 ins. by 8 feet, 220050 lbs. : Omnecttng Machxntr%
-"t 179 lbs. Cane carriers, etc. , 46 787 lbs.
MEMORANDA. 909
ITiltering Stone. ArtiJieiaX. ^Cl&y, 15 parts; Levigated Chalk, z. 5; ani
Glaas Sand, coarse, 83.5. Mixed in water, molded, and hard burned.
Fire-engine* IS team. Relative eflfect for equal cost oompared with a
hand engine, as x to 113. Each IIP reqaires about 112 weight of engine.
iriocttins Bodies, Velocities of*. At low speeds resistance increases
somewhat leas than square of velocity. In a Canal, at a speed of 5 miles per hour,
a large wave is raised, which at a speed of 9 miles disapi>ears, and when speed is
BU|ierior to that of the wave, resistance of boat is less in proportion to velocity, and
immersion is reduced.
Length of Veftek—The proper length for a vessel in feet (upon the wave-line
theory) is nfleen sixteenths of square of her speed in knots per hour.
Flo-^v or A.ir. 67 y/k = VdocUy per second X G. h representing column
oj waler in ins. , and C a coefficient ranging from 56 to loa
Circular orifices, thin plate 56 to .79
Cylindrical mouth-pieces, short • .81 " .84
do. do. rounded at inner end .92" .93
Conical converging mouth-pieces. *.... • .9 *' x
Conoidal mouth piece, alike to contracted vein 97 '•^ x
Flues, Corrugated. ( Wm. Parker.) ~ = Working stress in
lbs. per sq. inch. T representing thickness in j6ths of an inch^ and D diameter in ins.
Steel,- corrugations 1.5 ins. deep. Experiments upon a furnace 31.875 ins. in
diam., 6.75 feet in length, and with 13 corrugations.
Foundation Piles. When piles are driven to a solid fbandation, they act
as columns of support, and are designated Columns, and when they derive their
supporting power fVom the fViction of the soil alone, they are termed Files.
Authorities differ greatly as to the factor of safety for Piles, varying .1 to .01 of
Impact of ram. ( WeisbcKh. )
As columns, their safe load may be taken at from 750 to 900 lbs. per sq. inch.
Authorities give a higher value (Rankine and Mahon, 1000); but it is to be borne
in mind that when piles are driven to a solid resistance, they are frequently split,
and consequently their resistance is much decreased.
As a rule, the following coefficients for ordinary structures are submitted '
When the piles are wholly IVee from vibration consequent upon external impulse,
.33 to .4, and when the structures are heavy and exposed to Irregular loading, as
storehouses, etc., .15 to .3.
Ordinarily, the bearing of a properly driven pile not less than xo ins. in diam. may
be taken at 10 tons.
. Friotion of* Bottoms ofVessels. At a velocity of 7 knots per
hour, a foul bottom requires 2.42 IP over that for a clean bottom.
Friotion of Planed Brass Surraces Inmuddy wateris.4pressurei
G^as, Steam, and IXot-air Knsines. Relative costs of gas, steam,
and air engines per H*: Otto Gae engine, 8.75; Steam engine, 3.5; and Hot-air
engine, 4.
Ueat. Available heat I '643' 535
expended per IIP per hour J Total heat of combustion x Coefficient for fliel "^
GomnimptioD of coal per IW.
Coal X4000X773 units = 10808000. Theoretical evaporative power =15 Ibb.
water. Efficiency of Aimace = . 5 ; then 10 808 000 X • 5 = s 404 ooc, and ^—^^ — ^^
' 5404000
= 3.04 lbs. per IW per hour.
Toe Boats, Speed of. Mi^-Gen. Z. B. Tower, U. S. A., assigns the speed of
Ice boats at twice that of the wind, and the angle of sail, to attain greatest speed,
to be less than 90°.
Japan Coal. Analysis of Bitummous. — Specific Gravity, i. 231. Carbon,
77.50. Hydrogen, 5.28. Oxygen, 3.26. Nitrogen, 2.75. Sulphur, 1.65 Aab,84^
■ndlosa, 98.
Its evaporative efltet = 4. x6 lbs. water per lb. of ooeJ.
Ooal, Effeotiv
2564 units per hour, ai
in the generation of -
of coal reqalred per W
into atmospheric stcar
q,uired to change 30 lb-
The total heat devel-
ranges from .55 to .8, i
Cl^oast and Kn-
will scour and transpun
are very much less.
Oold, G^^eatest
liquid Nitrous Acid.
Oorrosiozi of I
AS a mean, fully one th
Oost of Famil
to $600 per annum, oi
cellaueous 8.
OrasHine; Re^
clay withstood a presdi..
SZavtl&'w-orlc. >
thrown horizontal, 12 i
When vertical, 6 to 10 t
WheeUarrow. —Prop.
I4'iAzxxl>ev of X..
-- *i-
Distance.
Trip..
No.
Voh.
FmL
Cub. ■
so
lao
2J
50
no
10.
70
100
14
100
98
l.-i
Volume of a barrow !■
Portable RaUroad at-
be transported per day.
Horse Care.— Vo]
DtaUuce.
Trip.. Vol..
F««t.
No.
Cub.
300
86
17-
11.
500
67
Volume of each load.
Ox Car
i is less i]
0 coj.;
SleotT^io I^i|>ht
Current with 30 Paur.-
like cells, 124 volts, auu
The elavated electri.
distance of 80 mUea
B2]
■C 1"
»i.
— Ilk. w,l*-
r *T of
^» -•t%j':'
:«c
«r li?-
■ .X
MBHOBANDJU
911
Pftmelter Steomey, Ordinary I>i«€Til3Utioix of I><ywer
in ». I'ower develope* liy fOgiJiw, 88 IIF; Poww ezpesAed in its operation, 13.
Percent. I ,. , „ ^•"^•"^
Friction of load 75 Power expended by slip of propeller. ... 14
" ofpropeller 7.5 I " '' in propulsion 71
T>«mT> Centrifugal, has lifted water 28 to 29 feet, drawn it horizontally 800
fe^ and then lifted it 15 feet. Also drawn it 24 feci, and projected it 50 feet
Tiailx^asr 'drains. Pommot and Metistanee. — A railway ^ain runaing at
raieef 6a »ites per bou* = 88 feet per aeecaid, and velocity a bo«ky would acqaire
in fUlinK from 88 feet = 88-^8.02 = 120. 3 feet Consequently, In adxHtion to power
expended in frictional and atmospheric resistance to train, as much power mnai be
expended to put it in motion at this speed, as woiiM lift it in mass to a height of
121 feet iD a second.
If the train weighed 100 tons = 224 000 lbs., then 224cx)oX 120.3 = 26747200
foot-lbs. , and if tbis resolt waa oMaincd ift a period of 5 minates, it would require
120.3^5X224000^33000=163.3 IP in addition to that required tor frict.onal
To ratBotbe speed «rfa train from 40 ($8.66 feet per second) to 45 (66 feet per sec-
ond) miles per hour, the power reqalr^l^in addition to tta»t of Irictioo would be as
5866-^8.02 = 53. 44 feet is to 66 -=-8^ = 67. 57 feet = 67. 57 — 53- 44 = "4- 1 3 feet.
Assume a train of 100 tons, running at rate of 60 miles per hour, ind total rotard-
init power at . i its weight 100 -r- 10 = 10. Then 224 000 X 10 X 120. 3 = 26 947 200 —
22 400 = 1203 feet, which train would run before stopping. If, however, tram was
ascending a grade of i in 100, the retarding force = ,11 (11 -H 100) of weight =
24640, distance in which traiji would come to rest would be 26947200-7- 24640 =
1093. 6 feet
Relative Non-oondnotiloility oT ftlaterials.
Matekiai..
Hair felt
Mineral wool. No. 2
" " and tar
Sawdust....
Per cent.
100
83.2
71-5
68
MAtneiAl.
Mineral wool, No. i
Charcoal
Pine wood
[X..oam«
Per ecHt.
67.5
63.2
55-3
55
Matkriai..
I Per cent.
liime, ^aeked .... 48
Asbestos 36.3
Coal ashes j 34.5
Air space, 2 ins. . . , 13.J6
K.esistaiice to a Steam-vessel in Air and "Water. 4n air
10 per cent of IIP. and in water, at a speed of ^ miles per hour, 90 per cent., or 8
IH* per sq. foot of immersed amidship section.
Saws, Circular. 30 ins. in diameter, are run at 2000 revolotlons per minute
■=: 3.57 miles.
Spur 0-ear has been driven ata velecity of i mile per minute.
Sugar 'M.ill Rollers. 5 feet by 28 ins., at 2.5 revokrtions per minote,
requires 20 H*, and 18 feet per minute is proper speed of such rolls.
Surface CoMdensation, I^xperiments on. (B. G. Nichol.)
Tube of Brass, .75 Indi External Diameter. No. \Z B W G. Surface = 1.0656
sq.feet. Duration of Experiment, 20 Minutes.
Steam.
IVmperatore
Pressare per sq. inch per gauge. . .
Condensation by tnbe snrfkce
"persq. ft. of •' per hour
Ver«c«l.
17.75 lbs,
18.5835 "
52.32
256 o
18.25 lbs
299585 "
84.34 "
130.4375 "
Horizontal.
253°
16.75 Iba
24.0835 "
67.8 "
24.5625 "
17.25 Ibt.
430835"
121.29 '*
43.5625"
Condensed during experiment ... 1 19.062^
Steamers' Kn^i^es, Weiglits Of. Engine, Boiler, Water, and aU
Fittings ready for Service per Iff.
IMercantilc iienmet 480 lbs. I Light draught 280 Ib&
English Naval " 360 " [Torpedoes 60 "
Ordinary Marine Boiler with Water 196 lbs.
1, Pressure of. Estimate of. upon Structures. -^^o lbs. per sq. Ibof^
ot of a locomottre train — 10 feet in height, 300 lbs. per sq. toQ\.
^as developed a pressure of 93 lbs. pef lineal fotff^.
912 MEMOBANDA.
"Via Snez Canal. Passages by Steamers.— 1^9^ *^ SHrUng OasUe^^^ Sbaog
hai to Gravesend, in 29 days 33 hmtrs and 15 mm. , inclading z day 33 hours and 3c
min. in coaling and detentions.
" Qlenare,^* Amoy to New York, N. Y., in 44 days and 13 hours, inclading deten-
tion at Suez. From Gibraltar in 11 days.
Zinu Foil in. Steam-boilers. Zinc in an iron steam-boiler consti-
tutes a voltaic element, which decomposes the water, liberating oxygen and hydro-
gen. The oxygen combines with fotty auids and maizes soap, which, coating the
tubes, prevents the adhesion of the salts left by evaporation. The mealy d^osit
can then be readily removed.
Piles. To Compute Extreme Load a Foundation Pile wiU Sustain.
.p , j^> =1* R representing weight of ram, P weight of pile, and L eaUreme
load, cUl in lbs.; h heigfit of fall of ram, and s distance of depression of pile with lasi
bUtwi, both in feet
Illustration. — Assume a ram 1000 lbs. to fall 30 feet upon a pile of 400 lbs.,
what resistance will the earth bear, or what weight wiU the pile sustain when
driven by the last blow, firom a height of 20 feet, .5 inchV
« = . 5 of 12 in& = .0416.
_. 10008X20 30000000 ^ ,.
Then r = — ^ = 343 406 lbs.
(400 -f 1000) X. 0416 58.24 ^*^'
Perim eter. The limits or bounds of a figure, or sum of all its sides.
Of a canal it is the length of the bottom and wet sides of its transverse section.
Flood "Wave. The flood wave of the Ohio River In March (1884) was 71
feet I inch at Cincinnati, being higher than that of any previous record.
Ice. Crushing Strength of, as determined by U. S. testing machine, ranged
firom 327 to 1000 lbs. per sq. inch
.A.tm08pliere. If pure air is exhausted of 3. 5 per cent of Hs oxygen, it will
not support the combustion of a candle.
Blasting Paper. Unsized paper coated with a hot mixture of yellow
prussiate of potash and charcoal, each 17. parts; refined saltpetre, 35; potaasium
chlorate, 70; wheat starch, 10, and water, xsoa
Dry, cut into strips, and roll into cartridgea
Circular Sa^vs. Speed, 9000 feet per minute. Thus, for an 8 Int., 4500
revolutions, and progressively up to a 72 ins. , 500 revolutiona (Emerson.)
IToods, Relative \^alue of, compared i^itli lOO I^los. of
Q-ood Hay,
Additional to page 303.
Lbt.
Acorns 68
Barley and Rye, mix'd 179
Barley straw • . . 180
Buckwheat 64
Buckwheat straw. . . . soo
LiM.
Linseed 59
Mangel-wurzel 339
Pease and Beans 45
Pea-straw 153
Potatoes.' 175
Rye 54
Turnips $04
Wheat 46
Wheat, Pea, and Oat-
chaff 167
Depth of tlie Ooean. Mean depth is estimated by Or. Krummel at
1877 fathoms =s 1.85 geographical miles.
d-as-engine. A gas-engine 1.5 actual H* will cost, with ga8.at 8 cents per
hour, 10 cents per hour for 10 hours. (Am. Engineer.)
X^ocomotive. Average daily run 100 miles at a cost of $ xs.So for driver,
fireman, ftiel, and repairs. [H, J. Central R. B, Co.)
Consumption of Fuel per Mile. Passenger, 2$ to 30 lbs. ooal. Frei^, 45 to 55
lbs., or one cord wood per 40 milea
HSMOBANPA. 9I3
iAumotxry. In laying stones in mortar or cement, they should rest upon the
course beneath them, more than upon the material of joint.
Steel Q-vin (ICrupp's). Bore, 15.75 ins. ; length of bore, 28.5 feet; of
gun, 32.66 feet. Weight, 72 tons. Charge, 385 lbs. prismatic powder; projectile,
chilled iron, z66o Iba, with an explosive charge of 22 lbs. of powder.
Moment of shot at muzzle, estimated at 31 000 foot-tons, and range 15 miles.
Sa^ve-AAill. 7723 feet of i inch Pillar boardt in One Hour.
Engine (Non-condensing). Cylinder. — 12 by 24 ins. strolce of piston.
Boilers. — Two (cylindrical flued), 38 in& in diam. by 26 feet in length, two 14 Ins.
return flues in each. Heating Surface. — 780 sq. feet. (?raf«s.— 42.5 sq. feet
Pressure of Steam. — 125 lbs. per sq. inch, cut off at 16.5 ins.
BevoktHons. — 350 to 350 per minute. Saws.— Two circular, 60 and 66 ins. in
diam.
NoTB.— Grates set s8 ins. Arora under side of boilers, without bridge-wall, and a
combustion chamber under boilers, 4 feet in depth. Fuel, sawdust.
Steam Keating. 62 500 cube feet of space requires 6000 sq. feet of heat-
ing Surface to attain a temperature of 70*^ in the vicinity of the city of New York
In its coldest weather.
Or, One sq. foot of iron pipe will heat 10.5 cube feet of space in an ordinary build-
ing, temperature of exterior air 70^. {Felix Campbell)
Velocity of* Steam. Steam at a pressure of 60 lbs. + atmosphere has
avelocity of efflux of 890 feet per second, and as expanded, a velocity of 1445 feet.
Slasting. In small blasts i lb. powder will detach 4.5 tons material, and in
large blasts 2.75 tons. (See page 443.)
Delta Metal (Iron and Bronze). Specific gravity 8.4. Melting point 1800°.
(See page 384.)
Jarrali 'Wood of A.vi8tralia. Impervious to insects and the Teredo
Navalis,
N'atural and Artifioial Gras. Relative water evaporating powers
differ ill localities, bat are assumed at 900^ and 600^ heat units (B.T. U.) :N'at-
viral oorapared xv-itli Bituxninous Coal is effective m the ratio
or2.38toi.
F'ree Soard of Vessels. For each foot of depth of hold (fW>m ceiling
lo under side of main deck), .1 inch added to 1.5 ina for a depth of 8 feet Thus,
for 24 feet depth i. 5 + . i x 8 00 24 = 3. i ins. {American. )
Or, 3 in& for 8 feet depth and . i fbr each foot in addition thereto. {Lloyd^s.)
Oolors fbr "Working DraMrings.
Brass Gamboge.
Bricks Oarmine.
^ay .Burnt Umber.
Toncrete. . . .Sepia with dark markings
Copper. Lake and Burnt Sienna.
Granite India Ink, light
Iron, cast . . .Neutral tint
** wrought . Prussian Blue.
Lead lad. Ink tinged with P. Blue.
Steel Neutral tint, lighi
Water Cobalt
Wood Burnt Sienna.
Burnt Umber.
Yellow Ochre.
" <' and Black.
" " and B't Umber.
Red and Indigo.
Burnt Sienna and Indigo.
Stones
and
Earths
Stowage of Chain Cal>le. Square of diameter of chain in ins. mul-
tiplied by .35 will give volume of space required to stow i fothom.
.A-splxalt ^4ortar. Asphaltura i part, powdered asphaltic limestone 7.5
parts, residuum oil .28 parts, stind .6 parts.
Melt asphaltum and add the rest in order named.
i^splxalt Concrete. Asphalt mortar 11 parts and broken stone 9 parts.
A.sl>e«tos is a fibrous variety of Actinolite orTremolite, composed of silica,
alumina, magnesia, oxide of iron, and water. It resists heat, moisture, and many
acids.
^14
JilSlfiCnEMitllllr
t>atay WoftiA dit eok K8q.i2ijQaa\ei# Ffe^ or a tea -toner 81,9 «M
Bread x.75 Iba, Soup 1.25, Spirits x, abA Water .9 pIM. (i8*r' W. R F^rry. f
Coignefs Concrete. For walls that resist moijt*ttre.~>~S&aiyQTa,'vetBnX
Pebbles, 7 parts; Argillaceous Earth 3 parts, and Quicklime i pari.
Hard and quick setting.— ^atid, Gravel, and Pebbfes, 8 parfd; Eartk, burned and
powdered Cinders, each i part, and Unslacked hydraulic Lime i 5 part& For a very
hard mixture, add cement i part.
^ransmissloxx or ConcLuotivlty of 'Pempdra.t-aim ia tike
JSartlSK. At Edinburgh therntiometers set at a depth of 16 feet in the enrth ai-
tained their maximum and minimum at about six months after the corresponding
maximum and minimum of the surface, being TowcsC or coldest in July.
The average rate of transmission of heat, as observed at Schenectady, N. Y.^
dowBwarcte, 2.9 feet per months and upwards 3.4 feet. (Olin H. Landreih,)
Shaflts. When loaded transversely, the diameters of the Journal should first
be determined, its dimensions tbett- »t any other point caiir be deducted from thfoee
dlattleters. It being obserted that tfte dfameterg at atrf fwo poMto sboortd be*prob
portional to the cube routs of the stress at those points.
Journals.— For operation at high speed a greater teBgtb Is required thaa-fer low
speed. The less their length, the less may be its diameter for a given stress, and
coOBeqafftttj tbe fri(;tiou wilt ber lesa
When in constant operation, a large sur&ce Is requlfed to reduce heating, and
as ft'iotion increases with diameter, not with length, for like stress, it is best to
lengthen.
Wrougfit Iron. — For 50 revolutions length to diameter as 1.2 to i, and Uttetety
50 revolutions additional . 2 ^ouM be added. Thus, for 1000 nvohiUoins the length
to diameter should be 5 times. Cast Iron. — Length to diameter as .9, and £iteef
as t. ^5 of above value. ( W. C. Unwin. )
Noxx-oondiiotiiig liCaterialis. By the investigations df Prof. J. M.
Ordway of New Orleans, he determined the relative non-conducting values of the
following materials, compared with a naked pip^, to be :
Hafr-f^lt, bfirlap j z 1 Cork in strips d
Asbestos paper, hair-felt, duck. ««<< 1,18 Rice-chaff.. •..«<. ..J a.a
Pine charcoal .........4.... i.ao 1 Clay and vegetable fibre ......... . a.8
Airspace , 4 | Naked pipe 31
{EnffineerinQj vol. 39, page 206.)
Miariiie Transportation Oi" Troops. Heig|bt fMtlreen deckn
(deck to under side of beam), men 6 feet, horses 7 feet. ffatchiMtfS.-^EoraeB at
least 10 by 10 feet. Vessels. — H(»^es. beam not lesi^ than 30 feel Men, all ranks,
2 to 2.5 tons capacity, horses, 10 tcM»s. Rations. — If biscuit in bags, loooo reqoire
950 cube feet of volume; if it is in barrels, 1350 cube feet.
Cabtm.— Officers, 30 tq. feet ai&d 19^ cube fe^ of volume, two men 42 sq. feei, and
270 cftfbe feet of volume, and for each additional nian lo sq. feet, ei&eluslve of bed
space of 6 by 2 feet.
Hammocks. —To wmpute mmkit* ttuU can be naung flmeUr a deck,
. rtj X -7 = n. { tepresendng length under deck in Jkef^ arid h breadth in Im,
6 16
[Sir G. WolseUy.)
Horse -"Povrer of Boilers. — 30 lbs. water evaporated into dry
steam, from feed at loo^, under a pressure of 70 lbs. per sq. inch merenrial gavge
per iiour. (Civntennkxl Exhibition, 1876.) 34^5 lbs. water as abore from frad at
212° into steam at 212°. (Am. Soc. Mechanical Engineers.)
lfIUCOBAJ<(DA.
9IS
]Pen«trati<»n of Zjiglit In Ttratef. Mediterranean, clear snnlighi
in March, at a depth of 1200 feet; in winter, 600 feet {M. M. Fol and Sararin,)
Railroad. Horse. First in operation In 1826-7.
Vina. First in use In England about 145^
Iron Steamers. First build in 183a
X^noifer Afatoh,. First made in x8s(^
'Watolie^. First constructed in 1476.
ILioad oix 6tone per sq. foot. Church of All Saints at Angers, 86000 Iba
Pantheon at Rome, 60000 lbs
1''le3til>le Faint fbr Canvae. Yellow soap 1.66 parts. Boiling
water i. Qrind while bot with .93 parte oil pftint.
B^ixel. Evaporation of 9 lbs. water flrom 212^:
1 lb. good coal .75 lb. petroleum.
2 lbs. dry peat e. 5 lbs. dry wood.
3.25" cotton stalk& 35 '^ brushwood.
3.75 " wheat straw. 4 *^ megass, or cane refuse.
Tram-ways or Street Railroads.
Resistance on straight and level tracks 15 to 40 lbs. per ton, or an average of
30 lbs.
Power required on a good track to start a oar, as determined by A. W. Wright,
M.W.S.E., 116.5 lbs., and to maintain it in motion 17.2 lbs C. E. Emery, Ph. D.,
made it 13 lbs. On a bad track, the power is 134.6 lbs. to start and 35 to maintain
it m motion.
Power required, as determined by Mr. Wright, to start a car is 33- 53 H*, with an
average load and day's work, and 133.22 to maintain it in motion.
Average work of a car-horse 5.75 hours per day for a term of service of 6 yeara
Strong draught- horses will exert a power of 143 lbs. (^ 3.75 miles per hour for 22
miles, and an ordinary one 121 lbs. for 25 milea {Guyffier.)
CabU Railway. Mr. Wright gives the power required per ton * at 1.92 EP.
* All tons h«f« and tlMwhcr* are givaa at 2240 lbs.
Ztesnlt of Sxperiments on IMotors fbr Street B-ailroadsi.
(1885.)
At Antwerp, by Capt. D. Galton, F R.S., etc.
X. Locomotive Engine and Car, Ordinary type of steam-engine, surface condensei
(Krauis).
*• Surface condenser, vertical boiler, escape super-
heated (Black and Hawthorn).
<* Compound engine, compressed air, water -tube
boiler (Beaumont).
** and car combined. Ordinary type of steam-engine, water-
tube boiler (Howan).
** combined- Electric Fausse Batteriea
.3-
4-
S-
<t
M
M
ii
Weight of Train per
Pi
Lba.
5. Electric... 1. 78
4. Steam ,2.3
3. Comp'd air, 3.55
Fael oonsumed
Per Mile of ConrM.
Lbs.
4. Rowan 5.32
5. Electric 6.16
3. Black and ) q «„
Hawthorn. . ) '*''
I. Krauss 9.x
3. CompM air,. 39. 48
Per Seat par
Mile of Course.
Lba.
.1
•23
•23
•as
.66
Oil, Tallow,
eto.
Lbe.
.038
.038
•073
.lOX
•355
Water
per Mile of
Course.
Galloni.
Rowan 75
Comp'd air. 1.06
Black and
Hawthorn
Krauss.,,.. 6. 52
Hawthorn f 5 S''
ffan. — The •eenomy «f tbe Rowan motor ocearred mainly from tk« aztvit of ita oon(
fewtft I9 wtdch warm watar waa supplied (0 the boiler.
gi6
MBMOBANDA.
on Steel or Iron*
Corrosive Sfibots of Salt-'virater
(J. Farqukarton.)
Lou of Hates Subm^gedjor Six Months. Area 12 Sq- Fed.
?^» »53lb. Steel ) combined
Iron 233 " Iron ) w»u»/i«v«
{:
07
445
Friotioxial Resistance or a Iiail\^a3r Train. (C. H, HwiMm.\
Resistance per ton, due to atmosphere at maximum speed, .133 lb \ to starts
17.07 1^ i ^^^^ ^ maintain in motion, 5.x lbs.
Blasting Ghelatiue. ((? McSdberU, FC.S.)
Is composed ( Nitro glycerine 93 parts > Effective nower tat^ rfMi.lbs.
by weight. . . . { Nitro-cotton 7 " J i^neciive power. . . . 1400 roM-iM.
It freezes hard at a low temperature (35 to 40O). At ordinary temperature above
flreezing, it does not explode by sbock, but when frozen it readily explodes. It is
insoluble in water Specific gravity i 55 to i 59.
Effective Povoer of some other Explosives.
Nitroglycerine, 1270 foot-lbs. ; Dynamite, No i, 900: Gun-powder, extra strong,
as Curtis and Harvey^s, 272; Dynamite, No. 2, of 18 nitroglycerine, 71 nitrate or
potash, 10 Qfcharcoal^and i of paraffin, 531, and Fulminate of Mercury, 367.
Soltfl
Diam.
ofBott.
1 of AVr
Tool.
ouglit I
Strength
strength
when cot.
.ron a(
(D.js;
ijter Sq^i
Lots.
^ .A^fTeo
Clark.)
%re Inch o^
Diam.
of Bolt.
ted by
fMetak
TooL
tl&e Tliread.
StrmKth 1 ,
wfaeticiit. 1 I^»«-
Iiu.
125
X.25
X
X
Dies.*
Chaser.
Old Dies.
New Dies.
Lb*.
40812
38528
55149
42650
per cent.
25
29
II
30
lot.
I
.625
.625
• 625
Chaser.
Old Diea
New Diea
Chaser.
Lbe.
44845
51005
43613
41888
Per cant.
28
14
26
33
* Die not given, evidently new.
^Approximate Sottoxn Velocities of Vlo^^ of "'Water in
Channels, at 'wliioli follcwring Alaterials begin J;o IbXove.
{Haupt)
Feet.
Milet.
Sm.
Honr.
.25
•»7
•5
X
!68
»-75
1. 19
9
«.39
Microscopic sand and clay.
Fine sand.
Coarse sand and fine gravel.
Pea gravel.
( Rounded pebbles, i inch in
( diam.
Feet.
See.
3
3'33
Milet.
Hour.
3.04
2.3
3-41
(Small stones, x.75 incb
( in diam.
(Flint stones, size of
( hen^B eggs.
{2-inch square brick-
bats.
Scouring force of the current is proportioned to the square of its velocity.
Transporting rapacity varies as sixth power of the velocity. Hence the impor-
tance of increasing botUm velocities, both to effect a scour and to prevent deposita
Cliimney. {Mettemick Lead Mining Co.)
Foundation 36 feet square by 11. 5 in height; base circular 24.6 feet by 39.37 in
height; shaft, 397. 5 feet In height, 24.6 feet at base, and 12.48 at top; flue 12.48 and
9.84 feet in diameter. Total height 441.6 feek
Evaporation of "Water. Mean, as observed at BosUm, Mass.
loa.
January 9
February. 1.2
March x.8
April.
May. .
June.
Int.
4.01
5.86
Total.
Int.
July 6.28
August 5.49
September... 4.09
... 39.11 ins.
Iniu
October a. 95
November ... i .63
December.... x.a
MSMOBANDA. QI^
Central Width, of pt R-oad-way in a Cut.
Feet. Feet.
Ranlwajr, single line. i8 to so | Public road 381030
" double line 30 "■ 33 | Turnpike road... 38 " 40
Kydrauliq H.ara.
l^ffidency under Heads of Supply from 2 to 24 Feet, and Ddivery of DUcharge at
Elemtions from 15 to 100 feet.
MeaguremerUs from Valves of Ram.
To Compute I*er Cent, of Total Volume of "Water Ex-
pended.
-—- C = Par cent H representing head of supply, and E elevation of discharge,
lit
bo<A in feet, and 0=8.
Illustration. — What is volume of water delivered with a head of 3z feet to an
elevation of 60 feet?
^ X .8 = .2S per eerU. Hence, if the volume of dischaiige is zoo cube feet, vol-
60
ume elevated is 100 X -aS = 28 cube feet.
Inversely. By formula of £. B. Weston, M Am. Soc. C. R
S C H
= V. S representing number of cube feet expended in ram per mintUe, h dif
xooA
ference in elevations of ram and delivery in feet, and V volume raised in cube feet
C =± 65 to JO.
Assume as preceding, H = sx feet, E = 60 feet, and S = 100 cube feet
_^ 100X65X31 136500 . - ^
Then, ^^—^-^ — = -^-^- = 35 cube feet
100x60 — 31 3900
Nonk—To eonferm t» tke precedtiiK fortoala C thoold be 53.
To Compnte Elements of a Screw Propeller*
Plif^T; ^i^ = T; ^^^^ = 1^; and 1^335^^^,
p ' pB. 33000 pR
P represerUing mean pressure on piston per sq. inch in lbs. , a area of piston in sq.
ins., p pitch ofpr<^ll^ and I length of stroke, both in feet, R number ^revolutions
per minute, and T thrust of propeller in Ws.
Illustration.— The elements of operation of a steam-engine are: Mean pressure
CD piston, having an area of looo sq. ins., is 30 lbs. ; length of stroke 3 feet ; revolu-
tions of engine 130 per minute; and pitch of propeller is feet. What is the thrust
of the propeller, and what the power of the engine?
3oX3X3X-ooo^^^^ ^^^3oX3X3XxoooXi3o^i56ooooo^ ^
Z3 33000 33000
Centrifugal I*nmp.
{SoutkuHirk Foundry and Machine Co. Non-condensing.)
Pumps.— f^o of 43 ins., with runners 68 ina in diameter; discharge pipe 43 in&
Engines.— Two of 38 ins. in diameter of cylinder, and 34 ins. stroke of piston.
Boilers. — 12 Horizontal tubular. Heating surface, 8568 sq feet; QraU, 330 sq.
feet; Combustion natural.
Pressure of Steam 70 lbs. per sq. inch, cut off at .635.
devolutions, 130 to 160 per minute.
Height of Delivery, o to 36 feet
ir«^A<.— Pumping plant exclusive of boilers 300000 lbs.
Discharge.— From Piy-doijk from a depth of water of o to 36 feet, mean per mi»
ate zzaQ33 gallons,
4H*
9i8
MEMOBANDA.
Friction of* a Noxi-condensing Sngine. (/Vo/ R. H. Thur$ton-\
Friction of a non condensing engine is given at from 2 to 4.75 lbs. per 8q. Inch of
piston, being least at low pressure. The conclusions drawn from a aeries of exper-
iments are as follows:
I. It is sensibly constant at any given sp^ed of engine at all loads.
3. It is variable with variation of speed of engine, increasing with the speed.
3. It increases with increase of pressure of steam.
NoTB.— This p«r cent, of friction is somewhat lees thftn that given ante at p. 7^
^iBil>ilit3r of* Vessel's Sidelights. The minimum distance ol
visibility assigned by the International regulations for green and red lights is 7
nautical miles.
'Weiglit or A.iivils. The weight of an anvil for forging iron should be
8 times that of the hammer, and for steel 12 times. {Prof. Fi-iedrick Rich.)
Temperature of* M.iiies. Temperature of copper mines of I^ke Su-
perior increases i** for every 100.8 feet of depth. The usual gradient is from 5c to
55 feet. (H. A. Wheeler.)
Plorse. In transportation by sea occupies the space of 10 tons measurement,
and requires that of 300 cube feet of air.
Stalls 6 feet in length in the clear of padding and haunch piece, 2 feet 2 ins. in
clear width between padding, 10 per cent, of this width 2 ins. narrower, and 5 per
ceilt of it 6 ins. longer.
Alule. A pair will draw, including cart, 1500 to 2000 lb&
^ss. Will carry 100 to 200 lbs. 15 miles per day.
*
Camel. The Arabian, or Dromedary, has one hump on back, the Bactrian has
two. I^rge animals will carry 1500 lbs. for 3 or 4 days, or xooo lbs. for several
days, and 450 to 600 lbs. for a long march.
One has travelled 115 miles in n hours.
Klephant. Weight, 3 to 5 tons; weight one can carry about 1450 lbs. ; 2000
lbs. have been carried. Occupies 55 sq. feet; will travel on a good road at a rale of
2. 5 miles per hour for 6 hours.
Wliales. Greenland Right, length 50 to 60 feet. Finner, 80 feet Speed, 10
to 12 miles per hour. Extreme weight, 74 tons. IP estimated at 145.
Cliimneys. Late experiments as to the draught of chimneys have developed
the result that an increase of its area near to the top increases the draught
Cost of ^laintenanoe of Street Itailroads, 1876.
Average of 16 roads, 102 mikt in lengthy with 1397 cars and 10300 horses,
{H. HcatpU)
Cast per horsCj and average number to a car eight
Repairs of harness. $ 4.06 Shoeing. $92.77
Feed x34*39 Stall expenses. 42.13
Replacing horses 22. i
Total.... $2is-45
Cost per month of each horse, $ 18. On one of the longest railroads in the City
of New York, on the least populous route, the daily cost per passenger, exclusive of
general expenses, was 2.88 cents, and inclusive of general expenses 4.1 cents.
AHagiiesia Covering for Steam-pipes and Soilers.
Experiments made by Bureau of Steam Engineering, U.S.N., developed the fol-
lowing comparative results:
Felt (as standard)... xoo | Sectiopal magnesia..., 203.07 | Sawdust 90.5
APP»NDi;5,
919
APPENDIX.
River Steamboat, "Wood. Side Wheels,
li^reiglit and. i^asseng^sr.
** BoeroNA. "— floRizoNTAL Lever Engines {Non-co)idetmng). — Length 4m -deck,
y)2/eet 10 ins.; beam, a feet 4 ins.; hoUL, tfeet. 2^pn«,-993.52.
Immersed section 0/ light draught of id ins., 83 sq.feet Capacity for freiglU, 120*
tons {2000. U>s.).
Cylinders.— Tvfo of 25 ins. in diam. by 8 feet stroke of piston.
Boilers. — Four of steel, 47 ins. in diam. by 30 feet in length, 6 flues in each.
Heating surface, 903 sq. feet. Grate surface, 98 s^. feeU
I'resture qf Steam, 154 Iba per sq. inch, out off at .625.
Revolutions, ^per minute. Speed, 10 miles per hour against current of upper
Ohio, 3 to 5 miloa
To Coixipute IVXeta-oeaiitre of Hull of a "Vessel.
Operation of Formula in Naval Architecture, page 660.
Assume a sharp- modelled yacht, 45 feet in length, 13.5 feet beam, and 9.5 feet
hold, with an immersed aniidship section of 42 sq. feet, and a displacement of 900
cube feet at a mean draiii^bt of water of 6 feet
2 py^ dx
- / = Meta-centre. See pages 650, 659.
3^ O
Ordinates (dx) taken at intervals of 2.5 feet are as follows:
y
y
ys
v6»_
,8
:= O = .0
= .63= .ai6
= 1.33= 2.197
= 2* = 8
= 2.83= 21.952
= 3.53= 46.656
5' =125
y7 =583=195.
113
y8*z= 6.5' = 287.496
ye' = 6.73 = 300.763
yto' =6.75 = 307.547
y"' = 6.5 =287.496
3
y" =6.25 =244.14
y«'=5.8 =195.1x3
y'4'^=5 =125
y»5 =:4.2 s= 7^.088
yi6 ^3.25 — 3^.328
y'7- = 2.4
yx8'=i.5
y»9 = .8
y»'= 0
= 13-824
= 3-375
= .512
= .0
2272.814
2.5
5082.035
Sammation of function of cubes of ordinates for value of /y > dx = 5683.035.
And ^ of 55??:^ = ± of 6.31 = 4.21 fiet.
3 900 3
Note.— The other elements of this vessel are:
Area of load-line, 401. 12 sq.feet ; JHqffUKement in toeight, 27.974 tons ; do. at loud-
draught, .9«;5 tons per inch ; Depth qf centre qf gravity of displaccmeut below load-
Une, i.^g feet; Volume of displacement, to volume of immersed dimewsiqns, s6.8
per cent.
To Compute Height of Jet in a Conduit !Pipe frora a
Constant IFIead. {Weisbach.)
H'^+'^m
V
^.0
h'
- = — —h.', and — = A". A, h', and A" representing heiglUs
due to vdoexty qfejgHux, loss of head and ofaseent, I length «fp^ or conduit, and '
and d' diameters of pipe and jet, all in feet, v relocibg i^ ed^m <in ^eeA per seeondy.O
and C coefficients of friction of inlet of pipe and outlet, and z a divisor determined
Jjy experiment with diameters of.^ to 1.25 inf., ranging from 1.06 io 1.08.
iLLrfiTRATiox.—Tf conduit pipe for a foimtnin is 350 feet in length, and 2 Ins. In
diameter, to what height will a Jot of .5 inch ascend under a head of 40 feet?
AarameCandr/.S and .5, h=i2sfeet, (I = 2tm. = .i66,and.5 = .5->x3=:.04i6
^5 =4.9/j«fc
Then
1 +
(«+3.V;)(°^4*Y
920
APPBKDIX.
To Coxnpixte Kead and I>isoliarge ofWater in Pipes of
G}-reat JLteiigth.,
It becomes necessarj first to determiue the velocity of the flow, which iss^
A V V
^ = V = S.373 -T^, independent of fViction. V rq^reseiUiim volume qf water
in cubefeet^ a»d d diameter of pipe in int.
When head, length, and diameter of pipe are given, — - — - — — = «,
n/'+*'+4
Coefficients of Mction G, for velocity of flow, range (h)m .0334 to .0191 for velocl<
ties fh>m 3 to 13 feet per second, and c that for the pipe as a mean at . 5. See Wei»
bach's Mechanics, VoL i., page 431.
Illustration. — What head must be given to a pipe 150 feet in length and 5 ina
in diameter, to dischaige 25 cube feet of water per minute, and what velocity will
it atUin at that head ? C = .024 and c = .5.
25 X 12'
Then x.373 -^^zj—a = '•273 X 2. 4;= ^055 feet velocity per second, and
(rfl+.o24 l^^^j |^ = x.5 + 8.64X.i4 = ..ai/erfA««l
Vd* - /i v
Or, 4-72 — _:^= — V in cu6c/crtj)cr mittttte, and. 538 f/— r- = d»«tia:
Vl-T-h V a
Illustration.— Assume elements of preceding case.
Then 4.7. -::^^iyi==4.7»X^=.S.67C«»«JH«i'«I-S38f^^^5^
Vi50-^i.42 'o-« ^ '•4a
5= -538X7^69 607 = .538X9. 301 =5 ifU.
To Coxnpnte Fall of a Canal op Open Condnit to Con-
duct and Discliarge a Given "Volnxne of "^Vater per
Second.
Coefficient 0/ friction in tuck case is assumed by Du Buat and others ai
.007 565.
C L?x — = *. h rqn-esenHng height qffaU, I length of eanaly and p net perime-
ter, all in feet ; A area of section of canal in sq. feet, and v velocity of flow in feet
per sfxxmd.
iLLrsTRATiON I.— What fall should be given to a canal with a section of 3 feet at
bottom, 7 at top, and 3 in depth, and a length of 2600 feet, to conduct 40 cube feet
of water per second ?
€=.0076, i>=3 + (V3»+2«Xa)=iaaiyferf, A=^^t22il=:,5,g./5e«, and
« = l^ = 2.66>fect
-,. , 3600 X xo,ax ^^ 2.66* ^ , « -,^
Then .0076 X> = 13.45 X. 11 = 1-48 /««.
' 15 64.33
3.— What Is volume of water conducted by a canal, with a section of 4 feet at
bottom, 13 at top, and 5 In depth, with a fall of 3 feet, and a length of 5800 feetf
_i-Xa^ft=«. A=-i^i^^ = 4o«?.>fe««,andi> = 4 + (V?T?X8)c*
\j ip a
i6.Z feet
40 X 3.23 feet velocity = 129.2 cube feet
For Dimensions of transverse profile of a canal, see Weisbach, page 493, voL L
Ji
APPENDIX. 921
MAGNESIA COVERING FOR STEAM BOILERS, HEATED PIPES, ETC.
Ro'bert A. Keasbesr, Jersey City and. Ne'w York.
This covering is devoid of organic matter, hence it possesses great <?apacit9
to resist a high temperature, combined with high rank in the order of non«
conductors.
It is furnished for pipes in the form of hollow cylinders divided longitu*
dinally, and covered with canvas *, for boilers, in. blocks ; and for covering
odd fittings, filling floors, etc., in dry mass in bags.
JElelative Value of* iN'on. - Conducting Coverings on
"WrrQu.gh.t-. Iron Steam. I*ipe. IDetermined "by. ^Tests
at St. X^ouis Watov-Wori^am
Conderuaiion in C?u6« CmHmeterg per Foot per Hour.— (John A. Laird, M. E.)
Material.
Magnesia, SectiODal
Magnesia, Plastic
Asbestos Fire Felt, Sectionai.
Asbesto-Sponge, Molded
Analysis.
I Carbonate of Magnesia .... 92 . 20
i Fibrous Asbestos 7 . 80=100
( Carbonate of Magnesia 92.20
i Fibrous Asbestos 7 . 80=100
(Asbestos 82.00
\ Carbonaceous 18.00=100
j Plaster of Paria 92. 80
) Fibrous Asbestoa 4. 20=100
NoTS— The test at the New York Post-Office gave Fire-felt superior to Magnesia
DISTANCES, VELOCITIES, AND ACCELERATION.
To Compute Velocities of an A.ccelerated Body.
C,C.
No.
33-53
33-4
36.75
37.13
Vw' -h (2 '»' 8)7 Or, » + t »' = V. V and »' reprtunting original and accelerated
veUtcUies. and X fmil velocity ^ aJl in feet per second : S distance or space passed over
t»4- V
infeetj and t time in seconds. — ' — = V. V representing average velocity in
feet per second, V « = S, and 2 V' — V = w.
Illustration l — A body moving with a velocity of 10 feet per second, is acceler-
ated at rate of 4 feet per second, per second, for a period of 6 seconds; wba.t are its
different velocities?
T = 10, «' = 4, t = 6.
10+34
Then, 10 + 6 x 4 = 34 feet fined velocity. '—^ = 22 feet average velocity.
23 X 6 = 132 feet distance passed over. Vio'^ -|- {2 x 4 X 132) = V^S^ = 34 /««'»
and 2 X 32 — 34 = 10 feet original velocity.
And,^ = r', I±^x« = S, I^^x< = 1^S, i,» -j- 2 d* S = V«,
V— «
= «, and VV2_2»'S =
V.
a.— A body is projected vertically with a velocity of 200 feet per second, and is
retarded at the rate of 30 feet per second, per second ; what height will it have
passed through when its velocity is reduced to 80 feet per second, and in what time?
v = aoo, »' = 3o, and V = 8o.
200 — 80 . 8o-4-2oo ^ ^ A
Then -— — — = 4 seconds. —^ X 4 = 56o/«*i
30 2
3.— A vehicle being drawn with a velocity of 25 feet per second, is accelerated
5 feet per second, per second; what is its velocity and time of operation at the end
of 100 feet ?
V = 25, v' = 5, and V = 100.
Then '°Q ~ ^S _ ^^ gfconds. - — — — x i5 = 937-5y^*'
922
APr£NDIZ.
4.— A stream of water, after flowiag a distaaee of 120 feet, ia ascertained to have
a velocity of 40 feet per second, with an accelerating velocity of 2 (ieet per secood,
per second ; what was its primitive velocity and time of flow ?
S=^190, V = 40^. 1>' = 2.
Then V4o» — 2 x 2 x 120 = 33. 47 fui. ^^""^S-^^ _. j, ^5 feoonda
2
JDeliverjr And. SViotion in. £Cose.
{JEL F, ffartfvrd, Am. Soe. C. E.}
HoK 3. 5 in*, in diameter. Aozde* not exeeedinp z. 5 ins.
Rubber or leather, .0408 rd» and .^gjed' y/P = G; J^^i^— and
y^,_G^^. ^^^g^^p ^ ^:-=»; '-^^=P; .oJ,7tG'l;
003 175 6 c» d« P I and .oooobi H»»a* =|»; P— ^ = 1"; P« = P'j
, ,„ , . t>» . 314.06(1— «) - 46750.89 P(i — x) _
2.306 (P—p) and =»; T^J ^^ and ^ ^^ - , /- ^=1:
^ ^ ^ 1.123X2^ * frc'rf* bv^d* *
hp _ _- ^
■rp-^rH, 1 — .003 175 6 c^ d* i and •p' = »- G repreunting gallons dis-
charged per second^ v velocity in feet per second^ P jnr«teure of stream at hydrant or
source of suppky^ p pressure last tn kose^ and P' pressure at nozzle, cUl in lbs. per sq.
foot^ d diameter of nozzle in ins., U head of supply at hydrant^ h head at nozzle^ and
I length of hose, all infeet^ x fraction of P*ai nozzle^ b coefficient of material of hose,
and cfor nozzle.
6 = I for rubber hose and 1. 167 for leathec
c = .82 for smooth nozzle and .64 for ring.
iLLusTRATTOir.— Assume length of a rubber hose 200 f^et, pressure at hydrant 100
lbs., diameter of ring nozzfe r.25 ins., and volume of discharge 4.97 gallons per
second; whut are the oilier elements to be obtained by preceding; formulas?
.497 X .64 X 1.25' X V»oo = 4-97 ffoUons. ^45i X 4 97 _ jy,^f^
/-±.S^^^-97^ /-_:^l2^^,,^,i^, 4-484X4:97! ^200^^^^
V * V .04 V 100 .64' X 1.25* 1
OI9 857 X I X 4.97' X 200 .- 63.52 lbs. xoo— 63.52 = 36.48 lbs.
100 X 3648 = 3'-48 lbs. 2.306 (ioo>-63.52) = 84.1a feet — ^Zli- — 84.i3/«et
1.123X2^?
I— .003175 X I X.64'X 1.25* X 200=1— .6352 = .3648 — X.
314.96 (I ~. 3648) __ 200 ^^^ 46750.82 X 100 (»~. 3648) _ 2^ f^^
IX. 642x1.25* 1 iX77 96»Xi.25« ''
36.48 , „ 84.12X63.52 ^ ^^
^ = .3648 =r m. ^ ^ := 146-47 yfeet
100 3^*40
For vertical Jets, see page 549.
d-auging of Weirs,
When there is an Initial Velocity. (H + A f — ft I) ^ = H'. H otid H' reprejeirt-
ing depth ofvoater on weir, and when corrected to include effect of initial velocity qf
approaching water, and h head to which this velocity is due, all in feet.
Velocity in Pipes. C VrT •= V. r representing mean radius or hydraulic mean
depth,* I sine of angle of inclination equal to loss rfheadper unit qf lengthy V velocity
mfeet per second, and C a mean co^cient ofi^a.
In small Channels. G = 30 to 5a
Note.— lectio
A* pipe, conduit
Note.— SeetloDkl unm 1^ » pip* or condaii, divided by perimeter, le termed mmom ratiimtfSad wbcf
, or channel !• but partially tilled, the area is termed kydrauKe Huan d^pA.
• ^ aleo pat;* 5^.
APPKNDIX. 923
■
Metric B^aotors. In addition to pp. 27-37.
By Act (if Oongress, July, 1866. By French Metric Computation
I Liter per cube mtUBt =s .007 ^B ffoUona per cube Jboi . . . | .007 48 gallont.
"^^eiglxts and Pressures.
I GeDtimeter of mercury per sq. inch = . 192 91 lb. per )
sq. inch )
I Atmosphere (14. 7 lbs.) = 6.6679 kilogranu ,
I Inch of mercury per sq. inch = 2. 54 centimeters
I Pound \>er sq. inch = 453.6029 gram* ,
I Cube foot per ton = .027^ cu6e meter ,
.192911 7 lb.
6.6678 kilogranu.
2. 54 centimetrei.
453' 5926 grammes.
.0379 cubic metre.
Heat.
t Caloric per Kilogram = 1.8 heat units per lb | 1.8 heat units.
"Velocity.
I Meter per second = 3. 280 833 /ee£|)cr second ) 3.2808697061
I*o"sver and. "^^orlc,
I Kitogrammeter (X; x m) = 2.2046 x 3- 28083
1 Po(>t-|)ouQd = . 138 26 kilogrammeters
t Kiiogmra per cheval ;= 2.2352 lbs. per H*
I Sq. foot per H* == .091 63 sq. meter per cheval
7.233 ^t-lbs.
.138 25 kilogrametre,
2. 2353 pounds.
.091 63 sq. m^re.
1 Sq. Foot = 092 903 sq. meter,
"i Cube Foot = 028317 ctdte meter.
1 Cube Yard = . 764 559 cube meter.
Ailisoellaneous.
1 Avoirs Lb.= .4536 kilogram.
1 Ton = 1.016057 tonne.
I Sq. Inch = 645. 161 29 sq. millers.
I Mile per hour = 26.8225 meters per minute.
1 Knot " " (6086.44 feet) = 30.9192 " " "
I Cube Meter per minute = 7.848 ctite^rcts per Aour.
I " Yard " " =45.8718 •' m^iters '' •'
Z^ooomotive XS rakes. -r and — 5 —distance in which a train is
644./ 30/
ttopped. V and V representing velocity in feet per second, and miles per hour, and
/proportion ofreMistanee of brakes to weight of train.
Brakes, self acting, on all wbeel8,/=:; . 14. Ordinary hand,/^ .023 to .031. As-
cending I in .5 resistance is/-f- 2 ; descending i in .5 /— 2'.
Hydraulic Kaxus. Efficiency decreases rapidly as height to which water
Vs to be raised increases above the fall or head.
Number of times the height to which the water is raiserl exceeds that of the head
of the supply and efficiency per cent. ( Walter S. Button, C. and M. E.)
Number ... 4 5 6 7 8 9 10 iz 13 13 14 15 16 18 19 20 25
Efficiency . . 75 72 68 62 57 53 48 43 38 35 33 28 33 17 15 xa a
Speed of water in pumps, 900 feet per minute.
To Compute "Weight of "Water at any Temperature.
= W. W and to representing weights of water per cube
T-I-461.2O 500
500 • T-f 46J.90
foot at temperature T, and ai maximum density 0/39.2^=162.425 lbs., and 461.2^
equal absolute temperature.
iLbUBTRATiON. — Required weight of a cube foot of water at temperature of 60°.
604-461.2 500
500 ' 60"^ 461.9
924
AFPXNDIZ.
Results of* ESxperiments or Perfbrmaxioes of
Steaxn-engines ancL IB oilers.
cylinders^ Ctd-off, Vacuum^ and Diameters in Inches^ Revolutions per MimUe^
Pressure^ Water ^ and Coal in Ubs., and Surfaces aind Areas in Sq. Ins.
Ei.nniim or EMSiwrn.
Cylinder.
Revolutions
Pressure in Pipe ......
Cutoff
Mean effective Pressure
IW
Friction^...........
Netff
Water per net W
per hour. . .
Croal per do. .
Coal per Iff per)
. hour .«•. I
Vacuum
\
I • • • I
Combustible per)
IIP per hour .J *
Relative efficiency .
* Weight of engine, 40 000 At*
Hakru.
CoaLiM. 1
Non-con-
Con-
Con-
denaing.
deiuiiig.
densing.
28X42
18X42
24X60*
74.29
73-6
59'$?
58.5
76.37
92.88
4-74
7.94
18.03
26.93
29.47
89.38
105-47
"5.43
270.58
12.64
13.07
13.55
92.83
102.36
18.59
25.39
—
a'34
3.18
—
3.07
2.82
x.98
—
—
26.4
—
1.83
1.83
—
.753
—
BOILBBS.
Number
Diameter............
Length
Tubes 50 ,...
Heating Surface
Orate *♦
Calorimeter..........
Heating to Grate
Grate to Calorimeter. .
Temperature of Feed .
Steam per Lb. of
Combustiblet . .
Steam per Lb. of ^
Coal
Coal per Sq. Foot
ofGrate per hour ^ "
Steam per Temp. 2x20
X0.3
9.64
t Steam per lb. of coal 8.31 Ibt., and oTaporaUoa 9 to i.
3
60
la
4
1536.92
51.75
1256.64
29.7
5-93
"4.3**
8.8s
8.3X
WINDMILLS. (Andre-w J. Corooran, New Tork.)
(Improved. Patented June and August, 1888; March and June, 1889.)
Volnme of "^^ater "P-umped. per Mlinute.
From 10 io 200 Feet.
>iaineter
of
Wheel
Vbktkal Dutamo fbom Watbb to Podit or DntTiav ni Fht.
10 15 25 50 75 100
Feet. Gallons.
8.5 15-242
10 48.262
12 86.708
X4 111.665
16 155-982
18 249.93
20 309.604
25 532 -5»7
30 1080. 112
Factory in Jer
Gallons.
10.163
32.175
57-805
74-44
103.98
'59-954
206.403
355 012
728.828
sey City,
Gallons.
6.162
19.179
33-941
45.139
64.6
97.682
124.95
212.381
430.848
Gallons.
3.016
9-563
»7-952
82.569
31-654
52.165
63.75
166.964
2x6.172
Gallona.
GftUooa.
6.638
4.25
11.851
8.485
»5.304
11.346
19.542
16.15
32.513
24-421
40.8
31.248
71.604
49-725
146.608
107.7x3
150
300
Gallona.
Galloiu.
5.68
7.807
4998
9.771
8.075
17-485
X2.21X
19.284
15-938
37.349
36.741
74.8
54-043
Velocity of "Wind.
The average over the United States, as determined by the Signal Service of the
U. S. Army, is 5769 mileft per month, or about 8 miles per hour.
Experience has determined that, to operate a windmill, there Is required an
average velocity of wind of six miles per hour.
1^ = pressure oj wind per sq. foot of surface in tbs,
461.2OX 32-16
Or, -— t)« and — o'«. v representing velocity of air in feet per second^ and »*
400 200
in miles per hour,
NoTB.— For Qieftil Ubles and formalaa see « Wfaidmllli at a PrlsM Mover/* bj A. R. Wolff, J. WUoy
k Sons, New Tork, 1885.
APPENBIE. 925
To Oompute Head In I^im. per Sq. Inoli to Realst S'fId-
y-Jig _. V'l, _ H|3.7d>'83.. _ . /HQ.? d)t 83.. _
a ^difcAfuvv in «f , int., and IP kortt-pouttv offiT^i
f3fat,aai (3,7 X ^s>' X 83.3=1
^/. 9360000
I'm.
,.„
...
[ H>
Ti,
».'""■
nerage...
Cub ft
Chn
Gburcbea ..
>oo
Cominerolal H> of C
Hf ijsr itf c*uBB<y (11 Ftn
■*:.-
SO
60
;o
,*".
go
iia.
II4
75
I
z
r
^t:*
^
Z
~
~
.:
-
t: Sfiun CbiniHT iMust oncDl ™U oa> l^Ru gTDknicUr of BnuDil, [u Shi.
Krlotloii of 'n'ater in £*ipeH. (irni^acA.)
i^^^^ C = A- I TtprtKnting Itngth qfpipa in ftft, v = — -^- — ,
infatwrtfand^'V votumf ^fiwXfTtn cube/iel tiftattd per v^^ond, d 1
jnpeliniru.. anaC a eoeffieienl^ ranging Jrom .069 wtf '
fa*, -ox-iipr ,,feH, awt .dtB=/dp »/«*,
iLLDSTBiTioM.— Assume Tolume 13; cube feel, nised 1; hel per liDur, Ibrough ■
plp«9 Ids. Jn diuaeCer ud joo (eel la length; baw nuiDf IMI of venlcil beid wil
tlu IHoltOD Id Uia pipe be aquil Ui I
Then — ^^^—"^ = 3.18 ™iocitr, «ndO = ,oiS.
Ham:*,-— '-^ '"''*''' X.M» = H-6 fat. "idJi + i«.6 = 3»6.^
926
APPENDIX
'WatejvXu'be Marine JBoiler.
Tests of the United States Oavemment on a Boiler built ^or the U. 3, Cruun
*'*' Aterf' Conducted by a Board of Naval Engineers, April, 1899.
Heating Surface, 2125 sq. ft. Orate Surface, 48 sq. ft. Ratio, 44 : i.
Tlxe BcblKJOoU and Wiloox Oompaiasr.
Elements
Moisture in coal per cent . .
Refuse in dry coal per cent.
Boiler pressure, lbs
Temperature of feed- water.
Draught at base of pipe. . . .
Draught in furnace
Blast pressure, ash pit
Temperature of gases in flue . .
Analyses of flue gases
(jfCO...
decimals
Moisture in steam,
of one per cent,..
Dry coal per sq. ft. grate per
hour, lbs
Water evap. per hr. fr. k at 3i2*, lb«. :
Per lb. dry coal
Per lb. combustible
Per sq. ft. heating surface . .
Per sq. ft. grate surface
Cumberland Mine Run
8th
5-25
9-56
203
'57-2
.61
•3
498
.09
21. z
10.97
12.13
5.23
231.9
nth
t3th
4.09 2.77
7-39, IO-5
219 219
93-4 I 91
'•43 1-4
Anthra
C«t«,eiw
t4th
— .
.26
+.5
t-5'
595
5<>7
II. 9
7.8
10.9
8.2
•5
^
.10
•x
45-4
41.9
9.41
XO.06
10. t6
11.24
9-65
9-Si
427.4
421.3
.0
12.33
2l8
110.5
.61
.07
+ •53
520
II. I
8.7
.0
.05
28.8
10.66
12.16
6.94
307-2
CuDiberland
90th
ai«t
Cardiff
24th
2
IX. 6
204
152.6
•23
•>5
410
10.2
8.8
.0
15-4
10.93
12.36
4
167.8
1.63
10
204
160
•55
.27
470
9-7
9-3
.2
.0
22.x
10.70
It. 89
5-34
236.3
7.88
204
160.5
.26
•»4
433
10.8
8.x
.X
.0
x6.a
"•33
13-8
4-i.'^
183.1
NoTB.— The test of April 13th was made with air heated ly the fine frases to 168*.
Proportions of Ghrat« and. Heatingr Surfaces of* AVater-
'J?ul>e Soilera, ai* X)cteirxniiied \>y Xests oi*
13at>oocl£ and Wilcox Boilers
from ISrS to 1884.
{CommiUu of U. S. Centennial EsOribitum and Individuals.)
Water evapomted from and at axa^.
Aah
per eeni.
Combiutible con-
Daratlon
Bar race a.
sumed.
of
Per
Grata.
Per
Teit.
Grate.
Heating.
Ratio.
Heating
Surface.
Houn.
Sq.Ft.
Sq Feet.
Sq.Faet.
.«^. Feet.
8
44-5
1676
37-7
8.88
.2^6
X20
50.7
1980
39- «
XI. 21
.26
2x6
54.7
2148
39- «
12.22
.29a
24
61.9
2760
44.6
8.22
.198
22
59-5
2757
46^3
14. 25
•307
13-5
39-7
1680
42.3
5.8
•137
4
25
1403
56.x
X2,4I
.276
X0.25
70
3126
44-7
18.15
.406
Coal per
Grate
Hour.
Erapoi
by Cotn-
htt«tible.
ration
Cokl.
Sq. Feet.
Lba.
Lba
—
12. 131
—
xa.99
XX. 62
XX .982
9.71
—
11.626
10.09
l^
"•43
12.495
9.96
"•53
»3.44
12.38
XX. 5a
20
12.42
11.32
»3-7
X3.a*
xa.9*
7-5tT
8.8*
Coals :* Anthracite, American, f Bituminous, Welsh* t Bituminous, Scotch. | Bitunliioo^
Powelton. f Teat in London.
A Galloway boiler of standard efficiency, at this exposition, having a ratio of beat.
ing surface to grate of 35 to x, and feed water at a temperature of 56*^, gave the fol-
lowing results:
Consumption of coal, 8.87 lbs. per hoar p^r sq. foot of grate. Pressare of steam,
70 lbs. per sq. inch. Water evaporated per hour per sq. foot of heating snifiuM^
SI lbs. ; water evaporated per lb. of combustible, 9.68 lbs., and per lb. of coal, 8.63
bs.
APPENDIX.
927
To Oompute ,A.reft or C^lintiei* of a Steam-engine and.
Gl-rate anxl Ueating Sttriaceei of a Boiler.
When Required Power is Given. —It is assumed that IP of a sieam-engine is at-
tained by eTu|)oratiOQ of 33.6 lbs. water per hour, at a temperature of 212° flrom feed
water at ioq<^.
N«T«.— Thii Is a dednction from the elements of the estimate as given by the Am. Soc of Mech'I
Engineers, In order to pat temperature of the feed at 100° instead of 21a*.
Man. ' aondenimff ( Sing/le Cylinder ).
V X 33-6 X Iff
X 1728 = orca of cylinder
60X 2R X S
in sq. ins. V representing volume ef 1 lb. of water ^ terminal presmre nf steam xn
cube feet, R numi>er 0/ revolutions p^ minute, and S stroke cf piston in feet.
ILLUSTRATION. — Required ff of an engine Is 300, initial pressure of steam 70 Ihg.
mercurial gange, c«t off at .5 stroke of piston t>f 4 feet, and number of revolutions
60 per minute. What should be areas of cylinder of engine and grate and heating
surfaces of boiler?
Clearance in cylinder and steam passages = 1.8 ins. =.15 foot, point of cutting
off = 4 -i- .5 = 2 ^e^
Then (formula p. 711), 70 X (2 + . 15 -i- 4 + . 15) = 36.26 lbs. terminal pressure, and
steam at thvs pressure has a density <>r volnme, whinti is its reciprocal (formula
table p. 708) of 11.26 cube feet for each lb. of water contained in it.
„ 1X26X36.26X300 ^ o 122486 0^.0 L
Henoe, — f m X '728 = ^^— =8.51 X 1728 = 14 705 cuJbe tns.,
60x60X3 X2
14400
which -^48 ins. s<rofce = 306. 35 sq. ins., to which is to be added for friction of en-
gine and load and waste of steam i § per cent. => 45- 95 + 30^* 3S = SS^- 3 *"'•
Grate Surface — Evaporation of Trush water in an efllceot marine boiler, f^om a
temperature of feed of ioo<^ as assumed, witi) a proportion of heating snrlkce to
grate of 30 to z, to be, with a combustion of 20 lbs. coal per sq. foot of grate per
hour, 213 lbs. per sq. foot of grate, and 10. 3 lbs. per lb. of coal.
„ Eff
Hence, —^— =. area.
L representing icaporation per sq. foot of grate per hour.
Illustration.
-Assume elements of preceding, with evaporation as abova
33.6X300
213
= 47.32#g(.>fee«.
Heating Surface.— Then 47. 32 X 30= 1419 sq.feet area.
For the several types of boilers the following units should be osed:
Ratio ef a«aU$ig Smf ace to OrOU
T T p«.
Marine ,
Stationary
Portable
Looemottve
" Ooke.
30 to z i I so to z
Coal oonmimed per Sq. Foot cf •Gcate per Hoar
in Lba.
J5
.64
«S9
X32
ISO
131
20
2x4
207
»74
197
170
30
3>4
299
257
290
247
«5
ao
30
183
242
339
183
241
333
145
187
27 z
164
2ZI
30s
»59
X97
276
Unit* of Heat izi S'uels.
AdUiractte 14500
Bituminous 14 200
PtotroteaBB, 4ig|it. 22 600
heavy 19 440
(t
Petroleum, reined ,.... 19960
" crude .....•••.. <9vzo
Coal Gas ...«. ..•»■.••»•-.<• 90200
Water Gas 8 500
Tm R«<9is4: Oxid«ition in CaBt-iroxi I'ipew-
A coating of hot lime, which is much preferable to tar.
* Half atroke or point of cutting off.
928
APPENDIX.
To Compute Relative Velocities of Steaxki ITaohte, fW^xn
Klexxxents of* tlieir CoiistrvLotioix, Capacity, and Op-*
eration.
Rule. — Multiply area of their grate surfaces by- CfmtAant due to the
character of the combustion of their furnaces, divide product by cube root
of square of their ^oss tonnage (U. S.)i and cube root of quotient will give
their relative velocities.
Or, 3/ — - =: y. G reprevente'np arta of grate surface in tq, feet^ T grou totmoffe^
and C a coMton^ vis. natural draught t. Jet or ea^aust 1.25, and blaxt 1.6.
In the application of this rale, as alike to all others when there is material differ-
ence in the elements, as with large and small vessels, those that approach each
other in general dimensions or caimcities, as determined by certain ranges or limits
of tonnage, should be classed together.
Illustration. —The grate sarface of a yacht is 27.5 sq. feet, her tonnage 71.24,
and the combustion in her furnaces, jet.
Hence,3Mi2<±£5^3/if:^^,,^g^
This result is an index of the capacity of the vessel, when compared with anothef
in like manner.
Thus, assume one to be a fkir exponent of her class, as fh)m 40 to 60, 60 to 80,
or 80 to 100, etc., tons, and her speed to be 12 knots per hour, or 60 minutea
If then a competitor possessed the elements that by the above formula would give
a result of 1.3, their relative capacities over a like course woald be as 1.26 : 1.3 :*
60 : 61.9, and 61.9 — 60 = 1.9 minute = 1 minute 54 secondSf which is the time the
yacht of greatest capacity would have to allow the other.
o_
If the course was for a greater distance, as for 80 knots, than — x i<9 = za w^
12
4 tee. the allowance.
For ILiarge Steamers.
3 . 96 -y - 2 = V- S rq^nresenting area of immersed amidship section in sq. meters.
V&n.—A »q. meter Is xo.764 sq. feet.
This formula is used in Europe, and is applicable only for vessels of great capaci-
ty and with a blast combustion.
Simple Water Tests.
For Hard or Soft TTafcr. —Dissolve a small quantity of soap in alcohol. Put a
tew drops of it in a vessel of water. If it becomes milky, it is hard, if not, it is soft.
For Earthy Matters or Alkali.— Dip litmus paper in vinegar, and if on immersios
in water, the pa))er returns to its true shade, the water is free from earthy mattei
or alkali. Syrup added to a water containing earthy matter will turn it green.
For Carbonic Acid.— T&ke equal parts of water and clear lime-water. Ifcom-
XiiUed or free carbonic acid is present, a precipitate is produced, to which, if a few
drops of muriatic acid be added, an effervescence occurs.
For Magnesia. — Boil the water to a twentieth part of its weight, drop a few grains
of neutral carbonate of ammonia and a few drops of phosphate of soda into it, and
if magnesia is present it will precipitate to the bottom.
For Iron. — (i.) Boil a little nutgall and mix it with the water; if it tarns gray 01
slate black, iron is present— (2.) Dissolve a little prussiate of potash, and mix it
with the water; if iron is present, it will turn blue.
For Lime. — Into a glass of water put two drops of oxalic acid and blow upon it
If it becomes milky, lime is present.
For ^ctd.— Immerse a piece of litmus paper in It. If it turns red, it is acid. If
it precipitates on adding lime-water, it is carbonic acid. If a Mue paper is turned
red, it is a mineral acid.
APTHmyix,
929
TOBIN BRONZE.
{Trade-mark registered,)
JPlie Aiisonia Srase and Copper Co., New York, N. Y.
Sole Manufacturer,
Specific gravity, 8.379. AVeight of a cube inch, .3021 of a lb. Tensile
strength i-inch round rod, 79600 lbs. per sq. inch. Elastic limit, 54 257 lbs.
per. sq. inoh. Elongation in a rod i inch in diameter and 8 ins. in length,
15.4 per cent. Reduction, 37.26 per cent. — Fuirhanks,
Is readily forged into bolts and nuts at a dark-red heat, Torsional strength
and Elastic limit equal to machinery steel.
rrorsional StrPiiRtli,
Boit .5 inch in diameter and 1 inch in lengthy load at end of lever ifoot.
Torsion, 2.67**. Elastic limit, 328 lbs. Rupture, 633 lbs. Torsion point
of rupture, 92.2°. — J, E. Denton, Stevens's Institute.
Crashing Strength, maximum, 181 000 lbs. per sq. inch. — Faii'barUcs,
Plates.
Weight per Square Foot
Thlckneu.
ThkknaML T Wcifrkt
Lb«.
Ins.
.0625
.125
.1875
.25
•3125
•375
2.72
5-44
8.i6
10.88
13-59
16.31
ThtckiMNft.
Weight. I
IM.
Lb«.
•4375
19.03
.5
21.75
.5625
24.47
.625
27.19
.6875
29.91
•75
32.63
IlM.
.8125
.875
•9375
I
1.0625
1.125
1 WelRht.
Thickness.
Lbs.
Ins.
35-35
1.1875
38.06
1.25
40.78
1.3125
43-5
1-375
46.22
1-4375
48.94
1.5
W«iRllt.
Lbs.
51-66
54.38
57^1
59-82
62.53
65.25
Bolts and
L Rod
8.
Weight per Lineid Fdot.
Miunster.
WeiRht.
Di.'imeter.
Ins.
Weight. I
Lbs. 1
Diameter.
Weight.
I.bs.
Diameter.
Weight.
Lbs.
jDiam.
Weiirht
Ins.
Lbs.
Ins.
Ins.
\ Ins.
Lbs.
•25
•177
-75
1.6 ; i.s
6.42
2.5
17.8
4
45.57
.3125
•279
.8125
1.88 1.625
7.5
2.625
19.6
4-25
51-44
.375
•399 1
•875 .
2.18 1.75
8.7
2-75
21.53 4.5 ; 5764
•4378
-544 1
•9375
2.5 , 1.875
10
2.875
2352 ; 4-75 64.24
•5
.711
I
2.84 2
11.38
3
2553 5
71.16
.5625
.899
1.125
3.6 1 2.125
12.87 j: 3-25
30.05 5.25
78.4^
.625
I.H
1.25
4.46 , 2.25
14.43 1 3-5
34-86 5.5
86.11
.6875
1.34
1-375
5-36
2.375
16.06
. 3-75
40.01
6
102.45
Owing to its great strength and non-corrosive properties the rods are ex-
tensively used for bolts, forgings, etc., Marine and Naval Machinery, Sugar-
houses, Breweries, Pump Fiston-Rods, and Yacht Shafting. The plates are
used for Pump Linings, Condenser Heads, Hulls of Yachts, Centreboards,
and Rudders.
Drop Forgings and Nails of every description can be made of it.
Weiglits of* Steam-euBiiieei and Boilers 'with Water.
Per Tndicaied H» in Lbs.
\f erch^t Steamer 480
Royal Navy " 360
Steamboats 280
4 1*
Tor|)o«!o Boats 60
Marine Boilers 196
Jx>comotive '* 60
930
APPBNI>IZ.
"Weislit and Strengrtl^
DidUneioD* of Link.
of Ord.i11.ar3r
Cable.
Stud-Ljiuk Cliain
Diam.
Int.
375
4375
5
5625
625
6875
75
875
z
1. 125
25
Lenfi^h.
IBS.
2.25
2.625
3
3-375
3-75
4- "5
4-5
5-25
6
6-75
7-5
Widtlu
Int.
x-35
IT
2.095
2.35
2-475
2.7
315
3.6
405
4-5
Weight
Fftthom.
Admiralty
Proof*
•treu.*
Lb«.
Lb«.
7-55
"•3
»3-4
7840
10080
17.2
2<
12320
15680
25.4
30.2
19 040
22680
41. 2
30800
84
40320
50960
63000
DimensioMj of Link.
DluD. Length. Width.
In*.
1-375
«-5
1.635
1.75
1-875
2
2.125
2.25
2-375
2.5
275
Ins.
8.25
9
9 75
10.5
11.25
13
»a-75
'3-5
14-25
»5
16.5
Ins.
4-95
5-4
585
6.3
6.75
7.65
8.1
8.55
9
9.9
Weight
Admlralff
per
P»«o*.
Fathom.
stress.*
Lbs.
Lbiu
101.6
76160
I3t
90720
143
96400
164.6
«S!4 330
189
141 680
2x5
161 280
343.8
182000
376.3
204 1 20
303-2
227360
336
252000
1 406.6
304940
* Adopted by Lloyds.
Note i.—Safe Working- stress is taken at half the Proof-stresaL
2 Proof-stress and Sc^ Working-stress fur close-link cbains aiv respect irely
two-thirds of those of stud-link chains.
3. — Average Proof-stress is 72 per cent, of altimate strength, or 17000 lb& per sq.
inch of section of both sides. Safe working-stress is half the proof-stress, or 8500
lbs. per sq. inch of section.
Weight of ckwe-link chain Is abont three times the weight of the bar fhMn wblcta
it is made, for equal lengths.
4. — UUinuiU Strength per sq. inch of section of metal is 35 000 lbs.
Comparing the weight, cost, and strength of the three materials, hemp, iron wire,
and chain iron, the proportion between the cost of hemp rope, wire ro|)e, and chain
is as 2 : X : 3; and, therefore, for equal resistances, wire rope is only half the cost
of hemp rope, and a third of the cost of chains. (Karl Ton Ott)
it
It
n
II
tl
Keifflxt and rtetrooession oT I^iagara ITalls.
1842. Height — American 167 feet
Horseshoe.... 158
Width. — American 600
Horseshoe 1800
1875. Receded. — American 60
Horseshoe 160
1886.— Average retrocession 3.5 feet per annum {Woodward).
200 feet in IX years, and 9 feet per year io 43 years.
Descent of the river below 15 feet per mile.
Sridice.— Over Oxus on Caspian sea, 6230 feet in lengths
{J. PoMman.)
J(U.HaU.
Lake Survey.
Coarse.
LENGTHS
Miles.
OP
NBWMARKST.
.4eroB8 the Flat
Beacon ».»..
Cambridge(Ain. . . . .
Cesarewltch
Round
Rowley Mile
Summer Course . . . .
Two-year old, new . .
yearling
1.292
4.206
1.136
3.366
3-579
X.009
3
.703
.377
ENGLISH
Coarse.
RACE-COURSES.
DONCASTBR.
Chrular
FNswilliiim
KtAUoimb,.,.
St Leger4«
Cup Course
SP80X.
Craven
Derby and Oaks. . « .
Metropolitan.
Miles.
'•9«5
X
.711
3.634
1.35
3.35
Coarse.
OOODWOOD.
Cnp Course ....
UVKRFOOL.
New Course. . . .
Newcastle...
OXVORD.
touk.
Stakes OoursA. .
Two-mils
MUes
2.5
«-5
X.796
a
M-75
x.9a3
Rail'wasr Speed in ICngland.
Mj.^Korfk Western BaiUoajf. To Crewe, 158.5 miles in X78 minutes witboot
a stop.
Caledonian. Carlisle to Edinbufgh, xoo. 75 miles, including 10 consecutive
miles of elevation of x in 80, tn 104 minatea
APFBJSfDOL,
931
2 •
OQ
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9
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g
0)
0 « ^
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m
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9
i
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^tftm co^ fOfO ro^ M^ focn co* coco fO
M aOK ChC.
'♦^
• • • • •
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♦ CO* com
tff*
1*1
^ Q O
-o ■♦ >n
io</> m o mo
m >/) tn m
ON m «
mo
N m
O O
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o
m
M
m m « mo m
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m «n
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MOM
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omro oojn-^mNOOk^NO cono
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iSm^- *'>■* «■«♦• mm cO'«- ro'* ro'^ «o<o rofo f^-*- ro-^
J!
3
p S. I £'so vovot^ooOkOtO 6 6 Oci M« wmwmmmmo
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m m
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>l 6 6 «« «| ml ml
M M M
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932
APPBNDIX.
^iaeara River I*o"w©r.
The caual through which the water is to be drawn commenceB at a distance of
1.5 miles above the Fays. The water-storage of the river is computed at 328855
square miles, viz. , 87 620 of lake and 241 235 of shed. The annual rainfall being 37
Inchea
Assuming the rainfall to be but 30 inches, the flow over the Falls would be 213 cop
cube feet per second. The I^ake survey computes it at 265000 cube feet
The H' designed to be used by the company constructing the canal is 12000a
A late and corrected determination of levels gives Lake Ontario 246 and Lake Erie
578 feet above mean tide at oity of New York.
Keiglit of rro-^vers. Spires, etc.
(Additional to page i8a)
Eiffel Tower, Paris 984.3 feeL I Cathedral, Strasburg. 465 feet
Cathedral, Kouen 492 ' ' | City Hall, Philadelphia. 535
it
Zenitlx and Aleridiau Distance and. iA.ltitude of Sixxi
at New York. C. H. (Lot 40° 42' 44".)
Jun« 2iBt, Zenith distance. . . ij^ 15' 44"
Meridian altitude. 72^ aa 16"
Dec. 2ist, Zenith distance. .. 64° 9' 44"
Meridian altitude . 25° 50' 16"
Water-puTXip.— -First in use 283 years B.C. Rotating introdaced iu zytli
century. Plunger pistons invented by Morland (England), 1674. ' DmUtle cu:Hng by
De la Hire (France).
SsTxabolic XJatching and IDesigxiatioiis.
As adopted by Engineer DqMirtmeatf U. S. Natry.
Cast Ibon. Wrought iboit.' Cast Stibl. Wrought Stskl. Brass.
Copper.
Lead.
V///////y
Briok.
Glass.
WiRS.
Stonb.
Earth.
Wood.
Lbathkr.
VCLCANITR.
riie following are designed and added "by the i^utlior.
\i
"it
1 jf
rf'
M||
<^i
IJli
ill
Babbitt. Niokbl. Goil
See Colors for Drawings, p. xo&
'mi^
tilnt
Znro.
C09CRBTB.
iSPBSDlX.
933
FtesuXts of Sxperixxieixts on Operation of* Steaxn-
JEGnsine. {C. E. Emery ^ M. E.)
Condenring.
CyliDdcr i6 X 42 ins.
Pressure 81.69 lb&
" meaD effective. 31.06 "
RevolutioDR per min. . . 60.3
Non-Coodensinj;.
x8 X 42 iOB.
73-37 lbs.
29.47
736
CondeDsing.
Cutoff. 189
H» 78.79
Friction H* 10.09
Net IP.... 68. 7
Wliterper IH* per hour in lbs , ..•..as.30
Coal " " " " , 3,8a
Coal per net IP per hour in lbs. ,, 3.23
Relative efficiency per steam ', i
Relative efflsiency per coal i
Safety Valves of Steaxu-Boilers.
Non-
Condensing.
.189
"S-43
13.07
102. 36
29.231
3.25
3.66
.8685
.8676
Boilers operated at a low pressure of steam require proportionately larger safety
/alves than when operated at a high pressure. Thus: If* steam at 20 lbs. pressure
per sq. inch is raised to 30 lbs., a valve nearly one half more capacity is required;
but if raised from 100 lbs. to no lbs., a valve of nearly one tenth more capacity is
required.
Belting. Double belts will transmit one' and one half times the power of
single.
Wide belts are less effective per unit of area than narrow. Long belts are more
effective than short. Driving belts may be driven at a velocity of 3500 feet per min-
uta Lathe belts from 1500 to 2000 feet. Economy of wear requires less velocitiea
N"on.-Coiiductors of Temperature*
Th.eir Comparative ISfflciezicjr.
MaUriait in Italic* are whoUy free from Carbonization or Ignition from slow car^
tact with Bailert or Steam-pipes.
Th.e folloiving A<laterials -veere used, aa Covering to a
Steam-pipe ii Ins. in Diameter.
Pounds of Water Healed xo^' per Hour through One Square Foot of the Material.
{J. M. Ordway.)
Material i Inch in Thickness.
1. Wool, loose
2. Feathers of live geese . .
3. Lamp Mackj loose
4. Felt of hair.
5. Ootton wool, carded . . .
6. Lamp black.compressed
7. Charcoal of cork ,
8. Hagnesia, calcined)
and loose )
9. Magnesia, carbonate)
of, and light }
to. Charcoal of white pine.
XI. Magnesia, carbonate)
of, and compressed |
12. Plaster of Paris
Lbs.
ReIatiT0
Solidity.
8.x
9.6
9.8
10.3
.56
X.85
X0.4
.2
X0.6
3-44
XX. 9
•53
X2.4
.23
»3-7
.6
'3-9
i.i9
15.4
i-S
30.9
3.68
Material x Inch in Tbickneas.
13
14
15
16
17
Anthracite coalpow- )
der }
Magnesia, calcined )
and compressed . . )
Air alooe
Asbestos, One
Sand
18. Stag wool, best (fine |
threads of brittle glass) j
19. Paper
2a Rice-chaff
21. Bit. coal-ashes, loose. .
22. Asbestos paper, tight.
23. Anth. coal-ashes, loose
24. Clay and veg'ble fibre.
Lbs.
RelatiTV
Solidity.
35.7
5.06
42.6
2.85
48
62.x
.81
5.27
13
—
14
18.7
z
21
—
2X.7
—
27
30.9
.^
irio-w of Several Rivers. AUnlmn-am Dry Weather.
In Cube Feet per Minute.
SL I/iwrence, at BrockvH'e, Ont, 18000000.
Ifississippi, at St. Pauls^ Minn. . . . 200000a
Connecticut, at Holyoke, Mass.. . . 300 000.
Jkio, at Pittsburgh, Penn. 100 000.
Illinois, at La Salle, IlL
Seine, at Paris, France looooa
Mohawk, at Cohoes, N. Y 58 80a
Thames, at London, England. . 36000
Chicago, at Chicago, IIL 36000
... 36 000.
954
AtPBNDir.
Standard TJ. S. AVelglits and Measures.
[V. S. Coast Survey.)
Xiixieetl.
Inch to
Mtllimetres.
Foot to
Metre.
Yard to
Metro.
Mile to
Kilometres.
25-4
.304801
•9»44
1.60935
Metre to
inches.
Mftre to
Foot.
Metre to
Yards.
Kilomotrs
to Miles.
39-37
3.28083
X.093611
.621 37
Chain = 20.1169 metres. Fathom = x.829 metre& Sa- mile = 259 hectare&
Knot = 1853.27 metrea
Square.
Inches to
Ceutimetre.
6.452
Feet to
Decimetre.
9.29
Y«rito
Metre.
.836
Acre to
Hectare.
,4047
Centimotr*
to Inch.
155
MetMto
Feet.
JO. 764
Metre to
Yards.
Z.196
Hectare
to Aci-ea.
3.47*
Pram to
MHII-
litres.*
3-7
Volume. (Fluid.)
Ounce to
Milli.
litres.
Qaartto
Litre.
Gallon to
Litres.
Milli-
litre t to
Dram.
Millililre
to Oance
Litres
to
Qnarts.
Decm-
lilre to
GaUons.
29.57
.94636
378544
.27
.338
1.0567
2.6417
Hecto-
litre to
Baabcls.
2.8375
Inch to
Centimetres.
Foot to
M^re.
16.38/ I .02832
Yard to
Metre.
.765
Cube.
Bushel to
Hectoliter.
•35242
Centimetre
to tnch.
.o6z
DecioMtr«
to Indhes.
61.023
Meti«to
F%«t.
35.3»4
Metre to
Yards.
1.308
Weight.
Grain to
Milligrams.
At. OnnoB
to Grains.
64.7989 I a8.3495
At. Pound to
Kilogram.
•453 59
Tr, Ounce
to Grains.
31.10348
MilliKnun
to Grain.
.01543
Kilocrram
to Grains.
15432.36
Hectofcramt I Kilogram
to At. Ounces, to Pounds
3 5274
2.20462
Quintal lo Av. Pounds, 220.46. Tonnes 8 to Av. Pounds, 2204.6. Grams to Tr.
Ounce, .032 15. Av. Pound = 453.592 427 7 grams. Kilogram = 15 432.35639 grain&
NoTB.— The U. S. yard is equal to the British yard. British gallon = 4. 543 4^
litres. Bushel = 36.3477 litres.
"Value of the Aletre in terms of the British Imperial Yard, and of the
Committee Metre (CM.) of the U. S. Coast and Geodetic Survey. (O. HATtUman.)
Authority.
Hassler »• . 39 . 380 91 7
Kater 370 79
Bailey 369 678
Clarke 3704^2
Comstock 369 85
Value.
39-36994
39-3699
39 369 73
39-3697
39.36984
Dead Hea and Valley of the Jordan.
1300 feet below the level of the sea. {B- E. Peary^ )
Mean.... 39.3698
Portions of these are
"Value of O-old. From 1501 to 1889 ihe ratio of gold and silver varied
from 1 1. 1 to 22.
Durability of "\Vood8. Wood columns or posts, set in earth opposite
to course of its growth, are more durable than when set with it.
* Cube centimetres.
t Cube centilitre.
X 100 Grams.
S HUlien.
APPENDIX.
935
Misoellaneous Oper^.tioiis.
To Remove Paint. Apply chloroform.
To Restore Color of a Fabric When destroyed by an acid ap-
ply ammonia to neutralize it, and then chloroform.
■ Sllver-ware. Warm, and cover with a mild solution of collodion in
alcohol, applying it with a soft brush.
Grilt Franaes. To restore, rub with a sponge moistened with spirits of
turpentine.
Ggg Stain. On, silver, rub with salt.
Iron. RnBt* To remove from white fabrics, saturate the spots with
lemon-juice and salt, and expose to the sun.
Ink Stains. Wash with pure fresh water, and apply oxalic acid, If this
changes the stain to a red color, apply ammonia.
Clinlcers on Brick. Apply oyster shells on the top of a clear Are.
Antidotes ft>r Poisons.
Additumaito paQ€ 185.
AfiUmomal Wint or Tartar Emetic. — Warm water to induce vomiting.
Arsenic or Fotoler^s Solution. — Emetic of mustard and salt, a tablcspoonfVU.
Then, butter, sweetoil, or milk.
Bed Bug. — Oil of vitriol, corrosive sublimate, sugar of lead.
Caustic Soda or Potash, and Volatile ii/A;a{i.— Drink flreely of lemon -Juice or
vinegar in water.
Carbolic ^ctU— Floor and water, and glutinous drinks.
Carbonate of Soda, Copperas, or CchaU, — Administer emetic; soap or mucilagi-
nous drinka
Chloroform.— kppXy cold water to bead and fbce, artificial respiration, and gal-
vanic battery.
Laudanum, Morphine, or Opium. — Administer strong coffee, mustard flour, butter
or oils in warm water, and exercise.
Muriatic or Oxalic Acid. — Give magnesia mixed, and soap dissolved with flresh
water.
NUrite of Silver.— Salt in water.
Sulphate of Zinc or Aed Precipitate.— G\yt milk or white of eggs OOplomsly.
Sulptturic Acid.—Aqwi fortia
Strychnine.— Kmetie of mustard or sulphate of zinc, aided by warm water.
Miotive Po\ver of tlie ^World,
Steaxn-engines. In Horu-Pavoer.
United State*. ... 7 500 000 I Germany 4 500000 I Austria 1 500000
England 7000000 | France. 3000000 | Other countries. Z9000000
Steam-boilers in Foreign, Countries.
France, including Locomotive. . 51 390 | Germany .... 60700 | Austria 19000
I^oooznotives in IToreisn Countries.
France 7000 | Germany. . . xoooo | Austria. . . . 2800 | Other countries. . . 85 200
The steam-engines of the world represent the power or work of 1 000000000 men.
{Bureau of Statistics^ Berlin, 1887.)
Destructive Stress of Beltingf. {Horace B. Cfdle.)
In Lbs. per 8q. Inch.
MuMrtol.
Mul-
mam.
MbUman.
Exten-
siM.*
Materia.
Mail-
mnB.
Minim nm.
Exton-
■Ion.*
Hest leather.
Rawhide —
Llw.
8000
6750
Lbt.
3850
3000
Ineh.
.018
.18
Robber
Cotton belt'g
Lba.
3886
«9>3
Lb*.
3000
9000
Inch.
.059
.OSf
• At 400 1^ ptr 19. Inch*
93^ APPENDIX
Xjargest CoTistruotioxis axid !N"atural Formations*
New Opera-House, Paris. — Covers 3 acres, and has a volume of 4 387000 feet
Popocatapetl^ Highest active V(Acano^ Mexico.— Has a crater one mile in diametei
and 1000 feet in depth. (See p. 182.)
Telegraph Wire over river Kistnah, India. — <6ooo feet in length and xooo feet in
elevation. (See p. 179.)
Chinese Wall, Built 220 B.C. (See p. 179.)
Lambert Coal Mine, Belgium. — 3490 feet in depth.
Mammoth Cave, Kentucky — Some of its chambers are traversed by navigable
branches of the subterranean river Echo.
St. Oothard Tunnel.— It8 summit is 900 feet below the surface at Andermatt, and
6600 feet below the peak of Kastlehorn. (See p. 179.)
Bibliothique NaJtionale, Paris. — Founded by liouis XIV., contains 1400000 vol-
umes, 300000 pamphlets, 175000 MSS., 300000 maps and charts, and 150000 coins
and medals. Engravings x 300000, contained in 1000 volumes, and looooo portraits.
Desert of Sahara, Africa. — Length 3000 miles, average breadth 900 miles, and
area 2 000 000 sq. miles.
Pyramid of Cheops, Egypt.— Volume of masonry 89038000 cube feet; weight of
stone computed at 6 316000 tons. (See p. 174.)
Bell, Moscow. — Circumference at base 68 feet, height 31 feet. (See p. xSi.)
Bridges.* RicUlo, Venice. — A single arch of marble, 98.5 feet in length.
Clifton Suspension, Bristol, Eng. — Span 703 feet, elevation 245 feet.
Niagara Suspension, XJ. S. — Cantilevers, of steel, length 8x0 feeL Elevation above
the rapids 245 feet.
Britanma, England. — 1512 feet in length, and elevation 103 feet
Forth, Frith of Forth, Scotland.— Length 8098.5 feet, exclusive of approaches of
5349.5 leet. Two Cantilever spans of 17x0 feet each. Piers 360 feet above water.
Roadway 150 feet in the clear above water. Iron and steel 54000 tons. Masonry
350040 tons.
Toy, Scotland. — Length 3 miles, 85 piers, and elevation 77 feet
Coluxnxia or Pillars.
When a column or pillar is without its vertical line; one with slightly rcNiiided
ends becomes capable of greater resistance than one with square end&
Experiments at the U. S. Arsenal at Watertown, Mass.. devel0|)ed that the ver-
tical resistance of timber, to transverse compression or crushing, was about one
third of its resistance to longitudinal compression, and hence, that the area of the cap
or the head of a timber column, should proportionately exceed that of the column.
Steaxn-engrine JN'otes.
Horse -poioer,f Nominal.— -la usually computed flrom the volume of steam dis-
charged ffom the cylinder. Its measure for an ordinary non-condensing engine is
about .4 of its actual power. It refers more to the dimensions of an engine than
its capacity.
Indicated. —Is the measure of the force exerted by an engine, and fh>m this ia to
be deducted fur leaks, friction of its partd, and of its connecting parts, about 10 per
cent.
Feed fTa^er.— Ordinarily 2 to 3.5 gallons or 17 to 30 lbs. of water are required for
each IH*.
Fuel.— the ordinary consumption of fliel may be taken at 3 lbs. per IIP for a
non- condensing engine, and 2 llis. for a condensing.
Boilers. — 13 to 15 sq. feet of heating surface, or .4 to .5 of grate surfkce, with
natural draught, will give one IH*.
Flow of Steam. — ^The velocity of it In feet per second, may be determined by the
formula, 60V 1' + 460° = V; or, 60 times the square root of the sum of the tem-
perature of it in degrees, and 460. ThQs for a pressure of xoo lbs. per sq. inch a*
velocity of 900 feet may be obtained. (John Bichards^ PhiUi. )
* AdcUtioDftl to page z8z. t See •Im pp. 733, 734.
APPENDIX. 937
i^tlantio and f>aolfio Oceans. There is not uty difference in tbe
mean levels of these Oceans at Aspinwall and Panama, as determined by Geo. IL
Totten, who constracted the Panama Railroad.
Origin and IPeriod of* GJ-reat Inventions.
See also C/iranoloffif, pp. 71, 72, 9x5.
Air-engine. — ^Amonton, 1699. Stirling, 1827. Ericsson, 1855.
Air-pump. — Otto Gaeriche, x65a Anemometer. — ^Walflus, 1709.
BaUoon.—FiT8ty Lyons, France, 1783. Barometer,* — ^Torricella, 1643.
Battery. — Electric, 1745; claimed by Kleist, Cunaeus, and Muschenbroch.
Bridges (Suspension) Of chains, China,.ioo R G.
Bayonets. — At Bayonne, 1670. Socket bayonet, 1699.
BeUs. — In Christian church, 400; in France, 550. BeUows. — Egypt, 1490 B.G.
Bessemer SteeL — Sir Heniy Bessemer, 1856. Blankets.*— England^ 1340.
jB2cu<in^.— Germany, 1620. Bullets.— Of stone, 1418 ; of iron, 155a
Calio) Printing. — Egypt; introduced in England 1696.
Camera Otfscura. — Roger Bacon, 1214; Newton, 1700; Dagoerre, 1839.
Candles. — Of tallow, x29a Cannon. — x 118; England, 1521. .
Carriages. — Vienna, 15x5; England, 1580.
Clocks.*— 'To strike, by Arabians, 800; by Italians, 120a
Coin.* — 1x84 B.C. ; China, x2oo B.C. ; Rome, 576; England, xzoi.
ComjMut.*— China, 2634 B.C. Cotton G'iVj.— Whitney, 1793.
Dyeing. — 1490 B.G. Prussian Blue, Berlin, 17x0.
/dynamite.— Sobrero, 1846; Nobel, 1867.
Electric Discoveries.*— hejden Jar, Cunseas, X746 ; Electric Light, Davy, xSoo;
fii'st patent of it, Greene & Staite, X846.
Electro-Magnetism. — Oersted, Copenhagen, X819.
Electrotyping. — Jacob! of Russia and Spencer of England, 1837.
Engraving.— Ch\nsLj xooo B.C. ; on metal, 1423; line or steel, 1450; etching, X5i2.
&CW.— Murdock Cornwall, X792; Meter, Clegg, 1807; Dry meter, Malam, x82a
Glass.*— Egypi^ X740 B.C. Windows, France, 12th century.
Gold Leaf. — Egypt, X700 B.C. Gunprnader. — Unknown; rediscovered 1324.
Horseshoes. — 300; of iron, 480.
Hydraulic fV«ss.^~Bramah, X796. Hydraulic Bam. — Whitehurst, 1772.
Hydrogen.— iBol&ied by Cavendish, 1766. Iron Vessels.-— J. Wilkinson, England,
1787; Ship, x82x; Steam-boat, 1830; Ship building, 1833.
Kaleidoscope.— Sir Daniel Brewster, 1814-17. iTntties.— Table, England, 155a
LifS'boaL— 1817. Litfiography.—Senefelder^ about X796.
Locomotive. — Watt, X769 and X784. Ciignot, 1769.
Matches. — Friction, 1829. Medicine.— From Greece, in Rome 200 B. G.
if trrorf. --Glass, Venice, X3th century. Newspaper. — First authentic, X494.
Omnibus. — Paris, X827.
Organs. — 755. England, 95X. Oajy^^en.— Priestley, 1774.
Paper.— From silk, China, 130. B.C.; flrom rags, Egypt^ 1085.
/%n«.— Of steel, 1803; gold, X825. /%»Jd7».— Of lead, 50. England, X565.
Pianoforte.— \\a\j^ X7fa Phonograph.— F,d\win, 1877.
photograph.— F,ufgL^rxd^ 1802; perfected, x84i. R>tt«!fy.— Oldest, Egypt, 2000 B. 01
PoH-Ojg^ — ^Vienna and Brussels, 1516. Stantp«. ^England, x84a
Printing.*— Tjpe&y K Comer, 1423.
Jiailroad.*— Passenger, England, Sept 27, 1825.
/S^eunn^-mocAw.— Patented, England, X755.
aUeping-car. — x 858 ; Pullman, X864. Soap. —England, 16th centaiy.
(S;pec<ac/e».— Italy, xsth century.
Telephone. — A. G. Bell and G. J. Blake, Boston, 1874.
Torpedo.— Ct^M^ to D. Bushnell, 1777.
jjtt 111 J - I ■■ wiiw
4K
938 ' APPENDIX.
Valued of* soxxxe Preoious MetaJs.
Per Ptmnd Troy.
%
Cobalt 9 JO
Gold ,. 250
Iridium 295
Osmiam S 590 Rhodium S41S
Platinum 102 Ruthenium 975
Potassium.... 25fi9iJvcr* 12
K-xpenditnre in. Kngland for Various Purposes aud of
Articles Compared witli tliat of Spirituous Liciiiors-
In MiUUms of Pound Sterling.
Missions i
Rducation xi
Fuel for Households. . 15
Linen anil Cotton 20
Tea, Coffee, etc 20
Sugar 25
Milk..... 30
Butter and Cheese. ... 35
Woollen Goods 46
BwaA 70
Rents. 130
liquors. Z36
AlunairLuin.
Elastic limit of bars in tension 14000 lbs. per sq. inch. Specific heat .2185. Melt
at 1400°. Malleable at from 200*^ to 300°.
Tensile strength, nUfmate, 26000 Iw. Modulns of elasticity, 12000000.
Shrinkage .022 per^ linear foot. It is comparatively unaffected by ezpostire to
air or water. Cuoe inch weighs .0926 lb. h cube foot weighs 160.013 Ibe.
KCtmtinued on pag6 976.)
Busliels of Seed Kequired per Acre.
In B%t9hel8 per Acre.
Flax 5 to 2
Grass, blue. . .695 " .875
orchard. 1.5 ''2.25
Barley 1.5 to 2.5
Beaiu9 1
Buckwheat 75 ''
Carrots 75 '*
Clover, red 16 "
" white.. .16"
Com, brown . . 1 **
Indian... .25
it
«t
3
1.5
1.5
•33
•?3
1.5
X
Ik
'' Herds'..
" Timothy
Hemp z
Millet I
Mustard 25
375'* .5
" .625
Oats
Parsnips. .
Pe«6e
Potatoes. .
Rice
Rye
Turnips...
Wheat. . . .
2
to
4
•5
kk
.'/
2.5
ik
3-5
5
xo
2
ti
2-S
Z
11
2
.06
u
.16
».s
k«
a
See also n«« t*8u
Domestic Rexiiedials.
CWor*.— Discharged by an acid, can be restored by Ammonia.
i^/t««. -CarlioMc Acid (20 drops), evaporated on a hot surface, as a shoye), will
drive them from a room.
Ink— To remove stains from a white fabric, wet with Milk and cover with Salt
Mildew stains.— 'M.&y be discharged by Buttermilk.
Jfwg'Mito.— Camphor (ium, vaporized over the chimney of a gas-burner 01
lamp, will drive them from a room.
Bati.— To drive them off, apply Chloride of Lime to their locality.
Sewer Gas.— The noxious effects removed by Chloride of Lime.
Snnstroke. Remove patient to a cod place, administer water Arerty, and
Quinine or Salleate of Soda.
Comparative "Valnes of Food for SHeep.
Wool and TaUow Produced.
Food. Wool. Tallow. Fooo. P Woo). Tallow.
Wheat X
Oats 04
Barley 89
Pease 88
Rye, with salt 87
Wool.
Tallow.
LlM.
Lbt.
■97
•99
•7«
•7
.78
1
X
.7
•97
.58 u
Gern-fneal, weti 83
BackwlMat «... .70
Rye, witboui salt .... .58
Potatoes, witli salt... .3
'< withoiU salt. .38
•93
•7
•97
•45
•45
Lb«.
.29
•55
•7«
.a
.19
APPENDIX. 939
Oroton i\.quedxiGt. New Torky 189a
X>ixnen8ion8, Xjengtli, and Capaoit^r.
Tunnel proper..... =9.63 miles} „ ,^ ,^^
Aqueduct m open trench 1.12 " j i"- /^ »«"«'» «« wur*.!.
Pipes to Central Pftrk reservoir, 3.37 miles in length.
Tunnel ander Harlem river, 307 feet below tide-water level.
Course— Vxom Crolon Lake, 350 feet above the Dam, and runs generally Southerly
through Westchester Co. and the 24th Ward of New York, to a point 7000 feet K. of
Jerome Park, with a uniform inclination of .7 fbet per mile; its general form, that
of a hdrse-sboe with curved invert ; being 13.3^ feet in height and 13.6 feet in
width ; having a computed capacity of 318 millions of gallons per day. From
thence, where it is contemplated to construct a large reservoir, for the supply of
the annexed districts of the city, to its termination at 135th Street and loth Avenue,
its capacity is reduced to 250 millions of gallons per day. and the Aqueduct which
tcova there is to be operated unddr pressure, is circular in its section, 12.3 feet fn
diameter, with varyiug inclinations, the portion under the Harlem river being
10.5 feet
From 135th Street it is connected to x2 cast-iron pipes, 48 in& in diameter, 4 of
which connect with the old Aqueduct, 4 with the present City distribution, and 4
leading through Convent, (gtb) and 8th Avenues to the Reservoir in Central Park.
The operating capacity of all being equal to that of the Aqueduct, 250 millions of
gallons.
The Aqueduct is for the greater portion of its length a tunnel, it raising to the
surface but at four points, fVom which it can be emptied through gates into the
adjacent rivera
Copoctfy.— The watershed ef the Croton, in extreme dry weather, with storage,
is 250 million gallons per day.
The present storage system includes Croton lake. Reservoir at Boyd's Comers,
the middle brunch Reservoir of the Croton valley, and several lakes, with a total
capacity of 10 000 million gallons: three dams being in progress of construction and
others contemplated, viz., one at Carmel and one at Quaker Bridge.
The Capacity of the Reservoir in Central Park is computed at 1000 million gallons.
loe.
Additional top. 195.
X.5 in& thick will support a man; 5 Ins., an 84-lbB. cannon; xo Ins., a body of
men; tS ina, a railroad train.
Rape 55
Almond, sweet 47
»' bitter 37
Turnip 45
Additional to pace 189.
Yield of* Oil in Seeds.
Percent
Mustard, white 37
Hemp 19
Linseed 17
tCom, Indian 7
Oats 6.5
Clover-hay 5
Flour- wheat 3
Barley 3.5
Historioal XCventa and Rotable F'aot*.
.^tMtro/ia.— Discovered x6a3.
Amano.^ Produce per acre 44 times greater than potato, and 131 times greater
tlian wheat
Camelf.— Some can travel 800 miles in 8 daya
CcKocoNidic.— Of Rome, remains of 6000000 bodiea
Cfttna.'-Aathentic history of it, 3000 B.C. Crucifixion,— yj.
Library of Alexandria — 47 B. C. contained 400000 books.
Peru. — Steel, consumption 4000000 per day.
<8Za«ery.— Abolished in Eng. West Indies, 1834; Russia, 1861.
N*. Uatitude reaolied \iy Sxplorers. 1884.— AdoIpbuB W. Qreelj,
U. 9- Army. %z^ 94'. The 4isUnce ttom this (0 the Pole is 4^6 oa mileg.
940
APPENDIX.
Roolc I>ril line.
Band DrUt Co.. New York.
Drill*.
No.
Kid
I
3 and 2 A
3 and 3 A....
3.25 and 3. 25 A
4 uiid 4 A
5
7
Cylinder.
DUin.
Usual
D«pth
Drilled.
Ins.
Feet.
1-875
1.5
2.85'
3.75
6 to ro
3- "5
iotoi5
335
3.625
15
20
4-5
20 to 30
5.5
Dlam
Deoth
of 1 Drilled
Diam.
Dlam.
steam
St«am
Bottom 1 in 10
of Hole.t Hours.
of
Hose.
of
Steel.
Boiler.
npe.
Ida. 1 p0et
Ins.
Ins.
IP
Ina
I : .•• .
.75
.625
3
•75
t.0695
50
•75
•75
5
I
IS
60
•75
I
7
1.25
1.75
70
z
1. 125
10
>-5
1-75
70
I
1. 185 to 1.25
10
i-S
3
70
X.25
1.375
12
2
2.35
70
1.5
1.5
15
2
[ • • • •
"•5
175
20 to 23
2.5
Capacity in
Free Air
per Minute.
Cube Feet.
670
1196
1562
1650
1920
2242
2395
2520
2897
3128
3960
4icx>
4530
5000
6000
6B20
Ptand A.ir Compressors,
RandrCwlUs Class "^J?,/'
Compound Steam Condensing. Compound Air.
StCHm Pressure 135 lbs.
Stroke.
Cylinder Diameters.
1
Steam.
Air. 1
Hl<fb.
ill
Hiffh.
Low.
Ins.
Ins.
Ins.
10
18
10.5
»7
12
22
»3
21
M
26
15
24
"4
26
»5
24
16
30
»7.5
28
16
30
»7S
28
16
30
17-5
28
18
34
20
32
18
34
20
32
18
34
20
32
20
3«
22.5
36
22
40
24
38
22
42
25
40
84
44
26.5
42
26
48
29
46
88
52
30
48
Ins.
30
36
36
42
36
42
48
36
42
48
48
48
48
48
48
48
Rand *' Impei-ialf'* Type X.
Duplex Steam Non- Condensing. Compound Air.
Terminal
Revolutions
Air
M(mit«.
Preasnre
at 80 lbs.
No.
IH>.
8S
102
83
182
83
238
75
252
75
a93
75
342
70
365
75
384
75
442
70
475
70
604
65
625
65
690
55
763
55
915
65
1040
Steam fr<
9ssure t» to 100 Itw.
BUmm
Capacity In
Free Air
Duplex
Diameter of
Revolution*
and Aft
Steam
AirCy
inders.
Stroke.
MHmte.
Pressor*,
per Min.
Cylinders.
Hllfh.
Low.
' at xoo Iba.
Cube Feet.
Ins.
Ina.
Ins.
Ins.
No.
IIP.
145
6
6-5
10
8
200
25
* 245
I
75
12
zo
190
4«
370
8
9
X4
12
175
63
535
zo
zo
x6
14
>65
9«
705
Z3
zz
18
z6
Z50
Z20
1050
14
13
22
z6
150
Z78
Rand
Capacity In
FVeeAIr
per Min.
AirCy
Diam. of
eacb.
Cube Feet.
Ins.
11.7
4
22.7
ll
93
163
5
6
I
xo
275
Z3
pe Ai. iiuj
pfex Atr vytu
utert. iMA i
inders.
Revolution*
Air Pr«*Mnr» p«r Sq. Inch.
Stroke.
per Min.
60 lb*.
100 lb*.
In*.
No.
IH».
IH»..
4
200
»-7
2.3
5
200
3-3
4-5
6
200
5-5
7.5
7
200
9
Z2
8
200
Z3.5
Z&.S
zo
z8o
'4
30
13
X75
40
53
appendix;
941
Pxn
Siaspeiisloxi furnaces— M!orison,
The Continental Iron Works, Brooklyn, N", Y.
Form-ula for Corrugated, yu.rp.aces.
Board of U, S. SupervUing Enffinctri^ October lothy 1891.
=T. P = working pretture in Ibs^ per iq. inch, D mean diameter of fux'
15 600
fiac«=i7mc2« dtameter-|-2, and T thicknest of metal, both in ins.
Corrugated Dot less tfaan 1.5 inctaoB in depth, and flat sarface of ends not exceed*
ing 6 incbes in length.
rFTiiokneHS of ^Cetal iix Suspensioii ITurnaoes fbr dif«
lereiit X>ian:ieterB and. "^Vorking X'resBu.res in. X^bs.
I*«r Sq.. In oil.
As Determined by the Formula in the Rules and ReguJaJtums oftheU.S* Board.
Inside
Diain.
Ini.
A
Ji
t
il
A
H
i
a
A
«
■f
ill
n
i
28
30
162
157
152
178
172
167
195
188
182
211
204
198
227
220
213
243
235
228
260
251
243
236
229
222
216
210
205
200
195
190
185
181
177
173
169
165
162
159
156
152
150
147
144
141
139
276
267
258
292
283
274
26s
258
250
243
237
225
219
214
208
204
199
19s
190
1 86
182
179
175
308
298
289
32s
314
304
341
330
319
310
301
292
284
276
269
262
255
249
243
238
232
357
345
335
325
315
306
297
289
282
275
268
261
255
249
243
390
377
365
31
32
33
34
35
36
147
143
139
135
131
128
162
157
153
148
144
141
177
172
167
162
158
J 53
150
146
142
139
136
132
130
127
124
121
119
117
192
186
181
176
171
166
206
200
195
189
184
179
175
170
166
162
158
155
151
148
14s
142
139
136
221
215
208
203
197
192
187
182
178
174
170
166
251
243
236
230
223
218
212
207
202
197
192
188
280
272
264
257
250
J'ii
237
231
225
220
215
SIC
295
286
278
270
263
256
250
243
237
232
226
221
216
211
207
203
198
195
354
344
334
325
3i6
307
37
38
39
40
41
42
125
121
118
116
"3
no
137
134
130
127
124
121
162
158
154
150
147
144
300
292
28s
278
372
26s
43
44
45
46
47
48
108
los
t03
lOI
99
97
IIQ
116
114
III
109
107
ro5
103
lOI
99
97
95
94
02
90
87
86
140
137
134
132
129
126
162
158
155
X52
149
146
143
140
137
135
132
130
128
126
123
121
119
117
184
180
176
172
169
i6s
162
150
156
153
150
147
20s
201
197
192
189
185
i8i
178
174
171
168
i6s
162
159
156
154
151
149
227
222
217
213
208
204
238
233
228
223
218
214
260
254
248
243
238
234
49
SO
51
52
53
54
95
93
91
90
88
87
85
84
8a
81
70
78
114
112
no
108
106
104
124
f 21
119
ri7
115
ti3
III
109
107
los
103
102
133
131
128
126
124
121
119
117
IIS
113
1 1 1
no
172
168
165
162
159
156
191
187
183
180
177
174
200
196
193
189
186
i8a
179
176
173
I70
167
i6s
210
206
202
198
19s
IQl
229
225
220
216
212
aog
55
56
57
58
59
60
102
100
99
97
95
94
136
134
132
130
127
I2S
145
142
140
138
135
133
153
151
148
146
143
141
171
168
165
162
159
157
-188
184
181
178
175
172
305
201
198
19s
I9X
188
942
APPENDIX.
InfLxience of th.e Rotation of the Kartfa. on lif ovln^
Bodies.
The Rotation of tbo E«rtti on its axis effects on appreciable displaoement of the
rails in a line of railroad.
In the case of an express train weighing 400 tons, running N. at the rate of 5c
miles per honr, the pressure on the right hand or Easleru rail is computed at 501
lbs., and with a steamer, alike to the Inman Line "City of New York," the press-
are is computed at 936 lbs. This lateral force increases to the Polea {T. Von Bavier.%
Bacteria in Kartli-soil.
In Virgin soil ; soli flrom beneath Roadways; from Gardens; a4}acent to Factories
from Courtyards and Cemeteriea
HI
09
Meter*.
I
No.
124800
Depth
below
Surface.
Germa
per Cube
Centi-
meter.*
Meters.
2
No.
ISO
Depth
below
Surfane.
Meters.
I
m% f er
55(51
No.
64300
^^1
Metre*.
a
go B J
No.
590
* .061 o23-cabe Inehee.
The number very rapidly decreases in the deeper layers of the earth, both in
virgin soil and in that which has been poUated. (John Reimtrs.)
w atexvxxieters.
■^ITortHinirton's. Ne-wr York.
Dtam.
ofRe-
eelvin^
Pipe.
Int.
• 625
•75
Vidome
delivered per
Minute.
Cube ft
1-5
3
Galls.
11-25
23.5
Diam.
ofPe-
celTinjf
Pipe.
Ins.
I
Volnme
delivered per
Minute.
Cube ft,
5
6
Galls.
37-5
45
Dism.
of Re-
ceiving
Pipe.
Ims.
2
3
Volume
delivered per
Minute.
Cube ft.
8
Galls.
60
172
Piam.
of Re-
ceivinc
Pipe.
Ins.
4
6
Volume
delivered per
Mlnat«.
Cube ft.
X30
Galls
435
goo
NoTS 1.— The volume of delivery here given, for each meter, can be exceeded.
2.— Extreme velocity of a meter produces incessant and improper resistances;
honce. in order that the instrument may operate only within a perceptible reductioc
of the head of the supply, it should be of a capacity to effect its duty ai a moderate
velocity of operation*
Telescopes,
Galileo^s first telescope magnified but three times; but by the addition of a c<Mt-
cave eye and convex object glass he attained a magnifying power of 30 times.
The construction of large lenses is at present limited by the chromatic aberration,
or separation of light in a telescope.
Euler was the first to discover the principle governing this aberration and the
method of abolishing it.
I^iameters of tlie Principal Ol^ective Q-Ia««es«
United Stales.
Loe«tloo.
Diameter.
Fowl
Length.
Ins.
la
la
12.56
Feet.
15
ao.a
LDcatien.
Rochester
Washington
University, Va...
Lick Observatory.
Diameter.
Ins.
16
26
26
36
Focal
Length*
Fett.
22
32-47»
as
56. t
West Point.
Wesleyan Untveraity . .
Harvard*
ICadifon, Win
University of Sontbem California contemplates the construction of one of 40 intt
The largest telescopes outside the U. S. are. Gates Head, England, 24 ina ; Viani*
Austria, 27 ins. ; Nice, France, 28 ins. ; Pulkowa, Russia, 30 ina
* To have foor leoMi of 34 inchei.
ABPsamx.
943
Manuffecture of loe.
Machinery and Apparatus.
ProdiM-
xion of
Ie« laS4
Hour*,
Toas.
Z
3
5
lO
ia.5
IS
ao
30
40
45
60
80
Stewi-£B(iiie.
Com-
preMon.
Ins. R«T.
Ina.
7X 9
8X16
Z0X20
90
80
75
SXiot
5X15
6X18
12X30
70
8X20
14X30
65
8X25
14X30
65
X0X20
16X30
35
10X30
18X361
20X36
24X36
26X48
50
45
45
12X30
15X30
12X30;
20X36
- ]
Blookfl of loe.
Ins.
BX" 8X28
8X15X28
8X15X28
1X22X281
iXiiX28f
1X22X28 t
1XHX28)
1X22X28 I
iXuXaSf
1X22X28 <
1X11X28)
1X22X28 (
iXnX28t
1X11X28
1X11X28
1X11X28
1X22X28
Water
required
P"
MinuU.
Coal.
Opcntwv
Es«i- Fire-
neers. men.
Ub-
orers.
Oallons.
T's.«
5
•5
2
2
—
15
z
3
2
2
20
1.5
2
2
2
30
2
2
2
3
35
2-5
2
2
3
40
3
2
2
4
50
4
2
2
5
60
5
2
2
6
90
6.5
2
2
7
—
—
2
a
8
—
—
2
a
9
100
13
2
a
zo
ofSnglne
and
ria^t.
Lbs.
20000
58000
69000
lOI OQO
129000
167000
190000
225 000
360000
360000
2000 lbs.
t One oomjinMor. { And one 16x36 ins. additionaL
All others two compressors, and all single acting.
Pressure of Steam.— For all 75 lbs. per pf^uare inch.
Cut-off. — For the three first, which are slide valves, three eighths. For the
others, as Corliss engines, one fifth.
The volumes of ice above given cover that lost in thawing the molds to release it
The coal given as that required is inclusive of that required to distil water from
which to make the ice.
NoTB.—In order that the proper dimensions of engine and plant may be arrived
at for a required volume of ice, it is necessary that the quantity and temperature
of the water supply should be furnished.
2.— The ice is produced fVom water of distillation ; hence, it is clear and trans-
parent.
'\Vh.exi a lk£aolxizi.e is operated. \>y 'Water-po'^ver. As the
water flrom which the ice is made is not distilled from steam, as in the case where
steam is the motive power, the ice produced is less clear or transparent, and is
known as ''white ice.''
Refrifceratingp.
Engines for Reft-igerating are in all respects alike to those for Ice-making, witli
two thirds more capacity. As distilled water is not required in refrigerating, the
saving of fuel in consequence is Ailly thirty per cent. Refrigerating by compression
involves a much less expenditure of water tbnn when it is attained by al>sorption.
Elements of a Test of Operation and Capacity of n
Refrigerating Machine.
i<» Liquid in 24 ConMcutivt Houn^ 78.41 Tons of ^000 Ibe.
Steam-engine.— Non-condensing, 18X36 ins. Compressors 12.375X30 int.
Pressure of Steam^ 86 lbs. Revolutions per minute, 56.5.
niT.—Steamrcy Under, 84.3. Of compressors, 67.78.
Temperature of condensing water, 76.20. of condenser room, 6a.5».
Volume qf condensing water per minute^ 21.19 gallons. Of brine per meUr^
35 670 cube feet » a 496 900 lbs,
^Operating pressure, 25.22 lbs. Condensing pressure, 157.12 lbs.
Anthracite coal, consumed, 6108 lbs. Combustible, 63,6^ per cent.
Coal per lHVper hour, 3.0a Uit Consumption equivalent to the liquefaciior
of (me ton of ice, 77.88 lbs.
944 APPKin)ix.
^splialt and. A^splialt Pavenaexit.
Barber Aiiphalt Paving Co.^ New York.
Rock Asphalt is amorphous limestone impregnated with asphaltum, whereas
Trinidad asphalt pavement is a mixture of sand, pulverized limestone, and asphal-
tic cement. The asphaltic cement is composed of refined Trinidad asphalt, with a
little residuum oil of petroleum, the pavement being an artificial asphaltic sand-
stone.
* In the cities of Europe, where asphalt pavement has been laid, the practice is to
spread trova 1.5 to 2.5 inches of it on a bed of concrete.
The process of preparing the material for use is to crush the rock to powder, heat
it to about 280*^, spread it on the concrete, and then compress it by rammers.
The use of natural asphaltum, found in the United States, as Albertite and
Grahamite, was resorted to, but without success, when the pitch or asphalt lake in
Trinidad, W. I., was discovered; by combining this material with highly refined pe-
troleum, a satisfactory cement was produced, which being mixed with a sharp sili-
cious sund and powdered limestone, a desired sandstone was formed; a compound
possessing the necessary firmness and resistance to the changes of temperature and
durability, under the wear of loaded vehicles, combined with smoothness, cleanli-
ness, and comparative freedom firom noise; without danger from the slipping of
horses' feet, usual with pavements with smooth surface. So evident was the useful
application of this construction, that in 1870 an essay of its merits was made in
Newark and New York, and in 1876 it was nirther essayed on an extended scale in
Washington, its merits being evidenced by a Board of U. S. Engineers. Since which
time it has been laid in over 100 other cities in the U. S. to an extent of about
20,000,000 square yards.
The advantages of such a pavement are the reduction of the resistance to traction,
economy of transportation, and fireedom trom jolting in travel, added to cleanliness
and public health, as it is without seams or joints wherein filth may-be collected.
Its durability in wear is less than granite, and greater than sandstone, wood, or
macadam.
As regards the cost of its maintenance, it is less than that of any other material
maintained in like ccmdition of repair.
Origin and IDevelopment.
The utility of asphalt for covering of a road was not discovered until 1849. As-
phalt rock, broken up, was laid in the manner of a macadamized road, and the re-
sult was such that in 1854 a street in Paris was laid with compressed asphalt on a
foundation bed of concrete.
In 1869 it was first laid in London, and is now extensively laid in the cities of
Europe to an extent in excess of 3,000,000 square yards.
Sultatitutes. — Tar. As a substitute for it ft wa6 essayed to use the Inex-
pensive tar, obtained ft*om gas-works; but as it is deficient in the required cement-
ing qualities, susceptible of being rendered viscid by the heat of summer, and brittle
by the cold of winter, the use of it was abandoned.
Wood. — Wood-pavement is laid in London and Paris on a foundation of concrete,
and it lasts firom 4 to 6 years.
Stone-blocks filled in with asphaltum water- proof filling has been practised with
success. In some of the principal cities of Europe, the uniformity in the dimen-
sions and shape of the blocks contribute tu their durability. The cost of such a
pavement is in excess of all others.
MaMidam. — Macadam pavement is unsuited for cities from the wear of heavy
Tehicles, and the great cost of maintenance.
firtcA;.— Brick, hard burned, laid in two courses on 6 inches of sand, the first
course on its face, and the second on its longitudinal edge, has been used in Holland,
Ohio, and Illinois. The duration of such a pavement depends wholly on the uni-
formity of the material and its burning. In general practice it was found to be
neither enduring nor economical.
GenM Gillmore, U. S. engineer, in his report (1879) submits the fbllowing:
Requisite of a Oood Pavement. —A good pavement must be smooth, and to promote
easy draught must give a firm and safe foothold for animals, and not polish or become
slippery under wear; must be, as nearly as possible, noiseless and fi-ee firom dust or
mud, and made of durable material, laid upon a firm foundation, and be susceptible
of repairs at moderate cost at all seasons of the year.
APPENDIX.
945
Suital}!* Xnoundatiorks Tov Pavements.
A firm and unyielding foundation is quite as necessary for stability and endurance
of a pavement as for any olb^ar structure.
Following are suitable foundations for street-pavements, in order of value, pro-
vided their thickness is adapted to character of subsoil and nature of traflSc, viz. :
X. hydraulic concrete 5 to 8 ins. in thiclcness; 2. rubble-stone set on edge side by side,
but not in close contact, with interstices filled in with hydraulic concrete , 3. an old
coal-tar pavement properly brought to slope and grade; 4. rubble-stone set on edge
and wedged closely in contact like sub- pavement of a Telford road; 5. un old pave-
ment of stone-blocka, cobble, or rubble stone; and 6. an old Macadamized or gravel
road, or a compost layer of broken stone or gravel, 8 or 10 inches thick.
Tb« beet pavements now prominently before the public, classified with respect to
the materials of w^hich they are made, are Asphalt, Stone block, Wooden block, and
Coal-tar pavement& The wooden-block pavement is not entitled to a place in the
list
Stone PavemenU.—The best is formed with rectangular blocks from 3- 5 to 4. 5 ins.
thick. 10 to 13 in length on wearing surface, and 8 to 9 inches deep, set upon febeir
longest edge across the street, upon a foundation of hydraulic concrete.
Ast^uxlt Pavements. — Best asphalt is one having for a foundatiop a bed of hy-
draulic cement, or somethiug equivalent thereto in firmness and durability, and for
its wearing surface either the natural bituminous limestone known as asphalt rock,
derived flrom the Jurassic region on the confines of Switzerland, or, preferable thereto,
an artificially compounded mixture of refined asphaltum and silico-calcareous sand,
in which the calcareous ingredient is finely pulverized limestone. As the material
for first-named pavement comes principally firom vicinity of Neiifchatel, the i>ave-
ment is known as the Neufchatel. Asphaltum for the other pavements referred to
comes firom Iskind of Trinidad, and the pavement is sometimes called the Trinidad
asphalt
Netifchatel pavement— Ba& been extensively laid in L9ndon, Paris, and other Eu-
ropean citiea
Although these two pavements represent the best type of street snrfkce, there is
a efaaracteristic and somewhat important difference between them, due to the fact
that the Trinidad contains nearly 75 per cent of sharp silicious sand, and does
Dot, therefore, become polishe4 and slippery by wear; while the Neufchatel, being
eumposed entirely of bituminous limestone (a species of amorphous pulverulent
chalk, without grit, impregnated with bitumen), is by no means free fVom this fault
i) variety of asphalt pavement adapted to streets of exceptionally steep grade, is one
Sormed with rectangular blocks of compressed asphalt concrete.
Comparative Aferits of* tlxe Several Pavements.
X. Their Firtl CScxf.— In cost of construction, wood is the cheapest; Coal tar com-
position second: Sheet asphalt like the Trinidad third; Stone-blocks fourth, and
Asphalt blocks fifth.
3. Their Durability. — Assuming each of the four pavements named to be the beb.
of its kind, stone and asphalt will {lossess the longest life, and wood and coal-tar
very much the shortest Between the first two and the last two there is a wide gap.
Unless the stone be of good quality, asphalt will take first place and stone second.
3. Cost of Maintenarux. — Order of merit under this head would plare stone and
asphalt first, and wood and coal-tar last If the asphalt is good, woll mixed and
laid, the stone must be both tough and hard in order to maintain the first place.
Relative I-«oa<ls fbr Roadv^ays and Pavements*
At Low Speed. (J. W. Howard, C. E.)
Loads which a Horse can draw on a level, eodi day of 10 hours, onfolUnoing roads.
" ' ' RMiatonce
Roadway.
Asphalt
stone Block
Ordinary Stone Block.
Hard Macadam
Hard Gravel
LtM.
6095
3006
1828
>39»
"79
RMUtance
In Term
of Ix>Rd.
•037
.076
.124
.164
.178
Roadwaj.
Hard Earth
Worn Stone Block
Cobble Stone
Ordinary Earth. . .
Sand
Lbs.
in Term
of Load.
1193
.191
"37
.2
730
338
•31
•5
946
APPBNDIX*
Formuia for Determination of Prettttre per Square Inch of VatUmB
Explosives at DijfercrU Distances.
V ( Id + oir*-'" ) ~ **' ^ representing angle with Vie vertical passing tkr<mgk
Oii& centre of the charge, made by a line drawn from it tn the surface exposed to the
shade, determined from the nadir* in degrees ; E a constant for the explosive, cu de-
termined by experiment ; C weight of the explosive in lbs.; D distance from centre of
the explosive to the surfajce exposed, in feet ; and P the mMn pressure, corresponding
to that which would be transmitted to a disc of copper, by a Rodman indenting-tool,
per square inch of surface exposed to the shock, in lbs. . {Brev. Brig. General H. L.
Abbott, U. S. A., iB8i.)
Value of E, or Relative Strength of Explosives Fired under Water,
EzplotfTe.
Dualin
Dynamite Xo. 1 1
" No. 2 .
Explosive Geldt.
Gun-cottoD
Electric No. i . . .
No. 2 . . .
Hercules No. i . .
" No. 2..
•0
>»
^1
l-o
l\
r^
* s
H
116
* ,
be
232
s
III
108
75
1B6
100
100
100
t
120
75
83
88
259
125
117
"3
'35
8j
27
91
33
67
51
69
77
28
43
38
62
72
77
211
109
106
105
42
118
74
83
87
4
Exploaive.
Nitr©-
lycerin
H
bL
333
Forcite No. 1 . .
Tonite
__
118
Rackarock....
^—
220
Nitre glyc'ne. .
100
III
Reudrock
20
lOI
4t
40
160
i(
60
166
Vulcan No. i. .
30
99
" No. 2..
35
"M
to
Sii
.^'1
0 A
71
Zi
67
78
9'
94
93
95
06
78
72
82
&<8
86
84
^1
3
86
Illustration. — Assorae the distance between the line or the centre of a charge
of dynamite No. i and the bottom of a vessel to be 5 feet, the angle between the line
of centre of the distance and the bottom, measured ftrom the naidir, to be 180*^, the
constant for the chtirge 186, and its weight 100 lbs. What would be the mean
pressure on the object in lb& per sq. inch?
A = 180°, E = 186, C = 100, and D = 5.
3/76636 (i8o -\- 186) ioo\» _ 3//
V V (5-Hoip't I ~\/\
2 428 736 X ioo\ _^
(5-Hoi)''t / V^ V 29.489
* A point of tha globe directly ander oar feet, or that opposite the tenitli.
t Standard of compariaoD.
X For (s + .ox)*- », «ee p. 310. Tha«, ^^
\ =^8 2362x0* = 40 784 ft*.
xo
3t
— X log. 5.0X = 3.1 X .699 837 = Numbtr 39.489
When the Object is not in a Vertical line with the Explosion,
Illustration. —Assume a charge of gun-cotton weighing 882 lbs., set in water, at
a horizontal distance of 24, and a vertical of 86 feet from the object; what would
be the effect?
- X24
To obtain a, or angle of divergence, 180O — Tan. - ^ = 15O 25', and 180® —
86
i/f
150 25' = 1640 35' = 164.58°. D = V24»-f 86a=:89,andE = x35. Hence,
3 /766^6 (164. 58 + 135) 882^ _ p
Log. of 89+ 01 = X. 949 43^
Log. of 89.0X'-' = 4.0938219
(89-f-.oi)a-»
Log. of 6636 =3.821906
" "164.58 + 135 = 2.476513
" " 882 =2.945469
Product
Qootient
= 9.243888
4.093 822
=55.150066
2
a^ioL 300 ijg
Off cnbe root of Quotient = 3.433 378 = Number 2712.5 tbs.BmT.
JkFPBNDIX
947
ICffioienoy of* '^^a.teivTa'be Steam-JB oilers.
In a late test bf J. J. Thorneycroft of his patented boiler, the following elements
and resalts are reported to the Institute of Civil Engineer& See Vol. XCIX., 1889.
Engine.— Triple exparuioHy Cylinders 14, 20, and 31.5, by x6 ina stroke of piston,
and jacketed. Independent engines for Circulating pump, Blower, Donkey, and
Sheering. All exhausting into engine condenser.
rtesiilts or Xrials.
Fuiiiace.
ElemeDto sad Dlmeniloii*.
feet.
}
Natural Dmoght.
1837
61.2
200.8
26.2
1837
70.x
196.3
192.8
XI.I
165.2
7-74
—
11.22
— .
1308
—
X.24
474°
2.22
2.28.
150-3
421O
69.3°
2.28
2-334
89.x
86.8
I
«43
Grate surfoc^e in sq
Heating '' "
«' sarficc to grate
Pressure of steam in boiler, p^r sq. In.
«' blast in fire-room in ins
Revolutions of engine per minute. .
Coal per sq. foot of grate per hour. .
Water evaporated from and at 212° )
per lb. of coal, ash utilized J
Do. do. per lb. of carbon..
Do. do. per*sq. foot of
beating surface |>er hour
Temperature of gases in chimney..
>' of air in fire room....
Fuel per IIP per hour.
Carbon " "
IIP •* " '
Efficiency of boiler per cent
Water used for jacket per JH* per)
hour in lbs. j
Fuel. Calorific value of 14900 thermal units per lb., equal to 1025 of a lb.
bon. Ea«:h lb. of coal, if completely consumed, is capable of evaporating 15.
water firom and at 2120.
Blast Dranffbt.
30
30
26.2
1837
1837
1837
61.2
61.2
70.1
186
164.9
1949
27
^§
2
2342
268.7
318.4
18.6
29.8
66.8
10.48
X0.2
8.89
12.18
II.7
xao4
3-2
4-7
8.05
540°
610C
777°
71.4O
60. 30
62. lO
1. 981
1.99
2.26
2.03
2.04
2.32
282.1
440.2
78.2
774 7
81.4
66.6
.84
.42
38
of car-
41 Iba
Sarbed Steel-'wire Fencing. {GcUmnized or painted.)
J. A. Roebling's Sons Co., New Fork.
Four points, barbs 6 inches apart, 15 feet = i lb.
u »» ♦» a '* *' 12 " = I ••
On Spools.— IS foet in length of the regular measures and 12 feet of the thickset,
we'fgh each one lb.
Spool, about 18 X 18 X 17 »n8., measuring 3.5 cube feet, weighing (Vom 60 to xoo
lbs., and length of wire ordinarily 1500 feet Thickset or Hog weighs .2 mora
Xo Compute Volume of Boards tHat can "be Sa'wed out
of a Round I^og. (M. J. Butler, C.E.)
RuLf.— From diameter of log in inches sobtract 4, multiply remainder by one
half of it, multiply proceed by length of log in feet, and divide product by 8; result
will give number in feet.
dTTI X — X?-?-8 = V. d representing least diameUr in inches^ I Un{ftk of log
2
xA/eet, and V volume in feet of board measure.
ljxu8TRATX».-~%Assume a log 3p in& in diameter and 15 feet in length.
30 — 4 X 26 -H 2 X IS -^ 8 = 633.75/«t B.M.
iroot-Pound-TF/i«n/or Unit of Work-Is t lb. lifted, thrust, or projected
through I foot, against gravity or inertl». and to expressed in pounds or tons, with-
out regard to the period bf its action.
When for Unit of Rate ofWork-lH i lb. lilUd, etc., as above, i foot tn a glvwB
period, as In X second or minute.
948
APPfiKDIX.
CfaltMinizing decreases strenglh of nuannealed wire 5 per cent, and its ductility
15 per cent
Breaking Weight of No. 20, B W6 (.035 in.) cracible steel rope of 6 strands, t.75
ins. in circumference: Wires, 78 to 102 tons per square inch, and Ropes 5.75 to
10.47 tons.
Annealed Wire is not affected by galvanizing, but its ductility is reduced from
179 twists to 58, = 68 |)er cent.
Annealing Wire reduces its strength 45 per cent., but increases its elasticity
77 per cent.
Tensile Strength of crucible steel wire averages 85 tons (80 to 90) per sq. inch.
Permanent set, Bessemer iron wire 12 tons per sq. in., or .25 of ultimate tenacity.
Variation of tensile strength of like pieces of steel wire, galvanized or plain, is
but 3 per cent, for the former and 8 for the latter
Modulus of Elcuticity (ME). Iron wire 22400000, Steel 35000000, and crucible
Steel 33 000 000.
Bending. Stress dae to it, in a wire of the material and dimensions given.
ME = 32000000.
Diam. of pulley 10.5 13*125 16.875 18.75 24 ins.
Stress per sq. inch 50 40 31.4 28.2 22 ton&
Durability. Life bf steel wire ropes over iron pulleys, of material and dimen-
sions above.
Numher of times rope passed over the pulleys without Breaking. Load 1568 lbs.
Ini. lat. Iiu. Int. In*. Ins. Ins.
Diam. of pulley .. . 5.25 7.875 10.5 13.125 16.875 18.75 24
Number of times. . 6075 10300 16000 '23400 46800 72700 74100
— — 53ioot 85200! — 392 soot 336600
Over Pulleys 24 Inches in Diameter. Load 1568 Lbt.
Number of Bends before Breaking.
Msnufsctore of T. k W. Smith.
Ordinary crucible steel.
Patent improved steel. .
Plough steel
Iron wire
Crucible steel
Crucible steel
n
No.
20
20
20
»9
18
22
Diameter.
Ins.
.035
•035
•035
.042
.049
.028
Wire and strands laid
in opiMMite direction.
1-24 Inch.
No.
74100
96000
109000
66000
87000
IIKOOO
3-24 Inch.
No.
51 000
57000
54000
32000
47400
48700
Wire and stranda
laid in same
dbecUon.
3-34 Inch.
No!
126000
142800
«344a>
79000
117 100
120300
NoTii— By author: diameter of pulleys should be = 10 circumferences of ropa
rTeuacity oi* Dovetail's.
White Pine, 6 inches square. Notch in Length equal to Depth of Tinker.
S and D each representing proportion or d^th qfcuts to width of
Destruction.
S .25 3.9 tonsL
41
<(
Destruction.
D
.125
.167
.208
6 tons.
6 "
6 '*
•33 5-75
.41 5-"
Greatest strength in a double dovetail is attained when D = . 167, and 1& a single,
when S = .33. {Gen' I 0. M. Poe, U. 8. E.)
Sbaftine; for X^tUes and MlilU.
Diaweter. — Should be given in inches or quarters only. Length. — ^Kot to exceed
20 feet. Velocity. — Machinery, 125 to 150 revolutions per minute; Woods, 200 to
300. Power. — Applied at middle of length of, shaft whenever practicable. Hangers.
—With ac^ustable boxes, in order the easier to maintain a shaft in line.
• From a paper by A. 8. Biggart. Ins'n C.E.
f Long's patent lay.
APPENDIX.
949
Granite .,
Bluestone
Sandstone
los.
12
8
36 to 40
Limestone,
magnesia,
oolite. ...
Int.
10 to 15
36
40 to 70
(R.J.
Cost of* Saivine and IDressitig Stone.
Per Cube Foot.
Bedfbrd Stone. — 20 centa At Chicago, Soft^ mediam, 8 to ro cents;
ILiiixiestone, Alagnesiaii, and Oolites. — Medium^ 13 to 17 cents;
Marble and Grranite, Hard^ 25 to 30 cents.
Rate in 10 Hours.
Ina.
Marble, Tenn. . . 9
" Vermont. 20
Brownstone 20 to 25
NoTB.— Depth of cut without reference to its length or number of saws.
Oooke,)
X>ressiiig.
Per Square Foot. Labor $ 3 per Day.
Hard Litnestone. — Bush hammered, rough, 25 cents; Medium work,
30 cents; Fine work, 35 cents.
Cost of Raising %Vater.
1000000 Impexial or 1 SOO 0.00 TJ. S. G>-allons 1 Foot.
Average cfis Years.
Low Service. j High Service.
By water, 1.23 cents. By steam, 13.2 cents. | By steam 25 cents.
.A-dliesion of Drifted Bolts.
Steely One Inch in Diameter. —Hole Six Indies in Depth.
Wood. UnXa. UnlA Uy.1. rT>.l» 1I..1« I tl-1- H-1- HoIb
i2-i6tba.
LU.
•53
•45
Hemlock in x5-i6tbs hole 415 lbs. per lineal foot to withdraw it, and White or
Norway Pine i2-i6ths hole 830 lbs.
To obtain maximum holding resistance of timber, diam.of hole to bolt as 13 to 16.
Relative bedding resistance between driving parallel or perpendicular to the fibre
Is as X to 2. {J. B. Tschamer.)
Kesistanoe ot tlie A.ir to Falling Bodies.
Yellow pine.
White oak..
Mean Holding Resistance per Lineal loci
.
Ratios.
Hole
Hole
Hole
Hole
Hole 1. Hole
Hole
i5-i6th».
Lbs.
i4-i6th8.
i3-i6thi.
i2-i6ths.
i5-i6thB. 1 i4-i6tha.
i3-z6thB.
Lbs.
Lbs.
Lb*.
Lbs.
. Lbs.
Lbs.
361
616
761
400
•47
.8
I
1300
1778
2499
"33
•52
•7»
I
Falling Body
Sm.
In Vaeoo.
Veloc-
Fall.
Feet.
Feet.
X
*
3
16
t
32
. 64
96
Lead Ball, 2 Ins. In
Diameter, Wdght i lb.
In Air.
Final
FaU.
Veloc-
ity.
Feet.
30
55
77
Feet.
15.5
43-5
67.5
Retar-
dation
per See.
Feet.
•5
4.5
"•5
Body Falling HorixonUlly.
Weight I lb.
One Foot Square.
Final
Veloc-
ity.
Feet.
28
35
38
Fall.
Feet.
1433
33
38.5
Retor-
datloii
per Sec.
FeeU
1.66
Two Feet Square.
Final
Veloc-
ity.
Feet.
>3-33
24
IS
4I-5
{P. H. Van Der Weyde.)
Retor-
Fall.
dation
per Sec.
Feet.
Feet.
1333
2.66
37-3
61
24
66.66
Retardation is Inversely as Density of Body. Velocity after &11 of one second
becomes measoreably uniform; the increased velocity being balanced by the in-
creased resistance.
Resistance of the air at moderate velocities, to the velocity of a falling body, is as
the square of its velocity.
ThuB^ when the velocity is doubled, the resistance is quadrupled, and when trip-
led, nine times greater. Applicable alike to a cannon ball in i^ir or a body in water
950
APPENDIX.
Cost of a Hors^-I'o'wer "by Steaxn.^
Joule's equivalent (p. 504) =: 772 tintto = heat required to raise i lb. water x^, =
elevation of i lb., z foot high.
Unit of evaporation, to evaporate i lb. water to steam at the preBsare of the at-
mosphere = 966. i British thermal units.
Horse-power 33000 lbs.
= 43.75 heat units = i ff i °, and 42.75 X 60 min. t=: 2565 per W per hour.
33000
772
---— = a.655 lbs. water required to generate i IP.
966.1
Anthracite coal has. ... 14 500 heat units. ) ^ ,. ^ , ««. n ^fWi^
Bituminous" British. 14320 " " J * or other fuels see p. 486.
Then ^| — =15.01 U)s. wcUer evaporated per lb. of coaL
900.1
Hence,
2-655
= .1769 lbs, coal per IP per hour, or
= 5.65 W per how per
15.0X ' " -1769
lb. of coal.
Assuming in all of the above, the normal condition, that there is neither expen-
diture of water or temperature in the operation.
Operalively. — From elements furnished, in part by Thos. Pray, C.E., the cost of a
IH* at the pressures and expansions given is as follows:
Co€U at%2 per 2000 lbs.
EniciB**
Condantlnr.
2o''X48'^
NoD-eoodMrinir,
i8*'X42^
lbs.
44
4(
58.5
4 74 ina-
8.12 lbs.
0.99 "
ii.59 "
3.07 "
6.21 centa.
Initial pressure of steam 83.6 lbs.
Cutoff — ins.
Terminal Pressure '8.71 Iba
Evaporation per lb. of coal 10. 31
" IP 16.84
Coal per IIP per hour 2.28
Cost per IIP per 10 hours 2.6 cents.
A Condensing Pumping Engine has been operated at a cost of 2.28 cents.
* For Hone-povtr ttt pp. 441, 733, 758, and 9x4.
Cost of "Water I*ower on IDriving Sliaft.
P«rIP.
Power is variable, depending upon variation in head of water, as when it Is de-
livered in a river subject to rise by fireshets, cost of water, and of plant In order
to attain an average daily power, the power must be increased to meet the loss of
head by back water in fresheta
Location.
Manchester, N. T. .
Lawrence, Mass. . .
FP
No.
890
1000
*t 9 Q —
Feet.
30
490
Cost
•
44
42
LocAnoN.
H?
No.
1000
1000
Fe«t.
28
Lowell, Mass. . . .
4i 11
• • •
FMt.
575
290
13
18
Coai
100
57
Cost of a 1000 H* Plant independent of cost of water about $ 45 per W.
Cost of a like
Plant uxxder different Kead4S.
From Supply to Discharge in Feet. |
From Supply to Dbebarge in FeoU
Head.
too
aoo
300
400
500
600
Head.
xoo
900
300
400
Soo
Feet.
$
t
t
•
1.
1
Feet.
$
$
1
•
1
10
95
IfO
"5
140
155
170
30
26
3a
39
45
Sx
20
3»
40
54
62
70
77
40
20
25
31
37
42
600
"•"
58
48
At lAwreQce and liowell. a Mill Power = 30 cube feet of water per second, with
a head of 35 feet At Manchester it is 38 cube feet, with a head of 20 feel
{Ch€is. T- Mmn, M.S.)
For Power of a Mill Wheel see pp. 565, 566.
951
Hia'bor in
Steam Plant.
Dally and YeaTly Cost of Coal and.
Operating a Plant of lOOO
Y'ear of 308 days of 10.26 liours, coal at ^3 per ton
of SOOO lbs.
Deduced from Reports of Chat. T. Main^ M.B.
KnaiirB.
•ExhikuU
tteain
used.
CJorapouDd.
Condensing .
Non Con-
densing. . .
I'er cent.
I''
(50
(50
(50
* For heatiDg.
Ccmlper
» |«r
hoar.
Attend
per
BoUer.
Lbt.
c
1-75
•S3
x-5
1.25
.45
.38
2-5
2.06
•75
.63
1.63
•49
3
.90
2.44
1.88
.56
per IF per Day.
Eaciiu.
c
60
60
60
40
40
40
35
35
35
1 Stores
Coml
>ay.
perH»
Storat.
Iter day.
e
•
.25
2.14
.25
1.84
•25
1-53
.sa
3.06
.22
2.52
.22
2
.20
367
.20
2.99
.20
2.3
^if
tDally
for
xoooH?
•
•f
3-5*
316
2.76
3520
3160
2760
4-43
376
4430
3760
3.XI
3i»o
5.12
5120
4.27
42701
3-47
3470
Tewly.
10 841 60
9732.80
8500.80
J 3 644. 40
1 1 580. 80
9578.80
15769.60
13x51.60
10687.60
t Ineladinp tMA.
Yearly Cost of lOOO :H> and of a
Year of 308 days of 10.26 hours. Coal at 9 3
of SOOO IL.t>8.
DodwMfrvm SUfvrU tf Chat. T. Main, M.B.
EltOINB.
Compound. . .
<^nden8ing . . .
Non-Condens-
in«
•ExkAMi
Engine
tOperat-
Steam
and
ingEx-
omA.
Hooaei.
piBMk
Percent.
%
%
0
40
5.02
25
40
5-02
SO
40
S-oa
0
33
4-M
25
33
4-14
50
31
3-95
0
29.50
3.70
25
29.50
3-70
(50
29.50
370
BoiJer-
honse add
Shed.
%
18.36
x6.i6
13.00
34.80
ai.x2
'7-33
24
24.28
19.46
fOpcra-
tor's
EzpeoM.
%
2.50
3.*30
X.]
3-
2.88
a. 36
3-95
3-3>
«.65
t.89
J. 38
;Coal and
Labor and
Stores.
per ton
STotal per
IP
xo 841.60
9732.80
1500.80
13644.40
1x588.80
9578.80
15769.60
13 151.60
10687.60
%
18361.60
16952.80
154x0.80
21 164.40
18608.80
16888.80
23 419.60
20161.60
17037.60
* For Heating.
t As per preTioas Table.
t Injector, Depredation, Taxes, Interest, and Tasamace.
I Net fneladiag Cost of Plani in eolomn 3 and 5.
Sugar in IMortar.
It has been demonstnited that the addition of saccharine matter to lime-mortar
is very beneficial, as it enables it to be laid in nrosty weather.
It is claimed also that H eaases the mortar to set rary soon and strengthens it,
and thai it can be laid with dry bricks.
As sugared water dissolves lime, it is necessary to dissolve the sugar first, and
then add the water to the lime slowly and cautiously. The mortar should be very
stiff.
ProporUont, — For mortar, eoarse broiWD sngar, 3 Ibe.; lime, i bushel; sand, c
bnsbeia
If sugar IB added to mixed mortar, it renders it too thin. (Jfantf/octerer cmd
BuOder.)
Seltins. Speed of belts, single and double, i inch in width, sbonid not ex-
ceed for the first, 800 feet per mioute, and for the second 500 feet, each = one ff .
Xlailroad Speed.
London, Xorth Western^ and CaUdrmian. — I<ondon to Edinburgh, 400 miiea
Speed, q5.4 miles per hour ; 3 stops 50.9 miles. Engine, tender, and cars,
348 000 lbs.
Chicajgo, Burlington, and Quincy.—i^B miles in 0 minutes.
952
APPBKDIZ.
Cost of Irrigation, per A.cre.
Calijvmia. — From $ 7. x8 to $ 53. 33. Colorado. — $3. 75 to $ zo.8<x CTtaA, $ 4.
France. —Average of several, $ 58. India. —Average of several, $ i. 75 to $ xol
Alloy
That expands in cooling: Lead 9 parts, Antimony 2, Bismuth x.
S^jEtrexnes of rTexxiperature.
Artificial, 135° {Faraday). Atmosphere, 77 ^ {Bade).
Kxtexxsion of "W^oodis by Water. (<fe VoUon Wood.)
Elongation. Pine 065 Lateral. Pine 2.6
Oak 085
ChestuaL. .165
Oak 3.5
Chestnut.. 3.65
SxxioUeless Powder. Gun 6 ibs. in diam. Charge 17.64 Iba Energy
at muzzle, 4609 foot tona Per lb. of powder 139.7, and per weight of gun 730.
Voluxxie of '^Tater Flo^viiif; over Niagara Falls.
270000 cube fnet per second. Since 1842, Horseshoe Fall has receded 140.5 feel,
and American 36.5 feet {J. Bogart, S. S.)
ROOFS.
'Po Compute Stress oxx Roofbr.
"Velocity axid Pressure of "^^ixid.
RuLS.— Multiply square orvelocity of wind in feet per second by .0023, or square
of its velocity in miles per hour by .005, and product will give pressure in pounds
per sq. foot
Or, »« X .0023 = P, and V« x .005.
Also, .0023 «* sin. X = P. P rqtreunting pressure per »q. foot in Ihs.^ x angle
of incidence of wind with plane of turf ace in degrees^ V velocity of wind in miles per
hour, and v velocity in feet per second.
Direction of wind usually makes an angle of 10° with the horizon, hence 10^ is
to be added to horizontal plane of direction of the wind.
Illustration i. — Assume wind with a velocity of 100 feet per second to impinge
upon a plane roof set at an angle of 45°; what would be the pressure per sq. foot?
Sin. 4S°4- »o° = -8i9. .0023 X ioo» X .819 = 18.837 **•
2.— Assume the wind to have a velocity of 150 feet per second, and angle of roof
60°; what would be the pressure per sq. foot ?
Sin. 600 -f xoo = .94. .0023 X 150 <* X .94 = 48.75 lbs.
!Pressu.re of Snovr.
This pressure decreases per square foot in Ratio of half space, to length of rafters,
or height divided by space.
I*ressures for Various Angles or f^atios.
At IS Pounds Weight per Square FooL
Degrea^
Lb*.
h-r-i
De|^«e«.
Lbt.
b-4>S
I>Bgreak
45°
33^40'
36° 34'
10.6
12.6
13-4
.2
.16
•14
21^ 48'
»5°39
13.9
'4-3
14-4
.X25
.XX
.xo
X4O2'
12O 3x'
1 1® 19'
.5
33
as
Single tiles 20
Slates, ordinary x 5
Asphalt on slaba .... 20
Pi^r, tarred. 6
»4-5
X4.6
«4-7
VP^eiglits 0x1 R.oof1s.
Per Square Foot in Lbt.
Iron, sheet 8
Zinc, sheet 8
Slates on iron 10
Iron, sheet on iron . . 5
Iron, corrugated, on iron 4.3
Zinc »' " 4.5
Snow ao
Wind c xo
APPENDIX.
953
Ooxnparative Operations of* a Sizvtple and a
I^oooinotive.
Compound
Brooklyn and Union Elevated Railway of Brooklyn^ N. Y. Forney Type.
KLnann.
Siukpl*.
Componnd.
Cylinders, in& . . . .
l«Xi6
11.5 18X16
Drivers, diam
43 ins.
42 ins.
" re vol u- 1
tions per mile j
480
480
Boiler, diam
42 ins.
43 ins.
Flaes, 0 D
1.5 ins.
«.5
Number.
124
124
Exhaust tip, diam.
3. 25 ins.
3 ina
Grates, water
—
—
Area, sq. feet. . .
15-6
>5.6
Heating surface, )
sq. feet J
289.46
289.46
Ratio of do. to)
grate ]
18.5
18.5
CJoal
3899 lbs.
2430 lbs.
Firing
Dmionation.
Expl. Gelat. (Vouge's).
Hellhomte
Nitro-glycerine (old)..
'* fresh . . .
" French .
Sm'less Powder (Nobel)
Gun-cotton, 1889.
** laboratory
Dynamite No. i
Emmensite No. i
Oxinite ft. Pieric acid.
Amide powder.
ELBMBim.
Coal per car mile.
Water
Gain in fuel
Evaporation )
fh>m 212°)
Gain in water....
Water per car )
mile J
Pressure of )
steam, ave' \
Revolu'sper min.
Miles per hour. . .
IP
Weight, loaded...
Miles run
Simpls.
11.05 ^^B-
26070 lbs.
8.09 lbs.
73.85 lbs.
136 Iba
45350
122
CompOBOd.
6.88 lbs.
19862 Iba
37-7^
9.97 lbs.
23-8j<
56.27 Iba
136 Iba
222
2773
223.6
45850
122
Higli Explosives.
[Point and H.elative Strength
DSSIQNATIOV.
Firing
Point.
Order of
Strength.
Deforce.
365
365
106.17
106.17
100
346
92-37
81.85
92.38
83.12
—
81.31
301
81.31
77.86
69.51
69.87
Tonito
Bellite
Kack-a-rock
Atlas powder.
Ammonia, dynamite. .
Volney's powder No. i
" " No. 2
Melinite
Fulminate, silver
*' mercury..
Mortar powd. , I)uiM)ut
Forcite No. x
FirliiR
Puiut.
I>egrees.
3»5
500
330
Order of
Strength.
68.24
65.7
61.71
60.43
6a25
58.44
53.18
50.82
50.27
49.91
a3->3
{Lieut. W. WdUet, U. S Army.)
Centrifusal Fump,
To Compute tlie Req.nired Velocity of the Outer ICdge
of* the Gladed^.
When the Height of the Required Lift of Water is Given.
The edge of Uie blades must have a velocity at least equal to that acquired by.,
body falling firom the given heiglit.
Then, to lift water 1 / — r- ,z « - ^
and sand 20 feet. / V2fliA = V64.4 X 2o = 35.89/«rf.
Comparison of* Operation and Cost ot a Oas and
Steam Kngine.
{In addition to page 587. )
Element*.
Steun.
Brake W
Thermal efficiency
<( ** or per cent, of heat in)
power, to total beat generated.. /
Mechanical efficiency of motor. . . .
Power to operate engine
Coal for B ff per hoar.
■^pace occupied, including gen* t
erator or boiler. )
76
( Generator, 70.5^
(do. and engine, 12.7^
i8j<
69JC
3iJ<
s. 34 lbs.
470 sq. feet.
i'lofeuor witc.
75
Boiler, 72JC
and engine, j%
9 75%
1S%
255t
2.6 lbs.
360 sq. feek
Bryan DorC
954 APPENDIX.
8TBAM-ENQINSS.
Ooxn pound.
» DuraHon of Operation 2 Hours.
Cyiffulert.— 5. 5, 9, and 15.5 Ins. in diameter. Stroke of piston !<. iit«
BevoltUiofu. — 150 per minute JIP 40-
Bo<Z«r«.— Fire tubular. TuJbes, 38 of 2 ins. ; 6.25 feet in length.
Heating Surface.^i$Z sq. feet. Grates.— $.7 sq. feet
Pressure 0/ Steam.— lys Ib^ per »q. inch.
Water. —Weight consumed, 1 140 lbs. Evaporation per lb. of coal, o. 8 Ib& Dmwq
fh>m jackete, 84 lb& Consumption per W per hour, 1.435 lbs. Temperature of
feed, 550.
Consamed 116 lbs. —per IIP per hour 1.45 lbs. ; per sq. foot of grate 10.2 lbs.
IndiaUor Diagrams.— Mwn ^ 54= 13.31 IH^; Intermediate 18=3 la IH*; GoU'
densing 7. 5 c= 14. 7 \W = 4cx
< Fly-wheel.—s-s feet in diameter and 10.5 ins. in width.
Weight of Engine and Boilers^ without water, 14 560 lb&
But7d«r«.— Marshall & Co., Kreigly, Eng.
PUMPING ENGINE.
Vertical Com pound.
Cy^vnders.—2\ and 66 ins. In diameter by 60 in& stroke of piston.
Pressure of Steam.— 7^.81 lb& per sq. inch. Vacuum^ 26.25 iu&
RewdtUimu. — 25. 51 per minute. Grate Surface. — 70 sq. feet
Pressure of Water by Gauge. —62.02 lbs. Head, including lift, i55.i7>l9ef s
67.62 lbs. Fuel— 67s *h8. per hour.
Duty.— 104 S20 4^1. Stack, in height, 125 ^t
Constrtutors.—The Edward P. Allis Co., Milwaukee, Wi&
ELECTRIC DYNAMO ENGINE.
Triple Sxpansion..
Arc Lights. — 500. Water entrained in steam 7.39](-
Cylinders.— 14, 25, and 33 ins. in diam. by 48 ins. stroke of piston.
Ooiufetu<;r.— Separate. Circulating Pump, 16 x 16 ins. ; Air-pump, single-acting,
24 X 16 ins. Cylinders, 12 x 16 in&, operating both pumps. Revolutions, 61.29.
IH» 16.4.
Pressure of Steam.— 12$ Iba per sq. inch; Revolutions^ engine, 99.12; Steam per
IH* per hour, 12.94 lbs. IH* 516. liyection Water. — 72°. Reservoir, 90®.
Constructors.— The Edward P. Allis Co,, Milwaukee, Wis.
Hailroad. Siffxials and Sigiiiiioation.8.
"Off breaks,'^ two whistles.
''Back up," three whistles.
'' Danger,'' continued whistles.
''A cattle alarm," rapid short whistles.
"Stop," one pull of bell-cord.
*'Go ahead," Two puUa
"Back up," three pulls.
"Down breaks," one whistle.
"Go ahead," a sweeping parting of the hands, on level with the eyes.
" Bark slowly, " a slowly sweeping meeting of the hands, over the head.
"Stop." downward motion of the hands with extended arms.
"Back," beckoning motion of a hand.
" Danger," a red flag or light waved up the track.
"Stop." red flag raised at a station.
"Start," lantern at night raised and lowered vertically.
"Stop," lantern swung at right angels across the track.
"Back the train," lantern swung in a circle.
Ikletropolitan Opera House, Ne-w ITorb:.
Copoctfy. .-.Seating, ^600. Standing, 40a If the saloons attached to the private
boxes were removed, tne total capacity would be 500a
APPKKDIX.
955
I>i8tlllatioii of SVesli *Water.
Process ofO. W. Boxrdy U. S. Natty, New York.
Marine Steamers for long voyages, operated under a high presdure of steam, are
neceesariiy provided with Evaporators, to replace the water expended in leaks and
▼ents, and to provide for the ordinary requirements for fresh water.
This process is an improvement upon existing methods, inasmuch as it furnishes
the water potable, and it is as follows:
The Evaporator contains a series of tinned metallic coils and a volume of sea-
Wttter; which is designed to be evaporated by the passage of steam fVom the engine
boilers through the coils. The water condensed in them is returned to the boilers;
the water vaporized from the sea-water, external to the coils, is either led to the
Engine condenser, to replenish that lost by leaks and vents, as fh)m gauge cocics,
etc. : or if required for potable purposes, is led to a DistiUcr, where it is aerated,
condensed, and filtered, f^om which it is drawn for use.
Aa the sea-water is evaporated in vacuo^ vi^wrization occurs at a temperature
below that at which much scale is precipitated. Hence the shell and ooilB are both
measurably free from it.
Restxlts of Bjx Sxperixnent.
Pressure in coils, 20 lbs. above atmosphere; temperature of steam in coUs, 259-3^;
temperature o/feed water, 131.66°; tempercUure of the wcUer vaporised, 212*^; water
vaporized per hour, 103.33 lbs. ; water condensed in the coils per hour, 112. 12 Iba;
total heat in the steam, 1193.7° and in the water vaporized, 1178.6°.
Oetpaoitiee of* liS-vaporators and X>istillers.
GaUonsper day cf^^ hours.
No.
X
9
Kntpo*
rator.
DIa.
tlllar.
No.
Evapo-
rator.
DIt-
tlllar.
No.
4
4*5
Evapo-
rator.
Dlt.
tiller.
No.
Evapo*
rator.
Oalloua.
600 .
X300 ]
Gallont.
600
1200
3
3*5
Gallont.
2000
3000
Gallont.
1600
1600
Gallont.
3000
3000
Gallont.
2000
2500
5
6
Gallont.
4cxx>
6000
Dft.
tillw.
Gallont.
2500
3000
Coal Produotion. and Consuzziptioii
0/the World Per Diem.
fVodtief ion. ^^Estlmated at 3 360000000 to 3 696000000 lbs.
0»n«ttinp<um.— Generation of steam, Land and Marine, 624000000 Ibe. ; Smelting
Iron Ore, s8 800000 lbs. ; other metals, 23000000 lbs. ; Forges, 20000000 lbs. ; Do-
mestic use, 57 600 000 lbs. Total, 2 700 000 000 lb&
Corrosioxi of "^^ro-aKKt Iron.
The purer the water, the more active it is in corroding and pitting Wrougbt-iroa
plates. This arises f^om the greater presence of i^ir in pure water, and hence a
greater proportion of Oxygen. {Locomotive. ) .
KaxrtH Soring and Heat of IMines.
Speren'ber^. near Berlin. Bore, 4173 feet in depth, about 1000 feet in ex<
cess of Artesian well at St Louis.
In lower levels of some of the shafts in theComstock mines, prior to the draining
tato the Sutro Tunnel, the water was at a temperature of iao°.
I*reservative» of Iron.
Pitch, Black Varnish, Asphalt and Mineral waxes are among the best, provident
the acid and ammonia salts, which frequently occur in tar and tar products, ar«
removed.
If in addition these substances are applied hot to warm iron, the bituminous and
asphaltic substances fonn on the surfkce of the iron an enamel, which, unlike to
other coatings, is not microscopically porous, and consequently it is imperriotw tn
water.
SpiriU and Naptha vamisheK are iqjurioua. (Prof. Itturit.)
95^
LIGHTNING-CONDUCTORS.
Code of* Rules for the jBreotioxi pf Light n in g-Gon*
duotors.'
Lightning-rod Conference,
Points. — Point of termiDal should not be sharp — not sharper than a cone of which
the height is equal to radius of its base. A foot lower down a copper ring should
be screwed and soldered on to the upper terminal, in which ring should be fixed
three or four sharp co])per points, each about 6 inches in length. It is desirable
that these points be platinized, gilded, or nickel-plated.
Upper Terminals. — Number of conductors or points to be specified will depend
upon size of the building, material of which it is constructed, and comparative
height of the several parts. No general rule can be given for this. Ordinary
chimney-stacks, when exposed, should be protected by short termiuals connected
to the nearest rod.
Insulators.— Rod. is not to be set off from building by glass or other insulators,
but attached to it by metal fastenings.
AttaehvMnt. — ^Rods should be led down the side of building which is most ex-
posed to rain. They should be secured firmly, but the holdfasts should not pinch
the rod, or prevent contraction and expansion.
Factory Chimneys. — Should have a copper band around the top, and stout, sharp
copper points, each about z foot in length, at intervals of 2 or 3 feet throughout the
circumference, and the rod should be connected with all bauds and metallic masses
in or near the chimney.
Ornamental Ironwork. — All vanes, ridge- work, etc., should be connected with
conductor, and it is not absolutely necessary to use any other point, than that
atlbrded by such ornamental iron-work, provided the connection be perfect and the
mass of iron considerable.
MateriaX. — Copper, weighing not less than 6 ozs. per foot in length, and the con-
ductivity of which is not less than 90 per cent, of that of pure copper, either in the
form of tape or rope of stout wires, no one wire being less than No. 12 B.W.6.
Iron may be used, but should not weigh less than 2.25 lbs. per foot in length.
Joints. — Bad joints diminish the efficacy of the conductor; therefore every joint,
besides being well cleaned, screwed, scarfed, or riveted, should be thoroughly sol-
dered.
/Voterfion. —Copper rods to the height of 10 feet above the ground should be
protected from injury and theft by being enclosed in an iron pipe reaching some
distance into the ground.
Painting.— Iron rods, whether galvanized or not, should be painted; copper ones
may be painted or not.
Cui'vaiure, — Rods should not be bent- abruptly. In no case should the length of
it between two joints be more than half as lopg again as the line joining them.
^Vhen a string course or other projecting stone- work will admitof it, the rod should
be carried through, instead of around, the projection. In such a case the hole
should be large enough to allow for expansion, etc.
Masses of Metal.— M far as practicable it is desirable that the conductor be con-
nected to extensive masses of metal, such as hot- water pipes, etc., both internal
and external; but it should be kept away ft-om all soft metal pipes, and ft-om in-
ternal gad-pip^. Bells inside well- protected spires need not be connected.
Earth Connection.— li is essential that the lower extremity of the conductor f)e
buried in permanently damp soil ; hence proximity to rain-water pipes and to
drains is desirable. U is a very good pllm to bifurcate the couductor close below
surface of the ground, and adopt two of following methods for securing escape of
the lightning to earth. A strip of copper tape may be led from the bottom of the
rod to t4)e nearest gas or water main— not merely to a lead pipe — and be soldered
to it;- or a tape may be soldered to a sheet of copper 3 feet X 3 feet and .0625 inch
thick, buried in permanently wet earth, and surrounded by cinders or coke; or
many yards of the tape may be laid on a trench filled with coke, taking care that
the surfaces of copper are, as in previous oafies, not lessAhap 18 square feet. Where
iron is used for the rod, a galvauized iron phite of similar dimensions should be
cmployod.
Initpection. — The conductor should be satisfactorily examined and tested by a
qiKililied person, as injury to it often occurs up to the latest period of the works
from Roeidontul causes and carelessness.
Collieries. — ^The head-gear of all shafts should be protected by proper lightning-
conductors to prevent explosion of fire-damp by sparks from atmospheric elec-
tricity being led to the mine by the wire ropes of the shaft and iron rails of the
galleries.
STONE fiREAKEB. — ORUSHllR. — STEAM HEATING. g^y
Stone Breaker and. Ore Cruslier.
Stone Breakers and Ore Crushers are used in' mak-
ing Macadam for construction of roads ; material for
concrete ; ballasting railroads, crushint^ ores, quartz,
corundum, and all brittle substances ; tbey can be ad-
justed to pass a mass from the size of a pea to larger
diameters, depending upon the capacity of the machine.
Crushed to Cubes qfn Indies. /Vr Hour.
Extreme
No.
Receiver.
Volume.
Weight
of Stone.
Weight
Produced.
J
length.
OimetiBioi
Breadth
Ins.
Cab. yds.
Lbs.
Lbs.
Ft. ins.
Ft. ins.
I
3X 1.5
—
40
100
X. I
. 6
2
6X 2
X
560
I 200
2.10
2. I
3
loX 4
3
1800
4900
4
3. 3
4
loX 7
5
3800
7800
5. >
3. 9
5
I5X 9
8
7400
15500
6. 6
5
6
15X10
9
7800
16000
6. 6
5. 5
7
20X 6
10
5300
II 200
5- 3
2. II
8
20X10
10
8100
18300
6.10
5. 9
9
12X30
16
14200
33000
7.10
8. 4
TO
»5X3o
20
14200
35000
.7.10
. 8. 4
t.
Height.
PuUey.
Speed.
IP
Ft. ins.
Ins.
No.
.10
SX 1
250
•5
2. 3
"X 5
250
4
3- 9
20X 6
250
6
4. 5
24X 7-5
250
8
5-"
30X 9
250
»5
5-II
30X10
250
15
4. 6
30X10
250
15
5."
36X12
250
20
6. 4
36X12
250
30
6. 4
36X12
250
30
Note.— The 30X15 and the 36X24 are preparatory Crushers, the former breaking
500 cube yards in 10 hours to 4 ins., and the latter 800 cube yards to 8 ins.
Crusher >vitli
Revolving Screen.
Dimen-
sions.
Volume.
Extreme
Weiglit
of Stone.
Weight
Produced.
I
Length.
NmensioDt
Breadth.
Depth.
Pulley.
Speed
jJlhi.
IP
Ins.
Cub. yds.
Lbs.
Lbs.
Ft. ius.
Ft. ins.
Ft ins.
Ins.
Kev.
No.
xoX 7
5
3800
10200
5- >
3-9
4. 5
2 X 7-5
250
8
15X 9
8
680U
17 700
6. 6
5
S-"
2.6X 9
250
15
X5X10
9
7300
18x00
6. 6
5-5
5"
2.6X10
250
za
20X10
10
7700
21 500
6.10
5-9
5. II
3 X X
250
M
Steaxxi Heating and Boilers.
Steam JH eating. — Is effected Directly or Indirectly. In
the first case, the steam is conveyed through a pii^e, or to a
cluster of them, at whatever point they are re(|uired, termed
a Radiator ; air being heated by contact with the exterior sur-
face of the pipes, and the water of the condensed steam flows
back (by gravity) through the return pipes discharging into
the boiler.
In the second case, steam is conveyed in like manner to a
cluster of pipes enclosed in a chamber, in the lowest part of the
building, usually the cellar, the air within the chamber, upon being heated,
ascends by its rarefaction, and is led to the space or apartment required to
be heated.
Hot- water Heating. — This system consists of circulating hot water
in the radiators instead of steam. The boiler, pipes, and radiators are fully
filled with water— the flow or circulation pipes attached to the top of the
boiler and the return pipes to the bottom. The water in the boiler, when
heated, rises and circulates through the pi|ies and radiators, and parting with
a portion of its heat it becomes denser, and gravitates through the return
pipe to the boiler, where it is again heated.
This system requires a much greater proportion of radiating surface than
that of steam.
958
BOILEBS. HTRDAULIC CEMBNT.
S oilers. In continuaHon.
ELBMBim. No.
Shell, diam Ins.
" over jacket. .. "
" height
<^ extreme . . .
Furnace, diam . . .
Tubes, No., do. 3 .
'' length
Steam-outl'ts 2,diam. ''
Chimney flue, diam.
Water-line flrom base
Heating surface. . Qfeet
Direct radiating ) («
surface supplied J
(I
i(
((
ti
C(
Wroaght>iroi
k Water Lags.
<
lut-bm
3
3
4
5 6
7
0
z
3a
35
41
43
5X
54
24
38
35
3a
45
46
55
57
30
31
33
69
37
72
1^
n
45
92
45
92
64
67
31
24
30
32
3«
40
18
19
44
56
84
9«
134
z6o
30
36
30
34
34
42
42
42
27
y>
2
2
2-5
2.5
3
3
1-5
1-5
8
8
zo
10
12
12
7
7
55
59
63
,11
73
74
51
54
75
los
140
360
320
45
60
450
630
830
X050
Z500
1900
260
350
32
35
33
69
2Z
44
30
2
8
55
75
450
35
38
37
72
24
56
34
3
8
59
«05
630
For Direct radiation, each G^oot of radiating surface will heat firom 50 to zoo cube
feet of air 8|iace, and for Indirect, ft'om 2<; to 50 cube feet; tbe range depending ui)uu
the conditions of construction of building and its exposure to external air.
HYDRAULIC CEMENT.
£«ortlancl«
In addition to pp, 589-590.
Some limestones when burned, ground finely, and made into paste, attain tbe
element of hardening in water, and are termed Hydraulic.
Cements are classed as Natural and Artificial. Tbe stone from whick
Portland or Hydraulic Cement is made iu tlie Uniied States is found in stratified
beds of aqueous de{>o8its, which iu extent cover about one-third of the area of the
State of New Yoric, the western part of Vermont, and also in New Jersey, I'eun
sylvania, Maryhmd, Virginia, and East Tennessee.
Analysis of Glens Falls and best German cement are nearly identical, both in
their quality and volumes, and all advantage chtimed for the former is that it is
finer grained, and that, in common with this, that it sets slowly, usually requiring
from 4 to 6 houra Consequently, the mixture can be made in a larger voluuie
without being rendered useless by setting before all of mass is required.
It is only in the stopping of joints leaking water under a pressure that the
quick setting of cement is better.
'Pensile Strengtli. Cement 1, Sand 3. Per square inch.
Work.
Aqueduct Na S
Vertical Wall .
Swing Bridge. .
Vertical Wall. .
Swing Bridge. .
Vertical Wall. .
Swing Bridge. .
Vertical Wall. .
Vertical W&IL .
Location.
Fort Miller
Glens Falls
Waterfbrd
Glens Falls
Waterford
Glens Falls
Waterford .
Glens Falls
Glens Falls
Sievo.
s«u.
M Day.* '
TmL
SB Days' 1
No.50.
No.lOO.
Inf.
U«l.
Min-
Hard.
Min.
Max.
Lba.
MIn.
Lb*.
Aver*
•He.
Max.
Lba.
Min.
Lbt.
Lba.
100 T
98.35
50
'42
347
254
309
394
300
zoo
9? 875
70
Z56
404
305
337
442
320
zoo T
56
Z36
369
303
342
3**§
330
zoo
99- "5
Z40
230
379
330
350
39*»
326
zooT
99
120
230
3B3
388
331
407
295
zooT
99
ISO
280
3^S
2K0
321
372
31a
zooT
99-125
'55
300
368
323
343
404
332
zoo
99
160
255
3«5
273
337
442
326
zoo T
99-125
los
Z90
374
3»3
33a
440
374
Wm. p. Judtttm, Deputy fitate Enginetr, N Y.
Oru.8h.lxLS Streiisth.. Per Square Inch.
ieets of strength made at New York and Brooklyn Bridge.
[n
WatM
LbiT
1409
Period.
In
Air.
In
Water.
Period.
In
Air.
In
Wat«r.
Period.
In
Air.
In
Water.
Period.
II
Air.
Lba.
1854
Day.
1
Lbi.
Lba.
385
Weeli.
X
Lba.
W8 i
Lba.
Wee)[B.
3
Lba.
750
Lba.
515
Weeka.
3
BLBCTKIC HOTOB
959
HJleotrio Motor. The Crockm'-Wkeeler^ New York.
This jMotor has be^n designed to remove difficulties
which experience has develu|)ed to be attendant upon
otlier instruments of like purpose.
Care has been taken in its design and construction.
J'he bearings are oiled aotoniatically, and magnetic
circuit is made as perfect as practicable. Its centre
uf gravity is low, machine strongly built, weight of
it comparatively low, and its efficiency high.
Designed to run at low speed, in order to reduce wear, heating journals, etc.
Between Bolt- SbafU.
H»
Weight
Vehw-
ity.
No.
LIM.
v..
18
2100
•"5
36
3000
.166
26
1800
•25
65
1300
.5
100
>350
'57
1050
t
290
1050
\
300
lOCX)
485
1000
run«9y.
Dfam.
IM.
Gi.
Fi.
G .
Fi.
2.
In*.
•375
•375
•25
DimenBionii.
Length.
lae.
7*375
9-75
Breadth HeiKhi.
Ids
5-5
7-5
Im.
7.875
8.5
8.5
hulea.
Length.
Ina.
4.625
6.375
6.375
Breadth
Ins.
2-75
3.375
Diam.
Ids
•25
•375
From
Base of
Motor.
Ibs.
3-375
3.6875
6875
75
75
0625
8.25
8.25
9- 25
9*75 7-5 8.5 6.3753.375 .375
3 2 14.75 9.5 10.75 9.75 4.3*25 .5625
3.53 18.25 I' »3 »».5 5-5 6875
4 3-5 19 »3-25 15.5 12.25 7 .875
63 25 12. 625 18.375 18.25 9.25
8 4 26.25 15.625 18.375 18.25 9.25
7.54.5 28 18.75121 18.75 9.75 I'las
a Grooved. F FkaU
Application qfthe Motor. ^For Printing-rooms and mechanical Shops of medium
capacity and Elevators, one of 5 IP is sufficient
To Compvite I*o>ver reQUired fbr Elevators.
Rule.— Multiply twice * prodact of weight to Inn raised in lbs., and height of as-
cent in feet per minute; divide by 33 000, and the quotient wrll gfve the number of
H* required.
Sixiall Af otors, of . 166, . 125, and .0833 IP are adapted for operating Fans,
Bloweis, Sewing maebinest Small loathes. Presses, Tools, Moflels in operation, Ro-
tating Advertisements, Organ blowing, Bafflng wheels, Knife sharpeners, Cloth and
Paper cutting, ExpertmeDtal models, etc., etc
miectrio Fans.
For Ventilation of OfLcos, Restaurants, Kitchens, Sick-rooffls, etc., etc.
Constructed in various styles, Plain and Nickel-plated.
Faru 12 Inches in Diameter
Regular, .0833 IP motor. — Fa^i^ .125 £P motor. — Double (a Fan at each side),
.1666 IP motor, or one i6-incb Fan.
Lm Kue ConUructum.—\ M\Able speed, Fan 24 ins.in diam.— 20 Inch, 125 H* motor.
ICleotric FuxnpH.
Pump, . 166 IP, will elevate 500 gall, water per day ot ro hours 100 feet in height
These pumps are arranged to operate automatically, so that when a receiving tank
is filled, the pump is arrested.
Capacitjr of I'll nip per Hour.
H»
Galhms.
H'
Oallons.
¥P
OAllons.
1670
2600
.166 100 .3 370 3
.25 230 1 750 5
Are Circnit !Motors.
Are 3tot'fr9 diflcr flroin all others. The ifianner of connecting the circuit ttid of
their operation varies Arom that of other motors .
They are famislied from .135 to 5 IP.
They sboaM ad ways be connected to the arc circa it by a competent lineman.
* Tk» twice k takn to coT«r lou of power by friciioa of all tho pttrtt.
960 DYNAMO LBATHBR BELTS. — WIBES AND GABLSS.
I>ynaxno Leatlier Belts.
Belting, — For Dynamos and Electric Light Machinery should be
double and endless, and not over ,^ inch thick, when run at a velocity of
4CXX) feet or more per minute ; should be perforated to prevent air-cushion-
ing, the perforations may be .093 75 inch in width, .281 25 inch in length,
and placed 1.5 inches apart; furnishing about 50 openings per sq. foot of
belt, without material injury to the tensile or operating strength of it.
■ In order to protect the surface of a Dynamo Belt it should be rendered
im{)ervious to the mineral oil used on it, which is destructive to the fibre of
the leather.
LEATHBB LINK BELTS.
Where Belts are run at right angles and at short distances apart, Leather
Link Belts are recommended, as they are very pliable and have uniform
oscillation.
Link Belts made .6875 inch thick, forming when combined two foil cir-
cles, assure the required uniform it v of oscillation.
WIRES AND CABLES.
Telegraph, Teleplione, aixd. Klectric ILiigb.t Wires
arid. Cables.
For A.eria,l, Su.'b.-xxiarine, and Underground..
The Okonite Company, New York.
Insulation. — In order to effect an enduring insulation this Company uses a
compound termed Okonite, a material possessing buili tenacity and resistance to
abrasion, while it is equally unafiected by extremes of temperature, commercial
acids, or alkalies, with insulating properties of the highest order.
Test Requirements for Insulated. 'Wires.
"Voltage Test.
SIZE
Thick
NESS
OP Insulatiok in Inches
A. W. G.
3/64
2f33
5/64
3133
4500
6000
6750
7/64
6000
7500
8250
4/3«
7500
9000
97SO
5133
6/32
7/32
8/32
9/32
10/32
4/0 to I
2 to 7
8 to 14
• • • •
■ • ■ •
2250
• • - •
3000
37SO
3000
4SOO
5250
10500
12000
12750
13500
ISOOO
IS7SO
16500
1 8000
18750
19500
3 1000
22500
24000
25500
27000
NoTK.— Elzperience proves that tbe above are sufficiently hi(;h voltages toemploy. Higher voltagM
although not necessarily caasing a breakdown of the insulation, are apt to Urain it.
Miegolims Fer 3VCile. 60 I>eg- F.
One Mliiiiite Eleotrifloation.
Strd.
II
4/0
3/0
2/0 •'
I/O -
1 Solid
2 "
i "
I "
8
9
10
12
14
Not*. — The above are conservative
resulu.
<«
it
(I
i<
3/64
2/32
• • a «
• • a •
• • ■ •
• • • •
• • • •
1200
1300
1400
. 1550
1700
1 60c
> 2000
i8o<
J 2200
200<
i 2400
230<
) 2800
3 70<
> 3250
5/64
800
850
950
1050
1300
1400
1500
1700
1850
2000
2400
3600
2800
3200
3700
figures,
3/32
7/64
4/32
S/32
950.
1050
1 1 75
1400
1050
1150
1300
T500
1 1 50
1275
1400
1700
1250
1400
IS50
1800
iSoo
1700
1900
3200
1600
1850
2050
3400
1800
3 000
3300
3600
3000
3300
3400
3800
3150
3400
3600
3000
2300
3600
2800
3250
3700
3000
3300
37SO
3900
3250
3500
4000
3150
3500
3750
4250
3600
39SO
4«SO
4800
4100
4SOO
4800
5350
6/32
good insalating oompoand
1600
1800
1900
2100
2500
2700
2950
3150
3400
3600
4150
4400
4700
5250
5850
should f^v
7/32
1800
3000
3150
2350
2800
3000
3250
3450
3700
3975
4SOO
4790
5050
5600
6250
lower
VOLTMETERS AND AMMETEBS. 01
JSlectrioal DMeasuring Instiraxuents.
The proper seleclion of indicating electrical measuring instruments which wUl
best meet the requirements of a particular case is a very important matter and
should receive careful attention. The most suitable types and ranges must be de-
termined by the kind of service for which they are to be used and the degree of
accuracy required; the sizes and styles must be determined by the length and
kind of scale desired, by the space available, and by the general finish of the
Bwitcbboard.
When selecting an electrical measuring instrument, the following six require-
ments should be borne in mind as essential to a satisfactory instrument:
1. It must be Direct Reading — this means that it be provided with a pointer
moving automatically over a divided scale marked directly in electrical units so
that the value of the indication of tho meter can be determined by a mere inspec-
tion of the position of the pointer upon the scale without manual operation or
calculation.
2. It must be Portable— ih\a means that it can be moved about from place to
place and used directly without previous levelling, calibrating,. or adjusting.
3. It must be ^ccuro^— this means that if it is used with reasonable care itB
indications will not diflTcr from the true value of the quantity measured by more
than a definite small per cent.
4. It must bePermanent — this means that its calibration will not change with time.
5. It must be Aperiodic or Dead- Beat— ihxB means that its pointer will immedi-
ately come to rest at its proper position on the scale without vibrating to and fro
about this position.
6. It must be Economical in Power Consumption — this means that it shall con-
sumo only a small amount of power for its operation, so that tho expense of operat-
ing is negligible.
Tbe Weston direct-current instrument consists essentially of a light rectangular
coil of copper wire wound on an aluminum fVame, pivoted in Jeweled bearings,
and capable of rotating in an annular space between a soft-iron core and tho
specially formed pole pieces of a permanent magnet A light tubular pointer
is attached to the coil and moves over a calibrated scale. The current is intro-
duced into the coil by means of two spiral springs which also serve to control
the movement. The movement of the coil is due to the dynamic action be-
tween the current flowing through the coil and the magnetic field of tlie per-
manent magnet. The iK)intcr assumes a position of equilibrium when the action
of the spring equals the tendency to rotation produced by the current and tho
magnetic field. Since the magnetic field is uniform and the torsion of the spring
proportional to the deflection, the scale is practically uniform.
The well-known aperiodic or **dead-beat" quality of Weston instruments is pro-
duced by foucault currents generated in the aluminum tntne when rotating
through the magnetic field. These foucault currents have a sufficient influence on
the movement of the moving coil to cause the pointer to come to rest almost in-
stantly and without friction.
The permanency of Weston instruments depends largely upon the small annular
gap between the pole pieces and core, and, as this is an important point, it sliould
be borne in mind when selecting electrical measuring instruments. Tbe small air
gap referred to necessitates the greatest accuracy in mechanical construction, and
it is a well-known fact that the product of the Weston Company is unapproached
in this respect.
The balance of the moving coil and pointer is also an important point, as an un-
balanced condition of tho moving system introduces forces which an electrical
instrument is not intended to measure, and therefore causes great errors in the in.
dications. The coils of Weston instruments are carefully balanced for all positions
BO that the indications are practically correct for all positions of tbe instrument.
4 M
962 VOLTMETERS AND AMMETERS. RAILROAD CRANE.
Weston instruments are extremely ec<»iomical in current consumption, and are
unexcelled in this respect. As a proof of this fact it may be stated that a volt-
meter of the standard type consumes only about .01 of an ampere.
The special alloy composing the series resistance of Weston Voltmeters has a
negligible temperature coefficient and consequently temperature corrections are
unnecessary. In addition to this the alloy has been carefully designed for absence
of thermo-electric effect with other metals of the circuit, and consequently errors
fh)m this source are avoided.
A great variety of models of electrical measuring instruments of the p(>rmanent-
mignct typo is manufactured by the Weston Electrical Instrument Co. adaptable
to the various conditions to be met with in engineering and central-station work.
Among thede are the highest-grade Laboratory Standard Instruments, Portable
Standard Testing Instruments^ and a complete line 0/ Switchboard Instruments.
Besides the direct-current Instruments described above, a new line of alternating-
current Instruments of the soft-iron type is manufactured by this company. They
are extremely accurate and permanent, and, by means of a well-designed air
damper, have the same "dead beat" action of the movable system as in the case of
the direct-current instruments. They are practically independent of temperature,
frequency, and wave form. They are made for both portable and switchboard use.
Complete catalogues describing all of the above apparatus will be supplied on
application to the company at Newark. N. J.
Portsklale I>ireot»Re€t<iiuK Voltmeters and 'WattmoterH
lor .A-lteriiatins axidi Direct** Cur reiiit Oirouits.
Voltmeters, 22 ranges, ft*om 7.5 to 3000 volts.
Wattmeters, 12 ranges, from 150 to 30000 watta
Swi tell "board. Ammete'rs and Voltmeters for Central
Stations and Isolated Plants.
Illuminated Dial Instruments, '' Round Pattern ^' Instruments, have sul)StantiaUy
the same characteristics as the Portable Standard Instruments. Are " dead beat,"
have uniform scales, can be kept in circuit continuously.
Railroad. Crane.
The FarreU Foundry and Machine Co.^ A nsoma^ Conn,
Post, — Of cast iron, in one piece, fitted to deck-plate, with
faced joints and secured by bolts running throagh a stone foun-
dation, set up on anchor plates on its under side.
JUf. — Of two wroaght-iron beams, bolted at head 4ind foot to
a bonnet and shoe, with tie bolts between them, and secured to
the post by bolts which lead from its head to a yoke, which
turns on a pin in the hub.
Hub. — With a pin is fitted into head of post-, on which the jib turns.
Tohe. — la secured by two bolts, which lead down through and arc secured
at the deck-plate on the foundation.
Gearing. — Double and set for both fast and slow motions, and detachable,
to admit of lowering load by a brake.
Chain, — Triple " B Crane,'* and all sheaves have roller bushes.
Capacity.
lUdiat.
FmU
13. 5
SO
Cnpadty.
Weijrht.
Lb*.
55<»
6500
15
Tubs.
6
10
Welr>)t.
Ltw.
10400
14D00
16
30
CnniiHtv.
T«ii>.
so
Tods.
3*
4
* I>wi|(n«d for operation on Wrecking and Coottractini; can.
Weiglit.
LbeT
17400
23800
VACrUM PUMPS.
963
Vaoiium Puxnpfl,
Vaouuzn P-axups. — Air pumps are so termed when they are used
in connection with vacuum pans, multiple effects, or filters.
It is impracticable to define a general rule for their capacity, as the cir-
cumstances of their operation vary in different cases. «
Vacuum Evaporators.— The\r dimensioDS depend upon the temperature to which
they are submitted, the evaporatton, character of the liquid concentrated, Tacuum
desired, and type and efficiency of the condenser.
J>ry Exhaustion. — When air alone is withdrawn.
( J M = Q. V and V rtprueiOing volwnes oj cylinder and receiver, II
volume of air in receiver at commencement of operaXion^ botk in cube feet, n nuv^^er
^Hrokes of piston^ and Q volume of air remaining after n strokes of piston.
Condensation.— There are two systems in operation for vacuum puns and multiple
effects, viz. —
Dry System.— Where the condenser is fitted with a leg pipe or barometric tube,
through which the injected water passes off by gravitation.
Wet System. ^Wheh the pump receives and discharges the condensing water, in
addition to its maintaining a vacuum.
In either system the pump is required to discharge: ist. The air contained in the
injection water, in the liquid, and in the pan, pipes, and condenser.— 2d. The incon-
densable gases evolved trom the liquid in operation.
Motes ^The Pan and its immediate connections are made of iron, copper, bronze,
or alloya
In designating the design and construction of pump required, the liquor, the
volume, the degree of concentration required, and the time in which the operation
must be completed, should be fUrnished.
To fhcilitate transportation, the bed plates of the large sizes are cast in two parts
and bolted together.
An order for a pump should state: ist What liquor, and volume of it, is to be evap-
orated in a given period, as an hour? 2d. What the diameter ofpan or evaporating
vessel, and what that of vapor pipe when it enters condenser? 3d. What the
heating surface ofpan, and has it a steam-jacket and coils, and if coils, what is their
diameter and length? 4th. If heating surlkce is of iron, brass, or copper? 5th.
What the average temperature of condensing water, and what the volume of it?
Duplex "Vacuuxn iPumps.
Fly-'veheel Typo for **I>ry»» op ••AVet*» Syetezn*
DfMBMSIONI.
Dt*in«t«r
DiameUr
ofVMonm
ofStoun
Cyllodm.
Cyliad*n.
Int.
Int.
6
5
8
6
10
7
10
8
la
8
la
9
«4
9
\t
10
to
16
la
18
za
18
«4
20
la
ao
>4
aa
14
aa
16
"4
16
a4
x8
DbplaMiDtBt, at 75
Diameter of PIpet.
Volnm*
FMt Pbton SpMd pM
BoctloD
Stroke.
par Rev-
olution.
Ml
Parlfla.
Inst*.
Per Hour.
and
Diieharfe.
steam.
***'l>Mtt
Int.
Cub. fact.
Cub. f«et.
Cob. feet.
IM.
Ins.
Int.
6
•589
29-45
1767
I
«-25
6
1.047
52.35
3M«
i
X-25
« 5
6
'•635
81. 8a
4909
1-25
9
6
9
1.635
2.356
81.82
117.81
5?a
»-5
a
a
9
2-356
X17.81
7068
1.5
a
9
3«o7
160.35
9621
1.5
a
9
3»?2
160.35
962Z
»-5
2.5
9
4.188
209.4
H564
1
«'5
2-5
9
4.188
009.4
"§
u
s
■•5
9
5.30'
265
X
a
2.5
9
5.301
265
,5898
i
a
2-5
9
6-545
327 -25
«9$35
s
a
2-5
9
6-545
327.25
'9635
M
a
2.5
9
7.919
395.95
23757
3
a
2.5
9
7.919
395-95
23757
2.5
3
9^
9 42»
471.21;
a8a75
a.5
3
9
9-424
I 47*«»ft
1 38375
2-5
3
964 DRAWING, TRACING, SECTION, ETC., PAPER.
Dra-wing, Tracing, Profile, Cross-section, I*h.oto-
printing Papers and. Clotlis.
Keuffel & Euer Co.^ AVio York^ Okicago^ SL LouU^ San J^VaneUea
In Blxeets.— WbatmaD*8 Haud made in all sizes, U P, C P, and R
Univei'scUf For general drawing and water-colors, six sizes, 14X17 ins. to 27X40
ins. — Normal^ Not Hand-made, but very similar to the Not Hot Pressed, in Koyal.
Imperial, and Double Elephant. — JJupltx, Cream color, for line detail and general
drawings, in Hoyal, imperial, and Double Klepbaut.— i>up/fa;. Drab color, heavy,
Double Elephant only— Faragun^ Medium rough, in Koyal, imperial, and Double
Elephant, «wM>o</t in Double Elephant only.— Bristol- Board (Keyuolds's), Ave sizes,
12.5X15.25 ins. to 21.5x28.75 ins., 2, 3, or 4 sheets in thickness. IL & E. Patent
Oniou Bristol-Board, 10X15 >i^ ^^^ 15X20 ins. K. &. K J3ond i'aper, light and
Very lough, three sizes, 19X24 to 27X40 >*^
TraoiiiK h*eLi>eir ft. — Vegetable (French), five sizes, 13X17 to 29X42 ins.—
Cfupola, very tough and transparent, 28X39 ius. — Hermex (slight grain), 20X30 and
30X40 ins.— C*;;r«, tough, 20X27 and 27X40 ins.— Corona, thick, 27X40 ina Of
these the Vegetable, Ceres, and Corona are natural Tracing ]>aper (not prepared).
In rolls: — J'archnynU, Thick Parchment, Abaetu, Patera^ Colonna, thin and
medium, 30, 36, 42 ins. in width (can often be substituted for tractug cloth),
Corinthian, Oothic, Doric^ AUba (for transferring), Lottu^ and Libra.
Drawing F»apers in ^toll^.— Duplex, medium, cream color, 30, 36,
42, 56, and 6a ins. in width. — />>., thick, drab color, 36 and 56 ins. in width.—
Uaiversal^tof general drawing, water colors, etc., 36, 42, 56, and 62 Ins. in width.—
Aawa, similar to Universal, pearl gray.— Anvil, medium and thick, surface and ap-
pearance similar to Whatman's Not Hot Pressed, medium, 36. 42, and 62 ins. in
width; thick, 62 and 72 ins. in width. —7'ara(/on, pebbled surface (similar to
egg shells), thin, medium, thick, and extra thick. All 58 ins. in width, except
rough, medium, which is also 36 and 42 ins. — With smooth surface (similar to
Whatman's N. U. P. on one side, smooth on the other), medium and thick, both
58 ins. in width, except medium, also 36 and 72 ins. All can be had by the
yard, in lo-yard lengths, or in rolls of about 35 lbs.
Detail.— £'conomVi 50-yard rolls, light 60 ins. in width, medium 36 and 60 ins.
^Simplex, light, medium, and heavy (Manila), 36, 42, 48, and 54 ins. in width, in
50 and 100 yard or loo-lb.. roll&
MIounted. — Unitfersaly Duplex, Lara, Anvil, and all the Paraxon Papers
are mounted on muslin, in all the widths; by the yard, or in 10, 20, or 30 yard
rolls. All the sheet pipers are also to be obtained mounted up to 20X30 feet
I*hoto-Priiitii\g Papers.— Prepared, in 10 or 50 yard rolls. Helios Blue
Print, medium and thick, 24 to 54 ins. in width. K. T. Paper, thin, for mailing,
34. 30t 36, and 42 in.s. in width. — Columbia, Blue Print Papers, medium, thick, and
thin (mailing), 24 to 4a ins. in width. Blue I*roces8 Cloth, prepared and unpre-
pared, in 10- yard rolls, 30, 36, and 42 ins. in width.— iVijTrorirw (Positive Black Proc-
ess), lo-yard rolls, 30. 36, and 42 ins. in width, prepared only — Umbra (Positive
Black Process) requires no developing bath. — ifaduro (Negative Brown Proc-
ess) Paper and Cloth, requiring ouly a fixing bath; 30, 36, and 42 ins. in width.
From Maduro prints on thin paper positive blue or brown prints can be taken.
Maduro is the latest.
Proflle Crosa - Section and Tracing Papers.— -Tracing and
Drawing Cloths printed in red, green, orange, or blue.
Oross-Seotion Papers.- 10X10, 16X16 per inch, 5X5 to the half-inch,
8x8 per inch millimeter, 12X12 per inch, all in sheets about 16X20 ins. 10X10,
x6Xi6 millimeter also continuous in rolls and in the usual variety of colors, and on
Tracing Paper, Tracing Cloth, and Drawing Clolh,
Traoing 0\ot\\B.— Excelsior, extra fine, very transparent, 30, 36, and 4a
ins. in width. — Imperial, both sides glazed or one side dull, 30, 36, 42 ins. in width,
and one side dull in 48 and 54 ins. in width. — Sagar''8, 30, 36, and 43 ins. in width.
— Dowse'' s, 30, 36, and 42 ins. in width.— Tnton, thick, for coarse tradings, 30, 37,
40, and 43 ins. in width.
NoTK,— A complete cntalogrue of Drawinf^ MnttriaU und Surveying loitramtnts, 660 pp., mailed
on application, . , .
BEFB16ERATION. ^6$
Adeoliaxiioal Refrigeration.
The De La Vergne RefHgerating Machine Co.y New York.
]MecfaLaiiica.l Refrigeration, is effected by Compressionf Condensa-
tion^ and Expansion of a liquefiable gas.
The Kefri^erating or Heat-absorbing agents are Ammonia, Ether, Sul-
phurous Oxide, Carbonic Acid, etc., which undergo the operations above
given. The De La Vergne Machine is operated with Ammonia.
Coixkpreseion. — The gaseous agent is compressed if Ammonia is used
to from 125 to 175 lbs. per sq. inch; during which operation heat is devel-
oped in proportion to the pressure exerted upon the gas, or the relative vol-
ume to which it has been reduced.
Condensation. — The heat developed in the operation of compression
is withdrawn from the compressed gas, which is forced through coils of
metal pipe, surrounded with cold water. As soon as the condition of satura-
tion is reached, the gas assumes a liquid state.
ICxpansion. — The liquefied gas is also passed through coils of metal
pipe, suspended or seated in a space where the substanee to be cooled, as air,
water, brine, beer, etc., is introduced ; the pressure in the interior of the coils
being at a lower point than that required for the maintenance of the gas
in the liquid state.
The liquefied gas, upon entering these coils, again expands, and extracts
from them and the substance around them the same quantity of heat that
was previously given up by the gas to the water of condensation.
The gas, having passed through this routine of operation of refrigerating,
is now m a condition to be used in a repetition of it.
The gas is forced through these coils by the pressure in the coDdenser, which, in
the use of Ammonia, is generally from 125 to 175 lbs. per sq. inch. Under this
pressure and the cooling action of the water, liquefaction occurs, and the resulting
liquefied gas flows to a stop-cock, having a minute opening, by which the pressure
is reduced from 10 to 30 lbs. per sq. inch in the expansion coils, and where the
liquid through reduction in pressure is again transformed into a gas. By the ex-
hausting operation of a gas pump, this pressure is maintained, and then the gas iEf
forced by compression into the condenser again.
Thus the expansion coils, although similar to those for condensation, are operated
for the reverse, which is the absorption of heat by the liquefied gas, instead of the
extraction of heat from it.
In Operation, heat is transmitted from the outside through the walls of the ex-
pansion or cooling coils, and is absorbed by the expanding liquefied gas withiu such
coils. This heat is Dorne by the gas through the pump into the condenser, where
it is in turn transferrred to the cooling water through the walls of the condenser
coils, and ultimately carried away by this water.
NoTV. — Uqaefied ammonta in ■ giiMoiu condiUon at atmoupberic precsare and temperature of 60",
•naadi about 1000 times, and upon ita ezpanaion re-absorba a quantity of heat equal in amount to t^at
originally held and OTolved frftm it during llqaofactioo.
The liquefied gas, entering the coils tL>rough the minute opening in stop-cock, is
immediately relieved of a pressure of 125 to 175 lbs., that requisite to maintain it
in a liquid state, when it boils and expaLds into gas. To obtain this, heat is re-
quired, and which alone can be supplied fh>m the substance surrounding the coils,
such as air, brine, water, etc.
As a result, the surrounding substance is reduced in temperature, the quantity
of heat withdrown by the gas being the same as that which was withdrawn flrom it
during its liquefaction in the condenser.
Consequently, if the expansion coils are set in an insulated space, it will be re-
frigerated; and if brine or any liquid surrounds the coils, it will be reduced in tem-
perature, and brine, in this condition led into a space through a pipe or open con-
duit, will refrigerate it.
in*
966
BEFBIGERAltON.— FOBCITE POWDER.
ResnltB of* Operation of H.eftrigeratit»g Mlaoliixiea
of 200* Tons.
At Lion Brewery^ New York. Duration of Test ii A 20 min.
Steam Cylinders.— D\a.meter, 36 ins. ; Stroke of Piston^ 36 ins. Pressure*
of steam (mean), 48.4 lbs.
Gas Compressors. — Two double acting; diam. 18 ins. ; Stroke of Piston^ 36 ins. ;
back-pressure, 38.22 lb& ; condenser, 180.78 lbs. persq. inch; BtoolutUms^ 39.55 pel
minute.
Test for cooling made by running water of a mean temperature of loags^' ovei
wort, Baudelot Cooler, and cooling same to a mean temperature of 50.77°.
Befrigeratum, equal to melting of 210 tons Ice per day of 24 hours.
Horse Power. — IH* = 313, and assuming consumption of coal at 3 Ib& per boui
per IIP, ratio of refrigeration = 20.84 lbs. ice per lb. of coal.
•
If operated under ordinary condensingpressure of 156 lbs., the IW would be 278,
and ratio 23.47 lbs. ice per lb. of coal ; 1& per ton of ice per day = z. 183.
Of a 26-Ton l^aohine. At Bohlen-Huse Machine and Lake Ice Co.^
Memphis^ Tenn. Duration of Operation 20 Days.
Steam Cylinder : Diameter, 22 ins. ; Stroke of Piston^ 28 ins. ; Steam, 93.49 lbs. per
84. inch. — Cfas Con^rensors^ Two single-acting: diam., 14 ins. ; Stroke cf Piston, 38
ins. — Revolutions^ 40 13 per min.— TemperaXures : Cooling water 63^', brine 18.62°;
coal consumed, 180597 lbs. ; Ice produced, i 221 172 lbs. — Ice-making, 26.83 ^'^ P®'
day of 24 hours.— Steam-boiler evaporated 5.5 lbs. water per lb. coaL
* All tons are giTen at 2240 lb*. See foot-note, p. zzri.
FORCITE POWDER.
A merican Forcite Powder M^fg Co,, New York,
ITorcite. — Is an improvement in Nitro-glycerine compounds, and it
presents the following elements :
It is less sensitive to shock than other explosives.
Assuming Dynamite No. 1 as (he Standard ^=. 100.
Forcite No. X, 95 per cent Nitro-glycerine, 133 per cent, intensity.
3t40 " " " 95 "
* 3$ per cent, stronger than Dynamite No. i. f Within 5 per cent, the strength of No. x, 75 per cant.
It is more powerful than any other known explosive in our market
See Report of Henry L. Abbott, Lieut.-Col. E. U. S. A.
It is safe in handling and transportation, quintuple force-caps being ap-
plied to explode it, and free from noxious fumes. Water-proof, ftise from,
tiie absorption of moisture, and is not injured by submersion in water.
Directions in Use,
In Blasting, fill the hole, and thoroughly tamp the charge.
Thaw it, if frozen, as frozen powder will not explode with its proper eflfbct
Exploder or caps should be maintained dry, and are not to be stored in samo
buildings as the powder.
Powder, ignited by weak caps, instead of being exploded, emits noxious vapors.
Per Cent, of Nitro««grl3roerine in Srande of I^oroite.
Gelatine 95 I No. i 75 I No. 2 50 I No. 3 40 I No. 3 B m
N0.1X 8o| "aX....6o| "3X....45I "3A....35I »' 3C 30
SURFACB CONDENSATION. — ^RSFBIGSRATING. 967
SURFACE CONDBN8ATION.
W?i€eler Condenser A Engineering Works^ New York,
Constrviotion. — The Wheeler Condenser, alike to others for the same
purpose, is an elongated vessel, cylindrical or cubical, with the neftssary at-
tachments for Steam and water connections.
Its disting^uishing features are : The exhausted steam, upon entering the
condenser, impinges upon a perforated scattering plate, which distributes it
generally over the tubes and thus diverts the deteriorating effect of the direct
impingement of it upon one portion of the tubes ; the steam, expanding
in a void above the tubes, is reduced in pressure, and consequent temperature,
before it tlows into contact with the surfaces of the tubes.
Each pair of tubes is composed of an external and internal tube, set hori-
zontally, the inner tube having an open end, the other end being screwed
into a removable head or vertical diaphragm, which is set at a space of a
few inches from a like head, into which one end uf this large tube is screwed,
the other end being closed by a screw cap.
This design permits the tubes to expand or contract, without the use of
tube i)ackings or ferrules of any kind, as only one end of each tube is fixed.
The tubes are tinned both externally and internally, and can be readily
withdrawn for cleaning, etc.
Operation. — The tubes are divided into two distinct tiers ; the condens-
ing water flowing through the small tubes in the lower division passes out
of their open ends and through the annular space between their external sur-
faces and the internal surfaces of the larger tubes, and from thence into the
upper division, and through its tubes in like manner to the 8{)ace between the
two heads referred to, and finally out through the discharge pipe.
The circulation of the condensing water is by this manner of fiowing ren-
dered very active, and consecjuently a less volume of it is required, and there
is less tube surface needed for a required volume of condensation.
HeHults o<* an Operation to Determine tlie Kfflcienoy
of* tlxis Condenser, -with, and -witliovit a Vaonum.
Steam Condensed per Hour per Sq. Foot 0/ Condensing Surface.
Coiidenter.
With
Vacuum
V«c-
■um.
In*.
24.5
In
Water.
T«inp«ratarM.
DIi-
charfT*
Wat«r.
56.5
98
RMer-
Tolr.
DtifC'a.
138
Steam '
Coo- I
dented.
Lbs.
101.8
CondanMr.
Without
Vacuum*
Teinperatarea.
In- DU-
jsction ' chftrir*
Water. Water.
D«K't.
J78.5
Deg's.
139
Rsacr-
▼olr.
DeK'..
201
Steam
Con-
d«nMd.
Lba.
204.2
* Aa a tlmple surface condans«r without air pump attached.
REFRIGERATING AND ICE-MAKING.
A Refrigerating Machine is one that produces as low a temperature as a
given volume of ice, at the temperature attained, would in melting from the
temperature of the air, or void to be refrigerated := 142° (142.6°) of temper-
ature are required to transfer one lb. ice at 32° to one lb. water at 32°, which
difference represents the Latent heat.
In order to operate such a machine for the formation of ice, there will be
requireil, instead of 142°, about 236°.
Thus, Assume the water (Tom which the ice is to be formed to be of an average
irnnpemture of 72^; Ihen to reduce it to 32*^, before Ice can be formed, 40° or 40
thermal units are to be abstracted flrom each lb. of water; Uien 143° are to be ab*
Viracted f^om the lb. of water of 32 ^ to reduce it to one lb. ice at ^2^.
q68 befbigkbatinq and ios-making, btc, etc.
If the ice is produced at the general temperature of iS^', and the Specific heat of
it is taicen at . 5° ; then, 32 — - 18 x • 5 = 7^. To reduce this water from 72° to 32°
there is a reduction of 40° or thermal units from each lb. of water.
If ice is produced at 18°, Then 7° additional, as deduced above, are required.
In practice it is observed that the avenge loss of temperature by radiation of it
from the freezing tank, melting the external surface of the ice, to withdruw it from
the molds, etc., is fully 20 per cent, of the total capacity of the machine. Hence, of
the 236^^ which are to be abstracted from the water per lb. of ice, in order to reduce
it to ice, 47.3° are lost by radiation. And 40+ 142 + 7-1-47=: 236° are to be ab-
stracted from each lb. of water of 72^, in order to produce i lb. ice at 18°.
Consequently, If 142° are required in Refrigerating machine und 236° in Ice-
making, the relative requirements are as i to i .66 or as 6 to 10.
Refrijgerating Capacity- — Of a machine is designated by the
number of lbs., or tons of Ice, which it is capable of producing.
One lb. of ice at 32° absorbs 142 <^ or thermal units in melting. Hence, one ton
of ice absorbs 142° X 2240 =2 318 000 o, and a machine of 50 tons' capacity absorbs
318000° X 50= 15900000° every 24 houre of its operation.
Ice-making Capacity. — Of a machine is also designated by the
namber of lbs., or tons of Ice, which it is capable of producing.
To freeze one lb. of water at 72° to ice at 18°, it requires the absorption of 236°
viz.. To reduce one lb. of water at 72° to 32°, it requires the ahsorption of 40°, to
freeze it requires 142°; to reduce ice from 32° to 18° requires 14 x -5 = 7° (Specific
heat of ice = .5). Reduction of temperature from surface-of freezing tank and
withdrawing the ice from its molds by the application of heat, about 20^ of total
capacity of machine = 20^ of 236 = 47°. Hence, Total heat to be absorbed per lb.
of ice = 4o-|-i42-|-7-|-47 = 236°.
Ratio 0/ Capacity 0/ Refrigerating to Ice-making. — As 142 : 236 : : 6 : 10, as pre-
ceding, or a Refrigerating machine of 9.97 tons capacity will produce about 6 tons
of ice in the same period.
l^igliest £21evation. of a I^alze.
Colorado. — '* Green Lake" is 10252 feet above level of the sea and 300 feet in
depth.
Afagnifying.
Bavaria^ Munich, possesses a microscope that magnifies 16000 diameters.
r*ower of* Screw Bolts.
Results of an Experiment
Wrought-iron. — Diameter^ 2 ina Thread, V. Pilch, .22 ina
Mean Power applied at a circumference of 78.85 ins., 213 Iba
Loss by friction, 10. 19 per cent.
{Jos. McBride, M. Am. Soc. M. E.)
IDuration of* Railroad Cross-ties.
Du.ration. of* IfolloAving "Woods.
Wood. I Yean. Wood. Yeara. I Wood.
White Cedar. .
White Oak. . . .
Black Cypress
Wood.
Yeara.
Chestnut
Red Spruce
Red Oak
I'
5.5
Yevt.
8.75 Chestnut 7.5 Yellow Pine 6
8 Red Spruce 6 Hemlock 5.5
8 Red Oak 5.5 Tamarack 4
The elements of durability are Resistance to decay and to wear. White Oak com-
bines both qualities to the highest degree. Yellow Pine resists wear, but not decay.
Red Cedar and Black Cypress resist decay, but not wear.
Ties should not be cut when the tree is in leaf, and should be well seasoned or
preserved by some antiseptic process before being laid.
Proper draining of a road-bed will add to the duration of ties, andall indentations
of their surface by tools, etc. , should be avoided, and all spike-holes plugged to
avoid the absorption of water. {H. W. RecU.)
GAS ASi> ELSCTBIO LIGHTING. — BAILBOAD SPBBD. 969
GAS AND ELECTRIC LIGHTINO.
{In AddUifm to pp. 583-587). Gras.
Csuidle JPo^w^er and Coxisuixiptioti of X>ifierent Sixrners.
Candle Peww.
Burner.
Bats wing
Flat I from
Flame j to...
CandU Power.
No.
10
"5
13-8
Per Foot
per Hoar.
No.
2-33
2.5
3
CoosamH
tioo
per Hoar
per Lamp,
FeeU
4-3
4.6
4.8
Bamer.
No.
Flat
Flame'
In I
CIub)
ters.!
60
150
Per Foot
per Hoar.
No.
4
5.5
5
Coneaaip*
tion
per Hoar
per Lamp^
Kleotric.
Am Xjaxups.
Current.
Ampera.
6
8
10
Candle Power.
WatU
Unite
Horix'tal.
Angle ;•.
Angle to*.
Angle 20*.
No.
Annie 40*.
Required.
per
No.
No.
No.
No.
No.
Hoar.
93
175
207
322
460
300
•3
156
300
350
546
780
400
.4
220
420
495
770
1 100
500
•5
Feet.
«5
30
30
Relative
Coeto*of
Gas. Eleo-
tricsi.
3.67
3-77
483
* Per Candle Power for Batowing Bonier.
Arc Lighte should be set high and for the following causes:
1. Their high candle power and distance apart being in excess of gaslighta
2. Light radiating at a depressed angle is greater than when cast horizontally.
3. Horizontal rays are not as steady as angular.
N<yrB.>-The greatest intensity with continuous currents is at an angle of 40° be*
low a horizontal line.
T*o Deterxnine tlie Coefficient of Mlixximixxn Xjiglitlxi^
Po-^wev ill Streets.
L H -H D3 = Co. L reprf tenting candle power of lamps, D maximum distance
Jrom lamp, and H height o/lamp^ both in feet, and Go, coefficient.
Usual standard for Gaslighting is assumed for a unit of pavement 50 fbet dis-
tant for a lamp of 12 candle power 9 feet in height. Hence,
12 X 9 -J- 50* = .000864.
Adopting this coeffl<^ent, the following capacities of arc lights will give the same
standard of light at the following h«ight and distance.
A minimum standard would increase the coefficient to .001 728.
NoTK.— One arc light can replace from 3 to 6 gas-lamps, according to locality and
standard of light adopted.
a. — Arc lighting, based on the substitution of one light for 3.5 to 4 gas-lamps,
would double the minimum standard of light; while the average standard would
be Increased from 10 to 12 time&
{Eliminaledy etc, from Papers of Henry IMrinson, M.I.C.E.)
Xlailroad Speed.
1891, Sept 14. N. T. Central and Hudson River R. R.— From Grand Central
Station to East Buflalo, N. Y. 416 miles in 426 minutes, actual running time =
61 . 404- miles per hour. Weight of Train 230 tons.
From Station to Fairport, 361 miles in 360 minutes, there delayed by a hot JoumaL
1891. Philadelphia and Reading R. R. — One mile in 39.75 Beoonds=:the rate of
90 . 54 miles per hour.
" Flying Seolshman,** London to Edinburgh, 400 miles; stops, 44 minutes ex-
eluded, in 8 . 5 honn :£ 47 .05 miles per hour.
Weight of Trains excluding locomotive, 80 tonsL
970
TMJfACl'XY AHfH BS6I9TANCS QF BOLTS.
rrenaoitsr of* Round and Square "^^rouglit-Iron Solts,
Round — .75-incb,4riTen into a ho]a at .695 iQcti, in White Pine, for 12 iii&,
required 6875 lbs. to withdraw it.
I -inch, driven into a hole ot .75 Inch, <n White Pine, for 12 ins., requited io6it
Ita. (o withdraw it; and in Norway Yellow Pine. 10830 \i».
i-incb, screwed, S-tbreads per inch into a bole . 8125 inch, in White Pine, for z? in&,
required 15 125 lb*, to withdraw it, and oiie of 19 threads required 15 250 lbs.
x.iss-ins., driven into a hole of .875 inch, in Hemlock, for 12 ine., required 8875
Iba. to withdraw it.
Square. ^Tbe differeoo^ belween that and Round, under like conditions, was
essentially diStorent, and when a hole wa« bored 10 ins. in depth, tb^ diflferwoa was
not essential -
Rail-vragr Spilces.
te
Tf«.
4.6
Ctiettont.
Lbs.
3*64
To Withdnwr
Y. Pine. W. Cedar. W. OA.
Lbs.
3«98
3305
Lbs.
4330
Hemlock,
Lbs.
3485
Remarltt.
Iq solid wood, sharp pointed.
6hip Spikes. — 37^ inch square and 7 ins. in doptb, driven 3 in& in White
Pine and drawn back, required 1617 lbs., their edge wit^ the grain of tbe wood, and
1317 lbs. with it across.
iVbfe.— The above are dedueed ftom Experiments ef Gen. Weitzel, U. S. E.,
1874-77.
BemHance 9/ BoUt, afVer being 7 piontbis driven ;== xo per c?nt. greater than im-
mediately after, and when driven through in direction of flbre it fs but 60 per
cent, of that of being withdrawn.
Smooth bolts have greater retention than ngged, efther driven or withdrawn.
Moderate " ragging " reduces their power 25 per «ent , and extreme 50 per cent.
Relation between diameters of bolt and hole showed that the resistance of a fooU
of f inch in a .6875-incb hple was greater tbA« in ope of .75 or .8x25 inph.
With a .75-inch bolt the reBistaaoe was gveator in a hole of .625 inch, and waa
one quarter greater than in one of a sixteenth greater or les£k
One-inch square bolt is a .875-inch hole was the same as a roviid boU in » >6875*
inch bole.
Screw-bolts are about 50 per ceat. more elfective than ptoin rownd.
Long pointed blunt bolts are more effective than short pointed.
ExperimeBta of Mr. F. Cottingwood a«d Wn. H. Paine, made in connection with
construction of the New York and Brooklyn Bridge, gave for a i-inoh round bolt,
driven in a .9375-)nch hole, in best Georgia Pine, a resistance of 15 000 lbs. per lineal
foot, and in a .875-inch hole 12 000 lbs. In lighter woods the tenacity was less.
Mr. J. B. Tscharner, in the laboratory of the University of Illinois, determined
that a like bolt (^-inch round), under like conditions in WliKe Pine, was 6cxx> lbs.,
and that a bolt driven paraillel to the grain of ttie wood has but hadf of the reaist-
ance of that drivon perpendievlar to ft. Furtiier, that amuraiDg a bolt of i imeh in
a .0375-hole as I, that if driven in a .75-inch hole it would be 1.69, and iaa.tiss-
incn sole 2.13.
Relative IDriving Resistance of* Round and Sq.uare
Steel IBolts.
One Inch in Diameter. Drive into Pine Wood, Six Inehe$ in Depth.
S^u«re.
Diam. of Holes in Ins.
Power applied in Lbs.
Tenacity per Inch of Depth
"k
•9375
426P
710
.875
4660
777
.8«^
40S0
675
Konnd,
•9376
9250
375
.875
3798
633
.8125
4728
788
(/. ff. Powell and A- E, Uarwy).
Non.— Inasmuch as the amount of matal jn Um fiovnd bolta is but .7854 that
of the square, Round drift bolts «c« lb» Iwat «SpaA^iF«.
MOBTAB. — SPKXD OV YS8SBLS, KTO.
971
MIortar.
K rick.— Clean and Sharp Sand, 3 parts; Ume^ t part; laid in a bed saffl-
cientlj large to admit of the composition being in a thin layer.
In slaking the lime, apply sufficient water to prevent its baming. Stir rapidly
and thoroughly, in order to enable the water to cover each lump of lime as it deli-
q06Kes; and when this operation is flilly efiteted, stir the substance into a condi-
tion alike to milk, and then mix it with the sand in the bedt with water sufficient
to render the mass semi-fluid.
In this condition it should remain fbr a period of at least 94 hours— a longer pe.
riod is preferable.
When required for use, add and thoroughly mix with it another part of sand.
Hair Iilortatr.—Lay the hair on a floor and beat it, in order to break the
bunches and remove (breign substances. Then soak and wash it in water for «4
hours, to remove all glutinous matter.
Spread it on a layer of sand in a bed, add lime, and proceed as directed for Brtck
Mortar.
Uar^^e Xreea in A.i3.stralia«
In VidoriOf Eucalyptas.— One 435 and one 450 feet in height.
6peed of* Vessels.
To I^eterxnine the True Spe^d oraV^essel \>y ConBeoutive
and A.lternate Runs over a Pleasured Distance.
Asmme the Runs asfMoun:
3
4
5
6
MilM or
KnoU.
15.6
10. a
»4-4
ti
13. a
II. 8
xrt
RMuIt.
ia.9
14.3
la.y
13. 1
"5
ad
RMolt.
ia.6
12.S
13.4
ia.3
3d
Result.
ia.55
ia.45
ta.35
RMalt.
ia.5
ia.4
Mean
of RmuIIs.
ia.45 =« Trtu Speed.
62.5-7-5 = la. 5 Ordinary mean Speed.
NonL^The mean of second result Is sufficiently accurate for ordinary determl-
nattona
Velocity o^ tlie €7ui*fent.
To I^oterxnine the Valooity of* the Ourrent in ILiitie of
the Vessel's Course.
From the observed speed of the vessel deduct her true speed, and the difference
Is the velocity of the current
iLunmuiTioif Assume preceding runs.
speed.
Rua.
X
3
4
I
Obaerved.
15.6
10.1
»4-4
II
13.3
II. 8
True.
' ■ » « «
ia.45
3-15
3.35
x>45
.65
Milee or Knotk
With the vessel
Against da
With do.
Against da
With da
Against da
Relative Corrosion of Wrought Iron in 8ea Water.
In Air i.
In contact with brass 34 i iQ contact with lead 5.5
" " copper 4.9) »' " gun-metal ©.5
In contact with tin. 8.7.
972 PILE-DRIVING. — RiNGrNG ENGIITB.
PILE-DRIVING.
{Continued from page 672.)
Xo Comp-ute Weight of R,a.xn. {MoleavHyrth.)
P ( — T-| — 1 ) = H. P rqareseTiiing weight of pile in lbs., h height of fall ofram^
ftp
and L Urtf^k of pile, both in feet, and A <wea of section of pile in sq. inis.
Piles are distinguished according to their position and purpose: thus,
Gauge Piles are driven to define limit of area to be enclosed, or as guides to
the permanent piling.
Sheet or Chse Piles are driven between gauge piles to fmrm a compact and
continuous enclosure of the work, and are driven as close and uniform to
each other as practicable of attainment, and the interA'ening space or joint,
however close, is made water-tight by the introduction of a " feather " driven
in a groove on the sides of the piles.
Ci-ushing. — Crushing resistance of a pile, unless of verv hard wood, should
not be estimated to exceed a range of from 500 to 1000 fbs, per sq. inch.
Refused of a pile intended to support a weight of 13.5 tons can be safely
taken with a ram of 1350 lbs., falling 12 feet, and depressing the pile .8 of
an inch at final stroke.
Pneumatic Piles.— A hollow pile of cast iron, 2.5 feet in diameter, was depressed
into the Goodwin Sands 33 feet 7 ins. in 5. 5 houra
Water Jets. — A stream of water )s ejected under pressure at the point of a pile,
and, rising around it, removes the end and surface resistance, so that it will be more
easily driven. Suited for sand or fine soil.
XasmyWs Steam Pile-hammer has driven a pile 14 ins. square, and 18 feet in
length, 15 feet into a coarse ground, imbedded in a strong clay, in 17 seconds, with
20 blows of ram, making 70 strokes per minuta
Shaw's Gunpowder Pile-driver is operated by cartridges of powder on head
of pile, which are ignited by fall of the ram. 30 to 40 blows per minut«
have been made under a fall of 5 and 10 feet.
Slieet lulling.
Bevelling 120° 1 Shoeing a^
To Coxupute Coetfnolexit ocf Resls^tauoe of th.& KartK.
—— = (X R representing resistance of the earth, h height offaU of ram, and d final
€L
depression, both infect.
I^inging ICngine
Requires i man to each 40 lbs. of ram, which varies from 450 to 900 lbs.
To Color Srasa (Copper and. Zino) Slue,
Mix in a close vessel 100 grains t= 6.5 oz. Troy, of Carbonate of Copper and 750
^ins = 4.o6 lbs. Troy, of Ammonia; shake until solution is effected and then add
distilled water; shake, and the solution is ready for' use.
Keep it coo) and elTectively stopped. If deteriorated, add a little Ammonia.
Articles to be colored, to be perfectly clean, suspended in motion in the solution;
remove tberefh)m in n-om 2 to 3 minutes, wash in pure water, and dry in sawdust
or like effective material.
Expose during the operation as little to the air as practicable.
Other alloys, as copper and tin and argei&tine, are not available.
{CJiemical JoumcU.)
SI^BBL SPRINGS. 973
STEEL SPRINGS. (Additional to page 779.)
To Comptxte Safe Blemeiits of Springs.*
.8Z3 /Dbt^n .813 ,/Jii -8^3 bt'n
FiT^-^' V~^8~"-'' d73^-^' V^ftli-'' 0673-"' 1T"~
D repr«<en<t7i0' deflection and t Uiickness 0/ plates, both in t6f^ of an inch; I length
of span or bearings when weighted^ and b breadth of plates of springs, both in ins.;
n numlter of plates, and L load or stress in 1000 Ws.
NoTB.— The plates are assumed to be similar and regularly formed.
Illustration.— A£su mo a sprmg of the following elements :
^ = 20 and b = i ins., t = ^ i6f^, n = 5, and L 24cx> lbs.
.8X203 ^6400^ , /6.66X 3X43X5, 3 /64°o_.^^.^ .
3X43X5 960 'V .8 -V .8 ""^ ****•'
3/ .8X2o3 ^,76400^ ^. -8 X 2o3 ^640o_
V 6.66X3X5 V ««> ' 6.66X3X43 "80 ^'
.8 X w3 6400 , .^. . 3 X 4' X 5 240 ,K
= - — = 3 + »««. ; - — - — - = -^ = 2.4 1000 ihs.
6.66 X 43 X 5 2133 ^ ' 5 X 20 ic»
NoTK.— When buck or short plates arc added, they are to be added to the number
of plates if of the ruling breadth and thickness.
When extra thick back or short plates are added, they are to be represented by
plates of ruling thickness having an equivalent resistance, prior to computation by
formulas for D and L, and are thus ascertained: multiply number of additional
plates by cube of their thickness, and divide product by cube of ruling thicknesa
Illustration.— Assume as preceding, thickness of p]ates=4 i6tb8, number of
litem 5, and 3 extra plates of 5 i6thi to be added.
Then, ^^^ = ^ = 5.86 = no. of plates, and 5 -f- 5.86 = ia86, the no. of platet
of 4 i6<*« in thickness. la 86 X 43 = 695, and 5 x 43 = 320 j Aqc
3X53 = 375) ^^'
Hence, 3 plates 0/5 i6<A» added to the s of 4 i6<** = to.B6 plates of ^ i6«*«.
Conversely, 695 -f- 53 = 5. 56 pHaUs of 5 i6«*« are equal to Vie 10.66 of 4 i6rt«.
Helical Steel Springs.
d3 L /d3 L D , . /CtAD ^ C M D
= L.
C<4 ' V C ' V L d3
i^D additbn of .135 to ^ slu>ald be add«d to the diameter or square to compeiuate far a set of the
jpringi.
Safe Load. 3 / — = t jor round, and 3 /— = tfor square.
d representing diameter or distance between the centres of the rod or bar of the
spring, and D compression of the spring, both in ins. ; L load or stress applied in lbs.;
I diameter of rod or side of square of bar in i6<^ of an inch, and C a coefficient =. aa
for round rods and y>for square bars.
Illustratiox.— Assume as follows: <i = 7 ins. square; L=:3363 lbs.; t = i6 lis-
ieenths, and C = 22. t
73x3363^1253434^3.^ 4/73 X 3363 X. 8^^/. 441792 ^,6 ,6^
23 X l64 I 441 792 V 22 V 22 *
3/22Xi64x.8^3yi,53434^ .^. 22 X i64 x .8^x^53434^ 33^3 „^
V 3363 V 3363 73 343
The load and deflection obtained for one coil are each to be multiplied by the
number of coils for the respective total load and deflection of the spring.
A square spring is approximately equal to a round of like area.
• EumittoUy from T>. K. Clark's Manual.
074
HKHOBAinU.
Slaat I>rauslit in. .AoBh-pit of* a Marine Soiler.
Of Blower
Engliic.
Iff
I
I
Of
CoiU
Per IH* Coiuamod
Water
Bvapormted
Relatire
EagiiM.
per hovr.
per hoar.
per n». of Coal.
No.
LU.
LN.
U»,
FtrCnt.
57-5
3-7»
SX4
xO-77
f
88.8
3.26
290
8.83
1. 186
100.5
3.12
314
8
1.05
106. r
?04
323
7.89
1.086
118. 8
a- 93
348
7.83
1. 172
1 19. 8
3.12
374
7-53
1.179
I. J 58
127.9
3'»
399
7
135-7
31
421
7-03
X.283
No.
Natural )
Draught / '
.96
3
a
4-2
5
6
7-4
When the Power toas Doubled. — ^Tbe fuel consumed was as 1.5 to x, the watei
evaporated as .73 to i, and the saving of coal was 19 per cent.
An average of the above results gave a saving of 15. 8 per cent.
By trials in the R N., it was ascertained that a blast draught increased the power
of the engines 53.5 per cent, and the bgilers 65 per cent, per ton of their weight
ITirBt SteamxXuaunoU*
*'SwnTRf(ART.''--W«8 built at the Navy Yard, New York, in 1837.
Lengthy 35 feet; beam. 4 35; depth, 1.83.
Engine, vertical cylinder beam, 4 ins. in diam. by 12 Ins. stroke of pistoQ.
Water-wheel*, 4 feet by lo ins. Boiler, horizontal Are tubular.
On her trial trip she was saluted by steamboats and a^emblages of people '>n
ferryboats and on the piers. Designed by and constructed under the direction of
the Author.
Searingfs vritb-out XiUbrioants.
Graphite or Plumbago— \b the essential clement in dry bearings.
^^ Fibre ^apAtfe '*— Consisting of finely-powdered plumbago mixed with moist
wood fibre, is pressed io a mold of the required form, tboo saturated with a drying
oil and oxidized in a hot dry air.
NoTB.— Thi> hearing * has beoa faTorsbly repertad on by a oooiiaHtae Vl the Franklin Inxtltote.
'' Car6oui{" — Is carbon mixed with finely-powdered steatite; its specific gravity
= 1.66, that of carbon being 1.48. It can be molded, turned, bored, and shaped to
any form.
NoTK.— The coefficient of friction with dry bearings is lower than thai of many oil
bearings in good condition.
Tests for Wat«r.
(A^itional to page 852.)
To A.soertain
Ij Hard or Soft. — Into a clean glass tube put a solution ot soap, add a si*, 'ill vol-
ume of the water, when, if hard, the mixture will become milky.
J/ Alkaline.— It will turn red litmus-paper blue.
^ Acid.— It will turn blue litmus- paper red.
If Carbonic Acid is preient— Equal volumes of it and lime-water will become
milky. Add a little hydrochloric acid to the mixture and it will become clear.
IfSulvhaU of Lime {Gypsum) it pr«<en/.<.-^ Add to it a little chloride of barium:
if a while precipitate is formed, which will not dissolve when a small volume of
nitric acid is added, it contains the sulphate.
AiioliorijiK BoltB iii. Stone.
A test of the relative value of Lead, Sulphur, and PorUand Cemontu tv the re-
tention of iron bolts in limestone rock, give similar results.
— ■ ■ ■ ■ ■■«■■■■■ ^ ■■ .1 , I ■-■■■■■ »i ,. ■-^■M. I .^p^^^p— ., ^ I
* rhtltp H. HQlin«s paunt.
GATE VALVES. — HVPRANTS.
975
G^ate Valves. SdOy Vaivi 0»., WaUrfbrO, N, T.
Oato Val-v-es, Doable Seated, have foces set at a
slight angle to line of stem, and as the gates, in consequence
of their angular faces, cannot fill the space between the
valve-seats until they are ftilly down to their position, the
adhesion of them to the valves in their progress down,
f^om the interposition of sediment or other obstructions,
is not only not arrested, bnt they are Imfiracticable of
arrest iMfore belDg tnWy seated, and left imrtially open,
under (lie iuapressioQ on the part of the operator that they
are in position and the flow of the fluid arrested.
The valves are attached to the stem by an articulated ball
joint, hence they are rendered free to revolve, and their
fiB«es varying with that of their valve - seats, cutting or
grooving is measurably avoided.
The valves are two independent pieces, whereby a single
defect involves the repair or removal of but one of them.
The stem rotates In a screw-collar connected to the ball
Joint, and hence it is not elongated outside its glands upon
the rafaing of ibe valves.
DUm*
et«r.
In*.
•5
•75
I
«-5
2
3
35
4
4-5
5
6
7
8
End to
End of
Screw
SoclieU.
, 300 Founds* Test I>ressure
Hab-«nd VaItm.
All lt«ia for Gm.
Iron Body Braaa
Mountml for Wat«r.
Knd to
ValT«. 8cr«Wfd asd FbiMwd
End*. Stationary Sum and Quick-
<»p«iin|f Rack and Pinion.
lua.
2-375
75
875
375
5
375
.125
375
2.
2.
3-
3
4-
5-
5-
6
6.625
7
7-25
r 75
8.25
9
Face to
Face of
Flangre.
Diameter
of Stan*
dard
Flanirv.
Ina.
2-5
3
3-2S
4
4
4-6a5
5-5
5.875
6.25
7
7.25
7-5
7-75
8.125
8.5
•5
•75
•25
•/5
lua.
3
4
4
5
5
5
6
^•5
7.125
8
9
9
II
12
«3
25
5
5
5
Diant-
eter.
Ina.
2
3
4
5
6
8
10
12
14
X5
16
18
20
22
24
30
36
Bad of
Hub
End*.
ina.
7-5
10.5
12
12.5
«3.5
14.25
15.5
16
I7.
»7
\l
19,
21
22
25
30
25
5
75
IrosBeAy
wUhBrM
■ or BrMM monnM
Valval.
Screwed and l^lMi|ad Biuta.
End to
Face to
Face of
PlauKe.
Diameter
DteBv
eter.
Endaf
Sorew
of Stan-
dard
Sorliett.
Flange.
lua.
Ina.
Ina.
Ii».
2
5-5
5-75
6
2.5
6
6.5
7
3
7^25
7-75
7-5
3-5
7.5
7-75
8.5
4
8
7-75
9
4-5
8.$
8.5
9-»5
5
9
9-25
10
6
?o.2S
9'75
II
7
II
II
12.5
8
II
II
»3-5
zo
13-25
12
16
12
M-75
13.5
'9
>4
15
2Z
»5
15
22.25
16
16.25
23^5
18
16.25
25
20
»7-75
27^5
22
»9
29.5
24
20
3»-5
30
22.5
^8
36
26.5
44.5
P:ddy hydrants- Xddy Valve Co., Water/ord, ^'. F.
Dfauncttraof |
Pip* Con-
Stud
8e*t
neelian.
Pipa.
Rlntr.
Ink
log.
las. .
3 or 4
4-5
3
3 or 4
5-5
4
6
5-5
4
4 or 6
6
4-5
4or6
6.625
5
6
7.625
6
8
7.625
6
8 or 10
9-75
8
laa.
Na.
1
I
I
Noxxlaa.
Steamer and
la*.
9-S
a-S
a-S
steam-
as
a-S
laa.
In«.
In*.
«r.
Ina.
Ina.
No.
No.
No.
Na.
No.
Ntf.
No.
2
3
—
I
2
2
3
—
—
I
2
2
3
—
—
I
a
a
3
4
—
I
2
2
3
4
—
I
2
2
3
4
—
I
a
—
—
—
6
—
—
•^
Eddy Valves and Hydrants are Mo|>Ma bjr i^ if? Insurance Companl^
« • • •
976
MEMORAKDA.
{Continued from page 938.)
The available properties of Aluminum are its relative lightness, fireedom fh>m
tarnish, not being affected by sulphurous fumes and being slowly oxidized by a
moist atmosphere, its extreme malleability, its facility of being cast, Its high' speci-
fic heut and electrical and heat conductivity, and its extreme ductility.
Its transverse and torsional resistances are very low, its maximum shearing re-
sistance for castings laooo lbs., and forgings 16000 lbs. per square inch.
It is adapted for structures under water, can be welded by electricity and an-
nealed if heated and gradually cooled Just below a red heat. The tensile strength
of its wire is greater than that of its rolled metaL
Its properties are materially changed and impaired by atloyiDg it with small per-
centages of other metals, and its tensile resistance, relative to its weight, is in
plates as strong as steel at 80000 lbs. per square inch^ and ia cold drawn wire as
strong as it is at 180000 lbs. (Alfred E, Htmt^.)
Ad agn eaiuxn .
Specific gravity 1.74, is .33 lighter than Aluminium; is harder, tourer, and
denser; less affected by alkalies, and takes a higher polish.
Stair. ' •
Staff is composed of Plaster of Paris, water, and hemp fibre, the latter used to
bind the mass.
For ornamental pieces, matrices of hardened gelatine are used.
It resists the weather and even frost after being saturated.
Boiler Setting.
The fire-brick should be laid with very thin Joints, and set in Kaolin * or pre-
pared fire-clay, so thin that it is necessary to lay it with a spoon instead of a
trowel.
Every fifth course should be a header course. (*' Tfte Locomotive.''^)
GMue. — Its tenacity varies from 500 to 700 lbs. per square inch.
IfViotion. of Engines aTid. Oearing,
(In addition to pages 469-478, etc^).
Deduced from ExperimenU of Alfred Saxton, Manchester Assn. of En^neen.
Spur Gearing 25.9 per cent t Belt Driving 28.6 per cent
Rope Driving 29.6 " | Direct Acting 23.8 "
Engines 6 and 10.3 per cent.
Spur gearing gave the best result when not complicated with rope driving.
Rope driving gave best results at high speeds.
Bel^t driving for developing large power is only equal to an average rope-driving
engine.
Itelative Value of varions "Woods, tlieir Cr-usliixxK
Sti^eiigthi and Stififnesei 'being Combined.
Teak 9.4
English oak ... 5.8
Ash 5.1
Elm 5
Beech 4.4
Quebec oak. ... 4. i
Mahogany..... 3.7
Spruce........ 3.6
Walnut....... 3.4
Yellow pine. . . 3
Sycamore 3.6
Cedar i
Comparative Value of* I^ong Solid Colvixnus of various
Mlaterials. (Hodgkinson.)
Cast Iron xooo | Cast Steel.... 3518 | Oak 108.8 | Pine. 78.5
Hence, To compute destructive weight of an Oak or Pine column, take weight foi
one of Cast iron of like dimensions, and if for Oak divide by 9, and for Pine by ta.f,
* A variety of clay, one of tbs two ingnstUeuto in Oriental poKeXain} th« otliflr is tmutd la Chiiu
pttutue.
SPIBALLT BIVBTED IBOIT OR STBBt. PIPE.
977
Spirally Rivetecl Iron, or Steel Pipe.
Abendroth & Boat MJ'g Cb., Newburgh, N. T.
Spirally Riveted A£etal Pipe.
Compared with Wrought or Cast iron Pip«, has the advantage of low
original cost and expense of transportation, maintaining a nearly equal
bursting pressure with that made of heavier material. It is made of Sheet
Iron or Sheet Steel, varying in thickness from No. 20 to No. 12 B.W.G., ac-
cording to diameter and pressure. The rivets in
the seam are set by compression, while the laps
are thoroughly coated with hydraulic cement to
make it water tight
Cojtneotioiis. — When a moderate pressure
is maintained, these pipes, their ends being
crimi)ed, are usually connected by a cement joint,
as shown in the annexed cut.
When the pressure is excessive, a lx)ltcd joint is resorted to, as also
shown, and which is in effect a stuffing box or sleeve joint, dispensing
with lead calking, and admitting of a slight flex-
ure of the pipe.
For service connections the collar may be
tap|)ed. Wtien lead calking is required, the
inner ends c^ the pipe are reinforced by an iroa
collar.
Bursting Pressure.
. ,
u .
u •
w .
h
5*3
^i
^1
Par Sq. Inch.
u
Par Sq. Inch.
1^
Per 84. In^li.
ag
Par Sq. Inch.
55
h
1
55
Int.
Int.
Lba.
lot.
Lba. 1
lo*.
Lba.
Lba.
3
900 to Z300
6
350 to 800
10
275 to 650
16
190 to 400
4
7c» " 1000
8
350 " 825
12
225 " 550
18
>5o " 375
5
550 " 800
9
300 " 750,
»4
200 " 470
20
14Q " 325
|«*
1*
Per Sq. Inch.
■as
Ina.
Lba.
22
125 to 300
24
no " 27s
—
—
In order to enable an estimate of the relative cost of these pipes, com-
pared with cast and ordinary wrought-iron pipes, the weights of each are
submitted.
'Weishts.
Hm
h
Td
^t
Hei
8pi
1
f
|5 ^&
•a
^
>
5
^
ina.
Lba.
Lbe. Lba.
Int.
Lba.
3
a
7 5
>3
8
8
i
a-5
10.75
20
10
10
5
18.75
30
12
«3
S »
Tb..'
Lba.
a8
40
40
55
49
70
Spi
ivy
ral.
h
31
Hai
8p
■J
h
31
1
i
Lba.
Lba.
E
Int.
Lba.
In>.
Lbi.
Lba.
Lbt.
M
20
58
94
20
28
—
180
16 , 23
—
109
22
3«
—
aoo
18
26
—
160
24
33
—
250
• StaadanL
»4N
tUstit
978
OBAPHITB AND DRAWING PENCILS.
Grraplilte as a Xjubrioant.
Joseph Dixon Crucible Co., Jersey City, N. J.
Results of Comparative Tests of its Operation
"WitU best Sperm Oil and I*erfe©ted C3-raplxite.
Lubricant.
Best Sp«rm (MI
P«tfected Graphite*.
WciKbt
of
Lobrieaot.
Graina.
5- 16
1-75
PreMora on
bcarinf;
p«T 84. Incfa.
Lb*.
48
4»
RevolutioM
per
Miliutfl.
No.
2000
90O0
UnMof
Duration of
TMt.
MlautM.
11
30
Frictleoal
SurflMX In
8q.
No.
7198
1963s
* Mixed with water enough to distribute it orer the bearing,
NoTB.— Hence it appears that Graphite, under like conditioBs, presaany aad vdoeltj of opMvite,
was 2.73 times more effective than the beet Sperm Oil.
With, best Sperm Oil, Xj-ubrioatixig GH'ease^ and lllCA
G^reasci, ooiitaining; 16 per cent, of* Perfbot«d Ghrapli-
ite.
Lobrlcant
Lnibricant.
PiMsoreon
Bearing
per 8q. Indk
RcToIutions
Minute.
Best Sperm Oil
Lubricating Grease. .
Same mixed with)
tiraphite. ...«...)
Grains.
5. .6
5.16
5.16
Lbs.
60
60
60
No.
9000
2ono
aooo
Time of
DurfttfoD of
Tekt.
MinutM.
d93
Frictioaal
Surface In
Sq. Feet.
No.
33360
33360
19494*
NoR.-^The grMM «rfthottt Graphite ftave only like resnlto wllll the tearm 0B{ bat whea tlw |Ms
cent, of Graphite was added, the time of operation of the beariafl WM 5.» time* longer wlth«ttt ail>
ting and at the same velocity. IVw/*. it. H. TkunCon.
To introduce in Steam Cylinders. The method preferred by experienced engi-
neers is to mix the graphite with oil for the yalres and iivject by a small hand oil
pump attached to steam pipe. The graphite must not be too coarsely ground.
P»tre Chraphitcy mixed with oil, applied to a scratched or cut sorface, as cylinder
or piston rod of an engine, valve seat or journal^ will arrest the catting of them.
The selection of the perfectly pure involves the experience of an Expert, or confi
dence in the manufaotorer
IDrawing !Penoils.
Engineers, A^roliiteots, A.T^ists, «to.
Joseph Dixon Crucible Co., Jersey City. N. J.
Hexagonal in Section and I^urnislxed in Xen Ghradev
of JHardness.
Trade
Not.
210
211
2191
913
914
216
217
918
2x9
Grade Stamps.
vvs
V s
s.
8 M
MB
M
M H
H
V H
V VH
Character.
(B B B.)
(BB.)
(Band No i.)
(H B and No. 9.)
(F.)
(Hand No. 3.)
(HH.)
(H H H and No. 4.)
(H H H H and No. 5.)
(H H H H H H.)
NoT>w~-The first 5 numbers, cio to 3x4, are especially designed for Artiste.
M H is designed for sketching, V H for ordinary drawinga, and V V H for very fin*.
Very, very soft. .
Very soft
Soa
Soft medium....
Medium black. . .
Medium
Medium hard....
Hard
Very hard
Very, very hard.
Bimllaf gnde to the EnropMS
•tamp of
lOIfOKANDA.
979
^'bsorptioxi of Ct-eologioal Stx^ata.
Water in loo Parts or Per Oml. of Volume.
Material.
From Where,
Per Cent.
Avthority.
Gub^ro , Dnluth. Minn
.29
•42
•55
2.1
4 4
25
4.81
6.25
6.6
12.5
12.
36.5
11.6
ia.15
23.98
Geo. P. Merrill.
GraDite Hornblende
Limestone
St. Cloud, Minn
((
Quincy. Ill
t(
Rockford, 111
Bedford. Ind
0. W. Mead.
C(
t(
Dolomito
SftoitsloDe
Red Wing, Minn
Geo. P. Merrill
Fond du I AC, Wis
Fort Snelling, Mi up
Berca, 0
{(
D. W. Mead.
((
Jordan. Minn
Geo. p. Merrill.
Dry Ctoy
R. J. Htinter.
Sand and Gravel
(t
Red Sandstone
Gloacestershire. Kng
Cheltenham, Eng
ti
E. Wetherell.
Oolite Limestone
'* Sandstone
Supporting Po^ver of S^nd and Clay,
Per Square Foot.
Sand with Loam, 4 to 5 tons. Clay, 2 tons. Friction resistance of sides
should be neglected.
NoTK.— The walls of the Capitol at Albany, N. Y., at some points settled at a
weight of 2 ton&
To Compnte tlie K* of* Ropee.
Rule. — Mnltiply sectional area of it in square inches by its velocity in
f(p«t per minute and divide product by 330.
Bjumplb. — Area of rope, 4.2 sq. ins., and velocity 72 feet per minate.
4.2 X 72 -4-330;=. 916 H*.
I^ooflng Slates.
Streng>t1i ftud. Qvialities.
t4 by la tfu. and ,1875 fo .35 ins. in thickness.
Qtwrry.
Albion
Old Bangor...
Pleach Bottom.
Modnlnt
of
Rapture.
Specific
Gravity.
Poroeity.
7»5o
9810
II 260
2775
2780
2894
.238
•M5
.224
Corrodibil-
«ty.
Denaity.
DafleetloB.
.208
.169
.086
80
128
90
Modulus of Rupture, in lbs. per sq. t'ncft,
3WI
2&d2
= M. W iutruetive loa4 in lbs.,
I distance between the supports, and b and d the breadth and depth, all in inches.
Porosity, per cent. 0/ water ahsm-bed in 24 hours. Corrodibflity, per cent, of tfeight
lost in 34 hours in on aeid soUttion. Density, grains atyradM oy 50 revoluifpni of a
smaU grindstone ; and Deflection, on supports as inches apart, in inches.
Slates are finished in varisd dimensions, ranging f^om 6 x 12 io 14 x 24 inf In
Roofing, with a slats of 24 ins, , 10. 5 ins. are exposed, 10. 5 coverad by the slafe above
it, and the balance of 3 is covered by the two above it The slates required to cover
an area of 10 x 10 feet in the above manner is termed a Square, which Is the
Uoiik For slates 12 X 34 ina, X14 are rwmirtd to make a Sftuarp, and for 8 x 16
Ina, #77 are requirtd. {M. M0rrim9n, M, 4m, ^, C. J7.)
98o
SINOTS^ HiTGHBSy ETC.
In Aleolxaziioal and. Snsineering Operation*.
Slip-Knok Square or Reef Knot Flemish Loop.
Bowline.
Harline-spilce
Hitch.
Sheet Bend, or
Weaver's Knot
Carrick Bend.
Stevedore's
Knot.
Bowline on a Bight.
Water Knot.
Sheepshank.
Halt Timber Clove Rolling
Hitch. Hitch. Hitch. Hitch.
Cat's-paw.
Chain Knot with Toggle.
Timber Hitch
and Round Turn.
Black-
wall
Hitch.
Ftsh'^rman'8 Bend.
Short Snlica
Racking, or Bound Turn Round
Frapping. and Half Hitcb. Seizing.
Cask Sling.
Selyagee
StrapL
SYMBOLS.
981
SYlVtBOLS
For Slexneixts and Forxnulae, proposed \>y tlie A-vitlior.
For the purpose of inducing a uniformity in their expresxion (1891).
Angle. ^
Of Incidence z
Calorimeter Cal.
Grate Gt
Heating surface Hs
Section. . Sen, H, Lor T
Superficial Sup.
Square Sq. or Q
Square foot, feet . . D^b-
Atmosphere, -s At
Barometric Be
Breadth, -s b. b'
Centrifugal force Cf
Centre of gravity Cg
Circumference, -s.. G.c.c'
Coefficient or Factor. . Co.
Compound Cpd
Cube Cub. org)
CyUndrical Cyl.
Dead flat {g}
Depth, -8 dp . dp'
Departure Dpt
Diameter, -b D . d . d,'
Distances. Inch, -es. ins.
Feet ft.
Yard, -s Yds
Chain, -s Cbn
Rood, -8 {Id
Knot, •& K
Mile, -8 ^8
Millimeter, -s. mm
Centimeter, -s cm
Decimeter, •&..... . dm
Meter, -8 m
Dekameter, -a da
Helctameter, -a hk
Kilometer, -a. . » . . . . km
Myriameter, -a mr
Centare orsq. meter, -s Ce
Are, -a... a
Hectare, -a Ha
Draught of water Dw
Elevation, -s Kl
Energy E
Equivalent, V. S. or
French
Electric. Ampere, -a Am
Farad, -acOiMk cap. phi) 4>
Microfiira<l,-a(Gn«k pbQ ^
} Eq,
Henry, -s H
Joule, -8 J
Kilojbule, -s KJ
Watt, -8 wt
Kilowatt, -8 kwt
Millihenry, -s mh
Milliampere, -a. .... ma
Megohm (Gr««kc. omega) il
Microvolt, -s Mv
Ohm, -8. .(Ore«k oaugn) «*
Volt, a Vo
Evaporation, ive.... Evp
Foot pound, -8, tons Fp.Ft
Force F
Friction Fn
Gravity g
Height, -8 H . h. fa'
Sum, -8 — Sm
Tangent...'. Tan.
Cotangent Cotan.
Thrust... Tt
Time, -s T . t . t'
Second, -s.Sec. sec. or "
Minute, -s Min. min. or '
Degree, -s Deg. or o
Hour, -a Ho . ho
Day, -8 Da
Month, -s Mo
t'ear, -s Ys
Triangle, -a a A'
Triple Tpl
Unit, a Heat Hu
Calorific or French .'. Cc
Vacuum Vm
Horsepower IP ' Velocity V
Efftective KIP
Indicated IH^
Nominal NIP
IncUnation In
Joule's Equivalent jE
latitude Lat
Length, -s L.l . 1'
Logarithm I.x>g.
Hyperbolic . . . Hyp. log.
Longitude Lon.
Mercurial gauge Mg
Meridian M
Modulus of Elasticity . MB
Moment, -s Mt
Number, -a No
Ordinate, -a 0 . o . o'
Perpendicular Pr
Pitch, -a Ph.Ph'
Pressure, -a P p . p'
Quadruple Qpl
Radius^ -ii R . r . r'
Revolution, -s.. Rev. rev.
Secant Sec.
Cosecant Cosec.
Sine Sin.
-Cosine Cosin.
SHp Sp
Solid Sd
Specific gravity Sg
Span Sn
Stability St
Steam Stro
Stroke S . s
V = 3 1416
v V
Versed sine v-sin
Vertical Vt
Volume, -8 Vol. vol.
Chaldron, -a. Ch
Chord, -a Co '
Buahel, -a Bl
Cube foot, feet Cf
Barrel, -s bbl
Gallon, -8 gl
Microliter (Greek lambda) \
Milliliter, -s ml
Centiliter, -s cl
Deciliter, -s dl
Liter, -a 1
Dekaliter, -a dal
Hektollter, -a hi
Kiloliter or Stere, -a Kr
Water-line v. Wl
Weight, -a W. w. w'
Ounce, -8 oz
Pound, -a lb. . Iba
Ton, -8 (2240) Tons
" (2000) . . . —Tons
Milligram, -s mg
Centigram, -a cg
Decigram, -s dg
Oram, -a g
Dekagram, -a dgm
Hektogram, -a hgm
Kilogram or Kilo, a. Kg
Myriagram, -a y
Quintal, -a...... q
Miller or Tonneaa, -a Mr
982
MEHOBANDA.
Relative £fBoieno3r of a r?on-ooud*n«ins Steam-Bncixia
and a 13i-Sulpb.ide of Car'bozi (C Sa) ICns^ixe.
With like Engine, Boiler, and Fuel, as developed by competitive tests of both at
Riverdale, near Chicago, 1892-94.
Cylinder, 16 X 42 ins. Jacketed and with automatic Cut-off. Boiler, horizostal
cvlindrical fire' tubular. Grates, 21.6 sq. feet, and Heating surface, loaS sq. feet.
Fuel, anthracite; Combustion, natural draught.
Steam. — Coal consumed per z W per hour, 4*399 lbs.
C St.— •' " •* a.49 " =42.08 p«r cen^., or as 1 to
1.7a 4-) or 942.6 lbs. coal in each ton.
Alortar for "M-BMoixry ly^lO'Vir KrAeKing^point.
Anhydrous Carbonate of Soda, '^Sodium carbonate" (Na2C0 3), 2.3 lbs. per
gallon, dissolved in water, maintained at 86 <3, mixed with equal volume of water.
Mix the mortar with 25 per cent, more of this Solution than if pure water was used.
Hands of operatives should be protected, as with ludia-rubber gloves. Extra cost
35 cents per cube yard of masonry. Setting of mortar accelerated. It will set at
30 below freezing point as readily as at 10° above.
{Coen and Vive- Saint Lo IPy.) Mom. Rabat.
Freestone.
RetuU of a Seriei 0/ Test* of Comnedicid BrowntUme to Ruiit CfruAing.
Per Sq. Inek of Crou Seotion.
Portland stone 6222 to 10928 lbs Colt's Firearms Mfg. Go.
New England Brownstone Co. . 7843 '* 13 297 " U. S. Ordnance Dept
Portland Shaler and Hall 9330 " 13980 " " "
Hisliest Hailwasr in ICurope.
Brienzer BotMombahn. — Alps, 7886 feet at Summit level.
Greatest grade, 1 in 4.
Rack and PinipD.
Slevation in Feet of* Uooalities in tlie XJpper Alissit
sippi and "West of JL<ake Miioliisan*
{In addition to page 58a.)
Davenport, la 615 | AshIand,Bay City, Wis. 610
Dubuque, **■ 665
Ft. Madison, la 600
Independence, la 850
Keokuk, '• 618
Monticello, *'. ... 880
Appletou, Wis 658
Cedar 2000 years.
Cyprus 800 "
Elm 300
Ivy 335
Larch 576
La Crosse,
Milwaukee,
FL Ridgely, Minn.
Ft. Snelling,
Minneapolis,
St. Paul,
744
697
1330
820
856
831
Ft. Ripley, Minn 1130
Chicago, 111 715
Galesburg, 111 795
Ottawa, '* 500
Peoria, " 475
Rockford, *' 800
St. Louis, Mo. 571
A.e>e of Trees,
Lime xioo years.
Maple 516 '*
Oak 1500
Olive 800
Orange 630
Oriental Plane. 1000 year&
Spruce laoo *'
Walnut 900 "
Yew 3aoo
((
Alonolith..
(In addition to page 179.)
Wisconrin.—Ai World's Fair, 10 feet square at bsM, 115 in height, and 4 at apex.
A-ngle of Repose of Sartlx.
o Gravel, clean ^99
with sand.... 26^
Sand, wet a6°
dry 34O
R. E. AideMimorie.
The co-efflclent ^f mc^oQ = t»n. of degrees, as co-efflclent of shinfle = tan. of
Clay, dry 29°
damp, well
drained 45°
16°
wet.
Earth, vegetable dry.. 29'
moist 47O
Shingle 39O
39*' = .8e.
I
MICMOBANDA, 983
To Oontypute tfi^ f£* ot a "Wrouglit-iron SHa^.
Rule. — Multiply cube of diameter of shaft in its journal in inches, by
number of its revolutions per minute and divide product by 80.
ExAMPLB. — Diameter of Journal 17 ius.,and revolutions of engine 30. What Is
its IP?
17 3 X aa = 98 360, which -r- fio rs ias6. 35 ff .
To 33etemaiiie the South, "by the Motir-hand. of a "Watch,
bet'^p^een the Irlourei of 8 ^.I^. and 4r P.l^.
When the Sun is VisibUi.
OrsBATMw.<~<Point the hour-hand to the sua, and half the diaUace belwaan thai
point and tha figure is is the South.
Nora.— The greatwt tutor ti In latHiule 38*, and Is about 15* to* Atr Baai at 8 a.h. aad 15* te» iv
Waal at 4 p.m. Hmio* allawanoaa ara to ba oorvaapoodlagly aiMa.
Ci-reateiit i:>epth8 »»»d £leis^ts»
{In a4iditi(m to pp. 179-184.)
Greatest depth of Ocean, Pacific 28000 foal
Deepest Well in North America, Wheeling, Va 4 560 '*
" Mine in " Cotnstock. Nev 3000 •'
Highest Mountain in North America, St. Elias 18 ocx> *'
'* flkruoUre, Washington MonuBM»ni. sgo «
" Tide, Bay ofFundy 50 "
Tests for *%Vater.
(fn addition to page 851.)
If Hard. — When mixed with a solution of soap, it will be rendered milky.
If Carbonic Acid u prtsent. — When mixed with Hme water it will be rendered
Wtiky.
If Sulphate of Lime {Oyptum) is present— it'ix with a little chloride of bariHMK,
and if a white precipijbate is formed, which will not diasolve when nitric acid is
added.
Comparati-ve Tenaoitsr of Out and "Wire Iron Nwdlm*
In Lengths from 1.135 <o 6 ww-, and Driven in Bpruoe w4 Pine Timlber.
In Spruce.— The tenacity ot ordinary cut nails exceeded that of wire 47.51 per
cent; of finishing, 72.22; luad of Iwx, 5a 8S.
In fViM.— Box aails taper perpendicular to grain of wood 125.2 per cent.; paral-
lel to it, 100.33; '■'^d driven in end of wood, 64.38.
Average of 58 series of tests, with 40 sizes of nails, 72.74 per cent
Maj. J. W. Reitty, U. 8. O. D.
»jf Wm. H. Burr^ a B.
Uydro-Greology.
U. a. Census Report, Vol. JTVII.
Upper MlspourU— The average annual Discharge of the principal tribn-
taries of it, to the precipitation on the basin == joS per cent.
Upper ^liHsinsippi — Average annual Kainfall in it and in the valley
west of Lake Michigan, 33.7 inchea
Avarafa flow per aeoo^d per square mile of drainage araa, .701 cube feet.
Klevation of ordinary low water at its extreme souree above the Ocean, 1680 feet
Draiaafe araa above moath of Missouri river, 969000 squave milea
J. L. Gresnleti/, C. X.
Cost of an Sleotrioal IP.
Avaitahte W, 84 per cent of Indicated. Coal at $3.75 per Ton.
Coal, 64 cents. Wages, water, etc., s6 cents.
Alea, Siemens, M. I. C. X.
984
MEMOBAKDA.
Capacity of Grirders and Floor Seams.
Loaded in their Centre, — Girders of single span of Georgia or Yellow Pine,
lo ins. in breadth, 12 ins. in depth, and 10 feet in length between its sup-
ports at both ends.
The mean rapacities of the woods in ordinary use in the floors of buildings for
one inch square) and one foot between supports are as follows:
Lbs-
Spruce 550
Canada Oak 560
N. E. Pine 500
Lbs. I Lbt.
Georgia or Yel. Fine. . 830 I White Pine 500
Hemlock 450 1 White Oak 650
Chestnut. 480 I Ash 900
In the computation of the strength of posts, girders, and floor beams in baiid-
ings, it is impracticable of assured safety at all times to assume their strength at
their mea*v value as determined by experiment, inasmuch as allowance is to be
made for defects, as knots and shakes, fungus growth and dry rot Hence a Factor
ofzafety or a deduction of capacity in each case must be resorted to.
In the case above given, the strength of the pine is assumed at 850 and coeffi-
cient of capacity at 4.
„ 10X122x850 . „ .30600 . „
Hence, — — = 30 600 Un. and = 3060 lb*»
4 X xo 10
If Uniformly Loaded^ this result would be doubled.
Sstimate of .'Paiai.t Required, ibr Open Iron "Worlc on
Bridges, etc.
First coat, .625 gallon per ton; second coat, .375 gallon.
(21 J. Sioijl, a K}
To Compute lr!P of a Stream of "^Vater.
When Maintained at a Uniform Height.
Illustration.— Assume section 22 sq. feet, velocity of flow 5 feet per second, and
&AI 25 feet.
22 X 5 = no euhefeei ttnUer in volume per geoond. no X 60 X 62.5 := 4x2 500 26s.
water per minute.
Then, *'^^°° — ^ = weight 0/ wcder in lbs. -f- 33 000 = 312. 5 theoretical W per
33000
minute, from which is to be deducted loss of efficiency of instrument of applica-
tion, and which are given. (See pp. 561-580. )
Assume a Turbine wheel at .7 of efficiency. Then, 312.5 X • 7 = 218.75 effective W.
If the surface is maintained (impounded) at a uniform height, the power of it,
for the period of working hours, will be 2x8.75 x 60 x N. N representing the num-
ber of hours.
The result, then, for a period of 10 hours would be 218.75 X 60 X 10 = 131 250 W.
If a stream has a supply equal to the expenditure of it, it will overflow in the
Intervals between working hours; but if it is unequal to the operating volume or
consumption required, there must be a storage reservoir, and the greater the
area of it the less the decrease of the head or level of it, when being drawn frouL
To Compute Slemeiits of a Flume.
2%e Volunu of Water, Area and Height being Given.
/ V y
- A y/^2 ghGss volume. I 2 n a 1 *^ agz=heighL V representing voihune in cube
3 V-CAy
feet, A area in sq. feety C co^fftderU of discharge, h height, and I length in fxL
Assume Volume 36.39 cube feet, Area 8 sq. feet, and G .6.
(-.6X8) ■^^4-33 = -6;^ = a'^»^'^^- -X 8 X \/64.33X3X.65F36.39»oliima
j^=i-=4i^ngthi Off --=- = 9 height.
MBMOBANDA.
985
Sfieot or Tappiiis of ILiongr-leaf Pine.
Late tests, conducted by the U. S. DepH of Agriculture, of 32 trees, have conclu-
sively evidenced that the timber of the Long-leaf Pine is in no wise aflected by the
tapping of it for turpentine. See Circular No. 9, Forestry Division.
Comparative Strength of Tapped and Untapped Long-leaf Fine.
In Founds per Sq. Incfi.
ConditioD.
Specific
Gravity.
Ten rile.
Trail srerM.
Crashing^. > Detmrive.
Tapjfed.
25 pieces, green . . .
dry
Z15 tests, mean... .
Untapped.
Z33 tests, menu
•759
.687
.76
•71
LIm.
15448
M757
15985
Lba.*
136
177
140
i4fl
Lbi.
4755
6627
5118
5661
Lba.
540
648
636
652
16429
* Oue inch squaiw and one foot in length, weight tupported from one end.
See Circular No. 8.
Tapped and untapped is known as "boxed" and " unboxed."
The pores of woo<l leading upward, or in the direction of its growth, facilitate
the Uow or passage of moisture in that direction. Hence, timber set inclined or
vertical, with the abut end up|)ermost and exposed to moisture, will decay at the
top more readily than if set with the abut down.
The effect of varying the set of wood is frequently observed in" the staves of a
cistern or tub, etc , some of them being saturated with moisture and others quite
dry.
ITo Compute "Weiglit or Flue etnid Xubuletr I^ariue
Steam Boiler.
To weight of the metal plates, as determined by tfieir area and thickness, add as
follows :
For Laps and Rivets. ~One lb. per sq. foot for each . 125 ins. in thickness of plate.
'* Bolts^.Stays, and Braces. — 20 per cent, of total weight of the plates in lbs.
" Mean and HandhoU Flaies.^yso ^ icno lbs.
^otes on. Portland Cement and Cement JMortars.
{In addUion to pp. 515, 589, 871, 907, 958.)
Cements that harden rapidly produce a brittle texture ; they should increase in
strength with uniformity. The strength at terminotion of one day should not ex-
ceed 45 per cent, that of the seventh day.
The addition of Sulphate of Lime and Gypsum to American Portland cement in-
creases the strength of the cement; with 3 per cent, of the former il increases it
64 per cent. ; from that it diminishes the effect; and with 5 per ce*t. of the latter
it increases it 33 per cent.
To English Portland cement 2 per cent, of Sulphate of Lime increased It 60 per
cent
Dry Sands.— Standard— Weight. 92 lbs. per bushel, and its voids are
47-5 PC*" cent. Natural or Bar. — 103 Um., and 41.25 per cent.
Requirements and Specificatunu. — Tensile Tests.— An average of 5 briquettes in
each case.
Fineneu.—qj.s per cent, through No. 50 sieve, and 87.5 through No. 100 sieve.
Specific Gravity. — To exceed 3.
Homogenefms.—D\aca, 3.5 ins. in diameter, and .375 thick at centre, tapering to a
sharp edge at the circumference ; they should not crack or warp.
Samples.— Ten per cent, of the quantity selected at random.
Tensile Strength.— lAm\t of results, 10 jier cent.
For Exposure in Salt-water. — Initial set with fresh-water not to exceed ten min-
ntea.
10
986
MSMORANDA.
ikl>«orptiv* Ponnrer of Okarooal*
Of Fint Boxwood. J3y VoluvMt.
Aimnonts 3:0
Carbonic acid 35
Carbonic oxide 9.4a
Carburetted hydrogen 5
Hydrogen 1.75
NUrottS oxide. 40
Oxygen 9.9$
NUrofeiL. ...•• 6.5 |Saly'dbydr(^ea... 55
Pop Safety and Relief "Valves. Crane Co., Chicago.
BUAB8.
H. P.
IRON BODY. BRASS SB AT
No.
3to 6
6 " to
10 *^ so
90 " 30
30 »♦ 40
40 " 75
it
Sq.FU
l<32
«.35
3-68
5-3
9.42
14.72
r
3-75
Ins.
«-5
3
3-5
4
4-5
5
6
H. P.
Mo.
40 to 75
75 " Joo
100 *' X95
125 ** 150
150 •• 175
175 " aoo
250 " 300
t
•«
li
£Sf
-^
Ifto
~5
05-3 -s
pS
>
S4. Ft.
Int.
14.79
3.75
21.9
4.375
98.86
4-75
3769
5.695
47' 7
6.375
58.9
6.375
84.83
7.125
Approved by U. S Board of Supervising Inspectors of Steam Ypssels. and
will be approved by all TiOcal Inspectors, on n bn«!}-» of On«^ s^iattre luc'i of area to
three squxre feet of grate surface. ,
^nierioan. "Woods.
With ike Order of their Strength.
Order,
i<
Ash, mountain, Pifvus Americana.. —
" Frax^inui pistacuefolia 234
" Oregon, Fraxinus Oregana... 210
red, " pubescens. .
white, " Americanum
priclcly, JTanUioxylum Ameri-
canum
Basswood, Li ndeo, Titia Americana
Beech, Fagu» fen-uginea 24
Butternut, Jufjlaws cinerea 205
Button- woo<i, Ctmocarpus ereeta. . . 76
Ceditr, while,*Z>t<M>ce(lnM decurrent,
*' red. canoe, Thuya gigantea.
Cherry, wild red, Prunus Pennsyl-
vanica
Cherry, wild blaolc, Prunus serUina
Chestnut, Castanea vulgaris
Cottonwood, Populus monilifera. . .
Cucumber, mountain, Magnolia acu-
minata 908
Elm, slippery, Ulmusfidva. —
** white, '* Americana.. 114
Fir, white, Abies grandis 280
Gam, sweet, Liquidambar styraci-
flua 222
Hemlock, Tsuga Mertensiana 87
Hickory, shell-burk, Cartfa aiba. . . 12
'* nutmeg, ** myritti-
coiformis x
105
29
949
300
119
150
Order.
Hickory, pignut, Carya porcina. ... 44
Iron wood, CyrUla racemijlora 305
Larch, hackmatack, Larix Ameri-
cana. 94
Laurel, big. Magnolia grandiflora.. 139
" white " glauca 170
LignumvitsB, Cfuaiactim sanctum. . . 143
Lime, wild, JTanthostyium Pterota.. —
Locust, Rwinia pBeudacaeits. 3
Maple, mountain, Acer spioatum. . . —
■ *■* sugar, hard, '•^ saecharinuvk
*^ Biiver, soft, " dasjfearpum.
" swamp, " rubrum.
Oak, black, Quereus tincUiria
'* live, '* vireni
'' white, " cUba
Pine, white, JVntM s^ro&tM. 332
'« yellow, •' Arizonica. —
•♦ pitch, •♦ rigida 168
•' scrub, " inops 914
Poplar, white'wood, Liriodendron
tuHjpifera. 215
Redwood, Stqwna sempervirens. . . . 946
Satinwood, jtanOmxylum cai-ifxpum 157
Spruce, wh Ite, Picea alba 163
Sycamore, PUUantu oecidentalii. . . 231
Tulip, yellow —
Walnut, bluck, Jufflans nigra. —
Willow, Salix Uemgata 394
21
56
X96
57
89
ELECTBIGAL. 987
I Sleotrioal.
CimpiUd l>y Prqf. A. E. KenneUy.
XJnits in Bleotrioal Ifingrlneering.
The faUowing units have bem legally adopted by the U, S. Oovemment, s^d Con-
gress, 1894:
XJnit of Hesistanoe The International Ohm, represented by the re-
sistance offered to an unvarying electric current by a column of mercury at the
temperature of melting ice* 14.4521 grammes in mass, of a constant cross-sec-
tioi»l area, und of tbe length one hundred and six and three- tenths centimetres.
"Unit of Current.— The Intfmalional Ampere, which is the one-tenth of
the unit of current of the centimetre gramme-second system of electro- magnetic
units, and is the practical equivalent of the unviirying current which, when passed
through a solution of nitrate of silver in water, in accordance with standard
specifications, deposits silver at the rate of .001 118 gramme per second.
XJiiit of* Eleotromotive Foroe. — The Intemaiionai Volt, which is
the electromotive force that, steadily applied to a conductor whose resistance Is
one international ohm, will produce a current of an international ampere, and is
practically equal to 1.434 times the electromotive force between the poles or elec-
trodes of the voltaic cell known as Clark's cell, at a temperature of xs** C, and pre-
pared in the manner described in the standard specifications.
TJnit of Quantity. — ^The International Coidomb, which is the quantity
of electricity transferred by a current of one international ampere in one second.
Unit of Capacity.— The IfUemaiional Farad, which is the capacity of a
condenser charged to a potential of one international volt by one international
coulomb of electricity.
Unit of T^orls.— Th6 Jouk, which is equal to io7 units of work in the
C.-6.-S. system, and which is practically equivalent to the energy expended m one
second by an international ampere in an international ohm.
. "Unit of I*ower. — The Walt, which is equal to io7 units of power in the
C.-G.-S. system, and equivalent to work done at the rate of one joule per second.
"Unit of Induction.— The Henry, which Is the induction in acircait when
the electromotive force induced in circuit is one international volt, while the in-
ducing current varies at one ampere per second.
The following list presents these nnits with their derivatives, and also other elec-
tro-magnetic units which are in use:
Resistauoe, Ohm. — Megohm, one million ohms- Begohm, one billion ohms;
Tregohm, one trillion ohms; Microhm, one millionth onm; Bicrohm, one billionth
ohm.
Current, >lmp«r«.— Bicro-ampere, one billionth ampere; Micro-ampere, one
millionth ampere; Milli-ampere, one thousandth ampere; Centi-ampere, one hun-
dredth ampere; Deci-ampere, one tenth ampere; Deka>ampere, ten amperes; Hecto-
ampere, one hundred amperes; Kilo-ampere, one thousand amperes.
£. "M.. IT*., Toft— Microvolt, one millionth volt; Kilovolt, one thousand volts.
Capacity, l^arod.— Bicrofarad, one billionth farad; Microfarad, one mill-
ionth farad.
Work, Jou^tf. — Kilojoule, one thousand Joules; Megajoule, one million Joules.
l?o"wer. Watt. — Kilowatt, one thousand watts.
Induction, ^enry. — Microhenry, one millionth henry; Millihenry^ one
thousandth henry.
Alagnetio F'lux, IKefrer.— Kiloweber, one thousand webers; Megaweber,
one million webers.
AAatsn^tio lieliiotanoe. Oersted — Millioersted, one thousandth oersted.
*' Intensity, Oauss. — Kilogauss, one thousand gausses.
AXaenetoxnotive F'oree, Gilbert —The O-ilbert is the M. M. F
produced by .7958 ampere-turn.
The Oersted is the reluctance of a cubic centimetre of air measured between
opposed parallel faces.
The Weber is the flux produced by a M. M. F. of one gilbert through a mag-
netic circuit in which the reluctance is one oersted.
The Ghauss is an intensity of one weber per normal sq. centimetre.
p88
ELEGTBTCAL.
Sjleotrioal. (BrUiah Association.)
H.esi0tanoe. — Unit of resistance is termed an Ohm, which represents resist-
ance of a column of mercury of i sq. millimeter ia section and 1.0486 meters in
length, at temperature o** C.
X 000000 Microhms = x Ohm.
I Microhm =5 ■ 1000 absolute electro-mAgnetic anits.
I Ohm = looooooooo " " " "
1 000000 Ohms = X Megohm or 10 «5 ♦' " <* *»
TCleotro-xnotive IToroe.— Unit of tension or difference of potentials is
termed a Volt.
1 000000 Microvolts. . = i Volt.
X VoU = loooooooo absolate electromagnetic units.
X Megavolt . . . = 1 000000 Volt&
Current. —Unit of current is equal to i AmperA^ or the current in a circuit
which has an electro motive force of i VoU and a resistance of one Ohsn.
Capacity-.— Unit of capacity is termed a Farad,
z 000000 Microfarads or io~9 absolute units of capacity = x Farad.
Heat. — Unit of heat is quantity required to raise one gramme of water ttom
''o C. to 1° C. of temperature,
Qiian tit3r. — Unit of Quantity, one CfouUmb, and Is the quantity of Electricity
transferred by one ampere during one second.
r
To X>eterxnine tbe Kast aticl TVest Aleridiaii.
Set up a rod vertically on a level area or plane in tlio approximating mer.Uian
and describe arcs, with a radius of about twice the height of the rod.* At any time
before M. mark the point in tbe arc where the shadow of the rod touches it, and in
the P.M., at the same length of time of before M., mark the point of the shadow on
the arc; remove the rod, and a line drawn through these points will give the true
bearing of E. and W.
1?o Coxxipute th.e Ixiorease o£ A.rea ojf a Circle or
"Volume of a Cul^e.
By Differential Calculus.
Circle, n x^=:u and 2 n x dx = du.
u representing area^ x radius of circle^ and du increase of area.
Illustrations. — i. Assume x 10 ins., and d x, or difference of radius, .05 inch.
Then, 2X3- 1416 X 10 X .05 = 3. 1416 sq. ins.
Circle of 10 ins. radius = 3. 1416 sq. ins.
Hence, . / - — - T - - = y/ 404 = 20.0997 ins. , the increased diameter.
V • 7°54
Cube, x^ = u and 2 x^dxtsidu,
2. Assume X side of a cube 22 ins. and d x increase of side .05 inch.
X representing side ofcube^ and du increase of volume.
Then, 3 X 12=^ X -05 — 21.6 cube ins.
Hence, •^'123-1-21.6 = 12.05 ins. the increased side.
du 3 da; .15 dx .05 ,, . .0125 _ ^ ,.^
— - - — = -^ =.- .0125 and - -= - ^- = .004166 and — — ~r = 3. Hence, tbe
u X 12 ar 12 .004166
cubical expansion is tliree times that nftfie linear.
— — — • — ■ — ■* ■
• Varyin;; with th« latitiiile of the location, as the more vertical the mu Uie gremUr the beiitht ol
thfl rod.
ENEB6T AND MOTION — KINETICS. 989
ICnergy and !M.otioxi.
The science of Motion is included in Mathematics, and is termed Kine-
malics; the science of V or ce^ Dynamics or Kinetics; and the investigation or
operati(Hi of forces in equilibrium, Statics.
All standards of Energy aud Motion are Units^ as the unit of liength may be an
inch, foot, yard, or mile, bul usually a foot ; that of Time a second, minute, hour,
or day, usually a second; aud Velocity by the number of units of lengths or opera-
tion in a unit of time.
Uniform Acceleraiion is the uniform increase or decrease of velocity per unit of
time or distance, but this increase or decrease of velocity is that whicli the force
produces in a unit of time ; hence -— =F. m representing unit of force, a unit
of accelei'alion, t the time, and F the force.
Illustration Assume a body moving at the rate of 50 feet per second, and at
the end of 10 seconds it has acquired a velocity of 75 feet per second, the increase
of velocity is 25 feet in 10 seconds, equal to 2. 5 feet per second in each second, or
2. 5 feet per second per second. *
2. Given a uniform acceleration of velocity of 40 feet per second per second;
what is the acceleration in yards per minute per minute?
40 feet perl ^40 x ^feet per min. per sec. > ^40X60'^
sec. per sec. f 40X60=* " " " " min.f 3 t 9 i
min. per min.
3. A train of cars 2 minutes after starting attains a uniform velocity of 15 miles
per hour ; what is the acceleration in miles per minute per minute?
15 miles per hour = .25 mile per minute, increase of velocity = .25 mileper minute
which occurs in 2 minutes.
Hence, acceleration = . 5 of .25 mile per minuie = . 125 milt per min. per min.
Kinetics.
Force and Mass.
If two bodies of equal dimensions and unequal weights be simultaneously pro-
jected with likeFe/oci^y, the heavier one will go farther than the lighter; but if these
bodies were projected with like Force, the lighter one would go the farthest.
The difference is in consequence of the difference^of the Mass or Matter, and as a
result it requires more force to stop the heavier body when started than the light
one.
In operation, there are two common Units of Mass, as there are two of Force.
The Poundal, or British absolute unit of force, is that which the action on a mass-
pound for one second produces in it a velocity of one foot per second.
The Dyne is that force wliich, acting on a mass-gram for one second, produces in
it a velocity of one centimeter per second.
Opk&ation. — If 15 poundals bear upon a mass of 70 lb&, in what time will it pro-
duce a velocity of 60 feet per minute?
I poundal = a velocity of i foot per sec. in i lb. in 1 second.
Hence, 15 poundals =3 a velocity of i foot per sec. in i lb. in — teamd.
70
15 poundals = a velocity of i foot per sec. in 70 lbs. in — seconds, and 15 poundals
= a velocity of 60 feet per sec. in 70 lbs. in ^= 280 uconds.
Hence, — r- = F, m representing unit offeree, v unit of velocity, t unit of time,
and F the force.
* Second per Mcond, Minute per minnte, etc., altboufrh nnaknal, )• proper. Thns, the enreetloii,
*' The train went with a velocity of 60 mliea per hour,*' is indefinite, as it may have gone at that rata
hat for a period of one minute, or 10 minntee ; wbereaa, 60 milea per hoar per aoar indicate* both the
rate of the velocity and of that per boor.
990 KINSTICS.'-raAB BNGINBS*
Impulse — Is when a force acts during a given time.
Thus, if a force of 5 lbs. bears upon an object during 3 seconds, 3 X 5 = 15 units
of effect, and — — = F, representing the number of units of impulse.
Momentum or Moment — Is the product of the number of units of velocity with
which the mass is moving.
Illvstratiom.— A mass of aoo lbs. is moved with a uniform velocity of 75 yards
per minute; during what time is a force of 80 lbs. required to arrest the mottpn?
7S X ^ 200 X 7^
>■ = 3-75 feet per second^ and -._^ = 750, which -i- 80 = 9.375 seconds.
2. A mass of 6.75 lbs. is acted ui)OU by a force of .5 lb. during 5 minutes ; what is
th« velocity acquired?
5 minute8=3oo seconds^ and 300-T-.5 (halfpouDd) = i5o units of impulse, and
^^ = 33. 2 feel ner McoRd.
6.75
3. A rod 8 feet in length, weighing 8 lbs., has a weight of 205 lbs. suspended fVom
one end and 60 lbs. from the other ; at what ))Oint in the bar will the effect of the
weights be equalized ?
By rule To Compute Position of Fulcrum, p. 624,
•OK 8
8-T- -r^ + i ;= — •= 1.8113 /ee<=dMtance of 305 Vbs. from its end. and 8 —
00 4.4107
1. 81 1 3 = 6. 1887 feet =. distance of 60 lbs. from its end.
Then, to include weight of rod—
205 -|-i.8ii3-r-6o-|-6. 1887 4-1=4- 1246, and 84-4. 1246 = i. 9396— /e«f = distance
of aos lbs. from its end, including its toeight of the rod. Hence, 8 — 1.9396 — =
6.0604 -\-feet =: distance of 60 lbs. from its end.
Verifcation. 205 4- 1-9396 X 1.9396 = 401.367 lbs., and 6o-|- 6.064 ~i~ X 6.064 -f- =
401.376 lbs.
GX& BNGINBS.
<3*as Kneines. Are divided into three types.
^^^ TlMoratleml. BllcUiiey.
I. Engines igniting at constant volume, without previous) _^
compression ) ^
3. Igniting at constant pressure, without previous compres- 1 ^ a
sion I ' — •'"
3. Igniting at constant volume, with previous compression. . . 3 = .34
In the first two types the cylindrical conditions are most favorable to cooling,
and a practical efficiency of .06 is attained. In the third the conditions for loss by
cooling are very favorable, and an actual efficiency of .17 is obtained.
The ordinary heat efficiency is 17 per cent of all the heat expended In ah en-
gine, and the highest obtained 25 per cent.
For powers up to 20 IIP, when gas is cheap, as in towns tod cities, it competes
with steam, as it is more economical and fnore convenient, and is most usually rs-
sorted to for a power of from 4 to 6 horses. Some engines have been constructed
and are in useof xoo H*.
Non-Coxxip7>e88ioTx HSngiixes. Are principally used for small power,
as up to .5 IP.
The pressure is applied only during a portion of the stroke.
In the I^eiioir the piston is moved only for about .5 its stroke, when it re-
ceives a mixed volume of gas and atmospheric air, which is ignited by an eleotrie
spark, the pressure rising to about 45 lbs. per sq. inch above the atmosphere. The
piston then is driven through the remaining portion of the stroke, and at the ead
of it the pressure falls to about 3 lbs.
The mean effective pressure being usually 8.5 lbs. per sq. lach.
OAS 8N<»IKfiS.
991
M.
n.
Reeixlts of* Operatiou of Thirtaen JKiAsixies of
Viire I>ifi«reut Ooustruccioos. ^
RMRlltB.
IIP
No.
Mean.
15-35
I^ast.
342
Extreme.
336
BH?
No.
1255
2.7
27-75
IIF
Cube feet.
22-21
16.92
30-9
Revolation
Heat Con-
per
per
vwrie4 iato
BiP
MiHntew
W«rk.
Cube feeL
No.
l*er cent.
28.05
180.7
17-43
23-58
132
10. s
33-4
223.8
21.2
This Type of engine \b heW to be -wasteftil of gas, as it consumes over 90 cube feet
of 16 caiidle-iwwcr gas per IH* per bour.
The Otto dc I^ati-s^v is a free- piston er atxnosoberic eogioe, admitting of
bigb piston speed and great cxpansiott, lieuce it is more ecQUonii^al.
An explosion of gus drives tbe piston upward, and by the projectile force of it
and the reduction of the temperature of tbe gas under it, a partial vacuum is
formed, the piston returning under atmospheric pressure.
In an engine with a cylinder of 12.5 ins. diameter and an observed stroke of pis-
ton of 40 ins. , 25 cube ffet of gas gave a maxitn.uiii gav^ preisure of 54 l)s. per sq.
inch, and a resuH of 2.9 per IH* per hour.
GompresHioxi JSix^iiies possess the advantage of furnishing greater
power with less vohioie and weigfai, as well as economy of operation.
The Otto. — It is a siog^e-acUog-pintoB engine, serving alternately as a pump and
a motor, and one explosion of gas is given for every two complete revolutions.
Opbratton. — The piston receives a volume or charge of gas and air, then returns,
compressing tbe volume into a space at end of its stroke, which mixture is ignited,
nnd Hie presavre ^erefeM foroes tip the piston, w)icn it i«turns with an exbanftt
valve open to fVee it from the forceand prodnots of combustion ; at the termination
of the stroke it is in position to receive a new charge.
Thus, one driving stroke of the piston is given for two revolutions of the rngine.
The Mean affective pressure^ with gas of 16 Ciindle-power, is about 55 to 60 lbs.
per sq. inch, the maxim«ai pressure of the explosion being from 140 to 160 lbs.,
and even up to 180 lbs.
In an engine rated at 6 fi? the coasimption of gas was 21 cube feet xvex IB?, .and
for brake W 29 cube feei.
The Clerk has a second cylinder, termed the charging, the function ef wfiieh
is to receive a charge of gas and atr at each stroke and deliver it into the motor
cylinder. The charge dispels the consaraetl gas of a previous operation and fills it
with mixture, to be compressed by the return stroke of the piston and ignited at
each revolution.
Tbe Me«M effective presmare ia an eagine of 12 IP is 65 lbs. per sq. incb, pressure
of compression 57 lbs., and maximum pressure of explosion 238 lbs. Gas consumed
24 ctibe feet of 24 candle-power per IH* i>er hour. One of oj^nch cylinder and 20
ins. stroke, at 132 revolutions per minute, developed 27.5 IH* per hour, or 23.2 IP
at the brake.
The Caxnp'bell and Midland, are of Chis type, and are alike to it in the
use of a charging cylinder.
Tbe Stoolcp-ut resembles it also, but the operation differs in the passing of
each charge ftom the gas pun»p, which is a combination of the motor -]»i8t»n, into
an intermediate reservoir, wbenoe it Mews out iato tbe motor cylinder and dis-
charges tbe buraed gas.
Three-Oyole engines are like the OUo in their operations, but give only
one impulse for every three revolutions, one extra doifble «troke being used in re-
ceiviBg a 'Charge of air and expelling it at the exhaust port, so that the comprea-
Bion space is cleared at each operation.
The eaxMrnt of tbeae eagiaes was kUMMm as iba Linfor^i those now in use are
the Or^n and tbe Barker,
992
GAS ENGINES.
The A-tkinson. Csrole gives an impulse at each revolution of the crank
shaft, and the piston, by a system of links, is connected so that it makes two out
and two in strokes for each revolution of the crauk-shafi, and one explosion is
given for each cycle of four strokes.
It resembles the Otto in using the same piston alternately for pump and motor
operations, but differs from it in making unequal strokes. This arrangement en-
ables the exhaust gases to be swept out of the cyUnder at every operation and great
expansion is obtained. This engine is held to be very economical, as in recent
trials it consumed but 22 cube feet of gas per brake W per hour.
(Ths Practical Engineer.)
The Crossley is a horizontal engine, with a single cylinder, and of nominal
powers from .5 to 30 B?, indicating from 2 to 85 ff : with double cylinders,^ ftom
16 to 170 IIP.
A 13 IP engine has developed 28 \W and 23 at the brake £= Z'2% of the indicated,
consuming 20 cube feet of gas per IIP per hour.
Hesults of* Xrials of* G-as Sug^nes.
Type.
Otto.
Clerk.
Beck.
IH».
No.
22.56
3- 4a
27.46
6.12
n>a ..^.
Heat
Revoln-
Gas per
Heat
Rerola-
1^ converted
*"^- 1 into Work
tiunt per
Type.
IFP.
converted
tions per
Minute.
into Work
Minnte.
Cube ft. Percent.
No.
No.
Cube ft.
Per cent.
No.
23.6
17-5
158.7
Griffin.
17.46
18.92
21.2
223.8
309
14.46
160.3
Forward.
5-54
20.79
19.3
—
20.39
I5-5
132
Fawcett.
11.49
18.4
19.6
—
20.67
21. 1
168.9
Atkinsoa
11.15
19.22
23.8
—
{T. L, JUaier.)
Results of* Trials of Crosslejr Sngixie iTvith. I.jOulcIoii
Coal O-ae.*
Pressures and Revolutions per minute. Pressures and Water in lbs., Ctas in cube
feel, and Efficiency and Heat per cent.
Power.
Revolutions per minute. . .
Explosions *' "
Mean initial pressure
Mean effective '■'■
Brake IP
Indicated H*
Mechanical efficiency
Gas per hour, total
Gas per IBP per hour
Gas per brake H* per hour.
Fall.
Hfilf.
160. 1
78.4
196.9
67.9
158.8
41.1
196.2
73-4
M-74
7.41
17.12
86.1
9-73
76.2
355-3
20.76
205.8
21.2
24.1
27.77
Power.
Water for cooling per hour
Mean pressure during
working stroke equiv-
alent to work in pump-
ing stroke
Corresponding IIP
Heat converted to work..
Heat rejected in jacket)
water. j
Heat rejected in exhaust.
Fall.
flalt
713
480
2.19
.58
—
22.1
ao.9
43a
41. 1
35-5
38
(D. K. Clark.)
I*ressures Produced, "by tHe lOxploeion of* Ghaseous
Miijctures in. a Closed Vessel.
Mixture of Air and Coal-Chis, TempertUure 64°.
Miztare.
6a>.
Volume.
1
I
Air.
Volumes.
5
7
Preesaret
per
Sq. Inch.
Lbs.
96
89
Mixture.
Gas.
Volume.
•I
1
Air.
Pressure
per
Sq. Inch.
Volumes.
9
II
Lbs.
63
Mixture.
Gas.
Volume.
I
Air.
Volumes.
X3
Pnssvre
per
Sq. Inch.
Lbs.
52
(2>. Clerk,)
• Set Xeport on Trialt of MXorafor BleeHt UghHngfor SoeUtf vf Art$f 1889,
t Maximum above the atmosphere.
DIMENSIONS OP BOLTS, NUTS. — ^TENACITY OF NAILS. 993
Standard. I>izxiensions of Iron and Copper Solts
and ^nts, TJ. S. Navy.
Sq.u.are and Hexagojaal Heads and Nuts,
J^nished,
From .25 Inch to 6 Inches in Diameter.
DiAMms.
BoiU
Effec-
tive.
Ina.
Ina.
•25
.,85
•3"S
•24
•375
.294
•4375
•345
.5
.4
•5625
•454
.625
•507
•75
.62
.875
•731
z
.837
1. 125
1.065
1.25
«-375
1. 16
i-S
1.284
1.635
1.389
«-75
I.49I
1.875
I.6I6
2
1. 712
2.35
1.962
a- 5
3.176
2.75
2.426
3
2.629
3*5
2.879
3 5
3-«
3-75
3-3»7
4
3567
4-25
3-798
4-5
4.038
4-75
4256
5
4.48
525
4-73
5 5
4-953
5.75
5-203
6
5-423
DiAMRIB.
Width.
Depth.
Effective
Area.
Be«d and Nut.
Head A Nat.
Hexagonal
HeuL
Hex.
Nut.
Hex.
Threada.
Hexagonal.
Square.
and
Square.
and
Square.
and
Square.
Sq.Iiw.
In*.
Ina.
Ini.
In*.
Ina.
No.
.026
9-16
23-32
•5
•'5 ,
•25
30
•045
ii'»z6
27-3«
19-33
19-64
.3«25
18
.067
25-33
31-32
ii-i6
11-32
•375
16
•093
29-32
I- 3-32
25-32
25-64
•4375
14
•125
I
1-25
•875
•4375
•5
13
.162
125
1.625
31-32
31-64
9-16
13
.202
I. 7-32
1-5
z. 1-16
17-32
.625
11
.302
I. 7-i6
1-75
1.25 ^
• 1635
•75
10
•4»9
1.21-32
2. 1-32
1. 7-16
23-32
.875
1
•55
1-875
2. 5-16
1. 5-8
13-16
1
•694
2. 3-32
2. 9-16
X. 13-16
29-32
1.125
7
.891
2. 5-16
3.27-32
3
1
1.25 •
7
«-o57
2.17-32
3- 3-32
3. 3-16
«• 3-32
'375
6
1.294
2-75
3- 1 1-32
2-375
1. 3-16
'•5
6
1. 515
2.3>-32
3.625
3. 9-16
1. 9-32
1.625
5-5
1.746
3- 3-16
3-875
2.75
>.37S
175
5
2.051
3- » 3-32
4. 5-32
3.15-16
1.15-32
187s
5
2.302
3.19-32
4.13-32
3- "5
1. 9-16
2
45
3-023
4- 1-32
4.i5-'6
35
»-75
2.25
4.5
3-7>9
4-«S-32
5-15-32
3.875
1.15-16
2.5
4
4.622
4.29-32
6
4-25
2.125
2.75
4
5-428
5.11-32
6.17-32
4-635
2. 5-16
3
3-5
6.51
5-25-32
7. 1-16
5
"•5 ^
3.25
3-5
Z§^7
6. 7-32
7.19-32
5-375
2.11-16
3.5
3-25
8.641
6.625
8.125
5-75
2.875
3-75
3
9-99
7. 1-16
8.21-32
6.135
3. 1-16
4
3„
11.329
7.5
9- 3-16
6.5
3-25 ^
4.25
3.87s
"743
7. 15-16
9-25-32
6.87s
3. 7-16
45
2.75
14.226
ia25
7-25
3.625
4.75
3.625
15-763
8.13-16
10. 25-32
7.625
3.i3-«6
5
2.5
17-572
9-25
11. 5-16
8
4
5.25
2-5
19.267
9.11-16
11.37-32
8.37s
4. 3-16
5-5
2.375
21.362
la 3-33
".375
8.7s
4-375 ^
5.75
a-37s
23.098
10.17-32
13.39-33
9.125
4. 9-16
6
3.35
For Rough Bolts and Nuts, add .066 to above dimensionB, and for other notes see
pp. 156-159.
Relative Tenacit^r of* WrougHt-Iron Out and 'Wire
M-ails.
Per Cent, of Cut and Wire Naiit,
Dimen.
aiona.
Spkccb.
Desiffoa-
tloo.
Per
Cent.
Dimen-
alona.
Ina.
J.25X4
Ina.
1.125X6
Ordinary.
47-5
X.125X4
Finish.
72.3
"•as X 4
X.135X4
Box.
50.9
«.2SX4
2X4
Floor.
80
1.25X4
DeaignU'
tlon.
Box.
Box.
Box.
Box.
Per
Cent.
135.2
loas
66.4
999
nirer.ilon of
Pmetratton.
• ■■ a «■ -> ■
In Spmce 40 tests of cat nails averaged 60 per cent.
In Spraee uid Pine combined the average was 73.7 per oeot
Taper porpeudlo^
ular to grain.
Taper parallel to
grain.
In end.
I In the three
\ wayg.
See p. 97a
(fTnk H. Burff CK.)
9^ COMPBESSION OF Al^
CoxMipre^^^d ap.d CoYnpression of ^tzAOspU^rio
Computations of IPlo-^r, Operation,' Bflfeot, l*o-W"er, etc.
For fuller information, see "Compressed Air," l)y Freclk..C. Weber, M.E., before
the Engineering Society of Columbia College, April 22d, 1806 ; Wm. L. Saanders,
N. y. ; also by Frank Richards, Mera. A.S.M.E. ; a lecture by R. A. Parke ; D. K.
Clark'0 Pocket- Book: $, treatise by W. C. Uuwin, iu V^ol. CV. of Proceedings of In-
stitution of 0. E. of Great Britain, and a treatise of The Norwalk Iron Works Co.,
etc.
Pressure and Xetnpeitature*
Under constant pressure the volume of air varies directly as the Absoluts
temperature. For constant volume the pressure is in direct proportion to
an increase in temperature.
Compression.
Heat and Mechanical energy are mntnally convertible ; when, therefore,
the piston of an air-compressing engine is in operation, heat is evolved
(theoretically) in exact proportion to the work performed, in the ratio of one
British thermal unit (B T U) for every 772* fu<^ pounds expended.
When atmospheric air is compressed, the degree of its comprrasion may
be indicated by a pressure gauge.
The heat evolved by the compression of air generates by expanding it an
increased resistance, and involves increased power to compress it. This
loss of power consequent upon the expansion of tlie air by the heat of com-
pression is so great that it is necessarily essayed to reduce the heat., and a
cooling medium is resorted to, to abstract it in the operation of compression.
The rate of increase of temperature of air during compression is not uni-
form, as the temperature rises faster during the primitive stages of compres-
sion tlian the later. Thus, in compresshig from i to 2 atmospheres, the
increase of temperature will be greater than in compressing from 2 to 3
atmospheres, ana in like ratios. The rate of increase also varies with the
initial temperature, as the higher it is the greater will be tlie rate of increaie
at any point of the compression. When air at atmospheric pressure and
0° is compressed to 15 lbs. gauge, the final temperature will be 100^, or an
increase of 100°. If at 60**, it will be 175°, an increase of xis°, and at 90°
it will be 210°, an increase of 130°.
The rise in temperature due to the compression of atmospheric air at 33^,
when it is reduced to one-fourth its volume, is given by Kimball at 344°.
TIm great reduoti(m of the temperature of oompressed air when it is dis-
charged from the compressing cvlinder, against a resistance, as the cylinder
piston vf an engine, precludes the economicji^l operation of using it expan-
sively alike to steam or any similar vapor. The available energy of com-
pressed air is that which it exerts against a resisting medium, in its increase
of volume by expansion.
When air is compressed, if it neither gains or loses temperature bjr com-
munication with any other body, the heat generated by compression, re-
maining and adding to it, the operation is termed AcUabatic conrnression.
When pressure is removed from compressed air and it expands wiuiout re-
ceiving heat externally, the air is termed to have expanded A diabaiicaUy,
If 'during the compression of air, it is maintained at a uniform tempera-
ture by thf reduction of it, coeval with its generation, the compression is
termed MhemcU. Hence when the air remains at a uniform tempera-
ture throughout the operation of compression or expansion, it is designated
as Isothermal,
■^..^■»^P*"»"~^^~»^*»-^"t»«— »«Wif»*w»WW»»^*i"^W^*«*ii^F^"^^H»^»#**
* JoaU't. L»t«r •zptriiMati put it at 77^
COUPBBHBIOtr OF AIB.
995
The specific heat of atmospheric air at constant pressure is .3 377. hence
the unit of beat tiiat would raise the temperature of i lb. of water i*^ would
raise the temperature of x lb. of air (i -f- .2377) = 4.307^.
(3.14X cube feet of air at 63*^ (table, p. 521) weigh i lb., and air. at 60*^
com|)ressed to half its volume evolves 116^ heat, and the specific heat of
air under constant pressure is .3 377, which x x 16 ss: 37.573 heat unittt, pro-
duced by the compression of i lb. or 13. 141 cui)e feet of free air into une-^
half its volume: Hence, 27.573 x 778 = 21452 foot IbH., and as heat and
mechanical energy are held to be convertible terms,
duced or lost by the compression of i lb« of air.
21452
33000
= ^5 H» pro-
"Voluxne, Adean Pressure, and 'Petnp^ratvire of* Ooxn-
pressed A.ir.
From % to 200 Lbt. and from 60° to 673°.
Air assumed cU 14.7 Ihs. and Temperature 60^.
Final T«m-
perator*,*
Air not
Cooled.
VOUIMB
09 AiB.
Prawnro
CoDsUnt
Not
in
LlM.
TauipMmtur*
Iao|o«rui»l.
Cooiikl.
A4iabatic
0
I
I
I
.9363
•95
• 3
.8803
.91
3
.8305
.876
4
.7861
.84
5
.7462
.81
10
•5953
.69
«5
.495
.6n6
30
.4237
.543
35
.3703
•494
30
.3289
.464
35
40
.2057
.2687
•42
.393
45
.2462
•37
50
.2272
.35
55
60
.■«io9
.■96I
.331
•3M
65
.1844
.301
70
• 1735
.288
P
,1639
.276
80
.1552
.367
85
•»474
.257
90
.1404
.248
95
.1281
.24
100
.232
»P5
.1228
,325
no
.1178
.219
"5
."33
.213
120
• 1091
.207
135
.1053
*203
130
.1015
.197
'35
.0981
.192
.188
140
•095
>45
150
.0921
.0893
.184
.18
160
.0841
.173
170
.0796
.166
180
•0755
.16
190
.0718
.154
300
.0685
.149
Constant
Not
T«fnu«rat«r«
lautluirinai.
Cooled.
Adiabatlc.
0
0
X
.975
1.91
B.78
8.8
3-53
3-67
4 3
4-5
7.63
8.37
1033
>i.5>
13.63
«4-4
«4-59
"0-34
17.01
19.4
17,93
31.6
19.32
23.66
20.52
25- 59
21.79
27.39
23.77
39.1 1
33.84
30-75
34 77
31.69
36
33-73
26.65
35.23
27.33
36.6
28.05
28.78
37-94
39.18
29-53
40-4
3a 07
41.6
30w8i
42.78
31.39
3i^98
43-91
44.98
3254
46.04
3307
47.06
33.57
48..
3405
49.1
34-57
50.02
35C9
3548
5'
51.89
36.29
53-65
372
55-39
3796
57.01
38.68
58.57
39-42
60.14
AlK PBK StBOKK.
During CoDipreaslon
only.
Oonalant
Not
T««par»tor«
CooUmL
0
0
•43
.95
:^
»-4
1.41
t.84
1.86
8.32
3.26
4»4
4.26
5-77
5.99
7.2
7.58
8.49
9.05
9.66
10-39
10.72
11.59
12.8
11.7
12.63
13-95
13.48
»505
»4-3
15.98
15-05
16.89
17.88
15-76
16.43
18.74
17-09
19-54
'2 7
20.5
18.3
21.22
18.87
33
'9-4
38.77
19.93
23-43
20.43
34.17
20.9
2485
21. 39
25-54
21.84
36.3
33.26
2681
22.69
23.08
3742
28.05
2341
2866
23-97
29.26
04.28
29.82
24.97
30.91
25-71 .
3«-o3
86.36 •
33-04
27.02
34- <*
27.71
35-02
600
88.9
98
106
«45
178
807
234
25s
281
302
321
339
357
375
389
405
420
432
447
459
478
485
496
507
518
529
540
%
570
580
589
607
634
64*
657
673
* Prodnead by oonpraailoB.
(Framk HicKardit'
990
COKPBB6SION OF AIB.
For detennination of absolute preesare add 14.7 lbs. to gauge preasitre.
Column 3 gives the volume of air (initial = 1), assuming that its temperatur«
has not risen during the compression, or that if the air has not been.wholly cooled
during the compression, it has been cooled to the initial temperature after the
compression. Or volume of one cube foot of free air at given pressure.
Absolute isothermal compression is not attainable, as it is impracticable in the
compression of air, simultaneously to abstract all the heat evolved in the compres-
sion. This column, however, does give the volume of air that will be realized, if it
is transmitted to such a distance fFom the compressor or in any manner that the
heat is abrtracled before it is used. Air radiates its heat very rapidly, and this
column may be taken to represent the volume of available air after compression.
Column 3 gives the volume of air at completion of the compression, assuming
that the air has neither lost nor gained during the compression, and that all the
heat developed by the compression remains in the air. The condition represented
by this column— adiabatic compression — is alike to that of isothermal compression,
never actually attained. In any compression, the air will lose some of its heat, and
consequently the air is not as heated at any period of the compression to the ex-
tent that theory assigns to it. Physically, the theory is correct, but practically it
fails. The slower a compressor is o|)erated, the more readily will the air radiate
some of its heat, and as a result, the less will be its volume and ItMs the power r«.
quired/or compression.
Column 4 gives the mean effective resistance to the piston of the air-comprrasor
cylinder in the stroke of compression, assuming that the air throughout the stroke
remains uniformly at its initial temperature— isothermal compression — but as the
air does not remain ut constant temperature during compression, the results in this
column are to be essayed to be attained in economical compression.
•
Column 5 gives the mean effective resistance to be overcome by the piston, as-
suming there is not any cooling of the air during compression — adiabatic compres-
sion— inasmuch as there is always some cooling of the air during compression, the
actual mean effective result will be somewhat less than that given in the column.
For the. computation of power required for the operation of the air-compressor
cylinder, the results given may be taken, with a per cent, added for f^'iction'"— o to
10 per cent. — and the result will very nearly give the power required to o|>erate the
compression.
Column 6 gives the mean effective resistance for the compression of the stroke
of the piston in compressing air— Isothermally— ft'om that of 14.7 lb& to any given
pressure.
Tllustration— Assume an air-compressing cylinder 20 ins. in diameter by 3
feet stroke of piston, making 75 revolutions per minute, with an adiabatic pressure
of 75 lbs. ■ ■
30»X.7 854X 35.23 (column 5) X 75 X 2 X 2-f-33ooo=ioa6 ff.
Illustration. —Assume an adiabatic pressure of 50 lbs. by gauge, the volume ot
air compressed and delivered will be (column 3) .35 for each stroke of the piston in
a cylinder fbll of free air; while for the compressing part of the stroke i — 35 = .65,
the mean resistance will be 15.05 lbs. (column 7). Thus, 15.05 x .65-^-50 X -35 =
37.28; corresponding very nearly w^ith 27.39 (column 5) for the whole stroke.
Comparing isothermal compression with adiabatic, to 50 lbs. as above, in column
6 is 13.48 which X i— 2272 = .7 728 (column 2) + 50 X •2272 = 21.78 or 21.79, as
given in column 4.
Columns 6 and 7 are useful in the computation of power in the first operation ot
oompression, as the fbnction of the first cylinder is that of compression only.
The results given in columns 7 and 8 are elements of computation for the IP of
the compressing engine, and a like computation applied to the result in the air
engine will give the power attained in the compression of the air. Column 7 gives
also the mean effective resistance for the compression of the stroke in compressing
air— isothermally— from a pressure of 14.7 lbs. to any given pressure, and column
8 gives the theoretic temperature of the air after compression — adiabatic — to the
given pressure.
* In MOM operation* th« air will bacoBio to cooled that It will, by the ranltiDK dacraaie of 1*41111%
meat of power 0/ operation, fully oompeiuale for the friction of the oompreaelng uiariilne
COMPRESSION OF AIR. 997
Xo Compute IIP ^w^itH tlie SSleznents of th.e Preoed-
ixkfs Table.
Assume a cylinder 40 ins. in diameter, with 4 feet stroke of piston, in which air
is compressed by 75 revolutions at 75 lljs. pressure per sq. inch. Area of cylinder,
less .5 that of piston rod, 1250. sq. ins. and mean pressure per stroke of piston as
per table (column 5) 35.23.
Then 1250 X 35- 23 X 75 X 4 X 2-i-33ooo=^8oo.6 IP.
*
Efficiency of Engine of Operation. — The efficiency of an enpne is the per
cent, of power develo[>ea by it^ tiiat it bears to that required to compress the
air, the loss by leaks, friction in pipes, of parts and heated air from the en-
gine-room (varying with the weather and the season), including that of the
driving engine.
Compressed air can be transmitted with great facility, provided the trans-
verse area of the conduit is pro[)ortioned to the volume and pressure of the
flow, and the suitability of the interior surface of it for its transmission.
Under such conditions, the volume of the external flow or discharge of air
may be computed by the volume of the cylinder of the air engine and the
number of strokes of its piston, less the loss and friction of the flow, which
may be estimated at 5 i>er cent.
Theoretical EflBciency of the compression and delivery of airT-7*t=E. T and
t repraenling the abgolute temperature* of the air at iti irUrance into the operaHng
cylinder and iti flow from the compressor.
In order, then, to increase the eflBciency, the heat evolved during compression
of the air must be abstracted, or by operating at a lower pressure.
Practical Efficiency is the difference between the iiower developed by the dis-
charged air and that expended in its compression, and in operation at a low speed
of compressing engine and under a pressure of but ft-om 60 to 75 lbs. an efficiency
of .9 has been attained.
Spray ii\jection of cold water into a cylinder is more effective than a water
Jacket, and by compressing the air In two or more cylinders, and cooling it between
them, the work lost or expended in the heating of the air by its compression is
much reduced. Hence compound compression with inter-coolers has been intro-
duced with advantage.*
If air is flowing with uniformity, a like weight of it flows through each trans-
verse section per section. Hence, G a V = W; 6 representing weight of a cube foot
of air in lbs. ; a, area of transverse section in sq. fut ; V, velocity in feet per second ;
and W, weight of air in lbs. per second.
Friction of Air in Long Pipes.
V«L ^ ixooood*Ch „ V»L .. ^ .iooood»CA _ „
= *'-v/ 1 = ^' r = a»C; and ==^ =L.
\ L loooo h " .
representing volume of air delivered in cube feet per minute; L = 2en^ of pipe ir%
feet ; d=. diameter of pipe in inches ; and C = coefficient cu per following table :
x" .35 «.5" -S' 1*5" .6513-5" -78715" -9348" 1.12512" 1.26)20" 1.4
1.25". 42 2'^ .56513'^ .73I4 .84 16" I. lo" i.a |i6" ..34I24" 1.45
For fifth power of d, see pp. 303, 304.
iLLUSTRjiTioy.— It is required to tnmsmit 1200 cube feet of flree air per minute,
at 75 lbs. gauge pressure, through a pipe 4 ina in diameter and 1000 feet in length ;
what is the additional pressure required to overcome the ftriction in the pipe ?
1200 y 1639 (col. 2, Table, p. 995) = 196.68 cube feet.
106.682X1000 -. • ,- , w%- X J* »
5r ^ s- ^ 30 Ofg, {Frank Richards. )
loooo X 1024 (45) X .84 ' ^^
Mr. Unwin gives the following : .0027 1 -f- 3 -H 10 d = C. d representing diameter
of pipe infeety and G a constant^ due to diameter of the pipe.
For pipes less than one foot in diameter, .5. € = .00435, .656 = .00393, and for
,98 feet ^=.00 351.
* tSSi. Norwalk Iron Worki Co. claim to haTe fint eonitroctad Compoond ComprflMort.
998
COMPRESSION OF AXR.
Xo Compute Ijosm of K^etd ixi Floipvr of JLiT in X^onfc
Pipes.
— C X -^ = A. V rqpresenting velocity of air in feet per second, C <u db&ve, I
length, d diametn' of pipe, and k head, all in feet.
• Assaroe a pipe having a diameter of .5 foot and a length of 1000 and the velocity
of the air 10 feet ^r second.
C==.ot>27 (1 + —) =00432. Then,- X 00433 X =53.71 feet.
\ 10/ 04.33 '5
Assnme the transmission of laoo cube feet of free atmospheric air per minute,
through a pipe 4 inches in diameter and 1000 feet in lesKtb, under a gauge press-
ure of 73.5 lbs. persq. inch; what will be the additional pressure or head required?
1200 cube feet of free air-^ -^'^"'"'^'^
»4-7
1034 and C for 4 ins. = .84.
3oo»Xiooo ^ ,^_ ^_j J y 10 000 X 1024 X. 84 X 4-65
-= 1200 -4- 6 = aoo feet at 73. 5 lb& 4* =
^-— - = 4.65 lbs. head, and ^ / ■
X.84 * ^ V
Then
looooX 1034 X ^H ' ~ ' V 1000
300 cube feet.
If, however, this volume of free air was, under a pressure, the volume of (V-ee air
during its transmission would be due to the pressure. Thus, if it was 58.8 Ibe. per
gauge, the volume would be t"'4-7 _ j^^^j ^oo X s = 1000 cube/set,
14.7
Loss of Pressure per Mile of Pipe*
P» /(i — ~- j = P. P* = conoentional presswre* qa given below ; V repre-
tenting initial velocity in feet per second, d diameter qfpipe in feet, and P termincA
pressure in lbs. per square inch.
Assuming initial velocities of 25, 50, and 100 feet per second and initial pressures
of 50, 100, and 200 lbs. absolute.
Diameter of Pipe, One Foot.
Initial
Velocity.
V.
Fe«t.
50
100
T«rniinal PreMHre=:P.
P« = 50. P<^=s:iOO.
Lbs.
48.8
45-3
26.9
LlM.
97-7
90.6
53-8
P'aiaoo.
Lba.
19*4
181. 2
Z07.6
Initial ^
f'reacare
lost in
Oi>« Mite
Per cent.
2.4
9-4
46.2
Diameter of Pipe, Two Feet,
Initial
Vel<»elty.
V.
Terminal pre«sqre = P.
P»a»SO.
Feet.
25
50
100
Lbc
49-4
47 7
40.1
piss 100.
Lba.
98.9
P> = aoo.
Lbs.
197.8
190.8
160.6
InUW
PressufQ
loetln
One MHa.
Per cent.
1.2
4-6
19.8
Illustration.— Assume initial pressure 50 lbs. per sq. ipch, velocity 100 feet per
second, diameter of pipe or conduit one foot.
50 / f I — )= 50 X V '39 = 26.93 lbs. terminal pressure.
Hence, if 50 — 26.92 = 23.08, 100 = 46.2 per cent, loss in mu mile.
The per cent, loss in one mile is the same, whatever the initial pressure, the
velocity increasing and the density decreaaing with the length of the pipe.
RestMs observed by Prof A. B. W. Kennedy, M.lnsLC.E., in the operation qf a
plant of six Compound cylinder engines, each operating two compressors, having a
combined capacity 0/2000 IP.
For a distance of 3. i mUes, through a pipe 11.8 inches in diameter.
At the terrainiitioD of the flow of air as it was about to enter the motor, it was
heated from a coke-burning stove. Compression of the air 88.a <73<5 4-14.7) lbs.
per sq. in. at a temperature of 150° reduced to 66.15 lba, and delivery of the com-
pression cylinders 348 cube feet of air at atmospheric pressure and 70^ tempera-
ture per IH* per hour.
The average loss was 3 per cent, velocity of air 1550 feet per minute, with an
UP of 1350.
COVPaMBIilOlf 0^ AIB.
999
Sammary of Results of two experiments, each with cold and heated air, in the
Transmission of Compressed air at Paris, 1889, for a distance of 4 miles. Motor
]o H* and presBttre of air reduced to 66 Uw. One IH* gave .845 liP in compressipn,
or 348 cube fbet of dir per hour H'om atmospheric pressure of 88.8 lbs.
A summary of other results showed that a small motor at a distance of 4 miled
from the oomiiressor iodicatoU i H* for a IP at the motor, or 2.5 IP When the air
w:is not heated before entering the motor.
Heating the air caused a saving of 225 cube feet of it per IIP, at a cost of 4 cents
per Iff.
The exhausted air from a motor, when that in the pipe is even but slightly heated,
will be so much reduced in temperature as to be available for coding and even
freezing application, so great is the effect of instantaneous expansion of the liir
when exhausted that ice is formed in the air-poris of the cylinder, and hen<)e the
operation of a plant at high pressures or above 90 lbs. is held to be objectionable. •
By operating at full pressure, the high velocity of the flow meohanically restricts
the deposit of ice crystals, but inasmuch as the useful effect decreases with an in
crease of pressure, it is held by Robert Zahner and others that 60 lbs. is the limit
unless the opetating air is reheated.
When air is o|)erated expansively at hulf-stroke^ the temperature falls 160°, and
at one-fourth stroke 284*^.
Compressed air is the only power of general application, as it can be applied,
extended, and distributed without restriction to distance, course, elevation, and
depression, and under ground or water, and under some of these conditions the
only power at all praotictible of operatioh. Alike to water it can be stored, which
condition is unattainable with steam.
Uealing Compressed A ir. — When compressed air has been transmitted to
the point wltere it is tO be employed^ an inerea99 of power is attainable b^
the addition of heat to it, befbre it is applied.
* Absolute temperature is 461.3°. Hence when the air is 60^, the absolute
temperature is 461.2 -{-60 = 521.2, and when it is — 30°, it is 431.2° abso-
lute.
Loss of JEfficienqf. IniticU TempetaMirt of Air 62°.
PraMar*.
! FinAl Tefh-
perature.
Lb«.
29.4
44- «
58.8
Degrees.
178
258
321
Eflleiency.
Rednced. Lom of.
Ptor cent.
82
73
67
Per cent.
18
27
33
Preuure.
Lbe.
73 5
'47
Finnt Tem-
perature.
Degrees.
373
559
Efflciencjrt
Redneed.
Per cent.
63
5'
Jjowof.
Pel- cent
37
49
Assuming eflBciency of Compression and also that of the Engihe at 80 per cent.
the resultatit efficiency of the combination at 147 lbs. pressure = -——? X 51 =
• 100
32 6 per cent. At 44. i lbs. thd efflclefifcy ^ -= x 82 =t 54. s ptr dmt.
««> (D. K. Clark.)
Air expands at constant presBure troxa 32° to 2i3<^ .00s 036 per degree of tem-
perature.
Ififfloiexioy or 'Cooling.
Cooling of compressed air effects a saving of power required for its compreission,
an^l aids in the lubriuation of the piston. It is most effective at low pl-essures.
Thus at 15 IbA pressure the temperature consequent upon compression is raised
from 60° to 177O and from 75° to 90*', but 39°.
When air is heated by compression and water is introduced it becomes saturated,
and when after perfonning itswork it is exhausted into the open air, it expands so
rapidly that its temperature is frequently reduced below zero, and, as a result, the
moisture in the air gravitates as ice in the exhaust passage of the engine, and its
capacity is choked and even closed. Rence It IB imperative that the air of com*
prewiOB should be maintained as dry as practicable.
lOOO
COMPBXSSION OlP AIB.
A.ir Receivers.
The operation of a Receiver, if of safflcieat volume, is to reduce the effect of the
pulsations consequent upon the stroke of the compressor, for without it the press,
ure of the air at its delivery from the compressor to a pipe would be -momentarily
in excess of the average pressure ot operation. This efl*ect may be reduced by in-
creasing the length of the pipe, also by the attachment of a second Receiver at the
termination of a long pipe.
As the presence of a Receiver -checks the flow of the compressed air, some of the
water which is in the air, which otherwise would be borne with the current, is
precipitated.
Kflloienoy of* OompreaaecL .A.ir Kzigriues.
At the ordinary pressure of 60 lbs. per sq. inch, the decrease in resistance effbcted
by the cooling of the air is held to be equal to the friction of the compressor. This
effect is greater with high than low temperatures of the air, in consequence of the
higher temperature at the higher pressures of the air.
AdiabcUic Expanrion,
The more air is in compression and the friction of its passage in the pipe in-
creased, the efficiency of compression is increased.
The following table gives the Lowest Pressures which should be operated in the
Compressor, with varying amounts of friction in the pipe:
^^
u
if
>l
fata
^1
SI
0
ll
0.
el
w •
P'rct.
55-7
53-9
Lbs.
ao.5
235
•s
Lbs.
26.4
29.4
Lht.
It
LbB.
20.5
29.4
P'rct.
70.9
64-5
Lb*.
8.8
11.7
Lb*.
38.2
47
P»rct.
60.6
57-9
Lbs.
17.6
Lbi.
52.8
61.7
Lbs.
705
76.4
P'rct.
52-5
513
Lbs.
82.3
88.2
P'rct.
50.3
49
Operation, and
M!ean XCesnlte of* a Hardie
Rome, N. Y., 180C
lifotor at
Elements.
Pressure iiersq. inch.
Distance run
Temperature of air
entering heater...
Temperature of air
leaving heater....
Temperature of air
at exhaust
Hea*t absorbed in
heater
One
Run.
1.41
358
65.2O
24a 3O
130-7°
175.1°
Mean of
Screw.
1 01 lbs.
a. 61 miles,
68.2°
219.50
X23.5O
137.1°
Elemento.
Difference in tem-
perature in heater
at start and fin«
ish
Iff
Water supplied. ....
Air per IH* per min-
ute
Power from heater..
One
Ran.
49"
12.45
29.37
6
43.3
Mauof
Screw.
29.80
9-47
21.46 lbs,
6.$ cube ft.
4o.ipercu>t
The power obtained fk-om the Reheater was about 45 per cent,
{Frederick C. Weber.)
Fo-^ver H.eq.u.ired to Compress A.ir at tlie XJnifbrm
Temperature of 62".
Pressure
per
Sq. Inch.
Lbe.
30
45
60
75
90
105
HP per
Cabe foot
of Com-
pressed Air
No.
.089
.211
.356
.5>6
.69
.874
Volume of
Compres'd
Air per
mtn.perIP
Cube feet.
11.25
4-73
2.88
X.94
1.45
1. 14
Pressure
per
Sq. Inch.
IP per
Cube foot
of Com-
pressed Air
Lbs.
120
135
X50
165
i8a
»95
No.
1.07
1.27
Z.48
Z.69
1. 91
a. 14
Volnme of
Compres'd
Air per
min.perH*
Cube feet.
.938
.788
.667
•59'
.523
.468
Pfeerare
per
Sq. Inch.
Lbs.
SIC
225
240
955
270
300
IP per
Cube foot
of Com-
preseedAir
No.
a.37
a. 61
a. 84
3.09
3.34
3.84
Volnme of
Compres'd
Air por
min.perH?
Cabe feet.
.4aa
•384
.35a
•3«4
•3
.a6
At the Mont Cents tunnel, 64 cube feet of compressed ftir per minute through « eMt>Iroit pipe 7.695
Ins. in diameter, 5325 feet in len|^h, and under a pressure of 838 lbs. : the loss of the head includiaf
leaks and fHctiou was bat 3.5 per cent., and in a length of pipe of 20000 feet the loss was but 5 per cent
of the initial preseore.
{D. K. Clark.)
COMPBESSION OF AlB,
lOOl
UI
"t^
^
R' 00
i?^
t*
§
5
«U1
90
IT
Q
o
w*:*
00
o«
CO
5 tt
o
0
s
oa
i
I
Gauge Prew-
ure at eii-
tnnce to the
Pipe. .
•s) "J VI vj .sa
V4 00 p0^p^O
i>. (>»» 00
Length of
Pipe fn Feet.
Diameter of
Pipe in Ins.
00"sl Ox*- M
'S
UI UI >> W M
^ H bvM ik
M
8
M M M M
pop 00>^ U)
M '-J M 0\
M
S
M
M M
M M \0 >4 OJ
1
UI
CO M M M
i
M M M M
M pOM<Sw
t
UI .^ M M i-i
M
Ui
0
M '
CO M M M
M 00>K C0\O
00 OOU) OJ M
• a • • ■
0\0\vO ►« vj
?
UI
•
Oaage Prea»>
are at en-
trance to the
Pipe
*4 >J ^ »J ^
UI yi UI ui p\
*^ b\boM
Length of
Pipe m Feet.
Diameter of
Pipe in Ina.
u! w »8\w
UI '^OJ
"S
00*4 <^ V] >4
M pOp^Ul M
<*< Ul>b M UI
M
8
OJO» U M M
M ov5 00^
M
8
M
M M M M M
O0>« ^ Q\UI
rf- P p^po
UI M 9\o^<>a
1
ijx
>. > OI OJ OJ
M 0\o ooo«
N| H M OJ UI
^bik oo«b bv
§
U U M M M
O^Ui 4^ 4k o*
*.+. pooJ «
UI o\ >■
•§
"^ 0\0>OhO»
M oj>p .^ 0>
b^boM UI 00
"8
t»
>• >• >- >. OJ
-^<Um OB
r
UI
Is
B
ft
»i
0
9
0
H)
<♦
9
9
Gauge PrsM.
are at en-
trance to the
Pipe.
00 00 00
M M H
?r
VI OvUl 4k. M
00 0\ M H OJ
. • • . •
M Ul UI M VI
Ul >. OJ M M
Ui>4 v|\0 p\
M M OO
OJ
M
M 00O\4>
M OOOOP
4> VI VI »«
SO VI 0\*- K
OJ <p M 00 00
i- C\ 00 bv4k
9 O
•s|
^4
UI
O
8
Ol
M M M M
Ui w O^OJ v|
O OJ 00 O o«
4i> N>0 ^ 4k
Ui OJ VI t^^O
M Ul UI Ul
Ui 4» OJ M M
OJ Ui Owl On
VI V| H ^ OJ
I
i
OJ » H M
M 0« M M UI
O0v»Ui ^ B
QkOJ OOUl Ov
>4 COM M OJ
UI ^ O) M M
O M OJ 0«Ul
OJ OOOOM OJ
OJ
w r
N Q OOOVOJ
0«*^ .K UI 00
M .^. v| OSOJ
^
OO'i 0»4k M
O 0> Q 0*>J
UI
OOUl H>6 UI
^ QkOJ Ui UI
O OvOwi 00
M ^ V4 OtOJ
ONOomo ui
M\C QUI M
-M \0 UI M
00-^ OJ ~
Ov 0\Ui
^2'
^
VI
<4J
»> O 00 0«OJ
4k 0\OJ Ol ««
vO 0J\0 O >0
OJ M M M
H QOtt <^'
^0 O M M '
N M O M '
wm 9m wm
VI UI W«0 UI
«0 OJ O OJ ^
<0 M OOOvOv
CO
00
i002
COMPRESSION OP AIR.
Voluzn« of f*ree .A.ir in Ctil^e P^eet Requiped in.
IVfotor per Ilf per ]\£iiiu.te.*
Without HeheaHng,
Gaage Pressure in Pounds at 60®.
20.3
16. 1
«5.«
135
12.9
>3-4
To these resqlts is to be added the per cent, of clearaoce as determined in each
Quse.
If the air is reheated, the volame in the table will be decreased, depending upon
the temperature of the air at admission, and it Is proportional to T-r T', T r^tre-
tenting absolut« temperature at 6o<3, and T' 460 -f temperaiure of air at a4misaion to
motor,
HeDce, if the air is reheated to 300^^, the volume in the table Is to be maltiplied by
460 + 60 ^5ao_ gg
460 -|- 300 760
To Aicertain the Eeonomieal point of Cutoff far the Gauge Preuwres in the l\ibU.
Avi inspection of it will show. Thus, at 60 lbs. the least volume of f^ee air per
Point
of
Cat-off.
«5
30
40
X
31-2
233
21.3
U
25.6
24.8
J7-85
16.2
.5
25.8
16.4
14.5
33
•25
37
»7S
2a 6
152
15.6
60
70
80
90
zoo
no
"5
150
19.4
18.8
18.42
18. 1
.7.8
17.63
17.4
17 05
1547
15
14.6
14-35
14-15
13- 9«
13-78
13-5
14-5
14.2
13-75
13-47
13-28
13.08
12.9
13.6
X3-8
12.3
II. Q3
10.8
11.7
11.48
"-3
ll.i
10.85
U.85
11.26
10.5
10.31
10. Q2
9.78
9^5
«3-3
11.4
10.72
10.31
10
9-75
9.42
9.1
TIP ip at .33 cut-off, and at 80 lbs. at .35.
{Frederick O. Weber.)
X^oes oi*Pre«sure by F'riotion of Compressed A.ir in Pipes,
In Pouadt per Square Inch for 1000 Feet of Pipe,
Volume of Free Air, Compressed to a Gauge Pressure of 60 lbs. per Square Inch,
Delivered per H inuta
Diam.
of Pip*.
50
75
zoo
»25
150
aoo
«S0
300
400
600
IlM.
Lbs.
Lta.
Lta.
Llw.
Lbs.
Lb«.
Lb*.
Lb«.
Lbi.
Lbs.
X
10.4
—
—
— .
—
—
—
—
—
—
1.25
a. 63
5.9
—
—
—
-^
.^^
—
-—
—
«-5
X.22
2.7s
4-59
7^65
If
—
—
—
— -
—
»
•35
•79
l.4«
2.2
3^i7
5-64
8.78
—
^
—
».5
•'4
•32
.57
•9
1.29
^•3«
3.58
5.18
9. a
—
3
. .11
.2
•31
•44
•75
1.33
1.77
3.«4
7.0s
3-5
—
—
—
•15
.21
.38
•59
•85
m:
3.4
4
—
—
—
— •
.8
■3«
•45
1. 81
5
—
—
—
—
—
.1
•15
.a6
•59
Diam.
•fPipe.
800
Lbs.
6.03
3 22
1.04
•41
.z
1000
Ins.
3-5
4
5
6
8
10
13
• Copyright«d.
Lb«.
5.02
1.63
.64
.16
Zmbe FtH
•
I90O
1500
z8oo
2000
3500
3000
4000
5000
Lb*.
Lba.
Lbs.
LU. .
Lbt.
Lb«.
Lba.
Lb*.
7-23
"•3
_
^.m
—
_
_«
.^
2.3s
•93
.23
3.66
1.46
•37
.13
5.28
2.09
•53
•>7
6-5
.31
XO.3
4.06
I.03
•33
•«3
sTsi .
1.47
•47
.19
10.3
3.61
.84
•34
4T08
1-3
•53
[Band DfiUCo., F. A. Halsey.)
COHFRESBIOM OF AJB.
j31ni«naloiiH and Klemeuta of A.ir C
Operuled bf SItam,
i.,.
t^
BlrolH
Si
ch.,^^.
su™.
E^.
"r
"w«,.
.
'"
»
s
If
■••.
lu
!"
**
"•jg
li
JO
.6
1
1
i6s9
1
-*
1
LIS
.i
1 CoiBpp*** One Cubfl I''oot
STTSK."
S'Zt.
p«.».
T3.
air.'
C«Hoi
iw..™.
■»
033'
::;i;
X'
£
"
X
Xi
.U99
-■4a5
70
l«
"
■3;;
1^37
:S
Mothn or the
■ Mj
L Points of flzpiuiBi
rtcn Mr nwnire i> £dii ttox Almniptert U U Oivm A
i
JZ
T„r,
^
""='-
~
;i;r
i
°tJ*
■?
1
is
Is
°%
11
Sii
4..6fl
9'
5
1004
COkPRSB^lOK OF AIR.
Heat Produoed lay Coxnoresuioxl of I>ry ^ir.
Witiunu vooting.
Preeenre
aboTe
Atmoe-
pliere.
Lbe.
o
«-47
367
7-35
II. II
M7
Volame.
Cube feet.
I.
.9346
.8536
•7501
.6724
.6117
Teinpera
ture of
the Air
O
60
74.6
94.8
124.9
i5».6
175-8
Preeenre
above
Atmoa-
phere.
Lbe.
22
29.4
367
44- «
58.8
73 5
1 Tempera-
Voinme.
ture of
\ the Air.
cane fMC.
0
.5221
218.3
.4588
255.x
•4»»3
287.8
.3741
3«7-4
.3194
369.4
.2806
414.5
Preeenre
above
Atmoe-
pbere.
Volnme.
Temper*
tnreof
the Air.
Lbs.
Cnbe feet.
0
88.2
102.9
.2516
.2288
454-3
490.6
Z17.6
.2105
5237
132.3
205.8
•1953
•M65
554
681
2793
•«i95
781
The presence of moisture will increase these resulte as it increases both the
specific heat and the heat-conductive caoacity of the air. ( IT. L. Saunders. )
lOffloienosr of* an ISxi£:ine.— With perfect expansion, without the air
receiving any increase of temperature, the efficiency at pressures above the at-
mosphere and friction in pipes are estimated as follows :
Friction
cetiinnted.
U-7
39.4
Lbe.
5.1
>4 7
Per cent
70^44
57.14
Per cent.
68.81
64.49
48.53
Per Cent.
44-X
Per cent.
64.87
62.71
55-13
58.8
Per cent.
61.48
60wI2
55-64
73.5
Per cent.
58.62
57-73
54-74
88.3
Per cent.
66.23
56.59
53-44
As firiction increases, the most efficient and economical pressures increase.
Lowest Pressures aJt Compression.
Friction.
Compres-
sion.
EUBoIency.
Friction.
Lbe.
si
8.8
Lbe.
20.5
38! 2
Per cent.
7a 92
Lbs.
11.7
17.6
Compree-
■ion.
£fllciency.
Friction.
Comprec-
•ion. .
Efficiency.
Lbe.
52.8
61.7
Per cent.
57.87
55-73
53-98
Lbe.
20.5
26.4
LU.
70.5
82.3
Per cent.
52.52
51.26
50.17
13.134 cube feet of air at 62*^ (table, p. 521) weigh i lb., and air at 60*^ compressed
to half its volume evolves ii6<^ heat, and as the specific beat of air under constant
pressure is .2377, which x 116 = 27.573 hecU units, produced by the compression of
I lb. or 13.134 cube feetof fVee air into one-half its volume : Hence, 27.573 X 778 ==
21452 foot-ibe., and as heat and mechanical energy are held to be convertible
terms, ^li^ =s .65 IP produced or lost by lbe compression of i tt>. of air. Inas-
33000
much, then, as the compression of air develops heat, and if the temperature of the
compressed air is reduced to that of the atmosphere from which it is drawn before
being used, the mechanical efl*ect of this difference in heat is work lost.
Work: I^ost "by Heat of* Compression.
Air assumed to be cooled to temperature of atmosphere between stages of com-
pression and without effect of Jacket cooling.
Second
Staff*.
Gauge
First
Second
Third
Fourth
Preeenre.
Stase.
Stage.
Stage.
Stage.
Lbe.
Per cent.
Per cent.
Per cent.
Per cwit.
60
23
11.8
4.45
80
25-3
13. 1
—
4.8
xoo
27.6
14.6
—
8.27
200
34-4
18.9
—
400
40.7
22.9
—
II
600
44.6
24.0
13 1
Oange
Pressure.
First
Stage.
Lbs.
800
1000
Per cent.
47-4
49-2
1200
51.6
1400
1600
1800
52
53-3
54
Per cent,
26.3
28.x
28.6
29.4
30
30.6
The power .of compressing at high pressure is not proportional to the pressure.
(Frederick C. Weber.)
Third
Stage.
Fourth
SUfB.
Per cent.
Per cent.
—
M-3
—
^^'i
—
14.8
—
15
__
x6.x
COMPRESSION OF AIR.
1005
XjOSs of* Pressure throiagh. IT'riotion. of ^ir in
l-'ipes.
Per 100 Feet of Length (Imtial Gauge
Pressure 80 Lbs. at
Receiver)
•
Eqaivalent
Volwne of
DiAURBB or Pipe.
Free Air
Diacbargad.
I
I-25
«.s
s
Ins.
2.3
3
4
5
Ins.
6
Ins.
7
8
10
1 "
M
Per minute.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ids.
Ins.
35
.24
.12
___
—
—
—
—
—
—
—
—
—
—
—
50
I
•45
.18
—
—
—
—
—
—
—
—
—
—
~-
75
2.4
I
•4
—
—
—
—
—
—
—
—
—
—
100
—
1-7
•7
•'3
—
—
—
—
—
—
—
—
—
200
— , —
3
•5
•175
—
—
—
—
—
—
—
—
— .
300
—
—
—
t.2
.3a
•'5
—
—
—
—
—
—
—
—
400
—
—
—
2. IS
•67
.27
.06
—
—
—
—
—
—
—
500
—
—
—
3-3
I.I
•4
.1
.03
.012
—
—
—
—
—
750
—
—
—
2-5
.:r
.22
.07
.03
•013
~
.—
—
—
1000
—
—
—
—
—
•4
.12
.05
.023
.012
—
—
—
X500
—
—
—
—
—
4
X
•3
.12
.052
.027
—
—
—
2000
—
-—
—
—
—
: —
i.6q
.5
.a
"95
.048
.017
_^
—
3000
—
—
—
—
—
—
3.70
I .2
^5
.22
•"5
.036
.015
—
4000
—
- —
—
—
—
—
—
2
.8
•39
.2
.07
.026
.012
5000
—
—
—
—
—
—
—
—
» 3
.6
•3
.1
.041
.018
6cxx)
—
—
—
—
—
—
—
—
1.9
•85
M
•15
.06
.028
7500
—
—
—
—
—
—
—
3
1-4
.22
.09 .04
xoooo
—
1
—
^—
—
—
—
— .
2.5
»-25
•4
•»7
•075
(Frederick C. Weber.)
Illustration. —Ad air compressor fYtniishes 500 cube feet of free air per tninnte
at a pressure of 80 lbs. per square inch in the receiver. If this air is used at the
end of a 3-inch pipe 1000 feet in length, the loss due to fViction will be 10 X .4 = 4
Iba If a like volume of air were supplied by the same compressor at a like press-
ure and passed through a 5-iDch pipe 1000 feet in length, the loss would be only
.03 X 10 = .3 lbs. ; thus illustrating the iipportance of using pipes of large diameter.
Strictly, the loss of pressure is not directly proportional to the length of the pipe,
but for all practical purposes it may be taken.
Elbows and irregularities in pipes increase the friction in excess of the figures
here given.
The results in the table represent the loss by friction in the pipes. There is also
a slight loss due to friction of the air with itself at the mouth of a pipe when it
leaves the Receiver.
Leakage,
All leaks in compressors or valves, air receivejre or pipes, should be -strictly
guarded against for economy, as they are Hilly as expensive as steam leaks. When
air, at 60 lbs. pressure, issues from a leaky Joint in a pipe at a velocity of over 500
feet per second the waste of it will become apparent.
M-eein. Kffeotive Pressures in the Compressing and
Delivery of* Free A.ir to a Ghiven G-auge Pressure
in a Single Cylinder.
Oaoge
Press-
are.
Lbs.
I
3
3
4
5
xo
Compression. {
Oange
Adia-
Isotber-
Press-
Iwtie.
mal.
are.
Lbs.
Lbs.
Lbe.
■^
•43
15
•95
29
1.41
'•4
25
1.86
X.84
30
2.26
2.22
35
4.36
4-14
40
Compression. |
Oange
Compreesion. {
Gannre
Cbiopressloii.
Adia-
Isother-
Press*
Adia.
Isotber-
Press-
Adia- Isothtr-
batic.
mal.
ftre.
batic.
inal.
ure.
batic.
mal.
Lbe.
Lbs.
Lbe.
Lbs.
Lbe.
Lba.
Lbs.
Lbs.
r??
5-77
45
«395
12.62
J^
19-54
17.09
Z'
50
X5.05
X3-48
2a 05
17.7
905
8.49
55
15.98
M3
85
21.22
i«-3
10.39
9.66
60
16.89
1505
15-76
90
22
18.87
".59
10.72
65
17.88
95
22.77
19.4
12.8
XI.7
70
18.74
16.43
xoo
23-43
1992
{Frank Bichards.)
1006 0OA£PBSSSIOK OF AIB.
To Goxnp-ate tb.e Steazxi Pressure and. foixit of Cutting
off* -for & O-iven i\.ir Compressor.
Assume steam and air cylinders each 22 X 24 ins. and temperatare of initial air
62°.
Area : — g — - = 5. 26 cube feet per stroke.
1720
= . 4 — 26<. , and, if compressed adiabaticaUy, 68 755 (see ante) X < 4 = 37 592
13.141
\HU-lbs.
lbs. resistance to be overcome by steam pressure.
Hence, „ ^' ^=41.2 lbs., which correspon
380.13 X 2t
are of 80 lbs. gauge pressure. (F. C. ITefter, Jf. E. )
Jbot-lbs., and assuming friction of operation at la per cent. • ^ ==31 352 foot-
.88
B overcome by steam pressure.
Hence,— —^^-^^^—-=41.2 lbs., which corresponds with .2 cut-off at initial press-
To Compute Volume of One Pound of Dry Air in Culje
Keet and Weight of One Cube IToot of it in Pounds,
At Various Temperatures and at Atmospheric Pressure,
T -\- T-T- 39. 819 = volume. T representing temperature of air and T' absahUe tern-
pertUure in degrees.
DrT = 620. 62O-|-46i0-J-39.8i9 = i3.i34Cu6e/e«t
Inversely. 39. 819 -»- 630+4610 = . 076 097 lbs.
NoT«.-~For Table of Voliimes, Preuures, and Density at 62* = i, and for Compatation of Volnme,
Weight, Preasure, Density, and Elasticity at other Temperatoree, see pp^ 531, 533.
When the Pressure and Temperature of Air both vary.
2. 7093 X P -7- T = cube feet in lbs. T representing absolute temperature and press-
ure in lbs. per sq. inch,
Illustsation — What is the weight of a cube foot of air at 60 Ib& pressure and
ioqO*
3.7093 X 6o+i4.7-!-46iO-|-iooO = .36o7 lbs.
. . 4610-f 100O-J-60+14.7 ,
Inversely. ■ ' — ^^=3.771 volume.
3.7093
Comparison of Singrle and Compound Compression.
Assume areas of cylinders for Single and Compound compression respectively
100 and 33.33 sq. ins. , and pressure of compression 100 lbs. per sq. inch. Resistance
to cylinder of single compression = 100 x 100 = loooo lbs., and to second cylinder
of compound compression = 33.33 X loo = 3333 lbs.
The resistance upon the large piston is its area multiplied by the pressure re-
quired to force the air from its cylinder into the less. In this case ft is 30 lbs. per
sq. inch; but inasmuch as this 30 lbs. presses upon the rev<^rsfl side of the less pis-
ton, and thus assists the operation, the net reeigtance to forcing the air fh>m the
large into the less cylinder is equal to the difference of the area of the two jiistons,
X the SQ lb& pressure, =66.66 X 30 = 2000 lbs.
Hence, the resistance to forcing the air from the larger into the less cylinder is
2000 lbs., and the resistance in the small cylinder to the compression of it to 100
lbs. =si 3333 lbs., the sum of the resistance = 5333 lbs.
{The Normaik Iron Works Co.)
The compression of air develops heat, and if the temperature of the oompressed
air is reduced to that of the atmosphere fhim which it is drawn before being used,
the mechanical effect of this difference in heat is work lost.
* Dedscting area of piston-rod. f a feet atroke.
OOMPBJSSSIOX OF ▲IB. tOOJT
Isotlverznal Compression.
P V hyp. log. -^ = F. P rtpreteMing atmokphtric praturt in Ihi. per Jrf. ^bof s:t
14.7 X 144 = 2116.8, V wlume of i Ih. air at , atmospheric pressure (62®) = i3.xai
CM6e/e«<, p and p' t^rmiruU and atmospheric pressures absolute in lbs. per sq. inch,
and V foot-lbs. per lb. qfair. Assume p =5 80 lbs. per gauge.
Then, aii6.8 X 13.X41 X Uyp. log. ^^=27 814.7 Xi.86as = 5> 8o4/i»aW6«.
A.<iia1>atio Oozxxpression. One Cytindtr,
n — I
py ...^ /:?-\ nr"—i « F. «, ouwftttiV w»Mr^^ ^jMefc^, =3* i-M
Thtto, as preoediMg, 27814.7 X 3-45 X f— ) — i =95^X 6.4429— 1«95.^
\«4-7/
X . 7165 = 68 755 foot-lbs.
Coxnpound Air Cylinders. Two Cylinders.
Air cooled to atmospheric temperature before admission to second cylinder.
*— I ,^ V «— I
uret in ist and ad cylindtrs. ..
PY— ^=595960, at prt«Jedlng, andj>a = VPiXJ»3=3 37.»5.
n — I
Then, 9596dX (^) **'+ (|^) "- « = 95 960 X 1.3096:^ »»3096-a=:.6i9«
X 95 960 = 59 4x8 foot-lbs. '
For N Cylinders, ^5960 X N X R •=*9^ i =»= F- N rq»r«eii«iV numfttr of cylinders
and R rofio of compression, equal in each cylinder.
Na«.-^Iililtal pMMur* in lit cylliidw « 14.7 *••? tort.toal37.2S »»• '^^l ^*^ ^ ** •'^"■**
Jp.aS, BMD« M tormioal in x«t, and ai termiDai in ad cylinder = 947 '*•• »»>«>»•»'
To Compute WorU per Povind of Air in Compressing
it to 000 IjUb., Oa«KO I^ressure, from an Initial
Tftmpek»at\iro of 6S«» in B'irtet Cylinder.
Coolina to Atmospheric Temperature before Air is admitted to next Cylinder, and
Jacket Cooling not considered, hence n = 1.408.
F = 9596oXNxR«»-i
Pi _^Pl-.Pl =:£♦ = R, p representing atmosphere in lbs. per sq. incfc = 14.7,
p Pi Pu P* I
p^ terminal presxure (oftw^wte) in ist cyKndtr and admission to 2d=VpXPi
= V»4.7X86.8 a= 35.7, Pt terminal in ad cyUnder and admission to 3d = y/pxp^=
^14.7 X S147 = 86.8, P3 terminal pressure in 3d cylinder and admission to ^th =
^^^3^=^86.8 X 514.7 = 2ix,j)4 terminal pressure ^SH 7 Hw., atkJ N = 4.
ac.7 86.8 an «„.! S14:7_. ,.
Heh«5, f^-^-43, 5;:V = «-43' 86:8 = »«' "^"^ -^ = '**-
95 960 X 4 X 2.43 a*- I = 95 9^ X 4 X 2937 = 1x2 7^4 footpoundk.
•ro Compute the Steam Pressure Reqllil^d irt tlie Steam
Cylinder of a Simple A.ir Compressor.
When the Air Pressure and Diamder of Both Cylinders are Given.
£ y^ /£\ '_. Pj. p and Fi representing mean effective air and steam pressures in
Ib^perlq.inch, E, mecfcomcaJ efficiency of Compressor, and d and d^ diameter of
air and steam eytind^t
ICX)8 OOMPBESSION OF AIR.
iLLCSTiUTioir. — Agsume pressure of air 60 lbs., diameter of steam and air cylin-
ders respectively 12 and 14 ins., and mechanical efficiency .85.
Mean eflective air pressure of air for adiabatic compression at 60= 3a 75 lb&
{see table, p. 995).
^—^ X (~) = 36. 18 X 1.36 = 49.2 lbs. per «g. inch.
Corresponding to a steam pressure of 70 lbs. gauge, at .375 cat-off.
Temperature is a direct function of the pressure, hence it is apparent that in the
multiple stiige compression, where the temperature, by the application of inter-
coolers, is reduced back to that of the atmosphere before admission to each cylin-
der, that the loss in radiation is reduced. In'compound compression, in ordjsr.to
divide the work equally, the ratio of compression should be the same.
The temperature of the air (theoretical) in the single stage compression here
given is about 400°, and that at the end oteach compression in the compound case
is about 200^.
The mean eifective pressure or resistance of the air of compression in a single
cylinder, and for the given pressure and temperature,* is Isoihermally — ~ —
= 27. 38, and AdiabcUicaUy — -~- — = 36. 33, and 51 804 -r- 68 755 = 75. 35. Hence,
144 X 13- '4'
AdiaitaUe compression is- but 75.35 per cent, as eflfective as IsotherwuU.*
For the heat evolved and given to the air by Adiabatic compression is difitised to
the surrounding media before the air is admitted to the Motor cylinder of an
engine, the extra work in compression is lost, and in the case here referred to, the
loss is 100 — 75.35 = 24.65 per cent.
In a water.jacketed cylinder, the loss is not so much, as the heat of compression
does not rise so high. iFrederick C. Weber.)
1?o Oozzipiite tlie AVeiglit of .A.ir -used in. a !M!otor i>er
IMinute for a Q-iven' .A.mo-axit of "Work.
5^^^- = — =: cube feet N r^aresenUf^ nu«U>er of H*. U = P V
I — •—■ M >« P initial and Px exhatut pressure in lbs. per sq. tncJk, V volume
P Ir
of air in cube feet^ n 1.408, and T and Tx dbsd^Mte tempertUwes at admission and
atmospheric temperature ; W weight (fair per minute to deliver^ N. W per minute^
and w weight per cube foot at atmospheric pressure in lbs.
N assumed 12, to .076, T and T, 63 -4- 460 = 523, and 300 -f 460 == 761, P 80 Oa. per
gatige, and volume at 62^ = 13. 141 cube feet
33000x12X5^3 _
14.7 X 144 X 13. 141 X —^1—- XI ^1408 X 761 X .0761
■ ^^' — — = 89.2 cube feet per minute.
95960 X ( I —.1552 ■'•) -4174 X 761 X .0761 = 2 319 510
89.2-i-.686=: 129.9 cu5e/ee< without reJieaiing ajad 129.9 X .686 = 89.1 cubefxi
when reheated.
1.408-1 t Log. 14.7 X. 29 = 1.167317 X. 293=. 338521
x^l±l X.408 = I— .1552" 94- 7 X. 29 =1.97635 X. 29 = .573141
94*7 — .234620
I — .23 462 = .76 538 and number of .76538 — i =.5826 — 1=:. 4174.
By Logarithms. ^5960=4^98209 33000=4.51851
.4174 = 1.62055 12 :i= 1.07 918
761=^88138 523 = 2.71850
.0761 = 2.88138 8.316x9
6-36540
Log. of z. 95079 = 89.28 cube feet. '•95079
* For an lUoitration of th« corvM of preuare, see Frank RichArds. Fr9ati^«c« aad p. 43.
i Bj Logarithms.
COMPBE6SION OF AIB.
1009
IDizuexisions of* "Valves, Pipes, and Clearanoe of A.ir
Cylinders.
DiacHABOS Valvcs.
Number. Area.
Pressure of Air ^ 75 Lbs,
Cylinder.
Ann. Fi
ree Air.
PreaBure,
75Lta.
Inlbt Pipe.
Diameter. | Ares.
Ids.
Sq. inu. P
er ceb V.
Percent
Int.
Sq. ins.
10.25 X 12
I 78
0098
.0086
.047
2
3- '4
12.25 X 14
"3
•043
2-5
4.9
14.25 X i8
154
0066
•033
3
7
16.25 X 18
201
0066
.023
3-5
9.6
18.25X24
255
0049
.0225
4
»2.5
2a25X24
JM
0049
.0225
4-5
159
22.25 X 24
380
0049
.0225
5
19.6
28.2
3a25 X 60
707
002
.01
6
36.25 X 48
1018
002
.Oz
7
38.5
No.
a
2
3
3
8
8
10
18
20
Sq. iu8.
5-4
8.8
13- 2
13 2
35-2
35-2
44
79.2
88
Clearance, .0625 ^^^^ ^^ '^^^^ ^^^ of cylinder. The area of the dischai|;e depends
upon the speed of the compressor; for a speed of 300 feet per minute, ten per cent,
of area of cyliHder; for a spaed of 450 to 500, fifteen per cent.
(W. L. Saunders.)
lOIO
TIDAJU OB FLUYIAI. BBFMCT.
Tidal or muvial JSfieot on Speed of a Steam or l^ike
^Propelled Vessel.
Deduced from the Experimenti and Notet of £dmn A. StevnUf Atsociate, and
C. P. Paulding J Junior ^ Members N. A. and M. E.
Xo Couipute Velocity of the Tide or Current iu Keet
per AdCiiiute.
R — ^
C 1. — - = V, repretenting the velocity in feet per minute ; C, Ungth qf course
in feet; R and r, T and <, respectively, whole number of revolutions of engine^ and
timet of run in minutts^ both against and witli a tide or current
I LLuBTRATiox.— Assume C one mile = 5 280 feei, R and r 970 and 548 number of
revolutioQs, aud T and t 8.43 aud 4.77 times. What is velocity of tide or current f
970 — 548
5280
970X4-77 + 548x8.45
=5280
422
- - — -
4 626.9 -|- 4630.6
= 240.7— /<e< velocity.
To Coxxipxite A.dvaiioe per Flevolution. of Kneiiie in.
Feet per ^linvite.
With Tide or Current.
C — \t
= A.
5280 — 240.7 X4'77 4«3«'9
548
Against Tide or Current.
C4-VT
= A.
5280+340.7 X8.45
548
7314
= 7-54/««'-
= 7.S4/«*-
R 970 970
NoTK.— If distance is given in knot of 6 080 feet, add 15. 151 per cent.
To Compute Speed of Vessel iu I^eet per ^lixiutek
» R + r _ „ 970 -H 548 „ 5181
rT-f-R<
= S. 5280
548 X 8. 45 + 970 X 4-77
= 5380
9»57-5
= 865.8/«e«.
Po Compute Number of Revolutions to Run one ACile
in Still W^ater and the Slip.
rT-\-Rt
^^ _ N. 548 X 8.454-970X4.77 ^ 9i57:5 ^ ^^ revolutions, imd
T-j-t 8.45-1-4.77 13.32 '
54 -t-970 _ y^ ^^ _ ^_5^ 700.26 = 58.74 lost in slip = 7.75 P^ cent.
2 2
NoTK. — In applying these formiilse, the number of revolutions in the run should
be as uniform as practicable.
Between runs, a variation of 5 per cent, will not materially affect the result.
STEAM SIPHON. A.n Independent J^ifting I*ump.
Capacity for a Discharge Pipe 2 Ins. in Diameier., per Minufe.
Water raised.
Preuure.
FMt. Ini.
14 6
13 3
13 3
Lbs.
30
40
50
Diacharfre.
Water rnlied.
Preasure.
Ditcbarii^.
Gallons.
63.54
85.71
lod
Feet. Ina.
13 2
13 2
13 a
Lba.
60
Gallons.
X19.68
'38 -44
»57.57
F'riotion Tjosses and T>isti»i"biatloii of* Powder in
"M^aoliiiiery.
Krom 8 to 400 I-P.
Losses Range from 55 to 65 per Cent
Per Cent.
flTrlctton of Engine 10 to 1 1. 8
" ofShafting 15 "17.7
» of Belts and Hearing. 15 »' 17.7
PbtOmM.
Friction of Lathes and Ma-
chinery 1510x7.7
Effective Operation , 45 *' 35. «.
CAST IBON, D^W-POINT, AND COLUMNS. lOI I
Strezifctli or Cast Iron.
At deUrmined by Tests on a Riehli Instrument at Lextr^fton^ Ky.
Aver<tge of i6 Tests.
Teniile,
ElMtie
Modolus of
Tmneverae,
Elastie
ModaloB of
p«r Sq. Inch.
Limit.
ElMticily.
p«r Sq. Inch.
Limit.
ElMticity.
Lb«.
Lba.
Lbs.
Lbs.
Lbs.
Lbs.
24436
, 21 469*
28 240 CXX)
Ann««led.
MalieabU.
4425
2508
21000000
41582
3104a
13000000
Refined.
2435
—
19300000
. {Janus H. WeUs.)
rTo iVsoertaiti the IDegree of A.'bsolu.te IDr^riiess in the
AAr and the I>eAV-I'oiiit.
Mason's Hygrometer.
11 ^
li
II
0
0
.08
1.17
•«7
2.33
•25
•33
42
4.67
5.83
•Is
.67
8.17
9-33
•75
•83
10.5
11.67
i|
II
ii
i|
H
3q
0
0
0
0
0
0
5-5
.92
12.83
10.5
"•75
245
6
I
«4
II
,.83
25.67
6.5
1.08
1517
"•5
1.92
26.83
7
1.17
16.33
12
2
28
7-5
1.25
»7-5
12.5
2.08
29.17
8
1.33
18.67
»3
2.17
30.33
«5
1.42
.9.83
»3,5
2.25
3>-5
9
'5.
21
14
2.33
32.67
95
i.5«
.22. 17
M-5
2.42
3383
lO t
1.67
2333
15
2.5
35
i^
Exceuof
DryneM.
l<
II
0 a
0
0
0
<5-5
2.58
3617
16
2.67
37-33
16.5
2-75
38.5
17
2.83
39-67
17-5
2.92
40-83
18
3
42
18.5
3.08
43-17
19
3«7
44-33
>9-5
325
45-5
20
3-33
46.67
o
•5
1
»-5
2
2-5
3
3-5
4
4 5
5
To Ascertain the DryneJis. —OytKATiOH. — From temperature of the air subtract
that of the wet thermometer, add excesB of dryness from the table for the differ-
ence, multiply sum by 2, and the result will give absolute dryness in degrees.
Illustratiox.— Temperature of air, 57; wet thermometer, 54. Hence, 57—54
= 3. Add ,5, flpom table, = 3.5 which X 2 =11 7 degrees.
To Ascertain the Dem - Point. —From temperature of the air subtract Absolute
Dryness and result will give the Dew-Point in degrees.
Illustkatiox— Temperature of air, 57; Absolute Dryness = 7. Hence, 57 — 7 =
yP Dew- Point.
Safe Orutsixing tStreriKth of Oolunine of a H^eight not ex-
ceeding 12 times their Diameter.
In Pounds per Square Inch of Transverse Section.
Material.
Basalt
Brick, hard
*■* common . .
Granito, hard
** common
Lbs.
2875
«75
58
1090
575
Iron, cast 28 750
Material.
Lbs.
14400
720
432
M35
43»
38
Material.
Mortar, common.
Oak, white
'* common
Sandstone
Spruce, red
'* white...
Lba.
36
432
280
«29S
540
240
Iron, wrought
Limestone, hard
*' common
Marble, hard
" common. . . .
Mortar, good and old
When the height of a column exceeds 12 times its least diameter in feet, or area
in square feet, divide the tabular weight by the number in the following table
corresponding to the length.
Height I 12 18
Divisor | 1.2 I 16
Illustration. —Assume height of a column of white oak 15 Inches in diameter
and 21 feet in length. What weight will it support ?
432 -f- X. 8 = 240 lbs. ,
21
24
27
3^
35
*?.
^l 50
6c
1.8
a
2-4
2.8
39
4.8
5.8 7-8
12
• TanaUa RfftMd Ultinntoi 03695.
PKEPETUAL AIM AS AC
flf=.ill-J
15 °5ll^m-
SS|||II
13
Pi
tis
i
liriH
fSa"
?'
SSI
^d;P
h
CEMSNT, HDMIDITT, METRIC
latlve Humidiiy and Dew Point of tl
At Delermiaed lig a Diy aad We< Themvnaeter.
■B or Tempenlure beliveen Iha Two TJiermoRiQtera sad ]
(OrwBioiri Otuemaliiry.)
ofMetrio Mea>
illgniilex i,B| + 3a = ilegree5"
ere-T- 5.69 = 8 ilrjchi
HeclolltereVyiji = cube tl
Hwlolilera X a.a, = huahela
Heclollwnx -ijr = i-ulie ys
KllaptrCi
r Ch«vj
KilomeMn-
< 33.84 ^OiDdouDO
<.a^j = pilluns
I0I4 CHIMNKY DRAUGHT, SITBAM YESSBLS, BTC.
Xo A.soertainL tb.e Ii!eifi;Ut of* ct Ch.ixxi.ja.ey for a Re-
q,xiired. IDrauglit.
Divide 7.6 by the absolute temperature of the external air, and 7.9 by the like
temperature or the gases in the chimney at the point of their delivery into it; sub-
tract this quotient n'om the former, divide the required draught by the diflerence,
and the quotient will give the height of the chimney in feet.
Or, —2 — =h. D representing the draught in inches ofwater^ T temperature
70 7-9
T t
of air -\- 460, t temperature qf gases -\- 460, and h height oj chimney in feet.
Illustration.— Assume temperature of air 20 o, and that of the gases 600^, and
required draught .6 inch /
.6 .6 ^ J. J
— = — — -— = nx.tfett
7^6 7.9 .00838 ' ''
20O + 460° 600° -f 460O
T*o Ascertain, tbe IDrauglit of* a CUizxixiey.
In Inches of Water.
Proceed as above to determine the difference of temperature, subtract the latter
Arom the former, and multiply the remainder by the height of tne chimney in feet
Illustration, — Assume like temperature and height of chimney as above.
!Resistan.oe of Steaxn Vessels.
The thrust of a pro|)elIer on the resisting collars of a propeller shaft is the meas-
ure of the power applied to the propulsion of the vessel.
a X llr 33000 33000 t» K.
Iff. P representing the titrust of the propeller in Z6»., S and S, the speed of the ves-
sel in feet per minute and knots per hour^ D disptaoement in tons (2240), A area of
immersed amidship section in square feet, and C and C, constants.
Assume the following elements of the steamer '* El SoP': Length betvjeen per-
pendiculars, ^j J. 2 feet; amidship section, g^^ square feet; displacement, 6760 tons;
S and S], i^.-j^feet and 14.5 knots; C and C|, 310 and Siq; and IIP z= 3500.
.66X33000^ 5. 69s X .475 ^6 Kg. 51695 Xi^ = 3«6 Iff.
1475 X 3500 ^^ 33 000 33 000
6760K X M- 53 ^ 357. 5 X 3048 ^ i^ 934X14.53^ I^,
310 310 ■"' 813
D. K. Clark gives — = EH*. W representing ufetted surface in square feeL
20000.
Coefiioieiits of* Radiation of* Heat.
For a Period of One Hour from 10.76 Square Feet* of Surface.
Silver, polished 16
Copper, red 20
Brass, polislied 32
Sheet- iron, polished. . . 56
Sheet-iron, leaded 81
Sheet-iron, black 345
Glass, polished 373
Cast-iron, rusted 419
Paper 470
Stone, building 499
Soot 500
Water 66a
{'■Home Study.^')
lEIeat Radiated, per Square F'oot per Hour.
From a Temperature of 180° to X59O in Units.
Tin-plate 1.37 | Sheet- iron 9.34 { Glass. ».z8
(TredgeUL)
—,1 I u_jii...ia..i
FORCED DBA.UGHT, GBOLOOICAL STRATA, RTt?. IOI5
IPoroed I>r»aglxt in Alarine Soiler.
C<mpre»Kd Air JSwhamting BUut in the S. & ''BewltUe."
Blowlnic
Engine.
Engine.
Coal
per hour.
Coal*
perI(P
per hour.
Water
evapo-
rated per
lb. or coal
Blowing
Engine.
Natural )
dniiRlit. f
.96
a
3
1H>
575
88.8
loas
106.1
Lba.
ai3
289
315
32i
Lba.
3-72
326
3.1a
304
Lba.
10-77
8.82
8
7.82
IR'
4-2
5
6
7.4
Engine.
I Coal
per hour.
Goal
perIH>
per boor,
IIP .
I18.8
1 19. 8
Jia7.9
135 7 '
Lbs.
348
374
400
430
Lbi.
2.93
3>a
3. 13
3.10
Water
evapo-
rateaper
lb. of coal
Lba.
783
7-53
7
7.03
{D.K. Clark.)
Formation.
A.b9orption or G^eologioal Strata.
P6r Cent, by Volume.
Locatlgn..
Dolomite
14
i(
l(
ti
Gabbro
Granite, Hornblende..
Freestone, Calcareous.
Limestone
Galena ....
Trenton . . .
Oolite
Devonian..
u
(i
*(
tl
Sandstone.
It
(I
u
((
it
il
it
Quartzose.
Oolite
Old red...
Clay, dry
Sand and Gravel.
Joliet, 111
Tieniont, III
Winonu, Minn
Red Wing, Minn
Mantorville, "
Duluth, »'
B. St. Cloud, '♦
Grand Beaucbamp, France
Bedford, Ind
llockford, III
Cheltenham, Eng
Boulogne, V ranee
Quincy, 111
Big Sturgeons Bay, Wis. .
Grand Beaudhamp, Prance
Water in
100 p^rta.
i(
Cheltenham, Eng. . . .
Gloucestershire, Bog.
Fond du Ijac, Wis. . . .
Fori SneiliDg, Minn. .
Jordan,
Berea, Ohio .
It
1.06
I 13
4.76
2-5
5-55
•29
•42
29
4 4
4-2
2.1
12.15
.08
Authority.
G. P.
Merrill.
(t
{ -in
•25
( 4 37l
M3 «5J
29
2395
II. 6
4.81
6.25
1.25
6.6
la
<(
C(
(I
u
M. Delessee.
D. W. Mead.
il
E. Welherel.
M Delesnee.
O. P. Merrill.
i(
u
M- Delessee.
C(
B. Wetberel.
li
6. P. Mtrrill
tl
it
D. W. Mead.
R. J. HInton.
il
tt
{II }
{Daniel W. Mead, C.E.)
Caet-iron. 'Water Pipes.
To Compute Tliiokness of IMetal.
Hd pd
-~— -f- . 25 = T, and ^ 1- .25 .= T. H representing head ofpretmre ofvMXter in
9000 425^
feet^ d internal diameter of pipe, and T thickneu, both in \nck99, and p interior preu-
ure in lb$. per $q. inch.
IiiLUBrRATioM.^AssnnM head of wateir 200 feet, diameter of pipe ^ ioa, and if-
terior pressure 86.83 lbs. per sq. inch.
200x8 , . 86.83 .
— r-— +»5=-4«7**»*M *°d ^ + -25 =.4134 int.
For faucet ends, the eqaiyaleQt length of pipe, equal in weight to that of the
faucet, 7 -|- d -7- 1 5 = ins.
See ante, p. 147. (D. K. Clark.)
^— ^ I I I I III. I ■ ^fc^.*.^^^..^^^.^.^.^^ ^^Hi»i.i ■ ■ ■ I ■ - ■
* Antin briguettea. Tha fuel coniaiiMd and the power were doubled, but the •▼aporative iMiimey
wH redocad.
10 1 6 PBICTION AND FLOW OF WATEB IN MKTAL PIPES.
Friction of B^low of 'Water in Sznootli ^Vletal Pipes,
From .5 to 3.5 Inches in Diameter.
To CoTxipute tbe I^oss of Xlead.
Per loo Feet.
^ • '0315 — .o6d I u^
.0126 + -^- , X -; X r = H. d, tntoma2 diameter, H, JoM 0/ Aeod due
to friction o/Jlow, dU in feet; t>, velocity of Jlow per secotui, and I repreeenUng
length of pipe.
Illustration.— Assume diameter of pipe 2.5 ins., lengtb, 100 feet, and velocity
of flow 36 feet per second, what will be the loss of head due to ftriction, velocity of
flow, influx, and efflux ?
i: I -0315 — .06x2.5-7-12 100 1296 ^ , « «,
•0126 H — i-2 . , X : X T-^ = .0126 + .003a = .0x58 X 480 X
V30 2.5-1-12 64.3
30. z := 1 32. 44 feet loss due toJHction.
Loss of Head Due to the InJUtx of the Water into the Pipe,
«** , t>* 1206 , E2q6 ^ ,
Hence, 152.44 -|- 30.34 = i82.6Sfeet, total head.
BViotioEL of Flow of "Water in Cast-iron Pii>es,
From 4 to 60 Inches in Diameter,
, .001666 t t>» „ „ .^ ,
.01989a + •— ^ — ^ 1 ^ — 77 ^ ^* "Sfyiroftoto CLs preceding.
iLLUSTRATioir. — ^Assume volume of water required 30000000 gallons per 24 hours,
diameter of pipe 16 inches, and length of it 1000 feet. What will be the loss of
head due to frictiop of the flow and what the loss by influx into the pipe in feet?
V 231
-7 X '- 720 = velocity in feet per minute. V representing votwrne of discharge
t a
in gaUons. <, time of flow in mintUes, a, area qf section of pipe in sq. tncftef, and 730^
lineai inches of flow per minute.
Gallon = 231 and area of pipe = aoi cube indus.
20000000 231
X;7;:;7-5- 12X60 = 13889 X 1. 149 -4- 720 = 22. 16 /Mt velocity per second.
388
627
34 X 60 aoi
Or, by table, p. 1016, ^—^ssaa.is/^
Hence, 32. 15' x .3465, flrom table, = 120.02 feet loss of heady and — -> X .505 — ^|— 5_
3 flr 64. 3
X . 505 = 3. 86 fe^ loss by ii\^ux to pipe.
Loss of Head Due to the Influx of Oie water into the Pipe.
V2 , ^ 22.162 22.l6» ^ M „
— ■ + -- X.5o5 = -T h-T — x.905 = "'SfB^- Hence, 120.944-11.5 = 133.44
3 gr sg 04.3 04.3
feet totai head.
20000000 gallons per 24 hours = 13889 per minute, By Coefficients in table, p.
Z017, for a pipe of 16 ins. 13 889 -7-627 = 22. 15 ^t velocity^ and 23.15^ X •2465 =
S3a94,^ loss of head due toJHction.
To Ooxnpute tlie ITlo-wr ot "W^t&r firozxi a G-iven. Heeui.
V -r- ^^ X 12X60 XT. T r^irreseniing time of flow in minutes,
a
Illustration. —Assume the elements of the preceding case.
231
22. 15 1 -?- -^- X 720 X 60 X 34 = 19 987 430 gaUons.
20I
— repreMnting the head required to produce the Telocitj, and — X .505 the loet doe to tlie «■•
a g ag
^nce of the water into the pipe.
By BeardnuuL, p. 548, « would s a3.6/*tt.
FRICTION AND PLOW OF WATBB IN MBTAL PIPSS. 101/
^^lien tlie GMven Xjeixgtli is X^ess or d-reater tUau tlie
Xjenstb. of* lOOO in tire foUo^wiiig Table.
The ratio of tbe given length to the length in the table is ascertained by dividing
the length in the table (looo) by the given length, and the inverse ratio to the
length in the table is awertained by dividing the given length by looa
Assume, as in the second of the preceding cases given, the length to be 1500 feet.
i^= 1.5. As the flriction head (for 1000 feet) of 130.94 corresponds to a veloc
_IOOO
ity of 22. 16 feet per second, 120.94 x i-5 = iSi. 41 feetj the Jrictional head in a pipe
of I ^oo feet in length.
Application of the Formulas in the following TcMe.
Assume a lake 1500 feet distant to discharge water through a cast-iron pipe 10
ins. in diameter under a head of 70 feet : What is the velocity in feet per second,
the loss of head to the influx into and flow through tbe pipe, and the discharge in
gallons per 24 hours?
_ , .00167 ^ Vq gh V64. 3 X 70
.oio8o4 ^=.o2i89=c — = g = • — •> -^ J .
10-^ " /I I 1500
sj i+.505-h 5 XC ^ i-h-5<^5+ ^^i^ X.02t89
ra ' — (!^ — ja48/«c< velocity.
Vi. 505-1- 1800. 7X.02189 ^-4
C = 352 512 X za48 = 3 694 326 galloni.
Assame a discharge of water of 2450 gallons per minute, through a cast- Iron pipe
10 ins. In diameter and 1500 feet in length : what will be tbe loss of bead due to
Ariction, and what the discharge in 24 hours?
2450-4-245 {from table) = jo /iet velocity per second, io« X .4084 {from table) x
-'— = 61. 26feetfrictum head, and lo X 35a 512 (from table) = 3 595 120 gallons.
1000
Hencei, 1 +.505+ .03189 X 1800 X ^^ = 4a8o7X 1.708 = 69.698 /erf total
04.3
head
Coeffloients ibr Computations of Velooitsr or IHo^v, X>is«
charge, and X^osa of Head, due to Friction of* F'lo'w
of ^Water in Pipes, lOOO Feet in Uength.
Velocity of Flow.
Discharge -i-CoefBcient=i»«an velocity of flow in feet per second, and velocity x
Coefflcient = discharge in gallons per nUmUe.
InchM.
Diameter..] 4 I 6 I 8 I 10 I 12 I 16 I 20 I 24 I 30 I 36 I 48 | 60
CoefflcientI 39 j 88 | 157 | 245 | 353 | 637 1 979 1 1410 1 2303 1 3173 1 5640 1 8813
Loss of Head due to Friction =iCo^eieni x Square of Velocity.
Diameter..! 4 | 6 I 8 I 10 I 12 I 16 | 20 1 34 I 30 I 36 I 48 | 60
Coefflcient 1 1 . 161 1 . 722 | . 5231I .4084I . 3353I . 2465I . 1949I . i6zi | . 1278I . 1060I •o7^l .0629
Discharge per 24 Hours = Coefficient x Velocity.
IncfaM.
Diameter I 4 I 6 I 8 | zo I 12 1 16
CoeffictoBt I 56403 I 126931 I 335608 I 353513 I 507617 I 903448
Diameter I 30 { 34 I 30 I 36 I 48 I 60
Coefflcient | 1410048 | 3030490 I 3173600 | 4568568 | 8x31859 | 13690400
Tabu, and, euentially, the computations from the v<Uuable work by Edmund B,
Weston, C.E. {D. Van Nottrand Co., 1896).
ioi8
BELTS AND BELTING.
T'o Cpnaptite tlie A.ot-u.al IDisoheirge of* Water tlirouslft
A Oouical Tulae (Nozzle). Coefficientsofi^docity andt^ftlffiiix.
Angle.
5<^26'
Velocity. Efflux.
.829
.919
.829
.924
Anprle.
12° 4'
J3O 24'
Velocity.
•955
•963
EfiSoz.
.942
.946
r-
Angle.
19O a8'
83°
Velocity.
•97
'974
Efflux.
.924
9M
{Home Study.)
{Contintied frqm poffe 443.)
Pulleys should have a slight convexity of surface. Authorities differ, from .5 inch
per fvot of br«fulth to .1 of breadth. Belts run at a high sp^ed are less liable to slip
than at low speed.
The best speeds for economy are f^om 1200 to 1500 feet per minute, and the best
for result not to exceed 1 8cx>.
Belts.— Le&iheVy toirside. . . . x I I<etiihier, fle&h-sidd. . . .74 | Rubber. 51
Guttapercha........ .44 | Canvas >.. » ^^4 .35 ... .
Coefficient of Friction of a Belt in oi>eration is assumed to be flnom .2 to .4.
Smooth-mirface belts are most eadurablo and soft most adherent.
Round belts .25 and .5 inch in diameter are fully equal in operation to flat of x
and 3 ins., and grooves in their pulleys should be angular or V shaped.
Long belts are more effective than short. *
The neutral point of a rope belt is at .33 of diameter from inside surface.
Friction of driving and pdlley bearings is about .025.
A fan-blower No. 6,* driven by a belt 3.875 in& in Width and .18 in thickness, at
a velocity of 2820 revolutions per minute, requires |)ower of 9.7 horse&
Area of belts per EP varies essentially, ranging from 25 to 100 square feet; the
mean is 75.
The average '' net effective stress " of k belt is the diflferen^e of len&ional Stress
between its driving and slock surfaces per lineal or sq. indh -of seotiod, iind this
stress over fast and loose pulleys was but >.4 of that ov^r- cones.
"Idlers/' are most effective on the sl^ck side of a belt.
Narrow and thick belts nre preferable to wide and thin. The Joining of the ends
of a belt should be by splieitig and cementing, and the length of the splict^ the same
as the width of the belt, and if the ends are cut slightly convex and so connected
the effect in operation will be that of equalizing the stress on the centre and edges.
The OuhI 'stretching of leather belts is 6 per cent.
A double belt with an arc of contact of 180° and i inch in width will sustain a
stress of 35 lbs., and the number of sq. feet of a double belt over a pulley per min-
ute to. transmit onf H* is 80..: >. • •. r . < : .
Tlie transmitting powet (resistanOB) of the ttrc'of contact i^ee^ntialiy ptupor-
tionate to the arcoftSa^. ' • • '
The average '' working load " on fast and loose pulleys was but .4 that of on cone
pulleys, and the ^' net working loa<! ** Is the difference in tension between the driv-
ing and slack.
The diameter of u pulley should be increased in proportion to the thiekness of,
or number of plus of, a belt.
A band wheel at the Amoskeag Mfg. Co., N. H., 30 feet in diameter and no ins.
face, drove three belts, havitig a lineal vf idth of 104 Ina, at-a speed of 5750 feet per
minute. Capacity of engine 1950 H*, trx>n\ which is to lie deducted the friction,
which is assumed largely at 5 per cent., leaving 185a net IP. .
Hence, ' -^ = 17.8 IP per inch of width of belt and ^^= 333 feet speed of bell
104 17'9
per H* per inch of width. ...
If a bell of its proper length slips, the under surface slwuld be moistened with
boiled linseed oiL *
When belts have become dry and hard, apply neat's-foot or liver oil, mixed with
a small quantity of resin.
Rubber belts are improved by the application with a brush of A composition of
litharge, red and black lead, in equal parts, mixed with boiled linseed oil, and var-
nish sufficient to cause it to dry quickly. They are less liable to slip than leather,
and are suited for service when exposed to mOiSture.
Cfvient. Gutta perclia. 16 parts, rubber 4, pitch 2, shellao x, and Unseed oil 3;
cut in small parts, melted, and well mixed. {Moletworth.)
For a table of Bells for Fan-blowen, etc., see J. H.Coopcr, in « Jour. Franklin Inst.,*' vol. jS6, p. 409.
OIL BN6IXKS. — BLAST AV1> A-XHAUST BLOWBES. IOI9
OTL KNGmKfe.
Oil TCn.g:in.es are In employ meni as Motors.
In tbc Priejtiniaa, mineral oil or petroleum, having a speciflo gravity of .8 Oimp*
9vardB, with a flushing-point from 75O to 150°, is umU.
The oil is mixed with air under a pressure, is drawn into the cylinder, and ig-
nited by an eleotrio ajKirk.
llie oonsamption of oil varies ftotn 1.25 ponnda per bralce ff per hour for large
engines to 1.6 lbs. for small.
An engine, cylinder 8.5 ins., Stroke la ins/, and 180 tevolntiobB per minote, de-
veloped 4.6 brake £P, with a consumption of .1.2 lbs. of oil per IP per hour.
The Hargredves motor is designed for the use of coal-tar or creosote as fuel.
It coqsists of nn air-compressing pump and motor cylinder, to which a regenera*
tor 18 adapted, which absorbs a portion of the heat of jibe exhausted gases, and
yields it to tbe incoming charge.
The compressed air is delivered tbreagb th« r^renerator into the motor cylinder,
where it is exposed to a jet of coal-tar or creosote, and being healed to redness ig>
nites the fUel.
In a trial, 40 IH* was generated by tbe consumption of .512 lbs. coal iar per hoar,
and 32.4 per ccnu of heat converted into work, and in another trial with a smaller
engine, 5.17 IIP was generated by tbe consumption of 1.3 lbs of creosote per hour,
and 14.4 per cent, of heat converted into work. {D. K. Clark.)
Slast and IGxh.au.st B^atx Slo^irers*
{In addition to pp. 447-448 and 898.)
The BUist Areay which fs the basis of all computations, is the diameter of the
tsLD (wheel) multiplied by the width of it at its periphery.
Exhaust Fan. — The area of its discb.trgc fcbould be about equal to three times
tbe blast area, or equal to tbe area of .the inlets, and the vtidtb of the fan 25 its
diameter at its greatest width.
Volume Blower. —For foroed draught tbe <lla<:harge «Ma sbontd be about equal
to the area of tbe blast, and the width of the fan 25 its diameter at its greatest
width.
Pressure Blotoer. — As for a Cupola, the discharge area should be .33 that of the
blast, and one-half the area of the ialet^ and the diaipeter of the fan should be pro-
portionally great, and the blades of the fun narrow at their extremity.
In ordinary practice the inlets are made about one-half the diameter of the fttn.
{American Blower Co.)
I>im«nsionii- of* F«tn«
Prkssurs.
From 3 lo 6 ovncetper Sq. Inch; or 5.3 to 10.4 Incke% of Waler.
Dfamatsrof
Fan. I Inlet*.
BlAilM.
Width.
Ft. Int.
Ft Ina.
\ Ft. Ins
3
1.6
.9
36
1.9
.10.5
4
a
I
Length.
Ft. Int.
■9
.10.5
I
Dfsinetor of
Fan.
Ft. In«.
4-6
5
6
InleU.
Ft \vm.
2-3
9.6
BladM.
Width.
Ft. Int.
1.1.5
'•3
1.6
Leniitth.
Ft Int.
1. 1.5
>-3
1.6
Ftintk 6 tog otmees per Sq. Inch; or 10.4 to 15.6 Inches of Water.
Dlami
Fan.
»t«t of
Inlet t.
Biai
Width.
Ft. Int.
4
Ft Int.
X
x.6
Ft Int.
.9.5
L«n^h.
Ft Int.
X
1. 1. 5
13-5
Diameter of
Fan.
Ft Int.
4-6
Inlett.
Ft Int.
1.9
2
2-4
Blades.
Width. I Length.
Ft Int.
.10.5
X
t.2
x.xo
{Mr. BudMi JSmperimenJU.)
Ft
I020 FLOOB BEAMS, GIBDEBS, COLUMNS, ETC.
To I>eterniine th.e Dixnensious of .Floor- Beaxns, O-ird-
ers. Columns, ITouiidat.ions, and Piling of* a Build-
ing to Sustain GKiven X^oads on tJb.e Floors.
Omsiruction, Dimengions, and Capacities as Assigned by (he Department of
BvUdings, CUy of New York,
Foundation. — Piles, not less than 5 ins. at point, spaced not to exceed
30 ins. from centres, and to support not to exceed 40000 lbs. = 5.714* tons
per sq. foot with two lines of piles, 8.57 tons with three lines, and 11.43 tons
with four lines, etc., or 2.857 tons per additional line.
WaUs and Piers. — Include all built below the first tier of beams, at or be-
low the level of the curb-stone. Masonry, of stone or brick, with lime mor-
tar, not to be subjected to a stress exceieding 16000 lbs., with lime and
cement 23000 lbs., and with cement 30000 lbs. per sq. foot
Side WaUs, — Their widths as determined by their height and the propor-
tional area of fiues and recess^ in them. If of stone, at least 8 ins. wider
than the wall first above them, to a depth of 12 feet below the curb, and for
each 10 feet or part thereof, an additional 4 ins. If of brick, for 8 ins. put
4 ; other requirements same as for stone. In buildings where the beams
are 25 feet in length or over, an addition of 4 ins. in width must be given to
the side walls from above the curb-stone. ^
Front and Rear WaUs* — Except where supporting a girder, for half the
distance between it and the column, are non-bearing, and may be 4 ins, less
in width.
Footing or Base Course and Piers, — Of stone or concrete, or both, and at
least one foot wider than base of wall or pier. Capacity of solid primitive
earth, estimated at 8000 lbs. per sq. foot.
When the instability of the ground is such as to render additional support
to piers necessary, they are to be connected by inverted arches of the full
widUi of the piers, but not less than 12 ins. in width.
Widtli of Walls for Ghiven Heiglits.
Height Measured from Level of Cwrb-Stone,
Height
V
Hdth.
Feet
IBB. Ft
Itia. Ft
Ins. Ft
iBt. Ft
40 to 60
z6 to 4ot
Then 12 to top.
— —
— —
60 to 75
30 to 25t
.. ,6 u
.— —
— —
75 to 85
24 to 20t
" 2oto6ot
Then x6 to top.
— —
85 to 100
28 to 25t
" 24 to sot
" 2oto75t
Then 16 to top.
If over 100 feet, each additioniU 25 feet, or part thereof, above the ctirb- stone to
be increased 4 ins., and if there is a clear span of over 25 feet between the walls, 4
ins. additional width for every 12.5 feet, or flraction thereof, that they are more
than 25 feet apart.
Nora.— For otiier ead fuller detidla of dinMOdoiu, see Lawi relating to Constraction of Boildingi.
Weight of Materials Per Cube Foot.
MaterUle.
Lbe.
Mnterialt.
Lbe.
Brick \
"5
160
160
White Marble
Cast-iron
160
^§°
480
487
35
Masonry )
Sandstone
Wrought Iron
Rolled Steel
White Pine
Granite or other)
stone 1
Mnterlale.
Lbe.
3«
23
54
54
Aoo^.— Weight assigned 50 lbs. per sq. ft. is addition to weight of its materials,
assumed in the following compatations at 15 lbs.
Spraoe
Hemlock.
Georgia or Tellow)
Pine t
White Oak
* 2240 lbe.
t Or neareet tier of beame to thai faelgbt
FLOOB BEAMS, GIRDEB8, COLUMNS, ETC. 1 02 1
Header and Trimmer Beams, of 4 fe«t or less in length, one inch deeper than
their adjoining floor or roof beams: when over 4 feet and not over 15 feet, to be
proportionately increased, or doubled in width; and when over 15 feet to be sup-
plemented with a wrought iron Fitch plate of suitable thickness securely bolted to
beams.
Crusliina: and Transverse Strengtlx and Coefiloients
of* Safety'.
Cnishbg per Sq. Inch.
Lbs.
Cast-iron 80000
Rolled Iron 40000
Rolled Steel 48000
White Pine 3500
Spruce 3 500
Georgia or Yellow)
Pine J5000
White Oak 6000
Trantvene Oba Inch Squara
•nd Loaded in Centre
between Supports.
Lbe.
Georgia or Yellow)
Pine JSSO
White Oak 550
White Pine 450
Spruce 450
Hemlock 400
If uniformly loaded doubled.
Coefflcientt or Factors of Safety
for Crushing and Tensile.
Columns and Vertical Sup-
ports of Wrought Iron
or Rolled Steel. ..Four.
All other materials, ./^ve.
For Tie-rods and all parts
sutjected to a Tensile
stress Six.
Illustration. — Assume a warehouse of stone and brick masonry, 25 feet in
width, 4 stories in height, with a cellar and sub-cellar, with one line of girders and
columns above and brick piers in sub>cellar, 8 feet apart ft-om centres, stairways 4
feet in width and 15 in length; ground, wet sand.
Heights between Levels of Floors, inclusive of Beams, and Required Capacity 0/
Beams.
Ft. Lbs.
Sub-cellar 8 . —
Ft.
ist story 15
Cellar 10 300 2d Story 12.83
Lbs.
300
250
Ft. Lbs.
3d Story «o-33 225
4th Story 9 300
Height of Buildistgfrom Curb hne, as determined by the Hei^s bdween the Floors.
To the upper side or level of the 4th floor 39' 9", and to the under side of the
roof 48' 2", hence the brick walls are to be x6 in width Arom ist to under side of
3d floor, and 12" above.
Foundation of Side ITaUf.— Sub-cellar, le^-f-S" for stone masonry = 24" for a
depth of 12 feet below the curb line, and for its part of 10 feet below this, 4"-)- 28"
= 2 feet 4 ins.
Cellar, i6"+ 8" for stond masonry = 24", or a feet.
ist, 2d, and 3d floors i6"= i' 4", and 4th floor 12"= i foot.
Floor beams, half lengths. Cellar 12' 6^—2' 4'= 10.16 feet, 2d, 3d, and 4th
stories 12' 6"— 1' 4"= i s,i6feet. xst story 12' 6"— 2'= 10. 5 feet
NoTS.— The ■nb^allar floor Is of oiaionry.
All Computations made for a Lineal Section of 8 feet of Length of Building.
Operation.— Weight to be supported by columns under roof. Lbs. Lbs.
8 feet apart from centres. Area of section 11' 5" x 8'= 92 sq.feet x 65
lbs. (stress on roof and weight of its materials) =
Girder, White pine 5"x 5" In breadth, depth = /iiii?^ =6.48 (6.5) ins,
V 225* X 5
To be supported by column
Column, Yellow pine, o feet, less oak cap and girder 8^.5 = Bfeet 3. 5 ins.
Diameter by approximation ttom table, p. 769, 4.7 ins., area = 17.4 sq.
ins., and by formula, p. 768, — 5000X1734 _^ ^^_ ^^^
5900
5963
85
\4-7/
004
Fourth .9fory.— Weight required to be supported 300 lbs. Area of sec-
tion 1 1'. 16 X 8'= 89. 33 sq. feet x 200 lbs. =
Floor beams, White pine a"x 10" and 19. i" apart flrom centres, capao-
ity not less than 200 lb8.r= 257 lbs. per sq. foU
17866
330
* Coefllcleni for While pine nniformlv Uiaded.
t For safety.
I022 FLOOB BKAMSy GIBDBBBy COWMNS, BTO.
« LiM. Lba.
Gfrder, TeUov pine, 7 ins breadth, depth = /— 1* ''^ =; 8. 7 ( 8.5 )
V «75*X7
int. and cap = 1^
To be supported by column 24438
Column, Yellow pine, 9' 6" less girder and cap := Zfttl 7 int 24 438
Diameter by approximation, 7.75 Ins., area — 47 «^. iiw., and by
formula, p. 768, 5«» X 47 _^^^ ^^^^
Weight of column and cap 172
Tkir^ iS^fory. ^Weight required to be supported, 245 lb& Area ot
section, 89. 33 x 295 lbs. = «o 100
Floor beams, White pine, same as preceding, t^ 257 lba per sq. foot, . . . 330
Girder, Yellow pine, 8 ins. breadth, depths / °*^° = 8.s ins,
' ' *^ V 275X8 ^
and cap =... , 220
To be supported by column 45260
Column, Cast-iron, 13 , less girder, cap, and sole plate i'= xnfeeL —
Diameters by appro^dmation, as preceding, 6 and 5.125 in& = 7.65
tq. int., and by formula, p. 768,. ^ ^' — = 50579
ProoMd in like manner for remaining oolumns and floom
Second Story. — Weight required to be supported ' ^ 22 333
Floor beams, White pine, 3 X " X 19'- 1 <ns 397
Girder, Yellow pine, 8 ins. in breadth, 9 ins. in depth 935
To be supported by column 68225
Column, Oast-iron, diameters 7X6 Ins., length 15', less girder, cap,
and sole plate =: 14/ipet 72 416
First Sffory.— Weight required' to be supported 96 800
Floor beams, White pine, 3 x 12 x 19.1 ins 397
Girder, Yellow plue, 9 ius. in breadth, 9. 5 ins. in depth 274
To bo supported by column '95696
Column, Cast-iron, diameters 7X6 Ins., length 9 feet, less girder, cap,
and sole plate = B/eet. .' 1 12 070
Cellar. — Weight required to be supported. 25 200
Floor beams. White pine, 3X 12X 19.1 ins. ' 397
To be supported by Pier. , < . , , 121 293
Sub-etUaar, Fier Brick maeonry in lima and cement mortar 30 int.
8q.=:6.25 sq. feet, which at 23cxx> lbs. per sq. foot = 143750
Weight. 6.25 X 6.33 feet in height and footing stone, 8 Ins. in depth x
42 Ins. square =s 5800
To be supported in addition to weight of piles 127093
Requiring 4, set at 30 ins. from centres, and driven at least to a refusal
of 30000 lbs., which, when they are In a quiescent condition, =
40000 lbs. z^ 160000
Side Walls and Footings. — Weight 01 each, Including one half ot
weight on Pier an 370
Requiring 7 piles, set and driven in like manner for the pier 280000
NoTB.— The «zecu of b«u1nfr raMcity of the piles it to meet any extraordfawry luullnc of the floon,
mad the poMibllity of edilsfr to tb« iMiKfat of Uw butUUng.
For dimenaiona of HMMler and Trimmer Beams, see pp. 834-«84i.
— • - - - — --^ — ' — — — ^ ■ — • ■ ■ ■ i»
• CoeOdwl /or Yellow piq^
^►-•—
NON-CONDUOTCKBS OF HEAT.
I033
HiOss of Presfiiar« of yio-w of Air for Vax»yiafif JDliajia.-'
elierH of Pipo axxd. Velooitiea.
' ' ' •
l«sa of prefimre per sq. ioch for varying Diameter of pipe and Velocities of fiow;
computed upon the basis that the friction is clii:^ct)y inverse to the innet siirface
of the circumference of tlie pipe. TUifi is not normally correct, inasmuch as whilst
the area of the inner surface is in a direct ratio with the diameter, that of the
transverse area of Uie pipe is as the square of its diameter. For ordinary reference
and for pipes of approximate diametors it is sulQcientty correct
The TaJ)le, with some addition to the velocity^ is for a pipe 0/2 ins. in diameter.
For. other JHqmtter thf Lots of Pressure is directly Inverse to the Diameter.
>
Feet^
100
200
Pressure
per Sq.
Foot
Veloeltyof
Air per
Miaute.
Lbs.
.0005
.0008
.CKKII
Feet.
•300
400
5QO
I3^i
s ^ o
Lbs.
.0031
.008
.oil
Velocity of
Air per
MiBute.
Pressure
per Sq.
Foot.
Velocity of
Air per
Miouta.
Velocity pf
Air per
Minute.
Pressure
per Sq.
Foot.
Feet.
600
750
900
Lbs.
.019
.Q28
Feet,
lioo-
1500
2000 1
Lbs.
.05
.078
.X04
Feet.
3400
30OQ
36cx>
Lbs.
.312
•45
Velocity 0
A4r per
Mitmte.
Pressure
per Sq.
Foet.
Feet.
4200
4800
6000
Lbs.
.612
.8
I 25
{American Blower Co.)
R.4&lative Efflcieuoy of I^on-Condxiotors of £Ieat<
Tiie. efflciency of substances for the retention of beat varies generally inversely
lo their power of conduction of it.
By experiment it was ascertained that the relative condensation of steam in a
metal pipe under the following conditions was :
Bare 100 | Oementoteied........ ^ | Hair-felt covered 27
Relative Cost of Steam I»oAver in l^ngiiies per 1^,
Based on cost of one of 1000 IP 1888.
Plant, Fuel, and Cost.
Nl)D
Condensing.
: $ cts.
RDgiiie itnd House complete 39- 50
Depreciation, Repairs, Interest, Taxes, and In-t
surance I 3. 70
Boilers, House, and Gbimney .<. | 39,
Pepreciation, Kepairs, Intere&t, Taxes, and In-
surance ; 3.95
Total yearly cost of Coal aad daily attend- 1
ance 308 days. . . . , — 25.595
33248
3
Total yearly cost
Coal per i H* per hour in lbs.
Co.a...U.,. ^a~Sj.
$ cts.
33-
4.14
.24.89
338
21.817
29-355
2.50
$ ct^
40.
so?
18.36
2.50
16. 570
24. 087
1-75
Chas. T. Main, A. S. M. E.
Non.<— If tb« «zlwait timm. ii otiUM4> tb« nt^ wUl tw GvrtwpaiuUwIy reduced.
'Po Grradiiate tlie Compass of a rTransit Th-ood-
olite to Coinoid« ^w^ltli tlie Xiine of Sifflit
• of tlie Telescope.
Bute a small hole in centre of cover of objeet-^ass and put it in place ;
deprt'Sd eye end of telescope to the graduated circle of the compaas. Pla^e
telescope parallel to the light, as Uiat from a window, and with a sheet of
white glazed paper, or like surface reflective of the light, a distinct view of
th^ graduations on the circle will be observed and so well defined that the
positions of 180° and j6o° with regard to the line of right can be obtaoieds
I024 APPENDIX*
To I!>et«i*zxiine tHm Diameter of Cylinder of a ITotx*
.Coixdensiiiif 8teatii*Ktigiiie^ and tlxe KlezxiezitB of* a
Fire-Flixe Sieaxxi Boiler, by Coxnputatioix of tliem
froixx th.e required Capacity of Kusixxe and of its
A.88igiied Operations.
Steam pressure by g^nge, 70 lbs. ; cut-off at one-third; stroke of piston,
3.5 feet ; revolutions, 50 per minute ; clearance^ or volume of space between
mean surface of piston and valve seat or o|)ening, .1; back pressure and
friction each assumed at 2 lbs. per sq. inch.
Hence, P = 7a; ^ = 42-^3-7- 12 = 1.16 ; r = i.z6-|->i = i'26 ; Lssj-s; c=:.i',
R= ^■^,"^*' =286; 6 = 2; and/=2.
1. 16 -f~ •*
Assume— Kvaporation of water = 10 lbs. per lb. of coal. Combustion, 15 lb& of
coal per Hq. foot of grate surfuce per hour. Heating to grate surface as 35 to x ;
and transverse area of tubes to grate surface, . 14.
Xo Compute Alean Sffeotive Pressure (p. 7x0-711)1
7o(i.26Xi-fhyP»log.g-86~.x) — -_x73.9
35 3-5
To Compute Diameter of CifUnder.
^-^ — ^^°°^ = 14 143, which -i- 45.7 {&f.= 309.5 im.= 19.85 (20) t4<. diameter.
5oX3-5Xa
Then, diam. 20 int. = 3x4. 16 sq. int. X 42 ins. stroke =. 13 195, steam cut-off at 33
= 4354 X 50 X 2 = strokes X 60 minutes = 26 124 000 cube ins. ; which -i- 1728 and
again by 5.05, the volume of one lb. of steam at the absolute pressure =2994 Ibe.
Assume feedwater at 50^. Then 2994 lbs. steam at 70 lbs. gauge = 85<) absolute
pressure, by Factor of Evaporation (see below), = x.201 (the equivalent value of
2i2<^) = 3596, and 3596 -T- 34.5 (the lbs. per hour evaporated at 2i2<^ at 70 lbs. gauge
pressure*) = 104 I£P.
Hence, 2094 lbs. water to be evaporated per hour ; 2994 -r- 10 lbs. water evapo-
rated per 16. of coal = 299.4 lbs. coal per hour; 299.4 -7- '.5 lbs. of coal expended per
sq. foot of grute= 19.9 sq. feet of grate surface; and 19.9 X 35 sq. feet of heating
surfiice per sq. foot of grate surface =606. 5 sq. feet of beating surface; and X9.9 x
.14, proportionate transverse area of tubes to grate surface, =2.78 sq. feet.
If engine were to be a condensing engine, the increase in the mean pressure in
the cylinder will correspondingly decrease the diameter of the cylinder, less the
increased friction of the operation of the air-pump, assumed at .71 Ite. pressure
per sq. inch.
To Compute ITaotor of lfi'vai>oration.
jl ^
. X F. H and h representxTig total keai of the tteam at given pressure and
965.7
temperatta-e offeedwater^ in degrees, and ¥ factor.
Illustration.— Assume gauge pressure of steam 70 lbs. per sq. inch, and tem-
perature of fecwlwater i loP.
1209.8 — XIO
— — = X. 139.
9657
Application.— Aaanme the volume of water evaporated at the temperature of the
feedwater of 110° to be 40000 lbs. in 10 hours ; steam, gauge pressure 70 lbs. per
sq. inch ; coal oonsnmed, 4000 lbs., and relVise flrom it 350 Ibi.
Tbexk, 40000-^4000=110 lb& water evaporated per lb. of coal consumed, and
40000-7- 4000 — 350 1= 10.96 lbs. water evaporated per lb. of combustible.
For this pressure of steam and temperature of feedwater, the factor of evapora-
tion t = X.139 ; which X 40000 (volume cf water) = 45 560 lbs. equivalent evapora-
tion at 212° ; and 45 560-f- 4000— 350 {lbs. of combustible) = 12.48 lbs. water evapo-
rated per lb. ofcnmbustiblejrom and at 212^.
If 34.5 lbs. water evaporated flrom and at 21 2P = one IH*, a boiler or boilers, oper-
ating with the given elements, will have developed 45 560-77 34.5 X 10= 132. x fi^.
" — I. - ■ ■ ■ ■ .
•Am. So&M. K- t Seep. 478. t Sm alto Am. Soc M. E.» 1884.
1
APPENDIX. 1025
Heating Sux*fkoe.
Of* a Steana Boiler, eto.
Heat is communicated to the transmitting surfaces of a steam boiler in the fol.
Vowing order of effect — viz. , incandescence, flame and gases of combustion ; and that
transmitted by radiation of it, (Vom one sorfbce to another, is reduced, in the ratio
as the square of the distance between the surfaces, and it is also reduced by a de-
pressed inclination of the surface upon which the current of the heat impinges,
and contrariwise increased by a raised inclination.
EvaporaUve Efficiency. — ^The evaporative efficiency of a boiler, or of an assigned
area of heating surface, as one sq. foot, depends .so entirely upon the thickness,
position, and condition of it that it is wholly impracticable to assign a determinate
valae to it It is also measurably affected by the duration of the time of the trans-
mission of the gases of combustion over it.
Theoretical and Attainable EvaporaMon. — If all the heat of the combustion of
coal in the fUmace of a steam boiler was utilized, the evaporation fh)m one pound
of best anthracite would be from and at 212^ abont 15 Iba of water, but only 80 per
cent, of that has been attained.
At the Centennial Exhibition in Philadelphia in 1876, the average evaporation
from 15 boilers of different types, with grate area as 35 to i, was 10.27 lbs. of water;
aud the averages of evaporation per sq. foot of heating surface per hour was 2.99
lbs., varying from 1.7^ to 9 ; aud of the temperature of the escaping gases, 410°.
Experiments with locomotive boilers by D. K. Clark, having from 52 to 90 sq.
feet of heating surface per sq. foot of grate, gave with coke an average evaporation,
at the ordinary temperature and pressures, 9 lbs. of water per lb. of fuel.
In horizontal tubular boilers, with heating to grate surface as 25 to z, the vol-
ume of water evaporal«d per lb. of fuel decreased as the fuel consumed per sq. foot
of grate area Increased.
Fnel
Water evaporated
Fnel
Water evaporated
from 3X3*
Tempera-
from 313*
Tempera-
per bour
p«r»q.
foot of
per lb.
persq.
foot of
tare of
escapioK
per hour
persq.
fe)tof
per lb.
Wof
ture of
escaping
^oot
bestiiiK
of coal.
heating
gases.
^t
heating
of coal.
heatiag
gases.
•f|Cnt«.
•urfiwe.
surface.
1 of grate.
surface.
surface.
Lbs.
Lbs.
Lbs.
Lbs.
Deg.
Lbs.
Lbs.
Lbs.
Lbs.
Deg.
6
•24
10.49
2.52
444
16
.64
8.21
5-25
897
8
.32
X0.3S
3-3«
472
18
.72
7.7
5-54
999
10
•4
10.05
4.02
fi^
20
.8
7-32
5-85
1074
12
.48
9-53
8.87
4.57
685
22
.88
7.04
6.19
1130
«4
.56
4.96
766
24
.96
6.82
6.54
1174
Bery. F. Ithervxiod, U. S. N.
The efficiency is also dependent upon the area of it for the contact of furnace
beat, flame, the gases, and the period of the application or transmission of the
beat over it ; and inasmuch as flame imparts more heat than the inflammable gases,
the diameter of tubes should be, so far as practicable, of a capacity to admit of the
flow of it
Radiation 0/ Heat to Surfaces. — If the thickness and surfaces of boiler plates and
lubes were uniform, or progressively reduced in thickness and resulting capacity
of radiation, their progressive effect and the proper temperature of the gases at the
point of delivery, as into a smoke-pipe or chimney-stack, could be readily obtained
by a dividend, of the difference of temperatures between that of the entrance of the
gases of combustion into the flues or tubes, and that of 212^, the divisor being that
of any assumed number.
Thus, assume the gases at the bridge wall at 1700°, which is the temperature
Assigned by Chief Engineer Benj. F. Isherwoodj U. S. N., being the result of his
observation and extended experiments.
Then, at six locations or divisions of the temperature.
1700
p_
212'^
= 248°;
and 17000—2480 = 14520 and
1452
o
212*^
= 207*^
14520—2070=12450 and
«245
o
212^
= 1730; 12450 — 1730 = 10720 and
1072
o
212^
=9280 and 9»8°-j2i20^^^, 9280 - 120O = 8080 and ^° 7 *"° =
= 1440; 10720 _,44«
-=990.
1026 APPBITDIX.
Thus, at termination of 6tb location, oqO are radiated in its passage tram the sth,
and the temperatare of exits 806° — 21 2^= 596^'.
ProfBsaor Bankine asserts that when the difference of temperature between the
water of evaporation and the gases of combustion is ver^ great, that the rate of
conduction increases faster than the ratio of the difference, and is nearly propor-
tional to the square of the difference of temperature, and which may be thus ex-
pressed.
T— «''-=- C = R T and t representing tht tempetatures of Vu ffiuei and tkt footer ^
C a oonakuu defitedfrotn experience^ t6o to geo, ami R raMo ofcondueUan in ther-
mai units.
Assume temperature of gases and water 1500^ and 2x2^ and C =r tSa
— — r r= 0216 ^rmal units.
x8o '
Robert Wilson^ London, i8q6. Gives for nMiltitubular and other boilers with
heating surface to grate area n'om 30 to 40 to i : 9 sq. feet heuting surface to evap-
orate I cube foot fresh water, or 4.5 so. feet of total beating surface per IP. In
locomotive and like boilers with a blast draugni, with heating surface to grate firom
60 to 80 to 1 : 6 sq. feet heating surface to evaporate i cube foot fresh water, or 3
sq. feet of total heating surface per IP ; and the highest average efRciency^ i sq.
foot of heating surfkce for 13.5 lbs. water, of 4.66 sq. feet for i culje foot of water.
And in ordinary externally fired boilers, with heating surn^e to grate 10 to 16 to x :
x8 sq. feet of heating sarfkce to evaporate i cube foot watei, or 9 feet per W.
Vertical Boilers. — Usually, are wasteful of fuel, but when in good condition and
the tubes properly spaced, 16 sq. feet of heating surfkce have evaporated r cube
foot of water or 8 sq. feet per Wy ^itfa a consumption of x lb. coal to evaporate 8
lbs. water = 7.75 lbs. per cube foot Usually ic to 12 sq. feet of heating surfkce are
required per H*.
Tubes.^The numl)er and 8ect|onal area of tubes in a boiler (horizontal multi-
tabular) and the spaces l>etweea them should be determined by the transverse area
over the bridge wall or the grate surface, and the required facility of the ascending
current of steam ftK>m over fbmace, and in all cases should be set in direct vertical
lines, and, in consideration of their efficiency, their lower or inner surface kept flree
fVom accumulation of the mechanical deposit of ashes and soot.
Inasmuch as the surface of a tube increases directly with its diameter and iUt
sectional area, or capacity as the sqaare of it, it l)ecomes necessary in order to at-
tain like economy of evaporation by them, when of diflbrent diameters, as i and 1
ins. . that the length of the greater diameter must be twice that of the less.
TnuB, the 2-inch tube having four times the sectional area or capacity for the
passage of flame or gases than the less, and but twice its heating surface, the length
of the greater must be twice that of the less.*
Lenff^ of Flues and Tubes.-^tbe greater the velocity of the current of the gaset
in a flue or tube, the greater will be it§ temperature at their exit, and consequently
the greater the waste of it, unless the length of them is proportional to the velocity
of the current
The absorption of the heat of the gases requires time, and hence Ibe longer tbd
course of them, if duly proportioned, the greater their efftectt
PicUt assigns tbe proportion of radiating beat fTom coal in its condition of per>
feot combustion at .5 of its latent beat
Length and Area of ru6««.— With ordinary smoke>pipe or chimney dvangbk, tba
length of a tube should not exceed 40 times its diameter. Experiment with a tube
8.5 ins. in diameter, the temperature of the gases at tlieir deliyery being 500°, the
length of it was 100 ins., or 40 times its diameter, and with a blast draught, as in a
locomotive boiler, or blower draught ; the length may be much increased. By
late experiments on a railway in France it was foond that greater economy was
attained by increasing the length of locomotive tubes above 12 feet In conse-
quence of which the Baldtoin Locomotive Worki, of Philadelphia, assign a length
of 14 and 14.5 feet for a 2-inch tube = 84 and 87 times the diameter. Prior to this
2-inch tubes were usually but 10 and X2 feet in length. In all cases, however, the
length should be in direct proportion to the diameter.
VerticeU Fire Tubes. — Are not as effective as horizontal or inclined, as the gasec
* Sm p. 743. t For the •Taponting capacity of tubM of difforont lengtlM, bm aUo p. 74a.
APPENDIX. 1027
which lose some of their temperature by contact with the surface of the tubes are
not replaced by the centre current, and the additional temperature of it imparted.
Water Tubes. — Whether vertical or inclined, enable the steam which is gener-
ated at their inner surftice to rise as fast as it is generated, and, as a consequence^
the velocity of the current of the water is increased.
Water or Masonry Bridge Walli.— At the termination of the grates, by diverting
the current of tbe gases of combustion, enable them to be better commixed, and
effect a more effective combustion and consequent economy.
In the computation of the area of heating surface, the areas of the furnace above
the grates, bridge wall if water, combustion chamber, flues, tubes (fire or water),
and connections to water-line are to be taken, and also two-thirds of all the gas
surfaces above it, inasmuch as they, as in the case of a steam chimney, are sur-
rounded by steam at a high temperature.
Steam Heatins*
{In addition to p. 527. )
1?o Ooxnpixte ^rea of Plate or Pipe Surface of* Cast-
Iron, to Coxnpexiaate the Reduotion of Xeznperature
in. an. B^noloeed Space by tlie Exposure of G)-laaa
to tlie Kxternal A.ir, or its ICq.uivalent in Kxpoaed
W^alls.
T — t
- — — = A. T and t representing degrees of required temperature of space and of
external air, H temperature of heating surface, and A area of radiating plate or
pipe maface in sq. feet.
Illustration.— Assume temperature of external air 70^, of heating surface i6<:^,
and required temperature of space 70*^.
70^ 20**
—-a 0= 667 sq.feet of heating surface for each sq,foot of glass. Hence, if
100^^7**
the area of the glass in windows or lights of a room is 80 sq. feet, then .667 X 80=
53.36 sq.feet additional radiating surface.
H-adiation.
One square foot of Direct Radiating surface will heat
Cube Feet.
In an ordinary domestic room
with glass windows 35 to 45
In an ordinary public room 45 '^55
*' small dormitories 50 "60
" large dormitories 45 "55
** hallway and passages 60 '* 80
" school and low-ceiled lecture-
rooms and offices. ■. . . . 60 "75
Cabe Feet.
In churches and high -ceiled
halls ,,.. 65 to 95
*' small low -ceiled factories
and workshops 50 '* (So
" small high -ceiled factories
and workshops 60 " 70
" large high -ceiled factories
and workshops 75 *^ 140
Steam. Bxlianst Irleating.
Exhaust steam, according to the condition in which it flows nrom an engine,
contains water and oil, varying from 10 to 20 per cent, of both combined. Conse-
quently they should be arrested before entering a heating plant ; and as any restric-
tion to the flow of the steam involves a resistance to it, or that which is termed
bttok pressure, the receiving and distributing pipes should have the greatest prac-
ticable capacity and least restriction to the flow of it by curves and angles.
To meet an emergent requirement for heat, a direct connection to the boiler,
through an automatic reducing pressure valve, must be furnished, and, contrari-
wise, a relief valve should be furnished, in order that when a reduced temperature
or volume of steam is required in heating, it may escape into the air.
To Design and Proportion an Exhaust Stenm IHant.—li is necessary flrat to
ascertain the area of radiating surface required to condense the exhaust steam, and
to obtain this the volume of the steam which the engine would exhaust must be
ascertained. To determine which (see table, p. 708), give weight of WAter evaporatef'
fk-om aia^ per sq. foot of heating surlkoe.
1028
APPENDIX.
Illustration.— Assume the area of the heating surface Is 9000 sq. feet, of grate
30, and fuel consumed 16 lbs. per sq. foot of grate per hour.
The water evaporated per hour per sq. (bot of grate = 8.21 (see table, p. 1035) X
16 = 131.36 lbs. water, which x 26.36 (the volume of i lb. steam at 212°) = 3462.65
cube feet of steam.
Water evaporated per hour per IH* in a non-condensing engine ranges Arom 25
to 40 lbs. , from which, for condensation and leaks, 10 per cent, should be deducteid
to obtain the volume of steam available for heating.
One square foot of Direct Radiating surCEU^e will heat
Cnbe Fett. 1 Cnbe Faet.
In dwelling-houses 45 to 55 I In factories, stores, and shops 90 to 100
" offices. 65 " 75 1 " churches, auditoriums, etc. 150 " 200
For Indirect Radiation deduct 20 per cent., and when the heat is transmitted by
blast ft'om a Blower add from 4 to 6 times, In accordance with its volume and con-
sequent velocity.
Hot- "Water Heatixif?.
The sectional area of the main pipe should, in all cases, exceed that of its
branches, and for each sq. inch of its section, if short, indirect, and at a slight in-
clination, 50 sq. feet, and if long, direct, and vertical; loo sq. fbet
One square foot of Direct Radiating surface will heat, the average temperature of
the water i6o<=>, from 80 to 100 per cent, more surfkce than by Steam.
Horse-Po'wer Required, to Drive IVtaoliinery.
In addition to Frictional Resistances, etc., pp. 475-478. See a very full table of
H* required in American MackinUt^ April 12, 1894, and February 6, 1896.
Referring to the following table, it will be noticed that the loss of power varies
between wide limits, but in all cases the mechanical loss is large, averaging over 41
per cent
MftcliiDery. Work.
Union Iron Worka
Frontier I. k B. Works. .
Baldwin Ix)c. Works
W. Sellers & Co
Pond Machine Tool Co. . .
Yale & Towhe Co
Ferracute Machine Co. . .
Bridgeport Forge Cc»
Hartford Mch. Screw Co.
Engines and Machinery.
Marine Engines, etc
Locomotive&
Heavy Machinery
Machine Tools
Cranes and Locks
Presses and Dies
Heavy Forgings
Machine Screws
Total
nwrmr
Slmfting.
ftlaehln-
ery.
Shafting,
percent.
400
^l
305
•23
25
8
»7
.32
2500
2000
500
.80
102.45
40.89
61.56
.40
180
75
«'°5
•41
»3S05
66.81
68.24
•49
35
II
24
•31
150
75
75
•50
400
100
300
•25
(Piof. J. J. Flather.)
Hef^ieevBLting DMLaoliiiiery.
For the cooling of Brine and other liquids by the alternate compression and ex-
pansion of air.
P T
T - 75^^Trrt=^
t — t
772CX^^ = P.
P r<5>re«<»i^»«flr jHmer required in footpounds, T ahsolute maximum t»nperaiure
of the air in the hot or compressive end of the refrigercUor, t abseUUe minimum tern-
peraiure of the air in the cold or expansion end, and-C cooling work in thtrmdl
units. {David Thornton.)
Illusteation.— Assume T = 80° t = 30° and C = 80° — 30°= 50°.
772 X 50 X^^^° = 38 600 X .625 = 24 125 =zfoot pounds, and ^i^ Xg^_^^
= 31.35 X 1.6 = 50°. •
Hence, the most economical results, as regards power used, are obtained when
the machine is operated within a small range of temperature, as in a brewery,
where the temperature of the water Is frequently reduced to but io<*.
These formul|9 are applicable to all refrigerating machines, whether operated l>y
kWRTfrniX.
1029
atr, other, ammonia, or any other liquid. - In ao ammonia machine, or any other
operated on the same principle, in which mechanical power is applied, the value
of P 18 the heat theoretically required, at the rate of i heat-unit for 772 foot-pounds
of power, and the formula i becomes (ammonia): Heat required for the operation,
w
The ammonia machine is, theoretically, economically superior, as heat is less ez<
pensive than its equivalent in mechanical power.
The nature of the vapor operated controls the capacity of the machine.
Relative Capacities of Cylinder Required.
Ammonia... x
Carbonic acid. ....••. 16
Methyl Chloride 1.8
Motbyl ether 1.8
Sulphuric acid 2.6
Ether 15. i
{D.K. Clark.)
Se-werage.
Tn order that an estimate of the volunio or oxcessive rainfalls may be nom-
)>uled, tbo folluwiDg data are derived from the valuable report of the Sewerage Com-
mission of Baltimore, 1897 :
Philadelphia, Jnly 23, 1887 4. 23 inches in 13 minntea
Chestertown, Md., Aug. 15, 1894 3.64 '* '* 30 **
Washington, DC, June 30, 1895 6.27 ** *' 10 **
The average of 26 fulls was 3 inches in 10 minutes.
In the city of New York a fall of i inch in xo minutes has fluently occarreda-
6 inches per hour.
Safe Transverse Strength,
Loaded tn Middle. Supported at Both Endt.
Slate, mean of 242 and 537 390
Glass 2IO
Bluestone 178
Granite, Quincy 131
fccf
c.
Freestone, Little Falls.. 121
*■'■ Belleville, N. J xoi
" Connecticut , 6$
Dorchester, Mass 50
it
To Compute Safe Load. — - X G = Load in Iba C representing one-tenth qf
hreaking weight
Assume a flag or block of Quincy Granite, 6 feet in width, 6 ins. In depth, and 3
feet in length between its supports.
6 X la X 6» ^ ^ „
3X12 X'3« = 7aXi3i=943a«>«-
Avftag* weight of 17 differcot Sanditaoei, m ascertained by Licnt-Col. Gilmon^ U JSJ^t >43 Un>
CAST-STEKL FLAT BOPBS.
John A. BoebUng's Son* Co.^ Nem York.
Dimenalooi.
Welrhl
per Foot.
Stiengtii.
Dimenalona.
Weight
per Foot.
Stmgtiu
Im.
Lbe.
U».
Int.
Lbe.
Lba.
•375 X 2
I.IO
1.86
35700
•5X3
a. 38
71400
89000
•375X2.5
55800
•5 X 35
a. 97
•375 X 3
9
60000
•5X4
3-3
99000
•375X3-5
*5
75000
85800
•5X4.5
4
X20000
.375 X 4
8.86
•5X5
4.27
128000
•375X4-5
3.xa
93600
•5X55
4.82
X4460O
•375 X 5
3 4
xooooo
.5X6
5«
153000
•375 X 5-5
3-9
xioooo
•5X7
5-9
177000
Steel Wire Flat Ropes are composed of a number of strands, alternately twisted
right and left, laid aside of each other and sewed toi;cilicr with sod iron wirea
They are used sometimes in place of round ropes in Bimris of mines: wound upon
a narrow drum, requiring less space than a round ro|)e. Soft-iron sewing.wires
wear out sooner than the steel stnuids, and then it 18 necessary to replace them
with new iron wires.
I030 APPENDIX.
niustratioYis in Hiossaritluns.
Xo Compute tbie Xjengtli of an ^ro of a Oirole to
Radius 1.
RuLB.— To log. of degrees in the arc, add 2.241 877, and sum is log. of length.
Nora.— When the arc la in miniitea, MConds, etc., take their decimal eqnlvaleots.
Illustration.— An arc of a circle is 57O xf 44'' 48" -)- ; what is its length?
17° 44" 48" = • 2957- Log- 57° • 2957 = 1.758 "3
Log. 3. 1416 -f- 180° = 2. 241 877
Log. 1= .000000
1?o Compute tlie IDegrees in an A.ro of a Circle -wlien
tlie Xjengtii Is Q-iven.
RcLK. — To log. of length of arc, add 1.758 123, and from the sum subtract log. of
its radius, and remainder will give log. of degrees.
Illustration.— How many degrees are there in an arc when the length is 2 and
the radius i ?
Log. 2 = . 301 030
Log. 180° -i- 3. 1416 = 1.758 123
a- 059 '53
Log. I = .000000
" 2.059 '53 = 114.59166 = 114° 35' 30 '— .
7o Compute tUe .A.n(;les of a Triangle, tlie Xjengtli
of tlie Sides l>eing Oiveii.
Rule i.— -To the logs, of the diflferences between any two sides and half the sum
of the sides, add the arithmetical complements of the logs, of half the sum of the
sides, and the difference between it and the remaining side, and divide the sum by 3,
the quotient is the logarithmic tangent of half the angle opposite to the latter side.
Rule 2.— To the logs, of half the sum of the sides, and the difference between it
and any side, add the arithmetical complements of the logs, of the two other sides,
divide tlie sum by 2, and the quotient is the logarithmic cosine of half the angle
opposite the former side.
Rule 3.— To the logs, of the diflferences between any two sides and half the sum
of the sides, add the arithmetical complements of the logs, of three sides, divfde
the sum by 2, and the quotient is the logarithmic side of half the angle opposite to
the remaining side.
Illustration.— The sides of a triangle are A 679, B 537, and C 429. What are
the angles ?
79 "T 537 -r 429 __ g^^ ^ ^^j 822.5 — 679 = 143.5 = cKjferewc« between two sidet
arid halfgum of sides. 822. 5 — • 429 = 393. 5 and 822. 5 — 537 = 285. 5 = differences cu
above chtained.
I. Log. 143.5 = 2.156853 3. Log. 833.5=3:2.915136
" 393- 5 = 2. 594 945 " 143.5 = 2.156852
Co. Log. 822. 5 — 10 = 7.084 §64 Co. Log. 537 — 10 = 7.970036
•* " 285.5 — 10 = 7.544394 " " 429 — 10 = 7.367543
2)19.381055 2)19.709557
9.690528 9-854779
Log. 143. 5 = 2. 1 56 852 I. 9. 690 528 = . 5 Log. c Sin. = 19° 35
" 285.5 = 2.455606 2. 9.854779 = .5 " Cos. =44° 17' 30
Co. Log. 679 — 10 = 7. 168 130 3. 9. 525 307 = . 5 " Tan. = 26° 7' 30
" " 537—10 = 7270026 90° o' o
2)19.050614
7?
9525307 i860 (/ o'
./I*
APPKJJW^
1031
To Camp'cite th^ Voluxn* of ck Pyr»mi4 or Coxx«.
RuLi.— To log& of area of base and haight add T.saa 879, and the sum is the log.
of the volume.
Ii,i,r4TRATioir.«*Tb6 largest Fyrfupid of Egrpl ba« a ha8« of 700 fee( oqu^rt. «
height of 50Q feet, and assuming itp faces \o be triangular, and to be constructed
90li(l of graqile weighing 2654 ^^' V^^ ^^^ '^^ ^^'^^ '^ ^'^ volume and weight?
Log.
»4
700:
ti
Log. volume ns 7.419 045
Log. 9054 B 3. 433 901
Log. 2240 -i- 16 = 5.44563a
: 5.6^ 196
500 =s 9.696 970
Lag. volume 7. 919045 Log. weight ^ 6. 781 578
Log. 7.91a 045 xa 81 666 667 cube feet.
6.781 578 SB 6.047 528 totu.
(»
Cexitrifugal Pumps*
Morris Machine Works, BaldwinsmlU, N, T.
Omln/iwal Fmnp».^Kf^ simple id construction, and for the raising of gr«fil yol-
Qmes of irat«r, to or from a low elevation, are superior to a piston pump, in thsir
dispeosingof valves, piston and its paokiog, eto. {
and as a result they will eO'eotlyeiy raiss gravel,
sand, paper pulp, sewage, silt, and like material :
all of which a piston pump is wholly impractical
ble of raising-
Tbs e£9ciency of one when properly propor*
tioned and constructed is fhlly 65 per cent, of
the power expended to o|)erate it, and they are
also applicable to furnish surface-water for the
condensers of marine and other engines, and
brine in fee- making machines, in dredging,
wrecking, et&, oto., at ft |«8s cost of opsration th»n 4Q7 other pnwp of like
<»pacity.
Standard HTorizontal p-anip.
No.
Capacity par Minntc.
Minimam Power for
each Foot of Lift.
a«ii*.
1^.
1.5
50 to 70
.094
«-75
75 to 100
•037
«
tio to 150
054
a-S
175 to 250
086
3
t5o . 350
45c Ji Ooo
194
4
««3
5
790 to 900
372
6
I /CO to I 400
.496
8
I 700 to 2 aoQ
844
10
2 200 to 3 000
I
093
12
3000(0 4QQO
I
49
15
4 800 to 6 000
2
38
♦15
4iQO to 6000
».38
18
7500 to lOOQp
3.73
♦18
7500 to 10 000
3 73
22
Z2000 to 14000
5
96
Diameter aad
Face of Policy.
6
8
8
8
8
6X
7X
8X
8X
8X
10 X 10
15X10
15 x1a
?oX 13
84 X la
30X14
40X15
30X15
40X M
30X16
48X20
Weight.
168
232
306
348
400
545
8a6
965
I 500
2 170
3050
7«op
3IS9
90OQ
3500
12000
* Refer* to low-lift pomn. The nnmber of pamp is alto diameter of diachaige opcDing in Inches.
iVh. re iii.>rtf tliifti ,13 f«wt •>( tliMk«f|ie pip* i# 4MmW to pWliPiOil* OV tWO aiiea l|||0K tkfW U)f pppip
Rail-way.
Speed. Chicago, Bsrliogton k Qpiqoy, psssanger train, Denver to Eckley, 14.fi
pilss In 9 minutes = 98.66 mUes per liowr.
1032 ASBESTOS PELTINGS, CBMBNTS, ETC.
j^sbestos B^l^rios, !F*elts, Oexxients, Ijooomotive
ILiagginSa JSto.
H. W. Johns ManviUe Co.. New York.
Steaxu-Pipe and Soiler Coverings, Packings, £]to.
In the protection of sarfoces trom loss of heat, Hair-Felt and other organic
materials, in consequence of their destructibility at high temperatures, have been
very generally superseded by Felts made from Asbestos.
Numerous tests of the relative non-conductivity of materials published by au-
thorities have given an impression that Asbestos is an inferior non-conductor of
heat This, however, is an error, as these tests are made with the dense or crude
forms of Asbestos, while in its fibrous state it contains numerous air-cells. The
best insulator known is air confined in minute cells, so that heat cannot be re-
moved by convection, and the value of insulating substances depends upon )he
power of holding minute volumes of air in a manner that precludes circulation.
Asbestos Fibrous Fabrics are claimed, therefore, to be the very best and most
durable non-conductors of heat
A-sbestos XTire-Felt
Is a fkbric "felted*' flrom Asbestos fibres. As its air-cells are fnnnmerable and
microscopic in size, Fire-Felt is a successful application of the air-space principle.
In addition to its superior insulating properties, it is fire-proof, flexible, light In
weight, susceptible of any desired mechanical arrangement, and indestructible. It
is particularly adapted for Marine, Mine, and Railway work, as moisture and vibra-
tion will not disintegrate it, and it will withstand much rough usage. It is sup-
plied in cylindrical sections for pipes, in sheets for boilers, drums, flues, etc., in
rolls for grouped pipes, cylinders, hot-air pipes, etc., and in blocks for Locomotive
and Boiler Lagging, etc.
.Asbestos STlre-Felt, Asbesto-Sponge Felted, and A.8*
Tsesto- Sponge !Molded Sectional Pipe Covering.
These are formed into cylinders, cut lengthwise, in order that they may be laid
over pipes, and are furnished with a canvas jacket, secured by metal bands. They
are suitable for both high and low ^team pressures. The Fire-Felt, being com-
posed wholly of Asbestos, is especially adapted for highest pressures and super-
heated steam.
Champion, Zero, Grine, and Auznznonia Sectional Pipe
Covering.
"Champion" is an economical covering for low-pressure steam and hot- water
pipes.
"Zero " eflfectually prevents water and gas in pipes (Vom f\reezing.
Brine and Ammonia Pipe Coverings prevent the formation of ice on the line of
pipe, and produce important economies in refrigerating and ice plants.
A-slsestos Cement Felting.
Composed of Asbestos fibre, inAisorial earth, and a cementing compound, ap-
plied to pipes, boilers, etc., while heated.
Furnished in bags or barrels. One bag contains Bufllcient material to cover
about 40 square feet of surface z in. in thickness, and weighs about 120 lbs. net
A-slaestos IL<agging for Xjooomotives.
Composed wholly of pure Asbestos, suitable for all styles of locomotives.
In slabs, 6 ins. in width by 36 ins. in length, flrom .5 in. to 2 ins. in thickneaa
Asl>esto-Sponge Hair-Felt
Is very elastic, and, in consequence of the large proportion of AsbestOB In It, it
is not liable to injury Arom steam heat.
In rolls of about 300 square feet, 6 It in width, and .375 in. in thickness.
ASBESTOS FBLTIKGS, CEMENTS, ETC.
1033
Kair-ITelt.
Of various thickpessea
In bates of 300 sqiuiro iiset, 73 ins. Id width.
i^s'bestos Cloth..
Pure fibres of Asbestos spun into threads and woven into clotha
various weights and widths.
Fine doth. 36 ins. in width, weighs 3.33 oz. per square foot.
Medium clotn, 36 ina in width, weighs 4.66 oz. per square foot
Heavy cloth, 36 ins. in width, weighs 6.25 oz. per square foot.
Frodnoed in
A.s'bestos lPekolcing9 and i^s'beeto-ACetallio Paokings.
These are especially adapted for the extreme high-pressure and high-speed en-
gines of modem times. They are supplied in flat, round, and special shapes to
meet all requirement&
A.8l>e8t08 ]5f£ill-Board.
Composed of pare Asbestos fibrea Valuable for sheet-packing and general
Joint-work, for gas flre-backs, screens, partitions, and general fire-proofing pur-
posea
In sheets 40 by 40 ina, firom .03x25 to .5 in. In thicknesa
c<
A.s'beetos NoTi^^vLm
Paper or Sailding 3Brelt.»»
Composed of pure Asbestos fibres. Used as fire-proof lining between floors, side-
walls, etc., of frame and other structures ; also for railroad-car partitions. It is
vermin, acid,/ and fire proof, and is also made damp-proof
Supplied in rolls weighing about 80 lbs., 36 ina in widtb. Three weights—
thin, medium, and heavy.
l^iokel Steel and Sliaf\;lxi9,
Nideel Steel is well adapted for shafting, as it has greater elasticity and tensile
strength than steel, it being fully 30 per cent, greater, the latter being 20. per
cent
With 4.7 per cent, of nickel in the ooay)OSition of steel, the elastic strength has
been increased fVom 36000 to 41 000 Iba per Q inch, and the transverse fh>m 67 000
toSgooolba
Sleotrioal £iZpression.s and l^^q.nivaletits.
One
BaU of Operation.
"Watt. One
B Ampere per sec.
at one volt
.7373 fooi-iba per sec
44.238 *' ** min.
1654.38 '' *' hood
<So^mile-lb& " "
One Kiloi^att.
737.3
14238
1.34 BP-
foot-lbs.
«t
per sec.
" min
M
foot-lba
it
5SO
33000
375 mile-lba
746 Walls
.746 Kilowatt
per sec.
*' min.
" horr
Q^CMltit!| of OpetaiMin.
One "^^att-Honr.
2654.28 foot-lbs.
.503 mile-lba
f ampere - hour X
one volt
hoar _Lff.hour
746
Q^amtily of Operation.
One If-Hour.
tgSoooob foot-lbs.
375. mile-lbs.
746. Watt-hour.
.746 Kilowatt-hoar
QuantUy of Current.
One Ainpere-
Kour.
One Ampere flowing for
one hour, irrespective of
the voltage.
Watt-hour -i-volta
Fvrce Moving in a Circle.
Torqvie. One poonj
I at a radius of one foot
I034 CHAINS.
Cliaiiis.
ITov Cables, Cranes, eto., <9f 'MTr^tiettt Irmk Ol* flHM^.
Cable obaina are designated afi Open or Stud link, and Crane, Sus«
pension, and Hauling Cld Slloit Of OpTO Mttk.
U>t, per square inch.
siiort-iink«* The average ultimate tetisile strength of the b'flk of a
chain is ascertained to be 1.695 times that of the rod or bar from whiob it is
forged, and to avoid injury to a cliain in testing it should not be subjected to
a stress in excess of one haJf of its tensile strength ; nor, in consequence of the
disastrous results of the rupture of a cable or crane chain, snould it be
8tibj«cted in operation to a stress in excess of one half of its testing stmigth.
The average tensile strength of i inch round and chain-rolled wrought iron
and steel, is further assumed at 440CX) lbs., and a link of such chain at 71 500
lbs., or 1.625 times greater Chan tlUlt of a rod or hmt,
Hence, a chain of i inch may be tested to 35 750 Ibi., f md labiiiittod to
a Working stress of 17 875 Ibc
Th« Peocoyd Iron Workaj[iv«i i7gao Ike., th« P«nD«Tly»nU B«ilro«d 15000, and Molwlrottft
•od D. K. Clark, both of Enfimi, gIve rMt>«etty6Iy 15 Md aUd t344b Ifii.
When the lead of a chain is inclined to the stress, as when it encompasses a
weight lb ttiasi,ori8iippnM to caat^bookfe, the grMt«r Ihr angle, ibe greater the
stress with a given load, as the stress on each chain will be in the same ratio to
half tbo load that the length of one half or side of the chain beafft to the vertical
distance tn a line between (he point of suspebglon of the chAIn and the losd.
TbUfl, M QlMply hilf the load by the length of one lead of the chain, divide
the product by the vertical distance and the result will give the capacity of the
ohaia
Load
Or, X seo. .5 angle ot spread of the chain = Streu.
rtUTBTKAfiroN.— Aisame the load to be t ooo lbs., the length of one tM« of tbv
cftiain to be 5 Ins., the vertical distance 4 ins., and the BpresuA of the chains 6 inft
Then 1 000 -h a X 5 ^4 ^=3 625 lbs. 00 each chain.
Stud-link. Authorities on the relative strength of this and a short or open
Hnk are very materially divided.
D. K. Clark gives the safe working load of the two links approximately aa:
Short-link D* -r- 10.7, Stud-link D* -i- 7.07. An okMm of strength for the stud-link.
D rqnrKefMmg dimmer qf rod in eSghtk^ t^ an inch.
Again, be ghres the oHimate safe workmg stress of a stud-link chain at 9 tons
(20 160 lbs. ) and of a short-link at 6 tons (13 440 tbt. ).
This is wholly at variance wHh the pMceOtag rale Ibr the deMrmthatlon of the
stress on a chain, wben it Is spread or divergil^ outward from the V«t«tcat; for aa
Hie stress of the load inci^eases in the profionion that the length of one lead of a
chain is to the vertical distance, as here illuslratcd, the length of the stud not
only spreads the span of the Imk, but subjects it to a stevere ConttAned fenile and
transverse stress on its ooter surface, in the direction of the central line of the
stud, as the tenetle and transverse strength of wroaght iron or steel benig lem than
that of their crushing streligth. the neutral axis is lowered and thd stress on the
enter surlace correspondingly Int^reAsed.
Chaining over Indlinod l&ijimfr«»
I . cosiii. A = 2. L rein'UenHng length itf line on tw/foMt A angle of incUnatUm^
xmd I Ungth iff Hm reduoed to thi korimmtal,
* Crane chaini tkn Vsually of thtt crtiairuclioiu
itht UbiM OQ p. 457 it lor £ugliah irou and il for 31 300 Um.
APPBITDIX.
1035
Hsrdrat&llos of a F'ive-BInsiiia«
With a ring nozzle the Confident of discharge is about .74.
Loss of Pressure by Friction in Hose.— horn of head varied as the square of the
velocity ot the flow and nearly as the length of the hose.
The effect of a difference in diameter of hose, even of .125 inch for 3.5 ins., may
cause a loss of 35 per cent.
"WTind. Pressure.
Normal pressure is estimated at 15 lb& per sq. foot and maximum at 30 lbs. ; but
on elevated structures, in consequence of the partial vacuum or minus pressure in
their rear, the effect of the wind is much increased.
At the summit of the Eiffel Tower, 1097 feet, the pressure has been observed to
be 5 times that at the Central Meteorological Bureau, at its height of 70 feet be-
low.—J2. KohfaM.
From observations of the St. Louis tornado in 1896, the pressure was computed
wo vary f^om 45 to 90 lbs. per sq. foot; and trom experiments of C. F. Martin at Mt.
W^BsbfngtoD, U. a, it was shown that rapid and intense fiuctnatioo occurs; and by
Kernot, that a marked differenoe results from the preseOBe of other buildings. -^
T. Bates.
Kfieot of*
BIctaL
HiOMT Temperat-ure on. Iron and Steel.
Jn Tons per Sq. Inck.
Wrought-
Iron Bar.
Steel,
Siemens*
Angle.
Malleable
Iron Bar,
•I
Tempsrmtars.
ElMtte UmU.
Brakkitif; Stren.
^<
Z8.2
25.8
-<
18.5
26. c
37.8
—112°
19-3
^*o
X5.2
25-7
-^r.
15.7
87.7
— H2O
Z8.9
28.7
K
19.0
25. 5
-^l
so
26.4
— 1130
30.3
27.4
Ten«il«
Ratio of ElMtle
Strang.
and BMaktng.
xoo
.73
105
•7
"07»5
.7
100
•59
Z02.9
•57
123.8
.66
100
.77
102.3
.7^
103.3
•74
The conclusions flrom these results are:
1. Elastic and ultimate limits are raised by low temperatures.
2. The variation in mechanical properties by a reduction of temperature is greaU
er in steel and least in malleable iron. The variations between 'the extremes at
temperatures given are, in j9«r cenl:
Metal.
Siemens* steeL....
Wrought-iron bar,
Malleable iron
Elaitle Umit.
IncraaM.
33.8
5.4
3i3
Teftatla Strangth.
Incrvau.
It. 9
7-5
7-5
ElongMtioQ.
DacnaM.
30
14. 1
5. a
3. The compression by impact diminishes with a reduction of temperature, in
like manner with elongation under tension.
4. The loss of malleability is 8 per cent, at 4<^, and 23 at 112°. The change being
least in hammered iron, and greatest in rivet iron.
5. The flexibility of iron is slightly changed in sod rivet at 4°, and in rolled bar
iron at 112^; but all other qualities were more or less iujuriously affected at the
lowest temperature. — M. BadLeloff.
Relative Hiardening* of Cement and Mortar in Freslx
and Salt M^ater.
From experiments with cement with varying proportions of sand, it was shown
that, when it war mixed with and submitted to fresh water, it became harder.-^
N. Jf . Koning and L, BienforL
Kvaporative Powers of*' Oolxe and Ooal.
From experiments at Colmar. The calorific values were z and .8933
IFefier.
1036
APPENDIX.
The tjlsHtest Ktxovim Sa1>stebn«le
Ib tbe pith of the Sunflower; its speciflo gravity .038. Elder pith, hitherto bald
to be tbe lightest, is .09 ; Reiadeer's hair .1, aod Ck>rk .34. Heace, Reindeer's
hair has a buoyancy of x to to, and Sunflower pith i to 35. — FroiUheim.
Ratio "bet-^veetx Surfboe and. ACean Velooity or the ^Vet
Section of a Alill-^iaoe,
As determined by a series of experiments, is .60 to .65, being less than that o'
.80, usaally taken, and that of .71 to .73 in channels with earth banks.— iS. J*. T-
TUiein Horthemua.
rrestine of Stonea.
OranUey Marble^ and SahdsUme lose strength by sntnration with water, aod
Sandstone and Granite are most afltBcted by frost& — Jtf, Gary.
liosiataxioe of WrousHtilron and, Steel Rivets in a Xjap
of not l^eaa than Tliree.
Elartldl
p«r aq. inc!
I.
Lb*.
Iron.
3«36o
25 536 J
31360)
How
Mad«
Htind. I
Hydrat)'
lie.
TMnpviAi
tare.
Bright
red heat
White
beat.
Per Sq. Inch.
ItMittaDMtoH ElMtidty t
Sb«ariDg.
Lbs.
{I
5800
6730
7168
8288
LlM.
Stbbl.
31 360
32704
31360
32704
The Iron submitted to an extension of 13 per cent, before ft-acture, and tbe Steel
18 per cenL — Dupuy.
per aq. inch.
How-
Made.
Hand.)
Hydrau-
lic
Tempera-
ture.
Bright
red bent.
White
beat.
{
llesiiteace to
Sbenring.
Lta.
6384
7168
8512
9408
Muzzle Velooity of the G^erznan Infantry H.ifle«
A series of experiments gave the following results :
Muzzle velocity 3070 feet per second, and the maximum at 10 feet trom the mns-
zle 3130 feet.— //urn. C. E,
BiTeot of a Diamond* Kdeed. Savir.
Result of its operation at the Paris Exposition.
In semi -hard nnd soa stone, 11. 8 Ins. per minuta Cost a cents per sq. foot;
cost by hand sawing, 15 cents. -^J. Laftargue,
S^oroed X>raneht,
«
For non-caking coal it is necessary to reduce the width of the air space between
the grates of a ftirnace to .135 inch.
The greater the force of tbe blast, the less Is the evaporative effect of the fuel,
as illustrated in a steam-boiler plant, where the evaporation with natural draught
was flrora 7 to 8 lbs. of water per lb. of coal: it fell to 4 lbs. upon tbe Introduction of
a blast draught, nnd although there was a length of fine of 400 feet, and a chimney
130 feet in height, flame was generated at the top of the chimney, evidencing that
carbonic oxide left the Aimace unc^onsumed. — D. K. O.
Sffioienoy of Hand 13 rakes.
From a series of experiments on the tender of a locomotive on the Northern
Railway of France, it was deduced that the (t-ictional resistance absorbed 83.3
per cent of the power applied.
In general U Is assumed that the efficacy of hand brakes does liot exceed eo pot
eent— />. K. C.
A.Qetylene IHorn^ula*
Ci Bi, end a SpaoiOo Gravity .91.— if. Uemj^
AI^PBMXIX. 1037
Sfi*eot or Kiln Drying; bn Pine and Heznlook.
White i\'n«.^Wflighl of a cube foot, 36.4 lbs. ; dried at 2i3<>, 33 lb«. RedPine.^
32.3 lbs. ; at aiao, 31 lb& H«mlocik.— 53 lbs. ; at 3ia<>, 31.3 Ib&^/Vo/. H, T. Btnqf,
LL.D.
m
Test of* an. Iron "Wire H.ope 3.6 ins. in IDiaxneter.
C&nstrttetion. — Six Btrands on a core of hemp, and each of six other strands on a
central core containing 108 wires, .058 inch in diameter. Tensile strength of wire
260000 lbs. per sq. inch, and united strength of nil 740000 lbs. Reduction of di-
ameter with a stress of 150 tons x.4 inch, and ultimate strength 560000 lbs., a coeffi-
cient of 75 per cent. ~.i. Martens.
Consolidation of* I^oose or ACade G^round
May be sacceBsfuIly attained by the driving of piles as close together as the earth
will admit withdrawing of them, and filling their holes with a weak Concrete.
In an instance recited, 8 piles, 30 inches apart, driven to a depth of 23 feet in
made ground, supported a brick chimney S13 feet in height 00 a base of 43 feet
square. — Hoffman.
For the foundation of the buildings of the Paris Exposition, the ground was
rammed by ooaical and suitable monkeys from a pile-driver, and the holes filled
with hard substances rammed down.—IhUar.
A. rTe-wr G^eneral Formnla for Train Resistance*
4 4- S f .2 -| ^j~\ = R. R repreunting rtaistance in lbs. per ton (aooo), S ve-
locity in miUs per hotur, and T weight of train in lons.-^H. L» /.
Resistance of*F*ast Passenger Trains on Straight Road.
Experiments on the Northern Railway of France at velocities varying 25 to 35
miles per hour. i. 45 -f .0008 V* = R. -De LahorietU.
AAagnaliun&.
A new alloy of aluminum. Spec, gravity, 2-3; Melting-point, iioo^^; Tensile
strength with 5 per cent, of magnesium, 30000 lbs., and, with an addition of from
5 to 30 per cent of it, the alloy becomes similar to brass and bronze, and, with 50
per cent it loses Its hardness and ceases to be useful for mechanical purposes;
but as it is capable of receiving a very high polish, it is eminently suited for op-
tical and like Instruments.— Ifve^Ase.
Alaximite.
Experiments by the IT. S. Government have shown that it possesses in a great
degree the two essential properties which render a high explosive suited for the
charge of projectiles, viz., insensibility to heat and shock. To test its susceptibil-
ity to chemical change, it is maintained at a temperature of 165° for a period of
15 minutes.
Ignited, it burns slowly without explosion, and its resistance to shock was de-
termined by a drop test and a loaded j-inch shell, which was projected through a
nickel -steel armor plate without exploding; but when armed with a fUse it ex-
ploded, burstinginto about 800 fi'agments, and a 12-inch shell, similarly exploded,
burst into 7000 firagments. It freezes below the boiling-point of water, and possesses
the advantage of expanding in passing firom a fluid to a solid.— ^. P. H.
Oarlinder Ratios fbv Ooxnporand and Triple Bxpansion
Steam - SSngineu.
By experiments of Mr. Greaoen. of Perth Amboy, N. J., uader differant Initial
pressures, and the bushing of the high-pressure cylinder, he delennined the ratios
to be: With 60 lbs. pressure per sq. inch, 1 to 4; with 85 Iba, 1 to 5: with no lb*..
I to 6; with 135 lbs., z to 7: rmd with 160 lbs., 1 to 8.— B. C BaiL
I038
APPBNDIX.
B«lt • I> ri vititf.
Belte fbr high spMd, ranBinf over 4000 fiset per mhiiite, should be of sfngle,
ttiln, pUaMe, and (ough leather; and if singly compounded, they may be rui at
9000 feet per minute, with less loss from slipping.
Narrow pulleys are more effective than wide; thus, two belts of ao las. .will
traiiBmit more power tbata one of 40 Ins. over a wide pulley. Great convexity of
pulley increasea wear of belt, and induces loss of power. .063s inch in coavexity
IS sufficient for a pulley of 6 ins., and a less driven pulley may be flat on its fiwe.
*/. TuUi*.
TTemperature in. JMCiues.
From observations made in Australia, the mean result in rock was an increase
of 1° to each 137 feet ef deseeot /. SterUmg,
At Lake Superior, U. S., at 105 feet, S9°i ^^ ^^45^ f®et, 79O, a differenoe oit^
for 323. 7 feeL At SL Gothard Tuanel U was a o for 60 feet.— .^i. Agattiz,
Relative E^fllcienosr of a Reoiprooating: Piston Puxup^ a
I^otary Pump, and. a Steam SipKon.
Wttter rmittd <• 4m AevsMon <tf 17.66 /«elj wnd I^mndt of WMer raited per
JRmnd of Steam.
Reciprocating Pomp, 135.6 lbs. ; Rotary, 108.6 lbs. ; and Steam Siphon (Giflkrd'S),
37.4 JbB.-~& if, Uherwood, U, S, M,
*]^ntmity of* M'alls and I>rift Solta.
Experimenlf ma4e txl ^SUNey Oetle^ fitmuh the foOmninff revnIE*.*
CtU Nails are superior to Wire in all positions ; and, as the pointing of a nail in-
flroaecB its ettcieacy, the p»iiitiflig of a c«i mii viould increase its teaaetty elbovt
30 per cent. Barbing decreases their tenaci^ about 33 per cent.
Wire iVaiTf.— Their tenacity decreases with time of service. Surface of a nail
should be slightly rough. Nails should be wedge-shaped in both directions, where
there are not special dangers of the splitting of the wood. Nails are 50 per cent
more effective when driven perpendiesta' ie Om grain of the wood than with it,
and most effective when driven perpendicular to the surface., and when submitted
to impact they hold less than .063 the stress tbey can withstand when it is ^grad-
vally apiAied.
I)r0 BoUg, when round, are sUjperior to square, and the boles ijoto which ihey
are to be driven should be respectively, .81.25 and .£75 of their diaaetar.
BeUUive Tenacity of Wood$.— While pine, i; jkissvood, c.s; F«liosr piao, x.5;
Chestnut) 1.6; Elm and Sycamore, 3; Beech, 3.3; and White oak, 3.—F. W. Clay.
Ijubrioation of Jdietal 8earin«a*
Trmti rewTlB of e-jrtended experlmeirts on thelWlB-Ljenrs- Heffiterraneaii Raflwagr,
MEfeendtDg Itmn 1B71 to 1*890, it was shown Hial:
tAibncfAi'ng Wicks of irooibave a delivery of oil over that of cotton of from 50
to 100 per cent ; that'their renewals were but as 68 to 100 of the cotton, and that
^fliey were less TinWe to "ftrlng.
Jiaarin^s.—T\ie wear of^ite Vetal was 50 percent less than niat of Branze,
end beariQgs of it diminished the resistance of trains of 300 tons, runnlQg from «6
to 26 mOes per hour, 30 per centi but as the speed was increased, this gain was
diminished, but It remained always al^ jier cent.— £. Ch^baL
ITnocHL.
A*eoiinntlt0e vftllie Avstrian 1!taii>n -eT ISngineers and Awhitedls, sthvr «fKteiided
«KperiiBeiit8, svlnhfrtea tlint l^oitteiid Oement wtfli 7 <fier oenA. «f ^omtmm «at
.te •eeld ^Miter, and Ibe -mooe «r lirick dry, 'ima flie 'mvA «ffectiipe, sod that Lime
mortar was uBelcM.~il>(^«il ^reO.
AFPBHDIX.
rabls tor R*anoiiiB Oltmi
■od I>atl7 VBrlBiloii of Needle
VBrlOilion of the Day.
r' and Oaidttic SMntqi. i8;S.
No
"=-*
HindUi.
V
!.».
£."^
Sf
yt
i.lL
t
h.
*.
K
k.
t
N....
■
h.
6
IS-t::::;:
3
*
■
;
*
1
;
Winter.
;
i
i
7
i
J
-
Blevatlona, at Varioua Looationa, of BenoH-Marks
Above Mean Level of the Ooean. at
Sandy Hook, N, J,
Ba Pnanirf Amiuai Ktfort Jar ,t^ of Surennltudail V. S. Cotut (pd
Alban)F, N.
AMii'driaB.,Ry.
Brookiyn.H.v'!!
Burllnglon, lows.
GllI(l,IIL
Cbeyauua. Hva.
Cblcaco, 111
ClDolniuiil, d'....
ColondoSp's.Col. i
Columbus, Kf....
CumlMrliBi}, Hd.
Dakota, Minn...
Actmlt, Uc'b,°
Dubuque, Iowa.
Emm. Ptfaa , .
Krlfl, Pi
Fort Jc^eRaD,«
GoVBDr'il.,N."y;
Harrlsburg, Pb..
Jaokoon. Tenn. .
:;C
!;i?S
•di ■
7.5«i.l
Lake HlchigaD. III.
a Rock' Art.'
leapoliiL hIud!
Uoblle.itli
HalcliBi.Misa.....
Mewpon Nskb.V*.
New Orlaana, li..
New York, N.r...
Qmaba, h'eb
[}nlarla,?t.IM.,Cu
Oewego. N. Y
tebanect*d«, N. V
g.■i^^i::.::
Rb- e»c( loaUiim and ifcwriiHum nfBtnt*Marla, lee Btport ai olivet, pp, 548-51
1040 APFSKDn^
Insulation of Steam Soileva and Plp«
From the experiments of several parties in England, St. Petersburg, and Canada,
the following results were obtained:
With steam at pressures ranging from 3 to 150 lbs. per sq. inch, and averaging
75 lbs., the condensation of steam in pipes, per sq. foot per hour, was: Uncovered,
.60 lbs. ; with mica insulation, with steam fh>m 47 to 344 lbs., averaging 150 Ibs.^
.143 lbs.
With steam at 150 lbs. permanent in the pipes, it was computed that each sq.
foot of uncovered surface involved an annual loss of $a.ii ; with ordinary and gocNl
bagging, 55 cents; and with mica insulation, 28 cents.
From experiments on the Canadian Pacific Railway, the rate of cooling of water-
tanks ftom the boiling point in 5 hours, the loss of temperature varying from 84°
in the uncovered to 20° in the one covered with mica; and from other experiments
on the Grand Junction Railway, with 5 locomotives, with steam at fVoro 140 to 150
lbs. pressure per sq. inch, the observed effects, after the fires were drawn, were:
The uncovered boiler lost 56 lbs. pressure in one hour, while the covered lost, re-
spectively, 24, ao, 13, and 6 lbs., the last with mica covering.->J?»?pinemfi^, 1901,
p. 234.
I^iq-aid XTuel.
From experiments made with crude Borneo oil,*of the composition: Carbon, 87.9
per cent; hydrogen, 10.78; oxygen, x.34; flash-point, 21 lO; boiling-point, 395°;
and caloric value, 18.831 B. T. U.
The constituents of fuel oils fflve off vapor at temperatures f^om loo^ up to boil-
ing-point of tlie oil, near which point a residuum of dense carbon is precipitated,
tending to choke pipes and to accumulate in the fbmace.
The following methods of using it are: i. Ii^ecting it into the furnace under
pressure, as spray; 2. Spraying it by air or steam; 3. Vaporizing it.
The evaporative eflBciency under the first was 12 lbs. water fi'om ; and at 312O per
lb. of oil, an excess of air and a large furnace being required for combustion.
Under the second, 13 to 14 lbs., less air being required. Under the third, 15 to 16
lbs., a minimum of air being required.
The conclusions deduced were: ist A reduction in consumption of fUel with the
oil, compared with coal, of about 40 per cent 2d. A reduction in bunker space ot
about 15 per cent, for equal weights of fuel. 3d. A reduction in furnace labor of
at least 50 per cent.
The oil should be filtered before being used.— i?. L. Orde.
Sffeots of Repeated Stress on tlxe Strenstln uf VITrousli-t
Iron.
Prom Teits Made on a Bridge that had been 24 Years in Service.
The maximum stress being 6.64 tonfi per square inch, no reduction in strength
or durability flrom its service was observed.— Ztmm«nnann.
Saf^B Static ILioad on Ordinar^r IToundations*
In Toni per Square Foot
Sand, sharp and clean i to 1.5
Gravel, dry 1 a.as
Stones, broken and concrete. . 3
Alluvial soil .5
Clay and sand, moist z .33
Clay, hard and dry 1*5^3
Earth, firm itos.5
-^Aide Memoirt and Rainkime
APPENDIX. • 1 04 1
A.ir«Puxnps of CoudensiziK Steam-Kngii^esi-
Are more'efTective wbeD operated independent of the engine, in consequence of
possessing the advantage of their operation being varied to meet their require-
ipents; and vertical single-acting, at a velocity of piston not exceeding 400 feet
per minute, are more effecU¥e than double-acting.
The required dimensions and resulting capacity of full flowing pumps may be
computed from the table of H. R. Worth ington on p. 738.
A displacement of pump cylinder of one-fifth of a cube foot per minute is held
to be proper for one IIP.
Sffeot of tlxe Use of* Oil or T*allo'w in a Steam-Boiler.
Oil or grease introduced in a steam boiler, c'ombiniug with alluvial or calcareous
sediments from the feed water, if not held in suspension by rapid circulation over
the heated surfaces, as the crowns of the fUruaces and tubes, and withdrawn by
pump or blown out as it subsides, will settle u|>on the upper surfaces of the fur-
nace and tubes, involving the burning uf lUe metal aud their consequent disruption
under pressure.
Stress on. Xrussed Seam or Rods.
In addition to pp. 621-623, S23.
Kins TruflB* To Gompute Stress on. Beam.
W / W
---- sec. t= — cosec » = S. W repre-
8a
-.. aa 4
I tenting weight unijormly distributed^ I length
' of t>eam between supports^ d depth of trtus^
both in feel, and i angle.
lLLU8TRATioir.— Assume W = 3ooo lbs., l = 2o, d = 3.03 feet t = 11^43', and
cotan. i = 5.i.
2000X20 -. 2000 ,.
3 ^ =2495 lbs., = — — X 5 > = 2 550 '^*-
1?o Compute Stress on Rods.
Wi . W ^ ^ ^ , W Vi2 + 4da
-— sec. » = — cosec. x. In absence of angle put -f^ — .
8d 4 ° 4 2d
Illubtration. ^Assume as preceding. Sec. > = 1.02, cosec. t = 5. i.
9000 ^^ ,, 2000 , ,.
X z.o2 = 3 445.4 2m.,= X =5-1 =2550 (M.
*JCo Compute Stress on Centre.
IllustraMOU.— 5 W as - X a COO = 1 250 Ibs.
8 o
Queen Xmss. To Compute Stress on Beam.
♦ » WI . 3„ , , , J. ^
-T-^ sec. » = I W cotan. i, c := 6.67 fett.
Illustration Assume as preceding.
d=2 feet, and angle i-=.ifP 42', sec. i —
1.044, and cotan. t = 3.4a.
2000 X go ^ ,.044 = 2 6io »*., and |2ooo= 750 X 3.42 = 2 565 it*.
8x2 o
Xo Compute Stress on Rods.
W< . 3W
-— - sec. I = — „ coseft ».
8d 8
Illcstratioh.— Assume as preceding, cosec. i = 3.56
44 = 3 610 Ihs. , a
3W v^T^ip^d"
12^2L??X 1.044 = 2610 H«., and 3L2l£???x 3. 56 = 2670 ftl.
In absence of angle put - .
8 3a
To Compute Stress on Centre,
!iw = a w=2oooi6.. ii2il^=,,oo»t.
so 20
I042 ORTHOGRAPHY OF TBCHKIOAL WORDS AND TEpM&
ORTHOGRAPHY OF TECHNICAL WORDS AND TERMa
Orthography in ordinary use of following words and terms is so varied,
bhat they are here given for the purpose uf aiding in the estabiishmeat QX
a uniformity of expression.
AbuL To meet, to aiUJoin to at the end, to border upon. Almt end of a log, etc.,
to tliat having the greatest diameter or side.
Alt and Butt tud, wh«n appUed in this nuuuier, ar* corruptioiia.
AdiL iji Mining^ the opening into.a mine.
AmidiMpt. The middle or centre of a vessel, either fore and aft or athwartshipa.
The amidship (hime of a vessel is at {§{< ^^^ ie termed 4ea4JkU.
Arabesque. Applied to painted and carved or sculptured ornaments of imaginary
Ibliage and animals, in which there are no perfect figures of either. Synonymoua
with Moresque.
Arbor. The principal axis or spindle of a machine of revolution.
Arris. A term in Mechanics, the line in which the two straight or curved aur-
Ikces of a body, forming an exterior angle, meet each other. The edges of a body,
as a bricK, are arrisea
Ashlar. In Masonry^ stones roughly squared, or when faced.
Athwart Across, from side to side, transverse, across the line of a vessePs
aourse.
Athtoartskips, readhing across a vessel, from side to sldeL
«
Bagasse. Sugar-cane in its crushed state, as delivered IVom the rollers of a mill
Balk. In Carpentry, a piece of tinjber from 4 to lo ins. square.
BcUuster, A small column or pilaster; a eoUectiOD of them, joined by a rail, forms
a balustrade.
JBmniattr U • corniptlon of b^lutnul*.
Bark. A ship without a mizsentopeail, and formerly a small ship^
Bateau. A light boat, with great length proportionate to its beam, and wider at
Its centre than at its ends.
Batten. Tn Carpentrif, a piece of wood from i to 2.5 ina thick, and from i to 7
Ina in breadth. When less than 6 feet in length, it is termed a deal-end.
Berme. In Fortifications and Engineering, a apace of ground between a fampart
and a moat or fosse' to arrest the ruins of a rampart. The level top of the embank-
ment of a oanal, opposite to and alike to the towpatb-
Bevel. A term for a plane having any other angle than 45° or 9o<>.
Binnacle. The case In which the compass, or compasses (when two are used), is
set on board of a vessel.
Bit. The part of a bridle which is put into an animaPs mouth. In Carpentry^ a
boring instrument.
Bitter End. The inboard end of a vessePs cable abaft the bitta
Bitts. A vertical frame upon a deck of a vessel, around or upon which is secured
(jables, hawsers, sheets, etc-
Bogie. Pivoted truck, to ease the running of an engine or oar around a curve.
Boomkin. A short spar projecting frt>m the bow or quarter of a vessel, to extend
the tack of a sail to windward.
Bowlder. A stone rounded by natural attrition ; a rounded mass of rock trans-
ported from Its original bed.
0
Buhr-stone. A Stone which is nearly pure silex, Ml of poNS and cavUies, and
used for Milla
Bunting. Woolen texture of which colors and flags are made.
Burden. A load. The quantity that a ship will carry. Hence fmrdenxome.
Cog. A small cask, diflering from a barrel only in slza Commonly written Keg,
ORTHOGRAPHY OF TKOHKICAL WORDS AND TBRMR. IO43
OaKhef. Aa inslrameiit with Bsmi oireaiar togs, to roeasure diameteni of Bpheree,
or exterior and interior diameters of cylinders, bores, etc
A p4dr «>f OKHbera U laperflaoin and Impropor.
CcUk. To Stop seams and pay ttem with pitph, etc. To ppjnt an iron phoe so 4fi
to prevent its slipping.
Cam. Aa irrfiguliM' curved instrument^ having ite axi«( eccentric to the eh^ft
npon which it is tlxed.
Camber. To camber is to cnt » bc»m or mold » stru<st^rfi archwise, as 4ec|t-
besms of a vessel.
Cambooge. The stove or range in which the cooking in a vesael i» effected. The
cooking- room of a vessel; this term is usually confined to merphAnt vessels; in
vessels of war it is tormed Galley.
Camel In Engineering^ a decked vessel, having great stability, designed for nse
in the lifting of sunken vessels or structures. Also to trjiniBpor^ ^o94& of great
weight or bulk.
A 8eow U open decked.
CanUe. A fragment; a piece; the raised portion of the hind part of a saddle.
Cantline. The space between the sides of two casks stowed aside of each other.
When a cask is laid in the cantline of two others, it i3 sajd to be stoi^ed bilge and
cantline.
Capstan. A vertical windlasa
Caravel A small vessel (of 25 or 30 tons' burden) used upon the coast of France
iM berring {Mierie&
CarUngs. Pieces of timber set fore and aft ttom $h£ deck beams of a vessel, to
receive ue ends of the ledges in framing a deck.
Carvel bnill^A term appUed to the manner of con8tr«»otian of small boats, to
signify that the edges of their bottom planks are laid to each other like to ti»e twi-
ner of planking vessels. Opposed to the term Clincher.
Cotter A fy^y" phial «r battle tor the tabje. Casters. Small wheels placed
oiMMi the tegs 4>ftabfcii^ eto-, to alinw them to ib« moved with facility
Catamaran A small raft of logs, usually consisting of three, the centre one be-
Ing tS^r and wide" than the oSSti, and designed tor use in an n'^n roadstead
and NpoB a wa-eoaat.
Chamfer. A slope, groove, or small gutter cut In wood, metal, or stone.
ChapeUing. Wearing a ship *»«n* without bracing her fore yai^s.
•l»d<VirnSes,«iHl«f««lal, as ill «fltea» boiler. So^Pipe.
Chime. To chinse id to calk slightly with a knife or chisel
- jOiflck. taAr«WJrcfc««peiw-4!,«B»Uj?M»€»9 4afwoDdu8fidto,m»ke
flciency in a piece of timber, frame, eta See i^itmn^*.
OMte. fb>«tofii,io«h0tnct,iolitodk«9,toihiNKter,eto.
aeaU Pieces of wood or metal of various shapes, according to «ieir uses, eitheir
to b^fay ropes upon, to resist or support weights or strams, as M«<, shoar, 4>eam
cleat^<A&
<»tffM»ar toM A term «wtte« t« «be ooostruolion of vessels' 'bettoms, wtcn
the lower edges of the planks overlay the wext ond^r them.
Cook. A cylinder cttbe, or trian^e ofhard wood let into the ends or faces of two
which the pin runs. In Naval ArehiUciure, the oblong ridges hawked an Uie omm
tfahipa
<yoaminfft. Rniied borders «roimd 'tbe edges ofliartches.
CobU. A small fishing boat.
Cocoon. The case wWch .cectaln inaocta m^9 «w # 4»wU»g >0mV th# fi^oi
•r their nietamorphosis to the pupa sUte.
I044 OETHOGBAPHY OF TECHNICAL W0BD8 AKD TBBMS.
Cng. In Mechanics, a short piece of wood or other mateiial let into the fhoes o!
B body to impart luotiuu to unother. A term applied to a tooth in a wheel when it
is made of a diOereut material than that of the wheel. In Mining^ an intrusion ot
matter into fissures of rocks, as when a mass of uustratitled rocks appears to be in-
jected into a rent in the stratified rocks.
Cogging. In Carpentry, the cutting of a piece of timber so as to leave a part
•like to a cog, and the notching of the upper piece so as to conform to and receive
It. ^iko to indetUing or tabling.
CoUer. The fore iron of a plough that cuts earth or sod.
Compass. In Geometi-y.ha instrument for describing circles, measuring figures, etc
A pair of Ct>mpat$et b aaperfliioiu and improper.
Connecting Bod. In Mechanics, the connection between a prime and secondary
mover, as between the piston-rod of a steam-engine and the crank of a water-wheel
or fiy-wheel shaft.
Th« t«rtn PUmmn b loe«), and alto|C«ther liiRpplieabU.
Contraritoise. Conversely, op)x>site. Orottwaf b a comptioa.
Corridor. A gallery or passage in or around a building, connected with variona
departmeuts. sometimes running within a quadrangle ; it may be opened or enclosed.
In Ibrtijcations, a covert way.
Cyma. A molding In a cornice.
Damasquinerie. Inlaying in metal.
DaviL A short boom fitted to hoist an anchor or boat
Deals. In Carpentry, the pieces of timber into which a log is cut or sawed qpl
Their usual thickness is 3 by 9 ins. and exceeding 6 feet iu length.
Improperly reatrlcted to the wood of flr-treet.
Dike. In Engineering, an embankment of greater length than breadth, imper-
vious to water, and designed as a wall to a reservoir, a drain, or to resist the influx
9f a river or sea.
Dingey {yaulicai). A ship or vessers small boat
Dock. In Marine Architecture, an enclosure in a haitor or shore of a river, for
ihe reception, repair, or security of vessels or timber. It may be wholly or only
partially enclosed. See Pier.
When applied to a aingle pier or Jetty, it b a inbiq;»plication.
Dowel. A pin of wood or metal inserted in the edge or fiu» of two boards or
pieces, so as to secure them together.
Thb fa very similar to ooakinK, bat it need in a diminatiTe aente. An Illottratlon of it b liad in tha
Banner a cooper aecnrea two or mora fdeeee in the head of * eaak.
Draught. A representation by delineation. The depth which a veasel or any
floating body sinks into water. The act of drawing. A detachment of men firom
the main body, etc
Ordinarily written draft,
Dutchman. In Mechanics, a piece of like material with the structure, let into •
slack place, to cover slack or bad work. See Shim.
Edgewise. An edge put Into a particular direction. Hence endtote and Hdewiit
have similar significations with reference to an end and a side
Eigewaift b a corruption.
Euphroe. A pieee of wood by which the crowfoot of an awning is extended.
FauU. In Mining^ a break of strata, with displacement, which interropti Ofiera-
tions. Also, fissures traversing the strata.
/Woe, Felloes, The pieces of wood which form the rim of a whe^.
Feiek. Length of a reservoir, pond, etc, along which the wind may blow towards
Ihe emtrankment or dam.
Flange. A projection fVom an end or ft'om the body of an instrument, or any
part com|K)Bing it, for the purpose of receiving, confining, or of secaring it to a snp^
port or to a second piece.
FKer. In Carpentry, a straight line of steps in a stairway.
Frap. To bind together with a rope, as toyrop a fiOI, etc
OBTHOOBAPHY OF TECHNICAL WOBDB AND TEBMS. IO4J
Friexe. In Architecture^ the part of the entiiblature of a column which is between
(he architrave and the cornice.
Frustum. The part of a solid next the huge, left by the removal of the top or
segment.
f)nutrum, altboagh u«d by •om* lexioographen, te erroneous.
Furrings. Strips of timber or boards fastened to fhimes, joists, etc., in order to
bring tboir faces to the required shape or level.
Guleting. Putting galets into pointing-mortar or cement
GiUeiB. Pieces of stone chipped off by the stroke of a chisel. See SpdU.
Oaliot. A small galley built for «peed, having one mast, and firom z6 to ao thwarts
for rowers. A Dutch-constructed brigantine.
Gate. In Meehemies^ the hole through which molten metal is poored into a mold
for casting. Gtmt and 0«U «ni corraplione.
Gearing. A series of teeth or cogged wheels for transmitting motion. To gear a
machine is to prepare to connect its parts as by an articulation.
Gingle, To shake so as to produce a sharp, clattering noise, commonly JingU.
Girt. The circumference of a tree or piece of timber. Girth. The band or strap
by which a saddle or burden is secured upon the back of an animal, by passing
around bis belly. In Printing, the bands of a pretis.
Gnarled. Knotty.
Grave. In Nautical language, to clean a vessel's bottom by burning.
Graving. Burning off grass, shells, etc., fh>m a ship's bottom. Synonymous
with Breaming.
Grommet. A wreath or ring of rope.
Gymbal JHna. A circular rynd for the connection of the upper mill-stone to the
spindle by which the stone is suspended, so that it may vibrate upon all sides.
Harping*. The fore part of ^he wales of a vessel which encompass her bows,
and are Ihstened to the stem. Cat harpingt, ropes which brace in the shrouds of
the lower masts of a vessel
Hogging. A term applied to the hull of a vessel when her ends drop below her
centre. See Sagging.
Horsing. In Naval Architecture, oalking with a large maul or beetle.
Jam. To press, to crowd, to wedge in. In NatUical language, to squeeze tight
Jamb. A pier; tiie sides of an opening in a wall.
Jib. The projecting beam of a crane from which the pulleys and weight are sus-
pended. A sail In a vessel.
Jibe. To shift a boom-sail flrom one tack to another; hence Jibing, the shifting
ofabooDL
Jigging. Waditeg minerals in a sieve.
Keelifm. The timber within a vessel laid upon the middle of the floor timbers,
and exactly over the keel. When located on the floors or at the sides, it is termed a
sisters or a side keelson.
Kerf. Slit made by cut of a saw.
KeveL Large wooden cleats to belay hawsers and ropes to, commonly CaoiL
Laequer, A spirituous solution of lac To varnish with lacquer. *
Lagan. Articles sunk in the water with a buoy attached.
Laitanee. A pulpy, gelatinons fluid washed fh>m the oement of concrete depos-
ited in water.
Lap-tided. A lerm expressive of the condition of s vessel or any body when it
will not float or sit upright
Lay-to. To arrest headway of a vessel, without anchoring or securing her to a
buoy, eUx, as by coanterbracing her yards, or stopping her engine.
Leat. A trench to conduct water to or trom a mill-wheel.
Leech. In NmuHoal Umguage, the perpendicular or slanUpK edge of a eaU wb«r
•oi secured to a spar or 9(§y. ^ ^
104^ ORTHOGRAPHY OF TECHNICAL WORDS AND TBRM8.
LhJ. ttie ftillest part of tbe bow of a Tessel.
Mail. A largu duuble-beaded wooden hammer.
Mantle. To expand, to spread. Mantdpiece, The shelf over a fireplace in front
of a chimney.
Marquetry. Checkered or inlaid work in wood.
Matrau. A chemical vessel with a body alike to an egg, and a tapering neck.
MaJttreu. A quilted bed ; a bed stuffed with hair, Inoss, etc., and quilted.
Mitred. In Mechanics^ cut to an angle of 45^^, or two pieces joined so as to make
a right angle.
MiMen-magt. The afterfnoet mast ta a three-masted vessel
Mold. In Mechanics, a matrix in which a casting is formed. A number of pieces
of vellum or like sutastance, between which gold and silver are laid fbr the purpose
of being beaten. Thin pieces of materials cut to curves or any required figure. In
Naval Architecture, pieces of thin board cut to the lines of a vessers timbers, etc
Fine darth, such as constitutes soil. A substance which forms upon bodies in
warm and confined damp air.
Tbto ortbofmpiiy to by Hulogy, m gM^ aoldf «iif, M<l, 9oU,fvld, clt.
Maiding. 1 n Architecture^ a prelection beyond a wall, flnom a eirfumn, wainscot, eta
Moresque. See Arabesque.
Mortise. A hole cut in any material to receive the end or tenon of another pieca
Muck. A mass of dung in a moist state, or of dung and putrefied vegetable matter.
MuUion. A vertical bar dividing the lights in a window ; the horizontal cjo
termed transomt.
Net Clear of deductions, as net weight
Newel. An upright post, around which winding st&ira tnm.
Nigged. Stone hewed with a pick or pointed hammer instead of a chisel
Ogee. A molding with a concave and convex outline, like to an S. See Oyma
4D4 Taion.
PaOUuse. Masonry raised upon a floor. Abed.
Pargeting. In Ardiitecture, rough plastering, alike to that upon chimneya
Parquetry. Inlaying of wood in figures. See Marquetry.
Parral. The rope by which a yard is secured to a mast at its centre.
PawL The catch which stops, or holds, or fUls on to a ratchet wheel
Peek. The upper or iwinted comer of a sail extended by a gaff, or a yard set ob<
liqueiy to a mast. To peek u yard is to point it perpendicularly to a mask
Pendant. A short rope over the head of a mast for the attachment of tacklae
thereto; a tackle, etc.
Pennant. A small pointed fiag.
Pier. In Marine Architecture, a mole or jetty, prqlecting lAto a river or am, to
protect vessels from the sea, or for convenience of their lading. See Ihck.
CrronMotly t«ratMl • J>oek,
Pile. In Engineering, spars pointed at one end and driven into soil to sanx»rt a
superstructure or hold&st e^u to a cormption.
Pipe. In Mechanics^ a metallic tube. The fine of a fireplace or Aimaoe when
constructed of metal; usually of a cylindrical form.
Th* tarm or appUtaliMi of Stack (whkh rofon soioly to maMiiTy) to • HMtaUie ptpe to • mtonp^U.
eation.
Piragua. A small vessel with two masts and two boom-eaU&
Commonly termed Pirry-iiugur.
Pirogue. A canoe formed from a single log, propeUed by peddles or by a sell,
with the aid of an outrigger.
JHoMtering. in Ar<Mleeturey covering with plaster cement or mortar upon walls
or laths. In England, termed laying^ if in one or two coat work • and pricking 19^
If in three-coat work.
Pluwtber block. A bearing to receive and support the jeiuriuU of a shalk
Pokwre, Tdcsts of one piece, withQut to|i4b
ORTHOORAPHT OF TECHNICAL WOBDS AND TGBMS. IO47
Poppelt. In Ifavol Arehittchu% pleees of Mniber Mt p«rp«ndicQltr to a Taflnrs
bilge- ways, and extending to her bottom, to support her in launching.
Porch. An arched vtUibuU at the entnince of a building. A vestibale supported
by columns. A portico.
PorUco, A gallery near to the ground, the sides being open. A pUutza enoom*
passed with arches supported by oolumns, where persons may walk; the roof may
be flat or vaulted.
Pouw^oMM. A loose, porous, volcanic substance, composed of sUicious, argilla.
ceous, and calcareous earths and iron. .
Prue. In JfecAantCf, to raise with a lever. To ;>ry and a pry are eomptloiu.
Proa, Flying. A narrow canoe, the outer or tee side being nearly flat. A (htttie-
work, projecting several feet to tne windward side, supports a solid bearing, in the
form of a canoe. Used in the Ladrone Islands.
Purlin. In Carpentry, a piece of timber laid horizontal upon the rafters «f a
roof, to support the covering.
Bump. In ArckUedwre., a flight of steps on a line tangential to the «tep& A
. concave sweep connecting a higher and lower portion of a railing, wall, etc A
sloping line of a surface, as an inclined platform.
BarefacUon. The act or process of distending bodies, bjr separating their parts
and rendering them more rare or porous. It is opposed to Condensation.
Rebate. In Mechanics, to pare down an edge of a board or a plate for the purpose
of receiving another board or plate by lapping. To lap and unite edges of boards
and plates. In NcuhU ArchxtecturCy the grooves in the side of the keel for receiving
the garboard strake of plank.
CramoBly written BMtt.
Remou. Eddy water without progressive action, in bed of a river; a return of
water agamst direction of flow of a river.
Bmdering. In Architecturef laying plaster or mortar upon mortar or walls.
Sendered and Set refers to two costs or layers, and Aemfered, FUmsML, «n4 Set^ to
three coats or layers.
Beniform. Kidney-shaped.
ILuin. The residuum of the distillation of turpentine, sodn is a eomptka.
Riband. In Navai ArchUedurt, a long, narrow, flexible piece of timber.
Rinur. A bit or boring tool for making a tapering hole. In Mechanics, to Rim*
is to bevel out s hold Riming. The opening of the seams between the planks of a
reesel for the purpose of calking them.
Rotary. Turning upon an axis, as a wheel
RynA. The tnetallie collar In the upper mlll-stone by which it is connected to
the spindle.
Sagging. A term applied to the hull of a vessel when her centre drops below her
snds The converse of Hogging.
SeaUop. To mark or cut an edge Into segments of circles
Bcareemeni. A set back In the face of a wall or in a bank of earth. A fboting.
Scar/. To Join ; to piece ; to unite two pieces of timber at their ends by running
the end of one over and upon the other, and bolting or securing them together.
Scend. The settling of a vessel below the level of her keel
Selvagee. A strap made of rope-yams, without being twisted or Iskl ap, snd re>
tained in form by knotting it at intervals.
Sennit. Braided cordage.
Sewage. The matter borne off by a sewer.
Sewe± In nautical language, the condition of a vessel aground ; she is said to bs
imoid by as nrneli ss the diffiBrenoe In depth of water around her sad her floattng
depth.
Sewerage. The system of sewers
Skakgk Crsolrad or splits or tm timber Ioofl«ly put together.
Mkammg. Leather fyrepsred ftom the skin of a chamois goat
I04^ OKTHOGEAPHY OF TECHNICAL WORDS AND TKBlCa
Sheer. In Naval ArtkUeeture^ llM earn w bend of a ahip^s dick or 8lde& Ta
fAe«r, to slip or wove asM*.
Shtert. Elevated spars connected at tiie upper ends, and used to elevuie lieavj
twdies, as masts, etc.
Skim. In Naval ArehUecture, a piece of wood or iron let into a slack place in e
frame, plauk, or plate to fill out to a foir surface or line.
Shoal. A great multitude; a crowd; a multitude of fish.
Sekotl is • corrapUoa.
Shoar. An oblique brace, the upper end reeling against the substance tc be sup*
ported.
SkoUt. Pieces of plank under tbe heels of shoars, eta
Shoot A passage-way on the side of a steep bill, down which wood, coal, etc., ara
thrown or slid. The artificial or uatunU oontraotioa Of a river. A young pig
Sidewite. aeeSdgcurise,
Signalled. Communicated by 8ignal&
Bigmimdt wfan applM to aigiials, U a miMppliealioti of irordt.
SiU. A piece of timber upon which a buildiug rests; the horizontal piece of tim-
ber or stone at the bottom of a tVamod case.
Sijpf^on. A curved tiibe or pipe designed U> draw fluids out of vessela
Skeg. The extreme after-part of the keel of a vessel; the portion that supportt
the rudder-post.
SkuUwiie. Oblique; not perpendicular.
Sleek. To make smooth. ReAise; small ooaL
Sleeker. A spherical-shaped, curved, or plane-surftced instrament with which to
smooth surfaces.
Slue. The turning of a substance upon an nxis within its figure.
Snying. A term applied to planks when their edges oi their ends are carved or
rounded upward, as a strake at the ends of a fliU-modelled vessel
filpeUl. A piece of stone, etc. , chipped off by the stroke of a hammer or the force
of a blow. SpalUng^ breaking up of ore into small piecea
SpandrH. In ArchiUctwre, tbe irregular triangular space between the outer lines
or extrados of an arch, a horizontal line drawn from its apex, and a vertical line
from Us springing.
Spomon, An addition to the outer side of the h nil of a steam vessel, commencing
near the light water-line and running up to the wheel guards; applied for the paf*
pose of shielding the deck-beams from Uie shock of a sea.
Spnruon-tided. The hull of a vessel is so termed when her frames have the out-
tine of a sponson, and the space afforded by the curvature is included in the hold.
JE^fomding, 8ponti»fi, ate., are corrnpttona.
Squilgee. A wooden fnstmment, alike to a hoe, Its edge fiioed with leather or
vulcanized rubber, used to focilitate tbe drying of wet floors, or decks of a vessel
Stack. In Maeanry. a number of chimneys, or pipes standing together. Tht
diimney of a blast fufnace.
Tha appllciitioii of thia word to the ainokfl-pip« of a steam-boiler ia wholly erroneous.
Slope. In Engineering, the interval or distance between two elevations, in shovil-
ling, throwing, or lifting.
Sleeving. The elevation of a vessel^s bowsiprit, cathead, etft
Stroke. A breadth of plank.
SirtU. An oblique brace to support a rafter.
Style. The gnomon of a san-dial
Sump. In Miningy a pit or well into which water may be led fh>m a mine or work.
Surcingle. A belt, band, or girth, which passes over a saddle or blanket upon ■
horse's back.
Svjoge. To bear or force down< An instrnmeot having a groove on Its under
side for the purpose of giving shape to any piece subjected to it wjhen receiving a
iMOw Arom a hammer.
OBTHOGBAPHY OF TSCHNICAJU WOSDS AND TBiKMS. IO49
8ff]^tered. Overtapplng the ehamftred edge of one pUnk upon the chamfered
edge of aoother in such a manner that the Joint shall be a plane mrlhce.
Talut. In Architecture, the slope or batter of a wall, parapet, etc. In Oeolofjy^
a sloping heap of rubble at foot of a qlifll
remptate. In Architeeture^ a wooden bearing to receive the end of a girder to
distribute its weight
TempleL A mold cut to an exact section of any piece or structure.
Tenon. The end of a pieoe of wood, cat into the form of a rectangular prism, dc
signed to be set into a cavity of a like form iu another piece, which is termed the
mortige.
Terring. The earth overlying a quarry
Tester. The top covering of a bedstead
Tholes. The pins in the gunwale of a boat which an OBed as rowlocka
Thwarts. The atbwartship seats in a boat
Tide-rode. The situation of a vessel at anchor, when she rides in directioii ot tti
current instead of the wind.
Tire. The metal hoop that binds the felloes of a wheel
Tompieu. The stopper ot a piece of ordnanocL The iron bottom to which grapo
■hot are secured.
Treenails. Wooden pins employed to secare the planking of a vesMl to the
Ckamee
Trepan. In Mining^ the Instrument nsed in the comminution of rock in earth*
boring at great depths.
Trestle. The flrame of a table; a m«/vable form of support In Mast-making^ two
pieces of timber set horizontally upon opposite sides of a mast-head
Tries. In Seamanship, to haul or tie up by means of a rope or tricing- lino.
TueiroH or Tuyere. The noszle of a bellows or blast-pipe in a foige or smelting*
fhrnace.
Vice, In Mechanics, a press to hold fast anything to be worked upon
^oyal In Seamanshipy a purchase applied to the weighing of an anchor, leading
to a capstan.
Wagon. An open or partially enclosed four-wheeled vehicle, adapted for the
transportation of persons, goods, etc.
Wear. In noMtieal language, to put a vessel upon a contrary tack by taming
her around stem to the wind.
Weir. A dam across a river or stream to arrest the water; a fence of twigs 01
stakes in a stream to divert the run of fish.
Whippletree. The bar to which the traces of harness are (kstened.
Wind-rode. The situation of a vessel at anchor, when she rides in direction of
the wind instead of the current
Windrow. A row or line of hay, etc , raked together.
Withe. An instrument fitted to the end of a boom or mast, with a ring, throajh
ivhlch a boom is rigged out or mast set up.
Woold. To wind ; particularly to bind a rope around a spar, etc
i^LcLdenda.
Astragal In ArdUteeture, a round molding, surrouuding the head or base or a
column. In Gunnery, a like. molding on cannon near the mouth.
Creosote: An oily colorless liquid, procured from coal-tar.
Flume, a chunnei for conducting water, as that by which the surplus water of a
canal is led to n lower level
Forebaif. The part of a Mill-race or Penstock, fkrom which water flows upon a
water- wheel.
Grillage. A frame, constructed of beams laid in parallel rows, and crossed at
right angles, with others notched over them.
Designed to unlforroty dlstribate or extend the area of a foundation.
I050 OKiUOQiUPHY OF TXOUNXCAl. WOKD8 AND UfiKMS.
ffupotenui^, GowmoQly, b«t incorrectly, hjpoiheattiQ:
Jetty In IVaml AroMUeiwrt, a pier that Juts out or projects into a river or a
sea, a lanaing place. » « v* »
Kibble. In Mining, a metallic bucket in which ore is drawn up to the surface.
X^wiiM. One or two ArustumBor a right-angled metaUic wedge, aet inverted or
dove -tailed and keyed in a wedge-formed slot, in stone or like solid subsSnce
whereby it may be lifted and laid without the \m of aliog& »uuBHuice,
or'vSd^ t^° -B»^««n»iflf, a cylindrical pillar terminating a wing wall of a brid^^e
Parcelled. NautieaL Wrapped with canvas or tarred rope, to resist wear fi-om
friction.
Payed. Nautical. Painted, tarred, or gfoaaed, to resiH moisture and wear.
penstock, xn wrtiflcial conduit for water to a water-wheel, and nimished with a
flood-gate.
RaveL To disentanfle, untwist, or unweavf. Tli« wul pif«» Un U wboUy w|^rflii<.a»
Boil. To render turbid, to stir or mix.
Scabble. The dressing of the faces of rough stones, w with » brond QhiseL
Served, Service, IfctutifaL The layer of wrappiug, as spun yarn, lines, etc.,
around a stay or rope, to resist friction and wear.
ShackU, or Clevis. An open link set in a chain, secured by a pin running through
eyes in its ends, which, when withdrawn, admits chain to be parted at that point
SoJjU. In Architecture, the under side of an opening ; the lower surface of a
vault or arch; also the under surface of an arch between columns.
Splay. In Architecture, a sloped eurface, or ope making an oblique angle with
another. A large chamber.
Strike, in Geology, is the compass direction of the intersection Of th^ pllWQ of
stratified rock with the plane of the liorizon.
Altart. In Naval Arektieeture, the steps on the sides and end of a marine dock.
Gin. An instrument operated by men of animals for the raising or drawing of
heavy bodies; usually a vertical revolving windlass and lever.
Sump. In SaM works, a pond in which the sea or saline water is retained fbr use
in the future.
Skeet. Nauticca. A Bcoop with a long handle, for use in weltiD| the sails or thf
sides of a vessel.
Wya. The vertloal standards on which the telescope j( a TbeoUolita or T^vel is
supported, and which admits of their being reversed by a reversal of its ends
When the telesoope ia reversed by roti^ion on its trunniow^ (ho instrument is
termed a Transit
Cantcdev&r. -ab angular lever, as a projecting bracket under a balcony, the eaves
of a building or the span of a bridge, when the intrados is defined by lines from the
abutments, at an angle eleva^ns ^om the hori^op.
Cuiwl, in ^ttvek^ Architfictur^. A d^lvoU atiij Ilot bottomed vessel, alike tp a
tcoio ; adapted for transportation of heavy materia), in the raising of sunl^en ves^
«els, etc., aud for tUe traiisportat ion of heavy materials, as armaments f^om vessels
to a shore^ etc., commonly, but erroueously, a scow.
Soma. An open and flat-bottome^ fOPSSli adapted for operation In sballow water.
^procffft. A, radial projection on the circumference of a whe^li U> ^Qgago the
links of a chaih, as thos9 Op the wheel base of a capstan.
Spud. In Mechanics, A spade-like instrument for recovering a tool in a tube
well, in Surveying. A nail driven in a monument or stake, to designate a line or
point
Beam. Iq MecJianics. When vibrating, as in a Vertical or Side-lever Steam or
other Engine, it is simply a Beam, as Main, Overhead, Side-lever, Air-pump, et&
Working Ii raperflaoai, and Walking Is a local vulgarism.
Swe. In Mining. A separation of coarse and fine grains or parts. In Jfec^iitof
or Arts. A weak, viscous, and glutinous substance or varnish. In Qeometrf^ or
Volume, the application of it to areas, structures, etc, is otdoctiraable.
Comiption of Assixe, a Statute of measun and price.
OBTHOGBAPHY OF TECHNICAL WORDS AND TERMS. 10$ 1
AdjiUage. An opening in a vessel for tbe efflux of a fluid.
Archean. Oldest period of, geological time. A term given to crystalline schists
and massive rocks underneath the oldest fossiliferous stratified rocks.
Bascule Bridge. A bridge structure for tbe passage of vessels in a river; by
which a single or divided floor is counterpoised by the weight of the inner end or
ends. The whole of the movable floor or floors resting on a transverse shaft.
Beton. Artificial stone made by the admixture of broken stone, shingle, gravel,
etc., with hydraulic cement and water. When mixed with lime it is termed Con-
crete.
Breast-summer. A beam of metal, stone, or wood, designed to sustain a wall over
a doorway or like opening or floor; a lintvl.
Chaplet.' A metallic support or Stud, set in a mold to sustain a core against the
pressure of the metal when fluid
Crab. A shafl, vertical or horizontal, constructed as a rope-drum; for the draw-
ing or raising of heavy bodies, and operated by a winch or handspikes in the
manner of a windlass or capstan.
Dolmen or Tolm,en. (Celtic.) A Druidical monument con.sisting of a large stone
set horizontal on two verticiU stones at a short distance apart, and a few feet in
height (Breton.) An excavated stone containing human remains. Also Cromlech.
A large flat and crooked stone, set horizontal upon four others set vertical, alike to
a table.
Firmer Tools. Short chisels and gouges, as distinguished from ordinary long-
bladed, and usually operated by hand. The gouge is ground upon its outer side;
the ordinary upon its inner.
Flitch. In Construction. —The combination of wood with iron, either in plates
or a flanged beiim.
Gantry. A frame of posts and header, to support a travelling winch, wherewith
heavy weights, as stone for foundation walls, or machines, may be raised and trans
ported.
Jag. A rough point or barb on the projecting surfaces of metal ; produced by
nicking it, as with a chisel, or l)y casting. Jaggers. The rough projections.
Jagging. The insertion of a jagged or serrated bar, shaft, or eye-bolt in a casting,
to prevent its being easily withdrawn.
Key. In Mechanics, a tapered wedge used in connection with a gib and strap,
and also with brasses; to a^ust the length of the rod to which they are attached.
A Cottar.
Lacustrine. Pertaining to a lake, and applied to deposits which are present in
hike basins.
Lewis. A combination of one or two d(»vetailed iron pieces, with a shackle eye
and bolt; set into a dovetailed under cut in a body of stone, marble, or cement
block, and set out and secured by the insertion of a wedge. Lewis BolL A bolt
with a jagged end, for insertion in a block of stone, etc., and leaded in.
LxUing. The laying or insertion of a paste, cement, or adhesive material of plas-
tic consistency, in or over a crevice or between Joints of a pipe, etc.
MawlreL A metal spindle for chucking lathe work. A tapered metal rod or
ibrmer on which nuts, etc., etc., are dressed to shape.
Moraine. Material as rocks, earth, etc., pushed or deposited by glaciers.
Pein. The lesser head of a hammer, and is termed Ball when it is spherical*,
Cross when in the form of a round-edged ridge, at right angles to the axis of the
handle; and Straight, when a like ridge is in the plane of the handle.
Pierre Perdue. Lost or random stone projected in water, usually for a base to a
superstructure, or to construct a Breakwater. Riprap.
Scrim. A screen or shade ; a thin, coarse cloth, used for temporary windows or
doors in a building in progress of completion.
' Seepage. Percolation ; oozing fluid or moisture; also, the volume of a fluid that
percolates.
Stope. A step, an excavation in a mine to enable ore to be rendered accessible
by a shaft or drift. To remove the contents of a vein.
SuUage. Scoriae, cinder, scurf, eto., which floats on the sarfooe ol molten metal-
TaMe, The oomieotioD oC two or more blocks and a rope
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