THE

STEAM ENGINEER'S
HANDBOOK^

A CONVENIENT REFERENCE BOOK
For All Persons Interested In

Steam Boilers, Steam Engines, Steam Turbines,

and the Auxiliary Appliances and

Machinery of Power

Plants

BY

International Correspondence Schools

SCRANTON, PA.

1st Edition, 18th Thousand, 3d Impression

\\ SCRANTON, PA.
INTERNATIONAL TEXTBOOK COMPANY

COPYRIGHT, 1913, RY

INTERNATIONAL TEXTBOOK COMPANY

COPYRIGHT IN GREAT BRITAIN

ALL RIGHTS RESERVED

PRESS OF

INTERNATIONAL TEXTBOOK COMPANY
SCRANTON, PA.

27463

PREFACE

This handbook is intended as a reference volume
for persons engaged in the actual management and
care of steam engines, steam boilers, and the auxil-
iary appliances to be found in the average steam-
power plant. The aim of the publishers has been
to select data of general interest from the vast store
of available material, and to combine therewith
information relating to the problems and difficulties
likely to be encountered in the daily work of the
engineer and the fireman.

In order to keep the book of such size as to be
carried conveniently in the pocket, the treatment
of many of the subjects has necessarily been brief;
but subjects of greater importance, as, for example,
the care and operation of boilers and engines, have
been dealt with more fully. The various tables have
been selected with great care, and only those
have been included which are likely to be consulted
most frequently. The numerous rules and form-
ulas are stated as simply and concisely as possible,
and their applications are clearly illustrated by the
full solution of many examples.

Another important feature is the inclusion of
abstracts from the license laws of the various cities

and states in which such laws have been adopted.
These abstracts serve to indicate how and to whom
applications for license must be made and what
qualifications are necessary in order to obtain
licenses of the various grades. The United States
marine license law is given in full.

Care has been taken to arrange the several por-
tions in a convenient and logical manner, and a
very full index increases further the facility with
which any given subject may be located.

This handbook was prepared by Messrs. R. T.
Strohm and C. J. Mason, under the supervision of
Mr. J. A. Grening, Principal of the School of Steam
and Marine Engineering.

INTERNATIONAL CORRESPONDENCE SCHOOLS

Nov. 1, 1912

NDEX

Absolute zero, 57.
Accidental oil fuel fires, 158.
Acids, 128.

Addition of decimals, 4.
of fractions or mixed num-
bers, 3.

Advantages and disadvan-
tages of injectors, 127.
of turbines, 224.
Air for atomizing oil fuels,

Steam and, 84.
in oil burning, Excess of,

85.
Mixtures of oil spray and,

84.

pump, Pounding in, 214.
required for combustion, 77.
Allegheny, Pa., license law,

252.
Angles or arcs, Measures of,

42.

Anthracite coal, 79.
Apparent, cut-off, 183.

slip, 231.
Approximate mean effective

pressure, 190.
Arcs, Measures of angles or,

42.

Area of chimney, 110.
of safety valve, 115.
Areas, Irregular, 35.

of circles, Table of circum-
ferences and, 38.
Arrangement of piping, 122.
Atlanta, Ga., license law, 252.
Atomic weight, 55.

weights of elements, Table

of, 55.

Atomization of oil, 83.
Attachment of indicator, 175.

of indicator cord, 180.
Automatic injectors, 123

Axially expanded pitch, 234.
Axle, Wheel and, 66.

i, 81.
Baltimore, Md., license law,

253.

Banking fires, 164.
Barrel calorimeter, 97.
Bearing, Refitting cut, 216.
Bearings, Brass-bound, 210.

Danger of increasing heat-
ing of, 215.

Dangerous heating of, 216.

Effects of external heat on,
222.

Grit in, 220.

Hot, 215.

Lubrication of turbine, 228.

Newly fitted, 217.

Oils squeezed out of, 220.

Remedies for increasing
heating of, 215.

Running engine with hot,

216.

Bed plate, Springing of, 222.
Belt pulleys, 66.
Belting, 69.
Belts, Horsepower of, 70.

Lacing of, 72.

Sag of, 69.

Speed of, 70.
Bends, Expansion, 121.
Bituminous coal, 80.
Blade area, 237.

area, Developed, 234.

area, Helicoidal, 234.
Blades, Clearance of turbine,
225.

Erosion of turbine, 226.

Stripping of turbine, 226.
Blow-off, Bottom, 119.-

-off cocks and valves, 119.

VI

INDEX

Blow-off, Inspection of water

gauge and, 170.
-off pipe, Protection of , 119.
Blowing down, 165.
Boiler efficiency, 144.
explosions, 170.
feed, Equalizing the, 148.
feeding, 123.
fittings, 113.
horsepower, Standard of,

141.

inspection, 165.
inspection, External, 165.
inspection, Internal, 167.
management, 145.
piping, 120.
Preparations for shutting

down a, 163.
test, Hydrostatic, 169.
trials, 140.
tubes, Dimensions of iron,

58.
tubes, Dimensions of steel,

52.

Boilers, Connecting, 147.
Filling, 145.
, 103.

Use of zinc in, 134.
Bottom blow-off, 119.
Brake horsepower, 191.

horsepower, Calculation of,

200.

horsepower, Data for, 199.
Prony, l«Mi.
I.ulU-ys, Cooling of, 198.

, 198.

Brass and copper tubes, Table
of weight, of, 49.

md bearings, 210.
Brasses and journals, Cut,

218.

Imperfectly fitted, 218.
Loose, 210.
pinching journal, Edges of,

218.

Reversal of pressure on, 213.
too long. 222.
too loose, 217.
too tight, 217.

• pt-d and crocked, 218.
chimneys, KM).
Bridge wall,

British thermal unit, 58.
Broken piston packing, 2J2.
Brumbo pulley, ITS.
Buffalo, N. Y., license law,

254.
Burner, Shutting down oil

fuel, l.is.
Burners, Location of oil, 151.

Calculating indicated horse-
power, 192.

Calculation of brake horse-
power, 200.

Calculations, Signs used in, 1.
Calorific value of fuels, 78.

value of oil fuels, ^.i.
Calorimeter, Barrel, 97.
Causes and remedies for
pounding of engines, 210.
Carbonate of lime, 127.
Centrifugal force, 63.
Chemical compounds, Table
of common names of, .56.
formulas, 55.
symbi >

Chemistry. f> \.

Chicago, 111., license law, 255.
Chimney, Area of, 110.
Form of, 109.
foundations, 109.
Height of, 110.
Chimneys, 108.
Bricki 109.
Iron and steel, 109.
Table of sizes of, 1 12.
Chloride of magnesium, 128.

of sodium. !2s.
Circle, W.

Circles, Table of circumfer-
ences and areas of, 3S.
Circular ring, ^7.
Circulating pump, Pounding

in, 214.
Circumferences and areas of

circles, Table of, :is.
Cities having license laws,

States and, 2M.
Classes of coal, 79.
Classification of injectors,

123.
Cleaning fires, 149.

INDEX

Clearance, 182.
Effects of, 182.
of turbine blades, 225.
Coal, Anthracite, 79.
Bituminous, 80.
Classes of, 79.
consumption to speed, Re-
lation of, 212.
Maximum combustion rate

of, 111.

Semianthracite, 80.
Semibituminous, 80.
Cocks and valves, Blow-off,

119.

Coefficients of linear expan-
sion, 57.
Coke, 81.

Combination of pulleys, Go.
Combustion, 76.

Air required for, 77.
Incomplete, 78.
rate of coal, Maximum, 111.
Common fractions, 2.
Comparison of turbines and

engines, 225.

Composition of crude oil, 82.
Compound engine, Starting
and stopping Corliss,
210.

engines, Horsepower of, 194.
slide-valve engine, Starting,

207.

slide-valve engine, Stop-
ping, 209.
Compounds, 54.
Table of common names of

chemical, 56.
Condenser, Injection water

for jet, 203.
Condensers, Cooling water

for surface, 202.
Surface, 200.
Types of, 200.

Condensing slide-valve en-
gine, Starting, 206.
slide-valve engine, Stop-
ping, 206.

Connecting boilers, 147.
Connection of steam gauge,

118.

Construction of oil tanks,
153.

Conversion of temperatures,

57.
Cooling of brake pulleys,

198.

water for surface condens-
ers, 202.

Copper tubes, Table of

weight of brass and, 49.

Corliss engine, Starting and

stopping compound, 210.

engine, Starting simple,

207.
engine, Stopping simple,

207.
Corrosion and incrustation,

127.

External, 131.
Internal, 130.
Prevention of incrustation

and, 133.
Uniform, 130.
Coverings, Pipe, 121.
Cracked brasses, Warped and,

218.

Crosshead, Pounding at, 213.
Crude oil, Composition of, 82.
Cube roots, 6.
Cubes, 9.

Cubic measures, 42.
Cut brasses and journals, 218.
-off, Apparent, 183.
-off, Real, 183.
Cylinder, 36.

heads, Piston striking, 212.
Frustum of, 37.
ratios, 194.
Cylinders, Water in, 211.

Danger of increasing heating

of bearings, 215.
of water hammer, 204.

Dangerous heating of bear-
ings, 216.

Data for brake horsepower,
199.

De Laval turbine, Care of

gears in, 230.
id plate. 104.

Dead plate,

Decimal equivalents of parts
of 1 inch, Table of, 45.
fractions, 4.

INDEX

Decimal, Reducing a common
fraction to a, 5.

to a common fraction,

Reducing a, 5.
Decimals, Addition of, 4

Division of, 5.

Multiplication of, 4.

Subtraction of, 4.
Delivered horsepower, 191.
Denver.Colo., license law, 256.
Detroit, Mich., license law,

257.

Developed blade area, 234.
Diagrams, Taking indicator,

181.

Diameter of propeller, Re-
quired, 237.
Differential pulley, Go.
Dimensions of iron boiler
tubes, 53.

of pipe flanges, 51.

of steel boiler tubes, 52.
Dirty and gritty oils, 219.
Disadvantages of oil fuel, 1GO.
Disk area, 234.
Division of decimals, 5.

of fractions, 3.

of matter, 54.
Double-tube injectors, 123.
Draft, Measurement of, 108.

Production of, 108.

required for oil fuel burn-
ing, 157.

Driven pulleys, 67.
Driving pulleys, 67.
Dynamometers, 195.

E

Economy of heating feed-
water, 138.
Edges of brasses pinching

journal, 218.
Effect of sulphur in oil, 80.

of vacuum in turbines, 223.
Effects of clearance, 182.
Efficiency, Boiler, 141.

of engine, Mechanical, 191.
Elements, 54.
Machine, 63.
Table of atomic weight of,

55.
Elgin, 111., license law. 258.

Ellipse, 36.

Engine management, 203.
Mechanical efficiency of,

191.

out of line, 221.
Overloading of, 221.
speed and ship speed, Rela-
tion between, 243.
Starting and stopping com-
pound Corliss, 210.
Starting compound slide-
valve, 207.

Starting condensing slide-
valve, 206.
Starting non - condensing

slide-valve, 205.
Starting simple Corliss, 207.
Stopping compound slide-
valve, 209.

Stopping condensing slide-
valve, 206.
Stopping non-condensing

slide-valve, 205.
Stopping simple Corliss,

207.
with hot bearings, Running,

216.

Engineers' license laws, 244.
Engines, Causes and remedies

for pounding of, 210.
Comparison of turbines

and, 225.
Horsepower of compound,

194.

Indicating of, 172.
Stating size of, 193.
Steam, 172.
Steam pipes for, 102.
Warming up, 203.
Equalizing the boiler feed,

148.

Equivalent evaporation, 141.
Erosion of turbine blades,

226.
Errors of reducing motion,

ISO.

Evaporation, Equivalent, 141.
Factor of, 142.
Table of factors of, 143.
Evaporative power of oil fuel,

86.
Evolution, 6.

INDEX

Excess of air in oil burning,

85.
Exhaust - steam feedwater

heaters, Types of, 139.
-steam turbine, 229.
Expanded pitch, Axially, 234.

pitch, Radially, 234.
Expansion bands, 121.
joints, 120.
Ratio of, 183.
Explosions, Boiler, 170.
External boiler inspection,

165.

corrosion, 131.
heat on bearings, Effects of,
222.

Factor of evaporation, 142.
Factors of evaporation, Table

9f, 143.

Feeding, Boiler, 123.
Feedwater by chemicals, Pur-
ification of, 136.
by filtration, Purification

of, 135.
by heat. Purification of,

138.
by settlement, Purification

of, 135.

Economy of heating, 138.
heaters, Types of exhaust-
steam, 139.
Impurities in, 127.
Purification of, 135.
Testing, 134.
Figures, Significant, 6.
Filling boilers, 145.
Finding horsepower of tur-
bines, 225.
the mean effective pressure,

184.

Fire, Starting an oil fuel, 155.
Firebrick lining of furnaces,

88.

Fires, Accidental oil fuel, 158.
Banking, 164.
Cleaning, 149.
in starting, Management of,

146.

Precautions in relighting
oil fuel, 158.

Fires, Starting, 164.
Firing point of fuel oil, 87.

with liquid fuels, 150.

with solid fuels, 148.
Fittings, Boiler, 113.

for oil tanks, 153.

Furnace, 103.

Fixed and movable pulleys,
64.

grates, 103.
Flanges, Dimensions of pipe,

51.

Flash point of fuel oil, 87.
Flow of steam, 99.

of water in pipes, 72.

Vetocity of, 72.
Foaming, 163.
Follower plate. Loose, 212.
Foot-pound, 62.
Force, Centrifugal, 63.
Form of chimney, 109.
Formation of scale, 128.

of soot with oil fuel, 157.
Formulas, 29.,

Chemical, 55.

for slip, 232.

Foundations, Chimney, 109.
Fraction, Reducing .a decimal
to a common, 5.

to a decimal, Reducing a

common, 5.
Fractions, 2.

Common, 2.

Decimal, 4.

Division of, 3.

Multiplication of, 3.

or mixed numbers, Addi-
tion of, 3.

or mixed numbers, Sub-
traction of, 3.
Friction horsepower, 191.

Mixtures for reducing, 215.
Frustum of cylinder, 37.

of prism, 37.

Fuel burner, Shutting down
oil, 158.

burning, Draft required for
oil, 157.

Disadvantages of oil, 160.

Evaporative power of oil,
86.

fire, Starting an oil, 155.

7:VDEX

Fuel fires, Accidental oil, 138.

fires, Precautions in relight-
ing oil, 158.

Firing with solid, 148.

Formation of soot with oil,
157.

Furnace, Proportions for
oil. 88,

Liqir

Objections to gravity feed-
ing of oil, 152.

oil, Pairing point of, S7.

oil, Flash point of, 87.

oil, Properties of, 83.

Pressure on oil, 152.

Separation of water from
oil, 151.

Specifications for oil, 87.

Straining oil, 151.

Thermal advantages of oil,

159.
Fuels, 7! i.

Calorific value of, 78.

Calorific value of oil, 83.

Firing with liquid, 150.

for steam making, 79.

Heating of oil, 152.

Solid, 7'.<.

Steam and air for atomi-
zing oil, si.
Furnace fittings, 103.
. Proportions for oil fuel, 88.
Furnaces, Firebrick lining of,

Fusible plugs, 116.
Fusing point, ">'.).
Fusion and vaporization,
Table of temperatures
and latent heats of, 60.
Latent heat of, 5<t.
Temperature of, 5(».

Gauge and blow-off. Inspec-
tion of water, 170.
Connection of steam, 118.
Testing st--:un, 170.
Gears in De Laval turbine,

Care of, _V.<>.
Goshen, Ind., license la

ii.-ir, Herrins,'l><>;]<', 101.
Grates, Fixed, lo.i.

Grates, Shaking, 105.
Gravity feeding of oil fuel,

Objections to, 152.
Specific, 45.
Grit in bearings, 220.
Gritty oils, Dirty and, 219.
Grooving, 131.

H

Head of water, Pressure due

to, 72.
Heat, 56.

in wet steam, 96.
Latent, 59.
Measurement of, 58.
Mechanical equivalent of,

59.

of fusion. Latent, 59.
Specific, 60.

Heaters, Types of exhaust-
steam feed water, 139.
Heating feedwater, Economy

of, 138.

of oil fuels, 152.
Heats of fusion and vaporiza-
tion, Table of tempera-
tures and latent, tiO.
Table of specific, ill.
Height of chimney, 110.
Helicoidal blade i
Herringbone grate bar, 10 1.
Hints for use of planimeter,

186.
Hoboken, N. J., license law,

260.
Honeycombing, Pitting or,

131.
Horsepower, 62.

and revolutions, Relation

of, 240.
and steam consumption,

191.

Brake, 11)1.

Calculating indicated , 192.
Calculation of brake, 2(K).
Data for brake, 199.
Delivered, 191.
Friction, 191.
Indicated, 191.

I'.tl.

of belts. 70.
of compound engines, 194.

INDEX

Horsepower of steam turbines,

Finding, 225.
Standard of boiler, 141.
when towing, Reduction of,

240.

Hot bearings, 215.
Huntington, W. Va., license

law, 262.
Hydraulics, 73.
Hydrostatic boiler test, 169.

I

fitted

brasses,

Imperfectly

218.
Improper steam distribution,

213.

Impurities in feedwater, 127.
Incomplete combustion, 78.
Incrustation and corrosion,
127.

and corrosion, Prevention

of, 133.
Indicated horsepower, 191.

horsepower, Calculating,

192.

Indicating engines, 172.
Indicator, Attachment of, 175.

cord, Attachment of, ISO.

diagrams, Taking, 181.

Inside-spring, 172.

Outside-spring, 174.

springs, 174.

Injection water for jet con-
denser, 203.

Injectors, Advantages and
disadvantages of, 127.

Automatic, 123.

Classification of, 123.

Double-tube, 123.

Lifting, 123.

Location of, 124.

Non-lifting, 123. '

Positive, 123.

Size of, 123.

Steam supply to, 124.

Troubles with, 125.
Inside-spring indicator, 172.
Inspection, Boiler, 165.

External boiler, 165.

Internal boiler, 167.

of safety valve, 169.

of turbines, 227.

Inspection of water gauge and

blow-off, 170.

Installation of oil tanks, 154.
Insufficient lead, 213.

oil, 219.
Internal boiler inspection, 167.

corrosion, 130.
Involution, 6.
Iron and steel chimneys, 109.

boiler tubes, Dimensions of,
53.

Table of weight of round
and square, 50.

Table of weight of sheet, 48.
Irregular areas, 35.

Jersey City, X. J., license law,

263.
Jet condenser, Injection water

for, 203.

Joints, Expansion, 120.
Journal, Edges of brasses

pinching, 218.
Journals, Cut brasses and,

218.

Kansas City, Mo., license

law, 205.
Kerosene as a scale remover,

129.
Kinetic energy, 62.

Lacing of belts. 72.
Lamination, 132.
Latent heat, .'!».
heat of fusion, 50.
heat of vaporization, 60.
heats of fusion and vapori-
zation, Table of tempera-
tures and, GO.
Law, Allegheny, Pa., license,

262.

Atlanta, Ga., license, 253.
Baltimore, Md., license,

253.

Buffalo, X. Y.. license, 254.
Chicago, 111., license, 255.
Denver, Colo., license, 256.
Detroit, Mich., license, 257.

xii

INDEX

Law, Elgin, 111., license, 258.
Goshen, Ind., license, 260.
Hoboken, N. T., license,

260.
Huntington, W.Va., license,

262.

Jersey City, N. J., license,
. 263.
Kansas City, Mo., license,

265.

Lincoln, Neb., license, 266.
Los Angeles, Cal., license,

267.

Massachusetts license, 244.
Memphis, Tenn., license,

268.
Milwaukee, Wis., license,

269.

Minnesota license, 247.
Mobile, Ala., license, 271.
Montana license, 248.
New Haven, Conn., license,

272.
New York, N. Y., license,

273.

Niagara Falls, N. Y., li-
cense, 275.
Ohio license, 249.
Omaha, Neb., license, 277.
Pennsylvania license, 250.
Pe9ria, 111., license, 278.
Philadelphia, Pa., license,

279.

Pittsburg, Pa., license, 280.
Rochester, N. Y., license,

280.
Santa Barbara, Cal. .license,

281.

Scranton, Pa., license, 285.
Sioux City, la., license, 285.
Spokane, Wash., license,

286.
St. Joseph, Mo., license,

282.

St. Louis, Mo., license, 283.
Tacoma, Wash., license,

287.

Tennessee license, 251.
Terre Haute, Ind., license,

288.

United States marine en-
gineer's license, 291.

Law, Washington and District
of Columbia license, 289.

Yonkers, N. Y., license,

289.
Laws, Engineers' license, 244.

States and cities having

license, 244.
Lead, Insufficient, 213.
Levers, 63.

License law, Allegheny, Pa.,
252.

law, Atlanta, Ga., 252.

law, Baltimore, Md., 253.

law, Buffalo, N. Y., 254.

law, Chicago, 111., 255.

law, Denver, Colo., 256.

law, Detroit, Mich., 257.

law, Elgin, 111., 258.

law, Goshen, Ind., 260.

law, Hoboken, N. J., 260

law, Huntington, W. Va.,
262.

law, Jersey City, N. J., 263.

law, Kansas City, Mo., 265.

law, Lincoln, Neb., 266.

law, Los Angeles, Cal., 267.

law, Massachusetts, 244.

law, Memphis, Tenn., 268.

law, Milwaukee, Wis., 269.

law, Minnesota, 247.

law, Mobile, Ala., 271.

law, Montana, 248.

law, New Haven, Conn.,
272.

law, Niagara Falls, N. Y.,
275.

law, New York, N. Y., 273.

law, Ohio, 249.

law, Omaha, Neb., 277.

law, Pennsylvania, 250.

law, Peoria, 111., 278.

law, Philadelphia, Pa., 279.

law, Pittsburg, Pa., 280.

law, Rochester, N. Y., 280.

law, Santa Barbara, Cal.,
281.

law, Scranton, Pa., 285.

law, Sioux City, la., 285.

law, Spokane, Wash., 286.

law, St. Joseph, Mo., 282.

law, St. Louis, Mo., 283.

law, Tacoma, Wash., 287.

INDEX

License law, Tennessee, 251.
law, Terre Haute, Ind.,

288.
law, United States marine

engineers', 291.
law, Washington and Dis-
trict of Columbia, 289.
law, Yonkers, N. Y., 289.
laws, Engineers', 244.
laws, States and cities hav-
ing, 214.

Lifting injectors, 123.
Lignite, 81.
Lime, Carbonate of, 127.

Sulphate of, 128.
Lincoln, Neb., license law,

266.
Linear expansion, Coefficients

of, 57.

measures, 42.
Liners, 210.
Lining for furnaces, Firebrick,

88.
Liquid fuel, 82.

fuels, Firing with, 150.
measures, 44.

Location of oil burners, 151.
of injectors, 124.
of safety valve, 116.
Loose brasses, 210.
piston, 211.
thrust block, 211.
Los Angeles, Cal., license law,

267.

Lubrication of turbine bear-
ings, 228.

Machine elements, 63.
Magnesium, Chloride of, 128.
Maintenance of a uniform

steam pressure, 160.
of vacuum in turbines, 230.
Management, Boiler, 145.
Engine, 203.
of fires in starting, 146.
Marine engineer's license law,

United States, 291.
Massachusetts license law,

244.

Materials, Weights and sizes
of, 45.

Mathematics, 1.
Matter, Division of, 54.

Organic, 128.
Maximum combustion rate

of coal, 111.

Mean effective pressure, Ap-
proximate, 190.
effective pressure by ordi-

nates, 187.
effective pressure, Finding

the, 184.
effective pressure, Referred,

195.

Measurement of draft, 108.
of heat, 58.
of pitch, 234.
Units of, 42.
Measures, Cubic, 12.
Linear, 42.
Liquid, 44.
of angles or arcs, 42.
of time, 45.
of United States money,

44.

of weight, 43.
Square, 42.

Mechanical efficiency of en-
gine, 191.

equivalent of heat, 59.
stokers, 105.
Mechanics, 62.
Memphis, Tenn., license law,

268.

Mensuration, 33.
Milwaukee, Wis., license law,

269.

Minnesota license law, 247.
Mixed numbers, Addition of

fractions or, 3.
numbers, Subtraction of

fractions or, 3.
Mixtures for reducing fric-
tion, 215.

of oil spray and air, 84.
Mobile, Ala., license law, 271.
Moisture in steam, 95.
Molecular weight, 55.
Money, Measures of United

States, 44.

Montana license law, 248.
Movable pulleys, Fixed and,
64.

INDEX

Mud, Removing, 130.
Multiplication of decimals, 4.
of fractions, 3.

N

Nature of combustion, 76.
Net horsepower, 191.
New Haven, Conn., license

law, 272.
York, N. Y., license law,

273.

Newly fitted bearings, 217.
Niagara Falls, N. Y., license

law, 275.
Non-condensing slide-valve

engine, Starting, 205.
-condensing slide-valve en-
gine, Stopping, 205.
-lifting injectors, 123.

O

Objections to gravity feeding

of oil fuel, 152.
Ohio license law, 249.
Oil, Atomization of, 83.
burners, Location of, 151.
burning, Excess of air in,

85.

Composition of crude, 82.
Effect of sulphur in, 86.
feed, Stopped, 219.
Firing point of fuel, 87.
Flash point of fuel, 87.
fuel burner, Shutting down,

158.

fuel burning, Draft re-
quired for, J">7.
fuel, Disadvantages of, 160.
fuel, Evaporative power of,

8G.

fuel fire, Starting a, 155.
fuel fires, Accidental, 15s.
fuel fires. Precautions in

relighting, 15s.
fuel, Formation of soot

with, i:.7.
fuel, Furnace proportions

for, 88.
fuel. Objections to gravity

feeding of. 152.
fuel, Pressure on, 152.

Oil fuel, Separation of water
from, 151.

fuel, Specifications f:.>-

fuel, Straining, 151.

fuel, Thermal advantages
of, 159.

fuels, Calorific value <

fuels, Heating of, 152.

fuels, Steam and air fur
atomizing, M.

Insufficient, 219.

Properties of fuel, 83.

spray and air, Mixtures of,
84.

tanks, Construction of , 153.

tanks, Fittings for, 153.

tanks, Installation of, 15}.
Oils, Dirty and gritty, 2i'i.

of poor quality, 219.

squeezed out of bearings,

220.

Omaha, Neb., license law. 277.
Operation of turM;ie>, 227.
Organic matter, 12S.
Outside-spring indicator, 174.
Overfeed stoker, 105.
Overheating, 132.
Overloading of engine, 221.

Packing, Broken piston, 212.
Pantograph reducing motion,

177.

Parallelogram, 34.
Parallelepiped, 37.
Peat, 81.
Pendulum reducing motion,

17(1.

Pennsylvania license law, 25o.
Peoria, 111., license law, 27s.

Philadelphia, Pa., license law,

279.
Pillow block. Springing or

shift inn of, 222.
Pipe coverniK :,, 121 .

dimensions, Table of extra-
strong wrought-iron, 49.
dimensions, Table of stand-
ard, is.

flanges, Dimensions of, 51.
materials, 120.

INDEX

xv

Pipe, Protection of blow-off,

119.

Pipes, Flow of water in, 72.
for engines, Steam, 102.
Piping, Arrangement of, 122.

Boiler, 120.
Piston, Loose, 211.

packing, Broken, 212.
speed, 192.

striking cylinder heads, 212.

Pitch, Axially expanded, 234.

Determining the kind of,

236.

Measurement of, 234.
of propeller, Required, 236.
Radially expanded, 234
Pitting or honeycombing, 131.
Pittsburg, Pa., license law,

280.
Planimeter, 185.

Hints for use of, 186.
Plate, Dead, 104.
Plugs, Fusible, 116.
Polygons, 34.
Positive injectors, 123.
Pounding at crosshead, 213.
in air pump, 214.
in circulating pump, 214.
of engines, Causes and rem-
edies for, 210.
Power, Work and, 62.
Powering of vessels, 238.
Powers, roots, and reciprocals,

Table of. 11.
Precautions in relighting oil

fuel fires, 158.
Preparations for shutting

down a boiler, 163.
Pressure, Approximate mean

effective, 190.
by ordinates. Mean effect-
ive, 187.

due to head of water, 73.
Finding the mean effective,

184.

Oil, 152.

on brasses, Reversal of, 213.
Referred mean effective,

195.
Prevention of incrustation

and corrosion, 133.
Priming, 162.

Prism, 37.

Frustum of, 37.
Production of draft, 108.
Products of combustion, 76.
Projected propeller area, 234.
Prony brake, 196.
Propeller area, Projected, 234.

Required diameter of, 237.

Required pitch of, 236.
Propellers, Screw, 232.
Properties of fuel oil, 83.

of steam, 89.

Propulsion of vessels, 231.
Protection of blow-off pipe,

119.
Pulley, Brumbo, 178.

Differential, 65,
Pulleys, Belt, 66.

Combination of, 65.

Cooling of brake, 198.

Driven, 67.

Driving, 67.

Fixed and movable, 64.

Solid, 66.

Split, 66.

Wooden, 67.
Pump, Pounding in air, 214.

Pounding in circulating,

214.

Purification of feedwater, 135.
of feedwater by chemi-
cals, 136.

of feedwater by filtration,
135.

of feedwater by heat, 138.

of feedwater by settlement,
135.

Quality of steam, 95.

R

Radially expanded pitch, 234.
Ratio of expansion, 183.
Ratios, Cylinder, 194.
Real cut-off, 183.
Reciprocals, 10.

Table of powers, roots, and,

11.

Rectangle, 34.
Reducing a common fraction

to a decimal, 5.

INDEX

Reducing a decimal to a

common fraction, 5.
motion, Errors of, 180.
motion, Pantograph, 177.
motion, Pendulum, 176.
motions, Slotted-lever, 177.
wheels. 178.
Reduction of horsepower when

towing, 240.

Referred mean effective pres-
sure, 195.

Refitting cut bearing, 216.
Relation between engine
speed and ship speed, 2 13.
of coal consumption to

speed, 242.

of horsepower and revolu-
tions, 240.

Remedies for increasing heat-
ing of bearings, 215.
for pounding of engines,

Causes and, 210.
Removing mud, 130.

scale, 130.
Reversal of pressure on

brasses, 213.
Revolutions, Relation of

horsepower and, 240.
Ring, 36.

Circular, 37.
Rochester, N. Y., license law,

280.
Roots, and reciprocals, Table

of powers, 11.
Cube, 6.
Square, 6.
Rope brake, 198.
Round and square iron, Table

of weight of, 50.
Rules, Safety-valve, 1 1 .">.
Running engine with hot
bearings, 216.

8

Safety valve, Area of, 1 1 .">.
valve, Inspection of, 169.
valve, Location of, 110.
valve rules, 115.
valves, 113.
Sag of belts. 69.
Santa Barbara, Cal., license
law, 281.

Saturated steam, 89.
Scale, 127.

Formation of, 128.
-forming substances and
their remedies, Table of,
133.

remover, Kerosene as a, 129.
Removing, 130.
Scales, Thermometric, .06.
Scranton, Pa., license law, 285.
Screw propellers, 232.
Sector, 35.
Segment, 36.
Semianthracite coal, 80.
Semibituminous coal, 80.
Separation of water from oil

fuel, 154.

Shaking grates, 105.
Sheet lead, Table of weight of,

50.
Shifting of pillow block,

Springing or, 222.
Ship speed, Relation between

engine and, 243.
Shutting down a boiler, Prep-
arations for, 1«)3.
down an oil fuel burner, 158.
down turbines, 230.
Significant figures, <i.
Signs used in calculations, 1.
Sioux City, la., license law,

285.
Sizes of chimneys, Table of,

112.

of engines, Stating, 193.
of injectors, 123.
of materials, Weights and,

45.

Slack follower plate, 212.
Slide-valve engine, Starting

compound, 207.
-valve engine, Starting con-
densing, 206.

-valve engine, Starting non-
condensing, 205.
-valve engine. Stopping

compound, 209.
-valve engine, Stopping

condensing, 206.
-valve engine. Stopping

non-condensing, 205.
Slip, Apparent, 231.

INDEX

Slip, Formulas for, 232.

True, 231.

Slotteri-lever reducing mo-
tions, 177.

Sodium, Chloride of, 128.
Solid fuel, Firing with, 148.
fuels, 79.
pulleys, 66.
Soot with oil fuel, Formation

oi, 157.

Specific gravity, 45.
heat, 60.

heats, Table of, 61.
Specifications for oil fuel, 87.
Speed of belts. 70.
of vessels, 238.
Piston, 192.
Relation between engine

and ship, 243.
Relation of coal consump-
tion to, 242.
Sphere, 37.
Split pulleys, 66.
Spokane, Wash., license law,

286.

Springing of bed plate, 222.
or shifting of pillow block,

222.

Springs, Indicator, 174.
Square iron, Table of weight

of round and, 50.
measures, 42.
roots, 6.
Squares, 8.

St. Joseph, Mo., license law,
282:

Louis, Mo., license law,
283.
Standard of boiler horsepower,

141.
pipe dimensions, Table of,

48.

Starting (an oil fuel fire, 155.
and Stopping compound

Corliss engine, 210.
compound slide-valve en-
gine, 207.

condensing slide-valve en-
gine, 206.
fires, 164.

non-condensing slide-valve
engine, 205.

Starting simple Corliss engine,

turbines, 228.
States and cities having

license laws, 244.
Steam and air for atomizing

oil fuels, 84.
boilers, 103.
consumption, Horsepower

and, 191.
consumption of turbines,

223.

distribution, Improper, 213.
engines, 172.
Flow of, 99.

gauge, Connection of, 118.
gauge, Testing, 170.
Heat in wet, 96.
Moisture in, 95.
pipes for engines, 102.
pressure, Maintenance of a

uniform, 160.
Properties of, 89.
Quality of, 95.
Saturated, 89.
Superheated, 95.
supply to injectors, 124.
turbines, 223.
Steel boiler tubes, Dimensions

of, 52.

chimneys, Iron and, 109.
Stripping of turbine blades,

226.
Stoker, Overfeed, 105.

Underfeed, 106.
Stokers, Mechanical, 105.
Stopped oil feed, 219.
Stopping compound Corliss
engine, Starting and, 210.
compound slide-valve en-
gine, 209.

condensing slide-valve en-
gine, 206.
non-condensing slide-valve

engine, 205.

simple Corliss engine, 207.
Straining oil fuel, 151.
Subtraction of decimals, 4.
of fractions or mixed num-
bers, 3.

Sulphate of lime, 128.
Sulphur in oil, Effect of, 86.

INDEX

Superheated steam, 95.

steam in turbines, 229.
Surface condensers, 200.
condensers, Cooling water

for, 202.
Symbols, Chemical, 55.

Table of atomic weights of
elements, 55.

of circumferences and areas
of circles, 38.

of common names of chem-
ical compounds, 56.

of decimal equivalents of
parts of 1 inch, 45.

of extra-strong wrought-
iron pipe dimensions, 49.

of factors of evaporation,
143.

of powers, roots, and recip-
rocals, 11.

of scale-forming substances
and their remedies 133.

of sizes of chimneys, 112.

of specific heats, 61.

of standard pipe dimen-
sions, 48.

of temperatures and latent
heats of fusion and vapor-
ization, 60.

of weight of brass and
copper tubes, 49.

of weight of round and
square iron, 50.

of weight of sheet iron,
48.

of weight of sheet lead,
50.

of weights of various sub-
stances, 46.
Tacoma, Wash., license law,

287.
Taking indicator diagrams,

181.

Tanks, Construction of oil,
153.

Fittings for oil, 153.

Installation of oil, 154.
Temperature, 56.

of fusion, .V.).

of vaporization, 60.

Temperatures and latent
heats of fusion and
vaporization, Table of,
60.

Conversion of, 57.
Tennessee license law, 251.
Terre Haute, Ind., license law,

288.

Test, Hydrostatic boiler, 169.
Testing feedwater, 134.

steam gauge, 170.
Thermal advantages of oil

fuel. 159.
unit, British, 58.
Thermometric scales, 56.
Thrust block, Loose, 211.
Time, Measures of, 45.
Towing, Reduction of horse-
power when, 240.
Trapezium, 34.
Trapezoid, 34.
Triangles, 33.

Troubles with injectors, 125.
True slip, 231.
Tubes, Dimensions of iron

boiler, 53.
Dimensions of steel boiler,

52.

Turbine bearings, Lubrica-
tion of, 228.

blades, Clearance of, 225.
blades, Erosion of, 226.
blades, Stripping of, 220.
Care of gears in De Laval,

230.

Exhaust-steam, 229.
troubles, 225.

Turbines, Advantages of, 224.
and engines, Comparison

of, 22.-,.

Effect of vacuum in, 223.
Finding horsepower of, 225.
Inspection of, 227.
Maintenance of vacuum in,

Operation of, 227.

Shutting down, 230.

Starting, 228.

Steam, 223.

Steam consumption of, 223.

Superheated steam in, 229.

Vibration of, 227.

INDEX

Turbines, Water in, 227.
Types of condensers, 200.
of exhaust-steam feedwater
heaters, 139.

U

Underfeed stoker, 106.

Uniform corrosion, 130.

Unit, British thermal, 58.

United States marine engi-
neer's license law, 291.
States money, Measures of,
44.

Units of measurement, 42.

Use of zinc in boilers, 134.

Vacuum in turbines, Effect of,

223.
in turbines, Maintenance

of, 230.

Valve, Area of safety, 115.
Inspection of boiler safety,

169.

Location of safety, 116.
rules, Safety, 113.
Valves, Blow-off cocks and,

119.

Safety, 113.
Vaporization, Latent heat of,

60.

Table of temperatures and
latent heats of fusion
and, 60.

Temperature of, 60.
Velocity of flow, 74.
Vessels, Powering of, 238.
Propulsion of, 231.
Speed of, 238.

Vibration of steam turbines,
227.

W

Wall, Bridge, 103.
Warming up engines, 203.
Warped and cracked brasses,

218.

Washington and District of
Columbia license law,
289.

Water from oil fuel, Separa-
tion of, 154.

gauge and blow-off, Inspec-
tion of, 170.

hammer, Danger of, 204.
in cylinders, 211.
in pipes, Flow of, 72.
in turbines, 227.
Pressure due to head of, 72.
Wedge, 37.
Weight, Atomic, 55.
Measures of, 43.
Molecular, 55.
of sheet iron, Table of, 48.
of sheet lead. Table of, 50.
Weights and sizes of materials,

45.

of elements, Table of atom-
ic, 55.
of various substances.

Table of, 46.
Wet steam, Heat in, 96.
Wheel and axle, 66.
Wheels, Reducing, 178.
Wood, 81.

Wooden pulleys, 67.
Work and power, 62.

Y

Yonkers, X. Y., license law,
289.

Z

Zero, Absolute, 57.
Zinc in boilers. Use of, 134.

The Steam Engineer's
Handbook

MATHEMATICS

SIGNS USED IN CALCULATIONS

+ Plus, indicates addition; thus, 10+5 is 15.

— Minus, indicates subtraction; thus, 10 — 5 is 5.

X Multiplied by, indicates multiplication; thus, 10X5 is 50.

•4- Divided by, indicates division; thus, 10 -f- 5 is 2.

= Equal to, indicates equality; thus, 12 in. = 1 ft.

Parentheses, ( ), brackets, [ ], and braces, { },have the same
meanings, and signify that the operation indicated within
them is to be performed first; or, if more than one pair is used,
that indicated within the inner one is to be effected first.
Thus, in the expression 5(7 — 2), the subtraction is to be made
first and the difference then multiplied by 5. Again, in the
expression %[7— (3 + f)l, the addition indicated within the
parentheses is to be performed first, the sum thus found is to
be subtracted from 7, and then half of the remainder is to be
found.

The vinculum, , is used for the same purpose as paren-
theses, brackets, and braces, but chiefly in connection with the
radical sign "V thus, "V .

The decimal point (.) is placed in a number containing deci-
mals, to fix the value of that number; thus, 12.5 is 12 and r^j;
1.25 is 1 and ^; and so on.

An exponent is a figure written above and to the right of a
number to indicate the power to which the number is to be

2 MATHEMATICS

raised. Thus, 82 means that 8 is to be squared; that is, 8X8
= 64. Again, 8" means that 8 is to be cubed; that is 8X8X8
= 512.

The radical sign, V , means that some root of the ex-
pression under the vinculum is to be found. If it is used
without a small index figure, it indicates square root; thus,
V64 = 8. The sign ^f~ indicates the cube root; thus, \27 = 3.

The signs : : : : indicate proportion; thus, 3 : 4 : : 6 : 8
is read 3 is to 4 as 6 is to 8. Instead of the sign : : the equality
sign = is often used; thus, 3:4 = 6:8.

The signs ° ' " mean degrees, minutes, and seconds, respec-
tively; thus, 60° 15' 15" is read 60 degrees 15 minutes 16 seconds.

The signs ' " also mean feet and inches, respectively; thus,
7' 6" is read 7 feel 6 inches.

The symbol TC (pronounced pi) means the ratio of the cir-
cumference of a circle to its diameter and has a value, near
enough for most practical purposes, of 3.1416.

FRACTIONS

COMMON FRACTIONS

The numerator of a fraction is the number above the bar,
and the denominator is the number beneath it; thus, in the
fraction f , 3 is the numerator and 4 is the denominator. Two
or more fractions having the same denominator are said to
have a common denominator. By reducing fractions to a com-
mon denominator is' meant finding such a denominator as will
contain each of the given denominators without a remainder,
and multiplying each numerator by the number of times its
denominator is contained in the common denominator. Thus,
the fractions J, i, and & have, as a common denominator,
16; then t = A; i = tl; A = &.

By reducing a fraction to its lowest terms is meant dividing
both numerator and denominator by the greatest number
that each will contain without a remainder; for example, in
H, the greatest number that will thus divide 14 and 16 is 2;

14-^2

so that, - = I, which is jj reduced to its lowest terms.

16-=-2

MATHEMATICS 3

A proper fraction is one in which the numerator is less than
the denominator, as 3.

A mixed number is one consisting of a whole number and a
fraction, as 7f.

An improper fraction is one in which the numerator is equal
to, or greater than, the denominator, as ¥. This is reduced
to a mixed number by dividing 17 by 8, giving 2 5.

A mixed number is reduced to a fraction by multiplying the
whole number by the denominator, adding the numerator
and placing the sum over the denominator; thus, If becomes,

(IX 8) +7 15

by reduction, • •= — .

8 8

Addition of Fractions or Mixed Numbers. — If fractions
only, reduce them to a common denominator, add partial
results, and reduce sum to a whole or mixed number. If
mixed numbers are to be added, add the sum of the fractions
to that of the whole numbers; thus, lf+2J = (l + 2) + (i+S)
= 41,

Subtraction of Two Fractions or Mixed Numbers. — If they
are fractions only, reduce them to a common denominator,
take less from greater, and reduce result; as, | in. — ^ in.

1-4-9

— = & in. If they are mixed numbers, subtract frac-
16

tions and whole numbers separately, placing remainders
beside one another; thus, 3i-2J = (3-2) + (f-f) = If. With
fractions like the following, proceed as indicated: STS — 1M
= (2+T§+&)-lH = 2«-lH = 1« = H; 7-4i=(6+*)-4f
-2i

Multiplication of Fractions. — Multiply the numerators
together, and likewise the denominators, and divide the for-

135 1X3X5 15

mer product by the latter; thus, ~X~X- = — — = — . If
248 2X4X8 64

mixed numbers are to be multiplied, reduce them to fractions
and proceed as shown above; thus, l|X3J-tXV-V*4|.

Division of Fractions. — Invert the divisor, that is, exchange
places of numerator and denominator, and multiply the divi-
dend by it, reducing the result to lowest terms or to a mixed
number, as may be found necessary; thus, 3-^j = jX$ = 3f = 3

4 MATHEMATICS

= lg. If there are mixed numbers, reduce them to fractions,
and then divide as just shown; thus, li^S^-^-J--1^, or -^XfS

-4*-*.

DECIMAL FRACTIONS

In decimals, whole numbers are divided into tenths, hun-
dredths, etc.; thus, iV is written .1 ; .08 is read rSff, the value of
the number being indicated by the position of the decimal
point; that is, one figure after the decimal point is read as
so many tenths; two figures as so many hundredths; etc.
Moving the decimal point to the right multiplies the number
by 10 for every place the point is moved; moving it to the
left divides the number by 10 for every place the point is
moved. Thus, in 125.78 (read 125 and J&), if the decimal
point is moved one place to the right, the result is 1,257.8,
which is 10 times the first number; or, if the point is moved to
the left one place, the result is 12.578, which is rV the first num-
ber, moving the point being equivalent to dividing 125.78 by 10.

Annexing a cipher to the right of a decimal does not change
its value; but each cipher inserted between the decimal point
and the decimal divides the decimal by 10; thus, in 125.078,
the decimal part is rV of .78. 101.257

Addition of Decimals. — Place the numbers so 12.965

that the decimal points are in a vertical line, and 43.005

add in the ordinary way, placing the decimal 920.600

point of the sum under the other points. „_ s__

Subtraction of Decimals. — Place the number to
be subtracted with its decimal point under that
of the other number, and subtract in the ordinary
way. 434.968

Multiplication of Decimals. — Multiply in the ordinary way,
and point off from the right of the result as many figures as there
are figures to the right of the decimal points in 21.72

both numbers multiplied; thus, in the example 34 j

here given, there are three figures to the right ~2172

of the points and that many are pointed off in sfiRS

the result. If either number contains no deci- 6516

mal, point off as many places as are in the num-
ber that does. 740.652

MATHEMATICS 5

If a product has not as many figures as the sum of the deci-
mal places in the numbers multiplied, prefix enough ciphers
before the figures to make up the required number of places
and place the decimal point before the ciphers. Thus, in .002
X.002, the product of 2X2 = 4; but there are three places in
each number; hence, the product must have six places, and
five ciphers must be prefixed to the 4, which gives .000004;
that is, .002 X.002 = .000004.

Division of Decimals. — Divide in the usual way. If the
dividend has more decimal places than the divisor, point off,
from the right of the quotient, the number of places in excess.
If it has fewer places than the divisor, annex as many ciphers
to the decimal as are necessary to give the dividend as many
places as there are in the divisor; if the dividend is a whole
number, annex as many ciphers as there are decimal places
in the divisor; the quotient in either case will be a whole num-

25.75 82.5 82.50 7.5

ber. For example, = 10.3; = = 30; — = 3.

2.5 2.75 2.75 2.5

Carrying a Division to Any Number of Decimal Places.

Annex ciphers to the dividend and divide, until the desired
number of figures in the quotient is reached, which are pointed
off as above shown. Thus, 36. 5 -5- 18.1 to three decimal places

36.5000

= = 2.016 +. (The sign + thus placed after a number

IS. 1

indicates that the exact result would be more than the one
given if the division were carried further; thus, if the division
were carried to six figures, the quotient would be 2.01657.)

Reducing a Decimal to a Common Fractioc. — Place the
decimal as the numerator; and for the denominator put 1 with
as many ciphers as there are figures to the right of the decimal
point; thus, .375 has three figures to the right of the point;
hence, .375 = f$& = f.

Reducing a Common Fraction to a Decimal. — Divide the
numerator by the denominator, and point off as many places
as there have been ciphers annexed; thus, & = 3.0000 -^16
= .1875.

6 MATHEMATICS

INVOLUTION AND EVOLUTION

SIGNIFICANT FIGURES

In any number, the figures beginning with the first digit*
at the left and ending with the last digit at the right, are called
the significant figures of the number. Thus, the number
405,800 has the four significant figures 4, 0, 5, 8 and the sig-
nificant part of the number is 4058. The number .000090067
has five significant figures, 9, 0, 0, 6, and 7, and the significant
part is 90067.

All numbers that differ only in the position of the decimal point
have the same significant figures and the same significant part.
For example, .002103, 21.03, 21,030, and 210,300 have the same
significant figures 2, 1, 0, and 3, and the same significant part
2103.

The integral part of a number is the part to the left of the
decimal point.

SQUARE AND CUBE ROOTS

By means of the accompanying table, the square, cube,
square root, cube root, and reciprocal of any number may be
obtained correct always to five significant figures, and in the
majority of cases correct to six significant figures.

If the number whose root is to be found contains fewer
than four significant figures, the required 'root can be found
in the table, the square root under Vn, or "VlOw, and the cube
root under 3ln, ^10n, or 'S'lOOn, according to the number of
significant figures in the integral part of the number. Thus,
\.;.l 1^1.772; >/31.4= \1(>X:U 1 = r,.C,(«r,7; V.'U l = 1.46434;
V'.M = ^10><3.14 = 3.15484; %14= ^100 XiU 4 = 0.79688.

In order to locate the decimal point, the given number must
be pointed off into periods of two figures each for square root
and three figures each for cube root, beginning always at the
decimal point. Thus, for square root: 12703, 1'27'03; 12.703,
12.70'30; 220000. 22WOO; .000442, .OO'04'42; and for cube
root: 3141.6, 3'141.ti; »i7L".Mi428. 67'296'428; .0000000217,
.000'000'021'700; etc.

*If ciphers are used simply to locate the decimal point, thev
must not be counted as digits.

MATHEMATICS 7

There are as many figures preceding the decimal point in the
root as there are periods preceding the decimal point in the given
number; if the number is entirely decimal, the root is entirely
decimal, and there are as many ciphers following the decimal
point in the root as there are cipher periods following the decimal
point in the given number.

Applying this rule, \220000 = 469.04, \.OG0442 = .021024,
•^518000 = 80.31 13, and ^.003073 = .04 18.

If the number has more than three significant figures, point
off the number into periods, place a decimal point between the
first and second periods of the significant part of the number,
and proceed as in the following examples:

EXAMPLE 1. — Find the results of the following:
(a) \3.1416 = ? (b) A/2342.9 = ?

SOLUTION. — (a) In this case, the decimal point need hot
be moved. In the table under n2 find 3.1329 = 1.772 and
3.1684 = 1.782, one of these numbers being a little less and
the other a little greater than the given number, 3.1416. The
first three figures of the required root are 177. 31 ,684 - 31,329
= 355 is the first difference; 31,416 (the number itself) — 31,329
= 87 is the second difference. 87 -4- 355 = .245, or .25, which
gives the fourth and fifth figures of the root. Hence, "V3.1416
= 1.7725.

(b) Pointing off and placing the decimal point between
the first and second periods, the number appears 23.4290.
Under n2 find 23.4256 = 4.842 and 23.5225 = 4.852. The first
three figures of the root are 484. The first difference is 235,225
-234,256 = 969; the second difference is 234,290-234,256
= 34; 34-H969 = .035, or .0-4, which gives the fourth and fifth
figures of the root. Since the integral part of the number
23'42.9 contains two periods, the integral part of the root
contains two figures, or V2342.9 = 48.404.

EXAMPLE 2. — Find the results of the following:
(a) ^.0000062417 = ? (b) -$50932676 = ?

SOLUTION. — (a) Pointed off, the number appears .000'006'-
241'700, and with the decimal point placed between the first
and second periods of the significant parts, gives 6.2417. Under
n* find 6.22950=1.843 and 6.33163 = 1.853. The first three
figures of the root are 1.84. The first difference is 10,213. and

8 MATHEMATICS

the second difference is 1,220; 1, 220 -5- 10,213 = .119, or .12,
which gives the fourth and fifth figures. There is one
cipher period after the decimal point in the number; hence,
^00000624 17 = .0184 12.

(b) Replace all after the sixth figure with ciphers, making
the sixth figure 1 greater when the seventh figure is 5 or greater;
that is, -^50932700 and %)932676 will be the same. Placing
the decimal point between the first and second periods gives
50.9327. Under n? find 50.6530 = 3.70* and 5 1.0648 = 3.7 13.
The first three figures of the root are 370. The second dif-
ference 2^797 4- the first difference 4. 118 = .679 or .68. Hence,
^'50932676 = 370.68.

SQUARES

If the given number contains fewer than four significant
figures, the significant figures of the square or cube can be
found under n2 or n3 opposite the given number under n. The
decimal point can be located by the fact that if the column
headed VlOn is used, the square will contain twice as many
figures as the number to be squared, while if the column headed
Vn is used, the square will contain twice as many figures as
the number to be squared, less 1. If the number contains
an integral part, the principle is applied to the integral part
only; if the number is wholly decimal, the square will have
twice as many ciphers, or twice as many plus 1, following the
decimal point as in the number itself, depending on whether
ViOn or Vn column is used.

To square a number containing more than three significant
figures, place the decimal point between the first and second
significant figures and find in the column headed Vn or \\()n
two consecutive numbers, one a little greater and the other
a little less than the given number. The remainder of the
work is exactly as described for extracting roots. The square
will contain twice as many figures as the mfmber itself, or
twice as many less 1, according to whether the column headed
\10n or Vn is used. The number of ciphers following the
decimal point in the square of a number wholly decimal is
determined in the same way.

EXAMPLE. — Find the results of the following:
(a) 273.42* = ? (b) .0524362 = ?

MATHEMATICS 9

SOLUTION. — (a) Placing the decimal point between the first
and second significant figures, the number is 2.7342, which
occurs between 2.73313= VrTi? and 2.73496=^7748, found
under \». The first three figures of the square are 747. The
second difference 107 -^ the first difference 183 = .584, or .58.
Hence, 273.422 = 74,758.

(&) With the position of the decimal point changed, the
number is 5.2436, which is between 5.23450 = \2.74 and
5.24404 = V2.75, both under "VlOn. The first three significant
figures of the root are 2.74, and the second difference 910-;-
the first difference 954 = .953, or .95, the next two figures. The
number has one cipher following the decimal point, and the
column headed VlOn is used; hence, .0524362 = .0027495.

CUBES

To cube a number, proceed in the same way, but use a
column headed ^n, ^lOn, or ^lOOw. If the number contains
an integral part, the number of figures in the integral part
of the cube will be three times as many as in the given num-
ber if the column headed ^100« is used; it will be three times
as many less 1 if the column headed A/lOn is used; and it will
be three times as many less 2 if the column headed 3jn is used.
If the number is wholly decimal, the number of ciphers fol-
lowing the decimal point in the cube will be three times, three
times plus 1, or three times plus 2, as many as in the given
number, depending on whether the >/100w, "VtlOn, or 3ln column
is used.

EXAMPLE. — Find the results of the following:

(a) 129.6843 = ? (b) 7.64423 = ? (c) .032425' = ?

SOLUTION. — (a) With the position of the decimal
changed, the number 1.29684 is between 1.29664 =
and 1.29862= "fe.19, found under -%». The second difference
20 -r- the first difference 198 = . 101 + , or .10. Hence, the first
five significant figures are 21810; the number of figures in
the integral part of the cube is 3X3 — 2 = 7; and 129.684s
= 2,181,000, correct to five significant figures.

(6) 7.64420 occurs between 7.64032=^446 and 7.64603
= ^447. The first difference is 571; the second difference is
388; and 388 -4- 571 = .679 + , or .68. Hence, the first five

10 MATHEMATICS

significant figures are 44668; the number of ciphers follow-
ing the decimal point is 3X0 = 0; and 7.64423 = 446.68, correct
to five significant figures,

(c) 3.2425 falls between 3.24278=^10X3.41 and 3.23961
= ^10X3.40- The first difference is 317; the second difference
is 289; 289 -=-317 = . 911 + , or .91. Hence, the first five sig-
nificant figures are 34091; the number of ciphers following the
decimal point is 3X1 + 1=4; and .0324253 = .000034091, cor-
rect to five significant figures.

RECIPROCALS

The reciprocal of any number is equal to 1 divided by that
number; thus, the reciprocal of 6 is £, because 1-4-6= |. The
product of a number and its reciprocal is always 1; thus, J is
the reciprocal of 8, and 8X J = 1.

The last column of the following table gives the reciprocals
of all numbers expressed by three significant figures correct to
six significant figures. The number of ciphers following the
decimal point in the reciprocal of a number is 1 less than the
number of figures in the integral part of the number; and if
the number is entirely decimal, the number of figures in the
integral part of the reciprocal is 1 greater than the number
of ciphers following the decimal point in the number.

EXAMPLE. — Find the reciprocal of the following:

(a) 379.426; (b) .0004692 j

SOLUTION.— (a) .379426 falls between .378788 = and

1 -'.lit

.380228 = — -. The first difference is 380,228-:

= 1,440; the second difference is 380,228-379, 12(1 = SOL';
802-=-l,440=.o">7, or .56. Hence, the first five significant
figures are 26356, and the reciprocal of 379.426 is .002- ;:;:,(,
to five significant figures. j

(b) .469200 falls between .469484 = and .H,72!«i

1 2-13

= . The first difference is 2,194; the second difference is

2.14 !

284; 284-=- 2,194 = .129 + , or .13. Hence, = 2,131.3,

.0004692

correct to five significant figures.

MATHEMATICS

11

71

7l2

7l3

4H

ViOtt

«£

•fton

3lOOn

1

n

1.01

1.0201

1.03030

1.00499

3.17805

1.00332

2.16159

4.65701

.990099

1.02

1.0404

1.06121

1.00995

3.19374

1.00662

2.16870

4.67233

.980392

1.03

1.0609

1.09273

1.01489

3.20936

1.00990

2.17577

4.68755

.970874

1.04

1.0816

1.12486

1.01980

3.22490

1.01316

2.18278

4.70267

.961539

1.05

1.1025

1.15763

1.02470

3.24037

1.01640

2.18976

4.71769

.952381

1.06

1.1236

1.19102

1.02956

3.25576

1.01961

2.19669

4.73262

.943396

1.07

1 1449

1.22504

1.03441

3.27109

1.02281

2.20358

4.74746

.934579

1.08

1.1664

1.25971

1.03923

3.28634

1.02599

2.21042

4.76220

.925926

1.09

1.1881

1.29503

1 .04403

3.30151

1.02914

2.21722

4.77686

.917431

1.10

1.2100

1.33100

1.04881

3.31662

1.03228

2.22398

4.79142

.909091

1.11

1.2321

1 36763

1.05357

3.33167

1.03540

2.23070

4.80590

.900901

1.12

1.2544

1.40493

1.05830

3.34664

1.03850

2.23738

4.82028

.892857

1.13

1.2769

1.44290

1.06301

3.36155

1.04158

2.24402

4.83459

.884956

l.U

1.2996

1.48154

1.06771

3.37639

1.04464

2.25062

4.84881

.877193

1.15

1.3225

1.52088

1.07238

3.39116

1.04769

2.25718

4.86294

.869565

1.16

1.3456

1.56090

1.07703

3.40588

1.05072

2.26370

4.87700

.862069

1.17

1.3689

1.60161

1.08167

3.42053

1.05373

2.27019

4.89097

.854701

1.18

1.3924

1.64303

1 .08628

3.43511

1.05672

2.27664

4.90487

.847458

1.19

1.4161

1.68516

1.09087

3.44964

1.05970

2.28305

4.91868

.840336

1.20

1.4400

1.72800

1.09545

3.46410

1.06266

2.28943

4.93242

.833333

1.21

1.4641

1.77156

1.10000

3.47851

1.06560

2.29577

4.94609

.826446

1.22

1.4884

1.81585

1.10454

3.49285

1.06853

2.30208

4.95968

.819672

1.23

1.5129

1.86087

1.10905

3.50714

1.07144

2.30835

4.97319

.813008

1.24

1.5376

1.90662

1.11355

3.52136

1.07434

2.31459

4.98663

.806452

1.25

1.5625

1.95313

1.11803

3.53553

.1.07722

2.32080

5.00000

.800000

1.26

1.5876

2.00038

1.12250

3.54965

1.08008

2.32697

5.01330

.793651

1.27

1.6129

2.04838

1.12694

3.56371

1.08293

2.33310

5.02653

.787402

1.28

1.6384

2.09715

1.13137

3.57771

1.08577

2.33921

5.03968

.781250

1.29

1.6641

2.14669

1.13578

3.59166

1.08859

2.34529

5.05277

.775194

1.30

1.6900

2.19700

1.14018

3.60555

1.09139

2.35134

5.06580

.769231

1.31

1.7161

2.24809

1.14455

3.61939

1.09418

2.35735

5.07875

.763359

1.32

1.7424

2.29997

1.14891

3.63318

1.09696

2.36333

5.09164

.757576

1.33

1.7689

2.35264

1.15326

3.64692

1.09972

2.36928

5.10447

.751880

1.34

1.7956

2.40610

1.15758

3.66060

1.10247

2.37521

5.11723

.74ti2«9

1.35

1.8225

2.46038

1.16190

3.67423

1.10521

2.38110

5.12993

.740741

1.36

1.8496

2.51546

1.16619

3.68782

.10793

2.38696

5.14256

.735294

1.37

1.8769

2.57135

1.17047

3.70135

.11064

2.3!I280

5.15514

.7295)27

1.38

1.9044

2.62807

1.17473

3.71484

.11334

2.39861

5.16765

.724638

1.39

1.9321

2.68562

1.17898

3.72827

.11602

2.40439

5.18010

.719425

1.40

1.9600

2.74400

1.18322

3.74166

.11869

2.41014

5.19249

.714286

1.41

1.9881

2.80322

1.18743

3.75500

.12135

2.41587

5.20483

.709220

1.42

2.0164

2.86329

1.19164

3.76829

.12399

2.42156

5.21710

.704225

1.43

2.0449

2.92421

1.19583

3.78153

.12662

2.42724

5.22932

.699301

1.44

2.0736

2.98598

1.20000

3.79473

.12924

2.43288

5.24148

.694444

1.45

2.1025

3.04863

1.20416

3.80789

.13185

2.43850

5.25359

.689655

1.46

2.1316

3.11214

1.20830

3.82099

.13445

2.44409

5.26564

.684932

1.47

2.1609

3.17652

1.21244

3.83406

.13703

2.44966

5.27763

.680272

1.48

2.1904

3.24179

1.21655

3.84708

.13960

2.45520

5.28957

.675676

1.49

2.2201

3.30795

1.22066

3.86005

.14216

2.46072

5.30146

.671141

1.50

2.2500

3.37500

1.22474

3.87298

.14471

2.46621

5.31329

.666667

12

MATHEMATICS

n

n«

7l3

•VE

^llQn

<»

•ft(r»

^100 n

1

n

1.51

2.2801

3.44295

1.22882

3.88587

1.14725

2.47168

5.32507

.662252

1.52

2.3104

3.51181

1.23288 3.89872

1.14978

2.47713

5.33680

.657895

1.53

2.3409

3.58158

1.23693 3.91152

1.15230

2.48255

5.34848

.653595

1.54

2.3716

3.65226

1.24097 3.92428

1.15480

2.48794

5.36011

.649351

1.55

2.4025

3.72388

1.24499 3.93700

1.15729

2.49332

5.37169

.645161

1.56

2.4336

3.79642

1.24900 3.94968

1.15978

2.49866

5.38321

.641026

1.57

2.4649

3.86989

1.25300 3.96232

1.16225

2.50399

5.39469

.636943

1.58

2,1964

3.94431

1.25698

3.97492

1.16471

2.50930

5.40612

.632911

1.59

2.5281

4.01968

1.26095

3.98748

1.16717

2.51458

5.41750

.62x931

1.60

2.5600

4.09600

1.26491

4.00000

1.16961

2.51984

5.42884

.625000

1.61

2.5921

4.17328

1.26886

4.01248

1.17204

2.52508

5.44012

.621118

1.62

2.6244

4.25153J

1.27279

4.02492

1.17446

2.53030

5.45136

.617264

1.63

2.6569

4.33075

1.27671

4.03733

1.17687

2.53549

5.46256

.613497

1.64

2.6896

4.41094

1.28062

4.04969

1.17927

2.54067

5.47370

.609756

1.65

2.7225

4.49213

1.28452

4.06202

1.18167

2.54582

5.48481

.606061

1.66

2.7556

4.57430

1.28841

4.07431

1.18405

2.55095

5.49586

.602410

1.67

2.7889

4.65746

1.29228

4.08656

1.18642

2.55607

5.50688

.598802

1.68

2.8224

4.74163

1.29615

4.09878

1.18878

2.56116

5.51785

.595238

1.69

2.8561

4.82681

l.SOOOO

4.11096

1.19114

2.5H623

5.52877

.591716

1.70

2.8900

4.91300

1.30384

4.12311

1.19348

2.57126

5.53966

.588235

1.71

2.9241

5.00021

1.30767

4.13521

1.19582

2.57631

5.55050

.584795

1.72

2.9584

5.0x845

1.31149

4.14729

1.19815

2.58133

5.56130

.581395

1.73

2.9929

5.17772

1.31529

4.15933

1.20046

2.5x632

5.57205

.578035

1.74

3.0276

5.26802

1.31909

4.17133

1.20277

2.59129

5.58277

.574713

1.75

3.0625

5.35938

1.32288

4.18330

1.20507

2.59625

5.59344

.571429

1.76

3.0976

5.45178

1.32665

4.19524

1.20736

2.60118

5.60408

.568182

1.77

3.1329

5.54523

1.33041

4.20714

i.-jo'.mi

2.60610

5.61467

.564972

1.78

3.1684

5.63975

1.33417

4.21900

1.21192

2.61100

5.62523

.561798

1.79

3.2041

5.73534

1.33791

4.23084

1.21418

2.61588

5.63574

.558659

1.80

3.2400

5.83200

1.34164

4.24264

1.21644

2.62074

5.6462J

.555556

1.81

3.2761

5.92974

1.34536

4.25441

1.21869

2.62558

5.65665

.552486

1.82

3.3124

6.02857

1.34907

4.26615

1.22093

2.63041

5.66705

.549451

1.83

3.3489

5.13849

1.35277

4.27785

1.22316

2.63522

5.67741

.546448

1.84

3.3856

6.22950

1.35647

4.28952

1.22539

2.64001

5.68773

.643478

1.85

3.4225

6.33163

1.36015

4.30116

1.22760

2.64479

5.69802

.540541

1.86

3.4596

6.43486

1.36382

4.31277

1.22981

2.64954

5.70827

.537634

1.87

3.4969

6.53920

1.36748

4.32435

1.23201

2.65428

5.71848

.534759

1.88

3.5344

6.64467

1.37113

4.33590

1 .23420

2.65900

5. 72*65

.531915

1.89

3.5721

6.76127

1.37477

4.34741

1.23639

2.66371

5.73879

.529101

1.90

3.6100

6.85900

1.37840

4.35890

1.23856

2.66840

5.74890

.526316

1.91

3.6481

6.96787

1.38203

4.37035

1 .24073

2.67307

5.75897

.523560

1.92

:j.68C>4

7.0778'J

1.3*564

4.38178

1.242x9

2.67773

5.76900

.520833

1.93

3.7249

7.18906

1.38924

4.39318

1.24505

2.68237

5.77900

.518135

1.94

3.7636

7.30138

1 .39284

4.40454

1.24719

2.68700

6.78896

.515464

1.95

3.8025

7.41488

1.39642

4.41588

1.24933

2.69161

5.79889

.512821

1.96

3.8416

7.52954

1.40000

4.42719

1.25146

2.69620

5.80879

.510204

1.97

3.8809

7.64537

1.40357

4.4:tx47

1.25359

2.70078

5.81865

.507614

1.98

3.9204

7.76239

1.40712

4.44972

1.25571

2.70534

5.82848

.505051

1.99

3.9601

7.8*060

1.41067

4.46094

1.25782

2.70989

5.83827

.502513

2.00

4.0000

8.00000

1.41421

4.47214

1.25992

2.71442

5.84804

.500000

MA THEM A TICS

13

n

7*2

«3

V^

VlOn

\tt

$Wn

-%100n

1
71

2.01

4.0401

8.12060

1.41774

4.48330

1.26202

2.71893

5.85777

.497512

2.02

4.0804

8.24241

142127

4.49444 1.26411 2.72343 5.86746

.495050

2.03

4.1209

8.36543

1.42478 4.50555 1.26619 , 2.72792 5.87713

.492611

2.04

4.1616

8.48966

1.42829 4.51664

1.26827 2.73239 5.88677 1 .490196

2.05

4.2025

8.61513

1.43178

4.52769

1.27033

2.73685 5.89637 j .487805

2.06

4.2436

8.74182

1.43527

4.53872

1.27240

2.74129 5.90594 .485437

2.07

4.2849

8.86974

1.43875

4.54973

1.27445

2.74572 5.91548 .483092

2.08

4.3264

8.99891

1.44222

4.56070

1.27650

2.75014 5.92499 .-JN'T*;!*

2.09

4.3681

9.12933

1.44568

4.57165

1.27854

2.75454 5.93447 .478*69

2.10

4.4100

9.26100

1.44914

4.58258

1.28058

2.75893

5.94392

.476191

2.11

4.4521

9.39393

1.45258

4.59347

1.28261

2.76330

5.95334

.473934

2.12

4.4944

9.52813

1.45602

4.60435

1.28463

2.76766

5.9H273

.471698

2.13

4.5369

9.66360

1.45945

4.61519

1.28665

2.77200 i 5.97209

.469484

2.H

4.5796

9.80034

1.46287

4.62601

1.28866

2.77633 5.98142

.467290

2.15

4.6225

9.93838

1.46629

4.63681

1 .29066

2.78065 5.99073

.465116

2.16

4.6656

10.0777

1.46969

4.64758

1.29266

2.78495 I 6.00000

.462963

2. IT

4.7089

10.2183

1.47309

4.65833

1.29465

2.78924 . 6.00925

.460830

2.18

4.7524

10.3602

1.47648

4.66905

1.29664

2.79352 ! 6.01846

.458716

2.19

4.79K1

10.5035

1.47986

4.67974

1.29862

2.79779

6.02765

.456621

2.20

4.8400

10.6480

1.48324

4.69042

1.30059

2.80204

6.03681

.454546

2.21

4.8841

10.7939

1.48661

4.70106

1.30256

2.80628

6.04594

.452489

2.22

4.9*84

10.9410

1 .48997

4.71169

1.30452

2.81051

6.05505

.450451

2.23

4.9729

11.0896

1.49332

4.72229

1.30648

2.81472

6.06413

.448431

2.24

5.0176

11.2394

1.49666

4.73286

1.30843

2.81892

6.07318

.446429

2.25

5.0625

11.3906

1.50000

4.74342

1.31037

2.82311

6.08220

.444444

2.26

5.1076

11.5432

1.50333

4.75395

1.31231 ! 2.82728

6.09120

.442478

2.27

5.1529

11.6971

1.50665

4.76445

1.31424 ; 2.83145

6.10017

.440529

2.28

5.1984

11.8524

1.50997

4.77493

1.31617 2.83560

6.10911

.438597

2.29

5.2441

12.0090

1.51327

4.78539

1.31809

2.83974

6.11803

.436681

2.30

5.2900

12.1670

1.51658

4.79583

1.32001

2.84387

6.12693

.434783

2.31

5.3361

12.3264

1.51987

4.80625

1.32192

2.84798

6.13579

.432900

2.32

5.3824

12.4872

1.52315

4.81664

1.32382

2.85209

6.14463

.431035

2.33

5.4289

12.6493

1.52643

4.82701

1.32572

2.85618

6.15345

.429185

2.34

5.4756

12.8129

1.52971

4.83735

1.32761

2.86026

6.16224

.427350

2.35

5.5225

12.9779

1.53297

4.84768

1.32950

2.86433

6.17101

.425532

2.36

5.5696

13.1443

1.53623

4.85798

1.33139

2.86838

6.17975

.423729

2.37

5.6169

13.3121

1.53948

4.86826

1 .33326

2.87243

6.18846

.421941

2.38

5.6644

13.4813

1.54272

4.87852

1.33514

2.87646

6.19715

.420168

2.39

5.7121

13.6519

1.545%

4.88876

1.33700

2.88049

6.20582

.418410

2.40

5.7600

13.8240

1.54919

4.89898

1.33887

2.88450

6.21447

.416667

2.41

5.8081

13.9975

1.55242

4.90918

1.34072

2.88850

6.22308

.414938

2.42

5.8564

14.1725

1.55563

4.91935

1.34257

2.89249

6.23168

.413223

243

5.9049

14.3489

1.55885

4.92950

1.34442

2.89647

6.24025

.411523

2.44

5.9536

14.5268

1.56205

4.93964

1.34626

2.90044

6.24880

.409836

2.45

6.0025

14.7061

1.56525

4.94975

1.34810

2.90439

6.25732

.408163

2.46

6.0516

14.8869

1.56844

4.95984

1.34993

2.90834

6.26583

.406504

2.47

6.1009

15.0692

1.57162

4.96991

1.35176

2.91227

6.27431

.404858

2.48

6.1504

15.2530

1.57480

4.97996

1.35358

2.91620

6.28276

.403226

2.49

6.2001

15.4382

1.57797

4.98999

1.35540

2.92011

6.29119

.401606

2.50

6.2500

15.6250

1.58114

5.00000

1.35721

2.92402

6.29961

.400000

MATHEMATICS

n

n*

| rcs

V^

VlOM >«

^TOnkfOOn *-

2.51

6.3001

15.8133

1.58430

5.00999 1.35902

2.92791

6.30799

.398406

2.52

6.3504

16.0030

1.58745

5.019% 1.36082

2.93179

6.31636

.396825

2.53

6.4009

16.1943

1.59060

5.02991 1.36262 2.93567

6.32470

.395257

254

6.4516

1 16.3871 1.59374

5.03984 1.36441 2.93953 6.33303

.393701

2.55

6.5025

! 16.5814

5.04975 1.36620 2.94338

6.34133

.392157

2.56

6.5536

16.7772 1.60000

.Vor.'.ir.l 1.36798

2.94723 6.34960

.390625

2.57

6.6049

16.9746

1.60312

5.0(i!»ri2 1.36976

2.95106

«.35786

.389105

2.58

6.6564

17.1735

1.60624

5.D7937 1.37153 2.9.'.»>s

6.36610

.387597

2.59

6.7081

17.3740

1.60935

5.08920 1.37330

2.95869

6.37431

.386100

2.60

6.7600

j 17.5760

1.61245

5.09902 1.37J07

2.96250

6.38250

.384615

2.61

6.8121

i 17.7796

1.61555

5.10882

1.37683 2.96629

6.39068

.383142

2.62

6.8644

17.9*47 1.6I>61

5. 11 -.",9 1.37*59 2.97007

6.39883

.381679

2.63

6.9169

If. 1914 1.62173

f,.l-j-:t:, 1 .3-11:14 2.97385

6.40696

.380228

2.64

6.9696

18.8W7

1.62481

5.13*09 1.38208 2.97761

6.41507

.378788

2.65

7.0225

18.6096

1.62788

5.14782

1.38383

2.98137

6.42316

.377359

2.66

7.0756

18.8211

1.63095

5.15752

1.38557

2.98511

6.43123

.375940

2.67

7.1289

19.0342

1.63401

5.16720

1.38730

2.98885

6.43928

.374532

2.68

7.1824

19.2488

1.63707

5.17687

1.38903

2.99257

6.44731

.373134

2.69

7.2361

19.4651

1.64012

5.18652

1.39076

2.99629

6.45531

.371747

2.70

7.2900

19.6830

1.64317

5.19615

1.39248

3.00000

6.46330

.370370

2.71

7.3441

19.9025

1.64621

5.20577

1.39419

3.00370

6.47127

.369004

2.72

7.3984

20.1236 t 1.64924

5.21536

l .:w:>9i

3.00739

6.47922

.367647

2.73

7.4529

20.3464 1.65227

5.22494

1.39761

3.01107

6.48715

.366300

2.74

7.5076

20.5708 1.65529

5.23450

1.39932

3.01474

6.49507

.364964

2.75

7.5625

20.7969 1.65831

5.24404

1.40102

3.01841

6.50296

.363636

2.76

7.6176

21.0246

1.66132

5.25357

1.40272

3.02206

6.51083

.362319

2.77

7.6729

21.2539 1.60433

5.26308

1.40141

3.02571

6.51X68

.361011

2.78

7.7284

21.4850 1.66733

5.27257

1.40610

3.02934

6.52652

.359712

3.79

7.7841

21.7176 1 1.67033

5.28205

1.40778

3.03297

6.53434

.358423

2.80

7.8400

21.9520

1.67332

5.29150

1.40946

3.03639

6.54213

.357142

2.81

7.8961

22.1880

1.67631

5.30094

1.41114

3.04020

6.54991

.355872

2.82

7.9.VJ4

22.4258

1.67929

5.31037

1.41281

3.04380

6.55767

.354610

2.83

8.0089

22.6652

1.68226

5.31977

1.41448

3.04740

6.56541

.353357

2.84

8.0656

22.9063

1.68523

5.32917

1.41614

8.00096

6.57314

.352113

2.85

8.1225

23.1491

1. 68*19

5.33854

1.41780

3.05456

6.58084

.350877

2.86

8.1796

23.3937

1.69115

5.34790

1.41946

3.05813

6.58853

.349650

•2 -7

23.0399

1.69411

5.35724

1.42111

3.116169

6.59620

.3IM32

2.88

8.2944

23.8879

1.0*706

:,.:t66:><;

1 .42276

3.06524

660385

2.89

8.3521

24.1376

1.70000

1.42440

8.06878

6.61149

.3461)21

2.90

8.4100

24.3890

1.70294

5.38516

1.42604

3.07232

6.61911

2.91

8.4681

24.6422

1.70587

5.39444

1.42768

3.07585

6.62671

.343643

2.92

8.5264

24.6971

1.70880

5.40370

1.42931

3.07936

6.63429

.342466

2.93
2.94

8.5849
8.6436

25.1538
25.4122

1.71172
1.71464

5.41295
5.42218

1.43094
1.43257

3.08287 6.64185
3.08638 I 6.64940

.341297
.340136

3.95

8.7025

25.6724

1.71756

5.43139

1.43419

3.08987

6.65693

.338983

2.96

8.7616

25.9343

1.72047

5.44059

1.43581

3.09336

6.66444

.337838

2.97

S.H2II9

26.1981 1.72337

5.44077

1.43743

3.09684 6.67194

.336700

2.98

8.HHH

26.4684 1.72627

;'i 4T.-9I 1.43904 3.10031 6.67942 .335571

299

8.9401

l,7-'!l]f,

5.46809 1.44065 3.10378 6.68688 .334448

9.00

9.1HMMI

1 73205

5.47723 1.44225 3.10723 6.69433 .333333

MA THEM A TICS

15

n

«2

n»

<&

VIow

«!

Wn

•^100 n

JL

n

3.01

9.0601

27.2709

1.73494 5.48635

1.44385

3.11068

6.70176

.332226

3.02

9.1204

27.5436

1.73781 5.49545

1.44545

3.11412

6.70917

.331126

8.03

9.1809

27.8181

1.74069

5.50454

1.44704

3.11755

6.71657

.330033

3.04

9.2416

28.0945

1.74356

5.51362

1.44863

3.12098

6.72395

.328947

S.05

9.3025

28.3726

1.74642

5.52268

1 45022

3.12440

6.73132

.327869

8.06

9.3636

28.6526

1.74929 5.53173

1.45180

3.12781

6.73866

.326797

3.07

9.4249

28.9344

1.75214

5.54076

1.45338

3.13121

6.74600

.325733

3.08

9.4864

29.2181

1.75499

5.54977

1.45496

3.13461

6.75331

.324675

8.09

9.5481

29.5036

1.75784

5.55878

1.45653

3.13800

6.76061

.323625

S.10

9.6100

29.7910

1.76068

5.56776

1.45810

3.14138

6.76790

.322581

8.11

9.6721

30.0802

1.76352

5.57674

1.45967

3.14475

6.77517

.32154*

3.12

9.7344

30.3713

1.76635

5.58570

1.46123

3.14812

6.78242

.320513

3.13

9.7969

30.6643

1.76918

5.59464

1.46279

3.15148

6.78966

.319489

3.H

9.8596

30.9591

1.77200

5.60357

1.46434

3.15484

6.79688

.318471

3.15

9.9225

31.2559

1.77482

5.61249

1.46590

3.15818

6.80409

.317460

3.16

9.9856

31.5545

1.77764

5.62139

1.46745

3.16152

6.81 28

.316456

8.17

10.0489

31.8550

1.78045

5.03028

1.46899

3.16485

6.81846

.315457

8.18

10.1124

32.1574

1.78326

5.63915

1.47054

3.16817

6.82562

.314465

8.19

10.1761

32.4618

1.78606

5.64801

1.47208

3.17149

6.83277

.313480

8.20

10.2400

32.7680

1.78885

5.65685

1.47361

3.17480

6.83990

.312500

8.21

10.3041

33.0762

1.79165

5.66569

1.47515

3.17811

6.84702

.311527

8.22

10.3684

33.3862

1.79444

5.67450

1.47668

3.18140

6.85412

.310559

8.23

10.4329

33.6983

1.79722

5.68331

1.47820

3,18469

6.86121

.30959&

3.24

10.4976

34.0122

1.80000

5.69210

1.47973

3.18798

6.86829

.308642

8.25

10.5625

34.3281

1.80278

5.70088

1.48125

3.19125

6.87534

.307692

8.26

10.6276

34.6460

1.80555

5.70964

1.48277

3.19452

6.88239

.306749

8.27

10.6929

34.9658

1.80831

5.71839

1.48428

3.19779

6.88942

.305810

3.28

10.7584

35.2876

1.81108

5.72713

1.48579

3.20104

6.89643

.304878

3.29

10.8241

35.6129

1.81384

5.73585

1.48730

3.20429

6.90344

.303951

8.30

10.8900

35.9370

1.81659

5.74456

1.48881

3.20753

6.91042

.303030

8.31

10.9561

36.2647

1.81934

5.75326

1.49031

3.21077

6.91740

.302115

3.32

11.0224

36.5944

1.82209

5.76194

1.49181

3.21400

6.92436

.301205

3.33

11.0889

36.9260

1.82483

5.77062

1.49330

3.21723

6.93130

.300300

8.34

11.1556

37.2597

1.82757

5.77927

1.49480

3.22044

6.93823

.299401

8.35

11.2225

37.5954

1.83030

5.78792

1.49629

3.22365

6.94515

.29850&

3.36

11.2896

37.9331

1.83303

5.79655

1.49777

3.22636

6.95205

.297619

8.37

11.3569

38.2728

1.83576

5.80517

1.49926

3.23005

ti.95894

.296735

8.38

11.4244

38.6145

1.83848

5.81378

1.50074

3.23325

6.90582

.295853

3.39

11.4921

38.9582

1.84120

5.82237

1.50222

3.23643

6.97268

.294985

3.40

11.5600

39.3040

1.84391

5.83095

1.50369

3.23961

6.97953

.294118

8.41

11.6281

39.6518

1.84662

5.83952

1.50517

3.24278

6.98637

.293255

8.42

11.6964

40.0017

1.84932

5.84808

1.50664

3.24595

6.99319

.292398

8.43

11.7649

40.3536

1.85203

5.85662

1.50810

3.24911

7.00000

.29154I>

844

11.8336

40.7076

1.85472

5.86515

1.50957

3.25227

7.00680

.29069S

8.45

11.9025

41.0636

1.85742

5.87367

1.51103

3.25542

7.01358

289855

8.46

11.9716

41.4217

1.86011

5.88218

1.51249

3.25856

7.02035

.289017

8.47

12.0409

41.7819

1.86279

5.89067

1.51394

3.26169

7.02711

.288184

8.48

12.1104

42.1442

1 .86548

5.89915

1.51540

3.26482

7.03385

.287356

8.49

12.1801

42.5085

1.86815 1 5.90762

1.51685

3.26795

7.04058

.286533

3.50

12.2500

42.8750

1.87083 5.91608

1.51829

3.27107

7.04730

.285714

16

MATHEMATICS

n

7»2

W3

^

VlOn

*s

•<flOn

•^Too.n

1

n

3.51

12.3201

43.2436

1.87350

5.92453

1.51974

3.27418

7.05400

.284900

3.52

12.3904

43.6142

1.87617

5.932%

1.52118

3.27729

7.06070

.284091

3.53

12.4609

43.9870

1.87883

5.94138

1.52262

3.28039

7.06738

.283286

3.54

12.5316

44.3619

1.88149

5.94979

1.52406

3.28348

7.07404

.282486

3.55

12.6025

44.7389

1.88414

5.95819

1.52549

3.28657

7.08070

.281690

3.56

12.6736

45.1180

1.88680

5.96657

1.52692

3.28965

7.08734

.280809

3.57

12.7449

45.4993

1.88944

5.97495

1.52835

3.29273

7.09397

.280112

3.58

12.8164

45.8827

1.89209

5.98331

1.52978

3.29580

7.10059

.279330

3.59

12.8881

46.2683

1.89*73

5.99166

1.53120

3.29887

7.10719

.278552

3.60

12.9600

46.6560

1.89737

6.00000

1.53262

3.3019S

7.11379

.277778

3.61

13.0321

47.0459

1.90000

6.00833

1.53404

3.30498

7.12037

.277008

3.62

13.1044

47.4379

1.90263

6.01664

1.53545

3.30803

7.12694

.276243

3.63

13.1769

47.8321

1.90526

6.02495

1.53686

3.31107

7.13349

.275482

3.64

13.2496

48.2285

1.90788

6.03324

1.53827

3.31411

7.14004

.274725

3.65

13.3225

48.6271

1.91050

6.04152

1.53968

3.31714

7.14657

.273973

3.66

13.3956

49.0279

1.91311

6.04979

1.54109

3.32017

7.15309

.273224

3.67

13.46*9

49.4309

1.91572

ti.OSHOi,

1.54249

3.32319

7.15960

.272480

3.68

13.5424

49.8360

1.91833

6.06630

1.54389

3.32621

7.16610

.271739

3.69

13.6161

50.2434

1.92094

6.07454

1.54529

3.32922

7.17258

.271003

3.70

13.6900

50.6530

1.92354

6.08276

1.54668

3.33222

7.17905

.270270

3.71

13.7641

51.0648

1.92614

6.09098

1.54807

3.33522

7.18552

.269542

3.72

13.8384

51.4788

1.92873

6.09918

1.54946

3.33822

7.19197

.268817

3.73

13.9129

51.8951

1.93132

6.10737

1.55085

3.34120

7.19841

.268097

3.74

13.9876

52.3136

1.93391

6.11555

1.55223

3.34419

7.20483

.267380

3.75

14.0625

52.7344

1.93649

6.12372

1.55362

3.34716

7.21125

.266667

3.76

14.1376

53.1574

1.93907

6.13188

1.55500

3.35014

7.21765

.265957

3.77

14.2129

53.5826

1.94165

6.14003

1.55637

3.35310

7.22405

.265252

3.78

14.2884

54.0102

1.94422

6.14817

1.55775

3.35607

7.23043

.264550

3.79

14.3H41

54.4399

1.94679

6.15630

1.55912

3.35902

7.23680

.263852

3.80

14.4400

54.8720

1.94936

6.16441

1.56049

3.36198

7.24316

.263158

3.81

14.5161

55.3063

1.95192

6.17252

1.56186

3.36492

7.24950

.262467

3.82

14.5924

55.7430

1.95448

6.18061

1.56322

3.36786

7.25584

.261780

3.83

14.6689

56.1819

1.95704

6.18870

1.56459

3.37080

7.26217

.261097

3.84

14.7456

56.6231

1.95959

6.19677

1.56595

3.37373

7.26848

.260417

3.85

14.8225

57.0666

1.96214

6.20484

1.56731

3.37666

7.27479

.259740

3.86

14.8996

57.5125

1.96469

6.21289

1.56866

3.37958

7.28108

.259067

3.87

14.9769

57.96(16

1.96723

6.22093

1.57001

3.3H249

7.28736

.258393

3.88

15.0544

58.4111

l.'.lii'.lTi

6.22H96

1.57137

3.38540

7.29363

.257732

3.89

15.1321

5.1 8639

1.97231

6.23699

1.57271

3.38831

7.29989

.257069

3.90

15.2100

59.3190

1.97484

6.24500

1.57406

3.39121

7.30614

.256410

3.91

15.2881

59.7765

1.97737

6.25300

1.57541

3.39411

7.31238

.255755

392

15.3664

fio.2:ifi3

1.97990

6.26099

1.57675

3.39700

7.81861

.255102

3.93

15.4449

fid. 69*5

1.98242

C.268JJ7

1.57809

3.39988

7.32483

.254453

3.94

15.5236

61.1630

1.98494

6.27694

1.57942

3.40277

7.33104

.253807

3.95

15.6025

61.6299

1.98746

6.28490

1.58076

3.40564

7.33723

.253165

3.96

15.6816

62.0991

1.98997

6.29285

1.58209

3.40851

7.34342

.252525

3.97

15.7609

62.5708

1.99249

6.30079

1.58342

3.41138

7.34960

.251889

3.98

15.8404

63.0448

1.99499

6.30872

1.58475

3.41424

7.35576

.251256

3.99

15.9201

63.5212

1.99750

6.31664

1. 5*601

3.41710

7.36192

.250627

4.00

16.00W

64.0000

2.00000

6.32456

1.58740

3.41995

7.36806

.250000

MATHEMATICS

17

n

712

n»

vs

VlOw

<i

-^10 n

"^lOO n

1

n

4.01

16.0301

64.4812

2.00250

6.33246

1.58872

3.42280

7.37420

.249377

4.02 16.1604

64.9648

2.00499 6.34035 1.59004

3.42564

7.38032

.248756

4.03 16.2409

65.4508

2.00749

6.34823

1.59136

3.42848

7.38644

.248139

4.04 16.3216

65.9393

2.0099ft

6.35610

1.59267

3.43131

7.39254

.247525

4.05

16.4025

66.4301

2.01246

6.36396

1.59399

3.43414

7.39864

.246914

4.06

16.4836

66.9234

2.01494

6.37181

1.59530

3.43697

7.40472

.246305

4.07

16.5649

67.4191

2.01742

6.37966

1.59661

3.43979

7.41080

.245700

4.08

16.6464

67.9173

2.01990

6.38749

1.59791

3.44260

7.41686

.245098

4.09

16.7281

68.4179

2.02237

6.39531

1.59922

3.44541

7.42291

.244499

4.10

16.8100

68.9210

2.02485

6.40312

1.60052

3.44822

7.42896

.243902

4.11

16.8921

69.4265

2.02731

6.41093

1.60182

3.45102

7.43499

.243309

4.12

16.9744

69.9345

2.02978

6.41872

1.60312

3.45382

7.44102

.242718

4.13

17.0569

70.4450

2.03224

6.42651

1.60441

3.45661

7.44703

.242131

4.14

17.1396

70.9579

2.03470

6.43428

1.60571

3.45939

7.45304

.241546

4.15

17.2225

71.4734

2.03715

6.44205

1.60700

3.46218

7.45904

.240964

4.16

17.3056

71.9913

2.03961

6.44981

1.60829

3.46496

7.46502

.240385

4.17

17.3889

72.5117

2.04206

6.45755

1.60958

3.46773

7.47100

.239808

4.18

17.4724

73.0346

2.04450

6.46529

1.61086

3.47050

7.47697

.239234

4.19

17.5561

73.5601

2.04695

6.47302

1.61215

3.47327

7.48292

.238664

4.20

17.6400

74.0880

2.04939

6.48074

1.61343

3.47603

7.48887

.238095

4.21

17.7241

74.6185

2.05183

6.48845

1.61471

3.47878

7.49481

.237530

4.22

17.8084

75.1514

2.05426

6.49615

1.61599

3.48154

7.50074

.236967

4.23

17.8929

75.6870

2.05670

6.50385

1.61726

3.48428

7.50666

.23640T

4.24

17.9776

76.2250

2.05913

6.51153

1.61853

3.48703

7.51257

.235849

4.2a

18.0625

76.7656

2.06155

6.51920

1.61981

3.48977

7.51847

.235294

4.26

18.1476

77.3088

2.06398

6.52687

1.62108

3.49250

7.52437

.234742

4.27

18.2329

77.8545

2.06640

6.53452

1.62234

3.49523

7.53025

.234192

4.28

18.3184

78.4028

2.06882

6.54217

1.62361

3.49796

7.53612

.233645

4.29

18.4041

78.9536

2.07123

6.54981

1.62487

3.50068

7.54199

.233100

4.30

18.4900

79.5070

2.07364

6.55744

1.62613

3.50340

7.54784

.232558

4.31

18.5761

80.0630

2.07605

6.56506

1.62739

3.50611

7.55369

.232019

4.32

18.6624

80.6216

2.07846

6.57267

1.62865

3.50882

7.55953

.231482

4.33

18.7489

81.1827

2.08087

6.58027

1.62991

3.51153

7.56535

.230947

4.34

18.8356

81.7465

2.08327

6.58787

1.63116

3.51423

7.57117

.230415

4.35

18.9225

82.3129

2.08567

6.59545

1.63241

3.51692

7.57698

.229885

4.36

19.0096

82.8819

2.08806

6.60303

1.63366

3.51962

7.58279

.229358

4.37

19.0969

83.4535

2.09045

6.61060

1.63491

3.52231

7.58858

.228833

4.38

19.1844

84.0277

2.09284

6.61816

1.63616

3.52499

7.59436

.228311

4.39

19.2721

84.6045

2.09523

6.62571

1.63740

3.52767

7.60014

.227790

4.40

19.3600

85.1840

2.09762

6.63325

1.63864

3.53035

7.60590

.227273

4.41

19.4481

85.7661

2.10000

6.64078

1.63988

3.53302

7.61166

.226757

4.42

19.5364

86.3509

2.10238

6.64831

1.64112

3.53569

7.61741

.226244

4.43

19.6249

86.9383

2.10476

6.655*2

1.64236

3.53835

7.62315

.225734

4.44

19.7136

87.5284

2.10713

6.66333

1.64359

3.54101

7.82888

.225225

4.45

19.8025

88.1211

2.10950

6.67083

1.64483

3.54367

7.63461

.224719

4.46

19.8916

88.7165

2.11187

6.67832

1.64606

3.54632

7.64032

.224215

4.47

19.9809

89.3146

2.11424

6.68581

1.64729

3.54897

7.64603

.223714

4.48

20.0704

89.9154

2.11660

6.69328

1.64851

3.55162

7.65172

.223214

4.49

20.1601

90.5188

2.11896

6.70075

1.64974

3.55426

7.65741

.222717

4.50

20.2500

91.1250

2.12132

6.70820

1.65096

3.55689

7.66309

.222222

\IA Til EM A TICS

n

n2

7*3

Vn

VlOw

*s

$Wn

•ftbOn

1

n

4.51

20.3401

91.7339

2.12368

6.71565

1.65219

3.55953

7.66877

.221730

4.52

20.4304

92.3454

2.12603

6.72309

1.65341

3.56215

7.67443

.221239

4.53

20.5209

92.9597

2.12838

6.73053

1.65462

3.56478

7.68009

.220751

4.54

20.6116

93.5767

2.13073

6.73795

1.66684

3.56740

.220264

4.55

20.7025

94.1964

2.13307

6.74537

1.65706

3.57002

7.69137

.219780

4.56

20.7936

94.8188

2.13542

6.75278

1.6f)827

3.57263

7.69700

.219298

4.57

1'0.884<J

95.4440

2.13776

6.76018

1.85648

7.701!62

.218818

4.58

20.9764

96.0719

2.14009

6.76757

1.66069

8.57788

7.70824

.218341

4.59

21.0681

96.7026

2.14243

6.77495

1.66190

8.58046

7.71384

.217865

4.60

21.1600

97.3360

2.14476

6.78233

1.66310

3.58305

7.71944

.217391

4.61

21.2521

97.9722

2.14709

6.78970

166431

3.58564

7.72503

.216920

4.62

21.3444

98.6111

2.14942

6.79706

1.66551

3.5*823

7.73061

.216450

4.63

21.4369

99.2528

2.15174

6.80441

1.66671

8.59081

7.73619

.215983

4.64

21.5296

99.8973

2.15407

6.81175

1.66791

3.59340

7.74175

.215517

4.65

21.6225

100.545

2.15639

6.81909

1.66911

3.59598

7.74731

.215054

4.66

21.7156

Ml. 195

2.15870

6.82642

1.67030

3.59856

7.75286

.214592

4.67

21.8089

101.848

2.16102

6.83374

1.67150

3.60113

7.75840

.214133

4.68

21.9024

102.503

2.16333

6.84105

1.67269

3.60370

7.76394

.213675

4.69

21.9961

103.162

2.16564

6.84836

1 .67388

3.60626

7.76946

.213220

4.70

22.0900

103.823

2.16795

6.85565

1.67507

3.60883

7.77498

.212766

4.71

22.1841

104.487

2.17025

6.86294

1.67626

3.61138

7.78049

.212314

4.72

22.2784

105.154

2.17256

6.87023

1.67744

3.61394

7.78599

.211864

4.73

22.3729

105.824

2.17486

6.87750

1.67863

3.61649

7.79149

.211417

4.74

22.4676

106.496

2.17715

6.88477

1.67981

3.61904

7.79697

.210971

4.75

22.5625

107.172

2.17945

6.89202

1.68099

3.62158

7.80245

.210526

4.76

22.6576

107.850

2.18174

6. 89928

1.68217

3.62412

7.80793

.210084

4.77

22.7529

108.531

2.18403

6.90652

1.68334

7.*1339

.'209644

4.78

22.8484

109.215

2.1X632

6.91375

I.I;-I.Y_>

3.62919

7.81885

.209205

4.79

22.9441

109.902

2.188ft]

6.92098

1 .68569

3.63171

7.V2429

.208768

4.80

23.0400

110.592

2.11)089

6.92820

1.68687

3.63424

7.82974

.208333

4.81

23.1361

111.285

2.19317

6.93542

1.68804

3.63676

7.83517

.207900

4.82

23.21124

111.WO

2.19545

6.9 42(12

1.68WO

3.63928

7.84059

.207469

4.83

23.3289

112.679

2.19773

6.94982

1 .69037

3.64180

7.-IC.ill

4.84

23.4256

113.380

2.20000

6.95701

1.69154

3.64431

7.85142

.206612

4.85

23.5225

114.084

2.20227

6.96419

1.69270

3.64682

7.85683

.206186

4.86

23.6196

114.791

2.20454

6.97137

1.69386

3.64932

7.86222

.205761

4.87

23.7169

115.501

2.206M

6.97854

1 .6H503

3.651M2

4.88

23.8144

116.214

2.20907

6.98570

1.69619

3.65432

7.872M

4.89

23.IM21

116.930

2.21133

1.697*4

.204»i.'.»

4.90

24.0100

117.649

2.21359

7.00000

1.69850

3.65931

,304081

4.91

i4.ua

IWJ71

2.21585

7.00714

1.69965

3.66179

7.88909

.203666

4.92

24.2064

119.095

•-'.21-11

7.01427

1.70081

3 66428

7.89446

.203252

fcM

24.3049

L19.8M

2.2203C,

7.02140

1.70196

3.66676

r.899W

4.94

24.4036

120.554

2 22261

7.02851

1.70311

3.66924

7.90513

.202429

4.95

24.5025

121.287

2.221*6

7.03562

1.70426

3.67171

7.91046

.202020

4.96

24.6016

122.024

2.22711

7.04273

1.70540

3.67418

7.91578

.201613

4.97

21.71X19

2.22935

7.0 IH-'.'

3.67665

7. !H! 110

.201207

4.98

24.8004

m.506

2.23159

7.05691

1.70769

3.67911

7.92641

.200803

4.99

21.90U1

7.06399

1.70--4

3.68157

7J8171

.200401

5.00

25.0000

125.000

2.23607

7.07107

1.76998

3.6x403

7.93701

.200000

MA THEM A TICS

19

n

n2

n*

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•9lOO«

1

n

5.01

25.1001

125.752

2.23830

7.07814

1.71112

3.68649

7.94229

.199601

5.02

25.2004

126.506

2.24054

7.08520

1.71225

3.68894

7.94757

.199203

5.03

25.3009

127.264

2.24277

7.09225

1.71339

3.69138

7.95285

.198807

5.04

25.4016

128.024

2.24499

7.09930

1.71452

3.69383

7.95811

.198413

5.05

25.5025

128.788

2.24722

7.10634

1.71566

3.69627

7.96337

.198020

5.06

25.6036

129.554

2.24944

7.11337

1.71679

3.69871

7.96863

.197629

5.07

25.7049

130.324

2.25167

7.12039

1.71792

3.70114

7.97387

.197239

5.08

25.8064

131.097

2.25389

7.12741

1.71905

3.70358

7.97911

.196850

5.09

25.9081

131.872

2.25610

7.13442

1.72017

3.70600

7.98434

.196464

5.10

26.0100

132.651

2.25832

7.14143

1.72130

3.70843

7.98957

.196078

5.11

26.1121

133.433

2.26053

7.14843

1.72242

3.71085

7.99479

.195695

5.12

26.2144

134.218

2,26274

7.15542

1.72355

3.71327

8.00000

.195313

5.13

26.3169

135.006

2.26495

7.16240

1.72467

3.71566

8.00520

.194932

5.14

26.4196

135.797

2.26716

7.16938

1.72579

3.7181C

8.01040

.194553

5.15

26.5225

136.591

2.26936

7.17635

1.72691

3.72051

8.01559

.194175

5.16

26.6256

137.388

2.27156

7.18331

1.72802

3.72292

8.02078

.193798

5.17

26.7289

138.188

2.27376

7.19027

1.72914

3.72532

8.02596

.193424

5.18

26.8324

138.992

2.27596

7.19722

1.73025

3.72772

8.03113

.193050

5.19

26.9361

139.798

2.27816

7.20417

1.73137

3.73012

8.03629

.192678

5.20

27.0400

140.608

2.28035

7.21110

1.73248

3.73251

8.04145

.192308

5.21

27.1441

141.421

2.28254

7.21803

1.73359

3.73490

8.04660

.191939

5.22

27.2484

142.237

2.28473

7.22496

1.73470

3.73729

8.05175

.191571

5.23

27.3529

143.056

2.28692

7.23187

1.73580

3.73968

8.05689

.191205

5.24

27.4576

143.878

2.28910

7.23878

1.73691

3.74206

8.06202

.190840

5.25

27.5625

144.703

2.29129

7.24569

1.73801

3.74443

8.06714

.190476

5.26

27.6676

145.532

2.29347

7.25259

1.73912

3.74681

8.07226

.190114

5.27

27.7729

146.363

2.29565

7.25948

1.74022

3.74918

8.07737

.189753

5.28

27.8784

147.198

2.29783

7.26636

1.74132

3.75158

8.08248

.189394

5.29

27.9841

148.036

2.30000

7.27324

1.74242

3.',5392

8.08758

.189036

5.30

28.0900

148.877

2.30217

7.28011

1.74351

3.75629

8.09267

.188679

5.31

28.1961

149.721

2.30434

7.28697

1.74461

3.75865

8.09776

.188324

5.32

28.3024

150.569

2.30651

7.29383

1.74570

3.76100

8.10284

.187970

5.33

28.4089

151.419

2.30868

7.30068

1.74680

3.76336

8.10791

.187617

5.34

28.5156

152.273

2.31084

7.30753

1.74789

3.76571

8.11298

.187266

5.35

28.6225

153.130

2.31301

7.31437

1.74898

3.76806

8.11804

.186916

6.36

28.7296

153.991

2.31517

7.32120

1.75007

3.77041

8.12310

.186567

5.37

28.8369

154.854

2.31733

7.32803

1.75116

3.77275

8.12814

.186220

5.38

28.9444

155.721

2.31948

7.33485

1.75224

3.77509

8.13319

.185874

5.39

29.0521

156.591

2.32164

7.34166

1.75333

3.77740

8.13822

.185529

5.40

29.1600

157.464

2.32379

7.34847

1.75441

3.77976

8.14325

.185185

5.41

29.2681

158.340

2.32594

7.35527

1.75549

3.78210

8.14828

.184843

5.42

29.3764

159.220

2.32809

7.36206

1.75657

3.78442

8.15329

.184502

5.43

29.4849

160.103

2.33024

7.36885

1.75765

3,78675

8.15831

.184162

5.44

29.5936

160.989

2.33238

7.37564

1.75873

3.78907

8.16331

.183824

5.45

29.7025

161.879

2.33452

7.38241

1.75981

3.79139

8.16831

.183486

5.46

29.8116

162.771

2.33666

7.38918

1.76088

3.79371

8.17330

.183150

5.47

29.9209

163.667

2.33880

7.39594

1.76196

3.79603

8.17829

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5.48

30.0304

164.567

2.34094

7.40270

1.76303

3.79834

8.18327

.182482

5.49

30.1401

165.469

2.34307

7.40945

1.76410

3.80065

8.18824

.182149

5.50

30.2500

166.375

2.34521

7.41620

1.76517

3.80295

8.19321

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20

MA THEM A TICS

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5.51

30.3601

167.284

2.34734

7.42294

1.76624

3.80526 8.19818

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5.52

30.4704

168.197

2.34947

7.42967

1.76731

380756 8.20313

.181159

5.53

30.5809

169.112

2.35160

7.436*0

1.76888

3.80986 8.20808

.180832

5.54

30.6916

170.031

2.35372

7.4*312

1.76944

3.80115 8.21303 .180505

6.55

30.8025

170.954

2.35584

7.44983

1.77051

3.81444

8.21797

.180180

5.56

30.9136

171.880

2.35797

7.45654

1.77157

3.81673

8.22290

.179856

5.57

31.0249

172.809

2.36008

7.46324

1.77263

3.81902

8.22783

.179533

5.58

31.1364

173.741

2.36220

7.46994

1.77369

3.82130

8.23275

.179212

5.59

31.2481

174.677

2.36432

7.47663

1.77475

3.82358

8.23766

.178891

6.60

31.3600

175.616

2.36643

7.48331

1.77581

3.82586

8.24257

.178571

5.61

31.4721

176.558

2.36854

7.48999

1.77686

3.82814

8.24747

.178253

5.62

31.5844

177.504

2.37065

7.49667

1.77792

3.83041

8.25237

.177936

5.63

31.6969

178.454

2.37276

7.50333

1.77897

3.83268

8.25726

.177620

5.64

31.8096

179.406

2.37487

7.50999

1.78003

3.83495

8.26215

.177305

5.65

31.9225

180.362

2.37697

7.51665

1.78108

3.83721

8.26703

.176991

6.66

32.0356

181.321

2.37908

7.52330

1.78213

3.83948

8.27190

.176678

5.67

32.1189

182.284

2.38118

7.52994

1.78318

3.84174

8.27677

.176367

5.68

32.2624

183.250

2.38328

7.53658

1.78422

3.84400

8.28164

.176056

6.69

32.3761

184.220

7.54321

1.78527

8.84636

.175747

6.70

32.4900

185.193

2!38747

7.54983

1.78632

3.84850

8.29134

.175439

5.71

32.6011

186.169

2.38956

7.55645

1.78736

3.85075

8.29619

.175131

6.72

32.7184

187.149

2.39105

7.56307

1.78840

3.85300

8.30103

.174825

5.73

32.8329

188.133

2.39374

7.56968

1.78944

8.85624

8.30587

.174520

5.74

32.9476

189.119

2.39583

7.57628

1.79048

3.85748

8.31069

.171216

6.75

33.0625

190.109

2.39792

7.58288

1.79152

3.85972

8.31552

.173913

5.76

33.1776

191.103

2.40000

7.58947

1.79256

3.86196

8.32034

.173611

6.77

33.2929

192.100

2.40208

7.59605

1.79360

3.86419

8.32515

.173310

5.78

33.4084

193.101

2.40416

7.60263

1.79463

3.88642

8.32995

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5.79

33.5241

194.105

2.4(1(124

7.60920

1.79567

8.86866

8.33476

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6.80

33.6400

195.112

2.40832

7.61577

1.79670

3.87088

8.33955

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5.81

33.7561

196.123

2.41039

7.62234

1.79773

3.87310

8.34434

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5.82

33.8721

197.137

2.41*47

7.62389

1.79876

3.87532

8.84818

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5.83

33.98*9

198.155

2.41454

7.63544

1.79979

3.87754

8.35390

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6.84

34.1056

199.177

2.ll(ilil

7.64199

1.80082

3.87975

8.35868

.171233

5.85

34.2225

200.202

2.41868

7.64853

1.80185

3.88197

8.36345

.170940

5.86

34.3396

201.230

2.42074

7.65506

1.80288

3.88418

8.36821

.170649

5.87

31.4569

202.262

2.42281

7.66159

1.80390

3.88639

8.37297

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5J6

34.5744

203.297

2.42487

7. r>i;- 12

1.80492

8.88859

8.37772

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5.89

34.6921

204.336

2.42693

7. 67163

1 .80595

3.89082

8.38247

.169779

5.90

34.8100

205.379

2.42899

7.68115

1.80697

3.89300

8.38721

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5.91

34.9281

206.425

2.43105

7.68765

1.80799

3.89520

8.39194

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5.92

35.0164

207.475

2.43311

7.69415

1.80901

3. 89739

8.39(167

.168919

6.93

35.1649

208.528

2.43516

7.70065

1.81003

389958

8.40140

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6.94

35.2836

209.585

2.43721

7.70714

1.81104

3.90177

8.40612

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5.95

35.4025

210.645

2.43926

7.71362

1.81206

3.90396

8.41083

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6.96

35.5216

211.709

2.44131

7.72010

1.81307

3.90615

8.41554

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6.87

36.6409

212.776

2.44336

7.72658

1.81409

3.90833

8.42025

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6.98

35.7604

213.847

2.44540

7.73305

1.81510

3.91051

8.42494

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6.99

35.880P

214.922

2.44745

7.73951

1.81611

3.91269

8.42964

.166945

6.00

36.0000

216.000

2.44949

7.74597

1.81712

3.91487

8.43433

.166667

MATHEMATICS

21

n

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1

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5.01

36.1201

217.082

2.45153

7.75242

1.81813

3.91704

8.43901

.166389

6.02

36.2404

218.167

2.45357

7.75887

1.81914

3.91921

8.44369

.16611$

6.03

36.3609

219.256

2.45561

7.76531

1.82014

3.92138

8.44836

.165838

6.04

36.4816

220.349

2.45764

7.77174

1.82115

3.92355

8.45303

.165563

6.05

36.6025

221.445

2.45967

7.77817

1.82215

3.92571

8.45769

.165289

6.06

36.7236

222.545

2.46171

7.78460

1.82316

3.92787

8.46235

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6.07

36.8449

223.649

2.46374

7.79102

1.82416

3.93003

8.46700

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6.08

36.9664

224.756

2.46577

7.79744

1.82516

3.93219

8.47165

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6.09

37.0881

225.867

2.46779

7.80385

1.82616

3.93434

8.47629

.164204

6.10

37.2100

226.981

2.46982

7.81025

1.82716

3.93650

8.48093

.163934

6.11

37.3321

228.099

2.47184

7.81665

1.82816

3.93865

8.48556

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6.12

37.4544

229.221

2.47386

7.82304

1.82915

3.94079

8.49018

.163399

6.13

37.5769

230.346

2.47588

7.82943

1.83015

3.94294

8.49481

.16313?

6.14

37.6996

231.476

2.47790

7.83582

1.83115

3.94508

8.49942

.162866

5.15

37.8225

232.608

2.47992

7.84219

1.83214

3.94722

8.50404

.162602

6.16

37.9456

233.745

2.48193

7.84857

1.83313

3.94936

8.50864

.16238ft

6.17

38.0689

234.885

2.48395

7.85493

1.83412

3.95150

8.51324

.162075

6.18

38.1924

236.029

2.48596

7.86130

1.83511

3.95363

8.51784

.161812

6.19

38.3161

237.177

2.48797

7.86766

1.83610

3.95576

8.52243

.161551

6.20

38.4400

238.328

2.48998

7.87401

1.83709

3.95789

8.52702

.161290

6.21

38.5641

239.483

2.49199

7.88036

1.83808

3.96002

8.53160

.161031

6.22

38.6884

240.642

2.49399

7.88670

1.83906

3.96214

8.53618

.160772

6.23

38.8129

241.804

2.49600

7.89303

1.84005

3.96426

8.54075

.160514

6.24

38.9376

242.971

2.49800

7.89937

1.84103

3.96639

8.54532

.160256

6.25

39.0625

244.141

2.50000

7.90569

1.84202

3.96850

8.54988

.160000

6.26

39.1876

245.314

2.50200

7.91202

1.84300

3.97062

8.55444

.159744

6.27

39.3129

246.492

2.50400

7.91833

1.84398

3.97273

8.55899

.159490

6.28

39.4384

247.673

2.50599

7.92465

1.84496

3.97484

8.56354

.159236

6.29

39.5641

248.858

2.50799

7.93095

1.84594

3.97695

8.56808

.158988

6.30

39.6900

250.047

2.50998

7.93725

1.84691

3.97906

8.57262

.158730

6.31

39.8161

251.240

2.51197

7.94355

1.84789

3.98116

8.57715

.158479

6.32

33.9424

252.436

2.51396

7.94984

1.84887

3.98326

8.58168

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6.33

40.0689

253.636

2.51595

7.95613

1.84984

3.98536

8.58620

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6.34

40.1956

254.840

2.51794

7.96241

1.85082

3.98746

8.59072

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6.35

40.3225

256.048

2.51992

7.96869

1.85179

3.98956

8.59524

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6.36

40.4496

257.259

2.52190

7.97496

1.85276

3.99165

8.59975

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6.37

40.5769

258.475

2.52389

7.98123

1.85373

3.99374

8.60425

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6.38

40.7044

259.694

2.52587

7.98749

1.85470

3.99583

8.60875

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6.39

40.8321

260.917

2.52784

7.99375

1.85567

3.99792

8.61325

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6.40

40.9600

262.144

2.52982

8.00000

1.85664

4.00000

8.61774.

.156250

6.41

41.0881

263.375

2.53180

8.00625

1.85760

4.00208

8.62222

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6.42

41.2164

264.609

2.53377

8.01249

1.85857

4.00416

8.62671

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6.43

41.3449

265.848

2.53574

8.01873

1.85953

4.00624

8.63118

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6.44

41.4736

267.090

2.53772

8.02496

1.86050

4.00882

8.63566

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6.45

41.6025

268.336

2.53969

8.03119

1.86146

4.01039

8.64012

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6.46

41.7316

269.586

2.54165

8.03741

1.86242

4.01246

8.64459

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6.47

41.8609

270.840

2.54362

8.04363

1.86338

4.01453

8.64904

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6.48

41 .9904

272.098

2.54558

8.04984

1.86434

4.01660

8.65350

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6.49

42.1201

273.359

2.54755

8.05605

1.86530

4.01866

8.65795

.154083

6.50

42.2500

274.625

2.54951

8.06226

1.86626

4.02073

8.66239

.153846

22

MATHEMATICS

n

n-

W3

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1

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6.51

42.3801

275.894

2.55147

8.06846

1.86721

4.02279

8.66683

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652

42.5104

277.168

2.55343

8.07465

1.86817

4.02485

8.67127

.153374

6.53

12 6409

278.445

2.55539

8.08084

1.86912

4.02690

8.67570

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6.54

42.7716

279.726

2.55734

8.0«703

1.87008

4.02*96

8.68012

.152905

6.55

42.9025

281.011

2.55930

8.09321

1.87103

4.03101

8.68455

.152672

6.56

43.0336

282.300

2.56125

8.0993S

1.87198

4.03306

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6.57

43.1619

2*3.593

2.56320

8.10555

1.87293

4.03511

8.69338

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6.58

43.2964

2S4.890

2.56515

8.11172

1.87388

4.03715

8.69778

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6.59

4:i.l2-l

2*6.191

2.56710

8.11788

4.03920

8.70219

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6.60

43.5600

2B7.496

2.56905

8.12404

1.87578

4.04124

8.70659

151515

6.61

43.6921

288.805

2.57099

8.13019

1.87672

4.04328

8.71098

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6.62

43.8244

290.118

2.57294

8.13634

1.-7767

4.04532

8.71537

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6.63

43.9569

291.434

2.57488

8.14248

1.87861

4.04735

8.71976

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6.64

44.0-96

292.755

2.57682

8.14862

1.87956

4.04939

8.72414

.150602

6.65

44.2225

294.080

2.57876

8.15475

1.8*050

4.05142

8.72852

.150376

6.66

44.3556

295.408

2.58070

8.16088

1.88144

4.05345

8.73289

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6.67

44.4*89

296.741

2.58263

8.16701

1.8*239

4.05548

8.73726

.149925

6.68

44.6224

298.078

2.58457

8.17313

1.8*333

4.05750

8.74162

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6.69

44.7:>61 299.418

2. 5*650

8.17924

1.88427

4.05953

8.74598

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6.70

44.8900

300.763

2.58844

8.18535

1.88520

4.06155

8.75034

.149254

6.71

45.0241

302.112

2.59037

8.19146

1.88614

4.06357

8.75469

.149031

6.72

45.1584

303.464

2.59230

8.19756

1.88708

4.06558

8.75904

.14-10

6.73

45.2929

304.821

2.59422

8.20366

1.88801

4.06760

8.76338

6.74

45.1276 i 306.182

2.59615

8.20975

1.86896

4.06961

8.76772

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45.5625 307.547

2.59808

8.21584

1.88988

4.07163

8.77205

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6.76

45.6976 ! 308.916

2.60000

8.22192

1.89081

4.07364

8.77638

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6.77

45.8329

31(1 2-9

2.60192

8.22*00

1.89175

8.78071

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6.78

45.9684

311.666

1.60884

8.23408

4107765

8.78503

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6.79

46.1041

313.047

2.60576

8.24015

1 39861

4.07965

8.78935

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6.80

46.2400

314.432

2.60768

8.24621

1.89454

4.08166

8.79366

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6.81
6.32

46.3761
46.5124

315.821
317.215

2.60960
2.61151

8.25227

8.25833

1.89546
1.89689

4.08365

4.0*565

8.79797
8.80227

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.146628

6.83

46.6489

31*612 2.61343

8.26438

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6.84

46 7-56

320.014 2.61534

8.27043

1 .-•>•_' i

4.0*96*

8.81087

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6.85

46.9225

321.419

2.61725

8.27647

1.89917 4.09164

8.81516

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6.86

T.06M 322.829

2.61916

8.28251

1.90009 4.09362

8.81945

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6.87

7.1969 ".21.213 2.62107

8.2**55

1.90102 4.09561

8.82373

.145560

«.88

7.3344 325.661 2.62298

8.29458

1.90194 4.09760

8.82*01

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6.89

7.4721 827.083 2.62 l*s

8.30060

1.90286 4.09958

8.83229

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«.90

7.6100

328.509

2.62679

8.30662

1.90378

4.10157

8.83656

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6.91

7.7481

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2.62869

8.31264

1.90470

4.10355

8.84082

.144718

6>2

331.374 2.63059

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1.90562

4.10552

8.84509

.144509

6.93

2.63219

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1.90653

4.10750

8.84934

.144300

6.94

2.63439

H.33067

1.9H715

4.10948

8.85360

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6.95

4BJOSS

335.702

2.63629

8.33667

1.90837

4.11145

8.85785

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6.96

48.4416

337.154

263818

8.34266

1.90928

4.11342

8.86210

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6.97

48.5809 ' 338.609 2.6400*

8.34*65

1.91019

4.11539

H.86634

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6.98

140.068 2.6H97

8.35464

1.91111

4.11736

8.87058

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6.99

48.8601 i 341.532

8.36062

1.91202

4.11932

8.874*1

.143062

7.00

49.0000 343.000 2.64575

8.36660

1.91293

4.12129

8.87904

.142857

A/,1 THEM A TICS

23

n

11-

W3

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Mo n

4S

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1

n

7.01 49.1401

344.472

2.64764

8.37257

1.91384

4.12325

8.88327

.142653

7.02 49.2804

345.948

2.C4953

8.37854

1.91475

4.12521

8.88749

.142450

7.03

49.4209

347.429

2.65141

8.38451

1.91566

4.12716

8.89171

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7.04

49.5616

348.914

2.65330

8.39047

1.91657

4.12912

8.89592

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7.05

49.7025

350.403

2.65518

8.39643

1.91747

4.13107

8.90013

.141844

7.06

49.8436

351.896

2.65707

8.40238

1.91838

4.13303

8.90434

.141643

7.07

49.9849

353.393

2.65895

8.40833

1.91929

4.13498

8.90854

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7.08

50.1264

354.895

2 .6KOS3

8.41427

1.92019

4.13695

8.91274

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7.09

50.2681

356.401

2.66271

8.42021

1.92109

4.13887

8.91693

.141044

7.10

50.4100

357.911

2.66458

8.42615

1.92200

4.14082

8.92112

.140845

7.11

50.5521

359.425

2.66646

8.43208

1.92290

4.14276

8.92531

.140647

7.12

50.6944

360.944

2.66833 1 8.43801

1.92380

4.14470

8.92949

.140449

7.13

50.8369

362.467

2.67021 8.44393

1.92470

4.14664

8.93367

.140253

7.14

50.9796

363.994

2.67208

8.44985

1.92560

4.14858

8.93784

.140056

7.15

51.1225

365.526

2.67395

8.45577

1.92650

4.15051

8.94201

.139860

7.16

51.2656

367.062

2.67582

8.46168

1.92740

4.15245

8.94618

.139665

7.17

51.4089

368.602 2.67769

8.46759

1.92829

4.15438

8.95034

.139470

7.18

51.5524

370.146 2.67955

8.47349

1.92919

4.15631 j 8.95450

.139276

7.19

51.6961

371.695

2.68142

8.47939

1.93008

4.15824

8.95866

.139082

7.20

51.8400

373.248

2.68328

8.48528

1.93098

4.16017

8.96281

.138889

7.21

51.9841

374.805

2.68514

8.49117

1.93187

4.16209

8.96696

.138696

7.22

52.1284

376.367

2.68701

8.49706

1.9327i7

4.16402

8.97110

.138504

7 23

52.2729

377.933

2.6S887

8.50294

1.93366

4.16594

8.97524

.138315

7.24

52.4176

379.503

2.69072

8.50882

1.93455

4.16786

8.97938

.138122

7.25

52.5625

381.078

2.69258

8.51469

1.93544

4.16978

8.98351

.137931

7.26

52.7076

382.657

2.69444

8.52056

1.93633

4.17169

8.98764

.137741

7.27

52.8529

384.241

2.69629

8.52643

1.93722

4.17361

8.99176

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7.28

52.9984

385.828

2.69815

8.53229

1.93810

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8.99588

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7.29

53.1441

387.420

2.70000

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1.93899

4.17743

9.00000

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7.30

53.2900

389.017

2.70185

8.54400

1.93988

4.17934

9.00411

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7.31

53.4361

390.618

2.70370

8.54985

1.94076

4.18125

9.00822

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7.32

53.5824

392.223

2.70555

8.55570

1.94165

4.18315 9.01283

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7.33

53.7289

393.833

2.70740

8.56154

1.94253

4.18506 1 9.01643

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7.34

53.8756

395.447

2.70924

8.56738

1.94341

4.18696

9.02053

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7.35

54.0225

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9.02462 .136054

7.36

54.16%

398.688

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8.57904

1.94518

4.19076 9.02871

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7.37 | 54.3169

400.316

2.71477

8.58487

1.94606

4.19266 9.03280

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7.3s 54.4644

401.947

2.71662

8.59069

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4.19455

9.03C89

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7.39

54.6121

403.583

2.71846

8.59651

1 .94782

4.19644

9.04097

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7.40 54.7600

405.224

2.72029

8.60233

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4.19834

9.04504

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7.41 54.9081

406.869 2.72213

8.60814

1.94957

4.20023

9.04911

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7.42 55.0564

408.518 2.72W7

8.61394

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9.05318

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411.831 2.72764

8.62554

1 ."5220

4.80689

9.06131

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7.45 55.5025

413.494 2.72947

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7.46 55.6516

415.161

2.73130 *.63713 1.95395

4.20965

9.06942

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7.47 55.8009

416.833

2.73313 8.64292 1.95482 4.21153 9.07347

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7.48 55.9504

418.509

2.73496 8.641*70 1.95569 4.21341 j 9.07752

.133690

7.49 56.1001

420.190 2.73679 8.65448 1.95656 4.21529 9.08156

.133511

7.50

56.2500

421.875 2.73861 8.66025 1.95743 4.21716

9.08560

.133333

MATHEMATICS

n

n«

na

1K

VlCfn

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k

7.51

56.4001

423.565

2.74044

8.66603

1.95830

4.21904

9.08964

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7.52

56.5504

425.259

2.74226

8.67179

1.95917

4.22091

9.09367

.132979

7.53

56.7009

426.958

2.74408

8.67756

1.96004

4.22278

9.09770

.132802

7.54

56.8516

428.661

2.74591

8.68332

1.96091

4.22465

9.10173

.132626

7.55

57.0025

430.369

2.74773

8.68907

1.96177

4.22651

9.10575

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T.56

57.1536

432.081

2.74955

8.69483

1.96264

4.22838

9.10977

.132275

7.57

57.3049

433.798

2.75136

8.70057

1.96350

4.23024

9.11378

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7.58

57.4564

435.520

2.75318

8.70632

1.96437

4.23210

9.11779

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7.59

57.6081

437.245

2.75500

8.71206

1.96523

4.23396

9.12180

.131752

7.60

57.7600

438.976

2.75681

8.71780

1.96610

4.23582

9.12581

.131579

7.61

57.9121

440.711

2.75862

8.72353

1.96696

4.23768

9.12981

.131406

7.62

58.0644

442.451

2.76043

8.72926

1.96782

4.23954

9.13380

.131234

7.63

58.2169

444.195

2.76225

8.73499

1.96868

4.24139

9.13780

.131002

7.64

58.3696

445.994

2.76405

8.74071

1.96954

4.24324

9.14179

.130i90

7.65

58.5225

447.697

2.76586

8.74643

1.97040

4.24509

9.14577

.130719

7.66

58.6756

449.455

2.76767

8.75214

1.97126

4.24694

9.14976

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7.67

58.8289

451.218

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8.75785

1.97211

4.24179

9.15374

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7.68

58.9824

452. 9K5

2.77128

8.76356

1.97297

4.25063

9.15771

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7.69

59.1361

454.757

2.77308

8.76926

1.97383

4.25M8

9.16169

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7.70

59.2900

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9.16566

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7.71

59.4441

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7.72

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K.7NJ35

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4.26351

9.18545

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7.76

60.2176

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7.77

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7.78

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7.79

60.6841

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60.8400

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60 .9%!

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8.81*73

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4.27995 1 9.22087

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7.86

61.7796

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7.87

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7.89

62.2521

491.169

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8.HH257

1.99079

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9.24043

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7.90

62.4100

493.039

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8.88819

1.99163

4.29084

9.24433

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7.91

62.5681

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7.92

62.7264

4!t6.7!>3

2.81425

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1.99331

4.29446

9.25213

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7.93

62.8849

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1.99415

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7.94

63.o4:m

500.566

2.H17M)

8.9KH17

1.99499

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7.95

63.2025

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9.26380

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7.96

63.3616

504.358

2.82135

8.92188

1.99666

4.30168

9.26768

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7.97

63.5209

506.262

2.82312

8.92749

1.99750

4.30348

9.27156

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7.98

63.6804

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1.99*33

4.30528

9.27544

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7.99

63.M401

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2.KJIK16

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1.99917

4.30707

9.27931

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8.00

64.0000

512.000

2.82843

3.94427

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9.28318

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MATHEMATICS

25

71

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ns

1ft

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lm

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1

n

8.01

64.1601

513.922

2.83019

8.94986

2.00083

4.31066

9.28704

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8.02

64.3204

615.850

2.83196

8.95545

2.00167

4.31246

9.29091

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8.03

64.4809

517.782

2.83373

8.96103

2.00250

4.31425

9.29477

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8.04

64.6416

519.718

2.83549

8.96660

2.00333

4.31604

9.29862

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8.05

64.8025

521.660

2.83725

8.97218

2.00416

4.31783

9.30248

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8.06

64.9636

523.607

2.83901

8.97775

2.00499

4.31961

9.30633

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8.07

65.1249

525.558

2.84077

8.98332

2.00582

4.32140

9.31018 I .123916

8.08

65.2864

527.514

2.84253

8.98888

2.00664

4.32818

9.31402

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8.09

65.4481

529.475

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8.99444

2.00747

4.32497

9.31786

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8.10

65.6100

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9.00000

2.00830

4.32675

9.32170

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8.11

65.7721

633.412

2.84781

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2.00912

4.32853

9.32553

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8.12

65.9344

535.387

2.84956

9.01110

2.00995

4.S3031

9.32936

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8.13

66.0969

537.368

2.85132

9.01665

2.01078

4.33208

9.33319

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8.14

66.2596

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9.02219

2.01160

4.33386

9.33702

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8.15

66.4225

641.343

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9.02774

2.01242

4.33563

9.34084

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8.16

66.5856

543.338

2.85657

9.03327

2.01325

4.33741

9.34466

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8.17

66.7489

545.339

2.85832

9.03881

2.01407

4.33918

9.34847

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8.18

66.9124

547.343

2.86007

9.04434

2.01489

4.34095

9.35229

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8.19

67.0761

549.353

2.86182

9.04986

2.01571

4.34272

9.35610

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8.20

67.2400

551.368

2.86356

9.05539

2.01653

4.34448

9.35990

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8.21

67.4041

553.388

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9.06091

2.01735

4.34625

9.36370

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8.22

67.5684

555.412

2.86705

9.06642

2.01817

4.34801

9.36751

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8.23

67.7329

557.442

2.86880

9.07193

2.01899

4.34977

9.37130

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8.24

67.8976 559.476

2.87054

9.07744

2.01980

4.35153

9.37610

.121359

8.25

68.0625

561.516

2.87228

9.08295

2.02062

4.35329

9.37889

.121212

8.26

68.2276

563.560

2.87402

9.08845

2.02144

4.35505

9.38268

.121065

8.27

68.3929

565.609

2.87576

9.09395

2.02225

4.35681

9.38646

.120919

8.28

68.5584

567.664

2.87750

9.09945

2.02307

4.35856

9.39024

.120773

8.29

68.7241

569.723

2.87924

9.10494

2.02388

4.36032

9.39402

.120627

8.30

68.8900

571.787

2.88097

9.11043

2.02469

4.36207

9.39780

.120482

8.31

69.0561

573.856

2.88271

9.11592

2.02551

4.36382

9.40157

.120337

8.32

69.2224

575.930

2.88444

9.12140

2.02632

4.36557

9.40534

.120192

8.33

69.3889

578.010

2.88617

9.12688

2.02713

4.36732

9.40911

.120048

8.34

69.5556

580.094

2.88791

9.13236

2.02794

4.36907

9.41287

.119904

8.35

69.7225

582.183

2.88%4

9.13783

2.02875

4.37081

9.41663

.119761

8.36

69.88%

584.277

2.89137

9.14330

2.02956

4.37255

9.42039

.119617

8.37

70.0569

586.376

2.89310

9.14877

2.03037

4.37430

9.42414

.119474

8.38

70.2244

588.480

2.89482

9.15423

2.03118

4.37604

9.42789

.119332

8.39

70.3921

590.590

2.89655

9.15969

2.03199

4.37778

9.43164

.119190

8.40

70.5600

592.704

2.89828

9.16515

2.03279

4.37952

9.43539

.119048

8.41

70.7281

594.823

2.90000

9.17061

2.03360

4.38126

9.43913

.118906

8.42

70.8964

596.948

2.90172

9.17606

2.03440

4.38299

9.44287

.118765

8.43

71.0649

599.077

2.90345

9.18150

2.03521

4.38473

9.44661

.118624

8.44

71.2336

601.212

2.90517

9.18695

2.03601

4.38646

9.45034

.118483

8.45

71.4025

603.351

2.90689

9.19239

2.03682

4.38819

9.45407

.118343

8.46

71.5716

605.4%

2.90861

9.19783

2.03762

4.38992

9.45780

.118203

8.47

71.7409

607.645

2.91033

9.20326

2.03842

4.39165

9.46152

.118064

8.48

71.9104

609.800

2.91204

9.20869

2.03923

4.39338

9.46525

.117925

8.49

72.0801

611.960

2.91376

9.21412

2.04003

4.39511

9.46897

.117786

8.50

72.2500

614.125

2.91548

9.21954

2.04083

4.39683

9.47268

.117647

MATHEMATICS

n

n*

W'

V^

.VlOn

^

•fton

-^00 n

I

n

8.51

72.4201

616.295

2.91719

9.22497

2.04163

4.39855

9.47640

.117509

8.52

72.5904

618.470

2.91890

9.2303*

2.04243

4.40028

9.4X011

.117371

8.53

72.7609

620.650

2.92062

9.23580

2.04323

4.40200

9.48381

.117233

8.54

72.9316

622.836

2.92233

9.24121

2.04402

4.40372

9.48763

.117096

8.55

73.1025

625.026

2.92404

9.24662

2.04482

4.40543

9.49122

.116959

8.56

73.2736

627.222

2.92575

9.25203

2.04562

4.40715

9.49492

.116822

8.57

73.4449

629.423

2.92746

9.25743

2.04641

4.40887

9.49*61

.110686

8.58
8.59

73.6164
73.7881

631 .629
633.840

2.92916
2.93087

9.26283
9.26823

2.04721
2.04801

4.41058 1 9.50231
4.41229 9.50000

.116550
.116414

8.60

73.9600

636.056

2.93258

9.27362

2.04880

4.41400

9.50969

.116279

8.61

74.1321

638.277

2.93428

9.27901

2.04959

4.41571

9.51337 ! .116144

8.62

74.3044

640.504

2.93598

9.2*440

2.05039

4.41742

9.51705 1 .116009

8.63

74.4769

642.736

2.93769

9.2*978

2.05118

4.41913

9.52073 .115875

8.64

74.6196

644.973

2.93939

9.29516

2.05197

4.42084

9.52441

.115741

8.65

74.8225

647.215

2.94109

9.30054

2.05276

4.42254

9.52808

.115607

8.66

74.9956

649.462

2.94279

9.30591

2.05355

4.42425

9.53175

.115473

8.67

75.1689

651.71 4

2.94449

9.31128

2.05434

4.42595

9.53542

.115340

8.68

75.3424

653.972

2.94618

9.31665

2.05513

4.42765

9.68908

.115207

8.69

75.5161

656.235

2.94788

9.32202

2.05592

4.42988

9.54274

.115075

8.70

75.6900

658.503

2.94958

9.32738

2.05671

4.43105

9.54640

.114943

8.71

75.8641

660.776

2.95127

9.33274

2.05750

4.43274

9.55006

.114811

8.72

76.0384

663.055

2.95296

9.33*09

2.05828

4.43444

9.55371

.114679

8.73

76.2129

665.339

2.95466

9.34345

2.05907

4.43614

9.66786

.114548

8.74

76.3876

667.628

2.95635

9.3i>*o

2.05986

4.48789

9.56101

.114417

8.75

76.5625

669.922

2.95804

9.35414

2.06064

4.43952

9.56466

.114286

8.76

76.7376

672.221

2.95973

9.35949

2.06143

4.44121

9.56830

.114155

8.77

76.9129

674.526

2.96142

9.364*3

2.06221

4. 11290

9.57194

.114025

8.78

77.0*84

2.96311

9.37017

2.06299

4.44459

9.57557

.113*95

8.79

77.2641

679.151

2.96479

9.37550

1.06378

4.44091

9 57921

.113766

8.80

77.4400

f,.-1.472

2.96648

9.38083

2.06456

4.44796

9.58284

.113636

8.81

77.6161

683.798

2.96816

9.38616

2.06534

4.44964

9.58647

.113507

8.82

77.7921

nun

0.89149

2.06612

4. 4 5133

9.69009

.113379

8.83

77.9689

68*. 465

2.97153

9.396*1

2.06690

4.45301

9.59372

.113250

8.84

78.1456

690.807

2.97321

9.40213

2.06768

I.4846S

9.59784

.113122

8.85

78.3225

693.154

2.97489

9.40744

2.06846

4.45637

9.60095

.112994

8.86

78.4996

695.506

2.97658

9.41276

2. 0692 I

4.45805

9.60457

.112867

8.87

78.6769

697.864

2.97*25

9.41807

•2 07002

4.45972

9.00818

.112740

8.88

700.227

2. 97993

9.4233H

2.070*0

4.46140

9.61179

.112613

8.89

79.o:-,2i

702.595

2.98161

9.42*6*

2.07157

4.46307

9.61540

.112486

8.90

79.2100

704.969

2.98329

9.43398

2.07235

4.46474

9.61900

.112360

8.91

79.3-M

707.348

2.98496

9.43928

2.07313

4.46642

9.62260

.112233

8.92

79.5664

709.7:12

2 9-061

9.i4i5*

2.07390

4.46-09

9 62620

.112108

8.93

79.7449

712.122

9.44981

2.07468

4.16976

9.63980

.1119*2

8.94

79.9236

714.617

MOM

9.45516

1.07648

4.47142

9.63339

.111*57

8.96

MM If.';-)

716.917

2.99166

9.46044

2.07622

4.47309

9.63698

.111732

8.96

80.2816

719.323

2.99333

9.46573

2.07700

4.47476

9.64067

.111607

8.97

*o.n;o9

7'-' 1. 734

2.99500

9.47101

2.07777

4.47642

9.64415

.111483

8.98

80.6404

7-Jt.ir,i

2.990(,0

9.47629

9.64774

.111359

8.99

MI>1'01

726.573

9.481M

2.o:9:il

4.47974

9.6S132

.111236

9.00

81.0000

729.000

3.00000

2.0*00*

4.48140

9.65489

.111111

MATHEMATICS

•21

n

W2

7l3

^

Vio^i

«

fto^

•^100 n

2,

n

9.01

81.1801

731.433

3.00167

9.49210

2.08085

4.48306

9.65847

.110988

9.02

81.3604 733.871

3.00333

9.49737

2.08162

4.48472

9.66204

.110865

9.03

81.5409

736.314

3.00500

9.50263

2.08239

4.48638

9.66561

.110742

9.01

81.7216

738.763

3.00666

9.50789

2.08316

4.48803

9.66918

.110620

9.05

81.9025

741.218

3.00832

9.51315

2.08393

4.48968

9.67274

.110497

9.06

82.0836

743.677

3.00998

9.51840

2.08470

4.49134

9.67630

.110375

9.07

82.2649

746.143

3.01164

9.52365

2.08546

4.49299

9.67986

.110254

9.08

82.4464

748.613

3.01330

9.52890

2.08623

4.49464

9.68342

.110132

9.09

82.6281

751.089

3.01496

9.53415

2.08699

4.49629

9.68697

.110011

9.10

82.8100

753.571

3.01662

9.53939

2.08776

4.49794

9.69052

.109890

9.11

82.9921

756.058

3.01828

9.54463

2.08852

4.49959

9.69407

.109770

9.12

83.1744

758.551

3.01993

9.54987

2.08929

4.50123

9.69762

.109649

9.13

83.3569

761.048

3.02159

9.55510

2.09005

4.50288

9.70116

.109529

9.14

83.5396

763.552

3.02324

9.56033

2.09081

4.50452

9.70470

.109409

9.15

83.7225

766.061

3.02490

9.56556

2.09158

4.50616

9.70824

.109290

9.16

83.9056

768.575

3.02655

9.57079

2.09234

4.50780

9.71177

.109170

9.17

84.0889

771.095

3.02820

9.57601

2.09310

4.50945

9.71531

.109051

9.18

84.2724

773.621

3.02985

9.58123

2.09386

4.51108

9.71884

.108933

9.19

84.4561

776.152

3.03150

9.58645

2.09462

4.51272

9.72236

.108814

9.20

84.6400

778.688

3.03315

9.59166

2.09538

4.51436

9.72589

.108696

9.21

84.8241

781.230

3.03480

9.59687

2.09614

4.51599

9.72941

.108578

9.22

85.0084

783.777

3.03645

9.60208

2.09690

4.51763

9.73293

.108460

9.23

85.1929

786.330

3.03809

9.60729

2.09765

4.51926

9.73645

.108342

9.24

85.3776

788.889

3.03974

9.61249

2.09841

4.52089

9.73996

.108225

9.25

85.5625

791.453

3.04138

9.61769

2.09917

4.52252

9.74348

.108108

9.26

85.7476

794.023

3.04302

9.62289

2.09992

4.52415

9.74699

.107991

9.27

85.9329

796.598

3.04467

9.62808

2.10068

4.52578

9.75049

.107875

9.28

86.1184

799.179

3.04631

9.63328

2.10144

4.52740

9.75400

.107759

9.29

86.3041

801.765

3.04795

9.63846

2.10219

4.52903

9.75750

.107643

9.30

86.4900

804.357

3.04959

9.64365

2.10294

4.53065

9.76100

.107527

9.31

86.6761

806.954

3.05123

9.64883

2.10370

4.53228

9.76450

.107411

9.32

86.8624

809.558

3.05287

9.65401

2.10445

4.53390

9.76799

.107296

9.33

87.0489

812.166

3.05450

9.65919

2.10520

4.53552

9.77148

.107181

9.34

87.2356

814.781

3.05614

9.66437

2.10595

4.53714

9.77497

.107066

9.35

87.4225

817.400

3.05778

9.66954

2.10671

4.53876

9.77846

.106952

9.36

87.6096

820.026

3.05941

9.67471

2.10746

4.54038

9.78195

.106838

9.37

87.7969

822.657

3.06105

9.67988

2.10821

4.54199

9.78543

.106724

9.38

87.9844

825.294

3.06268

9.68504

2.10896

4.54361

9.78891

.106610

9.39

88.1721

827.936

3.06431

9.69020

2.10971

4.54522

9.79239

.106496

9.40

88.3600

830.584

3.06594

9.69536

2.11045

4.54684

9.79586

.106383

9.41

88.5481

833.238

3.06757

9.70052

2.11120

4.54845

9.79933

.106270

9.42

88.7364

835.897

3.06920

9.70567

2.11195

4.55006

9.80280

.106157

9.43

88.9249

838.562

3.07083

9.71082

2.11270

4.55167

9.80627

.106045

9.44

89.1136

841.232

3.07246

9.71597

2.11344

4.55328

9.80974

.105932

9.45

89.3025

843.909

3.07409

9.72111

2.11419

4.55488

9.81320

.105820

9.46

89.4916

846.591

3.07571

9.72625

2.11494

4.55649

9.81666

.105708

9.47

89.6809

849.278

3.07734

9.73139

2.11568

4.55809

9.82012

.105597

9.48

89.8704

851.971

3.07896

9.73653

2.11642

4.55970

9.82357

.105485

9.49

90.0601

854.670

3.08058

9.74166

2.11717

4.56130

9.82703

.105374

3.50

90.2500

857.375

3.08221

9.74679

2.11791

4.56290

9.83048

.105263

28

MA THEM A TICS

n

71*

n3

V^

VlOn

ft

•fton

«S55| i

9.51

90.4401

860.085

3.08383

9.75192

2.11865

4.56450

9.83392

.105153

9.52

90.6304

862.801

3.08545

9.75705

2.11940

4.56610

9.83737

.105042

9.53

90.8209

865.523

3.08707

9.76217

2.12014

4.56770

9.84081

.104932

9.54

91.0116

868.251

3.08869

9.76729

2.12088

4.56930

9.84425

.104822

9.55

91.2025

870.984

3.09031

9.77241

2.12162

4.57089

9.84769

.104712

9.56

91.3936

873.723

3.09192

9.77753

2.12236

4.57249

9.85113

.104603

9.57

91.5849

876.467

3.09354

9.78264

2.12310

4.57408

9.85456

.104493

9.58

91.7764

879.218

3.09516

9.78775

2.12384

4.57568

9.85799

.104384

9.59

91.9681

881.974

3.09677

9.79285

2.12458

4.57727

9.86142

.104275

9.60

92.1600

884.736

3.09839

9.79796

2.12532

4.57886

9.86485

.104167

9.61

92.3521

887.504

3.10000

9.80306

2.12605

4.58045

9.86827

.104058

9.62

92.5444

890.277

3.10161

9.80816

2.12679

4.58203

9.87169

.103950

9.63

92.7369

893.056

3.10322

9.81326

2.12753 4.58362

9.87511

.103842

9.64

92.9296

895.841

3.10483

9.81835

2.12826 4.58521

9.87853

.103734

9.65

93.1225

898.632

3.10644

9.82344

2.12900

4.58679

9.88195

.103627

9.66

93.3156

901.429

3.10805

9.82853

2.12974

4.58838

9.88536

.103520

9.67

93.5089

904.231

3.10966

9.«3:it>2

2.13047

4.58996

9.88877

.103413

9.68

93.7024

907.039

3.11127

9.83870

2.13120

4.59154

9.89217

.103306

9.69

93.8961

909.853

3.11288

9.84378

2.13194

4.59312

9.89558

.103199

9.70

94.0900

912.673

3.11448

9.84886

2.13267

4.59470

9.89898

.103093

9.71

94.2841

915.499

3.11609

9.85393

2.13340

4.59628

9.90238

.102987

9.72

94.4784

918.330

3.11769

9.85901

2.13414

4.59786

9.90578

.102881

9.73

94.6729

921.167

3.11929

9.S6408

2.13487

4.59943

9.90918

.102775

9.74

94.8676

924.010

3.12090

9.86914

2.13560

4.60101

9.91257

.102669

9.75

95.0625

926.859

3.12250

9.87421

2.13633

4.60258

9.91596

.102564

9.76

95.2576

929.714

3.12410

9.87927

2.13706

4.60416

9.91935

.102459

9.77

95.45-29

932.575

3.12570

9.88433

2.13779

4.60573

9.92274 j .102354

9.78

95.6484

935.441

3.12730

9.88939

2.13852

4.60730

9.92612

.102250

9.79

95.8441

938.314

3.12890

9.89444

2.13925

4.60887

9.92950

.102145

9.80

96.0400

941.192

3.13050

9.89949

2.13997

4.61044

9.93288

.102041

9.81

96.2361

944.076

3.13209

9.90454

2.14070

4.61200

.101937

9.82

96.4324

946.966

3.13369

9.90959

2.14143

4.61357

9.93'.t«4 .101833

9.83

96.62*9

949.862

3.13528

9.91464

2.14216

4.61513

9.94801 .101729

9.84

96.*256

952.764

3.136*8

9.91968

2.14288

4.61670

9.94638 .101626

9.85

97.0225

955.672

3.13847

9.92472

2.14361

4.61826

9.94975

.101528

9.86

97.2196

958.585

3.14006

9.92975

2.14433

4.61983

9.95311

.101420

9.87

97.4169

961.505

3.14166

9.93479

2.14506

4.62139

0.96648

.101317

9.88

97.6144

964.430

3.14325

9.93982

2.14578

4.62295

9.95984

.101215

9.83

97.8121

967.362

3.144H4

9.94485

2.14651

4.62451

9.96320

.101112

9.90

98.0100

970.299

3.14643

9.94987

2.14723

4.62607

9.96655

.101010

9.91

98.2081

973.242

3.14802

9.95490

2.14795

4.62762

9.96991

.100908

9.92

98.4064

976.191

3.14960

9.95992

2.14867

4.62918

9.97326

.100807

9.93

98.6049

979.147

3.15119

9.96494

2.14940

4.63073

9.97661

.100705

9.94

9H.H036

982.108

3.15278'

9.96995

2.15012

4.63229

9.97996

.100604

9.95

99.0025

985.075

3.15436

9.97497

2.15084

4.63384

9.98331

.100503

9.96

99.2016

988.048

3.15595

9.97998

2.15156

4.63539

9.98665

.100402

9.97

99.4009

991.027

3.15753

<t.98499

2.15228

4.63694

<».98999

.100301

9.98

99.6004

994.012

3 15911

9.9*999

2.15300

4.63849

9.99333

.100200

0.99

99.*001

997.003

3.16070

9.99.MK)

2.15372

4.64004

9.99667

.100100

10.00

100.000

1000.00

3.16228

10.0000

2.15443

4.64159

10.0000

.100000

MATHEMATICS 29

FORMULAS

A formula is a brief statement of a rule, in which letters or
other symbols are used to denote the different quantities
involved. For example, the rule for finding the volume of a
rectangular prism is as follows: The volume of a rectangular
prism is equal to the product of the length, width, and height of
the prism. If the dimensions of the prism are taken in inches,
the volume will be in cubic inches; if they are taken in feet,
the volume will be in cubic feet; and so on. Suppose, however,
that the volume is denoted by v, the length by I, the width
by w, and the height by h. Then, the foregoing rule may
be stated much more simply and concisely by the formula
v = lXwXh. This formula indicates that the volume v is
equal to the product of the length I, the width w, and the height
h of the prism. Where several letters are multiplied together
in a formula, it is customary to omit the multiplication signs,
the multiplication then being taken for granted. The fore-
going formula, therefore, would ordinarily be written v = lwh,
The multiplication sign must not be omitted between numbers
that are to be multiplied together.

As may be seen from the example just given, a formula
consists of two parts separated by the sign of equality. The
letters or symbols denoting the quantities that are known are
usually placed at the right of the equality sign, and the letter
or symbol designating the value to be found is placed at the
left of the equality sign. To apply a formula to the solution
of an example a numerical value is substituted for each letter
that denotes a known quantity, and the indicated mathematical
operations are then performed. Care must be observed, in
using a formula, to have all weights, dimensions, or other
values expressed in the units required by the formula.

Letters with additional marks, such as O ', a", di, Ta, etc.,
are often found in formulas when similar quantities are to be
represented by the same letter and yet to be distinguished
from one another. The marks ' " are termed prime and
second, respectively, and the marks i and a are termed sub-
scripts or subs. The four examples just given are read large
C prime, a second, d sub one, and large T sub a. Parentheses
4

30 MA THEM A TICS

and brackets are used in formulas to indicate that the quan-
tities enclosed by them are to be subjected to the same opera-
tion. The sign — before an expression in parentheses or
brackets affects the entire expression, and if the parentheses or
brackets are removed, the signs + and — within them must
be interchanged; but if the sign + precedes the brackets,
they may be removed without changing any signs. For
example, the expression 212— (36+75 — 49) becomes, when
the parentheses are removed, 212-36-75+49; but the
removal of the brackets from the expression 65 + [20 +9— 14]
gives 65+20+9 — 14. The multiplication sign is ordinarily
omitted before and after parentheses or brackets, and before
the radical sign; thus, the expressions 36 X( 18 +22) ,[760 — 315J
X1.07, and .21 X VT40 — 27 would ordinarily be written
36(18+22), [760-315]1.07, and .21A/140-27. The following
examples will serve to illustrate the use of formulas.

EXAMPLE. — What is the volume of a block of cast iron 28 in.
long, 15 in. wide, and 12 in. high?

SOLUTION. — Applying the formula previously given, and
substituting 28 for /, 15 for w, and 12 for h, the volume is
r = 28X15X12 = 5,040cu. in.

One of the most familiar formulas, to the operating engineer,
is that used for finding the indicated horsepower of an engine.
This formula, as usually stated, is

PLAN

33,000

in which H = indicated horsepower;

P = mean effective pressure on piston, in pounds per
square inch;

L = length of stroke, in feet;

A =area of piston, in square inches;

N = number of working strokes per minute.
The formula as stated may be used to find the horsepower
of any engine, provided the values of the quantities denoted
by P, L, A, and N are known. But sometimes it is desired
to find some other quantity, as for example, the diameter of
cylinder required to produce a certain horsepower, or the mean
effective pressure necessary to produce the desired power.

MATHEMATICS 31

To find these quantities, the, order of the terms in the fore-
going formula must be altered, bringing the values to be
found to the left of the equality sign and the remainder to
the right. This operation is called a transformation of a
formula. The horsepower formula, transformed so as to give
the values of the piston area and the mean effective pressure
necessary to produce a desired horsepower, are

33,0007?
= PLN
and

33.00Qg

LAN

EXAMPLE. — Find the diameter of the piston of a steam engine
that is designed to produce 40 H. P., if the stroke is 30 in.,
the mean effective pressure is 28 Ib. per sq. in., and the speed
is 75 R. P. M.

SOLUTION. — The length of stroke in feet is L = 30-=-12
= 2.5 ft.; the mean effective pressure is P — 2S Ib. per sq. in.;
as there are two working strokes to each revolution, 2V = 2X75
= 150; and // = 40. Substituting these values in the formula
for the area of the piston,

33,000X40

The diameter of a circle having an area of 125.7 sq. in, is
about 12f in. The required diameter of the piston, or of the
cylinder, therefore, is 12| in.

If a segment of a circle is not greater than a semicircle, its
area may be found by the formula

irrzE c

A= --- (r-h),
360 2

in which A = area of segment ;
7r = 3.1416;
r = radius of circle;

E = angle, in degrees, obtained by drawing lines from
the center to the extremities of arc of segment;
c = chord of segment;
h = height of segment.

52 MA THEM A TICS

EXAMPLE. — A segment of a circle having a radius of 7.5 in.
is 1.91 in. high and its chord is 10 in. long. If the angle
subtended by the chord is 83.46°, what is the area of the
segment?

SOLUTION. — Substituting the given values in the foregoing
formula,

3.1416X7.52X83.46 10
360 2

= 40.97 — 27.95 = 13.02 sq. in., nearly.

If the lengths of the sides of a triangle are known, the area
may be found by the formula
b

in which A denotes the area of the triangle and a, b, and c
•denote the lengths of the three sides.

EXAMPLE. — What is the area of a triangle whose sides are
21 ft., 46 ft., and 50 ft. long?

SOLUTION. — In order to apply the formula, let a represent
the side that is 21 ft. long; b, the side that is 50 ft. long; and
-c, the side that is 46 ft. long. Then, substituting in the
formula,
50

_

= 25 V441 -8.252 = 25 \441 - 68.0625 = 25 \372.9375

= 25X19.312 = 482.8 sq. ft., nearly.

EXAMPLE.— When x = 8 and y = 6, what is the value of m in
the following: _

SOLUTION. — Substituting,
m

4X8X6
16+2.02 = 18.02

MA THEM A TICS

33

MENSURATION

MEANINGS OF SYMBOLS

In the following formulas, the letters have the meanings
here given, unless otherwise stated:
D = larger diameter;
d = smaller diameter;
R — radius corresponding to D ;
r = radius corresponding to d\
p — perimeter or circumference ;
C = area of convex surface = area of flat surface that can be

rolled into the shape shown;

5 = area of entire surf ace = C+ area of the end or ends;
A = area of plane figure ;
IT = 3. 1416, nearly = ratio of circumference of any circle to

its diameter;
V = volume of solid.
The other letters used will be found on the illustrations.

TRIANGLES

Using letters to denote the angles,
D =B+C
B =D-C

E' = E B' = B

For a right triangle, c being the hypotenuse,

If c = length of side opposite an
acute angle of an oblique triangle,
and the distance e is known,

-2be
h

If c = length of side opposite an obtuse angle
of an oblique triangle,

34

MA I II EM A TICS

Any triangle inscribed in a semicircle is a right triangle, and

c:b = a:h
fci\«. J

ab ce
c a

For any triangle,

2b

A1so. A =

in which s=$(a+b + c).

- a) (s - b) (s - c)

RECTANGLE AND PARALLELOGRAM

-7 A = ab

TRAPEZOID

TRAPEZIUM

Divide the figure into two triangles and a trapezoid; then,

or, A = \[bh'

Or, divide into two triangles by drawing a
diagonal. Considering the diagonal as the base
of both triangles, call its length /, and call
the altitudes of the triangles hi and fo; then,

REGULAR POLYGONS

Divide the polygon into equal triangles and
find the sum of the partial areas. Otherwise,
square the length of one side and multiply by
proper number from the following table:

MATHEMATICS

35

Name
Triangle

No.
Sides
3

Multi-
plier
.433

Name
Heptagon. .

No.
Sides

7

Multi-
plier
3.634

Square

4

1.000

Octagon

8

4.828

Pentagon

5

1.720

Nonagon. . .

9

6.182

Hexagon

6

2.598

Decagon . . .

.. 10

7.694

IRREGULAR AREAS

Divide the area into trapezoids, triangles, parts
of circles, etc., and find the sum of the partial
areas.

If the figure is very irregular, the approximate
area may be found as follows: Divide the figure
into trapezoids by equidistant parallel lines b, c, d,
etc., and measure the lengths of these lines. Then,
calling a the first and n the last length, and y the width of strips,

SECTOR

If I denotes the length of the arc, and E* the angle in degrees
and decimals of a degree,

Er

•• .0175 Er, nearly

V

Then,

57.296

A = -- = .008727r2£
360

CIRCLE

*If the angle E is stated in degrees, minutes, and seconds,
the minutes and seconds must be reduced to decimals of a
degree. To do this, divide the number of minutes by 60 and
the number of seconds by 3,600 and add the sum of the quo-
tients to the number of degrees. Thus, 28° 42' 18" = 28
8+.7+.005 = 28.7050.

36 MATHEMATICS

= 3.5449 ^A
2A 4A >

RING

77
4

SEGMENT
A = Wr-c(r-h)}

>^-°™E
B.«!!.WW-

wr r

ELLIPSE

P*-»Y

£)2-|_d2 (D-d)*

8.8

A = -Z?d = .7854Dd

CYLINDER

C = 7rdA

S = 2nrh+2*r*

4 7T

*The perimeter of an ellipse cannot be exactly determined
without a very elaborate calculation, and this formula is
merely an approximation giving close results.

MATHEMATICS

37

FRUSTUM OF CYLINDER

h = 5 sum of greatest and least heights

= Trdh+-d2+area of elliptic top

PRISM OR PARALLELOPIPED

C = Ph

S = Ph+2A

For prisms with regular polygons as
bases, P — length of one side X number of sides.

To obtain area of base, if it is a polygon, divide it into tri-
angles and find sum of partial areas.

FRUSTUM OF PRISM

If a section perpendicular to the edges is a
triangle, square, parallelogram, or regular poly-

gon, V

sum of lengths of edges

number of edges

— X area of right

section.

SPHERE

= 4.1888r3

CIRCULAR RING

D = mean diameter;
R = mean radius.

V = 27r2#r2 = 2.4674Dd2
WEDGE

MATHEMATICS

CIRCUMFERENCES AND AREAS OF CIRCLES FROM
1-64 TO 100

Diam.

Circum .

Area

Diam.

Circum.

Area

A

.0491

.0002

4

12.5664

12.5664

A

.0982

.0008

*i

12.9591

13.3641

A

.1963

.0031

4:

13.3518

14.1863

.3927

.0123

4

13.7445

15.0330

TS

.5890

.0276

4

14.1372

15.9043

£

.7854

.0491

4

14.5299

16.8002

-fg

.9817

.0767

4

14.9226

17.7206

•

1.1781

.1104

4

•

15.3153

18.6555

JL

1.3744

.1503

5

15.7080

19.6350

I

1.5708

.1963

5j

16.1007

20.6290

JL

1.7671

.2485

5

16.4934

21.6476

I

1.9635

.3068

5

16.8861

22.6907

1 h

2.1598

.3712

5

17.2788

23.7583

•

2.3562

.4418

5

17.6715

24.8505

H

2.5525

.5185

5

18.0642

25.9673

£

2.7489

.6013

5

18.4569

27.1086

! •'

2.9452

.6903

6

18.8496

28.2744

1

3.1416

.7854

61

19.2423

29.4648

l

3.5343

.9940

6

19.6350

30. (1797

3.9270

1.2272

6

20.0277

31.9191

4.3197

1.4849

6J

20.4204

33.1831

4.7124

1.7671

6

20.8131

3-1.-4717

5.1051

2.0739

61

21.2058

35.7848

5.4978

2.4053

6

21.5985

37.1224 "

5.8905

2.7612

7

21.9912

38.4846

2

6.2832

3.1416

7

22.3839

39.8713

2

6.6759

3.5466

7

22.7766

41.2826

2

7.0686

3.9761

7

23.1693

42.7184

2

7.4613

4.4301

7

23.5620

44.1787

2

7.8540

4.9087

7

23.9547

•{.->. <;<;;w

2

8.2467

5.4119

7-

24.3474

47.173]

2

8.6394

5.9396

7

•

24.7401

48.7071

2

9.0321

6.4918

8

25.1328

50.2656

3

9.4248

7.0686

8}

255255

51.8487

3

9.8175

7.6699

8

25.9182

53.4563

3

10.2102

8.2958

8^

26.3109

55.0884

3

10.6029

8.9462

8^

26.7036

56.7451

3

10. w-,r,

9.6211

8!

27.0963

58.4264

3

1 l 3883

10. :•(_'<)»)

8;

27.4890

60.1322

3

11.7810

11.0447

8

27.8817

61.8625

3

12.1737

11.7933

9

28.2744

63.6174

MATHEMATICS
TABLE — (Continued)

39

Diam.

Circurn .

Area

Diam.

Circum.

Area

9J

28.6671

65.3968

194

61.2612

298.648

91

29.0598

67.2008

191

62.0466

306.355

91

29.4525

69.0293

20

62.8320

314.160

94

29.8452

70.8823

201

63.6174

322.063

91

30.2379

72.7599

204

64.4028

330.064

9|

30.6306

74.6621

20 1

65.1882

338.164

31.0233

76.589

21

65.9736

346.361

ios

31.4160

78.540

211

66.7590

354.657

101

32.2014

82.516

214

67.5444

363.051

104

32.9868

86.590

211

68.3298

371.543

101

33.7722

90.763

22

69.1152

380.134

11

34.5576

95.033

221

69.9006

388.822

11*

35.3430

99.402

224

70.6860

397.609

• 114

36.1284

103.869

22|

71.4714

406.494

ill

36.9138

108.434

23

72.2568

415.477

12

37.6992

113.098

231

73.0422

424.558

12J

38.4846

117.859

234

73.8276

433.737

124

39.2700

122.719

23|

74.6130

443.015

121

40.0554

127.677

24

75.3984

452.390

13

40.8408

132.733

241

76.1838

461.864

13J

41.6262

137-887

244

76.9692

471.436

134

42.4116

143.139

24J

77.7546

481.107

131

43.1970

148.490

25

78.5400

490.875

14

43.9824

153.938

251

79.3254

500.742

141

44.7678

159.485

254

80.1108

510.706

144

45.5532

165.130

251

80.8962

520.769

14f

46.3386

170.874

26

81.6816

530.930

15

47.1240

176.715

261

82.4670

541.190

151

47.9094

182.655

264

83.2524

551.547

154

48.6948

188.692

261

84.0378

562.003

15*

49.4802

194.828

27

84.8232

572.557

16

50.2656

201.062

271

85.6086

583.209

161

51.0510

207.395

274

86.3940

593.959

164

51.8364

213.825

271

87.1794

604.807

16f

52.6218

220.354

28

87.9648

615.754

17

53.4072

226.981

281

88.7502

626.798

171

54.1926

233.706

284

89.5356

637.941

174

54.9780

240.529

28f

90.3210

649.182

171

55.7634

247.450

29

91.1064

660.521

18

56.5488

254.470

291

91.8918

671.959

181

57.3342

261.587

294

92.6772

683.494

184

58.1196

268.803

291

93.4626

695.128

18}

58.9050

276.117

30

94.2480

706.860

19

59.6904

283.529

301

95.0334

718.690

191

60.4758

291.040

304

95.8188

730.618

40

MATHEMATICS
TABLE — (Continued)

Diam.

Circum.

Area

Diam.

Circum.

Area

30|

96.6042

742.645

42

131.947

1,385.45

31

97.3896

754.769

42*

132.733

,401 .99

3li

98.1750

766.992

42*

133.518

,418.63

31*

98.9604

779.313

422

134.303

,435.37

311

99.7458

791.732

43

135.089

,452.20

32

100.5312

804.250

43*

135.874

,469.14

32*

101.3166

816.865

43*

136.660

,486.17

32*

102.1020

829.579

43 i

137.445

,503.30

32J

102.8874

842.391

44

138.230

,520.53

33

103.673

855.301

44*

139.016

,537.86

33*

104.458

868.309

44*

139.801

,555.29

33*

105.244

881.415

44 J

140.587

,572.81

33J

106.029

894.620

45

141.372

,590.43

34

106.814

907.922

45*

142.157

,608.16

34*

107.600

921.323

45*

142.943

,625.97

34*

108.385

934.822

452

143.728

,643.89

34J

109.171

948.420

46

144.514

,661.91

35

109.956

962.115

46*

145.299

,680.02

35*

110.741

975.909

46*

146.084

,698.23

35*

111.527

989.800

46J

146.870

,716.54

351

112.312

1,003.790

47

147.655

,734.95

36

113.098

1,017.878

47*

148.441

1,753.45

36*

113.883

1,032.065

47*

149.226

1,772.06

36*

114.668

1,046.349

47|

150.011

1,790.76

36J

115.454

1,060.732

48

150.797

1,809.56

37

116.239

1,075.213

48*

151.582

1,828.46

37*

117.025

1,089.792

48*

152.368

1 ,847.46

37*

117.810

1,104.469

48J

153.153

1 ,866.55

37J

118.595

,119.244

49

153.938

1,885.75

38

119.381

,134.118

49*

154.724

1,905.04

38*

120.166

,149.089

49*

155.509

1,924.43

38*

120.952

,164.159

49|

156.295

1,943.91

38 i

121.737

,179.327

50

157.080

1,963.50

39

122.522

,194.593

50*

158.651

2,002.97

39*

123.308

,209.958

51

160.222

2,042.83

39*

124.093

,225.420

51*

161.792

2,083.08

39j

124.879

.240.981

52

163.363

2,123.72

40

125.664

,256.640

52*

164.934

2,164.76

40*

126.449

,272.400

53

166.505

2,206.19

40*

127.235

,288.250

53*

168.076

2,248.01

40|

128.020

,304.210

54

169.646

2,290.23

41

128.806

,320.260

54*

171.217

2,332.83

41*

129.591

,336.410

55

172.788

2,375.83

41*

130.376

,352.660

55*

174.359

2,419.23

41!

131.162

1 ,369.000

56

175.930

2,463.01

MA THEM A TICS
TABLE — (Continued)

41

Diam.

Circum.

Area

Diam.

Circum.

Area

56*

177.500

2,507.19

78*

246.616

4,839.83

57

179.071

2,551.76

79

248.186

4,901.68

57*

180.642

2,596.73

79*

249.757

4,963.92

58

182.213

2,642.09

80

251.328

5,026.56

58*

183.784

2,687.84

80*

252.899

5,089.59

59

185.354

2,733.98

81

254.470

5,153.01

59*

186.925

2,780.51

81*

256.040

5,216.82

60

188.496

2,827.44

82

257.611

5,281.03

60*

190.067

2,874.76

82*

259.182

5,345.63

61

191.638

2,922.47

83

260.753

5,410.62

61*

193.208

2,9.0.58

83*

262.324

5,476.01

62

194.779

3,019.08

84

263.894

5,541.78

62*

196.350

3,067.97

84*

265.465

5,607.95

63

197.921

3,117.25

85

267.036

5,674.51

63*

199.492

3,166.93

85*

268.607

5,741.47

64

201.062

3,217.00

86

270.178

5,808.82

64*

202.633

3,267.46

86*

271.748

5,876.56

65

204.204

3,318.31

87

273.319

5,944.69

65*

205.775

3,369.56

87*

274.890

6,013.22

66

207.346

3,421.20

88

276.461

6,082.14

66*

208.916

3,473 24

88*

278.032

6,151.45

67

210.487

3,525.66

89

279.602

6,221.15

67*

212.058

3,578.48

89*

281.173

6,291.25

68

213.629

3,631.69

90

282.744

6,361.74

68*

215.200

3,685.29

90*

284.315

6,432.62

69

216.770

3,739.29

91

285.886

6,503.90

69*

218.341

3,793.68

91*

287.456

6,575.56

70

219.912

3,848.46

92

289.027

6,647.63

70*

221.483

3,903.63

92*

290.598

6,720.08

71

223.054

3,959.20

93

292.169

6,792.92

71*

224.624

4,015.16

93*

293.740

6,866.16

72

226.195

4,071.51

94

295.310

6,939.79

72*

227.766

4,128.26

94*

296.881

7,013.82

73

229.337

4,185.40

95

298.452

7,088.24

73*

230.908

4,242.93

95*

300.023

7,163.04

74

232.478

4,300.85

96

301.594

7,238.25

74*

234.049

4,359.17

96*

303.164

7,313.84

75

235.620

4,417.87

97

304.735

7,389.83

75*

237.191

4,476.98

97*

306.306

7,466.21

76

238.762

4,536.47

98

307.877

7.542.98

76*

240.332

4,596.36

98*

309.448

7,620.15

77

241.903

4,656.64

99

311.018

7.697.71

77*

243.474

4,717.31

99*

312.589

7,775.66

78

245.045

4,778.37

100

314.160

7,854.00

42 USEFUL TABLES

USEFUL TABLES

UNITS OF MEASUREMENT

LINEAR MEASURE

12 inches (in.) =1 foot ft.

3 feet =1 yard yd.

5} yards =1 rod rd.

40 rods =1 furlong .... I fur.

8 furlongs =1 mile mi.

mi. fur. rd. yd. ft. in.

1 = 8 = 320=1,760 = 5,280 = 63,360

There are various other units of length, such as the league
= 3 mi.; the nautical mile = 6,080 ft.; the fathom = 6 ft.; the
hand = 4 in.; the span = Q in.; the cubit = 18 in.

SQUARE MEASURE

144 square inches (sq. in.) =1 square foot sq. ft.

9 square feet =1 square yard sq. yd.

30 J square yards =1 square rod sq. rd.

160 square rods =1 acre A.

640 acres =1 square mile sq. mi.

sq. mi. A. sq. rd. sq. yd. sq. ft. sq. in.

1 = 640 = 102,400 = 3,097,600 = 27,878,400 = 4,014,489,600

CUBIC MEASURE

1,728 cubic inches (cu. in.) =1 cubic foot cu.

27 cubic feet = 1 cubic yard cu. yd.

128 cubic feet =1 cord cd.

24 J cubic feet =1 porch P.

1 cu. yd. = 27 cu. ft. = 46,656 cu. in.

MEASURES OF ANGLES OR ARCS

60 seconds (") =1 minute '

60 minutes =1 degree °

90 degrees = 1 rt. angle or quadrant . . D

360 degrees =1 circle

1 cir. = 300° -21, COO' = 1,296,000"

USEFUL TABLES 43

A quadrant is one-fourth the circumference of a circle, or
90°; a sextant is one-sixth of a circle, or 60°. A right angle
contains 90°. The unit of measurement is the degree, or ^ of
the circumference of a circle.

AVOIRDUPOIS WEIGHT

437J grains (gr.) =1 ounce oz.

16 ounces =1 pound Ib.

100 pounds =1 hundredweight cwt.

20 cwt., or 2,000 Ib = 1 ton T.

1 T. = 20 cwt. = 2,000 Ib. = 32,000 oz. X 14,000,000 gr.
The avoirdupois pound contains 7,000 gr.

LONG-TON TABLE

16 ounces (oz.) =1 pound Ib.

112 pounds = 1 hundredweight cwt.

20 cwt., or 2,240 Ib =1 ton T.

TROY WEIGHT

24 grains (gr.) =1 pennyweight pwt.

20 pennyweights =1 ounce oz.

12 ounces =1 pound Ib.

1 Ib. = 12 oz. = 240 pwt. = 5,760 gr.

DRY MEASURE

2 pints (pt.) =1 quart qt.

8 quarts =1 peck pk.

4 pecks =1 bushel bu.

1 bu. = 4 pk. = 32 qt. = 64 pt.

The U. S. struck bushel contains 2,150.42 cu. in. = 1.2444
cu. ft. By law, its dimensions are those of a cylinder 18| in.
in diameter and 8 in. deep. The heaped bushel is equal to
1J struck bushels, the cone being 6 in. high. The dry gallon
contains 268.8 cu. in., being f struck bushel.

For approximations, the bushel may be taken as 1J cu. ft.;
or 1 cu. ft. may be considered I bu.

The British bushel contains 2,218.19 cu. in. = 1.2837 cu. ft.
= 1.032 U.S. bushels.

44 USEFUL TABLES

LIQUID MEASURE

4 gills (gi.) = 1 pint pt.

2 pints =1 quart qt.

4 quarts = 1 gallon gal.

31* gallons =1 barrel bbl.

2 barrels, or 63 gallons , = 1 hogshead hhd.

1 hhd. = 2 bbl. = 63 gal. = 252 qt. = 504 pt. = 2,016 gi.
The U. S. gallon contains 231 cu. in. = .134 cu. ft., nearly,
or 1 cu. ft. contains 7.481 gal.

When water is at its maximum density, 1 cu. ft. weighs
62.425 Ib. and 1 gal. weighs 8.345 Ib.

For approximations, 1 cu. ft. of water is considered equal
to 7i gal., and 1 gal. as weighing 8$ Ib.

The British imperial gallon, both liquid and dry, contains
277.463 cu. in. = .16057 cu. ft., and is equivalent to the volume
of 10 Ib. of pure water at 62° F. To reduce British to U. S.
liquid gallons, multiply by 1.2. Conversely, to convert U. S.
into British liquid gallons, divide by 1.2; or, increase the
number of gallons $.

MEASURES OF UNITED STATES MONEY

10 mills (m.) =1 cent c.

10 cents =1 dime d.

10 dimes =1 dollar $.

10 dollars =1 eagle E.

m. c. d. $ E.

10= 1
100= 10= 1
1,000= 100= 10= 1
10,000=1,000=100=10=1

The term legal tender is applied to money that may be
legally offered in payment of debts. All gold coins are legal
tender for their face value to any amount, provided their
weight has not diminished more than ifor. Silver dollars also
are legal tender to any amount, but silver coins of a lower
denomination than $1 are legal tender only for sums not
exceeding $10. Nickel and copper coins are legal tender for
sums not exceeding 25c.

USEFUL TABLES

45

MEASURES OF TIME

60 seconds (sec.) =1 minute min.

60 minutes =1 hour hr.

24 hours =1 day da.

7 days =1 week wk.

4 weeks =1 month mo.

12 months =1 year yr.

100 years =1 century C.

yr. wk. da. hr. min. sec.

1 = 52 = 365 = 8,765 = 525,948 = 31,556,936

DECIMAL EQUIVALENTS OF PARTS OF 1 IN.

1-64

.015625

17-64

.265625

33-64

.515625

49-64

.765625

1-32

.031250

9-32

.281250

17-32

.531250

25-32

.781250

3-64

.046875

19-64

.296875

35-64

.546875

51-64

.796875

1-16

.062500

.5-16

.312500

9-16

.562500

13-16

.812500

5-64

.078125

21-64

.328125

37-64

.578125

53-64

.828125

3-32

.093750

11-32

.343750

19-32

.593750

27-32

.843750

7-64

.109375

23-64

.359375

39-64

.609375

55-64

.859375

1-8

.125000

3-8

.375000

5-8

.625000

7-8

.875000

9-64

.140625

25-64

.390625

41-64

.640625

57-64

.890625

5-32

.156250

13-32

.406250

21-32

.656250

29-32

.906250

11-64

.171875

27-64

.421875

43-64

.671875

59-64

.921875

3-16

.187500

7-16

.437500

11-16

.687500

15-16

.937500

13-64

.203125

29-64

.453125

45-64

.703125

61-64

.953125

7-32

.218750

15-32

.468750

23-32

.718750

31-32

.968750

15-64

.234375

31-64

.484375

47-64

.734375

63-64

.984375

1-4

.250000

1-2

.500000

3-4

.750000

1

1

WEIGHTS AND SIZES OF MATERIALS

SPECIFIC GRAVITY

The specific gravity of a substance is the ratio of the weight
of any volume of the substance to the weight of an equal
volume of water with solids and liquids, and air with gases.
The weight of 1 cu. ft. of any solid or liquid, in pounds avoir-
dupois, is found by multiplying its specific gravity by 62.425.
The weight, in pounds avoirdupois, of 1 cu. ft. of any gas at
atmospheric pressure and at 32° F. is found by multiplying
its specific gravity by .08073.
5

46 USEFUL TABLES

WEIGHTS OF VARIOUS SUBSTANCES

Metals

Aluminum

Antimony

Bismuth

Brass, common

Copper, cast

Copper, rolled

Gold, pure cast

Iron, cast

Iron, wrought

Lead, pure

Mercury, at 60° F

Silver, pure

Steel, hard

Steel, soft

Tin

Zinc..

Stones and Earth

Asbestos 1110

Brick 0723

Chalk 1006

Clay .0686

Coal, anthracite

Coal, bituminous .0488

Earth, loose 0491

Emery 1450

Glass, flint

Granite, Quincy 0958

Gypsum, opaque .0783

Limestone

Marble, common 0970

1012

Quartz 0961

Salt, common 0769

Sand 0957

1012

Soil, common .0717

Stone, common .0910

Sulphur, native <>7:<1

Weight per
Cu. In.
Pound

.096
.242
.352

.307
.314
.321
.696
.260
.281
.409
.491
.378
.286
.283
.256
.260

Weight per
Cu. In.
Pound

Specific
Gravity

2.660

6.712

9.746

8.500

8.700

8.878

19.258

7.207

7.780

11.330

13.580

10.474

7.919

7.833

7.351

7.101

Specific
Gravity

3 to 3.2
2.000
2.784
1.900
1.640
1.436
1.350
1.360
4.000
3.500
2.662
2.168
2.700
2.688
2.800
2.660
2.130
2.660
2.800
1.984
2.520
2.033

USEFUL TABLES

47

TABLE — (Continued)

Dry Woods

Weight per
Cu. In.

Pound

Specific
Gravity

Ash

.0305

.845

Beech

.0308

.852

Cedar American

.0203

.561

Cork

.0090

.250

.0441

1.220

Elm

.0202

.560

.0481

1.330

Mahogany Honduras

.0202

.560

Maple . ...

.0285

.790

Oak

.0343

.950

Pine Southern

.0260

.720

Pine White

.0144

.400 "

Poplar

.0138

.383

Spruce

.0181

.500

Liquids

Weight
per Cu. In.
Pound

Specific
Gravity

Acid, nitric
Acid, sulphuric
Acid, muriatic, or hydrochloric
Alcohol, commercial

.0440
.0665
.0434
.0301

1.217
1.841
1.200
.833

.0286

.792

Oil linseed

.0340

.940

Oil turpentine . .

.0314

.870

Water, distilled (62.425 Ib. per cu. ft.) .

.0361

1.000

Gases and Vapors
At 32° and a Tension of 1 Atmosphere

Weight
per Cu. Ft.
Grains

Specific
Gravity

565.11

1.0000

333.10

.."»894

Carbonic acid

859.00

1.5201

Carbonic oxide

546.60
39 10

.9673
.0692

Oxygen
Sulphureted hydrogen

624.80
663.80
548.90

1.1056
1.1747
.9713

Steam at 21 2° F

275.80

.4880

48 USEFUL TABLES

STANDARD PIPE FOR STEAM, GAS, AND WATER

Nominal
Inside
Diameter
Inches

Actual
Inside
Diameter
Inches

Thick-
ness

Inch

Internal
Area
Square
Inches

Threads
Per
Inch

Per
Foot
Pounds

|

.27

.068

.06

27

.24

.36

.088

.10

18

.42

|

.49

.091

.19

18

.56

i

.62

.109

.30

14

.84

i

.82

.113

.53

14

1.12

1

1.05

.134

.86

111

1.67

H

1.38

.140

1.50

111

2.24

ll

1.61

.145

2.04

11*

2.68

2

2.07

.154

3.36

lit

3.61

2*

2.47

.204 .

4.78

8

5.74

3

3.07

.217

7.39

8

7.54

3i

3.55

.226

9.89

8

9.00

4

4.03

.237

12.73

8

10.66

4J

4.51

.246

15.96

8

12.49

5

5.05

.259

19.99

8

14.50

6

6.07

.280

28.89

8

18.76

7

7.02

.301

38.74

8

23.27

8

7.98

.322

50.02

8

28.18

9

8.94

.344

62.72

8

33.70

10

10.02

.366

78.82

8

40.00

11

11.00

.375

95.03

8

45.00

12

12.00

.375

113.10

8

49.00

WEIGHT OF SHEET IRON PER SQUARE FOOT

Galvan-

Num-

Thick-

Black

Num-

Thick-

Black

ized

ber of
Gauge

ness
Inch

Iron
Pounds

ber of
Gauge

ness
Inch

Iron
Pounds

Iron
Pounds

1

.300

12.0

16

.065

2.6

3.0

2

.284

11.4

17

.058

2.3

2.7

3

.259

10.4

18

.049

2.0

2.3

4

.238

9.5

19

.042

1.7

2.1

5

.220

8.8

20

.035

1.4

1.7

8

.203

8.1

21

.032

1.3

1.5

7

.180

7.2

22

.028

1.1

1.3

8

.165

6.6

23

.025

1.0

1.2

9

.148

5.9

24

.022

0.9

1.1

10

.134

5.4

25

.020

0.8

1.0

11

.120

4.8

26

.018

0.7

1.0

12

.109

4.4

27

.016

0.6

0.9

18

.095

3.8

28

.014

0.6

0.7

14

.083

3.3

29

.013

0.5

0.7

Ifl

.072

2.9

30

.012

0.5

0.6

USEFUL TABLES

49

EXTRA-STRONG WROUGHT-IRON PIPE

Size , Nominal
of Inside
Pipe 1 Diameter
Inches '. Inches

Actual
Outside
Diameter
Inches

Thick-
ness

Inch

Weight

Foot
Pounds

Internal
Area
Square
Inches

i

.205

.405

.100

.29

.03

|

• .294

.540

.123

.54

.07

4

.421

.675

.127

.74

.14

i

.542

.840

.149

1.09

.23

3

.736

1.050

.157

1.39

.43

1

.951

1.315

.182

2.17

.71

H

1.272

1.660

.194

3.00

1.27

11

1.494

1.900

.203

3.63

1.75

2

1.933

2.375

.221

5.02

2.94

2i

2.315

2.875

.280

7.67

4.21

3

2.892

3.500

.304

10.25

6.57

3*

3.358

4.000

.321

12.47

8.86

4

3.818

4.500

.341

14.97

11.46

4J

4.280

5.000

.360

18.22

14.39

5

4.813

5.563

.375

20.54

18.19

6

5.750

6.625

.437

28.58

25.98

7

6.625

7.625

.500

37.67

34.47

8

7.625

8.625

.500

43.00

45.66

9

8.625

9.625

.500

48.73

58.43

\0

9.750

10.750

.500

54.74

74.66

11

10.750

11.750

.500

60.08

90.76

12

11.750

12.750

.500

65.42

108.43

WEIGHT OF IRON-PIPE SIZES OF SEAMLESS-DRAWN
BRASS AND COPPER TUBES

Nominal
Size

Outside
Diameter

Inside
Diameter

Weight, in Pounds
per Linear Foot

Inches

Inches

Inches

Brass

Copper

.27

.30

.31

.36

.43

.45

.49

.58

.61

i

H

.62

.80

.84

!

1&

.82

1.17

1.23

l

1A

1.04

1.67

1.75

u

1-

1.38

2.42

2.54

li

1-

1.61

2.92

3.07

2

2

2.06

4.17

4.38

2J

2

2.46

5.00

5.25

3

3

3.06

8.00

8.40

4

4

4.02

12.00

12.00

50 USEFUL TABLES

WEIGHT OF ROUND AND SQUARE ROLLED IRON PER
LINEAR FOOT

Side or
Diameter

Inches

Weight Pounds
per Foot

Side or
Diameter

Inches

Weight Pounds
per Foot

Round

Square

Round

Square

A

.010

.013

3J

39.864

50.756

i

.041

.053

4

42.464

54.084

JL.

.093

.118

4

45.174

57.517

i

.165

.211

4

47.952

61.055

.373

.475

4

50.815

64.700

?,

.663

.845

4

53.760

68.448

I

1.043

1.320

4f

56.788

72.305

i

1.493

1.901

4?

59.900

1

2.032

2.588

4 1

63.094

80.333

1

2.654

3.380

5

66.350

84.480

11

3.359

4.278

5i

69.731

88.784

1:

4.147

5.280

5

73.172

93.168

1!

5.019

6.390

5

76.700

97.657

1

5.972

7.604

5

80.304

102.2 10

1

7.010

8.926

5

84.001

io<i. <);>;•!

li

8.128

10.352

5

87.776

in. r.-.r.

1,

9.333

11.883

5

91.634

L16.671

2

10.616

13.520

6

95.552

121.664

2

11.988

15.263

6

103.704

132.040

2

13.440

17.112

6

112.160

142.816

2

14.975

19.066

6

120.960

154.012

2

16.588

21.120

7

130.048

165.632

2

18.293

23.292

7i

139.544

177.C.72

2

20.076

25.560

7i

149.328

190.130

2

21.944

27.939

7J

L59.456

203.024

3

23.888

30.416

8

169.856

21<i.33li

3j

25.926

33.010

8i

180.696

230.068

3

28.040

35.704

84

1 '.U. SOS

244.220

30.240

38.503

8f

203.260

2f>S.sOO

3

32.512

41.408

9

215.040

27:-S.7<>2

3

34.886

44.418

9

227.152

2S9.220

3

37.332

47.534

9

239.600

305.056

WEIGHT OF SHEET LEAD PER SQUARE FOOT

Thick-
ness
Inch

Weight
Pounds

Thick-
ness
Inch

Weight
Pounds

Thick-
ness
Inch

Weight
Pounds

.017

.o:5t
.051

.Olis

1
2
3
4

.085
.101
.118
.135

5

(i
7
8

.152
.169
.186
.203

9
10
11
12

USEFUL TABLES

g.s s

So*

CO 00 CO •* iO CO t^ |

'OOMOOXOONNININSCCO

C O O -* T)< 00 00

04 -M 01 01 04 01 01

Sss

10 «o o t^ oo o o O •-<

0 CO «O O 00 "-H CO ;

01 O) Ol Ol OJ ^ CO :

P.5

rtfe

Tj(Tj<iO<Ot»t>.aOOJO>O-H<NM«.'5®OS'-' « MS

222S3o1ol^cv

^-S.x

•* Ov- o

;oi?J^

52

USEFUL TABLES

DIMENSIONS OF PIPE FLANGES

The table on page 51 gives the dimensions of standard and
extra-heavy pipe flanges, the former being the pressure up to
125 Ib. per sq. in., and the latter for pressures above 125 and

STANDARD AND EXTRA-GAUGE STEEL BOILER
TUBES

r\..4.

Standard

Nominal Weight per Foot

Uut-
side

Thickness

Pounds

Di-

am-
eter

Near-

Stand-

One

Two

Three

Four

est

ard

Extra

Extra

Extra

Extra

In-

Birm.

Wirp

Inch

Thick-

Wire

Wire

Wire

Wire

ches

w ire
Gauge

ness

Gauge

Gauges

Gauges

Gauges

1

13

.095

.90

1.04

1.13

1.24

1.35

11

13

.095

1.15

1.33

1.45

1.60

1.74

H

13

.095

1.40

1.62

1.77

1.96

2.14

11

13

.095

1.66

1.91

2.09

2.31

2.53

2

13

.095

1.91

2.20

2.41

2.67

2.93

21

13

.095

2.16

2.49

2.73

3.03

3.32

2i

12

.109

2.75

3.05

3.39

3.72

4.12

2|

12

.109

3.04

3.37

3.74

4.11

4.56

3

12

.109

3.33

3.69

4.10

4.51

5.00

31

11

.120

3.96

4.46

4.90'

5.44

5.90

8|

11

.120

4.28

4.82

5.30-

5.88

6.38

31

11

.120

4.60

5.18

5.69

6.32

6.86

4

10

.134

5.47

6.09

6.76

7.34

8.23

4}

10

.134

6.17

6.88

7.64

8.31

9.32

5

9

.148

7.58

8.52

9.27

10.40

11.23

6

8

.165

10.16

11.19

12.57

13.58

14.65

7

8

.165

11.90

13.11

14.74

15.93

17.19

8

8

.165

13.65

15.04

16.91

18.28

19.73

0

7

.180

16.76

19.07

20.63

22.27

24.18

10

6

.203

21.00

22.98

24.82

26.95

29.47

11

5

.220

25.00

27.30

29.71

32.51

34.29

12

4i

.229

28.50

31.19

34.01

36.52

39.92

13

4

.238

32.06

35.25

38.57

40.70

45.98

not over 250 Ib. per sq. in. The dimensions of flanges and fit-
tings were arranged by joint committees from the American
Society of Mechanical Engineers and the National Association
of Master Steam and Hot-Water Fitters, and after revision
and amplification were adopted by the latter body and officially

USEFUL TABLES

e

as

T

-O'-iTt<'-HOt^d>~ r-xcNO'-'r^-t^o-^c:

-^ r. — — -' ~ ••' :•: n — c: c 5 x b io TJI -5 co

II
*

^1 O C5 O C2 "-O <-" L-5 O •* LO Tf iO CC t- O

'*t^~-r
i-< c; ci ~

CO i-i O X l> ^ '-t T«I L- TT -M M C5 1^. 1-1 >-~ C5 Tf T*<
^3 "H C5 '-C •* ^H l> TJH (N C t> (N t-. X O I-H ^H

II

c •* >oo »- »oo -H

i-ll-Hi-Hi-(C^CvlM'?0

Li C5 C5 C5 O O O "* •* X O »O 1C O

2 — — : s ^ ^ ^ w M "* ~ "-^ "^ x

54 CHEMISTRY AND HEAT

recommended by the former. Also, the American Society of
Heating and Ventilating Engineers recommended the values
for the use of its members. The table gives the dimensions
of flanges, but not of fittings. Another series of values is the
Manufacturers' 1912 Schedule, which was adopted July 10,
lltli', to take effect Oct. 1, 1912. The latter schedule agrees
with the table on page 51, so far as standard flanges are con-
cerned, but has slightly different values for extra-heavy flanges
for pipes over 8 in. in diameter.

CHEMISTRY AND HEAT

CHEMISTRY

Divisions of Matter. — Matter is anything that occupies
space, and it exists in three states, namely, solid, liquid, and
gaseous. It is made up of molecules and atoms. A molecule
is the smallest portion of matter into which a body can be
divided and exist without changing its nature. An atom is
an indivisible portion of matter, or the smaller particle pro-
duced by dividing a molecule. A molecule is simply a group
of two or more atoms that are held together by their natural
attraction for one another.

Elements and Compounds. — Every body, or every portion
of matter, is either an element, a compound, or a mixture.
Iron, silver, sulphur, and oxygen are elements; wood, coal,
salt, and water are compounds; and atmospheric air is a mix-
ture. An element is a substance that cannot be divided or
broken up into other substances; thus, if a piece of silver is
divided and subdivided, each particle will still be silver. A
compound is a substance that can be divided into other sub-
stances; thus, if an electric current is passed through water,
the water is decomposed into two gases, hydrogen and oxygen.
A mixture is simply a combination of elements or compounds
in which each preserves its own nature; thus, air is a mix-
ture of oxygen and nitrogen and minute proportions of
other gases.

CHEMISTRY AND HEAT

Symbols and Formulas. — Each of the known elements is
designated by a symbol, which is a letter or a pair of letters,
oftentimes the initial letter of the name of the element. Thus,
O is the symbol for oxygen, H for hydrogen, C for carbon, and
so on. When two or more elements unite to form a compound,
the symbols representing the elements in the compound may
be connected in a formula, which will show how the atoms of
the elements combined to form the compound. Thus, H and
O are the symbols of the elements hydrogen and oxygen.
When these two gases unite in certain proportions, they form
water, a compound whose formula is HiO. This formula
indicates, first, that water is composed of hydrogen, H, and
oxygen, O; and second, it indicates, by the subscript 2, that 2
atoms of hydrogen unite with 1 atom of oxygen to form 1

ATOMIC WEIGHTS OF ELEMENTS

Name of

Sym-

Atomic

Name of

Sym-

Atomic

Element

bol

Weight

Element

bol

Weight

Calcium

Ca

40.10

Nitrogen ....

.V

14.04

Carbon

C

12.00

Oxygen

0

16.00

Chlorine

Cl

35.45

Potassium . .

K

39.15

Hydrogen . . .

H

1.00

Sodium

Xa

23.05

Magnesium. .

Mg

24.36

Sulphur. ....

S

32.06

molecule of water. The formula for carbon dioxide is COi,
which indicates that a molecule of carbon dioxide consists of
1 atom of carbon, C, and 2 atoms of oxygen, O.

Atomic Weight and Molecular Weight. — The ratio between
the weight of an atom of any element and the weight of an
atom of hydrogen is termed the atomic weight of that element.
The symbols and the atomic weights of a number of the ele-
ments most commonly met with in steam engineering are
given in the accompanying table. By the aid of the atomic
weights, the composition of any substance, by weight, may be
determined. For example, water contains 2 atoms of hydrogen
and 1 atom of oxygen. Multiplying the number of atoms of
each by the atomic weight, it is seen that there are 2X1=2
parts of hydrogen, by weight, and, IX 16= 16 parts of oxygen,

56 CHEMISTRY AND HEAT

COMMON NAMES OF CHEMICAL COMPOUNDS

Chemical Compound

Common Name

Formula

Ammonium chloride. .
Ammonium hydrate . .
Calcium hydroxide
Calcium chloro-hypo-
chlorite

Sal ammoniac
Liquor ammonia
Slaked lime

Bleaching powder or

NHtCl

NH*OH

Ca(OH)i

Calcium oxide. . .

chloride of lime ....
Quicklime

Ca(ClO}Cl
CaO

Calcium sulphate ... .
Hydrochloric acid

Plaster of Paris
Muriatic acid

2CaSOi-H£>
HCl

Magnesium sulphate .
Nitric acid

Epsom salts
Aquafortis

MgSOi
HNOt

Potassium hydrate . .
Potassium nitrate ... .
Sodium carbonate . . .
Sodium carbonate

Caustic potash
Niter, or saltpeter
Washing soda
Soda ash

KOH
KNOt

NazCOs'lOHiO
NaiCOi

Sodium chloride

Common salt

NaCl

Sodium hydrate

Caustic soda

NaOH

Sulphuric acid

Oil of vitriol

//•2.SOl

by weight, and the molecule contains 2 -f 16 = 18 parts. The
weight of the molecule of a substance is termed the molec
weight.

HEAT

TEMPERATURE

Thermometric Scales. — Three different scales are used
designating temperatures, namely, the Fahrenheit scale, the
centigrade scale, and the Reaumur scale. The last-named
is little used, however. Temperatures on these scales are
usually indicated by the abbreviations F. or Fahr., C. or Cent.,
and R. or Reau., respectively. There are three standard points
on each scale, namely, the boiling point of water, at sea level,
the melting point of ice, and the absolute zero of temperature.
The last indicates the point of complete absence of heat. On
the Fahrenheit scale, the melting point of ice is marked 32
and the boiling point of water is marked 212, and the inter-
vening space is divided into 180 equal parts, called degrees.

CHEMISTRY AND HEAT

57

On the centigrade scale, the melting point of ice is zero, and the
boiling point of water is 100, and there are 100 divisions, or
degrees, between these points. On the Reaumur scale, zero
marks the melting point of ice, and 80 the boiling point of water.
Absolute Zero. — It has been found by experiment that all
perfect gases will expand I\R of their volume when heated
from zero to 1° above it. It is inferred, therefore, that the

CENTIGRADE AND FAHRENHEIT DEGREES

Deg.
C.

Deg.

F.

Deg.
C.

Deg.
F.

Deg.
C.

Deg.
F.

Deg.
C.

Deg.
F.

0

32.0

26

78.8

51

123.8

76

168.8

1

33.8

27

80.6

52

125.6

77

170.6

2

35.6

28

82.4

53

127.4

78

172.4

3

37.4

29

84.2

54

129.2

79

174.2

4

39.2

30

86.0

55

131.0

80

176.0

5

41.0

31

87.8

56

132.8

81

177.8

6

42.8

32

89.6

57

134.6

82

179.6

7

44.6

33

91.4

58

136.4

83

181.4

8

46.4

34

93.2

59

138.2

84

183.2

9

48.2

35

95.0

60

140.0

85

185.0

10

50.0

36

96.8

61

141.8

86

186.8

11

51.8

37

98.6

62

143.6

87

188.6

12

53.6

38

100.4

63

145.4

88

190.4

13

55.4

39

102.2

64

147.2

89

192.2

14

57.2

40

104.0

65

149.0

90

194.0

15

59.0

41

105.8

66

150.8

91

195.8

16

60.8

42

107.6

67

152.6

92

197.6

17

62.6

43

109.4

68

154.4

93

199.4

18

64.4

44

111.2

69

156.2

94

201.2

19

66.2

45

113.0

70

158.0

95

203.0

20

68.0

46

114.8

71

159.8

96

204.8

21

69.8

47

116.6

72

161.6

97

206.6

22

71.6

48

118.4

73

163.4

98

208.4

23

73.4

49

120.2

74

165.2

99

210.2

24

75.2

50

122.0

75

167.0

100

212.0

25

77.0

ultimate limit of contraction will be found at 460° below zero
on the Fahrenheit scale, and that at this point all motion of
the molecules ceases. This point is called the absolute zero,
and temperatures measured therefrom are called absolute
temperatures.

58 CHEMISTRY AND HEAT

The temperature that is indicated by the Fahrenheit ther-
mometer may be converted into absolute temperature by
adding it to 460°. Thus, a temperature of 85° by the Fahren-
heit thermometer corresponds to the absolute temperature
of 85+460 = 545°. On the centigrade scale the absolute zero
is 273 J° below the zero point. On the Reaumur scale it is
2 18 1° below zero. When the thermometer indicates tem-
peratures below the zero point of its graduation, the indicated
temperature must be subtracted from 460, 273 i or 218 §,
respectively, to find the absolute temperature; that is, absolute
zero is -460° F., -273|° C., and -218f° R.

Conversion of Temperatures. — A degree on the Fahrenheit
scale is equal to TS& = I of a degree centigrade and to /& = $ of
a degree Reaumur. Temperatures according to any one of
these scales, therefore, may be converted into the correspond-
ing temperatures on the other scales by using the following
simple formulas:

Temp. F. = f Temp. C.+320 =| Temp. R. + 320.

Temp. C. = | (Temp. F.-32°)=f Temp. R.

Temp. R. = a (Temp. F.-32°)=^ Temp. C.

The table on page 57 shows the equivalents of centigrade
temperatures on the Fahrenheit scale.

COEFFICIENTS OF LINEAR EXPANSION

The coefficient of expansion of a body is its expansion per
degree rise of temperature. The coefficient of surface expan-
sion is double, and that of cubic expansion three times the
coefficient of linear expansion. The table on page 59 shows
the coefficient of linear expansion for various substances.

For example, a 30-ft. steel rail in warming from 20° F. below
zero to 100° F. will expand (20+100) X .0000059!) X30X 12
38 in.

MEASUREMENT OF HEAT

British Thermal Unit. — The unit most commonly used for
the measurement of heat is the British Thermal Unit, abbre-
viated B. T. U. This is the amount of heat required to raise
the temperature of 1 Ib. of pure water 1° F. at or near the tem-
perature 39.1° F., whi,ch is the point of maximum density of
water. Heat is a form of energy, and it may be transformed

CHEMISTRY AND HEAT

59

into other forms of energy. The equivalent of 1 B. T. U. in
foot-pounds is 778 ft.-lb., and this value, 778 ft.-lb., is termed
the mechanical equivalent of heat. It is the number of foot-
pounds of mechanical energy that would be produced by
transforming 1 B. T. U. without any losses.

COEFFICIENTS OF EXPANSION FOR VARIOUS
SUBSTANCES

Substance

Coefficient of Linear

Expansion in Inches per

Degree F.

Aluminum

Brass '.

Brick

Cement and Concrete {£ro™

c°PPer

Glass

Gold

Granite

Iron, cast

Iron, wrought

Lead

Marble

Masonry

Mercury

Platinum

Porcelain

Sandstone {fro™

Steel, untempered

Steel, tempered

Tin

Wood, pine

Zinc...

.00001140
.00001040
.00000306
.00000550
.00000780
.00000961
.00000399
.00000521
.00000841
.00000460
.00000587
.00000677
.00001580
.00000400
.00000206
.00000490
.00003334
.00000494
.00000200
.00000400
.00000670
.00000599
.00000702
.00001160
.00000276
.00001634

Latent Heat. — The heat expended in changing a body from
the solid to the liquid state, or from the liquid to the gaseous
state, without change of temperature, is called its latent heat.

The temperature at which a body changes from a solid to
a liquid state is called its temperature of fusion, or its fusing
point; and the number of B. T. U. required to effect this change
in a body weighing 1 Ib. is called its latent heat of fusion. The

CHEMISTRY AND HEAT

temperature at which a body changes from a liquid state to a
vapor or a gas is called its temperature of vaporization; and the
heat required to effect this change in 1 Ib. of the liquid is called
its latent heat of vaporization.

When a vapor changes back to a liquid, it is said to con-
dense, and when a liquid changes back to a solid, it is said to
freeze; in either case, an amount of heat, equal to the latent
heat of vaporization or of fusion, as the case may be, must be
abstracted from, or given up, by the body.

TEMPERATURES AND LATENT HEATS OF FUSION
AND OF VAPORIZATION

Substance

Temper-
ature
of
Fusion
Deg. F.

Latent
Heat
of
Fusion
B. T. U.

Temper-
ature of
Vapori-
zation
Deg. F.

Latent
Heat of
Vapori-
zation
B. T. U.

Aluminum

1,160.0

51.4

Carbon
Copper ....

Infusible
1.930.0

Ice

32 0

144 0

212

Iron, cast
Iron, wrought
Lead
Mercury

2,192.0
2,912.0
626.0
— 37.8

233.0

9.7
5.1

662

157

Platinum
Steel
Sulphur

3,227.0
2,520.0
2390

46.0
16.9

824

Tin . . .

446.0

25.7

Zinc

6&0.0

50.6

1 900

493

The accompanying table shows the latent heats of fusion
and of vaporization for 1 Ib. of various substances, they having
first been raised to the temperature at which the change takes
place, and the pressure being one atmosphere, or 14.7 Ib. per
sq. in. The temperature of vaporization in the table is the
boiling point of the liquid under the ordinary atmospheric
pressure of 14.7 Ib. per sq. in.

Specific Heat. — The specific heat of a body is the ratio be-
tween the quantity of heat required to warm that body 1°
and the quantity of heat required to warm an equal weight of

CHEMISTRY AND HEAT

61

water 1°. The number of B. T. U. required in order to raise
or required to be abstracted in order to lower, the temperature
of a body a certain number of degrees may be found by the
formula Q=Ws (ti-h),

in which Q = number of B. T. U. required;

W= weight of body, in pounds;

s = specific heat of body;

ll = higher temperature, in degrees P.;

tz = lower temperature, in degrees P.

The specific heats of various solids, liquids, and gases are
given in the accompanying tables.

SPECIFIC HEATS OF SOLIDS AND LIQUIDS

Substance

Specific
Heat

Substance

Specific
Heat

Aluminum

.2143

Lead, melted

.0402

Ashes, average
Brass

.2100
.0939

Mercury
Platinum

.0333
0324

Charcoal

.2410

Steel

.1170

Copper
Glass
Ice...

.0951
.1937
.5040

Sulphur
Sulphur, melted
Tin

.2026
.2340
.0562

.1298

Tin melted

0637

Iron, wrought. . .

.1138

Water

1.0000

Lead . ..

.0314

Zinc

.0956

SPECIFIC HEATS OF GASES

Specifi

:Heat

Name of Gas

Constant
Pressure

Constant
Volume

Air ..

23751

16902

Carbon dioxide

.21700

.15350

Carbon monoxide

.24500

.17580

Hydrogen

3 40900

2 41226

24380

17273

Oxygen

.21751

.15507

62 MECHANICS

MECHANICS

WORK AND POWER

Work is the overcoming of resistance through a distance.
The unit of work is the foot-pound; that is, it equals 1 Ib.
raised vertically 1 ft. The amount of work done is equal to
the resistance in pounds multiplied by the distance in feet
through which it is overcome. If a body is lifted, the resist-
ance is the weight or the overcoming of the attraction of grav-
ity, the work done being the weight in pounds multiplied by
the height of the lift in feet. If a body moves in a horizontal
direction, the work done is the friction overcome, or the force
needed to move a resistant body or combination of bodies,
multiplied by the distance moved through.

It must always be kept in mind that motion in itself is not
work and that the mere application of a force also is not work ;
a force must act through a distance overcoming resistance in
order that work be done.

Power is the rate of doing work, or the quantity of work
done in unit time. The ordinary unit of mechanical power
is the horsepower, which is equivalent to 33,000 ft.-lb. per min.,
or :>:»<) ft.-lb. per sec. The term horsepower is commonly
abbreviated H. P.

The work necessary to be done in raising a body weighing
W Ib. through a height of h ft. equals W h ft.-lb. The total
work that any moving body is capable of doing in being brought

i iv

to rest equals its kinetic energy, or - , in which v is the velocity

of the body, in feet per second, and g = 32.16.

The kinetic energy of a 200,000-lb.. train running at 40 mi.
per hr., or .r>S.7 ft. per sec., is 200,000X58.7^(2X32.16)
= 10,714,220 ft.-lb.; the retarding force necessary to stop
the train within 2.000 ft. is 10,714.220H-2,000 = 5,357.1 Ib.,
and the average power required to stop the train in i min.
is 10,714.220-5-} = 21. l-'s. tin ft.-lb. per min., or 21,428,440
-^ 33,000 = 649.3 H. P.

MECHANICS 63

CENTRIFUGAL FORCE

If a ball is fastened to a string and is whirled so as to give
it a circular motion, there will be a pull of greater or less amount
on the string, according as the speed of the ball increases or
decreases. If the string is cut while the ball is in motion,
the ball will fly off, away from the center of the circle in which
it is whirling. The force that acts to draw a body away from
the center around which it revolves is termed the centrifugal
force of the body. It may be found by the formula

F = . 00034 WRN*,
in which F = centrifugal force, in pounds;

IT' = weight of revolving body, in pounds;

R = radius, in feet, of circle in which the center of

gravity of the revolving body moves;
2V = revolutions per minute of revolving body.

MACHINE ELEMENTS

LEVERS

A lever is a bar that may be turned about a pivot, or point,
as shown in Figs. 1, 2, and 3. In each case, the object W to

FIG. 1 FIG. 2 FIG. 3

be lifted is called the load , or weight; the force that accomplishes
the lifting is represented by F; and the fulcrum, or pivot, is
indicated by C. The distance / from the weight to the fulcrum
is termed the -weight arm and the distance L from the force
to the fulcrum is termed the force arm. • The distance between
the force and the weight is denoted by a. Whenever the force
f is just great enough to balance the load lifted, it will be
found that the force times the length of the force arm is equal

€4 MECHANICS

to the weight times the length of the weight arm. That is,
in each of the forms of levers shown in Figs. 1 to 3, F:W = l:L,

or FL=Wl. From this it follows that F = — and W= — .

L I

If the force and the weight are known, and it is desired to
calculate the lengths of the weight and force arms so that the
lever may balance, the following formulas may be used:
For the style of lever shown in Fig. 1,
Fa Wa

For the style of lever shown in Fig. 2,
Fa Wa

For the style of lever shown in Fig. 3,
Fa Wa

FIXED AND MOVABLE PULLEYS

A pulley consists of a grooved wheel on an axle held in a
frame, or block, and is very useful in moving or hoisting loads.
A fixed pulley is one whose block is not movable. Such a pulley
is shown in Fig. 1. A rope passes over the pulley and carries
the load W at one end, the hoisting force F being applied

FIG. 1 FIG. 2 FIG. 3 FIG. 4

at the other end of the rope. Neglecting the friction of the
pulley in its block, the force required to lift a load is equal
to the load; that is, F = W.

A movable pulley is one whose block is movable, such as that
shown in Fig. 2. In this case, one end of the rope is fastened

MECHANICS 65

to an overhead support and the hoisting force is applied at the
other end in an upward direction. With this arrangement, a
pull of 1 Ib. at F will lift a weight of 2 Ib. at W. If the free
end of the rope is. carried up over a fixed pulley, as shown in
Fig. 3, the effect will still be the same; that is, a weight of
2 Ib. can be raised by a force F of 1 Ib.; that is, in Figs. 2
and 3, F=±W.

A double movable pulley is shown in Fig. 4; that is, the
movable block attached to the load W carries two pulleys.
A similar pulley is fixed to an overhead support, and one end
of the rope is attached to it, the other end being carried around
the several pulleys as shown. With this arrangement, a force
F of 1 Ib. is sufficient to raise a weight W of 4 Ib.; that is,
F = \W.

Combination of Pulleys. — By increasing the number of fixed
and movable pulleys over which the hoisting rope or chain
passes, the force required to lift a given load may be lessened.
In Fig. 5 is shown a quadruple movable pulley, or one hi which
the movable block has four pulleys, and a force of 1 Ib. at F
will lift a weight of 8 Ib. at W. The following general rule
applies to any combination of pulleys:

Rule. — When a single rope is used with a combination of
pulleys, a pull on the free end will balance a load on the movable
block as many times as great as the pull as there are parts of the
rope supporting the movable block

For instance, in Figs. 2 and 3, there are two parts of the
rope supporting the movable block, and the load balanced by
the pull F is twice as great as the pull F. In Fig. 4 there are
four parts of the rope supporting the movable block, so that
W=±F, or F = %W. In Fig. 5, W=8F, as there are eight
parts of the rope supporting the movable block.

Differential Pulley. — The arrangement shown in Fig. 6 is
known as a differential pulley. The two fixed pulleys have
different radii r and R. The hoisting chain passes around the
larger of the fixed pulleys, then around the movable pulley
carrying the weight W, and then around the smaller fixed
pulley. The chain is joined at its ends, thus forming a con-
tinuous piece. The two fixed pulleys are fastened together
so that they must turn as one piece on their axle. When a

66 MECHANICS

pull P is exerted on a chain, the fixed pulleys are rotated.
The chain winds up on one side of the large pulley and
unwinds, at a slower rate, from the small pulley. As a result.

FIG. 5

FIG. 6

FIG. 7

the load W is lifted slightly at each turn of the fixed pulleys.
The weight W that can be lifted by a force P is found by the
formula

R-r

the letters R and r designating the radii of the large and small
fixed pulleys, respectively.

Wheel and Axle. — The device known as the wheel and axle
consists of two cylinders of different sizes connected rigidly,
so that they turn together. The rope carrying the load to
be raised is fastened to the smaller cylinder and the rope on
which the pulling force is exerted is wound on the larger cylin-
der, as shown in Fig. 7. The pull F causes the larger cylinder
to turn, rotating the smaller cylinder at the same rate. The
rope attached to the weight W is thus caused to wind on the
smaller cylinder, and the load is raised. If R and r represent,
respectively, the radii of the large and small cylinders, the
force F required to lift a weight W, and the weight W that may
be lifted by a force F, are given by the formulas

F = — and W =
R r

BELT PULLEYS

Solid and Split Pulleys. — Besides being used with ropes or
chains for the hoisting of loads, pulleys are extensively employed
with belts for transmitting power. Belt pulleys may be divided

MECHANICS

67

into two classes, namely, solid pulleys and split pulleys. A
solid pulley is one in which the arms, hub, and rim are cast
in one solid piece, as shown in Fig. 1. A split pulley is one that
is cast in halves that are afterwards bolted together, as shown
in Fig. 2. The latter style of pulley is more readily placed on
or removed from a shaft than is the solid pulley. Pulleys are
generally cast in halves or parts when they are more than
6 ft. in diameter. This is done on account of the shrinkage
strains in large pulley castings, which renders the pulleys liable
to crack as a result of unequal cooling of the metal.

FIG. 1

FIG. 2

Wooden Pulleys. — Although most belt pulleys are made of
cast iron, wrought iron, and steel, wooden pulleys have come
into extensive use. These are built of segments of wood
securely glued together, maple being the wood ordinarily
used. It is possible to procure wooden split pulleys that are
fitted with removable bushings, thus allowing the same pulley
to be adapted readily to shafting of different diameters.
Wooden pulleys are somewhat lighter than cast-iron pulleys
for the same service.

Driving and Driven Pulleys. — The pulley that imparts
motion to the belt is called the driving pulley, or the driver,
and the one that receives motion from the belt is called the
driven pulley, or simply the' driven. When two pulleys are
connected by a belt, the speeds at which the pulleys run are
inversely proportional to their diameters. Thus, if two
pulleys have diameters of 12 in. and 24 in., the speed of the
smaller is to the speed of the larger as 24 to 12, or as 2 to 1«

68 MECHA NICS

The speed of a pulley or of a shaft is usually stated in revo-
lutions per minute, abbreviated R. P. M.

Diameter and Speed of Driver. — It often becomes necessary
to calculate the size or the speed of a pulley that drives or is
being driven by a machine.

Let D = diameter of driving pulley, in inches;
d = diameter of driven pulley, in inches ;
N = number of R. P. M. of driving pulley;
« = number of R. P. M. of driven pulley.
Then, if the diameter of the driven and the required speeds
of both pulleys are given, the diameter of the driver may be
found by the formula

dn
D-- U>

If the speed of the driver is to be found, it is necessary to
use the formula

dn
X-- (2)

EXAMPLE. — A 12-in. pulley on a certain machine is to run
at 160 R. P. M. and is to be driven by belt from a pulley on
the shaft of an engine that makes 96 R. P. M. What must
be the diameter of the pulley on the engine shaft?

SOLUTION. — Substituting in formula 1,

12X160
D = =20 in.

Diameter and Speed of Driven. — If the diameter of the
driving pulley and the desired speeds of both pulleys are
known, the required diameter of the driven pulley may be
found by the formula

DN

d= (1)

n

If the speed of the driven pulley is to be found, it is necessary
to use the formula

DN

n = -~ (2)

a

EXAMPLE 1. — A 30-in. pulley on a line shaft running at
120 R. P. M. is to drive a pulley on a machine at 300 R. P. M.
What must be the diameter of the pulley on the machine?

MECHANICS 69

SOLUTION. — Substituting in formula 1,
30X120

i=^T-12ta'

EXAMPLE 2. — A driving pulley 48 in. in diameter makes
175 R. P. M. and is connected by belt to a driven pulley 14 in.
in diameter. What is the speed of the driven pulley?

SOLUTION. — Substituting in formula 2,

48X175

» = — 600 R. P.M.

14

BELTING

A belt is a flexible band by which motion is transmitted
from one pulley to another. The materials most commonly
used for belts are leather, cotton, and rubber, although thin,
flat bands of steel are coming into use. Leather belts are
usually made either single or double. A single belt is one
composed of a single thickness of leather, and a double
belt is one composed of two thicknesses of leather cemented
and riveted together throughout the whole length of the belt.
Still heavier belts, consisting of three or four thicknesses of
leather, and known as triple or quadruple belts, are sometimes
made for heavy drives. Cotton belts are made up of a number
of layers, or plies, sewed together and treated with a water-
proofing substance. They are termed two-ply, three-ply, etc.,
according to the number of plies they contain. Four-ply cot-
ton belting is usually considered equal to single leather belting.
Rubber belts are particularly adapted for use in damp or
wet places. They withstand changes of temperature without
injury, are durable, and are claimed to be less liable to slip
than are leather belts.

Sag of Belts. — The distance between pulley centers depends
on the size of the pulleys and of the belt; it should be great
enough so that the belt will run with a slight sag and a gently
undulating motion, but not great enough to cause excessive
sag and an unsteady flapping motion of the belt. In general,
the centers of small pulleys carrying light narrow belts should
be about 15 ft. apart and the belt sag 1J to 2 in.; for large
pulleys and heavy belts the distance should be 20 to 30 ft.
and the sag 2£ to 5 in. Loose-running belts will last much

70 MECHANICS

longer than tight ones, and will be less likely to cause heating
and wear of bearings.

Speed of Belts. — The higher the speed of a belt, the less
may be its width to transmit a given horsepower; consequently,
it follows that a belt should be run at as high a speed as con-
ditions will permit. The greatest allowable speed for a belt
joined by lacing is about 3,500 ft. per min., for ordinary single
and double leather belts. For belts joined by cementing,
when the joint has about the same strength as the solid belt,
the velocity may be as high as 5,000 ft. per min. Higher
speeds than these have been used, but there is little to be gained
by exceeding about 4,800 ft. per min. In choosing a proper
belt speed, due regard must be paid to commercial conditions.
Although a high speed of the belt means a narrow and cheaper
belt, the increased cost of the larger pulleys that may be
required may offset the gain due to the high speed of the belt,
at least so far as the first cost is concerned. The speed of a
belt, in feet per minute, may be found by multiplying the
number of revolutions per minute of the pulley by 3.1416
times the diameter of the pulley, in inches, and dividing the
product by 12.

Horsepower of Belts. — The pull on a belt is greatest on the
tight, or driving, side, and least on the slack side. The dif-
ference between the tensions, or pulls, in these two sides is
called the effective pull. The effective pull that may be allowed
per inch of width for single leather belts with different arcs
of contact is given in the accompanying table. The arc of
contact is the portion of the circumference of the smaller pulley
that is covered by the belt. The horsepower that can be
transmitted by a single leather belt may be found by the
formula

cwv

~ 33, 000*
in which // = horsepower of belt;

C = effective pull, taken from table;
H' = width of belt, in inches;
T' = speed of belt, in feet per minute.
If it is desired to find the width of single belt required
transmit a given horsepower, the formula becomes

MECHANICS

71

W--

33,000 H

CV

(2)

EXAMPLE 1. — What horsepower can be transmitted by a
single leather belt 4 in. wide running at a speed of 2,500 ft.
per min., if the belt covers one-third of the circumference of
the small pulley?

SOLUTION. — The fraction of the circumference covered by
the belt is | = .333. From the table, the allowable effective
pull corresponding to this value is 28.8. Substituting in
formula 1,

EXAMPLE 2. — A single leather belt is to run at a speed of
3,000 ft. per min. and is to transmit 18 H. P. Find the width
of the belt, if the arc of contact is 150°.

SOLUTION. — The effective pull corresponding to an arc of
contact of 150°, from the table, is 33.8. Substituting in
formula 2,

33,000X18

W=— — = 5.9 in.

33.8X3,000

A 6-in. belt would be used.

ALLOWABLE EFFECTIVE PULL

Arc of Contact

Allowable

Effective Pull

Degrees

Fraction of
Circumference

Pounds per
Inch of tyidlh

90

.250

23.0

112|

.312

27.4

120

.333

28.8

135

.375

31.3

150

.417

33.8

157£

.437

34.9

180 or over

.500 or over

38.1

The horsepower of a double leather belt may be taken as
1^ times that of a single leather belt of the same width running

72

MECHANICS

under the same conditions. Accordingly, the width of a double
leather belt required for any service is only T^ that of a single
belt for the same service.

Lacing of Belts. — A very satisfactory way of lacing belts
less than 3 in. wide is shown in Fig. 1, in which A is the outside
of the belt and B is the side that runs against the face of the
pulley. The ends of the belt are first cut square, and then
holes are punched in the ends, in corresponding positions
opposite one another. The number of holes in each row
should always be odd, in the style of lacing shown, using 3
holes in belts up to 2 in. wide and 5 holes in belts between
2 and 3 in. wide. The lacing is first drawn through one of
the middle holes from the under side, or pulley side, as at 1.
Then it is drawn across the upper side and is passed down
through 2, across under the belt to 3, up through 3, across and
down again through 2, back under the belt and up through 3
again, then across and down through 4 and finally up through
5, where a barb is cut in the edge of the lacing to prevent it
from pulling out. This completes the lacing of one half.
The other end of the lacing is then carried through the holes
in the other half, in the same order.

tt \N\V\\\V

FIG. 1

FIG. 2

For belts wider than 3 in., the lacing shown in Fig. 2 may be
used. In this case, there are two rows of holes in each end of
the belt to be joined. The row nearer the end of the belt should
have one more hole than the row farther away. For belts
up to 4} in. wide, use 3 holes in the first row and 2 holes in
the second row. For belts up to 6 in. wide, use 4 and 3 holes,
respectively. For wider belts, make the total number of holes

MECHANICS 73

in both rows either one or two more than the number of inches
of width of the belt, the object being to get an odd total number
of holes. For example, a 10-in. belt would have 10+1 = 11
holes, and a 13-in. belt would have 13+2 = 15 holes. The
outside holes of the first row should not be nearer the side
edges of the belt than f in. and not nearer the joint edge than
| in. The second row should be at least If in. from the joint
edge. In Fig. 2, A is the outside face and B the face next the
pulley. The lacing is first drawn up through 1 from the pulley
side, and then is carried through 2, 3, 4, 5, 6, 7, 6, 7, 4, 5,
2, 3, 8, and out at 9 to be fastened. The other end of the
lacing is used on the other half of the belt in the same way.

HYDRAULICS

Pressure Due to Head of Water. — Hydraulics treats of
liquids in motion. When a tank is filled with water, its
bottom and its sides are subjected to pressure due to the
weight of the water. The distance from a point at any given
level in the tank to the surface of the water, measured vertically,
is termed the head of water for that level. The pressure
exerted by the water is directly proportional to the head. A
cubic foot of water weighs approximately 62.5 lb., so that, if
a tank 1 sq. ft. in cross-section were filled with water to a
depth of 1 ft., it would contain 1 cu. ft., or 62.5 lb., of water.
The pressure on the bottom, having an area of 1 sq. ft., would
be 62.5 lb., or the weight of 1 cu. ft. of water; consequently,
the pressure per square inch would be 62.5 = 144 = .434 lb. In
other words, a column of water 1 ft. deep, or having a head of
1 ft., exerts a pressure of .434 lb. per sq. in. Knowing this
fact, the pressure due to any given head of water may be
found by the formula

p = .434 h,

in which p = pressure in pounds per square inch ;
h = head of water, in feet.

If it is desired to find the head of water necessary to produce
a certain pressure, the formula becomes

74 MECHANICS

Velocity of Flow. — If a hole is made in the side of a tank
filled with water, the water will issue therefrom with a velocity
depending on the head of water above the opening.

When water flows in a pipe, a ditch, or a channel of any
kind, the velocity is not the same at all points, because the
cross-section of the channel is not the same at all points, and
also because of friction. In such cases, the mean velocity is
taken in all calculations. The mean velocity is that velocity
which, being multiplied by the area of the cross-section of
the stream, will equal the total quantity discharged.

Flow of Water in Pipes. — For straight cylindrical pipes of
uniform diameter, the mean velocity of discharge may be calcu-
lated by the formula

in which Vm = mean velocity of discharge in feet per second ;
h = total head in feet = vertical distance between
the level of water in reservoir and the point
of discharge;

I = length of pipe, in feet;
d = diameter of pipe, in inches;
/ = coefficient of friction.

The head is always taken as the vertical distance between
the point of discharge and the level of the water at the source,
or point from which it is taken, and is always measured in
feet. It matters not how long the pipe is, whether vertical or
inclined, whether straight or curved, nor whether any part of
the pipe goes below the level of the point of discharge or not;
the head is always measured as stated above.

EXAMPLE. — What is the mean velocity of efflux from a
C-in. pipe, 5.780 ft. long, if the head is 170 ft.? Take /=. 021.
SOLUTION. — Substituting in formula 1,

Fm = 2.315 \/ — -- =6.69 ft. per sec.

\.021X5,780+(.125X6)

When the pipe is very long compared with the di
as in the foregoing example, use may be made of the formula

iameter,
y be made of the

fu
V?

Vm = '-'.:; I >\ .. (2)

MECHANICS

75

in which the letters have the same meaning as in the preceding
formula. This formula may be used when the length of the
pipe exceeds 10,000 times its diameter.

The actual head necessary to produce a certain velocity
Vm may be calculated by the formula

(3)

If the head, the length of the pipe, and the diameter of the
pipe are given, to find the discharge, use the formula

Q = . 09445 <#

hd

(•*)

'/H-.125<*

in which Q = discharge in U. S. gallons per second.

To find the value of /, calculate Vm by formula 2, assuming
that /= .025, and get the final value of /from the following table:

Y

/

Vm

/

Vm

/

.1

.0686

.7

.0349

2

.0265

.2

.0527

.8

.0336

3

.0243

.3

.0457

.9

.0325

4

.0230

.4

.0415

1

.0315

6

.0214

.0

.0387

H

.0297

8

.0205

.6

• .0365

H

.0284

12

.0193

EXAMPLE. — The length of a pipe is 6,270 ft., its diameter is
8 in. and the total head at the point of discharge is 215 ft.
How many gallons are discharged per minute?

7.67 ft. per sec.,
« = 8 (see table),

1.025X6.270

nearly. Using the value of /= .0205 for V-,

. 09455X82

215X8

•- 22.03 gal. per sec.

.0205X6,270 + (.125X8)
= 22.03X60 = 1,321.8 gal. per min.

If it is desired to find the head necessary to give a discharge
of a certain number of gallons per second through a pipe

76 COMBUSTION AND FUELS

whose length and diameter are known, calculate the mean
velocity of efflux by using the formula

24.51Q
Vm = -- -; (5)

d2

find the value of / from the table, corresponding to this value
of Vm , and substitute these values of / and Vm in the formula
for the head.

EXAMPLE. — A 4-in. pipe, 2,000 ft. long, is to discharge 24,000
gal. of water per hr.; what head is necessary?

24,000 24.51X61

SOLUTION.— Q = - = 6 j gal. per sec. V

= 10.2 ft. per sec. From the table, /=.0205 for Vm = S, and
.0193 for Vm = 12; assume that /= .02 for Vm = 10.2. Then

ft.

COMBUSTION AND FUELS

COMBUSTION

Nature of Combustion. — Combustion is the very rapid
chemical combination of two or more elements, accompanied
by the production of light and heat. The atoms of some of
the elements have a very great affinity or attraction for those
of other elements, and when they combine they rush together
with such rapidity and force that heat and light are produced.
Oxygen, for example, has a great attraction for nearly all the
other elements. For carbon, oxygen has a particular liking,
and whenever these two elements come into contact at a
sufficiently high temperature, they combine with great rapidity.
The combustion of coal in the furnace of a boiler is of this
nature. The temperature of the furnace is raised by kindling
the fire, and then the carbon of the coal begins to combine
with oxygen taken from the air.

Products of Combustion. — When carbon and oxygen com-
bine they form CO*, or carbon dioxide; when hydrogen and

COMBUSTION AND FUELS 77

oxygen combine they form water, HzO. These are called the
products of combustion. The oxygen required for combustion
is usually obtained from the air, which is a mixture composed
of approximately 23 parts of oxygen and 77 parts of nitrogen
by weight. The nitrogen that enters the furnace with the-
oxygen takes no part in the combustion, but passes through
the furnace and up the chimney without any change in its
nature.

Air Required for Combustion. — When carbon is burned to
carbon dioxide, COz, 1 atom of carbon unites with 2 atoms of
oxygen. Carbon has an atomic weight of 12 and oxygen has
an atomic weight of 16, so that the molecular weight of COi is
(1 X 12) + (2 X 16) = 44 ; hence COi is composed of 12 -^ 44 = 27.27
per cent, of carbon and 32 -=-44 = 72. 73 % of oxygen. To
burn a pound of carbon to COz, therefore, requires 32 -hi 2
= 2f Ib. of oxygen. If the oxygen is taken from the air, it
will take 2f -h. 23 = 11.6 Ib. of air to supply the 2f Ib. of oxy-
gen. This is because only 23% of air is oxygen. The com-
bustion of a pound of carbon to COz may be represented as
follows:

Mixture Elements Products

in Pounds in Pounds in Pounds

Carbon, 1.0 Carbon, l.OOl _ ,

Air 1,6 -I0"""' 2.6r)-Carbo"d'-de' 3'67

I Nitrogen, 8.93 Nitrogen, 8.93

12.6 12.60 12.60

That is, 1 Ib. of carbon requires 11.6 Ib. of air for complete
combustion. Of this air, 2.67 Ib. is oxygen which combines
with the pound of carbon, forming 3.67 Ib. of carbon dioxide.
The 8.93 Ib. of nitrogen contained in the air passes off with
the CO-i as a product of combustion.

Take, next, the complete combustion of 1 Ib. of hydrogen.
The product of the combustion is water, HiO. It has been
shown that HzO is composed by weight of 2 parts hydrogen
to 16 parts oxygen. Hence 1 Ib. of H requires 16 -=-2 = 8 Ib.
of O to unite with it. The air required to furnish 8 Ib. of O is
8 -T-. 23 = 34.8 Ib. The process of combustion is, therefore, as
follows:

78 COMBUSTION AND FUELS

Mixture Elements Products

in Pounds in Pounds in Pounds

Hydrogen, 1.0 Hydrogen, 1.0 1

Air 348=(°Xygen' 8-0/-Water'

\Nitrogen, 26.8 Nitrogen, 26.8

35.8 35.8 35.8

Incomplete Combustion. — There is one other case that may
occur; the combustion of carbon may not be complete. If
insufficient air or oxygen is supplied to the burning carbon,
it is possible for the carbon and oxygen to form another gas,
carbon monoxide, CO, instead of carbon dioxide, COz. The com-
bustion of 1 Ib. of carbon to form CO, of course, requires only
one-half the oxygen that would be necessary to form COz. This
is because in CO gas 1 atom of carbon seizes 1 atom of oxygen
instead of 2. To burn 1 Ib. of carbon to COz requires 11.6 Ib. of
.air. To burn it to CO would, therefore, require but 5.8 Ib. of air.
Calorific Value of Fuels. — The amount of heat, in B. T. U.,
developed by the complete combustion of 1 Ib. of a fuel is
termed the calorific value of that fuel; it is also sometimes
called the heat value or the heat of combustion. It may be
determined most accurately by burning a known weight of
the fuel with oxygen in an instrument known as a calorimeter.
The gases resulting from the combustion are passed through a
known weight of water and give up their heat to the water.
By noting the rise of temperature of the water, it is possible
to calculate the amount of heat absorbed, and thus to determine
the heat that would be produced by the combustion of 1 Ib.
of the fuel. The calorific values of the elements most commonly
found in fuels are as follows:

B. T. U. per Lb.

Hydrogen, burned to water, H->O 62,000

Carbon, burned to COi 14,600

Carbon, burned to CO 4,400

Sulphur, burned to SOi 4,000

If the various percentages, by weight of the elements, com-
posing a fuel are known, the approximate calorific value of
that fuel may easily be calculated by the formula

X=14,600C+62,000 \H ) +4,0005,

H

COMBUSTION7 AND FUELS 79-

in which X = calorific value of fuel, in B. T. U. per pound;
C = percentage of carbon, expressed as a decimal;
H = percentage of hydrogen, expressed as a decimal;
O = percentage of oxygen, expressed as a decimal;
5 = percentage of sulphur, expressed as a decimal.
EXAMPLE. — A coal contains 85% of carbon, 4% of oxygen,
6% of hydrogen, 1% of sulphur, and 4% of ash. What is
the heat of combustion per pound?

SOLUTION.— Applying the formula, X = 14, 600 X. 85+62,000

- — I +4,000 X. 01 = 15,860 B. T. U.

FUELS

SOLID FUELS

Fuels for Steam Making. — The fuels used in the generation-
of steam are chiefly coal, coke, wood, petroleum, and natural
gas. Other fuels, such as the waste gases from blast furnaces,
straw, bagasse, dried tan bark, green slabs, sawdust, peat, etc.,
are also used. All these fuels are composed either of carbon
alone or carbon in combination with hydrogen, oxygen, sulphur,
and non-combustible substances.

Classes of Coal. — Coal is the fuel most extensively used in
steam-plant work. Its different varieties may be classed in
four main groups, namely, anthracite, semianthracite, semi-
bituminous, and bituminous coal.

Anthracite Coal. — Anthracite coal contains from 92.31 to-
100% of fixed carbon and from 0 to 7.69% of volatile hydro-
carbons. It is rather hard to ignite and requires a strong
draft to burn it. It is quite hard and shiny; in color it is a
grayish black. It burns with almost no smoke, and this fact
gives it a peculiar value in places where smoke is objectionable.
Anthracite coal is known to the trade by different names,
according to the size into which the lumps are broken. These
names, with the generally accepted dimensions of the screens
over and through which the lumps of coal will pass, are as
follows: Culm passes through A-in. round mesh. Rice passes
over Ts-in. mesh and through j-in. square mesh. Buckwheat

SO COMBUSTION AND FUELS

No. 2 passes over J-in. mesh and through &-in. mesh. Buck-
wheat No. 1 passes over ^-in. mesh and through J-in. square
mesh. Pea passes over £-in. mesh and through f-in. square
mesh. Chestnut passes over f-in. mesh and through If-in.
square mesh. Stove passes over If -in. mesh and through 2-in.
square mesh. Egg passes over 2-in. mesh and through 2 f-in.
square mesh. Broken passes over 2 f-in. mesh and through
3i-in. square mesh. Steamboat passes over 3J-in. mesh and out
of screen. Lump passes over bars set from 3J to 5 in. apart.

Semianthracite Coal. — Semianthracite coal contains from
87.5 to 92.31% of fixed carbon and from 7.69 to 12.5% of vola-
tile hydrocarbons. It kindles easily and burns more freely
than the true anthracite coal; hence, it is highly esteemed as
a fuel. It crumbles readily and may be distinguished from
anthracite coal by the fact that when just fractured it will soil
the hand, while anthracite will not do so. It burns with very
little smoke. Semianthracite coal is broken into different sizes
for the market; these sizes are the same and are known by the
same trade names as the corresponding sizes of anthracite coal.

Semibituminous Coal. — Semibituminous coal contains from
75 to 87.5% of fixed carbon and from 12.5 to 25% of volatile
hydrocarbons. It differs from Semianthracite coal only in
having a smaller percentage of fixed carbon and more volatile
hydrocarbons. Its physical properties are practically the
same, and since it burns without the smoke and soot emitted
by bituminous coal, it is a valuable steam fuel. Semibitumi-
nous and bituminous coals are known to the trade by the fol-
lowing names: Lump coal includes all coal passing over screen
bars 1J in. apart. Nut coal passes over bars f in. apart and
through bars li in. apart. Pea coal passes over bars | in.
apart and through bars f in. apart. Slack includes all coal
passing through bars f in. apart.

Bituminous Coal. — Bituminous coal contains from 0 to
75% of fixed carbon and from 25 to 100% of volatile hydro-
carbons. It may be divided into three classes, whose names
and characteristics are as follows: Caking coal is the name
given to coals that, when burned in the furnace, swell and fuse
together, forming a spongy mass that may cover the whole
surface of the grate. These coals are difficult to burn, because ,

COMBUSTION AND FUELS 81

the fusing prevents the air from passing freely through the
bed of burning fuel. When caking coals are burned, the spongy
mass must be frequently broken up with the slice bar, in order
to admit the air needed for its combustion. Free-burning
coal is a class of bituminous coal that is often called non-caking
coal from the fact that it has no tendency to fuse together
when burned in a furnace. Cannel coal is a grade of bituminous
coal that is very rich in hydrocarbons. The large percentage
of volatile matter makes it valuable for gas making, but it is
little used for the generation of steam, except near the places
where it is mined.

Lignite. — Lignite, or brown coal, contains from 30 to 60% of
carbon, a small quantity of hydrocarbons, and a large amount
of oxygen. It occupies a position between peat and bituminous
coal, being probably of a later origin than the latter. It has
an uneven fracture and a dull luster. Its value as a steam
fuel is limited, since it will easily break in transportation.
Exposure to the weather causes it to absorb moisture rapidly,
and it will then crumble quite readily. It is non-caking and
yields but a moderate heat, and is in this respect inferior to
even the poorer grades of bituminous coal.

Miscellaneous Fuels. — Coke is made from bituminous coal
by driving off the volatile matter. It consists of from 88 to
95% of carbon, i to 2% of sulphur, and from 4 to 12% of ash.
It is little used for steam-boiler fuel.

Wood is used for fuel in localities where it is plentiful. It
contains from 20 to 50% of moisture when cut, and this per-
centage is not reduced much below 20% by drying. Wood
has a calorific value of 6,000 to 7,000 B. T. U. per Ib.

Peat consists of vegetable matter that is partly carbonized and
is found at the surface of the earth. It contains from 75 to 80%
water when cut, and must be dried before it can be used as fuel.

Bagasse is the refuse left after the juice has been extracted
from the sugar cane by means of the rolls. It is used to some
extent in tropical and semitropical countries. Naturally, its
use is limited to the places where the sugar cane is grown.

Dried tan bark, straw, slabs, and sawdust being refuse, their
use is local and usually confined to tanneries, planing and saw-
mills, and threshing outfits.

82 COMBUSTION AND FUELS

The Babcock & Wilcox Company state that on the average
1 Ib. of good bituminous coal may be considered as the equiva-
lent of 2 Ib. of dry peat, 2£ Ib. of dry wood, 2£ to 3 Ib. of dry
tan bark or sun-dried bagasse, 3 Ib. of cotton stalks, 3J Ib. of
straw, 6 Ib. of wet bagasse, and from 6 to 8 Ib. of wet tan bark.

LIQUID FUEL

Nature of Petroleum. — The fuel most extensively employed
in the generation of steam is coal, the most valuable of the solid
fuels. In some parts of the world, however, it has been found
convenient and economical to use liquid fuel. This is obtained
chiefly from petroleum, which is a natural oil obtained from the
earth. In its original state it is usually of a dark-green color
when viewed in the sunlight; but when held up to the light, so
that the light passes through it, it has a reddish-brown color.
The appearance of the oil will vary somewhat, depending on
the locality from which it is derived. In some cases it is
almost as clear and colorless as water, and in other cases it is
black; but American petroleum is commonly brown or red-
dish-brown with a green luster.

Composition of Crude Oil. — Petroleum in the form in which
it issues from the earth is known as crude oil. It usually con-
tains from 83 to 87% of carbon, from 10 to 16% of hydrogen,
and small percentages of oxygen, nitrogen, and sulphur. Some
crude oils are devoid of sulphur and nitrogen, but all those
obtained along the Pacific coast contain oxygen, sulphur,
nitrogen, and a small percentage of moisture. The presence of
sulphur in an oil is manifested by a very disagreeable odor.
The following analyses of crude oils from Beaumont, Texas,
and Bakersfield, Cal., will serve to give an idea as to the compo-
sition of the oils from these fields.

Constituents
of Crude Oil

Carbon
Hydrogen

Texas California
Per Cent. Per Cent.

84.60 85.0
10.90 12.0
1 63 8

Oxygen
Nitrogen
Moisture . .

2.87 1.0
.2
1.0

COMBUSTION AND FUELS 83

Properties of Fuel Oil. — Owing to the great demand for
gasoline in all its various grades, the better grades of petroleum,
such as those obtained in Pennsylvania, are treated so as to
recover the lighter hydrocarbons. Of these, gasoline is among
the early distillates, and when the gasoline, naphtha, and kero-
sene have been separated, the residue contains the lubricating
oils, paraffin, and coke. This residue may be further dis-
tilled, so as to obtain the several products named; or, it may be
used as a fuel, being then termed fuel oil. In other words, fuel
oil is simply the heavier compounds of carbon and hydrogen
contained in crude petroleum, the lighter compounds having
been driven off by distillation. The analysis of a fuel oil
derived from Beaumont crude oil is as follows:

Constituents Per Cent.

Carbon 83.26

Hydrogen 12.41

Sulphur .50

Oxygen 3.83

On comparing this analysis with that of Beaumont crude oil
previously given, it will be seen that the relative proportions
of hydrogen and carbon have been changed and that a large
part of the sulphur has been eliminated by the treatment of
the crude oil.

Calorific Values of Oil Fuels. — The combustible elements
contained in oil fuels are the same as those in coal, namely,
carbon and hydrogen, and possibly a small proportion of sul-
phur. The heat of combustion per pound of oil, or the calorific
value, may be found approximately from the chemical analysis
of the oil by the same formula as that used for rinding the heat
value of coal. A more accurate method, however, is to burn a
known weight of oil in a calorimeter and to measure the heat
generated, from which the heat per pound of the oil may readily
be calculated. From the results of available tests it is found
that the heat of combustion per pound of oil fuel varies between
17,000 and 21,000 B. T. U. The average calorific value of
Texas and California crude oils seems to be about 18,600
B. T. U. per Ib.

Atomization of Oil. — When coal is used under steam boilers,
the furnace contains a considerable amount of fuel; but early

84 COMBUSTION AND FUELS

experiments with liquid fuel soon proved that the methods
adopted for solid fuel were not applicable to liquid fuel, and
that the latter could not be burned successfully in bulk. To
insure satisfactory burning of oil fuel, it must first be changed
to a vapor, and this is now accomplished by atomizing the oil,
or converting it into the form of a very minutely divided
spray. It is the vapor that burns, and not the liquid oil
itself. If a sliver of burning wood is thrust into an open pan
of fuel oil, the oil will not ignite, and the flame of the stick
will be extinguished. The reason is that insufficient oil sur-
face is exposed to the action of heat, and vaporization does
not occur rapidly enough to supply the necessary quantity of
inflammable gases to support combustion. By atomizing the
oil, each minute particle is exposed to the air, thus providing
for rapid evaporation and complete combustion.

Mixture of Oil Spray and Air. — Having changed the oil to
a spray or to a vapor, it is next necessary to mix it intimately
with air in the correct ratio to produce complete combustion.
There are different methods by which the air is admitted so
as to accomplish the mixing. Sometimes it is allowed to enter
through holes surrounding the spraying devices and some-
times through openings from the ash-pit into the furnace;
combinations of both methods may also be used. In any event,
the main object to be attained is the thorough mixing of the
spray and the air, so that each particle of oil shall be surrounded
by the oxygen required for its perfect combustion.

Comparison of Steam and Air for Atomizing. — In stationary-
boiler practice the agent most extensively used for the atomi-
zation of oil fuel is steam, air being used in rare or special cases.
There seems to be little, if any, saving of fuel by using com-
pressed air for atomizing, for the reason that it requires
about the same amount of steam to operate the air compressor
as to atomize the oil directly. Moreover, with the direct use
of steam there is less complication of apparatus than when a
compressor is installed, and there is a correspondingly smaller
risk of accidents that may interrupt the service. Also the
installation required for atomization by air is considerably
more expensive than that required for the application of
steam.

COMBUSTION AND FUELS 85

Amount of Steam Used for Atomizing. — During 1902 and
1903 the Bureau of Steam Engineering of the U. S. Navy
Department made an extensive series of tests of oil burners
using steam and air as atomizing agents. From the results of
these tests it is found that the atomization of each pound of oil
required the use of from .15 to 1 Ib. of steam, the average value
being about .55 Ib. For good performance, the value should lie
between .3 and .5 Ib. The amount of steam used for atomiza-
tion, expressed as a percentage of the total amount of steam
generated by the boiler, ranged from 1 to 10%, but the aver-
age was approximately 2%. The foregoing values refer to the
steam used for atomization only, whether directly or through
the medium of the compressor, and are representative of aver-
age practice. They do not include the steam required for the
oil-pressure pumps, which amounts to another 2%, approxi-
mately. Hence, in calculating capacities for an installation,
it will be safe to assume that 5% of the steam generated will
be utilized by the atomizing and pressure systems.

Effect of Steam on Combustion. — The steam that is used
for the purpose of atomizing the oil does not increase the total
heat resulting from combustion, although it may affect the
character of the chemical changes in certain parts of the
flame so as to produce a higher temperature at those points.
An impression that seems to have gained credence is that the
steam, under the effects of the high furnace temperature, is
dissociated into its elements, oxygen and hydrogen, and that
the combustion of the hydrogen thus set free increases the heat
of combustion. The impression is wrong, for it takes just as
much heat to break the steam up into its elements as is obtained
by the subsequent uniting of those elements. Consequently,
if the combustion is perfect, the steam that enters the furnace
passes up the stack as steam, carrying away heat with it, and
the greater the amount of steam introduced, the greater will
be the heat loss. Thus, the introduction of steam into the
furnace decreases the available heat rather than increases it.

Excess of Air in Oil Burning. — A pound of oil fuel of average
composition requires about 13 or 14 Ib. of air for its complete
combustion; however, a greater amount must be admitted to
the furnace to insure complete combustion, as the mixture of

M, COMBUSTION AND FUELS

the air and the oil is not perfect. The excess of air is required
in order that the combustible elements may be surrounded
by sufficient oxygen during the subsequent mixing in the com-
bustion chamber. The percentage of this excess should be as
small as can be obtained without forming smoke. In some
boiler tests the excess has amounted to only 10%, which is
extremely low; but under average conditions the excess of air
is usually over 15%. When coal is used as fuel, the excess of
air is from 50 to 100%, or more; therefore, it is not surprising
that a fireman accustomed to burning coal should admit too
much air when burning oil fuel. To serve as a guide to the
fireman in the regulation of combustion, it is a good plan to
install a COz recorder, which will give a continuous record of
the percentage of COz in the flue gases. The amount of COt
formed bears a known relation to the amount of air admitted,
and by instructing the fireman to obtain as high a percentage
of COz as possible, the economy of operation may be increased.
In practice, about 15% of COz indicates the best performance
obtainable, and an average of from 12 to 13% may be consid-
ered very satisfactory.

Evaporative Power of Oil Fuel. — Owing to its higher calo-
rific value, oil fuel has a greater evaporative capacity, per lb.,
than is possessed by coal. Moreover, the conditions under
which oil fuel is burned enable a greater proportion of the
heating value to be obtained for evaporation of the water than
is the case with coal. As a consequence, the number of pounds
of water evaporated per lb. of oil is greater than the evapora-
tion per lb. of coal. Tests of boilers using a good grade of
coal have shown an evaporation of slightly more than 1 1 lb.
of water per lb. of coal and, under particularly favorable condi-
tions, even better results have been obtained. On the other
hand, an average evaporation of from 12 to 13 lb. of water per
lb. of oil has frequently been obtained with oil fuel, and in some
cases an evaporation of 16 lb. has been reached.

Effect of Sulphur in Oil. — The presence of sulphur in oil
fuels, particularly in crude oils, has caused some engineers to
fear that the plates and tubes of oil-burning boilers would be
pitted and corroded by the sulphurous gases generated. Their
fears, however, seem to have been groundless, inasmuch as the

COMBUSTION AND FUELS 87

boiler inspection and insurance companies, who would be most
likely to know, have made mention of no cases of excessive
pitting or corrosion directly traceable to the presence of sul-
phur in oil fuel. Some of the lower grades of bituminous-
coal, containing from 2 to 4% of sulphur, have been used in
steam-boiler furnaces without detriment to the boilers, although
the grate bars may have been affected. Consequently, there
seems to be no good reason why oil containing sulphur cannot
be burned with the same freedom from deteriorating effects
on the boiler.

Flash Point and Firing Point. — If a sample of fuel oil or of
crude oil is placed in an open cup and heat is applied, the oil
will begin to vaporize and inflammable gases will be driven
off. If, while the heating proceeds, a lighted match is passed
at intervals over the surface of the oil and about § in. from it, a
point will be reached at which the vapor rising from the oil
will ignite and burn with a flicker of blue flame. The tempera-
ture of the oil when this flame first becomes apparent is
termed the flash point of the oil. If the heating of the sample
is continued, the vapors will be given off more rapidly and
eventually they will ignite and burn continuously at the sur-
face of the oil when the lighted match is brought near. The
temperature of the oil when the burning becomes continuous
is termed the firing point of the oil. The flash point and the
firing point of an oil depend on the composition, specific grav-
ity, and source of the oil.

Specifications for Oil Fuel. — An oil to be used as a fuel for
steam boilers may be either a crude oil of uniform composition
or a fuel oil. If it is the latter, all constituents having a low
flash point will have been removed by distillation. The dis-
tillation should not have been carried on at a temperature high
enough to burn the oil or to cause particles of carbon to sepa-
rate from the oil; for these carbon particles will eventually clog
the pipes and burners and cause trouble. The flash point of
an oil fuel, as determined by a standard testing apparatus,
should not be below 140° F.; otherwise, there will be danger
from the inflammable vapors given off. The percentage of
water in the oil should be less than 2, and the percentage of
sulphur should not exceed about 1. If these proportions are

88 COMBUSTION AND FUELS

exceeded, the oil will be more troublesome to use and should
be purchasable at a correspondingly lower price.

Firebrick Lining of Furnaces. — It is possible to burn oil fuel
by spraying the oil directly into the metallic firebox of an
internally fired boiler or the ordinary furnace of an externally
fired boiler; but, although it may be done and .occasionally is
done, it is not good practice and is not recommended. The
spray of oil issuing from the burner should not strike the tubes
or the comparatively cold metal surfaces of the boiler, but
should first be completely burned in a combustion chamber of
ample size, after which the hot gases may be led into contact
with the heating surface of the boiler. A carefully designed
furnace is either partly or wholly lined with firebrick, which
protects the boiler from the direct action of the flames, prevents
the hot gases from being chilled before combustion is complete,
and tends to produce a more uniform transmission of heat to
the boiler.

Effect of Firebrick Lining on Combustion. — Under the effect
of the high temperature of combustion of oil fuel, the firebrick
lining of the furnace is maintained in an incandescent state,
which is of advantage in that it tends to promote a more nearly
uniform flow of heat to the boiler. If there is dirt or water in
the oil supply, or if the oil pumps do not act properly, so that
the oil supply is variable in pressure or not continuous, the
burners will act in a gusty, erratic manner. Under such cir-
cumstances, with an unlined firebox or furnace, it would be
difficult and troublesome, if not impossible, to maintain com-
bustion; but with a lining of incandescent firebrick there is a
reserve of heat in the furnace, so that combustion will be
restarted in case the fuel supply is momentarily interrupted
by dirt or water. Moreover, the firebrick, acting as a heat
reservoir, makes the flow of heat to the boiler more regular,
without seriously reducing the heat-transmitting efficiency of
the plates or tubes that it covers.

Furnace Proportions for Oil Fuel. — It is not necessary to
observe any definite ratio of length to breadth or length
to depth of the combustion space. The important point is to
provide ample volume, and then to insure that the gases fill it in
all parts and have the same velocity of flow throughout it.

STEAM

STEAM

PROPERTIES OF STEAM

Saturated Steam. — If water is put in a closed vessel and
heat is applied until boiling occurs and steam is given off, the
pressure and the temperature of the steam will be the same as
those of the water. The steam thus produced is known as
saturated steam; that is, saturated steam is steam whose tem-
perature is the same as that of boiling water subjected to the
same pressure. Its nature is such that any loss of heat will
cause some of the steam to condense, provided the pressure is
not changed. Saturated steam that carries no water particles
with it is called dry saturated steam; if it contains moisture,
it is called wet steam. At every different pressure, saturated
steam has certain definite values for the temperature, the
weight per cubic ft., the heat per lb., and so on. These various
values, collected and arranged in order, form the table of the
Properties of Saturated Steam, more commonly termed the
Steam Table. This table is shown on the following pages.

The various properties of steam, with their symbols, as given
in the Steam Table, are as follows:

1. The temperature, t, of the steam, which is the boiling
point of the water from which the steam is formed.

2. The heat of the liquid, q, which is the number of B. T. U.
required to raise the temperature of 1 lb. of water from 32° F.
to the boiling point corresponding to the given pressure.

3. The latent heat of vaporization, r, often termed the latent
heat, which is the number of B. T. U. required to change
1 lb. of water at the boiling point into steam at the same
temperature.

4. The total heat of vaporization, H, often termed the total
heat, which is the number of B . T. U. required to raise 1 lb. of
water from 32° F. to the boiling point for any given pressure
and to change it into steam at that pressure. It is the sum of
the heat of the liquid and the latent heat.

90

STEAM

PROPERTIES OF SATURATED STEAM

Abso-

British Thermal Units

I

lute

Wpiaht

Press.
Lb.

E

In.

Fahren-
heit
Temper-
ature

Heat
of the
Liquid
from
32° F.

Total
Heat
from
32° F.

Latent
Heat of
Vapori-
zation

Volume
of 1 Ib.
in
Cu. Ft.

w t ignt
of 1
Cu. Ft.
in
Pounds

P

f

Q

H

r

V

w

1

101.99

70.0

1,113.1

1,043.0

334.6

.00299

2

126.27

94.4

1,120.5

1,026.1

173.6

.00576

3

141.62

109.8

1,125.1

1,015.3

118.4

.00844

4

153.09

121.4

1,128.6

1,007.2

90.31

.01107

5

162.34

130.7

1,131.5

1,000.8

73.22

.01366

6

170.14

138.6

1,133.8

995.2

61.67

.01622

7

176.90

145.4

1,135.9

990.5

53.37

.01874

8

182.92

151.5

1,137.7

986.2

47.07

.02125

9

188.33

156.9

1,139.4

982.5

42.13

.02374

10

193.25

161.9

1,140.9

979.0

38.16

.02621

11

197.78

166.5

1,142.3

975.8

34.88

.02866

12

201.98

170.7

1,143.6

972.9

32.14

.03111

13

205.89

174.6

1,144.7

970.1

29.82

.03355

14

209.57

178.3

1.145.8

967.5

27.79

.03600

14.7

212.0

180.8

1,146.6

965.8

26.60

.03760

16

216.32

185.1

1,147.9

962.8

24.59

.1110117

18

222.40

191.3

1,149.8

958.5

22.00

.04547

20

227.95

196.9

1,151.5

954.6

19.91

.05023

22

233.06

202.0

1,153.0

951.0

18.20

.05495

24

237.79

206.8

1.154.4

947.6

16.76

.05966

26

242.21

211.2

1,155.8

944.6

15.55

.06432

28

246.36

215.4

1.157.1

941.7

14.49

.06899

30

250.27

219.4

1,158.3

938.9

13.59

.07360

32

253.98

223.1

1,159.4

936.3

12.78

.07820

34

257.50

226.7

1,160.4

933.7

12.07

.OS2XO

36

260.85

230.0

1,161.5

931.5

11.45

.08736

38

264.06

233.3

1.162.5

929.2

10.88

.09191

40

267.13

236.4

1,163.4

927.0

10.37

.09644

42

270.08

239.3

1,134.3

925.0

9.906

.1009

44

272.91

242.2

1.165.2

923.0

9.484

.1054

46

275.65

245.0

1,166.0

921.0

9.907

.1099

48

278.30

247.6

1,166.8

919.2

8.740

.11 H

50

2x0. sr,

2.50.2

1,167.6

917.4

8.414

.1188

52

283.32

252.7

1.168.4

915.7

8.110

.1233

54

285.72

255.1

1,169.1

914.0

7.829

.1277

56

2XX.O:>

257.5

1,169.8

912.3

7>>f,8

.1321

58

200.31

259.7

1,170.5

910.8

7.323

.1366

60

292.51

261.9

1.171.2

909.3

7.096

.1 10'.)

62

294.65

264.1

1,171.8

907.7

6.882

.1453

64

2W.74

266.2

1.172.1 '.«)<;._> 6.680

.1497

STEAM
TABLE — (Continued)

91

p

t

Q

H

r

V

w

66

298.78

268.3

1,173.0

904.7

6.490

.1541

68

300.76

270.3

1,173.6

903.3

6.314

.1584

70

302.71

272.2

,174.3

902.1

6.144

.1628

72

304.61

274.1

,174.9

900.8

5.984

.1671

74

306.46

276.0

,175.4

899.4

5.834

.1714

76

308.28

277.8

,176.0

898.2

5.691

.1757

78

310.06

279.6

,176.5

896.9

5.554

.1801

80

311.80

281.4

,177.0

895.6

5.425

.1843

82

313.51

283.2

,177.6

894.4

5.301

.1886

85

316.02

285.8

,178.3

892.5

5.125

.1951

90

320.04

290.0

,179.6

889.6

4.858

.2058

95

323.89

294.0

,180.7

886.7

4.619

.2165

100

327.58

297.9

,181.9

884.0

4.403

.2271

105

331.13

301.6

,182.9

881.3

4.206

.2378

110

334.56

305.2

,184.0

878.8

4.026

.2484

115

337.86

308.7

,185.0

876.3

3.862

.2589

120

341.05

312.0

,186.0

874.0

3.711

.2695

125

344.13

315.2

,186.9

871.7

3.572

.2800

130

347.12

318.4

,187.8

869.4

3.444

.2904

135

350.03

321.4

,188.7

867.3

3.323

.3009

140

352.85

324.4

,189.5

865.1

3.212

.3113

145

355.59

327.2

1,190.4

863.2

3.107

.3218

150

358.26

330.0

1,191.2

861.2'

3.011

.3321

155

360.86

332.7

1,192.0

859.3

2.919

.3426

160

363.40

335.4

1,192.8

857.4

2.833

.3530

165

365.88

338.0

1,193.6

855.6

2.751

.3635

170

368.29

340.5

1,194.3

853.8

2.676

.3737

175

370.65

343.0

1,195.0

852.0

2.603

.3841

180

372.97

345.4

1,195,7

850.3

2.535

.3945

185

375.23

347.8

1,196.4

848.6

2.470

.4049

190

377.44

350.1

1,197.1

847.0

2.408

.4153

195

379.61

352.4

1,197.7

845.3

2.349

.4257

200

381.73

354.6

1,198.4

843.8

2.294

.4359

205

383.82

356.8

1,199.0

842.2

2.241

.4461

210

385.87

358.9

1,199.6

840.7

2.190

.4565

215

387.88

361.0

1,200.2

839.2

2.142

.4669

220

389.84

363.0

1,200.8

837.8

2.096

.4772

225

391.79

365.1

1,201.4

836.3

2.051

.4876

230

393.69

367.1

1,202.0

834.9

2.009

.'4979

235

395.56

369.0

1,202.6

833.6

1.968

.5082

240

397.41

371.0

1,203.2

832.2

1.928

.5186

250

400.99

374.7

1,204.2

829.5

1.854

.5393

260

404.47

378.4

1,205.3

826.9

1.785

.5601

275

409.50

3S3.6

1,206.8

823.2

1.691

.5913

300

417.42

391.9

1,209.3

817.4

1.554

.644

325

424.82

399.6

1,211.5

811.9

1,437

.696

92 STEAM

5. The specific volume, V, which is the volume, in cubic ft.,
of 1 Ib. of steam at the given pressure.

6. The density, w, which is the weight, in pounds, of 1 cu. ft.
of steam at the given pressure. It is the reciprocal of the
specific volume.

The pressures, p, given in the first column of the Steam
Table, are absolute pressures. The pressure registered by the
gauge on the boiler is the gauge pressure, or the pressure of the
steam above that of the atmosphere. The pressure of the
atmosphere at sea level, with the barometer at about 30 in.,
is approximately 14.7 Ib. per sq. in. Therefore, the abso-
lute pressure at sea level is equal to the gauge pressure
plus 14.7. In using the Steam Table, the atmospheric pres-
sure, 14.7 Ib. per sq. in., must always be added to the gauge
pressure.

Use of Steam Table. — For any absolute pressure p given in
the first column of the Steam Table, the corresponding temper-
ature /, total heat H, or other property is found in the same
horizontal line, under the proper column heading; but if the
pressure lies between two of the values given in the first column,
the corresponding temperature, total heat, etc. must be found
by the process known as interpolation, as illustrated in the
following examples:

EXAMPLE 1. — Find the temperature corresponding to a
pressure of 147 Ib. per sq. in., absolute.

SOLUTION. — Referring to the Steam Table,

for/>=1501b., / = 358.26°

and for p = 145 Ib., t - 355.59°

Difference, 5 Ib., 2.67°

2.67°

Difference for 1 Ib. difference of pressure is = .534°.

5

147 lb.^145 lb. = 2 Ib., the given difference of pressure; and
for this, the difference in temperature is 2 X. 534°= 1.068° or
1.07°, taking two decimal places. Hence, the increase of 2 Ib.
from 145 Ib. to 147 Ib. is accompanied by an increase in temper-
ature of 1.07°. Therefore, adding the increase 1.07° to the
temperature 355.59° corresponding to 145 Ib., the temperature
for 147 Ib. is 355.59° +1.07° = 356.66°.

STEAM 93

EXAMPLE 2. — The pressure in a steam boiler as shown by
the gauge is 87 Ib. per sq. in. What is the temperature of
the steam?

SOLUTION. — The absolute pressure is 87+14.7 = 101.7 Ib.
per sq. in. This pressure, in the Steam Table, lies between,
the values 100 and 105.

for £ = 1051b., f = 331.13°
for £ = 100 Ib.. * = 327.58°
Difference, 5 Ib., 3.55°
For 1 Ib. change of pressure, the difference in temperature

3.55°

is — — = .71°. From 100 Ib. to 101.7 Ib., the change of pres-
5

sure is 1.7 Ib., and the corresponding change of temperature
is .71°X 1.7 = 1.207°, or 1.21° as the values in the Steam
Table contain but two decimal places. For 101.7 Ib., therefore,
the temperature is 327.58° + 1.21° = 328.79°.

EXAMPLE 3. — What is the pressure of steam at a temperature
of 285° P.?

SOLUTION. — From the Steam Table,

for/ = 285.72°, £ = 541b.
for / = 283.32°, p = 52 Ib.
Difference, 2.40°, 2 Ib.

From t = 283.32° to / = 285°, the increase of temperature
is 1.68°. Now, since an increase of temperature of 2.40° gives
an increase of pressure of 2 Ib., the increase of 1.68° must give

1.68
an increase of pressure of — X2 lb. = 1.4 Ib. Hence, the

required pressure is 52 lb. + 1.4 lb. = 53.4 Ib.

EXAMPLE 4. — Find, from the Steam Table, the total heat of
a pound of saturated steam at a pressure of 63 Ib. per sq. in.,
gauge.

SOLUTION. — The absolute pressure is 63 + 14.7 = 77.7 Ib. per
sq. in. From the Steam Table,

for p = 78 Ib., H = 1,176.5 B. T. U.

for p = 76 Ib., H = 1.176.0 B. T. U.

Difference, 2 Ib., .5 B. T. U.

Difference, 1 Ib., .25 B. T. U.

8

«J4 STEAM

The difference between the given pressure and 76 Ib. is 77.7
— 76 = 1.7 Ib. For a difference of 1.7 Ib., the change of total
heat is 1.7 X .25 = .425 B. T. U. Hence, for 77.7 Ib., H = 1,176.0
+ .425=1,176.425, say 1,176.4 B. T. U.

EXAMPLE 5. — Find the volume occupied by 14 Ib. of steam at
30 Ib. gauge pressure.

SOLUTION. — Absolute pressure = 30+14.7 = 44.7 Ib. per sq. in.
From the Steam Table,

for £ = 44 Ib., V = 9.484 cu. ft.

for £ = 46 Ib., F = 9.097 cu. ft.

Difference, 2 Ib., .387 cu. ft.

.387
The difference for 1 Ib. is = .1935. 44.7-44 = .7 Ib.

actual difference in pressure. . 1935 X. 7 = .135 difference in
volume. As the pressure increases, the volume decreases;
and to obtain the volume at 44.7 Ib., it is necessary to sub-
tract the difference .135 from the volume at 44 Ib.; thus, for p
= 44.7, v = 9.484 -.135 = 9.349 cu. ft. The volume of 14 Ib.
is 14X9.349 cu. ft. = 130.89 cu ft.

EXAMPLE 6. — Find the weight of 40 cu. ft. of steam at a
temperature of 25-4° F.

SOLUTION. — From column 10 of the Steam Table, the weight
w of 1 cu. ft. of steam at 253.98 is .07820 Ib: 254 — 253.98 = .02.
Neglecting the .02°, the weight of 40 cu. ft. is therefore
,07820X40-3.128 Ib.

EXAMPLE 7. — How many pounds of steam at 64 Ib. pressure,
absolute, are required to raise the temperature of 300 Ib. of
water from 40° to 130° P., the water and steam being mixed
together?

SOLUTION. — The number of heat units required to raise 1 Ib.
from 40° to 130° is 130° -40° = 90 B. T. U. Actually, a little
more than 90 would be required but the above is near enough
for all practical purposes. Then, to raise 300 Ib. from 40°
to 130° requires 90X300 = 27,000 B. T. U. This quantity of
heat must necessarily come from the steam. Now, 1 Ib. of steam
at 64 Ib. pressure gives up, in condensing, its latent heat of
vaporization, or 906.2 B. T. U.; but, in addition to its latent
heat, each pound of steam on condensing must give up an

STEAM 95

additional amount of heat in falling to 130°. Since the original
temperature of the stealn was 296.74° F. (see Steam Table),
each pound gives up by its fall of temperature 296.74 — 130
= 166.74 B. T. U. Consequently, each pound of the steam
gives up a total of 906.2+166.74 = 1,072.94 B. T. U., and

'- = 25.16 Ib. of steam will therefore be required to

1,072.94

accomplish the desired result.

SUPERHEATED STEAM

If saturated steam is contained in a vessel, out of contact
with water, and heat is added to it, its temperature will begin
to rise and its weight per cu. ft. will begin to decrease, pro-
vided the pressure remains constant. As more heat is added,
the temperature rises farther above that of saturated steam
at that pressure, and the steam is then called superheated
steam. Superheated steam cannot exist in contact with water.

The following distinction is usually made between saturated
and superheated steam: For a given pressure, saturated steam
has one temperature and one weight per cu. ft., neither of
which can change so long as the steam remains in immediate
contact with water. Superheated steam at the same pressure
has a greater temperature and less weight per cu. ft. than sat-
urated steam, and both the temperature and weight per cu. ft.
may vary while the pressure remains constant if the volume
increases or decreases accordingly. In other words, .both the
pressure and the volume of superheated steam must be con-
stant in order to maintain a constant temperature and a con-
stant weight per cu. ft.

QUALITY OF STEAM

Moisture in Steam. — The steam furnished by the average
steam boiler is not dry saturated steam, but is usually wet
steam. A good boiler should not show more than 2 or 3%
of water in the steam. In a quantity of wet steam, or a mix-
ture of steam and water, the percentage of dry steam, expressed
as a decimal, is called the quality of the steam. For example,
suppose that a certain boiler generates wet steam that con-
tains 3%, or .03, of moisture; then the quality of the steam.

36 STEAM

•or the percentage of dry steam, is .97. In other words, the
quality of the steam is equal to 1 minus the percentage of
moisture, expressed decimally. This rule may be stated
simply by the formula

Q=l-m,
in which Q = quality of the steam;

m = percentage of moisture, expressed decimally.

EXAMPLE. — What is the quality of steam that contains 2.7%
of moisture?

SOLUTION. — Expressed as a decimal, 2.7% = .027. Then,
substituting this value for m in the formula, Q = 1 — .027 = .973.

Heat in Wet Steam. — The total heat contained in 1 Ib. of
dry steam is the sum of the heat required to raise 1 Ib. of water
from 32° F. to the boiling point and the heat required to change
the boiling water into steam of the same temperature. That
is, in the Steam Table, each value given in the fourth column
is the sum of the values given in the third and fifth columns
and lying in the same horizontal row. In a mixture of 1 Ib. of
steam and water at the same temperature there is less heat than
in 1 Ib. of dry steam at the same temperature; for all the water
has not been changed to steam, and consequently the latent
heat of 1 Ib. of steam has not been utilized. Instead, there is
present only that part of the latent heat which is used to evap-
orate the portion of the mixture that is dry steam, which is
represented by the quality of the steam. Thus, using the
symbols given in the Steam Table,

H = q+r (1)

which is the formula for the total heat of 1 Ib. of dry steam.
But if the steam is wet, and Q represents the quality of the
steam, expressed decimally, the total heat of 1 Ib., represented
by//', is Hl = q+Qr (2)

EXAMPLE.— What is the total heat of 10 Ib. of steam at
150 Ib. gauge pressure, if the steam contains 5% of moisture?

SOLUTION. — From the Steam Table, the heat of the liquid
of lib. of dry steam at 150 Ib., gauge, or 150+14.7 = 164.7 Ib.,
absolute, is q = 337.84 B. T. U., and the latent heat of 1 Ib. at
the same pressure is r = 855.71 B. T. U. As the moisture is 5%,
the quality of the steam is 1.00 — .05 = .95. Then, applying
formula 2, //' =337.84 + .95X855.7 1 = 1,150.76 B. T. U.

STEAM

97

Barrel Calorimeter. — It is a rather difficult matter to make
a very exact determination of the moisture contained in steam.
The apparatus or instrument used for this purpose is called a
calorimeter. There are many more or less complicated calori-
meters, but about the simplest and most available one for
general use is the so-called barrel calorimeter, shown in the
accompanying illustration. A
barrel or tank a holding 400
or 500 Ib. of water is placed on
a platform scales b, filled with
water, and weighed. The tem-
perature of the water is regis-
tered by a thermometer inserted
in the side of the barrel. Steam
from the boiler is led through
a hose c into the barrel until
the temperature of the water

reaches 130° to 140° F. The steam is then turned off and the
barrel and its contents are again weighed. The difference
between this weight and the original weight is the weight of
the steam led in from the boiler and condensed in the barrel.
The average steam pressure throughout the process must be
observed. It is well to have the tube bent as shown in the
figure.

The weight of the cold water and the rise in its temperature
are known, and so also is the weight of the mixture of steam
and water that is led in from the boiler. From the Steam
Table, the temperature of the steam can be found, since the
average pressure is known. Now, if dry steam comes through
the hose c, the condensation of this steam should raise the
temperature of the cold water in the barrel a certain amount.
If the temperature is not raised that much, it must be because
some of the mixture led into the barrel was water.

Let Q = quality of steam;

W = weight of cold water in barrel, in pounds;
w = weight of mixture run into the barrel, in pounds;
t = temperature of steam corresponding to the observed

pressure ;
ti = original temperature of water, in barrel;

98 STEAM

tz = temperature of water in barrel after steam is con-

densed;
L = latent heat of 1 Ib. of steam at observed pressure.

Then, Q = — -

EXAMPLE. — In a calorimetric test, the weight of cold water
was 420 Ib., and of steam condensed, 36 Ib. The initial
temperature of the cold water was 40° F., the final tempera-
ture was 130° F., and the average steam pressure was 60 Ib.
Find the quality of the steam.

SOLUTION. — Absolute pressure = 60+ 14.7 = 74.7 Ib. per sq. in.
Latent heat of steam at this pressure, from Steam Table, is
898.5. The temperature of steam at this pressure is 307.2°.
Hence, by the formula

-- .9714

898.5

That is, the boiler generates a mixture that is composed of
97.14% of dry steam and 2.86% of water.

If the result found by the foregoing formula shows that Q
is greater than 1, the conclusion is that the steam, instead of
being wet, was superheated, and therefore gave up, in con-
densing, a greater amount of heat per pound than would have
been given up by 1 Ib. of dry saturated steam at the same
pressure.

The barrel calorimeter must be used very carefully in order
to obtain accurate results. The operation should be repeated
once or twice before the actual test is made so as to warm up
the barrel. The most important observation is the tempera-
ture. This should be taken by a thermometer graduated to
fifths or tenths of a degree. The weights should be as accu-
rate as possible. The chief merit of the barrel calorimeter is
its availability. It can be rigged up in almost any situation.

The quality of the steam having been determined, the actual
amount of water evaporated by a steam boiler is found by
multiplying the observed amount of feedwater by the quality
of the steam expressed decimally.

STEAM 99

FLOW OF STEAM

Weight of Steam Discharged. — The number of pounds of
steam that will flow continuously through a pipe of given
diameter in 1 min. at specified pressure may be calculated
by the formula

in which W = weight of steam discharged , in pounds per minute ;

w = weight of 1 cu. ft. of steam at the pressure Pi ;
Pi = pressure of steam at entrance to pipe, in pounds

per square inch;

P2 = pressure of steam at discharge, in pounds per
square inch;

L = length of pipe, in feet;

d = diameter of pipe, in inches.

In applying the preceding formula in determining the diam-
eter of the steam pipe for an engine, it must be remembered
that, in steam-engine work, the steam is drawn intermittently
from the pipe. Thus, assume that an engine of 100 H. P., con-
suming 30 Ib. of steam per horsepower per hour, cuts off at J
stroke. In that case, the steam consumption per hour would
be 100 X 30 = 3,000 Ib. But as the steam used at each stroke is
drawn into the cylinder during only one-fourth of the time
required to complete the stroke, the 3,000 Ib. of steam flows
through the pipe in J hr. Then, in order to determine the
quantity of steam that would flow continuously at the same
velocity at which it flows during admission to the cylinder,
the actual steam consumption per hour should be divided by
the fraction representing the cut-off and the quotient should be
taken as the weight of steam discharged per hour. This value,
divided by 60, should be substituted for w in the formula.
Thus, in the case mentioned, the amount of steam discharged
per hour, flowing continuously at the same velocity as during the
admission period, is 3,000 -f- i = 12,000, and the value of W to
be used in the formula is therefore 12, 000 -=-60 = 200 Ib. per
min. Knowing the pressures, the length of pipe, and the

100 STEAM

•weight of the entering steam per cubic foot, different values
of d may be assumed, until a value is found that will give the
necessary discharge W. This is the required pipe diameter.

The approximate weights of steam delivered per minute
through 100 ft. of pipe of various diameters, with a drop of
pressure of 1 lb., are given in the accompanying table. On
the whole, these values are slightly higher than those which
would be obtained by the foregoing formula for the same con-
ditions. If the drop of pressure is more or less than 1 lb., the
value in the table must be multiplied by the square root of the
drop, to obtain the discharge. Also, if the length of the pipe is
more or less than 100 ft., divide 100 by the length, in feet, and
multiply the square root of this quotient by the value given
in the table. The following example illustrates this point.

EXAMPLE. — How many pounds of steam will be discharged
per minute, with an initial gauge pressure of 120 lb. per sq. in.,
through a pipe 3 in. in diameter and 400 ft. long, with a drop of
pressure of 2 lb. ?

SOLUTION. — From the table, the amount discharged through
100 ft. of 3-in. pipe with a drop of 1 lb. and an initial pressure
of 120 lb. per sq. in., is 53.6 lb. per min. But as the drop
is 2 lb., the table value must be multiplied by ^2 and as the
length is 400 ft., it must also be multiplied by "V^. Hence,
the discharge for the given conditions will be 53.6 X "V2X \igg
= 37.9 lb. per min.

Resistance of Elbows and Valves. — The presence of elbows,
bends, and valves in a steam pipe increases the resistance to
the flow of steam and thus increases the drop of pressure
between the inlet and outlet ends. It has been found that the
resistance caused by an elbow or a sharp bend is approxi-
mately the same as the resistance of a length of pipe equal to
60 times the diameter, and that a stop-valve has a resistance
equal to that of a length of pipe of 40 diameters. In using
the foregoing formula for the weight of steam discharged,
therefore, the value of L should be the equivalent length of pipe,
taking into account the bends and valves. The method of
doing this is illustrated by the following example:

EXAMPLE. — What is the equivalent length of 300 ft. of 3-in.
pipe containing four elbows and six stop-valves?

STEAM

101

s

PER
DROP OF

ute
ure

vered per
Drop of

fl6COb-i-l"500i-l«O

t~00 00 O5OJO5OO

C^5 S 05 ^ ^ Ǥ o5

OiMecco^H

-

ts»OO1M|C10'^»OOt

c^c^cocococococo

cOt>'30c:OO^c<iro

CO OS <N <N O> •* t> t-; 5

(N 10 «O l> I> O •* N OJ

102 STEAM

SOLUTION. — Each elbow has a resistance the same as that
of 60 diameters of pipe, or 60X3 = 180 in. = 15 ft., and four
elbows have the resistance of 4X15 = 60 ft. of pipe. Each
stop-valve has a resistance that is equivalent to adding 40X3
= 120 in. = 10 ft. of pipe, and, as there are six valves, their com-
bined resistance is that of 6 X 10 = 60 ft. of pipe. The equiva-
lent length of pipe is, therefore, 300 + 60+60 = 420 ft.

Steam Pipes for Engines. — In practice, the velocity of flow
of steam in the supply pipes of engines and pumps is usually
not greater than 6,000 ft. per min., although it is increased to
as much as 8,000 ft. per min. in some cases. For exhaust
pipes, a common value is 4,000 ft. per min. The assumptions
made are that the cylinder is rilled with steam at boiler pressure
at each stroke and that a volume of steam equal to the volume
of the cylinder is released at each stroke, so that the flow is
practically continuous. The areas of the steam and exhaust
pipes may then be calculated by the formula

A S

a — —,
s

in which a =area of steam or exhaust pipe, in square inches;
A =area of cylinder, in square inches;
5 = piston speed, in feet per minute;
s = velocity of steam in pipe, in feet per minute.
EXAMPLE. — Find the areas of the steam and exhaust pipes
for an engine whose cylinder is*20 in. in diameter and whose
piston speed is 450 ft. per min.

SOLUTION. — By the formula, the area of the steam pipe,
assuming that 5 = 6,000 ft. per min., is
.7854X202X450

600

Similarly, for the exhaust pipe, assuming that 5 = 4,000, the
area is

.7854X202X450

4,000

= 35.3 sq. in.

STEAM BOILERS 103

STEAM BOILERS

FURNACE FITTINGS

Bridge Wall. — The bridge, also termed the bridge wall, is a
low wall at the back end of the grate; it forms the rear end
of the furnace and causes the flame to come in close contact
with the heating surface of the boilei It is usually built of
common brick and faced with firebi :k. The passage between
the bridge and the boiler shell should lot be too small; its area
may be approximately one-sixth the ar;?a of the grate. The
space between the grate and the shell should be ample for com-
plete combustion, and the distance between the grate and the
boiler shell may be made about one-half the diameter of the
shell.

Fixed Grates. — The grate, which is nearly always made of
cast iron, furnishes a support for the fuel to be burned and
must be provided with spaces for the admission of air. The
area of the solid portion of the grate is usually made nearly
equal to the combined area of the air spaces.

FIG. 1

The common type of fixed grate is made of single bars a,
Fig. 1 , placed side by side in the furnace. The thickness of
the lugs cast on the sides of the bars determines the width of the
open spaces of the grate. It is the general practice to make
the thickness across the lugs twice the thickness of the top of the
bar. For long furnaces, the bars are generally made in two
lengths of about 3 ft. each, with a bearing bar in the middle
of the grate. Long grates are generally set with a downward
slope toward the bridge wall of about f in. per foot of length.

104

STEAM BOILERS

For the larger sizes of anthracite and bituminous coal, the
air space may be from f to f in. wide, and the grate bar may
have the same width. For pea and nut coal, the air space may
be from f to $ in., and for finely divided fuel, like buckwheat
coal, rice coal, bird's-eye coal, crlm; and slack, air spaces from
& to | in. may be used.

FIG. 2

The grate bar shown n Fig. 2, and known as the herring-
bone grate bar, has in r.iany places superseded the ordinary
grate bar, because they will usually far outlast a set of ordi-
nary grate bars. Herring-bone grate bars can be obtained in
a great variety of styles and with different widths of air spaces.
They are usually supported on cross-bars, and, like many

FIG. 3

other forms of grate bars, may be arranged with trunnions, so
as to rock the individual bars by means of hand levers.

A form of cast-iron grate bar for the burning of sawdust is
shown in Fig. 3. The bar is semicircular in cross-section and
is provided with circular openings for the introduction of air.
Lugs are cast on each side of the bar to serve as distance pieces

in providing air spaces between

the bars.

Dead Plate.— The front ends

of the grate bars are usually
FIG. 4 supported on the dead plate,

which is a flat cast-iron plate

placed across the furnace just inside the boiler front and on a
level with the bottom of the furnace door. The purpose of
the dead plate is twofold: It forms a support for the firebrick

STEAM BOILERS 105

lining of the boiler front, and a resting place on which bitumi-
nous coal may be coked before it is placed on the fire. To
support the grate bars, the inner edge of the dead plate is
either beveled or a lip is provided, as at a, Fig. 4.

Objection to Stationary Grate Bars. — The greatest objec-
tion to stationary grate bars is that with them the furnace
door must be kept open for a considerable length of time
when the fire is being cleaned. Cleaning fires when the boiler
has a stationary grate not only severely taxes the fireman, but
the inrush of cold air chills the boiler plates, thus producing
stresses that in the course of time will crack them.

Shaking Grates. — There are on the market many designs of
shaking grates for large steam boilers, differing chiefly in detail
and arrangement. Usually the grate bars are hung on trun-
nions at each end and are connected together with bars to
which are attached shaking rods that extend forwards through
the furnace front. Levers or handles are attached to the
shaking rods, and by working them back and forth the grats
bars receive a rocking motion that breaks up the bed of coal
on the grate and serves to shake the ashes through into the
ash-pit. The fires may thus be kept clean without the neces-
sity of opening the fire-doors.

Classes of Mechanical Stokers. — A mechanical stoker is a
power-driven rocking grate arranged so as to give a uniform
feed of coal and to rid itself continuously of ashes and clinkers.
The principal designs of mechanical stokers and automatic
furnaces may be divided into two general classes, overfeed and
underfeed.

Overfeed Stoker. — In overfeed stokers the fixed carbon of
the coal is burned on inclined grates. The coal is pushed on
to these grates, which are given a sufficiently rapid vibratory
motion to feed it down at such a rate that practically all
the carbon is burned before reaching the lower end, where
the ashes and clinkers are discharged. In Fig. 5 is shown
a sectional view of a stoker of this class. The coal is fed into
the hopper a, from which it is pushed by the pusher plate b
on to the dead plate c, where it is heated. From c it passes
to the grate d. Each bar is supported at its ends by trunnions
and is connected by an arm to a rocker bar i, which is slowly

106

STEAM BOILERS

moved to and fro by an eccentric on the shaft s, so as
rock the grates back and forth; the grates thus gradually
move the burning fuel downwards. The ashes and clinkers
are discharged from the lower grate bar on to the dumping
grate e. A guard / may be raised, as shown by the dotted
lines, so as to prevent coke or coal from falling from the grate
bars into the ash-pit when the dumping grate is lowered. Air
for burning the gases is admitted in small jets through holes in
the air tile g, and the mixture of gas and air is burned in the

FIG.

hot chamber between the firebrick arch h and the bed of burning
coke below.

Underfeed Stoker. — The stoker shown in Fig. f> illustrates
the principle of operation and the construction of the under-
feed stoker. Coal is fed into the hopper a, from which it is
drawn by the spiral conveyer b and forced into the magazine d.
The incoming supply of fresh coal forces the fuel upwards to the
surface and over the sides of the magazine on the grates, where
it is burned. A blower forces air through a pipe / into the

STEAM BOILERS

107

chamber g surrounding the magazine. From g the air passes
upwards through hollow cast-iron tuyere blocks and out through
the openings, or tuyeres e. The gas formed in the magazine,
mixed with the jets of air from the tuyeres, risdfe through the
burning fuel above, where it is subjected to a sufficiently high
temperature to secure its combustion. Nearly all the air for
burning the coal is supplied through the tuyeres, only a very
small portion of the supply coming through the grate. The

FIG.

ashes and clinkers are gradually forced to the sides of the grate
against the side walls of the furnace, from which they are
removed from time to time through doors in the furnace front
similar to the fire-doors of an ordinary furnace. In other
words, owing to the construction of the underfeed stoker,
the fire must periodically be cleaned from clinkers and the
ashes removed by hand.

108

STEAM BOILERS

CHIMNEYS

Production of Draft. — It is well known that any volume of
gas is lighter when heated than the same volume of gas when
cool. When hot gases pass into the chimney, they have a tem-
perature of from 400° to 600° P., while the air outside the chim-
ney has a temperature of from 40° to 90° F. Roughly speak-
ing, the air weighs twice as much, bulk for bulk, as the hot
gases. Naturally, then, the pressure in the chimney is less
than the pressure of the outside air. The production of draft
and the satisfactory operation of a chimney
depend on this pressure difference. The pres-
sure of the draft depends on the temperature
of the furnace gases and the height of the
chimney. Chimney draft is affected by so
many varying conditions that no absolutely
reliable rules can be given for proportioning
chimneys to give a certain desired draft pres-
sure. The rules given for chimney proportions
are based on successful practice rather than on
pure theory.

Measurement of Draft. — The intensity
the draft may be measured by means of
water gauge such as is shown in the accom-
panying illustration. As will be seen, it is a
glass tube open at both ends, bent to the shape
of the letter U ; the left leg communicates with
the chimney. The difference in the two water
levels H and Z in the legs represents the intensity of the draft,
and is expressed in inches of water.

The draft produced by a chimney may vary from J in. to
2 in. of water, depending on the temperature of the chimney
gases and on the height of the chimney. Generally speaking,
it is advantageous to use a high chimney and as low a chimney
temperature as possible. The draft pressure required depends
on the kind of fuel used. Wood requires but little draft,
say J in. of water or less; bituminous coal generally requires
less draft than anthracite. To burn anthracite, slack, or culm,
the draft pressure should be about H in. of water.

STEAM BOILERS 109

Form of Chimney. — The form of a chimney has a pronounced
effect on its capacity. A round chimney has a greater capacity
for a given area than a square one. If the flue is tapering, the
area for calculation is measured at its smallest section. The
flue through which the gases pass from the boilers to the. chim-
ney should have an area equal to, or a little larger than, the
area of the chimney. Abrupt turns in the flue or contractions
of its area should be carefully avoided. Where one chimney
serves several boilers, the branch flue from each furnace to
the main flue must be somewhat larger than its proportionate
part of the area of the main flue.

Brick Chimneys. — Chimneys are usually built of brick,
though concrete, iron, and steel are often used for those of
moderate height. Brick chimneys are usually built with a flue
having parallel sides and a taper on the outside of the chimney
of from ^ to j in. per ft. of height. A round chimney gives
greater draft area for the same amount of material in its
structure and exposes less surface to the wind than a square
chimney. Large brick stacks are usually made with an inner
core and an outer shell, with a space between them. Such
chimneys are usually constructed with a series of internal
pilasters, or vertical ribs, to give rigidity. The top of the
chimney should be protected by a coping of stone or a cast-iron
plate to prevent the destruction of the bricks by the weather.

Iron and Steel Chimneys. — Iron or steel stacks are made of
plates varying from £ to | in. thick. The larger stacks are
made in sections, the plates being about J in. thick at the top
and increasing to £ in. at the bottom; they are lined with fire-
brick about 18 in. thick at the bottom and 4 in. at the top.
Sometimes no lining is used on account of the likelihood of
corrosion and the difficulty of inspection, and also because
the inside of lined stacks cannot be painted.

Chimney Foundations. — On account of the great concentra-
tion of weight, the foundation for a chimney should be care-
fully designed. Good natural earth will support from 2,000
to 4,000 Ib. per sq. ft. The footing beneath the chimney
foundation should be made of large area, in order to reduce
the pressure due to the weight of the chimney and its founda-
tion to a safe limit.

110 STEAM BOILERS

Height of Chimney. — The relation between the height of
the chimney and the pressure of the draft, in inches of water, is
given by the formula

_./7.6 7.9^
P = -

in which P = draft pressure, in inches of water;

H = height of chimney, in feet;
Ta and Tc = absolute temperatures of the outside air and of

the chimney gases, respectively.

EXAMPLE. — What draft pressure will be produced by a
chimney 120 ft. high, the temperature of the chimney gases
being 600° P., and of the external air 60° F.?
SOLUTION. — Substituting in the formula,

/ 7.6 7.9 \

^ = 120 (— —I =.859 in.

\460+60 460+600/

To find the height of chimney to give a specified draft pres-
sure, the preceding formula may be transformed. Thus,
P

7.G 7.9

U

EXAMPLE. — Required, the height of the chimney to produce
a draft of \\ in. of water, the temperature of the gases and of
the external air being, respectively, 550° and 62° F.

SOLUTION. — Substituting in the formula,

„,

7.6 7.9
522 ~ 1,010

In determining the height of a chimney in cities, it should
be borne in mind that it must almost always be carried to a
height above the roofs of surrounding buildings, partly in
order to prevent a nullification of the draft by opposing air-
currents and partly to prevent the commission of a nuisance.

Area of Chimney. — The height of the chimney being decided
on, its cross-sectional area must be sufficient to carry off
readily the products of combustion. The following for-
mulas for rinding the dimensions of chimneys are in common
use:

STEAM BOILERS 111

Let H = height of chimney, in feet;
H. P. = horsepower of boiler or boilers;

A = actual area of chimney, in square feet;
£ = effective area of chimney, in square feet;
5 =side of square chimney, in inches;
d = diameter of round chimney, in inches.

o rr r>

Then, E=^p = A-.6VZ (1)

H. P. = 3.33E Vff (2)

S=12V£+4 (3)

d =13.54 Vfi+4 (4)

The accompanying table has been computed from these
formulas.

EXAMPLE 1. — What should be the diameter of a chimney
100 ft. high that furnishes draft for a 600-H. P. boiler ?

.3X600
SOLUTION. — Substituting in formula 1, E = — —— = 18.

VlOO
Now, using formula 4, d= 13.54 Vis +4 = 61.44 in.

EXAMPLE 2. — For what horsepower of boilers will a chimney
64 in. sq. and 125 ft. high furnish draft ?

SOLUTION. — By simply referring to the table, the horsepower
is found to be 934.

Maximum Combustion Rate. — The maximum rates of com-
bustion attainable under natural draft are given by the
following formulas, which have been deduced from the
experiments of Isherwood:

Let F = weight, in pounds of coal per hour per square foot

of grate area;

H = height, in feet, of chimney or stack.
Then, for anthracite burned under the most favorable con-
ditions,

F = 2\//-l (1)

and under ordinary conditions,

F=1.5V//-1 (2)

For best semianthracite and bituminous coals,

F = 2.25V'// (3)

and for less valuable soft coals,

F = 3\// (4)

112

STEAM BOILERS

11

> § 8

i*J !

Ill IS

^

s. "~ c — c i-
r-i o — rc i- c-i

STEAM BOILERS 113

The maximum weight of combustion is thus fixed by the
height of the chimney; the minimum rate may be anything
less.

EXAMPLE. — Under ordinary conditions, what is the maxi-
mum rate of combustion of anthracite coal if the chimney is
120 ft. high ?

SOLUTION. — By formula 2,

F = 1.5>/120- 1 = 15| Ib. per sq. ft. per hr.

BOILER FITTINGS

Types of Safety Valve. — The safety valve is a device
attached to the boiler to prevent the steam pressure from rising
above a certain point. When steam is made more rapidly than
it is used, its pressure must necessarily rise; and if no means of
escape is provided for it, the result must be an explosion.
Briefly described, the safety valve consists of a plate, or disk,
fitting over a hole in the boiler shell and held to its place by a
dead weight, by a weight on a lever, or by a spring. The
weight or the spring is so adjusted that when the steam reaches
the desired pressure the disk is raised from its seat, and the
surplus steam escapes through the opening in the shell.

FIG. 1

Weight of Ball for Lever Safety Valve. — A simple diagram
of a lever safety valve is shown in Fig. 1. The valve stem and
the bail are attached to the lever at C and B, respectively,
and the fulcrum is at F.

114 STEAM BOILERS

Let d = F B = distance from fulcrum to weight, in inches;
c = F G = distance from fulcrum to center of gravity

of lever, in inches;
a = F C = distance from fulcrum to center line of

valve, in inches;
A =area of orifice beneath bottom of valve, in square

inches ;

W = weight of ball P, in pounds;
Wi = weight of valve and stem, in pounds;
Wt = weight of lever, in pounds;

p = blow-off pressure, in pounds per square inch.
Then, if the position of the ball P on the lever is fixed, the
required weight of the ball may be found by the formula
a(pA-Wi)-Wic

~7~

EXAMPLE. — The area of the orifice is 10 sq. in., the distance
from the valve to the fulcrum is 3 in., and the length of the
lever is 32 in. The valve and stem weigh 5 lb., the lever
weighs 12 lb., and the gauge pressure is 90 lb. What should
be the weight W, if placed 2 in. from the end of the lever,
assuming the lever to be straight ?

SOLUTION. — In this case, c = 3£=lG in., and d = 32 — 2 = 30 in.
Then, substituting in the formula,

Position of Ball for Lever Safety Valve.— If the ball of a
lever safety valve has a known weight and it is desired to find
at what distance from the fulcrum it must be placed so as to
give a required blow-off pressure, the formula to be used is

in which the various letters have the same meanings as before.
EXAMPLE. — Suppose all the quantities to remain the same
as in the solution of the preceding example, except that it is
desired that the boiler should blow off at 75 lb. gauge pressure,
instead of 90 lb. What will be the distance of the weight
from the fulcrum ?

STEAM BOILERS 115

SOLUTION. — Applying the formula

83.1

Roper's Safety-Valve Rules. — Some inspectors of the United
States Steamboat Inspection Service prefer to have lever
safety-valve problems worked out by the rules that follow,
known among American marine engineers as Roper's rules.
A candidate for a marine engineer's license should always use
Roper's rules when he knows that they are preferred by the
examining inspector.

Let A = area of valve, in square inches;

D = distance from center line of valve to fulcrum, in

inches;

L = distance of weight from fulcrum, in inches;
P = steam pressure in pounds, per square inch;
W= weight of load or weight on lever, in pounds;
V = weight of valve and stem, in pounds;
w = weight of lever, in pounds ;
1 = distance from fulcrum to center of gravity of lever,

in inches.

Then, the pressure at which the safety-valve will blow off is
found by the formula

r_WL+wl+VD

A D

If the distance L is known, the weight W to be hung on
the lever is found by the formula

L

The distance L from the fulcrum to the point at which the
weight W is hung is found by the formula
APD-(wl+VD)
W

Area of Safety Valve. — By area of safety valve is meant the
area of the opening in the valve seat; that is, the area of the
surface of the valve in contact with steam when the valve
is closed. The size of the valve relative to the size of the
boiler and the working pressure is prescribed by law in
many localities, and must be made to conform to the law

11G STEAM BOILERS

wherever such law is in existence. In localities having no
law governing this matter, the size of the safety valve may be
calculated by the accompanying formulas, which are based on
practice and recommended by leading authorities.
For natural draft,

For artificial draft,

1.406 w

in which G = grate surface, in square feet;

p = steam pressure, gauge, in pounds per square inch;
w = weight of coal burned per hour in pounds;
A = least area of safety valve, in square inches.

Location of Safety Valve. — The safety valve should be
placed in direct connection with the boiler, so that there can be
no possible chance of cutting off the communication between
them. A stop- valve placed between the boiler and safety valve
is a very fruitful cause of boiler explosions. Again, the safety
valve must be free to act, and to prevent it from corroding
fast to its seat, it should be lifted from the seat occasionally.
Care must be taken to prevent persons ignorant of the impor-
tance of safety valves from raising the blow-off pressure by
adding to the weights or increasing the tension of the sprir
To this end, the weights of lever safety valves are often loci
in position by the boiler inspector.

Use of Fusible Plugs. — Fusible plugs are devices placed
the crown sheets of furnaces or in similar places to obviate
danger from overheating through lack of water. The plug
often consists of an alloy of tin, lead, and bismuth, which melts
at a comparatively low temperature. In many localities, the
law requires that fusible plugs shall be attached to all high-
pressure boilers.

Forms of Fusible Plugs. — The fusible plugs in common
are shown in section in Fig. 2. They consist of brass or ir
shells threaded on the outside with a Standard pipe thi
The plugs have some form of conical filling, the larger end of 1
filling receiving the steam pressure. The conical form of the

STEAM BOILERS

117

filling prevents it from being blown out by the pressure of the
steam. Fusible plugs applied from the outside differ from
those applied from the inside, as Fig. 2 clearly shows.

Location of Fusible Plugs. — According to the rules issued by
the Board of Boiler Rules of the State of Massachusetts,
fusible plugs must be filled with
pure tin, and the least diameter
shall not be less than $ in.,
except for working pressures
over 175 lb., gauge, or when it
is necessary to place a fusible
plug in a tube, in which cases
the least diameter of fusible
metal shall not be less than
f in. The location of fusible pIG

plugs shall be as follows:

In horizontal return-tubular boilers, in the back head, not
less than 2 in. above the upper row of tubes and projecting
through the sheet not less than 1 in.

In horizontal flue boilers, in the back head, on a line with
the highest part of the boiler exposed to the products of com-
bustion, and projecting through the sheet not less than 1 in.

In locomotive-type or star water-tube boilers, in the highest
part of the crown sheet and projecting through the sheet not
less than 1 in.

In vertical fire-tube boilers, in an outside tube, placed not
less than one-third the length of the tube above the lower
tube-sheet.

In vertical submerged -tube boilers, in the upper tube-sheet.

In water-tube boilers of the Babcock & Wilcox type, in the
upper drum, not less than 6 in. above the bottom of the drum
and projecting through the sheet not less than 1 in.

In Stirling boilers of standard type, in the front side of the
middle drum, not less than 6 in. above the bottom of the drum
and projecting through the sheet not less than 1 in.

In Stirling boilers of the superheated type, in the front
drum, not less than 6 in. above the bottom of the drum, and
exposed to the products of combustion, projecting through the
sheet not less than 1 in.

118 STEAM BOILERS

In water-tube boilers of the Heine type, in the front course
of the drum, not less than 6 in. from the bottom of the drum,
and projecting through the sheet not less than 1 in.

In Robb-Mumford boilers of standard type, in the bottom
of the steam and water drum, 24 in. from the center of the rear
neck, and projecting through the sheet not less than 1 in.

In water-tube boilers of the Almy type, in a tube directly
exposed to the products of combustion.

In vertical boilers of the Climax or Hazelton type, in a
tube or center drum, not less than one-half the height of the
shell, measuring from the lowest circumferential seam.

In Cahall vertical water-tube boilers, in the inner sheet of
the top drum, not less than 6 in. above the upper tube sheet.

In Scotch marine-type boilers, in the combustion-chamber
top, and projecting through the sheet not less than 1 in.

In dry-back Scotch-type boilers, in the rear head, not less
than 2 in. above the top row of tubes, and projecting through
the sheet not less than 1 in.

In Economic-type boilers, in the rear head, above the upper
row of tubes.

In cast-iron sectional heating boilers, in a section over
in direct contact with the products of combustion in
primary combustion chamber.

In other types and new designs, fusible plugs shall be pi
at the lowest permissible water level, in the direct path of
products of combustion, as near the primary combusti
chamber as possible.

Connection of Steam Gauge. — A steam gauge should
connected to the boiler in such a manner that it will neither
injured by heat nor indicate incorrectly the pressure to which
it is subjected. To prevent injury from heat, a so-called
siphon is placed between the gauge and the boiler. This'
siphon in a short time becomes filled with water of condensa-
tion, which protects the spring of the gauge from the injury
the hot steam would cause. Care should be taken not to
locate the steam-gauge pipe near the main steam outlet of the
boiler, as this may cause the gauge to indicate a lower pressure
than really exists. In locating the steam gauge, care must
also be taken not to run the connecting pipe in such a manner

STEAM BOILERS 119

that the accumulation of water in it will cause an extra pressure
to be shown.

Bottom Blow-Off. — For the double purpose of emptying
the boiler when necessary and of discharging the loose mud and
sediment that collect from the feedwater, each boiler is pro-
vided with a pipe that enters the boiler at its lowest point.
This pipe, which is provided with a valve or a cock, is com-
monly known as the bottom blow-off. The position of the blow-
off pipe varies with the design of the boiler; in ordinary return-
tubular boilers, it is usually led from the bottom of the rear end
of the shell through the rear wall. Where the boiler is fitted
with a mud-drum, the blow-off is attached to the drum.

Blow-Off Cocks and Valves. — While in many boiler plants
globe valves are used on the blow-off pipe, their use is objection-
able, because the valve may be kept from closing properly by a
chip of incrustation or similar matter getting between the valve
and its seat. As a result, the water may leak out of the boiler
unnoticed.

Plug cocks packed with asbestos are widely used, the asbestos
packing obviating the objectionable features of the ordinary
plug cock. Gate valves are also used to some extent, but are
open to the same objection as globe valves. In the best modern
practice, the blow-off pipe is fitted with two shut-off devices.
The one shut-off may be an asbestos-packed cock and the other
some form of valve, or both may be cocks or valves, the idea
underlying this practice being that leakage past the shut-off
nearest the boiler will be arrested by the other.

Protection of Blow-Off Pipe. — When exposed to the gases of
combustion, the bottom blow-off pipe should always be pro-
tected by a sleeve made of pipe, by being bricked in, or by a
coil of plaited asbestos packing. If this precaution is neglected,
the sediment and mud collecting in the pipe, in which there is
no circulation, will rapidly become solid. The blow-off pipe
should lead to some convenient place entirely removed from
the boiler house and at a lower level than the boiler. Some-
times it may be connected to the nearest sewer. In many
localities, however, ordinances prohibiting this practice are in
force; the blow-off is then connected to a cooling tank, whence
the water may be discharged into the sewer.

120 STEAM BOILERS

BOILER PIPING

Principal Considerations. — The piping of an engine and
boiler plant requires that careful attention be paid to all the
details as well as to the general design, not only in order to
make it suitable for the purpose, but also in order to reduce the
likelihood of a breakdown. The main considerations regarding
steam piping are the size of the pipes; the arrangement and
construction of the piping system; the method of providing for
expansion; and proper drainage.

Materials for Pipes. — Most of the piping for steam and
water is built up of wrought-iron or steel pipe of standard size.
The various grades of wrought-iron and steel pipe are known
as standard, extra strong, and double extra strong. Both wrought-
iron and steel pipe are used in the piping systems of power
plants. Formerly, wrought iron was chiefly used, but of late
steel has been employed, especially for the larger sizes of steam
pipes. The two kinds are equally reliable when made into
expansion bends, copper bends as a general rule being used
only for very heavy work.

Expansion Joints. — In installing steam piping, provision
must be made for expansion and contraction, which ordinarily
amounts to about li in. per 100 ft. of pipe. Generally, this
may be provided for in the arrangement of the piping; but
for great lengths that are straight, or nearly so, it is necessary
to use expansion joints, which may be made in various ways.

One form, shown in Fig. 1,
is called the slip joint. The
ends a and b of the sections
of pipe come together in a
stuffingbox c in order to

_, make a steam-tight joint.

The stud bolts are extra

long, so as to extend through holes in a flange d riveted to the
pipe b. Check-nuts e on the ends of the studs prevent the two
ends of the pipe from being forced apart by the steam pressure.
The nuts e are not intended ordinarily to be in contact with the
flange; their distance from the flange is adjusted so that the
proper expansion may occur.

STEAM BOILERS 121

In Fig. 2 is shown a corrugated expansion joint, which is some-
times used on large exhaust pipes. It consists of a short
section of flanged corrugated
pipe, usually copper, which is
put in the steam pipe wherever
necessary. The elasticity of FIG. 2

this section, due to the corrugations, permits expansion and
contraction.

Expansion Bends. — The best way of allowing for expan-
sion is by using expansion bends, or bent pipes; but the space
they occupy often limits their use. The forms of bends more
commonly used are shown in Fig. 3, the trade name being given
below each bend. Where a bent pipe is used, the radius r of
the bend should not be less than six times the diameter of the
pipe, for wrought iron or steel; to secure the proper spring in
bends used on long lines of piping, the radius should be greater
than this. Bends of copper pipe may be of shorter radius,
as copper yields more readily than iron or steel.

Bends made from iron or steel pipe must be bent while red
hot. Iron and steel pipe bends generally have iron flanges
fastened on; copper bends either have composition flanges riv-
eted and brazed on, or have steel flanges, the edges of the pipe
being turned over. The piping is usually installed so that it is
under a slight tension when cold; when filled with steam, the
expansion of the pipes removes the tension, and there is no
stress on the pipe except that due to the steam pressure.

Pipe Coverings. — To prevent loss of heat by radiation, steam
pipes are covered with various kinds of materials that are poor
conductors of heat. As a rule, the covering is manufactured
in short sections molded in halves to fit the pipe, the valves and
fittings being covered with the same material in a plastic state.
After the covering is properly secured in place, it is frequently
covered with a heavy duck or canvas jacket sewed on and
painted, and sometimes ornamented by brass bands placed at
regular intervals.

The substances used for covering steam pipes for this pur-
pose are very numerous and vary considerably in efficiency.
Among the best and most widely used non-conducting materials
are hair felt, cork, magnesia, asbestos, and mineral wool.

122

STEAM BOILERS

Frequently, pipe cover-
ings are made up of
combinations of two or
more of these sub-
stances. For pipes laid
in trenches, where a
cheap covering is de-
sired, such materials as
sawdust, charcoal, coal
ashes, coke, loam, and
slaked lime are some-
times used.

Arrangement of Pi-
ping.— The pipes and
fittings must be so pro-
portioned as to permit
a free flow of steam or
water. Water pockets
should be avoided; and
where such pockets are
unavoidable, they must
be drained to free them
from water. By-pass
pipes should be arranged
around feedwater heat-
ers, economizers,
pumps, etc. The sys-
tem must be so designed
as to give perfect free-
dom for expansion and
contraction.

Perfect drainage must
be provided in order that
all water of condensa-
tion shall be fully sepa-
rated from the
Reliability is
by careful design and
superior workmanship,

STEAM BOILERS 123

combined with the use of high-class materials and fit-
tings and the judicious placing of cut-out and by-pass valves.
Drainage is best effected by arranging the piping so that all
the water of condensation will flow by gravity toward a point
close to the delivery end of the pipe, and then providing a drip
pipe at that point. A trap may be placed at the end of the
drip pipe for automatic draining.

BOILER FEEDING AND FEEDWATER
INJECTORS

Classification of Injectors. — Injectors may be divided into
two general classes, namely, non-lifting and lifting injectors.
Non-lifting injectors are intended for use where there is a head
of water available. When the water comes to a non-lifting
injector under pressure, as from a city main, it can be placed
in almost any convenient position close to the boiler. Lifting
injectors are of two distinct types, called automatic injectors
and positive injectors. As positive injectors generally have
two sets of tubes, they are frequently called double-tube inject-
ors. Automatic injectors are so called from the fact that they
will automatically start again in case the jet of water is broken
by jarring or other means. Positive, or double-tube, injectors
are provided with two sets of tubes, one set of which is used for
lifting the water, and the other set for forcing the water thus
delivered to it into the boiler. A positive injector has a wider
range than an automatic injector and will handle a hotter
feed-water supply; it will also lift water to a greater height than
the automatic injector.

Size of Injector. — Most engineers prefer to select a size of
injector having a capacity per hour about one-half greater
than the maximum evaporation per hour in order to have some
reserve capacity. The maximum evaporation, when not
known, may be estimated in U. S. gallons by one of the follow-
ing rules, which hold good for ordinary combustion rates
under natural draft:

Rule I. — For plain cylindrical boilers, multiply the Product of
the length and diameter in feet by 1.3.

124 STEAM BOILERS

Rule II. — For tubular boilers, either horizontal or vertical,
multiply the product of the square of the diameter in feet and
the length in feet by 1.9.

Rule in. — For water-tube boilers, multiply the heating sur-
face in square feet by .4-

Rule IV. — For boilers not covered by the foregoing rules,
multiply the grate surface in square feet by 12.

Rule V. — // the coal consumption in pounds per hour is
known, it may be taken as representing the number of gallons
evaporated per hour.

No standard method of designating the size of an injector is
followed by all makers; therefore, such an instrument must be
selected from the lists of capacities published by the different
makers.

Location of Injector. — An injector must always be placed in
the position recommended by the maker. There must always
be a stop-valve in the steam-supply pipe to the injector.
While lifting injectors, when working as such, scarcely need a
stop-valve in the suction pipe, it is advisable to supply it.
When the water flows to the injector under pressure, a stop-
valve in the water-supply pipe is a necessity. A stop-valve
and a check-valve must be placed in the feed-delivery pipe,
with the stop-valve next to the boiler. The check-valve
should never be omitted, even if the injector itself is supplied
with one. No valve should ever be placed in the overflow
pipe, nor should the overflow be connected directly to the
overflow pipe, but a funnel should be placed on the latter so
that the water can be seen. This direction does not apply to
the inspirator or to any other injector that has a hand-operated,
separate overflow valve. In the inspirator, the overflow pipe
is connected directly to the overflow, but the end of the pipe
must be open to the air. In general, where the injector lifts
water it is not advisable to have a foot-valve in the suction
pipe, as it is desirable that the injector and pipe may drain
themselves when not in use. A strainer should be placed on
the end of the suction pipe.

Steam Supply to Injector. — The steam for the injector must
be taken from the highest part of the boiler, as it must be
sup'plied with dry steam. Under no consideration should the

STEAM BOILERS 125

steam be taken from another steam pipe. The suction pipe
should be as straight as possible and must be air-tight. In
connecting up an injector, the pipes should be cleaned by
blowing them out with steam before making the connection,
"because if a small bit of dirt gets into the injector it will inter-
fere seriously with its operation.

Injector Troubles. — In the discussion of injector troubles as
given in succeeding paragraphs, the suction pipe, strainer,
feed-delivery pipe, and check- valve are considered as parts of
the injector. In searching for the cause of a trouble, therefore,
the suction and delivery pipes should be carefully inspected as
well as the injector.

Failure to Raise Water. — The causes that prevent an injector
from raising water are:

1. Suction Pipe Stopped Up. — This is due, generally, to a
clogged strainer or to the pipe itself being stopped up at some
point. In case the suction pipe is clogged, steam should be
blown back through the pipe to force out the obstruction.

2. Leaks in Suction Pipe. — This prevents the injector form-
ing the vacuum required to raise the water. To test the
suction pipe for air leaks, plug up the end and turn the full
steam pressure on the pipe; leaks will then be revealed by
the steam issuing therefrom. Have the suction pipe full of
water before steam is turned on, as the presence of small
leaks will be revealed better by water than by steam.

3. Water in the Suction Pipe Too Hot. — A leaky steam
valve or leaky boiler check- valve and leaky injector check-
valve may be the cause of hot water or steam entering the
source of supply and heating the water so hot that the injector
refuses to handle it.

4. Obstruction in Tubes. — There may be an obstruction in
the lifting or combining tubes; or, the spills (or openings) in
the tubes through which the steam and water escape to the
overflow may be clogged up with dirt or lime.

Injector Primes, but Will Not Force. — In some cases an
injector will lift water, but will not force it into the boiler; or,
it may force part of it into the boiler and the rest out of the
overflow. When it fails to force, the trouble may be due to
one or the other of the following causes:
10

126 STEAM BOILERS

1. Choked Suction Pipe or Strainer. — If the suction pipe or
the strainer is partly choked, the injector, in either case, will
be prevented from lifting sufficient water to condense all the
steam issuing from the steam valve. The uncondensed steam,
therefore, will gradually decrease the vacuum in the combining
tube until it is reduced so much that the injector will not work.
The remedy in case the supply valve is partly closed is to open
it. In the case of a choked suction pipe, the obstruction should
be blown out.

2. Suction Pipe Leaking. — The leak may not be sufficient
entirely to prevent the injector from lifting water, but the
quantity lifted may be insufficient to condense all the steam,
which, therefore, destroys the vacuum in the combining tube.
A slight leak may exist that will simply cut down the capacity
of the injector. In such a case an automatic injector will
work noisily, on account of the overflow valve seating and
unseating itself as the pressure in the combining tube varies,
due to the leak.

3. Boiler Check-Valve Stuck Shut.—U the boiler check-valve
is completely closed, the injector may or may not continue to
raise water and force it out of the overflow; this depends on
the design of the injector. If the boiler check is partly open,
the injector will force some of the water into the boiler and the
remainder out of the overflow. In case the check-valve cannot
be opened wide, water may be saved by throttling both steam
and water until the overflow diminishes, or, if possible, ceases.
The steam should be throttled at the valve in the boiler steam
connection. If a check-valve sticks, it can sometimes be made
to work again by tapping lightly on the cap or on the bottom
of the valve body.

4. Obstruction in Delivery Tube. — Any obstruction in the
delivery tube will cause a heavy waste of water from the over-
flow. To remedy this, the tube will have to be removed and
cleaned.

5. Leaky Overflow Valve. — A leaky overflow valve is indi-
cated by the boiler check chattering on its seat. To remedy this
defect, grind the valve on its seat until it forms a tight joint.

6. Injector Choked \Vilk Lime. — It is essential to the proper
working of an injector that the interior of the tubes be

STEAM BOILERS 127

perfectly smooth and of the proper bore. As in course of time
they become clogged with lime, the capacity of the injector
decreases until, finally, it refuses to work at all. If the water
used is very bad, it becomes necessary frequently to cleanse
the tubes of the accumulated lime. This may be done by
putting the parts in a bath consisting of 1 part of muriatic
acid to 10 parts of water. The tubes should be removed from
it as soon as the gas bubbles cease to be given off.

Advantages and Disadvantages of Injectors. — The advan-
tages of the injector as a boiler feeding apparatus are its cheap-
ness, as compared with a pump of equal capacity; it occupies
but little space; the repair bills are low, owing to the absence
of moving parts; no exhaust piping is required, as with a
steam pump; it delivers hot water to the boiler. The dis-
advantages of the injector are that it will not start with a
steam pressure less than that for which it is designed, and
that it will stand but little abuse, being poorly adapted for
handling water containing grit or other matter liable to cut
the nozzles.

INCRUSTATION AND CORROSION

Incrustation. — Broadly speaking, any deposit that is formed
on the plates and tubes of a boiler is termed scale, or incrusta-
tion; it is caused by impurities that enter with the water and
that are left behind in the boiler when the water is evaporated.
In passing through the soil, water dissolves certain mineral
substances, the most important of which are carbonate of
lime and sulphate of lime. Other substances frequently pres-
ent in small quantities are chloride of sodium, or common
salt, and chloride of magnesium. It also often contains other
troublesome substances.

Impurities in Feedwater. — Some of the more common impu-
rities found in feedwater, together with their properties, are
given in the following paragraphs:

Carbonate of lime will not dissolve in pure water, but will
dissolve in water that contains carbonic-acid gas. It becomes
insoluble and is precipitated in the solid form when the water
is heated to about 212° F., the carbonic-acid gas being driven
off by the heat.

128 STEAM BOILERS

Sulphate of lime dissolves readily in cold water, but not in
hot water. It precipitates in the solid form when the water
is heated to about 290° F., corresponding to a gauge pressure
of 45 Ib.

Chloride of sodium will not be precipitated by the action of
heat unless the water has become saturated with it. Since it
generally is present in but very small quantities in fresh water,
it will take a very long time for the water in a boiler to become
troublesome, and with the ordinary blowing down of a boiler
once a week or every 2 wk., there is little danger of the water
becoming saturated with it. Consequently, it is one of the
least troublesome scale-forming substances contained in fresh
water.

Chloride of magnesium is one of the worst impurities in water
intended for boilers, for while not dangerous as long as the water
is cold, it makes the water corrosive when heated, and when
present in large quantities, it becomes dangerously corrosive,
attacking the metal of the boiler and rapidly corroding it.

Organic mailer by itself may or may not cause the water to
become corrosive, but will often cause foaming; when it is
present in small quantities in water containing carbonate or
sulphate of lime, or both, it usually serves to keep the deposits
from becoming hard.

Earthy mailer, like organic matter, is not dissolved in the
water, but is in mechanical suspension. It is very objection-
able, especially when the earthy matter is clay, and when other
scale-forming substances are present is liable to form a hard
scale resembling Portland cement.

Acids, such as sulphuric acid, nitric acid, tannic acid, and
acetic acid, are often present in the feedwater. The sulphuric
acid is the most dangerous one of these acids, attacking the
metal of which the boiler is composed and corroding it very
rapidly. The other acids, while not so violent in their action
as the sulphuric acid, are also dangerous, and water contain-
ing any one should be neutralized when it must be used.

Formation of Scale. — The small solid particles, due to pre-
cipitation of substances in solution or matter in mechanical
suspension, remain for a time suspended in the water, especially
the carbonate of lime that for some time after precipitation

STEAM BOILERS 129

floats on the surface of the water. These particles will gradu-
ally settle on the plates, tubes, and other internal surfaces. A
large part of the impurities will be carried by the circulation
of the water to the most quiet part of the boiler and there
settle and form a scale. In a few weeks, if no means of pre-
vention are used, the inner parts of the boiler will be covered
with a crust from rj to -| in. in thickness.

Danger of Scale. — A scale & in. or less in thickness is
thought by many to be an advantage, as it protects the plates
from the corrosive action of acids in the water. When, how-
ever, the scale becomes J in. thick or more, heat is transmitted
through the plates and tubes with difficulty, more fuel is
required, and there is danger of overheating the plates. The
chief danger from a heavy incrustation is the danger of over-
heating the plates and tubes; it also prevents a proper examina-
tion of the inside of the boiler, since it may hide a dangerously
corroded piece of plate or a defective rivet head that would
otherwise be discovered.

Scale Containing Lime. — The carbonate of lime forms a
soft, muddy scale, which when dry, becomes fluffy and flour-
like. This scale may be easily swept or washed out of the
boiler by a hose, provided it is not baked hard and fast. A car-
bonate scale is much harder to deal with when grease is allowed
to enter the boiler. The grease settles and mixes with the
floury scale, making a spongy crust that remains in contact
with the plates, being too heavy to be carried off by the natural
circulation of the water. The sulphate of lime forms a scale
that soon bakes to the plates.

Kerosene as Scale Remover. — Some substances seem to
soften and aid in detaching scale. Of these, kerosene oil has
met with much favor. Its action appears to be mechanical
rather than chemical, the oil penetrating or soaking through
the scale and softening and loosening it. It is somewhat
useful, too, in preventing the formation of scale, enveloping
the fine particles of the scale-forming substances that, after
precipitation, float on the surface of the water for a little
while. It seems that this prevents the particles from adher-
ing firmly to one another and to the metal when they finally
settle.

130

STEAM BOILERS

Removal of Scale by Chipping. — A hard scale, when once
formed, is generally removed by chipping it off with scaling
hammers and scaling bars; soft scale can be largely removed
during running by a periodic use of the bottom and surface
blow-offs, and the remainder can usually be washed out and
raked out when the boiler is blown down and opened. In
order to prevent the scale-forming substances deposited on
the metal from baking hard, it is advisable to let the boiler
cool down slowly until entirely cold preparatory to blowing
off, whenever circumstances permit this to be done. This
cooling process will generally take from 24 to 36 hr.

Removal of Mud. — Mud and earthy matter by itself will
not form any hard scale, but will often do so when carbonate
of lime and sulphate of lime are present. An accumulation
of such matter can be prevented, and most of it can be
removed, by a periodic use of the bottom blow-off, removing
the remainder whenever the boiler is opened.

Internal Corrosion. — Corrosion of boiler plates may be defined
as the eating away or wasting of the plates due to the chemical
action of water. Corrosion may be internal and external.

FIG. 1

FIG. 2

Internal corrosion may present itself as uniform corrosion,
pitting or honeycombing, and grooving.

Uniform Corrosion. — In cases of uniform corrosion large areas
of plate are attacked and eaten away. There is no sharp line
of division between the corroded part and the sound plate.

STEAM BOILERS 131

Corrosion often violently attacks the staybolts and rivet heads.

Pitting or Honeycombing. — Pitting or honeycombing is
readily perceived. The plates are indented in spots with
holes and cavities from 3*5 to \ in. deep. The appearance of a
pitted plate is shown in Fig. 1. On the first appearance of
pitting, the surface so affected should be thoroughly cleaned
and a good coating of thick paint made of red lead and boiled
linseed oil should be applied. This treatment should be given
from time to time to insure protection to the metal.

Grooving. — Grooving, which means the formation of a dis-
tinct groove, is generally caused by the buckling action of the
plates when under pressure. Thus, the ordinary longitudinal
lap joint of a boiler slightly distorts the shell from a truly
cylindrical form, and the steam pressure tends to bend the
plates at the joint. This bending action is liable to start a
small crack along the lap, which, being acted on by corrosive
agents in the water, soon deepens into a groove, as shown in
Fig. 2.

External Corrosion. — External corrosion frequently attacks
stationary boilers, particularly those set in brickwork. The
causes of external corrosion are dampness, exposure to weather,
leakage from joints, moisture arising from the waste pipes or
blow-off, etc. External corrosion should be prevented by
keeping the boiler shell free from moisture, and the stoppage of
all leaks as soon as they appear.

Leakage of rivets and the calking edges of seams may be
caused by the delivery of the cold feedwater on to the hot
plates; another cause is the practice of emptying the boiler
when hot and then filling it with cold water. The leakage in
both cases is due to the sudden contraction of the plates.

In horizontal water-tube boilers of the inclined-tube type,
external corrosion principally attacks the ends of the tubes,
especially the back ends, close up to the headers into which
they are expanded. In the course of time the tubes will leak
around the expanded portion in the headers.

If leaks are attended to as soon as they occur, no corrosion
will take place, as the gases of combustion are harmless unless
acting in conjunction with water or dampness, or unless the
coal is rich in sulphur. Should, however, the ends of several

132

STEAM BOILERS

tubes be found badly corroded but not yet leaking from that
cause, the tubes should by all means be removed and replaced.
Lamination. — Sometimes what is called lamination, or the
splitting of a plate into thin layers, is revealed by the action of
the fire in causing a bag or blister to appear. Laminations
due to slag and other impurities in the metal, which become

FIG. 3

flattened out when the plates are rolled, are shown at a, Fig. 3.
Under the action of the heat the part exposed to the fire will
form a blister, which may finally open at the point b or c. If
the laminated portion of the plate is small, it may be cut out
and a patch put in its place. If there are a number of lamina-
tions in the same plate, it is advisable to put in a new plate.

Overheating. — The heating of a plate beyond its normal
temperature is called overheating, and may be caused by low
water or by incrustation. When the plate is covered by a
heavy scale, the plate becomes overheated, so that it yields to
the steam pressure, forming a pocket, as shown in Fig. 4,
which represents the shell sheet, or the sheet of a horizontal
return-tubular boiler directly over the fire. If the pocket is

FIG. 4

not discovered in time for the plate to be repaired, it stretches
until finally the material becomes too thin to withstand the
steam pressure; the pocket then bursts with more or less lia-
bility of an explosion. The vegetable or animal oils carried
into the boiler from a surface condenser are particularly liable
to cause the formation of pockets.

STEAM BOILERS

133

Prevention of Incrustation and Corrosion. — Incrustation
can best be prevented by purifying the feedwater prior to its
entering the boiler, and can be fairly satisfactorily prevented
by a chemical treatment of the water in case there is no puri-
fication of the water prior to its entering the boiler. When

SCALE-FORMING SUBSTANCES AND THEIR
REMEDIES

Troublesome Substance

Trouble

Remedy or Palliation

Sediment, mud, clay, etc.

Incrustation

Filtration

Blowing off

Readily soluble salts

Incrustation

Blowing off

Heating feed

Bicarbonates of lime, mag-
nesia, iron

Incrustation

Addition of caustic
soda, lime, or mag-
nesia

Addition of carbon-

Sulphate of lime

Incrustation

ate of soda or ba-

rium chloride

Chloride and sulphate of
magnesium

Corrosion

Addition of carbon-
ate of soda, etc.

Carbonate of soda in large
amounts

Priming

Addition of barium
chloride

Acid (in mine water)

Corrosion

Alkali

Heating feed

Dissolved carbonic acid
and oxygen

Corrosion

Addition of caustic
soda, slaked lime,
etc.

Grease (from condensed

Corrosion

Slaked lime and fil-
tering. Carbonate

water)

of soda

Substitute mineral

oil

Precipitate with

Organic matter (sewage)

Priming

alum or chloride of

iron and filter

Organic matter

Corrosion

Same as last

the water contains large quantities of substances that float
on the surface, mechanical means may be resorted to, using
the surface blow-off at frequent intervals or some equivalent
skimming device. Corrosion is prevented by neutralizing
the corrosive acids by an alkali; corrosion due to a perfectly

134 STEAM BOILERS

fresh water can be prevented by giving a protective coating to
the metal, which may be a thick red -lead paint made up with
boiled linseed oil, or a thin coating of scale. Sometimes organic
substances containing tannic acid, such as oak bark, hemlock,
or sumac, are used to loosen or prevent scale. They are liable
to injure the plates by corrosion and hence should not be
used. The preceding table gives a list of troublesome scale-
forming substances and the means of preventing or neutralizing
them.

Use of Zinc in Boilers. — Zinc is much used in marine boilers
for the prevention of both incrustation and corrosion. The
scale may acquire thickness and hardness, but can easily be
removed from the plates. The zinc is distributed through the
boiler in the form of slabs. About 1 sq. in. of zinc surface
should be supplied for every 50 Ib. of water in the boiler.

TESTING OF FEEDWATER

Testing for Corrosiveness. — It is a good plan to test the
feedwater and also the water in the boiler occasionally for cor-
rosiveness. This may be done by placing a small quantity in
a glass and adding a few drops of methyl orange. If the sam-
ple of water is acid, and hence corrosive, it will turn pink. If
it is alkaline, and hence harmless, it will be yellow. The
acidity may also be tested by dipping a strip of blue litmus
paper in the water. If it turns red, the water is acid. This
method is not so sensitive as the previous one, which should be
used in preference. If litmus paper is kept in stock, it should
be kept in a bottle with a glass stopper, as exposure to the
atmosphere will cause the paper to deteriorate. If the water
in the boilers has become corrosive and corrosion has set in,
the water in the gauge glass will show red or even black. As
soon as the color is beyond a dirty gray or straw color, it is
advisable to introduce lime or soda to neutralize the acid.

Testing for Carbonate of Lime. — Pour some of the water
to be tested into an ordinary tumbler. Add a little ammonia
and ammonium oxalate, and then heat to the boiling point.
If carbonate of lime is present, a precipitate will be formed.

Testing for Sulphate of Lime. — Pour some of the feedwater
into a tumbler and add a few drops of hydrochloric acid.

STEAM BOILERS 135

Add a small quantity of a solution of barium chloride and slowly
heat the mixture. If a white precipitate is formed, which will
not redissolve when a little nitric acid is added, sulphate of lime
is present.

Testing for Organic Matter. — Add a few drops of pure sul-
phuric acid to the sample of water. To this add enough of a
pink-colored solution of potassium permanganate to make the
whole mixture a faint rose color. If the solution retains its
color after standing a few hours, no organic substances are
present.

Testing for Matter in Mechanical Suspension. — Keep a
tumblerful of the feedwater in a quiet place. If no sediment
is formed in the bottom of the tumbler after standing for
a day, there is no mechanically suspended matter in the water.

PURIFICATION OF FEEDWATER

Means of Purification. — Water intended for boilers may be
purified by settlement, by filtration, by chemical means, and
by heat. Filtration will remove impurities in mechanical sus-
pension, such as oil and grease, and earthy matter, but will
not remove substances dissolved in the water. Chemical
treatment of the water will render the scale-forming substances
and corrosive acids harmless, and may be applied either before
or after the water enters the boilers, but preferably the former.
Purification by heat is based on the fact that most of the scale-
forming substances become insoluble and precipitate when
the water containing them in solution is heated to a high
temperature.

Purification by Settlement. — For feedwater containing much
matter in mechanical suspension, one of the simplest methods
of purifying it is to provide a relatively large reservoir, or a
large tank for small steam plants, where the impurities can
settle to the bottom. While this method is fairly satisfactory,
as far as earthy matter is concerned, it will not clear the water
of finely divided organic matter, which is usually lighter than
the water and often so finely divided as to be almost dissolved
in it.

Purification by Filtration. — Organic and earthy matter in
mechanical suspension is most satisfactorily removed by a

136 STEAM BOILERS

filter, passing the water through layers of sand, gravel, hay, or
equivalent substances, or through layers of cloth. Hay and
cloth are of service especially where the feedwater contains oil
or grease, as is the case where a surface condenser is used and
the condensed steam is used over again.

Purification by Chemicals. — Chemical purification may
take place before or after the water enters the boiler, the former
method being somewhat more expensive. However, the
purification is better carried out before the water enters the
boiler for the reason that the amount of impurities enter-
ing the boiler will be greatly reduced. The chemical pro-
cess to be adopted depends on the substances present in the
water.

Use of Quicklime. — When the water contains only car-
bonate of lime, it may be treated with slaked quicklime,
using 28 gr. of lime for every 50 gr. of carbonate of lime present
in the water, the quicklime precipitating the carbonate of
lime and being transformed into carbonate of lime itself during
the process.

Use of Caustic Soda. — Water containing carbonate of lime
may be treated with caustic soda, which precipitates the car-
bonate of lime and leaves carbonate of soda, which is harmless.
For every 100 gr. of carbonate of lime 80 gr. of caustic soda
should be added.

Use of Sal Ammoniac. — Sal ammoniac is sometimes added
to water containing carbonate of lime and will cause the latter
to precipitate. Its use is not advisable, however, on account
of the danger of the formation of hydrochloric acid, which will
attack the boiler. The formation of this acid is due to the use
of an excessive quantity of sal ammoniac.

Treatment of Sulphate of Lime. — While slaked lime will
precipitate carbonate of lime, it will have no effect on sulphate
of lime, and water containing the latter, either alone or in con-
junction with carbonate of lime, must be treated with other
chemicals. The most available ones for water containing both
are carbonate of soda and caustic soda. These are often fed
into the boiler and will precipitate the carbonate of lime and
sulphate of lime there, requiring the sediment to be blown out
or otherwise removed periodically.

STEAM BOILERS 137

Quantity of Chemicals to Use. — When treating water con-
taining carbonate of lime and sulphate of lime, caustic soda
may be used either by itself or in combination with carbonate
of soda, depending on the relative proportions of carbonate of
lime and sulphate of lime present in the water. The amount
of caustic soda or carbonate of soda to be used per gallon of
feedwater can be found as follows:

Rule I. — Multiply the number of grains of carbonate of
lime per gallon by 1.36. If this product is greater than the
number of grains of sulphate of lime per gallon, only caustic
soda is to be used. To find the quantity of caustic soda required
per gallon, multiply the number of grains of carbonate of lime
in a gallon by .8.

Rule n. — Multiply the number of grains of carbonate of lime
per gallon by 1.36. If this product is less than the number of
grains of sulphate of lime per gallon, take the difference and
multiply it by .78 to obtain the number of grains of carbonate of
soda required per gallon. To find the amount of caustic soda
required per gallon, multiply the number of grains of carbonate of
lime in a gallon by .8.

EXAMPLE. — A quantitative analysis of a certain feedwater
shows it to contain 23 gr. of sulphate of lime and 14 gr. of car-
bonate of lime per gallon. How much caustic soda and carbon-
ate of soda should be used per gallon to precipitate the scale-
forming substances?

SOLUTION. — By rule I, 14X1.36 = 19 gr. As this product
is less than the number of grains of sulphate of lime per
gallon, rule II is to be used. Applying rule II, (23 — 19) X. 78
= 3.12 gr. of carbonate of soda, and 14 X .8 = 11.2 gr. of caustic
soda.

Use of Carbonate of Soda. — Water containing sulphate of
lime, but no carbonate of lime, may be treated with carbonate
of soda. The amount of the latter that is required per gallon
to precipitate the sulphate of lime is found by multiplying the
number of grains per gallon by .78. When using soda, it is
well to keep in mind that it will not remove deposited lime from
the inside of a boiler. All that the soda can do is to facilitate
the separating of the lime, that is, cause it to deposit in a soft
state. This sediment must be removed periodically

138 STEAM BOILERS

Use of Trisodium Phosphate. — For decomposing sulphate of
lime, tribasic sodium phosphate, more commonly known as
trisodium phosphate, is often used. This is claimed to act on
the sulphate of lime, forming sulphate of sodium and phos-
phate of lime, the former of which remains soluble and is
harmless, and the latter of which is a loose, easily removed
deposit. Trisodium phosphate also acts on carbonate of lime
and carbonate of magnesia, forming phosphate of lime and
phosphate of magnesia, at the same time neutralizing the car-
bonic acid released from the carbonate of lime and magnesia,
and the sulphuric acid released from the sulphates.

Neutralization of Acids. — Acid water can be neutralized by
means of an alkali, soda probably being the best one. The
amount of soda to be used can best be found by trial, adding
soda until the water will turn red litmus paper blue.

Purification by Heat. — Carbonate of lime and sulphate of
lime become insoluble if the water is heated, the former pre-
cipitating at about 212° P. and the latter at about 290° P.
This fact is taken advantage of in devices that may be called
combined feed water heaters and purifiers; as they generally
use live steam, they are also called live-steam feed-water heaters.
Since no feedwater heater can effect a direct saving on fuel
except when the heat is taken from a source of waste, it follows
that a live-steam feedwater heater can affect the fuel con-
sumption but indirectly. This it does by largely preventing
the accumulation of scale in the boiler and the attendant loss in
economy due to the lowering of the rate of heat transmission
through a plate heavily covered with incrustation.

Economy of Heating Feedwater. — The feedwater furnished
to steam boilers must of necessity be raised from its normal
temperature to that of steam before evaporation can commence,
and if not otherwise accomplished, it will be done at the expense
of fuel that should be utilized in making steam. At 75
Ib. gauge pressure the temperature of boiling water is about
320° P., and if 60° is taken as the average temperature of feed-
water, 320- (50 = 200 B. T. U. is required to raise 1 Ib. of water
from 60° to 320°. It requires 1,151.5 B. T. U. to convert
1 Ib. of water at 60° into steam at 75 Ib. gauge pressure, so
that the 260 B. T. U. required for heating the water represents

STEAM BOILERS 139

260-7-1,151.5 = 22.6% of the total. All heat taken from a
source of waste, therefore, that can be imparted to the feed-
water before it enters the boilers is just so much saved, not
only in cost of fuel but in boiler capacity.

Types of Exhaust-Steam Feedwater Heaters. — The impuri-
ties contained in the water will largely determine the type of
exhaust-steam heater to be used in any given plant. These
heaters are divided into two general classes, namely, open
heaters and closed heaters.

An open heater is one in which the water space is open to
the atmosphere. In a direct-contact open heater, the exhaust
steam comes in contact with the water, which, by means of
some one of a number of suitable devices, is broken into spray
or thin sheets so that it will readily absorb the heat of the
steam. In a coil heater, the exhaust steam passes through
coils of pipe submerged in a vessel containing the water to be
heated, and open at the top.

A closed heater is a heater in which the feedwater is not
exposed to the atmosphere, but is subjected to the full boiler
pressure. The steam does not come in contact with the water;
the latter is heated through contact with metallic surfaces,
generally those of tubes, that are heated by the exhaust steam.

Selection of Heater. — When the boiler feedwater is free
from acids, salts, sulphates, and carbonates, so that no scale is
formed at a high temperature, the closed feedwater heater will
be found satisfactory. Heaters of the coil type may be used
with pure water, but should not be used with water that
will precipitate sediment or scale-forming matter of any kind.
The coil heater is very efficient as a heater, as the water cir-
culating through the coils is a long time in contact with the
surface surrounded and heated by the exhaust steam. Heaters
of the closed type, with straight tubes and sediment chamber,
can be cleaned more readily than those having curved tubes,
but the curved tubes allow more freedom for expansion and
contraction. Heaters of the tubular type should have ample
sediment chambers and may be used with water that contains
organic or earthy matter, but not with water containing scale-
forming ingredients. Carbonate of lime is likely to combine
with earthy matter and form an exceedingly hard scale.

140 STEAM BOILERS

Heaters of the open exhaust-steam type have the advantage
of bringing the exhaust steam in direct contact with the feed-
water; some of the exhaust steam is condensed, thus effecting
a saving in feedwater, and sediment and scale-forming ingre-
dients, except sulphates of lime and magnesia, are precipitated
or will settle to the bottom of the heater. The oil in the
exhaust steam must be intercepted by special oil extractors,
filters, or skimmers, generally combined with the heater and, by
automatic regulation, sufficient fresh feedwater must be added
to make up the total quantity required. When the system is
properly arranged, all live-steam drips and discharges from
traps are led to the heater.

BOILER TRIALS

Purposes of Boiler Trials. — A boiler trial, or boiler test,
as it is often called, may be made for one or more of several
purposes, the method of conducting the trial depending largely
on its purpose. The boiler trial may vary from the simplest
one, in which the only observations are the fuel burned and the
water fed to the boiler in a stated period of time, to the elabo-
rate standard boiler trial, in which special apparatus and sev-
eral skilled observers are essential. The object of a boiler
trial may be to determine the efficiency of the boiler under
given conditions; the comparative value of different boilers
working under the same conditions; the comparative value of
fuel; or the evaporative power, or horsepower, of the boiler.

Observations During Trial. — The essential operations of a
boiler trial are the weighing of the feedwater and fuel, and
the observations of the steam pressure, temperature of feed-
water, and various other less important pressures and tempera-
tures. In conducting a boiler trial, the various observations
of temperatures, pressures, etc. should be made simultaneously
at intervals of about 15 min.

Weighing the Coal. — The coal supplied to the furnace is
weighed out in lots of 500 or 600 Ib. It is a convenient plan
to have a box with one side open placed on a platform scale.
A weight is then placed on the scale beam sufficient to balance
the box. The scale may then be set at 500 or 600 Ib., the coal

STEAM BOILERS 141

shoveled in until the beam rises, and then fed directly from the
box to the furnace. After the test, the ashes and clinkers
must be raked from the ash-pit and grate and weighed. This
weight subtracted from the weight of the coal used gives the
amount of combustible.

Measurement of Feedwater. — The amount of water evap-
orated in a test for comparative fuel values may be taken as
equal to the amount of feedwater supplied without introducing
any serious error. The most reliable method of measuring the
feedwater delivered to the boilers is to weigh it.

Standard of Boiler Horsepower. — When making a horse-
power or an efficiency test, a more elaborate method of pro-
cedure is required than for a comparative fuel-value test.
The reason for this is that different boilers generate steam at
different pressures, different feedwater temperatures, and dif-
*erent degrees of dry ness; hence, to compare the performances
of boilers so as to determine their comparative efficiencies, it
is necessary to reduce the actual evaporation to an equivalent
evaporation from and at 212° F. per pound of combustible.

A committee of the American Society of Mechanical Engineers
has recommended as a commercial horsepower an evaporation
of 80 Ib. of water per hour from a feedwater temperature of 100°
F. into steam at 70 Ib. gauge pressure, which is equivalent to 34*
units of evaporation; that is, to 34 5 Ib. of water evaporated
from a feedwater temperature of 212° F. into steam at the
same temperature.

Since 965.8 B. T. U. is required to evaporate a pound of
water from and at 212°, a boiler horsepower is equal to 965.8
X 34| = 33,320 B. T. U. per hr.

Equivalent Evaporation. — The equivalent evaporation is
readily determined by means of the formula

965.8

in which W = actual evaporation, in pounds of water per hour;
H = total heat of steam above 32° F. at observed pres-

sure of evaporation;
t = observed feedwater temperature;
Wi = equivalent evaporation, in pounds of water per

hour, from and at 212° F.
11

142 STEAM BOILERS

EXAMPLE. — A boiler generates 2,200 Ib. of dry steam per hour
at a pressure of 120 Ib. gauge. The temperature of the feed-
water being 70° F., (a) what is the equivalent evaporation?
<6) what is the horsepower of the boiler?

SOLUTION. — (a) According to the Steam Table, the total heat
H corresponding to a gauge pressure of 120 Ib. is 1.188.6 B.T.U.
Applying the formula,

(b) The horsepower, which is obtained by dividing the total
equivalent evaporation by 34.5, the equivalent of 1 H. P., is,
2,621 -=-34.5 = 76 H. P., nearly

TT _ | I OQ

Factor of Evaporation. — The quantity : - that

96o.o

changes the actual evaporation of 1 Ib. of water to equivalent
evaporation from and at 212° F. is called the factor of evapora-
tion. To facilitate the calculating of equivalent evaporation,
the accompanying table of factors of evaporation is inserted.
The equivalent evaporation is found by multiplying the actual
evaporation by the factor of evaporation taken from the table.

EXAMPLE 1. — A boiler is required to furnish 1,800 Ib. of steam
per hour at a gauge pressure of 80 Ib.; if the temperature of the
feedwater is 48° F., what will be the rated horsepower of the
boiler?

SOLUTION. — From the table, the factor of evaporation for
80-lb. pressure and a feedwater temperature of 40° is 1.214,
and for the same pressure and a feedwater temperature of
50° it is 1.203; the difference is 1.214- 1.203 = . Oil. The
difference of temperature is 50° — 40° =10°, and the difference
between the lower temperature and the required temperature
is 48°- 40° = 8°. Then, 10°: 8° = . Oil : x, or x = .009; 1.214 — .009
= 1.205. 1,800X1.205 = 2,169 Ib., and 2,169 + 34.5 = 63 H. P.,
nearly.

EXAMPLE 2. — What is the factor of evaporation when the
feedwater temperature is 122° F. and the gauge pressure 72?

SOLUTION. — In the table, under the column headed 70 and
opposite 120 in the left-hand column is found 1.128; in column
headed 80 and opposite 120 is found 1.131; difference is .003.

STEAM BOILERS

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144 STEAM BOILERS

In the same vertical columns and opposite 130 are found 1.117
and 1.120; difference is .003; same as above. Hence, for an
increase of 10 Ib. in gauge reading, there is an increase of .003
in the factor of evaporation, or an increase of .0003 for 1 Ib.
and of .0003X2 = .0006 for 2 Ib. Therefore, for a feedwater
temperature of 120° and 72 Ib. pressure, the factor of evap-
oration is 1.128 + .0006 = 1.1286. The difference between the
numbers opposite 120 and 130 in the two columns headed 70
and 80, respectively, is 1.128- 1.117 = .011, and 1.131-1.120
= .011, showing that, for an increase of temperature in the
feedwater of 10°, there is a decrease in the factor of .011, and
for 1° a decrease of .0011, or for 2° of .0022. Hence, the value
of the factor for a temperature of 122° and a gauge pressure of
72 Ib. is 1.1286-. 0022 = 1.126.

Boiler Efficiency. — The efficiency of a boiler may be defined
as the ratio of the heat utilized in evaporating water to the
total heat supplied by the fuel. The efficiency thus calculated
is really the combined efficiency of the furnace and boiler, as
it is not easily possible to determine separately the efficiency
of each.

The amount of heat supplied is determined by first accurately
weighing the fuel used during the test and deducting all the
ash and unconsumed portions. This weight, in pounds, is
multiplied by the total heat of combustion of 1 Ib. of the fuel,
as determined by an analysis, the product being the total
number of heat units supplied during the test under the
assumption that combustion was perfect. The heat usefully
expended in evaporating water is obtained by first weighing
the feedwater and correcting this weight according to the
quality of the steam; the corrected weight is then multiplied
by the number of heat units required to change water at the
temperature of the feed into steam at the observed pressure.
The efficiency of a boiler, expressed in per cent., may be found
by the formula

in which E = efficiency of boiler;

A =heat utilized in evaporating water;
B = total heat supplied by fuel.

STEAM BOILERS 145

EXAMPLE. — A boiler trial shows a useful expenditure of
186,429,030 B. T. U. and a total supply of 270,187,000 B. T. U.
What is the efficiency of the boiler?

SOLUTION. — Applying the formula,

186,429,030

£=— — = .69 = 69%

270,187,000

Standard Code. — For elaborate boiler trials, the standard
code recommended by the American Society of Mechanical
Engineers should be used.

BOILER MANAGEMENT

FILLING BOILERS

Preparation for Filling Boiler. — Before starting the flow of
water into the boiler, the manhole plates or handhole plates
that were removed preparatory to cleaning and overhauling
must be replaced, and the blow-off valve must be closed.
The gaskets, and also the surfaces with which they come in
contact, should be examined to see that they are in good con-
dition. It is customary to place a mixture of cylinder oil and
graphite on the outer surface of each gasket, so that it may be
removed without tearing. It is important that the manhole
plates and handhole plates be properly replaced and secured
in order to prevent leakage.

Height of Water. — In some cases the water can flow in and
fill the boiler to the required height by means of the pressure
that exists in the main supply pipe. In other cases, it may be
necessary to use a hose or to fill the boiler with a steam pump
or a hand pump. The boiler should be filled until the water
shows half way up in the gauge glass.

Escape of Air. — While filling a boiler it is necessary to make
provision for the escape of the contained air, since otherwise
the pressure caused by the compression of the air may prevent
the boiler from being filled to the proper height. Most boilers
have some valve that can be used for this purpose; a gauge-
cock may be left open until water issues therefrom, when it
may be closed. Sometimes the manhole plate, if the manhole
is on top, is left off while filling a boiler.

146 STEAM BOILERS

MANAGEMENT OF FIRES IN STARTING
Precautions in Starting. — After the boiler has been filled and
before starting the fire, the attendant should see that the water
column and connections are perfectly clear and free, that is,
that the valves in the connections and the gauge-glass valves
are open so that the water level may show in the glass; he
should also see that the gauge-cocks are in good working
order and open the top cock or the safety valve; he should
take care that the stress on the stop-valve spindle is relieved
by just unscrewing the valve from the seat without actually
opening it. He should make sure that the pump, or injector,
or whatever device is used to feed the boiler, is in good working
order, and ready to start when required.

Starting the Fires. — It is customary to cover the grates with
a layer of coal first, and then to add the wood, among which
may be thrown oily waste or other combustible material that
may be at hand. To start the fire, light the waste or other
easily ignited material and open the damper and ashpit doors
to produce draft. Then close the furnace door. After the
wood has started to burn well, spread it evenly over the grate
and add a fine sprinkling of coal, until this in turn begins to
glow, when more coal may be added and the fire occasionally
leveled until the proper thickness of fire has been obtained.
It sometimes happens that the chimney refuses to draw; the
draft can be generally started, however, by building a small
fire in the base of the chimney.

Value of Slow Fires. — Wljen getting up steam, the fire should
not be forced, but, instead, should be allowed to burn up
gradually. By forcing the fire, the plates or tubes that are
nearest the fire suffer extreme expansion, while those parts
that are remote from the fire are still cold; under such condi-
tions the seams and rivets, and also the tube ends, which are
expanded into the tube plates, are liable to be severely strained,
and, possibly, permanently injured. It is not desirable to
raise steam in any boiler, except in steam fire-engines, in less
than from 2 to 4 hr., according to the size, from the time the
fire is first started. When steam begins to issue from the
opened top gauge-cock or the raised safety valve, as the case
may be, the cock or the valve may be closed and the pressure

STEAM BOILERS 147

still allowed to rise slowly until the desired pressure has been
reached.

Trying the Fittings. — After the pressure at which the boiler
is to run has been reached, and before cutting it into service,
all the valves and cocks should be tried. The safety valve
should be raised and its action noted; the water column should
be blown out and the gauge-cocks tested; the feeding apparatus
should be tried; and it should be noted particularly whether
the check-valves seat properly and the valve in the feedpipe
is open. All the accessible parts should be examined for leaks.

CONNECTING BOILERS

Cutting Boiler Into Service. — Cutting a boiler into service
is accomplished by opening the stop-valve, thus permitting
the steam to flow to the engine or other destination. The stop-
valve should be opened very slowly to prevent a too sudden
change in the temperature and consequent expansion of the
piping through which the steam flows, and also to prevent
water hammer. The steam-pipe drain should be kept open
until the pipe is thoroughly warmed up. In large plants with
many boilers and long steam mains it takes several hours to
warm these pipes thoroughly by a slow circulation of the
steam, but not until then should the main stop-valve be fully
opened.

Connecting Boilers to Main. — Before connecting the differ-
ent boilers of a battery to the same steam main, the precaution
of equalizing the pressures in the different boilers must be
observed in order to prevent a sudden rush of steam from one
boiler to another. All the pressures should be equal within a
variation of about 2 Ib. before an attempt is made to connect
the boilers.

Changing Over. — In plants where there are duplicate sets of
boilers, one set being in operation while the other is under-
going repairs, overhauling, and cleaning, the method of chang-
ing over, or connecting, is as follows: Start the fires and raise
steam in the boilers that are to be cut into service. Allow
the pressure to rise in all to within 5 Ib. of that which is in the
boilers in operation. All arrangements before changing over
should be made with a view to getting all the heat that can be

148 STEAM BOILERS

obtained from the fires in the boilers that are to be cut out.
This can be accomplished by running until the fires have given
up all of their available heat for making steam, as indicated by
the gradual fall in pressure when the dampers are wide open,
and then making the change. While the fires in one set of
boilers are burning low and the pressure is falling, the pressure
in the boilers to be cut in is gradually rising and meeting, so
to speak, the falling pressure of the set in operation. When
the difference of 5 Ib. is reached, change over. A man should
be stationed at each stop-valve, and while one is being opened
the other should be closed; the engine will continue running
uninterruptedly while the change is being made.

EQUALIZING THE FEED

When the boilers of a battery have been cut into service and
hence are all connected together through the steam main,
the regulation and equalization of the feedwater becomes an
important factor. Each boiler has its own check-valve and
feed stop- valve, and generally all the boilers are supplied from
one pump, which is running constantly. The quantity of
water admitted to each boiler is regulated by its feed stop-
valve. When the water gets low in any boiler, the feed stop-
valve should be opened wider, while at the same time the feed
stop-valves on one or more of the other boilers in operation
may be closed partly and thus divert the feedwater to the one
most requiring it. Some boiler plants have check-valves with
an adjustable lift; in that case the feed is equalized by adjust-
ing the lifts of the check- valves, the stop- valves being left
wide open while running. It will be understood from the
foregoing that the object in view is the maintaining of an equal
water level in all the boilers through the manipulation of the
feed stop-valves or check-valves. A boiler that is not doing
its legitimate share in generating steam may be known by the
fact that the feed stop-valve or check-valve on that boiler
will be nearly, if not entirely, closed most of the time.

FIRING WITH SOLID FUEL

General Remarks. — The safe and economical operation of
steam boilers calls for careful and intelligent management.
The fires should be kept in such condition as to maintain the

STEAM BOILERS 149

desired pressure and to burn the fuel with economy. Different
fuels require different handling and hence only general rules
can be given; much will depend on the skill and judgment of
the attendant, who must himself discover in each case by
actual trial the best method to pursue. The fires must be
cleaned at intervals; the time and method of cleaning depend
on conditions such as the nature of the fuel, the rapidity with
which it is being consumed, the style of grate in use, and the
construction of the furnace. Here much is left to the choice
and judgment of the attendant, who should readily discover
what is best to be done in any particular case.

Cleaning of Fires. — There are two methods employed in
cleaning the fires: first, that of cleaning the front half and then
the rear half; second, that of cleaning one side of the fire and
then the other side. In the first method, previous to cleaning,
green fuel is thrown on and allowed to burn partly until it
glows over the entire surface. The new and glowing fuel is
then pushed to the back of the furnace with a hoe, leaving
nothing on the front half of the grate but the ashes and clinkers,
which are then pulled out, leaving the front end of the grate
entirely bare. The new fire which had been pushed back is
now drawn forwards and spread over the bare half of the grate.
The ashes and clinkers that are on the rear half of the grate
are then pulled over the top of the front half of the fire
and out through the furnace door; this leaves the rear half
of the grate bare, which must be covered by pushing back
some of the new front fire. The clean fire having been
spread evenly, some new fuel must be spread over the entire
surface.

The second method referred to is substantially the same in
principle as that just described, with the difference that the
fire is pushed to one side instead of to one end of the furnace,
as in the first method described. The condition of the fires
themselves and the nature of the service of the plant will
determine just how often and at what time the cleaning of
fires should take place. In general, the fires in stationary
boilers require cleaning at intervals of from 8 to 12 hr. Fires
require cleaning more often when fqrced draft is used than when
working with natural draft.

150 STEAM BOILERS

Rapidity in Cleaning Fires. — Rapidity in cleaning fires is of
great importance, as during the operation a large volume of
cold air enters the furnace and chills the metallic surfaces with
which it comes in contact; consequently, the boiler is damaged,
however slightly. It is the greatest advantage of shaking
grates that they allow the fire to be cleaned without opening
the furnace door; the inrush of cold air and consequent chilling
of the plates, etc. is thus avoided.

Before starting to clean fires, the steam pressure and the
water level should be run up as high as is safe and the feed
should be shut off in order to reduce the loss in pressure v/hile
cleaning. The condition of the fire during cleaning and the
opening of the furnace doors cause the pressure to drop quite
rapidly, but the rapidity and the amount of drop will be reduced
by taking the precautions mentioned and cleaning quickly.

Drop of Pressure During Cleaning. — The amount of drop
in pressure while cleaning fires depends on several conditions.
For example, with a boiler that has a small steam space and,
in addition, is too small for the work required of it without
forcing, it is to be expected that the drop in pressure will be
much more than if the reverse conditions exist. Furthermore,
it may be necessary to clean fires while steam is being drawn
from the boiler, instead of being able to clean at a time when
the engine is stopped. In that case a greater drop must be
expected than when cleaning while no steam is being drawn
from the boiler. It is advisable when possible to do the clean-
ing at a time when no steam is being drawn from the boiler or
when the demand for steam is light.

FIRING WITH LIQUID FUEL

Number of Oil Burners Required. — The number of oil
burners to be installed in a given boiler depends on the type of
burner to be used and .the width of the furnace. The object
to be attained is a uniform distribution of heat throughout the
furnace. A straight-shot burner will produce a long, compact
flame, whereas a fan-tailed burner will produce a wide, short
flame; hence, one burner of the latter class may be sufficient for
a furnace that would require two burners of the former class.
One fan-tailed burner will ordinarily be sufficient for a furnace

STEAM BOILERS 151

6 ft. or less in width; two such burners may be used in furnaces
from 6 to 14 ft. wide; and for furnaces over 14 ft. in width
three burners should be installed. If narrow-flame burners
are used, their number will have to be greater.

Location of Burners. — The burners may be installed in the
centers of the fire-doors, if desired, and this practice is fre-
quently followed. In case only one burner is employed, it
may be placed in a suitable opening in the boiler front, between
the fire-doors. Another method that has been used is to insert
the burners below the fire-doors. So far as combustion is
concerned, the location of the burner is of little importance,
provided there is a sufficient air supply admitted under proper
conditions; but the heat developed may be utilized to better
advantage by exercising care in placing the burners. The
flames should not be directed against the side walls, but should
be approximately parallel thereto, with the tip of the burner
about 6 or 8 in. above the brick covering of the grate. It is
the usual practice to direct the flame from the front to the
back of the furnace; but in some installations of water-tube
boilers of the Stirling and Babcock & Wilcox types, the burners
have been placed at the rear of the furnace, so as to direct the
flames toward the front. This was found to be advantageous,
as the combustion was completed in the portion of the furnace
having the greatest cross -section, where the rapid expansion
of the gases due to the heat generated could be accommodated
most readily.

Necessity for Straining of Oil Fuel. — The crude oils used for
fuel come from wells drilled in the earth, and as a result they
contain varying proportions of sand and dirt. The denser
and more viscous the oil, the greater is the tendency for it to
retain impurities in suspension. If the oil is stored for some
time in tanks, and is left undisturbed, some of the heavier
dirt will settle to the bottom and thus be separated from the
oil; but if the oil is taken direct from the wells to market,
little or none of the dirt will be removed. Even fuel oil,
which undergoes a preliminary heat treatment to separate
the more volatile hydrocarbons from it, may not be free from
foreign matter. It may be assumed, therefore, that all oil
fuel contains dirt and sand, and as a consequence there arises

152 STEAM BOILERS

the necessity of straining the oil before admitting it to the
oil-burning system. The presence of sand and grit in the oil
supply vri.ll cause wear of the pump and erosion of'the burner
nozzles and orifices, and may result in the clogging of small
orifices.

Oil Pressure. — One of the requirements for the efficient
operation of an oil-burning plant is uniformity of the oil sup-
ply; for, if the oil supply is intermittent or varies in amount,
the combustion will be irregular and incomplete. To obtain
a uniform rate of feed it is customary to supply the oil at a
constant pressure by means of an ordinary duplex feed-pump.
The pressure at which the oil is delivered to the burners varies
in different plants and under different conditions. It may
range from 1 or 2 Ib. to 150 Ib. per sq. in., although the pressure
is usually between 10 and 40 Ib. per sq. in. The type of
burner employed will have some influence on the pressure
required; also, forcing of the boiler above its normal rating will
necessitate an increase in the oil pressure, to produce an
increased flow of oil.

Objection to Gravity Feeding of Oil. — When a standpipe is
used as a pressure regulator, the oil flows to the burners by
gravity. Some insurance companies refuse to insure plants
in which gravity feeding is practiced, on the ground that, if
a valve is left open, the boiler room may be flooded with oil,
thus greatly increasing the danger from fire. To overcome
the objection to having a considerable amount of oil held in
reserve above the level of the burners, a new form of apparatus
has been produced. This consists of a pump having a relief
valve between the suction and delivery sides. The relief
valve is set at the desired oil pressure, so that, if that pressure
is exceeded, the valve will lift and the excess of oil will be
returned to the suction side of the pump. When a standpipe
is used, it should be fitted with an automatic drain valve that
will open and drain out all the oil when the steam pressure falls
below the lowest pressure at which the oil can be atomized.
The flooding of the burners, with the attendant danger of
explosion, will thus be averted.

Heating of Oil Fuel. — The viscosity of certain crude oils
at ordinary atmospheric temperatures is very great, and it

STEAM BOILERS 153

increases as the temperature becomes lower. Below 40° F. the
oil is so sluggish that it can scarcely be forced to the burners
by the oil pump. Consequently, in all localities where low
temperatures are likely to occcur, provision must be made for
heating oil fuel, so that it may flow readily through the pump
and the pipes. The flow of oil from the storage tank to the
pump may be facilitated by surrounding the end of the suc-
tion pipe with a coil through which steam is led. The oil in
the vicinity of the pipe is thus heated and made more fluid.
Oftentimes, the oil is heated after leaving the pump, to aid in
obtaining better operation of the burners. In any case, how-
ever, the heating must not be carried to a temperature suffi-
cient to cause decomposition. The temperature at which the
decomposition begins depends on the nature and source of
the oil. Ordinarily the oil is not heated beyond a tempera-
ture of about 140° F.

Construction of Oil Tanks. — The size of the boiler plant
will determine the character of the oil-storage tanks. For
plants of small or medium size, the tanks used are generally
cylindrical in shape, built of steel plates, and coated with a
protective covering of tar. For large plants, rectangular tanks
made of reinforced concrete are frequently used. The penetra-
tive properties of petroleum necessitate tight joints, and conse-
quently it is advisable to entrust the construction of a steel
tank to a boilermaker. The rivet holes should be drilled rather
than punched, so that the rivets will properly fill them, and the
seams should be calked. There should be no openings in the
bottom, ends, or sides of the tank; all inlets and outlets should
be in the top. The manhole opening should be of such size
as to permit ready entrance to the tank when required, and
reinforcing flanges of steel or wrought iron should be riveted
to the tank at the various openings. Concrete tanks are
usually made with partitions, so that deposits of sediment or
of viscous matter may be removed at intervals without inter-
fering with the continuity of the fuel supply.

Fittings for Oil Tank. — Even at ordinary temperatures, oil
undergoes a slow process of evaporation, during which gases
are evolved; consequently, every oil-storage tank should be
fitted with a ventilating pipe to permit the escape of the gases

154 STEAM BOILERS

thus set free. This pipe will also serve to lead off the air in
the upper part of the tank during the operation of filling, and
will thus prevent undue pressure from accumulating. The
cross-sectional area of the ventilating pipe should be equal to
that of the rilling pipe. Care should be taken in locating the
ventilating pipe to see that no naked light can approach its
upper end; moreover, the openings in this end should be pro-
tected by a return elbow having wire gauze firmly fastened
over it. The gases rising from the oil, when mixed with air in the
correct ratio, form an explosive mixture, and could be ignited
by a naked flame. This flame, however, would not pass
through the fine meshes of the gauze, and the latter therefore
forms a safety device; also, the downward curving of the elbow
prevents any sparks from dropping into the opening. In addi-
tion to the ventilating pipe there should be a telltale, which is
a device for indicating the amount of oil in the tank at any
specified time.

Installation of Oil Tanks. — To conform with the require-
ments of underwriters and city ordinances, any oil-storage
tank located above the surface of the ground should be at least
200 ft. from inflammable property. Moreover, the top of the
tank should be at a lower level than the lowest pipe in the oil-
burning system, so that, in case a valve is inadvertently left
open, the plant will not be flooded with oil. If the tank is
placed underground, as is usually the case, its top should be
at least 2 ft. below the surface of the ground, and it should be
30 ft. distant from the nearest building; also, the top of the
tank should not be at a higher level than the lowest pipe in the
oil system. These, precautions in locating the tank or tanks
are necessary because of the highly inflammable nature of crude
oil and fuel oil.

Separation of Water From Oil. — The crude oils invariably
contain water in greater or less proportions. When the oil is
run into the storage tank, the water, being heavier, sinks to
the bottom of the tank and gradually accumulates. If the
suction pipe extends to the bottom of the tank, some of this
water will be drawn to the pump and forced to the burners,
extinguishing the fires. To prevent this trouble, provision
should be made for the removal of water from the oil tanks.

STEAM BOILERS 155

There is no practicable device that can be used to separate the
water from the oil. The best thing to do is to let the water
settle by gravity to the bottom of the tank- and then to pump
it out at intervals, as required. The oil being somewhat lighter
than water, will float on top of the latter, and by watching the
discharge of the pump it will be easy to discontinue the pump-
ing as soon as the flow of water ceases and oil appears.

Starting an Oil Fire. — Assuming that the oil pump has been
put in operation and that the desired oil pressure has been
obtained, the first step in starting an oil fire in a cold boiler is
to open the damper. The valve in the oil supply pipe leading
to the burner should be closed tightly. The needle valve, or
oil-regulating valve, on the burner should be opened one turn,
and the by-pass valve should be fully open. The steam valve
is now opened, admitting steam to the burner, and the valve
is left open until the steam blowing through appears dry. This
operation heats up the burner, cleans the oil passages, and
removes all water from the steam passages and pipes. The
by-pass valve is now' closed and the steam is almost, but not
wholly, shut off. A bunch of oily waste is next lighted and
thrown into the furnace, and the fire-door is closed. The oil-
regulating valve is closed slightly, and the valve in the oil-
supply pipe is opened fully. Steam and oil then pass through
the burner and the spray is ignited by the burning waste. The
condition of the fire is regulated by adjusting the steam valve
and the oil-regulating valve, in conjunction with the ash-pit
doors and the damper. The fire should not be forced, but
should be increased slowly, so as to permit the boiler to accom-
modate itself to the increasing temperature.

The procedure just outlined is based on the assumption that
a supply of steam for atomizing is available from an active
boiler in the battery, or else from a small auxiliary boiler
intended solely for the purpose. In case there is but a single
boiler in the plant, the method of starting a fire will be some-
what different from that just described. The ash-pit doors
and the fire-doors should first be opened, and a wood fire should
be built in the furnace. This fire should be kept going until
the gauge on the boiler shows a pressure of about 20 Ib. Then
the steam may be admitted to the burner and the latter may

156 STEAM BOILERS

be started in the manner already described, using the wood fire
to light the oil spray. The wood fire should be built on the
bottom of the furnace; or, in case it is a coal-burning furnace
converted for oil burning, the fire should be built on the brick
paving covering the grates. It is not necessary to remove the
bricks, nor must the burner be taken out while the wood fire
is burning, Care should be taken, however, to keep the fire
about a foot from the burner, to prevent overheating of the
latter. After the oil burner has become well started, the wood
fire may be raked out.

Furnace Conditions With Oil Burning. — When the brick-
work of the furnace has become heated and the burner is work-
ing normally, the furnace space should appear to be filled with
flame. In every properly arranged oil-burning boiler there
should be peep-holes at different points, to enable the fireman
to determine the conditions of combustion in the furnace. It
is also advantageous to have the top of the chimney visible to
the fireman, as the conditions at that point serve as a guide in
the regulation of the fire. The flame in the furnace should be
white or golden white in color, and should be steady. A prop-
erly adjusted steam burner will give a dazzling flame, whereas
an air burner will produce a duller, yellower flame. If the
burner passages are not kept clean, or if the burner is improp-
erly adjusted, the flame will become irregular and smoke will
be produced. No smoke should appear at the top of the chim-
ney; instead, there should be a light, grayish haze when the
burner is properly adjusted.

Smoke will be produced if there is too great a supply of oil,
or too little air, or insufficient steam for atomization. The
remedies to be applied to rectify these faults of operation are
obvious. If the burner hisses or spits, it is probable that the
steam used for atomizing contains moisture, or that there is
water in the oil supplied to the burner, or that a leak has devel-
oped in the suction pipe, so that air is being forced into the
burner with the oil. As a rule, oil burning in steam-boiler
furnaces is accompanied by a roaring noise of greater or less
intensity, and firemen experienced in the burning of oil fuel
are able to detect changes in the furnace conditions merely by
the altered roaring of the burners. An excessive supply of

STEAM BOILERS 157

cold air will increase the noise greatly and at the same time
will cause loss of heat; hence, as a general rule, it is safe to
assume that, the quieter the fire, the more nearly perfect is the
combustion. This is further corroborated by the fact that
preheating of the air, which is conducive to better combustion,
reduces the roaring. Sputtering of the flame from the burner
may be due to the heating of oil to such a point as to cause it
to be vaporized.

Draft Required for Oil Burning. — The draft of the chimney
performs the function of drawing air into the furnace and of
pushing the gaseous products of combustion through the boiler
and out into the air. When solid fuel is used, a large part of
the draft pressure is required to force the air through the layer
of fuel on the grates, the remainder serving to overcome the
resistance to the flow of the hot gases through the furnace,
tubes, flues, and chimney. When oil is used, there is no resist-
ance due to a fuel bed on a grate, and the draft pressure sim-
ply overcomes the resistance due to the flow of the air and hot
gases; consequently, the draft pressure required is much less
than for solid fuel. It follows, then, that when a boiler is
changed to use liquid fuel instead of solid fuel, the chimney
"that was satisfactory for the latter gives too strong a draft for
the former, and care must be exercised to prevent the admis-
sion of an excess of air. The draft pressure necessary for the
burning of oil fuel ranges from .1 to .5 in. of water, the former
corresponding to economical firing and the latter to firing with
a large excess of air. If the boiler is overloaded, the draft
must be increased above that required for normal working.

Formation of Soot. — An insufficient supply of air or an exces-
sive feeding of oil will result in the formation of soot, which will
by deposited on the heating surfaces and will reduce the effi-
ciency of heat transmission from the hot gases to the water in
the boiler, and may result in the overheating of some parts.
If such accumulations occur, they must be cleaned away, to
maintain the evaporative efficiency of the boiler. With care-
ful management of fires, boilers burning oil have been run at
full capacity for weeks without the formation of a troublesome
amount of soot. On the other hand, with coal as a fuel, it
would have been necessary to clean the tubes daily.
12

158 STEAM BOILERS

Shutting Down an Oil Burner. — To shut down an oil-burner
that is in active operation in a furnace, the oil valve in the sup-
ply pipe should be closed. The steam valve should next be
nearly closed, so that only a small amount of steam passes.
The oil-regulating valve should then be opened a full turn, and
the by-pass valve should be fully opened, after which steam
should be turned on again by manipulating the steam valve.
Steam will thus be discharged through the oil passages of the
burner, and all oil in them will be blown out, thus preventing
baking or carbonizing of the oil and the clogging that would
otherwise result. When the burner has been blown out, the
by-pass valve should be closed, and finally the steam should
be shut off completely. The burner will then be put out of
action, but will be in condition to be started again at short
notice.

Precautions in Relighting Fires. — If the fire should go out
completely, the fireman should not open the fire-door to look
for the cause of the trouble. His first act should be to shut off
the oil, and this should be followed by shutting off of the steam.
Then the furnace door may be opened, a piece of waste may be
set on fire and thrown in, and the fire may be restarted in the
usual way. The damper should be wide open when this is
being done. When the fire goes out for only a moment, as may
happen if a slug of water comes through the burner, it will
generally be reignited by the heat of the incandescent walls.
It is dangerous to leave the steam turned on and to increase
the amount of oil fed, in order to restart the fire in an incan-
descent furnace; for the explosion at the instant of reignition
may blow open the doors of the furnace, knock down the brick-
work, or cause other damage. The safest methed is to relight
the fire with burning waste.

Accidental Oil Fires. — If oil should escape in quantities
from the system and should become ignited, no attempt should
be made to put out the fire by spraying it with water, as this
will serve merely to spread the blazing oil and will make mat-
ters worse. Instead, sand or loose earth should be thrown on
the burning oil, to smother the flames. In some plants, boxes
of sand are kept at convenient points, in readiness for emergen-
cies of this nature. Also, in some cases, steam pipes are run

STEAM BOILERS 159

to the oil-storage tanks, so that,. if the oil in the tanks should
take fire, steam could quickly be run in to smother the blaze.

Thermal Advantages of Oil. — The calorific value of a pound
of oil fuel is about 30% higher than that of a high-class coal,
so that, by using oil instead of coal, the same amount of heat
may be obtained with a smaller weight of fuel. As has already
been shown, it is possible to obtain more nearly perfect com-
bustion, using less excess of air, with oil than with coal, which
increases the efficiency, Again, there is no repeated opening
and closing of the fire doors when oil is used, and this prevents
loss of heat and at the same time gives a better distribution
of heat in the combustion chamber. Also, there is less soot
deposited on the heating surfaces, in consequence of which the
transfer of heat is rapid and there is less heat lost up the chim-
ney. The capacity of the boiler may therefore be increased
from one-third to one-half by changing from coal to oil, while
for short periods the capacity may be doubled. Owing to the
uniformity of combustion of oil, the metal of the boiler is not
subjected to such severe conditions as when solid fuel is used.

Rapidity of Regulation. — Another great advantage of oil
fuel is the quickness and ease with which the intensity of com-
bustion may be altered. This is of particular importance in a
plant that may be subjected to quick increases in the load.
The fire in the furnace of an oil-burning boiler may be brought
very quickly from a moderate heat to a most intense heat, to
meet a sudden demand for more steam. Also, in case the load
falls off very suddenly, the burners may be adjusted rapidly to-
produce a correspondingly smaller quantity of heat. In emer-
gencies, the fires may be put out instantly, and may be almost
as quickly relighted when the danger is past. The closeness
with which the combustion may be made to follow the demand
for steam enables an almost uniform steam pressure to be
maintained by the use of automatic regulators for the oil pres-
sure and air supply.

Economy of Storage and Handling. — Oil fuel may be stored
and handled with less labor and at less cost than is possible
with coal. The volume occupied by a given weight of oil is
less than the volume of an equal weight of coal; also, because
of the greater calorific value of oil, it is possible to store 50%

160 STEAM BOILERS

more heating value, in the form of oil fuel, in a given space,
than can be done if coal is the fuel. Oil possesses the addi-
tional advantage that it does not deteriorate or lose its heating
value when stored for some time. Coal, on the other hand,
not only deteriorates but is liable to spontaneous combustion.
The cost of handling oil is less than that of handling coal, for
the reason that oil is run into the storage tanks by gravity, or
else is pumped into and out of storage.

Saving of Labor and Equipment. — When oil is employed for
fuel, instead of coal, there is no necessity for cleaning fires, and
consequently the boiler can be operated continuously at maxi-
mum capacity. There is a lower temperature in the boiler room,
because the fire-doors are kept shut. There is less wear and
tear on the pumps and other machinery that may be installed
in the boiler room, inasmuch as the absence of coal dust and
ashes enables the boiler room to be kept clean. The expense
of removing ashes is avoided, and there is a great saving in
labor, as fewer firemen and attendants are necessary. There
is no formation of clinker on the grates or side walls, and no
firing tools are used, so that the damage to furnace linings by
careless handling of tools is obviated.

Disadvantages of Oil Fuel. — One of the disadvantages of
oil as a boiler fuel is its low flash point; however, if oil having a
flash point of not less than 140° F. is used with care and judg-
ment by firemen of ordinary intelligence, there should be no
serious danger. The regulations as to the location of storage
tanks for oil fuel may be found irksome; for, in the case of a
plant situated in a thickly populated district in a city, it may
be wholly impossible to place the storage tanks at least 30 ft.
from the nearest building, and also underground. The tem-
perature of the fire obtained from oil fuel is greater than that
of a coal fire, and if the feedwater used contains much scale-
forming matter, the intense heat may cause more rapid deposit
of scale, and thus increase the cost of tube cleaning and repairs.

UNIFORM STEAM PRESSURE

Desirability of Uniform Pressure. — The attendant should
-aim to carry the pressure in the boiler as uniform as possible.
The reason why a steady steam pressure and a steady water

STEAM BOILERS 161

level are conducive to economy in the use of a fuel is to be found
in the fact that with these conditions in a properly designed
plant there will be a fairly steady temperature in the furnace,
which, under normal conditions, is sufficiently high to insure
a thorough ignition of the volatile matter in the coal. Now,
with a constant demand for steam, a fluctuation in the steam
pressure is caused by a change in the furnace temperature,
assuming the feedwater supply to be constant, and whenever
the steam pressure is down, the furnace temperature is low at
the same time. In consequence of this, large quantities of the
volatile matter in the coal often escape unconsumed and cause
a serious loss of heat. Furthermore, with a steady steam pres-
sure the stresses on the boiler are constant, and herlce the life
of the boiler will be increased and repair bills will be smaller
than otherwise.

Maintenance of Uniform Pressure. — During the period of
time between the cleaning of the fires, the pressure may be car-
ried nearly uniform by observing the following instructions:
Manipulate the feed apparatus so that just the necessary
amount of water constantly enters the boiler and thus main-
tains a constant level. Intermittent feeding is practiced under
certain local conditions, as, for example, where there is an injec-
tor or a pump that is so large that it would be impossible to run
it continuously without increasing the height of the water level.
In such a case, stop feeding just before firing; that is, do not
feed while firing nor resume feeding until the new fire begins to
make steam, as indicated by the rise of pressure on the gauge.
If the pressure tends to rise above the standard or normal
pressure, partly close the dampers and increase the quantity
of feed, assuming in this case that no damper regulator is fitted
and that hence the damper is regulated by hand. A damper
regulator, systematic firing, and proper feeding are essential
for carrying a practically uniform pressure. Should the pres-
sure continue to rise, throw on more green fuel, close the
damper, increase the feed, and only as a last resort open
the furnace door.

A uniform steam pressure cannot be kept without proper
firing. To maintain such a pressure the following directions
should be observed: Keep the fire uniformly thick; allow no

162 STEAM BOILERS

air holes in the bed of fuel. Fire evenly and regularly; be care-
ful not to fire too much at a time. Keep the fire free
from ashes and clinkers, and do not neglect the sides and cor-
ners while keeping the center clean. Do not, however, clean
the fires oftener than is necessary. Keep the ash-pit clear.

Keeping Water Level Constant. — In connection with the
maintenance of a constant water level, the following instruc-
tions should be followed : On starting to work, remember that
the first duty of the fireman is to examine the water level. Try
the gauge-cocks, as the gauge glass is not always reliable.
If there is a battery of boilers, try the gauge-cocks on each
boiler.

PRIMING AND FOAMING

Priming. — The phenomenon called priming is analogous to
boiling over; the water is carried into the steam pipes and
thence to the engine, where considerable damage is liable to
take place if the priming is not checked in time. There are
several causes for priming, of which the most common ones are
the following: Insufficient boiler power; defective design of
boiler; water level carried too high; irregular firing; and sudden
opening of stop-valves.

When the boiler power is insufficient, the best remedy is to
increase the boiler plant; the next best thing to do is to put in
a separator, which, obviously, will only prevent the entrained
water from reaching the engine, and will not stop the priming.

Defective design of a boiler generally consists of a steam
space that is too small or a bad arrangement of the tubes,
which may be spaced so close in an effort to obtain a large
heating surface as to interfere seriously with the circulation.
In horizontal return -tubular boilers, a sufficiently large steam
space can be obtained by the addition of a steam drum; some-
times the top row of tubes can be taken out to advantage,
which permits a lower water level. Defective circulation in
horizontal fire-tube boilers is difficult to detect and to remedy;
if it is due to a too close spacing of the tubes, a marked better-
ment may be effected by the removal of one or two vertical
rows of tubes. The remedy for a water level that is too high
is to carry the water at a lower level.

STEAM BOILERS 163

Evidences of Priming. — Priming manifests itself first by a
peculiar clicking sound in the cylinder of the engine, due
to water thrown against the heads. In cases of very violent
priming, the water will suddenly rise several inches in the gauge
glass, thus showing more water in the boiler than there really
is. When priming takes place, it can be checked temporarily
as follows: Close the damper, and thereby check the fires until
the water is quiet ; the engine stop-valve should also be partly
closed to check the inrush of water. Observe whether the
water drops in the gauge glass, and then, if more feed is needed,
increase the feed. To prevent damage to the engine, open the
cylinder drains. Regular and even firing tends to prevent
priming.

Foaming. — The phenomenon called foaming is not the same
as priming, though frequently considered so. Foaming is the
result of dirty or greasy water in the boiler; the water foams
and froths at the surface, but does not lift. A boiler may prime
and foam simultaneously, but a foaming boiler does not always
prime. Foaming while taking place is visible in the gauge
glass and is best remedied by using the surface blow-off. If
no surface blow-off is fitted, the bottom blow-off may be used
in order to get rid of the dirty water. Like foaming, priming,
will cause a wrong level to be shown, and hence the first thing
to do in case of foaming is to quiet the water by checking the
outrush of steam, either by slowing the engine down or by
checking the fire, or by both.

SHUTTING DOWN AND STARTING UP
Preparations l:or Shutting Down. — Before shutting down for
the night it is advisable to fill the boiler to the top of the glass,
so as to be sure to have sufficient water to start with in the
morning. The presence of possible leaks through the valves,
tube ends, or seams necessitates this course of action. Even
if no leaks exist, it is good practice to do this, if for no other rea-
son than to admit of blowing out a portion before raising steem
in the morning. All the gauge cocks should be tried and the water
column should be blown out to insure their being free and clear.
Banking of Fires. — The fires may be banked at such a time
that there will be about enough steam to finish the day's run,

164 STEAM BOILERS

thus shutting down under a reduced pressure with only a remote
possibility of its rising again through the night. If the fires
are properly banked and the steam worked off while the feed
is on, it will be remotely possible for the pressure to rise during
the night to a dangerous extent. To bank the fires they should
be shoved to the back of the grate and well covered with
green fuel, leaving the front part of the grate bare, thus pre-
venting any possibility that the banked fire will burn up through
the night.

Closing Valves and Damper. — The steam stop-valve, feed
stop-valve, whistle valve, and other steam valves should be
closed ; the valves at the top and bottom of the gauge glass also
should be shut off to prevent loss of water, etc. in case the glass
should break during the night. If there is a damper regulator,
it should be so arranged that the damper may be left closed,
but not quite tight, because a small opening must be left to
permit the collecting gases from the banked fire to escape up
the chimney; otherwise there is danger that the accumulated
gas will ignite and cause an explosion. It is very important
to take this precaution and also to make a mark by means of
which the distance the damper is open can be ascertained at a
glance. In fact, a damper should be so made that when shut
to the full extent of its travel there will be still sufficient space
around it to allow the gas to escape. The damper regulator
should be rendered positively inoperative in any manner per-
mitted by its design so that the damper when closed will remain
in that position until connected properly by the attendant
in the morning.

Starting the Fires. — On entering the boiler room in the morn-
ing, the quantity of water in the boiler should first be noted.
The gauge glass and the gauge-cocks should be tried and the
water level determined. After it has been found that the
water is not too low, the banked fires may be pulled down and
spread over the grates and allowed to burn up slowly, the
damper regulator, if one is fitted, in the meantime having been
connected.

Blowing Down. — While the fires are burning and before the
pressure begins to rise, the blow-off cock or valve should be
opened and the boiler blown down; that is, a small quantity of

STEAM BOILERS 165

the water should be blown out. This should be done every
morning, so that any impurities in mechanical suspension in
the water that settled during the night may be blown out.
Great care should be exercised while blowing down that too
much water is not blown out; from 3 to 4 in. as shown by the
gauge glass, is sufficient. Under no circumstances should the
attendant leave the blow-off while it is open. Disaster to the
boiler is liable to follow a disregard of this injunction. Next,
all the valves, except the stop-valve, which were shut the night
before should be opened and tried to see that they are free and
in good working order.

BOILER INSPECTION

NATURE OF INSPECTION

The inspection of a boiler usually consists of an external
examination of the complete structure, and of the setting if
the boiler is externally fired, and an internal inspection. The
examination of the boiler consists of an ocular inspection for
visible defects, and a hammer test or sounding for hidden defects
of plates, stays, braces, and other boiler parts. The hammer
test is made by tapping the suspected parts with a light ham-
mer and judging the existence and extent of defects from the
sound produced by the hammer blow. If the examination
discloses marked wear and tear, a series of calculations is often
required to find the safe pressure that may be allowed on the
worn parts, using such formulas or rules as laws, ordinances,
and regulations may prescribe for the particular official inspec-
tors. In the absence of officially prescribed formulas and rules,
the inspector should use such rules as he deems best appli-
cable or in best accordance with good practice. The inspec-
tion is usually, but not always, completed by a so-called
hydrostatic test, which is generally prescribed by official
regulations.

EXTERNAL INSPECTION

Preparation. — Before a boiler that has been in use can be
inspected, it must be blown out and must be allowed to cool off.

166 STEAM BOILERS

As soon as the water has been removed, the manhole covers,
handhole covers, and washout plugs should be taken out and
all loose mud and scale washed out with a hose. If the boiler
is externally fired, the tubes must be swept and the furnace,
the ash-pit, the smokebox, and the space back of the bridge
wall must be cleaned out. Any removable insulating cover-
ing that prevents the inspector from having free access to the
exterior of the boiler, must be removed to the extent deemed
necessary by him; it may even be necessary to take down some
of the bricks of the setting.

Inspection of Externally Fired Boilers. — In the inspection
of an externally fired fire-tube or flue boiler, the exterior is first
examined. The seams are gone over inch by inch; the rivet
heads and calking edges of the plates are carefully scrutinized
for evidence of leaks; and possible cracks are looked for between
the rivet heads, especially in the girth seams and on the under
side of the boiler. The plates must also be examined for cor-
rosion, bulges, blisters, and cracks. The heads are inspected
for cracks between the tubes or flues, cracks in the flanges,
leaky tubes, and leaks in the seams. The condition of the fire-
brick lining of the furnace and bridge and the top of the rear
combustion chamber is noted while making the exterior exami-
nation of the under side of the boiler. Every defect that is found
should be clearly marked. Attention must also be paid to the
condition of the grate bars and their supports.

Inspection of Internally Fired Boilers. — The inspection of
the shell and heads must be followed by examination of the fire-
box or furnace tubes or flues, and of the combustion chambers
if these are fitted inside the boiler. In fireboxes, special atten-
tion must be paid to the crown sheet. The ends of the stay-
bolts require close examination; if such ends are provided with
nuts, these must be examined, as they are liable to loosen and
are also liable to be burned off in time. Each stay bolt should
be tested for breakage, which is done by holding a sledge against
the outside end of the staybolt and striking the inner, or fire-
box, end with a light hammer; in making this test on the boilers
of locomotives it is customary, when practical, to subject the
boiler to an internal air pressure of from 40 to 50 Ib. per sq. in.
The internal pressure, by bulging the sheets, separates the ends

STEAM BOILERS 167

of a broken staybolt, which renders it comparatively easy to
find them by the hammer test.

Inspection of New Boilers. — As made in boiler shops, the
external inspection of new boilers, whether fhey are internally
or externally fired, and whether they are of the water-tube or
the fire-tube type, usually consists of a thorough examination
for visible defects and testing under water pressure to locate
leaks, if any. If a new boiler subject to official inspection during
construction successfully passes such a hydrostatic test as the
regulations prescribe, it will usually be permitted the working
pressure it was designed for, the design having been approved
officially before construction. The working pressure will be
reduced, however, if the inspection discloses poor workmanship.

In the external inspection of water-tube boilers that have
been in use, the tubes that are exposed directly to the heat of
the fire must be particularly well examined for evidence of
overheating. The plugs or handholes placed in headers to
permit the insertion of the tubes and the cleaning of them are
inspected for leakage, and the headers are inspected for cracks.
Steam drums and mud-drums should be examined as carefully
and for the same defects as the shells of externally fired fire-
tube boilers. The firebrick lining of the furnace, and the
interior of the brick setting in general, as well as the baffle
plates controlling the direction of flow of the gases of combus-
tion, must be examined for cracks and any other defects. The
external inspection of the setting can usually be made very
rapidly, as everything is in plain sight.

INTERNAL INSPECTION

Preparation. — Before the internal inspection is begun all
loose mud should be washed out with a hose. In a horizontal
return-tubular boiler and flue boiler, the shell plates and heads
should be examined for corrosion and pitting; if the boiler has
longitudinal lap seams, these should be inspected at the inside
calking edge for incipient grooving and cracks. All seams
should be examined for cracks between the rivet holes. Ob-
viously, if the boiler is scaled to an appreciable degree, the
scale must be removed before inspection. The tubes or flues
should be examined for pitting, as well as for uniform corrosion.

168 STEAM BOILERS

All braces should be inspected by sounding them with a
hammer, and if they are attached by cotter pins, it should
be seen to that these are firmly in place. All defects found
should be marked1; it is good practice to make a memorandum
of them as well. If any of the bracing seems to have worn
considerably,' it should be measured at the smallest part in
order that the safe working pressure thereon may be calculated
afterwards. To determine to what thickness a plate attacked
by uniform corrosion has been reduced the inspector will have
one or more holes drilled through the plate in the worn part to
enable him to measure the thickness. These holes are after-
wards plugged, generally by tapping out and then screwing in
a plug.

Inspection of Locomotive-Type Boilers. — In internally fired
boilers of the firebox and locomotive type, particular atten-
tion must be paid to the crown bars, crown bolts, and sling
stays, and in boilers having the crown sheet stayed by radial
staybolts, to these. As a general rule the inspector can make
only an ocular inspection of most of them, as they are beyond
his reach; where the outer sheets of the firebox contain inspec-
tion or washout holes above the level of the crown sheet, a
lighted candle tied or otherwise fastened to a stick can usually
be introduced through these holes from the outside by a helper.
In inspecting above the crown sheet, the inspector should look
for mud between the crown sheet and crown bars and sight
over the top of the bars to see if any have been bent. As the
inspector can reach from the inside of the boiler only a few of
the staybolts staying the sides of the firebox, he must rely on
the hammer test applied from the inside of the furnace for
finding broken staybolts.

Flues and Combustion Chambers. — In boilers having cir-
cular furnace flues and internal combustion chambers the top
of the furnace flues must be carefully inspected for deposits of
grease and scale, which are especially liable to be found if the
feedwater is obtained from a surface condenser. Even a light
deposit of grease on the furnace flue is liable to lead to over-
heating and subsequent collapse of the top. The tops of the
combustion chambers, together with their supports, are usually
easily inspected, there being ample space to reach every part.

STEAM BOILERS 169

Inspection of Vertical Boilers. — Vertical boilers as a general
rule, except in the largest sizes, have no manhole to admit a
person to the inside, and such internal inspection as is possible
must be made through the handholes. Defects to be looked
for are pitting and uniform corrosion of the shell and tubes
near the usual water-line, and cracks in the heads between the
tubes, the lower head being especially liable to show this injury.

HYDROSTATIC TEST

Value of Test. — While a hydrostatic test is usually demanded
by boiler laws and official rules and regulations, it does not at
all follow that a boiler that has successfully stood this test will
be safe. The chief value of the test lies in showing leaks.
Under no consideration should the test pressure be such as to
strain the parts of the boiler beyond the elastic limit of the
material.

Care in Making Test. — When applying the hydrostatic test,
the escape of air from the boiler while filling it with water
should be provided for, as by raising the safety valve. After
the boiler is full, all outlets must be tightly closed and the
safety valve so blocked that it cannot open; the pressure must
then be pumped up very slowly and carefully, the gauge being
watched for any drop of pressure, which denotes a sudden
yielding of some part of the boiler. When the desired test
pressure has been reached, the boiler is inspected for leaks, and
if any are found they are marked. Before calking to stop a
leak, the pressure must be left off by opening some convenient
valve or cock. In cold weather, when subjecting the boiler
to the hydrostatic test, it is customary to heat the water to a
lukewarm temperature.

Use of Blank Flange. — If the boiler to be tested is one of a
battery, and the others are to be in use while this one is being
inspected and tested, it is unwise to rely on a closed main stop-
valve to break communication with the other boilers. It is
good practice to put a blank flange between the boiler to be
tested and its main stop-valve.

INSPECTION OF FITTINGS

Inspection of Safety Valve. — The safety valve requires very
careful inspection. If this valve is known to leak, it should be

170 STEAM BOILERS

reseated and reground before the hydrostatic test is made.
After a boiler passes the hydrostatic test, the clamp locking the
safety valve is removed, and by running the pressure up once
more, the point at which the safety valve opens can be noted by
watching the steam gauge, which is supposed to have been tested
and corrected. If the safety valve does not open at the work-
ing pressure allowed or opens too soon, it is readjusted. If the
safety valve is locked by a seal, as is often required by official
regulations, the seal is applied after adjustment of the valve.

Testing of Steam Gauge. — The steam gauge should be tested
before the hydrostatic test, and at each inspection, with a so-
called boiler inspector's testing outfit. If the gauge under test
is more than 5% incorrect, most inspectors will condemn it,
although some will condemn gauges showing a much smaller
error. In most cases the gauge can be repaired at small expense
by the makers.

Inspection of Water Gauge and Blow-Off. — The connections
of water columns and water-gauge glasses require examina-
tion in order to see that they are clear throughout their whole
length. The blow-off pipe also requires examination in order
to see that it is clear.

BOILER EXPLOSIONS

As a boiler inspector is usually called on to investigate the
circumstances of a boiler explosion, and to render an opinion
concerning it, he must be familiar with the causes of such explo-
sions. Boiler explosions are really due to overpressure of steam.
This may occur because the boiler is not strong enough to
carry safely the working pressure used, or because the pressure,
through some cause, such as sticking or overloading of the safety
valve, has been allowed to rise above the ultimate strength
of the boiler. A boiler may be unfit to bear its working
pressure, for any of the following reasons : defective design ;
defects in workmanship or material; corrosion, and wear and
tear in general; and mismanagement in operation.

The common faults in design that have led to boiler explo-
sions are: insufficient staying, the stays being too small or too
few in number; the cutting away of the shell for the dome,
manhole, and other mountings, without reinforcing the edge

STEAM BOILERS 171

of the plate around the hole; fixing the boiler too rigidly in
its setting, thus causing it to be fractured on account of unequal
expansion; defective water circulation in a boiler, which may
lead to excessive incrustation and thus indirectly to 'explosion;
and a poorly designed feed apparatus or safety valve. Defects
in workmanship and material may include the use of faulty
material containing blisters, lamination, etc. ; careless punching
and shearing of plates; burning and breaking of rivets; burning
or otherwise injuring the plates in flanging, bending or weld-
ing; scoring of the plates along the joints by sharp calking
tools; and injury of the plates by the use of the drift pin.
Old boilers may, while being patched with new plates, be injured
by the operation of removing the old rivets and putting in
new ones, and also by the greater expansion and contraction
of the new plate as compared with the old plate. The strength
of the shell may be weakened by corrosion, pitting, and groov-
ing. In some exploded boilers, the plates have been found to
have wasted to little more than the thickness of wrapping
paper. Fractures that ultimately end in explosion may be
produced by letting the cold feedwater come directly into con-
tact with the hot plates.

If a boiler fractures while undergoing the hydrostatic test,
the water escapes through the rent in the plate and no explo-
sion takes place, because the cold water has little or no stored
energy. But when a boiler filled with steam and water at a
high temperature fractures, a violent explosion generally
follows. The steam escaping through the opening diminishes
the pressure, and, consequently, a new body of steam is formed
from the water, which, by escaping, lowers the pressure still
more, allowing the formation of another new body of steam
at a lower pressure, and this operation is continued until the
pressure reaches that of the atmosphere. The formation of
several successive large bodies of steam in this way, which
occurs almost instantaneously, produces a 'Disastrous explosion.
Generally speaking, the larger the body of the contained
water, the more disastrous is the result. For this reason
water-tube boilers, which contain a relatively small amount of
water, are generally considered to be much safer than fire-
tube boilers.

172

STEAM ENGINES

STEAM ENGINES

INDICATING OF ENGINES

Inside-Spring Indicator. — The indicator is an instrument
that is used to determine the action of the steam in the cylin-

FIG. 1

der of an engine. A form of indicator having its spring inside
the barrel, or cylinder, is shown in Fig. 1. The instrument
consists essentially of a cylinder a containing a piston and a

STEAM ENGINES 175

helical spring for measuring the steam pressure, a lever 6 for
transmitting the motion of the piston to a pencil point c, and
a drum d that carries paper on which this motion is recorded.
The card e is held close to the drum by clips /, so that the pencil
can easily trace the outline of the diagram. The piston, shown
at g, must work in the cylinder as nearly frictionless as possible,
the spring h being the only resistance to the upward motion of
the piston. This spring is calibrated; that is, it is tested so as
to determine the pressures required to move the pencil to vari-
ous heights against the resistance of the spring. Hence, it is
possible to find the pressure in the cylinder by the position of
the pencil point. By turning a cock in the small pipe con-
necting the indicator with the engine cylinder, steam may be
admitted to, or shut off from, the cylinder of the indicator at
pleasure. When steam is admitted through the nipple *', its
pressure causes the piston g to rise. The helical spring h is
compressed, and resists the upward movement of the piston.
The height to which the piston rises should then be in exact
proportion to the pressure of the steam, and as the steam pres-
sure rises and falls the piston must rise and fall accordingly.

To register this pressure, a pencil might simply be attached
to the end of the piston rod, the point of the pencil being made
to press against a piece of paper. It is desirable, however, to
restrict the maximum travel of the piston to about J in. while
the height of the card may advantageously be 2 in. To give
a long range to the pencil while keeping the travel of the piston
short, the pencil is attached at c to the long end of the lever b.
The fulcrum of the lever is at j, and the piston rod is connected
to it at k through the link /. The pencil motion is thus from
four to six times the piston travel.

The indicator, however, not only must register pressures,
but it must register them in relation to the position of the pis-
ton. This is accomplished by means of the cylindrical drum
shown at d. This drum can be revolved on its axis by pulling
the cord m that is coiled around it. When the pull is released,
a spring on the drum spindle, inside the drum, turns the latter
back to its original position. If the cord is connected with some
part of the engine that has a motion proportional to the motion
of the piston, the motion of the drum also will be proportional
13

174 STEAM ENGINES

to the motion of the piston. The outline then drawn by the
pencil, termed an indicator diagram, shows the pressure on
the piston at every point of the stroke. The slip of paper
on which the diagram is drawn is called an indicator card.

Outside-Spring Indicator. — The spring of the indicator
shown in Fig. 1 is subjected to the heat of the steam, and,
when highly superheated steam is used in the engine, the spring
may be rendered inaccurate by the heating due to the steam.

FIG. 2

An indicator with its spring located outside the barrel is shown
in Fig. 2. This form obviates the danger of heating the spring
and thus introducing eriors, and at the same time it has the
advantage of allowing the spring to be changed for a heavier
or a lighter one, with less trouble. In other details this indica-
tor is similar to that shown in Fig. 1.

Indicator Sptings. — The height to which the piston will rise
under a given steam pressure depends on the stiffness of the
spring. Indicators are usually furnished with a number of

STEAM EXGIXES

175

springs of varying degrees of stiffness, which are distinguished
by the numbers 20, 30, 40, etc. These numbers indicate the
pressure, in pounds per square inch, required to raise the
pencil 1 in. Thus, if a 40 spring is used, a pressure of 40 Ib. per
square inch raises the pencil 1 in., and therefore, the vertical
scale of the diagram is 40 Ib. per in. That is, the vertical
distance, in inches, of any point on the diagram from the
atmospheric line, multiplied by 40, gives the gauge pressure
per square inch at that point. The scale of the spring chosen
should not be less than half the boiler pressure, because it
is not desirable to have the indicator card more than 2 in. in
height.

Attachment of Indicator. — To attach the indicator to the
engine, a hole is drilled in the clearance space of the cylinder

FIG. 3

and tapped for a $-in. nipple, which should be as short as
possible. The nipple has an elbow, into which is screwed a
cock. The indicator may then be attached directly to the
cock by the nut n. Fig. 1, the conical projection i of the indi-
cator wedging tightly into the cock to prevent the leakage
of steam. It is preferable to have an indicator at each end
of the cylinder, but if that is not convenient, one indicator
may be connected with both ends of the cylinder by means
of a three-way cock, as shown at k, Fig. 3. This construction
is undesirable, however, if the engine has a long stroke, as the

176

STEAM ENGINES

long pipes will cause considerable resistance to the flow of the
steam. The pipe connections between the indicator and the
engine should be short and direct, and care should be taken
to see that the piston at the end of the stroke does not cover
the hole tapped for the attachment of the indicator pipe.
Before attaching the indicator, it is advisable to open the cock
slightly, to blow out any dirt or rust that may have accumu-
lated in the pipe.

Pendulum Reducing Motion. — The motion of the drum cord
is usually obtained from the crosshead. As the stroke of the

FIG. 4

FIG. 5

engine is nearly always greater than the circumference of the
drum, the cord cannot be attached directly to the crosshead,
and an arrangement called a reducing motion is used. A pen-
dulum reducing motion is shown in Fig. 3. The upright a is
fastened to the engine frame, and the lever b is pivoted at c
to the upright. Another upright d is fastened to the cross-
head or to the piston rod near the crosshead, and the link e
is connected at / to the piece d and at g to the lever b. The
cord, which should be parallel to the axis of the cylinder, is
attached to the point h on the lever b, which point must be
on the straight line connecting c and g.

STEAM ENGINES

177

Slotted-Lever Reducing Motions. — A form of reducing
motion consisting of a swinging slotted lever is shown in Fig. 4.
The lever a is pivoted at b to a stationary frame or girder and
is slotted at c so as to fit over a pin d fastened to the crosshead
e. The indicator cord / is attached to the lever at g.

Another form of slotted-lever reducing motion is shown in
Fig. 5. The lever a is pivoted at b and is slotted at its lower
end to fit over the pin c attached to the crosshead. The
indicator cord d is fastened to a bar e that slides in the guides /.

FIG. 6

FIG. 7

A pin g fixed in the bar e fits in a short slot in the upper end
of the swinging lever. As the crosshead moves to and fro, the
bar e , and hence the indicator cord also, copies the motion of
the crosshead to a reduced scale.

Pantograph Reducing Motion. — The type of reducing
motion shown in Fig. G is termed a pantograph. It consists of
four straight bars a, b, c, d joined together with pin joints to
form a parallelogram. One of the end bars d is prolonged, as
shown, and is pivoted to the crosshead of the engine at e.

• 178

STEAM ENGINES

The uppermost corner of the parallelogram is pivoted at / to
a stationary support, and the indicator cord g is attached to
the bar c at the point h, which lies on the straight line joining
the points e and /.

Brumbo Pulley. — A familiar form of reducing motion is
that shown in Fig. 7, as it is easy to construct. The lever a is
connected with the crosshead b by the bar c, pivoted at d and e.
At its upper end the lever a is pivoted on a stationary pin /
and has firmly fixed to it the sector g. The indicator cord h
is fastened to the sector at the corner * and lies against the
curved face j of the sector, which is an arc of a circle having

its center at /. As the crosshead moves back and forth, the
cord h is given a similar but reduced . motion by the sector.

Reducing Wheels. — Instead of a reducing motion composed
of levers, a reducing wheel may be used. Such a device is
illustrated in Fig. 8, as attached to the engine and to the
indicator, ready for use. A rigid upright is firmly fastened
to the crosshead, and to this upright is tied a cord, th<
end of which is wound on the wheel a. As the cr<
moves back and forth, the cord rotates the wheel a. Evidently
the linear movement of a point on the rim of this wheel in any
period is the same as that of the crosshead in that period.
Fixed to the wheel a and turning with it on the same shaft is

STEAM ENGINES 179

a smaller wheel c, on which is wound the cord leading to the
indicator b. Hence, as the wheel a turns, the drum of the
indicator is given a rotary motion that is proportional to
the motion of the wheel c, and hence proportional to the
crosshead movement also. But since the wheel c is so much
smaller than wheel a, the movement of a point on the drum
surface is much less than the movement of the crosshead.
On the forward stroke, the wheel a is rotated against the
resistance of a spring at d; but on the return stroke, this
spring rotates the wheel in the opposite direction. Both
wheels a and c are made as light as possible, in order that their
inertia may not affect the accuracy of the reduction. The

FIG. 9

cord leading from the wheel a to the upright on the crosshead
must be parallel to the axis of the cylinder, but the cord from
the wheel c to the indicator may incline upwards or downwards.
Reducing wheels, employing gears, are often made of alumi-
num for the sake of lightness. Such a wheel is shown in Fig. 9.
It really consists of two wheels; on the larger one, shown at a,
is wound the string that is attached to the arm on the cross -
head, and from the smaller one b runs the cord to the indicator.
A spring in the horizontal case c takes up the slack in the string.
Frequently, the reducing wheel is attached directly to the
body of the indicator, as shown in Fig. 2, thus avoiding the
necessity of fastening it to the engine frame, as in Fig. 8.

180 STEAM ENGINES

Attachment of Indicator Cord. — The cord leading from a
reducing motion to the indicator drum should be in two pieces
with a hook on one of the free ends, preferably the end next to
the indicator, and a loop in the end fastened to the reducing
motion. This makes it possible to disconnect the indicator
from the reducing motion when desired, and decreases the wear
on the instrument. The length of the string should be care-
fully adjusted so as to give the drum the correct amount of
motion. If the string is too short, it will be broken; and if
too long, there will be lost motion and the card will not repre-
sent the true length of the engine stroke. It may also result
in damage to the indicator.

A convenient arrangement is shown in Fig. 10. The hook a
is attached to the indicator cord, and the cord e from the
reducing motion is passed through a plate b, as shown. By

FIG. 10

slackening the cord at the point d, the plate may be slipped
to any position along the cord. The length is thus easily
adjusted. When the indicator is in operation, the hook is
hooked into the loop. By unhooking the two cords the indi-
cator may be stopped to put on a card.

The stretching of the indicator cord may introduce serious
errors in the diagram. Hence it is better, if possible, to use
a wire instead. If a cord is used, it should be as short as
convenient. It should also be thoroughly stretched before
being used.

Errors of Reducing Motions. — The forms of reducing motions
shown in Figs. 3, 4. and 7 are imperfect, because the motion
imparted to the cord is not exactly proportional to the move-
ment of the crosshead. The only forms of reducing motion
that are absolutely accurate are those in which the distance
from the pivot to the point of attachment of the cord always

STEAM ENGINES 181

bears a constant ratio to the distance from the pivot to the
point where the lever is connected to the crosshead. This
ratio must be the same at all points in the stroke, or at every
position of the crosshead; if it is not, the reducing motion is
not exact. In the reducing motion shown in Fig. 4, for instance,
the distance from the pivot b to the center of the pin d is
variable, depending on the position of the crosshead, whereas
the distance from b to g, where the cord is attached, is always
the same; in other words, the length of the long arm of the
lever changes while the length of the short arm remains con-
stant. As a result, the motions of the crosshead and the
cord differ at different parts of the stroke, and the indicator
diagram is correspondingly distorted. The reducing motions
shown in Figs. 5 and 6, and the reducing wheels shown in Figs.
8 and 9, are accurate, inasmuch as the motion of the cord is at
all times proportional to the motion of the crosshead.

Reduction of Errors. — For ordinary work with the indicator,
the amount of error caused by the - inexactness of reducing:
motions like those in Figs. 3, 4, and 7 is not serious and may
be ignored. To secure a minimum of distortion of the diagram,
the long lever should always be pivoted in such a position that
it will be perpendicular to the line of movement of the cross-
head when the latter is at the middle of its stroke. The
accuracy of the motion will, in general, be increased by increas-
ing the lengths of the long lever. For most purposes it is
sufficient to use a lever whose length is twice the stroke of the
engine.

Taking the Diagram. — After the instrument is properly
attached, a blank card is slipped over the drum so as to fit
smoothly, as in Fig. 1. The hook on the indicator cord is
then engaged with the loop on the cord from the reducing
motion, and the drum is allowed to rotate back and forth several
times, to see that it works properly and that the cord is adjusted
correctly. The cock is then opened and the indicator is allowed
to work freely while the engine makes several revolutions.
This warms up the parts to the working temperature. The
pencil is then pressed lightly against the card during a single
revolution. Next, the cock is closed and the pencil is again
pressed against the card, recording the atmospheric line.

182 STEAM ENGINES

Finally, the cord is unhooked, and the card is removed from
the drum.

If but one indicator and a three-way cock are used, as
shown in Fig. 3, the cock is opened to admit steam from one
end of the cylinder, and the diagram from that end is taken;
then the cock is turned to admit steam from the other end,
and another diagram is taken; finally, the steam is shut off
-entirely, and the atmospheric line is drawn.

CLEARANCE AND CUT-OFF

Clearance. — The term clearance is used in two senses in
connection with the steam engine. It may be the distance
between the piston and the cylinder head when the piston is
at the end of its stroke, or it may represent the volume between
the piston and the valve when the engine is on dead center.
To avoid confusion, the former is called piston clearance, and
the latter is termed simply clearance. Piston clearance is
always a measurement, expressed in parts of an inch. Clear-
ance, however, is a volume.

The clearance of an engine may be found by putting the
engine on a dead center and pouring in water until the space
between the piston and the cylinder head, and the steam port
leading into it, is filled. The volume of the water poured it
is the clearance. The clearance may be expressed in cut
feet or cubic inches, but it is more convenient to express it
as a percentage of the volume swept through by the piston.
For example, suppose that the clearance volume of a 12"X18"
is found to be 128 cu. in. The volume swept through
by the piston per stroke is 1 2-' X .785-1X18 = 2,035.8 cu. in.
Then, the clearance is 128 -=-2,035.8= .063 = 6.3%. The cl
ance may be as low as \% in Corliss engines, and as high
It', in high-speed engines.

Effects of Clearance. — Theoretically, there should be
clearance, since the steam that fills the clearance space does
no work except during expansion; it is exhausted from the
cylinder during the return stroke, and represents so much dead
loss. This is remedied, to some extent, by compression. If

STEAM ENGINES 183

the compression were carried up to the boiler pressure, there
would be very little, if any, loss, since the steam would then
fill the entire clearance space at boiler pressure, and the amount
of fresh steam needed would be the volume displaced by the
piston up to the point of cut-off, the same as if there were
no clearance. In practice, however, the compression is made
only sufficiently great to cushion the reciprocating parts and
bring them to rest quietly.

It is not practicable to build an engine without any clear-
ance, on account of the formation of water in the cylinder due
to the condensation of steam, particularly when starting the
engine. Automatic cut-off high-speed engines of the best
design, with shaft governors, usually compress to about half
the boiler pressure, and have a clearance of from 7 to 14%.
Corliss engines require but very little compression, owing to
their low rotative speeds; they also have very little clearance,
since the ports are short and direct.

Apparent Cut-Off . — The apparent cut-off is the ratio between
the portion of the stroke completed by the piston at the point
of cut-off, and the total length of the stroke. For example, if
the length of stroke is 48 in., and the steam is cut off from the
cylinder just as the piston has completed 15 in. of the stroke,
the apparent cut-off is if = tV

Real Cut-Off. — The real cut-off is the ratio between the volume
of steam in the cylinder at the point of cut-off and the volume
at the end of the stroke, both volumes including the clearance
of the end of the cylinder in question. If the volume of
steam in the cylinder, including the clearance, at the point of
cut-off is 4 cu. ft., and the volume, including the clearance,
at the end of the stroke is 6 cu. ft., the real cut-off is $=?.

Ratio of Expansion. — The ratio of expansion, also called the
real number of expansions, is the ratio between the volume of
steam, including the steam in the clearance space, at the end
of the stroke, and the volume, including the clearance, at the
point of cut-off. It is the reciprocal of the real cut-off. For
example, if the volume at the end of the stroke is 8 cu. ft.,
and the cut-off is 5 cu. ft., the ratio of expansion is 8-4-5 = 1.6;
in other words, the steam would be said to have one and six-
tenths expansions. The corresponding real cut-off would be f .

184 STEAM ENGINES

Let e =real number of expansions;

i = clearance, expressed as a per cent, of the stroke;
k =real cut-off;
^1 = apparent cut-off;

r = apparent number of expansions = — .

ki

Then, «--and* = - (1)

k e

EXAMPLE. — The length of stroke is 36 in. ; the steam is cut off
•when the piston has completed 16 in. of the stroke; the clear-
ance is 4%. Find the apparent cut-off, the real cut-off, and
the real number of expansions.

SOLUTION.— Apparent cut-off = £f = | = .444.

ki+i .444 + .04 .484

Real cut-off = k = - = - = - = .465.
1+t 1 + .04 1.04

Real number of expansions = e = - = — - = 2.15.

MEAN EFFECTIVE PRESSURE

Finding the Mean Effective Pressure. — In order to find the
horsepower of an engine, it is necessary to know the mean
effective pressure, abbreviated M. E. P., which is defined as
the average pressure urging the piston forwards during its
entire stroke in one direction, less the pressure that resists
its progress. The mean effective pressure is usually found
from the indicator diagram in one of two ways.

1. The area of the diagram in square inches may be meas-
ured by an instrument called a planimeterj the M. E. P. is
then found by dividing the area of the diagram in square inches
by the length of the diagram in inches, and multiplying the
quotient by the scale of the spring.

2. Where a planimeter is not available, the M. E. P. may
be found with a fair degree of accuracy by multiplying the
length of the mean ordinate by the scale of the spring.

STEAM ENGINES

185

Planimeter. — A common form of planimeter is shown in
Fig. 1. It consists of two arms hinged together by a pivot
joint at j. One arm carries a recording wheel d, which rolls
on the surface to which the card is fastened, while the outline
of the diagram is being traced by the point /. The needle
point p is fixed in the paper or drawing board, and remains
stationary during the operation.

The indicator card should be fastened to a smooth table or
a drawing board that has previously been covered with a
piece of heavy unglazed paper or cardboard. The point p
should be placed far enough from the card to enable the
wheel to roll on the unglazed paper without touching the card,
as it will slip if rolled over a smooth surface. Set the zero of

FIG. 1

the wheel d opposite the vernier e; then, with the tracing
point /, follow the line of the diagram carefully, going around
the diagram in the direction of the hands of a watch, and stop
exactly at the starting point.

Reading the Vernier. — The' area is read from the recording
wheel and vernier as follows: The circumference of the wheel
is divided into 10 equal spaces by long lines that are consecu-
tively numbered from 0 to 9. Each of these spaces represents
an area of 1 sq. in. and is subdivided into 10 equal spaces,
each of which represents an area of .1 sq. in. Starting with
the zero line of the wheel opposite the zero line of the vernier
and moving the tracing point once around the diagram, the
zero of the vernier will be opposite some point on the wheel;
if it happens to be directly opposite one of the division lines

STEAM ENGINES

on the wheel, that line gives the exact area in tenths of a squ
inch. The zero of the vernier, however, will probably be
between two of the division lines on the wheel, in which case
write down the inches and tenths that are to the left of the
vernier zero, and from the vernier find the nearest hundredth
of a square inch as follows: Find the line of the vernier that is
exactly opposite one of the lines on the wheel. The number
of spaces on the vernier between the vernier zero and this line
is the number of hundredths of a square inch to be added to
the inches and tenths read from the wheel. An example is
presented in Fig. 2, where the 0 of the vernier lies between
the lines on the wheel representing 4.7 and 4.8 sq. in., respect-
ively, showing that the area is something more than 4.7 sq. in.
Looking along the vernier it is seen that there are three spaces
between the vernier zero and the line of
the vernier that coincides with one of the
lines on the wheel; this shows that .03
sq. in. is to be added to the 4.7 sq. in.
read from the wheel, making the area
4.73 sq. in., to the nearest hundredth of a
square inch. The reading thus taken is
the area of the diagram, in square inches.
The M. E. P. is found by dividing this
area by the length of the diagram on a line parallel with the
atmo spheric line, and multiplying by the scale of the spring.

EXAMPLE. — The area of the diagram is 4.73 sq. in., the length
is 3.5 in., and a 40 spring is used; find the M. E. P.

4.73

SOLUTION.— M. E. P. = - - X40 = 54 1 Ib. per sq. in.
3.o

Hints for Use of Planimeter. — It is well to place the fixed
point p. Fig. 1, so that, as the tracing point moves around the
diagram, the arms will swing about equally on each side of a
position at right angles with each other. A slight dot is gen-
erally made with the tracing point to mark the point a'
its motion around the diagram begins; when the tracing point
reaches this dot in the paper, the operator knows that the
motion around the diagram has been completed. The Hirer -
tion of motion of the tracing point must always be the
same as that of the hands of a watch; motion in the opposite

STEAM ENGINES 187

direction will move the wheel in the wrong direction and give a
negative reading for the area. When measuring diagrams with
loops, like Fig. 3, move the tracing point so that it will follow
the outline of the loops in a direction opposite to the direction
of motion of the hands of a watch, as is indicated by the arrow-
heads on the diagram. This will cause the instrument auto-
matically to subtract the areas of the loops from the area of the
main part of the diagram.

An excellent check on the work is to start with the recording
wheel at zero and pass the tracing wheel around the diagram
two or three times, noting the reading of the wheel each time
the tracing point returns to the point of starting. Each read-
ing of the wheel divided by the number of times the outline

FIG. 3

of the diagram has been traced should give, very nearly, the
value of the first reading; if there is considerable difference
between the first reading and the value obtained by dividing
the second reading by 2 or the third reading by 3, it is an indi-
cation that an error has been made, and the work should be
repeated. If the difference is small, the work may be assumed
to be satisfactory and the value to be used for the area or the
M. E. P. may be taken as the average found by dividing the
last reading by the number of times the tracing point passed
around the diagram.

Finding M. E. P. by Ordinates. — The M. E. P. may be
found from the diagram by the aid of two triangles, a scale,
and a hard lead pencil; if two triangles are not available, a

188

STEAM ENGINES

single triangle and a straightedge will suffice. Lines perpen-
dicular to the atmospheric line and tangent to the two ends of
the diagram must first be drawn. The perpendicular distance
between these tangents will be the length of the diagram, and
this length must be divided into some number of equal parts;
10 or 20 parts are the most convenient, but any other number
may be used. Midway between each pair of points of dndsion
draw a line parallel to the two tangents; the part of this line
included between the lines of the diagram is the middle ordinate
of its corresponding space. The sum of the lengths of all of
these middle ordinates divided by the number of ordinates is
the mean ordinate and gives, approximately, the average
height of the diagram. The length of the mean ordinate

FIG. 4

should agree very nearly with the value obtained by dividing
the area of the diagram, as measured by a planimeter, by the
length of the diagram. The M. E. P. is found by multiplying
the length of the mean ordinate by the scale of the spring
with which the diagram was taken. A diagram thus divided
into equal parts, with the lengths of the ordinates marked
thereon, is shown in Fig. 4. The sum of the lengths of the
ordinates is 9.06 in. As there are 14 ordinates the length of

9 06
the mean ordinate is — — in., and if the diagram was taken

9.06

with an 80 spring, the M. E. P. is X80

51.77 Ib. per sq. in.
If a scale graduated to correspond with the scale of the

STEAM ENGINES 189

spring is available, the M. E. P. may be obtained by measuring
the ordinates in pounds instead of in inches; the sum of the
lengths of the ordinates as so measured divided by their number
gives the M. E. P. of the diagram. For example, let the scale
of the spring be 40; then each -fo in. in the length of an ordinate
represents a pressure of 1 Ib. per sq. in., and by measuring the
length of an ordinate with a scale graduated in fortieths of an
inch, the number of pounds of pressure represented by that
ordinate is found.

A convenient method of finding the sum of the lengths of
the ordinates of a diagram, and one that is especially to be
recommended when a decimal scale is not available, is the
following: Take a strip of paper having a straight edge a little
longer than the sum of the lengths of the ordinates. Lay this
strip along the first ordinate. From the point on the strip
representing one end of the first ordinate lay off the length of
the next ordinate. In the same way lay off on the strip the
length of each of the ordinates in succession. The length of
the strip included between the extreme, or first and last, points
so marked will be equal to the sum of the lengths of the ordi-
nates, and this length divided by the number of ordinates will
give the length of the mean ordinate.

Locating the Ordinates. — The length of the diagram will
seldom be divisible into equal parts that can readily be laid
off by a scale, and to divide the length into equal parts by a
cut-and-try process will be found very tedious. These diffi-
culties may, however, be overcome by an application of a
simple geometrical principle, in the manner illustrated in Fig. 4.
The tangent lines at the ends of the diagram are drawn perpen-
dicular to the atmospheric line AZ. Suppose, now, that it is
desired to have fourteen ordinates. Draw any other line from
A, as AB, at a small angle to AZ, and then lay off any con-
venient distance AC fourteen times successively, along AB.
Connect the last point B with Z, and from the other points
D, E, etc. draw lines parallel to BZ until they intersect AZ.
These points of intersection will divide the line AZ into four-
teen equal spaces. The middle points of these spaces can
then be located by direct measurement and the ordinates may
be erected at these middle points.
14

190

STEAM ENGIXES

Approximate M. E. P. — If an indicator is not available, so
that diagrams may be taken in order to determine the M. E. P.
of an engine, the value of the M. E. P. may be estimated by
the formula

in which P = M. E. P., in pounds per square inch;

C = constant corresponding to cut-off, taken from

accompanying table;
p = boiler pressure, in pounds per square inch, gauge.

The foregoing formula applies only to a simple non-
condensing engine. If the engine is a simple condensing
engine, the formula should be altered by substituting for 17
the pressure existing in the condenser, in pounds per square
inch.

CONSTANTS USED IN CALCULATING M. E. P.

Cut-off

Constant

Cut-off

Constant

Cut-off

Constant

j

.545

1

.773

f

.943

i

.590

.4

.794

7

.954

*

.650
.705

J

.864
.916

J

.970
.981

*

.737

;

.927

.993

In this table, the fraction indicating the point of cut-off is
obtained by dividing the distance that the piston has traveled
when the steam is cut off by the whole length of the stroke;
that is, it is the apparent cut-off. It is to be observed that
this rule cannot be applied to a compound engine or to any
other engine in which the steam is expanded in successive
stages in several cylinders.

EXAMPLE. — Find the approximate M. E. P. of a non-con-
densing engine cutting off at $ stroke, if the boiler pressure is
80 lb., gauge.

SOLUTION. — According to the table, the constant correspond-
ing to cut-off at J stroke is C = .864. Then, applying the for-
mula, P = .9[.864(80+ 14.7) -17] = 58.34 lb. per sq. in.

STEAM ENGINES 191

HORSEPOWER AND STEAM CONSUMPTION

Indicated Hors'epower. — The indicator furnishes the most
ready method of measuring the pressures on the piston of a
steam engine and, in consequence, of determining the amount
of work done in the cylinder and the corresponding horsepower.
The power measured by the use of the indicator is called the
indicated horsepower. It is the total power developed by the
action of the net pressures of the steam on the two sides of the
moving piston. The indicated horsepower is generally repre-
sented by the initials I. H. P.

Friction Horsepower. — The part of the indicated horsepower
that is absorbed in overcoming the frictional resistances of
the moving parts of the engine is termed the friction horse-
power. If the engine is running light, or with no load, all the
power developed in the cylinder is absorbed in keeping the
engine in motion, and the friction 'horsepower is equal to
the indicated horsepower. This principle furnishes a simple
approximate method of finding the friction horsepower of a
given engine; as, however, the friction between the surfaces
increases with the pressure, the power absorbed in over-
coming the engine will be greater as the load on the engine is
increased.

Net Horsepower. — The difference between the indicated
horsepower and the friction horsepower is the net horsepower.
It is the power that the engine delivers through the flywheel
or shaft to the belt or the machine driven by it, and is sometimes
called the delivered horsepower. Since the power that an engine
is capable of delivering when working under certain conditions
is often measured by a device known as a Prony brake, the net
horsepower is frequently called the brake horsepower, abbrevi-
ated B. H. P.

Mechanical Efficiency. — The mechanical efficiency of an
engine is the ratio of the net horsepower to the indicated horse-
power; or it is the percentage of the mechanical energy devel-
oped in the cylinder that is utilized in doing useful work. To
find the efficiency of an engine, when the indicated and net
horsepowers are known, divide the net horsepower by the
indicated horsepower.

192 STEAM ENGINES

General Rule for Calculating I. H. P. — Knowing the dimen-
sions and speed of the engine and the mean effective pressure
on the piston, all the data for finding the rate of work done
in the engine cylinder expressed in horsepower are at hand.
Let H — indicated horsepower of engine;

P= M. E. P., in pounds per square inch;
A = area of piston, in square inches;
L = length of stroke, in feet;
N = number of working strokes per minute.
PLAN

Then- H=

In a double-acting engine, or one in which the steam acts
alternately on both sides of the piston, the number of working
strokes per minute is twice the number of revolutions per
minute. For example, if a double-acting engine runs at a
speed of 210 R. P. M. there are 420 working strokes per minute.
A few types of engines, however, are single-acting; that is,
the steam acts on only one side of the piston. Such are the
Westinghouse, the Willans, and others. In this case, only
one stroke per revolution does work, and, consequently, the
number of strokes per minute to be used in the foregoing
formula is the same as the number of revolutions per minute.
Unless it is specifically stated that an engine is single-acting,
it is always understood, when the dimensions of a steam engine
are given, that a double-acting engine is meant.

Piston Speed. — The total distance traveled by the piston
in 1 min. is called the piston speed. It is customary to take
the stroke in inches. Then, to find the piston speed, multiply
the stroke in inches by the number of strokes and divide by 12;

or, letting 5 represent the piston speed, S = rr^t where / is

the stroke in inches. But N =2 R, where R represents the
number of revolutions per minute. Hence,

_M _IX2JR l_R

~ 12~~12~ " 6

EXAMPLE. — An engine with a 52-in. stroke runs at a speed
of (id R. P. M. What is the piston speed?

52X06
SOLUTION. — By the formula, 5- — =572 ft. per rr.in.

STEAM ENGINES 193

The piston speeds used in modern practice are about as

Small stationary engines ...... ........ 300 to 600

Large stationary engines .............. 600 to 1,000

Corliss engines ....................... 400 to 750 '

Marine engines ....................... 200 to 1,200

Allowance for Area of Piston Rod. — It is generally consid-
ered sufficiently accurate to take the total area of one side of
the piston as the area to be used in calculating the horsepower
of an engine. The effective area of one side of the piston is,
however, reduced by the sectional area of the piston rod, and
if it is important that the power be calculated with the greatest
practical degree of accuracy, an allowance for the area of
the piston rod must be made. This is done by taking as the
piston area one-half the sum of the areas exposed to steam
pressure on the two sides of the piston. Thus, if a piston is
30 in. in diameter with a 6-in. piston rod, the average area is

302 x .7854 + (302 X .7854 - 62 X .7854)

- - — — = 692.72 sq. in. If the

piston rod is continued past the piston so as to pass through the
head-end cylinder head, that is, if the piston has a tailrod,
allowance must be made for the tailrod. Thus, with a piston
30 in. in diameter, a piston rod 6 in. in diameter, and a tailrod
5 in. in diameter, the average area is

(302 x .7854 - 52 X .7854) + (3Q2 X .7854 - 6* X .78.54)

- - - — =682.9sq.in.

Stating Sizes of Engines. — The size of a simple engine, that
is, an engine having but one cylinder, is commonly stated by
giving the diameter of the cylinder, followed by the length of
the stroke, both in inches. Thus, a simple engine having a
cylinder 12 in. in diameter and a stroke of 24 in. would be
referred to as a 12"X24" engine, the multiplication sign in
this case serving merely to separate the two numbers. The
sizes of compound and multiple-expansion engines are desig-
nated in a similar fashion. Thus, a compound engine with a
high-pressure cylinder 11 in. in diameter, a low-pressure

194 STEAM ENGINES

cylinder 20 in. in diameter, and a stroke of 15 in. would be
referred to as an 11" and 20" XI 5" compound engine. In
the same way, a 14", 22", and 34"X18" triple-expansion
engine would be one in which the diameters of the cylinders
are 14 in., 22 in., and 34 in., and the stroke is 18 in.

Cylinder Ratios. — The cylinders of compound and multiple-
expansion engines increase in diameter from the high-pressure
to the low-pressure end, and it is customary to refer to their
relative sizes by means of cylinder ratios. As all the cylinders
have the same length of stroke, the volumes of the several
cylinders are in proportion to the areas of the cylinders, and
therefore in proportion to the squares of the diameters. The
area of the high-pressure cylinder is taken as unity, and the
other areas are referred to it, and the ratios of these areas, or
the ratios of the squares of the diameters, are called the
cylinder ratios. For example, a triple-expansion engine having
cylinders 12 in., 20 in., and 34 in., in diameter will have the cyl-
inder ratios of 12* : 20" : 34=, or 144 :400 : 1,156, which reduces
to 1 : 2.78 : 8.03; that is, the intermediate cylinder is 2.78 times
as large as the high-pressure cylinder, and the low-pressure
cylinder is 8.03 times as large as the high-pressure cylinder.
If there are two cylinders to one stage of expansion, as, for
example, two low-pressure cylinders, the sum of their areas
must be used in rinding the cylinder ratios. Thus, if there
had been two 24-in. low-pressure cylinders instead of one 34-in.
cylinder, in the foregoing case, the cy Under ratios would have
been 12* :2Q2 : 2X242, or 144 : 400 : 1,152, which reduces to
1 : 2.78 : 8.

Horsepower of Compound Engines. — The indicated horse-
power of a compound or triple-expansion engine may be cal-
culated from the indicator diagrams in exactly the same manner
as with any simple engine, considering each cylinder as a simple
engine and adding the horsepowers of the several cylinders
together. In taking the indicator cards from a compound
engine, the precaution of taking the cards simultaneously
from all cylinders must be observed, especially when the engine
runs under a variable load, because, otherwise, an entirely
wrong distribution of power may be shown, and there may also
be a great variation between the indicated horsepower really

STEAM ENGINES 195

existing and that calculated from diagrams taken at different
times.

Referred Mean Effective Pressure. — The indicated horse-
power of compound engines is sometimes found by referring
the mean effective pressure of the high-pressure cylinder to
the low-pressure cylinder and calculating the horsepower of
the engine on the assumption that all the work is done in the
low-pressure cylinder. To do this, the mean effective pressures
of the two cylinders are found from indicator diagrams; the
mean effective pressure of the high -pressure cylinder is then
divided by the ratio of the volume of the low-pressure cylinder
to that of the high -pressure cylinder; and the quotient is
added to the mean effective pressure of the low-pressure cyl-
inder, the sum being the referred mean effective pressure. This
sum is then taken as the mean effective pressure of the engine,
and the area of the low-pressure piston as the piston area;
with these data, the length of stroke and the number of strokes,
the horsepower is computed as for any simple engine. In the
case of a triple-expansion engine, the mean effective pressures
of the high-pressure and intermediate cylinders are referred
to the low-pressure cylinder and added to its mean effective
pressure. Thus, suppose that in a 12", 20", -and 34"X30"
engine the mean effective pressures are 83.2 lb., 27.8 lb., and

83 2
10.6 lb., respectively. Then, the referred M. E. P. is —

8.03

27 8 10.6

— I = 10.4 + 10+10.6 = 31 lb., and this value must be

2.78 1

substituted for P on finding the horsepower of the engine.
While this method shortens the labor of computing the horse-
power, it obviously does not show the distribution of work
between the cylinders.

Dynamometers.— Dynamometers are instruments for meas-
uring power. They are divided into two main classes: absorp-
tion dynamometers and transmission dynamometers. The most
common form of absorption dynamometer is the Prony brake,
which consists simply of a friction brake designed to absorb
in friction and measure the work done by a motor, or the power
given out by a shaft. A transmission dynamometer is used

196

STEAM ENGINES

to measure the power required to drive a machine or do other
work; thus, to determine the power required to run the shafting
in a mill, a transmission dynamometer would be interposed
between the shafting and the source of power, and by suitable
belt connections the shafting would be driven through the
dynamometer, from which the power could be determined. As
transmission dynamometers do not enter into the work of the
steam engineer, they will not be treated of here.

Prony Brake. — The brake horsepower of steam engines is
commonly determined by means of some form of friction
brake. One construction of Prony brake is shown in Fig. 1.
It consists of two wooden blocks a and b formed so as to fit

FIG. 1

the face of the iron pulley c on the shaft of the engine to be
tested. To the blocks are fixed the two long arms d and e,
and the whole is clamped together by means of the bolts / and g
and the nuts h and «. By tightening these nuts the blocks
a and b may be pressed more tightly against the face of the
pulley, thus increasing the friction at the surface of the
pulley. If the engine rotates so as to turn the pulley in the
direction indicated by the arrow, the friction on the face of
the pulley will tend to drag the blocks around in the same
direction; but as the end of the arm d carries a spring balance j
attached to a stationary support k, the tendency to turn is
indicated by a pull on the spring balance. The tighter the

STEAM ENGINES

197

nuts h and i are screwed up, the greater will be the pull exerted
on the spring balance. The arm e is extended and fits between
two stops I and n, so as to prevent excessive movement of the
brake. While a test is being made, the arm e should not
touch either stop. This can easily be attained by regulating
the tightness of the nuts h and i. The stops, however, should
never be dispensed with, as a sudden reversal of the engine or
an unexpected gripping of the pulley by the wooden blocks
might swing the brake arms around and injure the workmen.
The distance n from the center of the pulley c to a plumb-
line suspended from the center of the bolt o should be measured
very accurately, with the arm d in a level position. This

FIG. 2

distance n is used in determining the brake horsepower, as will
be explained later.

Another form of friction brake is illustrated in Fig. 2. In
this type, there are a number of wooden blocks a fastened to an
iron band b and surrounding the pulley c. The friction
between the blocks and the pulley may be altered by loosening
or tightening the nut d on the bolt e that joins the ends of
the band b. To the bands are fastened the arms /, which are
bolted together at their outer ends and rest on a knife edge g
fastened to a block h resting on a platform scales *. When the
pulley is rotated in the direction indicated by the arrow, the
outer ends of the arms / press down on the block h and

198

STEAM ENGINES

the pressure may be measured by the scales. The distance
between the center of the shaft to which the pulley is keyed
and the knife edge g should be measured carefully, as it repre-
sents the effective length of the brake arm.

Rope Brake. — A form of brake requiring less space than the
Prony brake is the rope brake, shown in Fig. 3. It is used in
determining the horsepower of engines of moderate size. The
pulley a on the engine shaft is encircled by a double rope b to
which are fixed blocks c that bear against the face of the

pulley. One end of the
rope is attached to a
spring balance d sus-
pended from a beam e,
and the other end car-
ries a weight / that may
be varied. The friction
of the brake on the
pulley is increased by
adding to the weight /.
The direction of rota-
tion is indicated by the
arrow. The brake arm
in this type of brake is
the distance from the
center of the pulley to
the center of the rope,
and this distance should
be measured very care-
fully and quite accu-

,

FIG. 3

rately, as it is required in calculating the horsepower.

Cooling of Brake Pulleys. — It is essential that the pulleys of
brakes should be well lubricated and for all except small powers,
means must be provided for conducting away the heat generated
by friction. If there are internal flanges on the brake wheel,
water can be run on the inside of the rim, the flanges serving
to retain the water at the sides and centrifugal force to keep it
in contact with the rim. A funnel-shaped scoop can be used
to remove the water. It should be attached to a pipe and
placed so as to scoop out the water, which should flow

STEAM ENGINES 199

continuously. An arrangement of this kind is shown in Fig. 2,
in which water is led into the rim of the pulley by the pipe j
and is scooped out and led away by the pipe k.

Data for Brake Horsepower. — It is necessary to know three
factors in order to determine the brake horsepower. These are

(1) the net pull or pressure exerted at the end of the brake arm,

(2) the length of the brake arm, and (3) the number of revo-
lutions per minute of the brake pulley. The work done by
the engine is converted into heat by the friction between the
wooden blocks and the face of the pulley, and the resistance
offered by the brake to the rotation of the pulley is a meas-
ure of the work done. This resistance cannot always be
measured conveniently at the surface of the pulley, but it can
be measured at the end of the brake arm by the scales or the
spring balance.

Net Pull or Pressure. — With the brake shown in Fig. 1,
there will be a pull in the spring balance due to the weight of
the arm d, when the nuts h and i are slacked and the brake is
loose on the pulley. This pull should be observed carefully,
and should be subtracted from the pull registered by the spring
balance during a test. The difference will be the net pull,
from which the brake horsepower is calculated. If the arm d
is counterbalanced accurately by adding weights to the arm e,
as shown dotted at p, it will be unnecessary to perform this
subtraction. The net pull will then be indicated directly by
the reading of the spring balance.

The net pressure must also be calculated if the brake shown
in Fig. 2 is used. The nut d should be loosened, and the arms /
should be worked up and down, to make sure thnt the blocks
are loose on the pulley. The ends of the arms should then be
rested on the knife edge g and the reading of the scale beam
should be observed. This weight represents the pressure due to
the block h and the unbalanced arms /, and it must be sub-
tracted from the reading of the scale beam observed during a
test in order to determine the net pressure.

In the case of the rope brake shown in Fig. 3, the net pull
is easily determined by subtracting the reading indicated
by the spring balance from the weight, in pounds, applied
at/.

200 STEAM ENGINES

Calculation of Brake Horsepower. — When the necessary
data, as previously noted, have been determined, the brake
horsepower may be calculated by the formula
2,r R WN

Hb

in which /?& = brake horsepower;
7T = 3.1416;

R = length of brake arm, in feet;
W = net pull or pressure, in pounds;
N = number of revolutions per minute.

EXAMPLE. — A Prony brake with an arm 6 ft. long was placed
on the flywheel of an engine running at 200 R. P. M. What
brake horsepower was being developed when the net pressure
was 140 lb.?

SOLUTION. — Applying the formula,

2X3.1416X6X140X200

33,000

CONDENSERS

Types of Condensers. — There are two types of condensers
in general use, namely, the surface condenser and the jet con-
denser. In the former, the exhaust steam comes in contact
with a large area of metallic surface that is kept cool by con-
tact with cold water. In the latter, the exhaust steam, on
entering the condenser, comes in contact with a jet of cold water.
In either case, the entering steam is condensed to water, and
in consequence a partial vacuum is formed. If enough cold
water were used, the steam on entering would instantly con-
dense and a practically perfect vacuum would be obtained
were it not for the fact that the feedwater of the boiler always
contains a small quantity of air, which passes with the exhaust
steam into the condenser and therefore partly destroys the
vacuum. To get rid of this air, the condenser is fitted with an
air pump, which pumps out both the air and the water formed
by condensation.

Surface Condensers. — In the surface condenser, the exhaust
steam and the injection water are kept separate throughout

STEAM ENGINES 201

their course through the condenser; and the condensed steam
leaves the condenser as fresh water, free from the Impurities
contained in the injection water. The water of condensation
from a surface condenser is therefore fit to be used as boiler
feed, except that it contains oil used for cylinder lubrication,
which can be eliminated by means of an oil separator, regardless
of the quality of the water used to condense it. It is for this
reason that the surface condenser, in spite of its greater com-
plication, cost, size, and weight, as compared with the jet
condenser, is used instead of the latter where the supply of
injection water is unfit for use as boiler feed. Thus, the
surface condenser is used altogether in marine work, except
for vessels navigating clean fresh water like that of the Great
Lakes, in order to avoid the use of sea-water in the boilers.

In the surface condenser the steam may be outside and the
water inside the tubes, or the reverse. If the water is inside
the tubes, it should enter at the bottom of the condenser and
be discharged at the top. This brings the coldest v/ater into
contact with the partly condensed steam, and the warmest
water into contact with the hot entering steam. When the
water is outside the tubes, it is necessary to fit baffle plates
on the water side to force the water into a defihite and regular
circulation, and to prevent it from going directly from inlet
to outlet and also to prevent the water from arranging itself
in layers according to temperature, with the coldest water on
the bottom and the hottest water on top. The outlet should
be well above the top- row of tubes. A solid body of water
above the top row of tubes is thus assured, and the accumula-
tion of a stagnant body of hot water in the top of the condenser
is prevented by its being continually drawn off by the circu-
lating pump and replaced by cooler water from beneath.

Air tends to accumulate in the top of the water side of a
surface condenser. This is particularly inconvenient where the
water is inside the tubes, as the air fills the top rows of tubes and
excludes the water, destroying their value as cooling surfaces.
To prevent this, an air valve must be provided , as high up on
the water side as possible, in all surface condensers, by which
the air can be drawn off whenever it becomes troublesome.
Drain valves and pipes should be provided at the bottom.

202 STEAM ENGINES

As the condensed steam from the surface condenser is gen-
erally pumped back into the boiler as feedwater, it is desirable
to have it as hot as possible; but it must be remembered that
it is impossible to get the feedwater from the condenser at a
higher temperature than that of saturated steam at the abso-
lute pressure existing in the condenser.

It will be considerably cooler than this if, after being con-
densed, it is allowed to lie in the bottom of the condenser
and give up its heat to the circulating water. The heat
thus given up is a total loss, and should be avoided by con-
necting the air-pump suction to the lowest point of the con-
denser and by shaping the bottom of the condenser so that the
water will drain rapidly into the air-pump suction.

Cooling Water for Surface Condenser. — The amount of
cooling water required in the case of a surface condenser may
be found by the formula

H- (/-32)

t»-h '
in which Q = number of pounds of cooling water required to

condense 1 Ib. of steam;
H = total heat above 32° of 1 Ib. of steam at pressure

at release;
<— - temperature of condensed steam on leaving

condenser;

t\ = temperature of cooling water on entering con-
denser;

*2 = temperature of cooling water on leaving condenser.
EXAMPLE. — Steam exhausts into a surface condenser from
an engine cylinder at a pressure of fi Ib., absolute; the tempera-
ture of the condensing water on entering is 55° P., and on leaving
it is 100° F. ; the temperature of the condensed steam on leaving
the condenser is 125° F. How many pounds of cooling water
are required per pound of steam?

SOLUTION. — The total of 1 Ib. of steam at 6 Ib., absolute,
from the Steam Table, is 1,133.8 B. T. U. Then, substituting
the values of H, t, t\, and fj in the formula,

l.i:«..X-(125-32) 1.040.8
'--• ,«,, " 45

STEAM ENGINES 203

Injection Water for Jet Condenser. — The quantity of injec-
tion water required for a jet condenser may be found by the
formula

H-(t-32)

t-h '
in which Q = number of pounds of injection water required to

condense 1 Ib. of steam;
H = total heat above 32° of 1 Ib. of steam at pressure

at release;
t = temperature of mixture of injection water and

condensed steam on leaving the condenser;
ti = temperature of injection water on entering the

condenser.

EXAMPLE. — Steam is exhausted into a jet condenser from
an engine cylinder at a pressure of 10 Ib., absolute; the temper-
ature of the injection water on entering is 60° P., and on leaving
140° F. How much injection water is required per pound of
steam?

SOLUTION. — The total heat above 32° of 1 Ib. of steam at
10 Ib. absolute, from the Steam Table, is 1,140.9 B. T. U.
Then, substituting the values of H, t, and h in the formula,
1,140.9-(140-32)_1.032.9
140-60 80

ENGINE MANAGEMENT

STARTING AND STOPPING

Warming Up. — About 15 or 20 min. before starting the
engine, the stop-valves should be raised just off their seats
and a little steam should be allowed to flow into the steam
pipe. The drain cock on the steam pipe just above the throttle
should be opened. When the steam pipe is thoroughly warmed
up and steam blows through the drain pipe, the drain cock
should be closed and the throttle opened just enough to let a
little steam flow into the valve chest and cylinder; or if a
by-pass around the throttle is fitted, it may be used. The
cylinder relief valves, or drain cocks, and also the drain cocks

204 STEAM ENGINES

on the valve chest and the exhaust pipe should be opened,
if the engine is non-condensing. If the cylinders are jacketed,
steam should be turned into the jackets and the jacket drain
cocks should be opened. While the engine is warming up,
the oil cups and the sight-feed lubricator may be filled. A
little oil may be put into all the small joints and journals that
are not fitted with oil cups. The guides should be wiped off
with oily waste and oiled. By this time the engine is get-
ting warm. If the cylinder is fitted with by-pass valves, they
should be used to admit steam to both ends of the cylinder.
In general, all cylinders, especially if they are large and intricate
castings, should be warmed up slowly, as sudden and violent
heating of a cylinder of this character is very liable to crack
the casting by unequal expansion.

An excellent and economical plan for warming up the steam
pipe and the engine is to open the stop-valves and throttle
valve at the time or soon after the fires are lighted in the
boilers, permitting the heated air from the boilers to circulate
through the engine, thus warming it up gradually and avoiding
the accumulation of a large quantity of water of condensation
in the steam pipe and cylinder. When pressure shows on the
boiler gauge or steam at the drain pipes of the engine, the stop-
valves and throttle may be closed temporarily, but not hard
down on their seats. When this method of warming up the
engine is adopted, the safety valves should not be opened
while steam is being raised.

Danger of Water Hammer. — Stop-valves and throttle valves
should never be opened quickly or suddenly and thus permit
a large volume of steam to flow into a cold steam pipe or cylin-
der. If this is done, the first steam that enters will be con-
densed and a partial vacuum will be formed. This will be
closely followed by another rush of steam with similar results,
and so on until a mass of water will collect, \vhich will rush
through the steam pipe and strike the first obstruction, gener-
ally the bend in the steam pipe near the cylinder, with great
force, and in all probability will carry it away and cause
a disaster. This is called -water hammer and has caused many
serious accidents. Before turning steam into any pipe line or
into a cylinder, all drain valves should be opened.

STEAM ENGINES 205

Easing of Throttle Valve. — Another precaution that should
be taken is the easing of the throttle valve on its seat before
steam is let into the main steam pipe; otherwise, the unequal
expansion of the valve casing may cause the valve to stick
fast and thereby give much trouble. Even if a by-pass pipe
is fitted around the throttle, it would be better not to depend
on it. Considerable space has been devoted to the subject
of warming up and draining the water out of the steam pipe
and engine on account of its importance. Water being non-
compressible, it is an easy matter to blow off a cylinder head
or break a piston if the engine is started when there is a quan-
tity of water in the cylinder.

Oil and Grease Cups. — The last thing for the engineer to do
before taking his place at the throttle preparatory to starting
the engine, provided he has no oiler, is to start the oil and
grease cups feeding. It is well to feed the oil liberally at first,
but not to the extent of wasting it; finer adjustment of the
oiling gear can be made after the engine has been running a
short time and the journals are well lubricated.

Starting Non-Condensing Slide-Valve Engine. — A non-
condensing slide-valve engine is started by simply opening the
throttle; this should be done quickly in order to jump the
crank over the first dead center, after which the momentum
of the flywheel will carry it over the other centers. The
engine should be run slowly at first, gradually increasing the
revolutions to the normal speed. When the engine has
reached full speed, the drain pipes should be examined; if dry
steam is blowing through them, the drain cocks should be
closed. If water is being delivered, the drain cocks should
remain open until steam' blows through and should then be
closed.

Stopping Non-Condensing Slide-Valve Engine. — To stop
a non-condensing slide-valve engine, it is only necessary to
shut off the supply of steam by closing the throttle, but care
should be taken not to let the engine stop on the dead center.
After the engine is stopped, the oil feed should be shut off and
the main stop-valve closed. The valve should be seated,
but without being jammed hard down on its seat. The
drain cocks on the steam pipe and engine may or may not
15

206 STEAM ENGINES

be opened, according to circumstances. It will do no harm
to allow the steam to condense inside the engine, as the engine
will then cool down more gradually, which lessens the danger
of cracking the cylinder casting by unequal contraction. All
the water of condensation should be drained from the engine
before steam is again admitted to it.

Starting Condensing Slide-Valve Engine. — Before the main
engine is started, the air pump and circulating pump should
be put into operation and a vacuum formed in the condenser;
this will materially assist the main engine in starting promptly.
Prior to starting the air and circulating pumps, the injection
valve should be opened to admit the condensing water into
the circulating pump; the delivery valve should also be opened
at this time. If an ordinary jet condenser is used, no circu-
lating pump is required, the water being forced into the con-
denser by the pressure of the atmosphere. If the air pump is
operated by the main engine, a vacuum will not be formed
in the condenser until after the engine is started and at least
one upward stroke of the air pump is made. In this case
the injection valve must be opened at the same moment the
engine is started; otherwise the condenser will get hot and a
mixture of air and steam accumulate in it and prevent the
injection water from entering. When this occurs, it is neces-
sary to pump cold water into the condenser by one of the
auxiliary pumps through a pipe usually fitted for that purpose;
if such a pipe has not been provided, it may be found neces-
sary to cool the condenser by playing cold water on it through
a hose.

Stopping Condensing Slide-Valve Engine. — The operation
of stopping a slide-valve surface-condensing engine is precisely
similar to that of stopping a non-condensing engine of the same
type, with the addition that after the main engine is stopped
the air and circulating pumps are also stopped, and in the
same way, that is, by closing the throttle, after which the
injection valve and the discharge valve should be closed and
the drain cocks opened. With a jet condenser, the operation
of stopping the engine is the same as the above, with the
exception that the injection valve should be closed at the same
moment that the engine is stopped.

STEAM ENGINES 207

Starting Simple Corliss Engine. — In the Corliss engine, the
eccentric rod is so constructed and arranged that it may
be hooked on or unhooked from the eccentric pin on the wrist-
plate at the will of the engineer. After all the preliminary
operations have been attended to, the starting bar is shipped
into its socket in the wristplate and the throttle is opened.
The starting bar is then vibrated back and forth by hand,
by which the steam and exhaust valves are operated
through the wristplate and valve rods; as soon as the cylinder
takes steam, the engine will start. After working the starting
bar until the engine has made several revolutions and the
flywheel has acquired sufficient momentum to* carry the
crank over the dead centers, the hook of the eccentric rod
should be allowed to drop upon the pin on the wristplate.
As soon as the hook engages with the pin, the starting bar is
unshipped and placed in its socket in the floor. The way to
determine in which direction the starting bar should be first
moved to start the engine ahead is to note the position of the
crank, from which the direction in which the piston is to move
may be learned. This will indicate which steam valve to-
open first; it will then be an easy matter to determine in which
direction the starting bar should be moved. If the engine is
of the condensing type, the same course of procedure in starting
the air and circulating pumps should be followed as with the
simple condensing slide-valve engine.

Stopping Simple Corliss Engine. — A Corliss engine is stopped
by closing the throttle ahd unhooking the eccentric rod from
the pin on the wristplate; this is done by means of the unhook-
ing gear provided for the purpose. As soon as the eccentric
rod is unhooked from the pin, the starting bar is shipped into
its socket in the wristplate and the engine is worked by hand
to any point in the revolution of the crank at which it is desired
to stop the engine. The procedure is then the same as for the
simple slide-valve engine. After stopping a Corliss condensing
engine, the same course should be followed as with a slide-
valve condensing engine in regard to draining cylinders, closing
stop-valves, etc.

Starting Compound Slide-Valve Engine. — Before starting
a compound engine, the high-pressure cylinder is warmed up

208 STEAM ENGINES

in the same manner as a simple engine. To get the steam
into the low-pressure cylinder is, however, an operation that
will depend on circumstances. If the cylinders are provided
with pass-over valves, it will be necessary only to open them
to admit steam into the receiver and from thence into the
low-pressure cylinder. If the cylinders are not fitted with
pass-over valves, the steam can usually be worked into the
receiver and low-pressure cylinder by operating the high-
pressure valves by hand. Sometimes compound engines are
fitted with starting valves, which greatly facilitate the oper-
ations of warming up and starting. Usually a compound
engine will start upon opening the throttle.

If the high-pressure crank of a cross-compound engine is
on its center and the low-pressure engine will not pull it off,
it must be jacked off. If the pressure of steam in the receiver
is too high, causing too much back pressure in the high-pressure
cylinder, the excess of pressure must be blown off through the
receiver safety valve; if the pressure in the receiver is too
low to start the low-pressure piston, more steam must be
admitted into the receiver. If the engine is stuck fast from
gummy oil or rusty cylinders, all wearing surfaces must be
well oiled and the engine jacked over at least one entire revolu-
tion. If the cut-offs are run up, they should be run down,
full open. If there is water in the cylinders, it should be blown
out through the cylinder relief or drain valves, and if there
is any obstruction to the engine turning, it should be removed.

If the crank of a tandem compound engine is on the center,
it must be pulled or jacked off. If the high-pressure crank
of a cross-compound engine is on the center, it may or may
not be possible to start the engine by the aid of the low-pressure
cylinder, depending on the valve gear and the crank arrange-
ment. When the cranks are 180° apart, which is a very rare
arrangement, the crank must be pulled or jacked off the center.
When the cranks are 90° apart and a pass-over valve is fitted,
live steam may be admitted into the receiver and thence into
the low-pressure cylinder, in order to start the engine. When
no pass-over is fitted, but the engine has a link motion, suffi-
cient steam to pull the high-pressure crank off the center can
generally be worked into the low-pressure cylinder by working

STEAM ENGINES 209

the links back and forth. When no pass-over is fitted, but the
high-pressure engine can have its valve or valves worked by
hand, steam can be got into the low-pressure engine by work-
ing the high-pressure valve or valves back and forth by hand.
If no way exists of getting steam into the low-pressure cylinder
while the high-pressure crank is on a dead center, it must be
pulled or jacked off.

If the air and circulating pumps are attached to and operated
by the main engine, a vacuum cannot be generated in the
condenser until after the main engine has been started. Con-
sequently, in this case, there is no vacuum to help start the
engine; therefore, if it is tardy or refuses to start, it will be
necessary to resort to the jacking gear and jack the engine
into a position from which it will start. A vacuum having
been generated in the condenser beforehand, the pressure in
the receiver acting on the low-pressure piston causes the engine
to start promptly, even though the high-pressure crank may
be on its center.

Stopping Compound Slide-Valve Engine. — Compound slide-
valve engines, whether condensing or non-condensing, are
stopped by closing the throttle, and, if a reversing engine, throw-
ing the valve gear into mid-position. If the stop is a permanent
one, the usual practice of draining the engine, steam chests, and
receiver, closing stop- valves, stopping the oil feed, etc. should be
followed. If the engine is intended to run in both directions in
answer to signals, as in the cases of hoisting, rolling-mill, and
marine engines, the operator, after stopping the engine to signal,
should immediately open the throttle very slightly, in order to
keep the engine warm, and stand by for the next signal. If
the engine is fitted with an independent or adjustable cut-off
gear, it should be thrown off, that is, set for the greatest
cut-off, for the reason that the engine may have stopped in a
position in which the cut-off valves in their early cut-off posi-
tions would permit little or no steam to enter the cylinders,
in which case the engine will not start promptly, and perhaps
nut at all. While waiting for the signal, the cylinder drain
valves should be opened and any water that may be in the
cylinders should be blown out. When dry steam blows through
the drains, the cylinders are clear of water.

210 STEAM EXGIXES

When the signal to start the engine is received, it is only
necessary to throw the valve gear into the go-ahead or backing
position, as the signal requires, and to operate the throttle
according to the necessities of the case, for which no rule can
be laid down beforehand, as the position of the throttle will
depend on the load on the engine at the time.

Starting and Stopping Compound Corliss Engine. — The
operation of starting and stopping a compound Corliss engine
is precisely similar to that of starting and stopping a simple
Corliss engine. The high-pressure valve gear only is worked
by hand in starting, the low-pressure eccentric hook having
been hooked on previously. The low-pressure valve gear is
worked by hand only while warming up the low-pressure cylin-
der. The directions given for operating the simple condensing
engine apply to the condensing Corliss engine, so far as the
treatment of the air pump, circulating pump, and condenser
is concerned.

POUNDING OF ENGINES

Loose Brasses. — Loose journal brasses are the most frequent
cajse of pounding in engines. The remedy for pounding of
this nature is obvious. The engine should be stopped and
the brasses set up gradually until the pounding ceases. In the
case of shaft journals, they may be set up without stopping
the engine, provided the engineer can reach them without
danger of being caught in the machinery.

Brass-Bound Bearings. — It may so happen that the boxes
or brasses are worn down until the edges of the upper half
and those of the lower half are in contact and cannot be set
up on the journal any farther; they are then said to be brass
and brass, or brass-bound. In a case of this kind, the journal
must be stripped, as it is called, when the cap and brasses
are removed from a journal. The edges of the brasses are
then chipped or filed off, in order to allow them to be closed in.

Liners. — It is a most excellent plan in practice to reduce
the halves of the brasses so that they will stand off from each
other when in place for a distance of J to A in. and to till this
space with hard sheet-brass liners from 20 to 22 Birmingham
wire gauge in thickness, or even thinner. Should the journal
become brass-bound, the cap may be slacked off and a pair

STEAM ENGINES 211

of the liners slipped out without the necessity of stripping the
journal.

In some instances journal-boxes are fitted with keepers, or
chipping pieces, as they are sometimes called. These usually
consist of cast-brass liners from i to | in. in thickness,
having ribs or ridges cast on one side, for convenience of
chipping and filing. These keepers are sometimes made of
hardwood and are capable of being compressed slightly by the
pressure exerted upon them during the setting-up process.
When the boxes are babbitted, the body of the box is occasion-
ally made of cast iron, in which case iron liners and keepers
are used instead of brass ones.

Loose Thrust Block. — In engines fitted with some types of
friction couplings, there is a thrust exerted upon the shaft
in the direction of its length. This will necessitate having a
thrust bearing, or thrust block, as it is sometimes called. There
are a number of types of thrust bearings, but the most common
is the collar thrust, which consists of a series of collars on the
shaft that fit in corresponding depressions in the bearing.
If these collars do not fit in the depressions rather snugly,
the shaft will have end play and there probably will be more
or less pounding or backlash at every change of load on the
engine. This can be remedied only by putting in a new
thrust bearing and making a better fit with the shaft collars,
unless the rings in the bearing are adjustable, in which case
the end play may be taken up by adjusting the rings.

Water in Cylinders. — Pounding often occurs in the cylinders
and is frequently caused by water due to condensation or
carried over from the boilers. This may be a warning that
priming is likely to occur in the boilers or has already com-
menced. If the cylinders are not fitted with automatic relief
valves, the drain cocks should be opened as quickly as possible
and the throttle closed a little to check the priming.

Loose Piston. — Another source of pounding in the cylinder
is a piston loose on the rod; this will result if the piston-rod
nut or key backs off or the riveting becomes loose, permitting
the piston to play back and forth on the piston rod. If due
to backing off of the nut, the engine should be shut down
instantly. There is generally very little room to spare between

212 STEAM ENGINES

the piston-rod nut and the cylinder head; therefore, it cannot
back off very far before it will strike and break the cylinder
head. After the engine is stopped and the main stop-valve
is closed, the cylinder head should be taken off and the piston
nut set up as tightly as possible. As a measure of safety,
a taper split pin should in all cases be fitted through the piston
rod behind the nut or a setscrew should be fitted through the
nut.

Slack Follower Plate. — A slack follower plate or junk ring
will cause pounding in the cylinder. It seldom happens, how-
ever, that all the follower bolts back out at one time, but
it is not an infrequent occurrence that one of the follower
bolts works itself out altogether. This is a very dangerous
condition of affairs, especially in a horizontal engine. If the
bolts should get end on between the piston and cylinder
head, either the piston or the cylinder head is bound to be
broken. Therefore, if there is any intimation that a follower
bolt is adrift in the cylinder, the correct procedure is to shut
down the engine instantly, take off the cylinder head, remove
the old bolt, and put in one having a tighter fit.

Broken Piston Packing. — Broken packing rings and broken
piston springs will cause noise in the cylinder, but it is more of
a rattling than a pounding, and the sound will easily be recog-
nized by the practiced ear. There is not so much danger of
a breakdown from these causes as may be supposed, from
the fact that the broken pieces are confined within the space
between the follower plate and the piston flange.

Piston Striking Heads. — Pounding in the cylinders of old
engines is often produced by the striking of the piston against
one or the other cylinder head. One of the causes of this
is the wearing away of the connecting-rod brasses. Keying
up the brasses from time to time has the effect of lengthening
or shortening the connecting-rod, depending on the design,
and this change in length destroys the clearance at one end
of the cylinder by an equal amount. The remedy is to restore
the rod to its original length by placing sheet-metal liners
behind the brasses; this obviously will move the piston back
or ahead and restore the clearance. A rather rare case of the
piston striking the cylinder head is due to unscrewing of the

STEAM ENGINES 213

piston rod from the crosshead, in case it is fastened by a thread
and check-nut. To obviate any danger, the check-nut should
be tried frequently.

Improper Steam Distribution. — The primary cause of another
source of pounding is the improper setting of the steam valve,
or possibly its improper design. In the case of improper
setting of the valve, insufficient compression, insufficient lead,
cut-off too early, and late release may all cause pounding on
the centers.

Reversal of Pressure. — The effect of a reversal of pressure
is clearly shown in the accompanying illustration. With the
crankpin at a and the engine running in --^^ir-^

the direction indicated by the arrow,
the connecting-rod is subjected to a
pull, but after the crankpin has passed
the dead center c, the connecting-rod is
subjected to a push, in which case the
rear brass, as shown at b, bears against

the crankpin, while in the former case, ^" *'

as shown at a, the front brass bears against the crankpin.
By giving a sufficient amount of compression, the lost motion
in the pins and journals is transferred gently from one side
to the other before the crankpin reaches the dead center. If
the compression is insufficient, there will be pounding.

Insufficient Lead. — Insufficient lead causes an engine to
pound because the piston has then little or no cushion to
impinge on as it approaches the end of its stroke, and it is
brought to rest with a jerk. A similar effect will be produced
by a late release; the pressure is retained too long on the
driving side of the piston. The ideal condition is that the
pressures shall be equal on both sides of the piston at a point
in its travel just in advance of the opening of the steam port.
The position of this point varies Vvith the speed of the piston
and other conditions that only the indicator card can reveal.

Pounding at Crosshead. — The crosshead is a source of
pounding from various causes, of which the loosening of the
piston rod is one of the most common. There are several
methods of attaching the piston rod to the crosshead. The
rod may pass through the crosshead with a shoulder or a

L>1 5 STEAM EXC.IXES

taper, or both, on one side of the crosshead and a nut on the
other; or the rod may be secured to the crosshead by a cotter,
instead of the nut; or the end of the rod may be threaded and
screwed into the crosshead, having a check-nut to hold the rod
in place. In the case first mentioned, the nut may work
loose, which would cause the crosshead to receive a violent
blow, first, by the nut on one side and then by the shoulder
or taper on the other at each change of motion of the piston.
The remedy is to set up the nut. A similar effect will be
produced if the cotter should work loose and back out. In
case the piston rod is screwed into the crosihead and the rod
slacks back, the danger is that the piston will strike the rear
cylinder head. The check-nut should be closely watched.
Pounding at the crosshead may be due to loose wristpin brasses,
in which case they should be set up, but not too tightly. In
case a crosshead works between parallel guides, pounding may
be caused if the crosshead is too loose between the guides,
and the crosshead shoes should therefore be set out.

If pounding results from the wearing down of the shoe of
a slipper crosshead, a liner should be put between the shoe and
the foot of the crosshead or the shoe should be set out by the
adjustment provided.

Pounding in Air Pump. — Pounding in the air pump is gener-
ally produced by the slamming of the valves, caused by an
undue amount of water in the pump, which will usually relieve
itself after a few strokes. The pump piston, however, may
be loose on the piston rod or the piston rod may be loose in
the crosshead. A broken valve may also cause pounding in
the air pump, all of which must be repaired as soon as detected.

Pounding in Circulating Pump. — In a circulating pump of
the reciprocating type, pounding may be caused by admitting
too little injection water, and the pounding n:ay be stopped
by adjusting the injection valve to admit just the right quantity.
It may so happen, however, that the injection water is very
cold, and to admit enough of it to stop the pounding in the
circulating pump will make the feedwater too cold. To
meet this contingency, an air check-valve is often fitted to the
circulating pump to admit air into the barrel of the pump as
a cushion for the piston; this check- valve may be kept closed

STEAM ENGINES 215

when not needed to admit air. A broken valve, a piston loose
on its piston rod, and a piston rod loose in the crosshead will
all cause pounding in the circulating pump; they should be
treated in the same manner as was specified for similar troubles
in the air pump.

HOT BEARINGS

Mixtures for Reducing Friction. — Should any of the bearings
show an inclination to hsat to an uncomfortable point when
felt by the hand, the oil feed should be increased. If the
bearing continues to get hotter, some flake graphite should be
mixed with the oil and the mixture should be fed into the
bearing through the oil holes, between the brasses, or wherever
else it can be forced in. A little aqua ammonia introduced
into a hot bearing will sometimes check heating by converting
the oil into soap by saponification, soap being an excellent
lubricant. Mineral oils will not saponify.

Danger of Increasing Heating. — If, after trying the remedies
just mentioned, the bearing continues to grow hotter, to the
extent, for instance, of scorching the hand or burning the oil,
it indicates that the brasses have been expanded by the heat
and that they are gripping the journal harder and harder
the hotter they get. At this stage, if the engine is not stopped
or if the heating is not checked, the condition of the bearing
will continue to grow worse as long as the engine is running,
and may become so bad as to slow down and eventually stop
the engine by excessive friction. By this time the brasses
and journal will be badly cut and in bad condition generally,
and the engine must be laid up for repairs.

Remedies for Increasing Heat. — The state of affairs just
mentioned should not be permitted to be reached. After
the simple remedies previously given have been tried and
failed to produce the desired results, the engine should be
stopped and the cap or key of the hot bearing should be slacked
back and the engine allowed to stand until the bearing has
cooled off. If necessity requires it, the cooling may be hastened
by pouring cold water oil the bearing, though this is objection-
able, as it may cause the brasses to warp or crack. Putting
water on a very hot bearing should be resorted to only in an
emergency, that is, when an engine must be kept running.

216 STEAM ENGINES

Water may be, used on a moderately hot bearing without doing
very much harm. It is quite common in practice, when
sprinklers are fitted to an engine, to run a light spray of water
on the crankpins when they show a tendency to heat, with very
beneficial results.

Dangerous Heating. — Should a bearing become so hot as
to scorch the hand or to burn oil before it is discovered or
because of the necessity of keeping the engine running from
some cause, it is imperative that the engine should be stopped,
at least long enough to loosen up the brasses, even though it
is necessary to start up again immediately; otherwise the
brasses will be damaged beyond repair and deep grooves
will be cut into the journals. If the brasses are babbitted,
the white metal will melt out of the bearing at this stage.
The engine will then be disabled, and if there is not a spare
set of brasses on hand, it will be inoperative until the old
brasses are rebabbitted or until a new set is made and
fitted.

Running Engine With Hot Bearing. — If it is absolutely
necessary in an emergency to keep the engine running while
a bearing is very hot, the engineer must exercise his best
judgment as to how he shall proceed. After slacking off the
brasses, about the best he can do is deluge the inside of the
bearing with a mixture of oil and graphite, sulphur, soap-
stone, etc., and the outside with cold water from buckets,
sprinklers, or hose, taking the chances of ruining the brasses
and cutting the journal.

Refitting Cut Bearing. — The wearing surfaces of the brasses
and journal must be smoothed off as well as circumstances
will permit; but if the grooves are very deeply cut, it will
be useless to attempt to work them out entirely, and if the
brasses are very much warped or badly cracked, it will be best
to put in spare ones, if any are on hand. If not, the old ones
must be refitted and used until a new set can be procured.
As for the journal, it is permanently damaged. Temporary
repairs can be made by smoothing down the journal and
brasses; but at the first opportunity the journal should be
turned in a lathe and the brasses properly refitted or replaced
with new ones.

STEAM ENGINES 217

Newly Fitted Bearings. — The bearings of new engines are
particularly liable to heat, as the wearing surfaces of the
brasses and journal have just been machined and hence are
comparatively rough. The conditions just mentioned also
exist with new brasses and the journals of an old engine. If
a new engine or one with new brasses is run moderately, in
regard to both speed and load, and with rather loose brasses,
there will be little danger of hot bearings, provided proper
attention is given to adjustment and lubrication. This is
what is familiarly termed wearing dawn the bearings.

Brasses Too Tight. — When the brasses of an engine bearing
are set up too tight, heating is inevitable. It is often the
case that an attempt is made to stop a pound in an engine by
setting up the brasses when the thump should be stopped in
some other way. The brasses should be slacked off as soon
as possible. As a matter of fact, hot bearings should never
occur from this cause.

Brasses Too Loose. — Bearings may heat because the brasses
are too loose. The heating is caused by the hammering of the
journal against the brasses when the crankpin is passing the
dead centers. The derangement is easily remedied, however,
by setting up the cap nuts or the key. Most engineers have
their own views regarding the setting up of bearings. One
method is to set up the cap nuts or key nearly solid and then
slack them back half way; if the brasses are still too loose, they
are set up again and slacked back less than before, repeating
this operation until there is neither thumping nor heating.

Another method of setting up journal brasses is to fill up
the spaces between the brasses with thin metal liners, from
18 to 22 Birmingham wire gauge in thickness, and a few paper
liners for fine adjustment. Enough of these should be put
in to cause the brasses to set rather loosely on the journal
when the cap nuts or keys are set up solid. The engine should
be run for a while in that condition; then a pair of the liners
should be removed and the brasses set up solid again. This
operation should be repeated until there is neither thumping
nor heating. It may require a week or more, and with a large
engine longer, to reach the desired point. If this system is
carefully carried out, there will be very little danger of heating.

218 STEAM ENGINES

In removing the liners, great care should be exercised not
disturb the brasses any more than is absolutely necessary.

Warped and Cracked Brasses. — Warped and cracked brasses
will cause heating, because they do not bear evenly on the
journal, and hence the friction is not distributed evenly over
the entire surface. If the distortion is not too great, the
brasses may be refitted to the journal by chipping, filing, and
scraping; but if they are twisted so much that they cannot,
within reasonable limits, be refitted, nothing will do but new
brasses.

Cut Brasses and Journals. — Brasses and journals that have
been hot enough to be cut and grooved are liable to heat up
again any time on account of the roughness of the wearing
surfaces. As long as the grooves in the journal are parallel
and match the grooves in the brasses, the friction is not greatly
increased; but if a smooth journal is placed between brasses
that ara grooved and pressure is applied, the journal crushes
the grooves in the brasses and becomes brazed or coated with
brass, and then heating results. The way to prevent heating
from this cause is to work the grooves out of the journal and
brasses by filing and scraping as soon as possible after they
occur.

Imperfectly Fitted Brasses. — Faulty workmanship is a com-
mon cause of the heating of crankpins, wristpins, and bear-
ings. The brasses in that case do not bear fairly and squarely,
even though they appear all right to the eye. A crankpin
brass must fit squarely on the end of the connecting-rod and
the rod itself must be square. If the key, when driven, forces
the brasses to one side or the other and twists the strap on the
rod, it will draw the brasses slantwise on the pin and make
them bear harder on one side than on the other, thus reducing
the area of the bearing surfaces. The same is true of the shaft
bearings. If the brasses do not bed fairly on the bottom of
the pillow-block casting or do not go down evenly, without
springing in any way, heating will result.

Edges of Brasses Pinching Journal. — Brasses, when first
heated by abnormal friction, tend to expand along the surface
in contact with the journal; this would open the brass and
make the bore of larger diameter were it not prevented by the

-

STEAM ENGINES 219

cooler part near the outside and by the bedplate itself. If
the brass has become hot quickly and excessively, the resist-
ance to expansion produces a permanent set on the layers of
metal near the journal, so that on cooling, the brass closes and
grips the journal. This is why some bearings always run a
trifle warm and will not work cool. A continuance of heating
and cooling will set up a bending action at the middle of the
brass, which must eventually end in cracking it. Heating
produced in this way may be prevented by chipping off the
brasses at their edges parallel to the
journal, as shown at a in the accom-
panying illustration, in which b is -a
section of the journal and c and d
represent the top and bottom brasses,
respectively.

Stopped Oil Feed. — It does not take
long for a bearing to get very hot if it
is deprived of oil. The two principal
causes of dry bearings are an oil cup
that has stopped feeding, either by reason of being empty or
by being clogged up from dirt in the oil, and oil holes and
oil grooves stopped up with dirt and gum.

Insufficient Oil. — The effect produced upon a bearing by
an insufficient oil supply is similar to that of no oil, but in a
less degree. Of course, it will take longer for a bearing to heat
with insufficient oil than with none at all, and the engineer
has more time in which to discover and remedy the difficulty.

Dirty and Gritty Oils. — Oils that contain dirt and grit are
prolific sources of hot bearings. There is a great deal of dirt
in lubricating oils of the average quality; therefore, all oil
should be strained through a cloth or filtered, no matter how
clear it looks. All oil cups, oil cans, and oil tubes and channels
should be cleaned out frequently. Oil may be removed from
the cups by means of an oil syringe, and all oil removed from
the cups and cans should be strained or filtered before being
used.

Oils of Poor Quality. — There are on the market many
lubricating oils whose quality cannot be definitely decided
on without an actual trial, and it is a difficult matter to avoid

220 STEAM ENGINES

getting a bad lot of oil sometimes. About the only safe way
to meet this trouble is to pay a fair price to a reputable dealer
for oil that is known to be of good quality, unless the purchaser
is expert in judging oils.

Oil Squeezed Out of Bearings. — Bearings carrying very
heavy shafts sometimes refuse to take the oil; or, if they do,
it is squeezed out at the ends of the brasses or through the oil
holes, and then the journal will run dry and heat. Large
journals require oil of a high degree of viscosity, or heavy oil,
as it is popularly called. Oil of this character has more diffi-
culty in working its way under a heavy shaft than a thin oil
has, but thin oil has not the body necessary to lubricate a
large journal.

This difficulty may be met by chipping oil grooves or channels
in the brasses. A round-nosed cape chisel, slightly curved, is
generally used for this purpose; care should be taken to smooth
off the burrs made by the chisel, which may be done with a
steel scraper or the point of a flat file. The grooves are usually
cut into the brass in the form of a V if the engine is required
to run in only one direction; if it is to run in both directions
the grooves should form an X. In the first instance, care
must be taken that the V opens in the direction of rotation
of the shaft; that is, the grooves should spread out from their
junction in the same direction as that in which the journal
turns. The oil grooves may be about J in. wide and J in. deep,
and semicircular in cross-section.

Grit in Bearings. — Grit is an ever-present source of heating
of bearings, and only by persistent effort can the engineer
keep machinery running cool in a dirty atmosphere. The
machinery of coal breakers, stone crushers, and kindred indus-
tries is especially liable to be affected in this way. Work done
on a floor over an engine shakes dirt down upon it at some
time or other; hence, all floors over engines should be made
dust-proof by laying paper between the planks. If the engine
room and firerooms communicate, and piles of red-hot clinkers
and ashes are deluged with buckets of water, the water is
instantly converted into a large volume of steam, carrying
with it small particles of ashes and grit that penetrate into
every nook and cranny, and these will find their way intc the

STEAM ENGINES 221

bearings sooner or later. Hot clinkers and ashes should be
sprinkled, and the fireroom door should be closed while the
ashes and clinkers are being hauled or wet down or while the
fires are being cleaned or hauled. As an additional precaution,
all open oil holes should be plugged with wooden plugs or
bits of clean cotton waste as soon as possible after the engine
is stopped, and should be kept closed until ready to oil the
engine again preparatory to starting up. Plaited hemp or
cotton gaskets should also be laid over the crevices between
the ends of the brasses and the collars of the journals of every
bearing on the engine and kept there while the engine is stand-
ing still.

Overloading of Engine. — The effect produced by overloading
an engine is this: the pressure on the brasses is increased to-
a point beyond that for which they were designed, the friction
exceeds the practical limit, and the bearing heats. In case
an engine is run at or near its limit of endurance, or if the
journals are too small, it would be a wise and economical
precaution to have a complete set of spare brasses on hand
ready to slip in when the necessity arises.

Engine Out of Line. — If an engine is not in line, the brasses
do not bear fairly upon the journals. This will reduce the
area of the bearing surfaces in contact to such an extent as to
cause heating. If the engine is not very much out of line,
matters may be considerably improved by refitting the brasses
by filing and scraping down the parts of those which bear
most heavily on the journal. If this does not answer, the heat-
ing will continue until the engine is lined up.

The crosshead guides of an engine out of line are apt to heat,
and they will continue to give trouble until the defect is rem-
edied. The guides may also heat from other causes; for instance,
the gibs may be set up too much. The danger of hot guides
may be very much lessened by chipping zigzag oil grooves
in their wearing surfaces and by attaching to the crosshead
oil wipers made of cotton lamp wicking arranged so as to dip
into oil reservoirs at each end of the guides if they are hori-
zontal, and at the lower end if they are vertical. These
wipers will spread a film of oil over the guides at every stroke
of the crosshead.
16

222 STEAM EXGINES

Effect of External Heat on Bearings. — Bearings may get hot
by the application of external heat. This may be the case
if the engine is placed too near furnaces or an uncovered
boiler, or in an atmosphere heated by uncovered steam pipes
or other means. The excessive heat of the atmosphere
will then expand the brasses until they nip the journals,
which will generate additional heat and cause further expan-
sion of the brasses, and so on until a hot bearing is the
result. The remedy obviously depends upon the conditions
of each case.

Brasses Too Long. — If the brasses are too long and bear
against the collars of the journal when cold, they will mosjt
surely heat after the engine has been running a while. It is
hardly possible to run bearings stone cold. They will warm
up a little and the brasses will be expanded thereby, which
will cause them to bear still harder against the collars. This,
in turn, will induce greater friction and more expansion of the
brasses. The evil may be obviated by chipping or filing a little
off each end of the brasses until they cease to bear against the
collars while running. A little side play is a good thing for
another reason, which is that it promotes a better distribution
of the oil and prevents the journal and brasses from wearing
into concentric parallel grooves.

Springing of Bedplate. — If the bedplate of an engine is not
rigid enough to resist the vibration of the moving parts, or if
it is sprung by uneven settling or the instability of the founda-
tion, the engine will be thrown out of line either intermittently
or permanently, and the bearings will heat. But it will do no
good to refit the brasses unless the engine bed is stiffened in
some way and leveled up.

Springing or Shifting of Pillow-Block. — The effect of the
springing or shifting of the pedestal or pillow-block is similar
to the springing of the engine bed; that is, the bearing will
be thrown out of line, with the consequent danger of heating.
As the pedestal is usually adjustable, it is an easy matter to
readjust it, after which the holding-down bolts should be
screwed down hard. If a pedestal is not stiff enough to resist
the strains upon it and it springs, measures should be taken to
stiffen it.

STEAM TURBINES

223

STEAM TURBINES

ECONOMICAL CONSIDERATIONS

Steam Consumption.— The relation between the brake
horsepower of the steam turbine at full load and the steam
consumption is shown in the accompanying table. The values
in this table are taken from published tests of steam turbines

STEAM CONSUMPTION PER HOUR OF TURBINES

Brake
Horsepower

Pounds of
Steam Used

Brake
Horsepower

Pounds of
Steam Used

100
200
300
400
500

18.2
17.5
16.9
16.3
15.8

600
700
800
900
1,000

15.3
14.8
14.3
13.7
13.2

that have attained the greatest commercial success. The
turbines used saturated steam of from 115 to 140 Ib. per
sq. in., gauge pressure, and exhausted into a vacuum of from
26 to 28.5 in. of mercury. Better results than those noted
in the table can be obtained by the use of highly superheated
steam.

Effect of Vacuum. — The better the vacuum, the greater is
the economy in the use of steam, both in the steam engine
and in the steam turbine. A high vacuum is of greater value
to the turbine, however, because the turbine can take advantage
of a greater range of expansion. The degree of vacuum to be
carried is a matter of dollars and cents; that is, it may cost
more to create and maintain a high vacuum than may be saved
in steam consximption. In a comparative test of a turbine
and a triple-expansion engine under like conditions, it was
found that, in the case of the reciprocating engine, little or
nothing was to be gained by carrying a greater vacuum than

224 STEAM TURBINES

56 Of

.about 26 in.; but the economy of the turbine in the use
steam increased rapidly as the vacuum was increased above
26 in. The conclusion is that high degrees of vacuum are more
desirable for turbines than for engines.

Advantages of Turbines. — The steam turbine possesses the
following advantages over the reciprocating engine:

1. The ability to use highly superheated steam, resulting
in greater economy.

2. Reduced cost per unit capacity of the electric genera-
tor because of increased speed and smaller weight per horse-
power.

3. Reduced floor space, resulting in less cost for land and
power-station building.

4. Reduced cost of lubrication, as no cylinder oil is needed
and less oil is used for bearings.

5. Saving in labor, as no oilers are required and one engineer
can attend to more output than on reciprocating engines.

6. Reduced cost of foundations, as the turbine is balanced
-and has no reciprocating parts.

7. Good steam economy over a wider range of load than
the reciprocating engine. This is particularly advantageous
in power stations, where the load is variable; thus, a turbine
can be operated at one-fourth or one-half load with smaller
increase of steam consumption than would be the case with
a reciprocating engine under the same renditions. Also, the
turbine is more efficient than the engine under overloads.

The foregoing advantages apply mainly to turbines used on
land. The steam turbine, however, is also used for the pro-
pulsion of ships. Among the advantages claimed for it in this
class of service are the following:

1. For the same power, the turbine plant has less weight
than the engine installation.

2. There is less danger of breakdowns, because of the smaller
number of parts in a turbine installation.

3. The balancing obtained almost eliminates vibration.

4. With fast vessels, it is possible to obtain a higher
speed than with reciprocating engines, at the same steam
consumption.

5. Less headroom is required than with steam engines.

STEAM TURBINES 225

Comparison of Turbines and Engines. — If the matter of
steam consumption alone is considered, the average condensing
turbine of less than about 700 H. P. is not so economical as
the average compound or triple-expansion condensing engine,
although the turbine may be preferred to the engine for other
reasons. In larger sizes, however, and particularly in very
large units, the economy of the turbine is very noticeable.
The turbine possesses the ability to expand the steam to the
lowest available condenser pressure without difficulty; bat
to do this in a reciprocating engine would require very large
valves, and ports and heavy pistons, because of the great
volume of steam to be handled at very low pressures.

Finding Horsepower of Turbines. — There is no way of
finding the indicated horsepower of a steam turbine, because
no form of indicator applicable to the turbine has been invented.
Nor is any such instrument likely to be developed, owing to
the very great difficulty of determining the energy given up
to the blades of a turbine from a jet of steam. The usual
way of finding the power of a steam turbine is to use a brake
or a dynamometer and thus to determine the brake horse-
power, or else to connect an electric generator to the turbine
and measure the electrical output at the switchboard. In
case the latter method is used, the efficiency of the generator
and the turbine together is involved.

TURBINE TROUBLES

Clearance of Blades. — To obtain free running, it is necessary
to allow clearance between the stationary and the moving
rows of blades, as well as between the ends of the blades and
the casing or the rotor. In impulse turbines, such as the
Curtis and the Rateau, the clearance between the rows of blades
is important; however, if it is made no greater than is neces-
sary for mechanical reasons, the efficiency will not be affected
seriously. In the reaction turbine, such as the Parsons, the
clearance between the rows is of small consequence as com-
pared with the clearance between the ends of the stationary
blades and the rotor and between the ends of the moving

226 STEAM TURBINES

blades and the casing. The former may vary from J to 1 in.
or more from the high-pressure to the low-pressure stage;
but the tip clearance must be kept between a few hundredths
and a few thousandths of an inch.

Stripping of Blades. — The stripping of the blades is one of
the troubles to which turbines are subject. It may be due
to the interference of the stationary and the movable blades,
or to the rubbing of the blades against the shell or the rotor.
In either of these cases the existing clearances are reduced,
by wear of the parts, shifting of the rotor, or unequal expansion
of the rotor and the casing, until the blades touch and tear
one another loose. The same result will occur if some foreign
solid, as a stray nut or bolt, is carried along with the steam
into the turbine. If a turbine is started too quickly, without
being properly warmed up, the sudden unequal expansion set
up in the heavy casing and the lighter rotor may cause the
blades to come in contact and be stripped. Stripping is claimed
by some engineers to be more common in turbines in which the
blades are not supported at their outer ends. To prevent it,
therefore, shroud rings and metal lacings are applied to the
blades at their outer ends, by some manufacturers of steam
turbines.

Erosion of Blades. — As there are no valves, pistons, or piston
rings in the turbine to be maintained free from leakage, about
the only thing that can affect the steam consumption is the
condition of the blades. The blades of steam turbines are
subjected to the cutting action of steam flowing at high veloci-
ties, and often carrying water particles with it. This cutting,
or erosion, wears away the edges and surfaces of the blades.
From the data available, it appears that the erosion is very
slight if the steam is dry or superheated, no matter what
velocities are used; but if the steam is wet, erosion will take
place, and it will be greatly increased if the velocity of the
steam is high. The horsepower is not affected to any great
extent by blade erosion, according to the results of experience.
In the case of a 100-H. P. De Laval turbine, the steam inlet
edges of the blades were worn away about A in-, yet the
steam consumption was only about 5% above that with new
blades.

STEAM TURBINES 227

Slugs of Water. — If the boiler supplying steam to a recipro-
cating engine primes badly, a slug of water may be carried
over into the cylinder, resulting in a cracked piston or cylinder,
a buckled piston rod or connecting-rod, or a wrecked frame.
In case a steam turbine is used, however, the danger is greatly
lessened. In turbines in which the blades are not supported
at their outer ends, the \vater may cause stripping of the blades;
but this is not very likely, as the blades at the high-pressure
end of the turbine are short. A rush of water from the boiler
has been known to bring a turbine almost to a stop without
damaging the blades.

Vibration. — On account of the high speeds attained in tur-
bine practice, the rotors are balanced accurately, so as to reduce
vibration. But in spite of this careful balancing, vibration
may manifest itself during ordinary running. It may be caused
in any one of several ways, but the fundamental cause is lack
of balance. If the rotor is warmed up too rapidly, the shaft
or the wheels may be warped by unequal expansion, producing
an unbalanced effect. The stripping of a blade or two will
affect the balance of the wheel and tend to produce vibration.
Even water carried into the turbine with the steam will bring
about an unbalanced condition and will lead to vibration.
When vibration is observed, it is well to reduce the speed a
little, and to note whether this causes the vibration to cease.
If it does, but comes back again as soon as the speed is increased,
the source of the trouble should at once be determined.

OPERATION OF TURBINES

Inspection.— If the steam turbine is a new one, or if it has
been standing idle for a long period, it should not be started
until it, together with its auxiliary apparatus, has been thor-
oughly inspected. The bearings should be properly adjusted
and free from dirt, and the entire lubricating system should
be clean and filled with clean oil. The steam pipe from the
boilers should be blown through, so as to clear it of any foreign
matter that could be carried into the turbine by the steam.
The governor mechanism should be examined, to see that it

228 STEAM TURBINES

is in good order; the oil pump should be looked after, to
ascertain whether it is in condition to maintain a continuous
supply of oil; and, finally, before the turbine is started, the
shaft should be turned over by hand, to insure that the rotor
will turn freely in the casing.

Starting. — A steam turbine should be started slowly, and
before it is allowed to turn over under steam it should be
warmed up. This is accomplished by opening the throttle
valve just enough to let steam flow into the turbine. The
drains should be kept open until the turbine is well started.
The length of time required for warming up depends on the
size of the turbine, a large unit requiring more time than a
small one. As the warming up proceeds, the throttle may
gradually be opened more, and the auxiliary machinery may
be started. Once it has been started, the turbine should be
brought up to speed slowly. If it is speeded up too rapidly,
vibration will result. After the normal running speed has
been reached, the load may be thrown on; but this, also, should
be done gradually, to prevent a rush of water from the boiler
with the steam.

If superheated steam is used, extra caution must be employed
in starting, for during the warming up, with the throttle valve
only slightly opened, the passing steam will be cooled consider-
ably. But when the valve is opened wider, the greater volume
passing will not lose so much of its superheat, and if care is
not exercised the turbine will be subjected to sudden expan-
sion because of the higher temperature of the steam. The
main point in starting is to avoid any sudden changes of
temperature in the turbine. If a turbine must be ready to
be put in operation at short notice, steam may be allowed to
flow through it continually, by means of a by-pass around
the throttle valve. It will always be warmed up, then, and
can be brought up to speed with less danger and more rapidly.
Lubrication of Bearings. — The shaft or spindle of a turbine
rotates at high speed, and therefore the bearings should be
kept well lubricated; for if the oil supply fails, or if a bearing
begins to heat because of grit carried into it, the resulting
trouble will come very quickly. The presence of a hot bearing
will usually be evidenced by the smell of burning oil or by

STEAM TURBINES 229

the appearance of white smoke. When these signs are observed
the oil supply should immediately be increased to the greatest
possible amount. If this does not reduce the temperature of
the bearing or prevent its further heating, the turbine should
be shut down. To continue will result in burning out the
bearing, and it is better to stop before this happens. The high
speed of the shaft renders it impossible to nurse a hot turbine
bearing along as is done frequently in the funning of recipro-
cating engines.

Use of Superheated Steam. — As there are no internal rub-
bing surfaces in the steam turbine, superheated steam may be
employed without causing any of the lubrication troubles
attending its use in reciprocating engines. Because of the
greater amount of heat contained in a pound of superheated
steam, the economy of a turbine working with superheated
steam is greater than that of one working with saturated
steam; also, the efficiency is increased because the superheated
steam causes less frictional resistance to the motion of the
blades. To show the value of superheated steam in turbine
work, it may be stated that 50° F. of superheat reduces the
steam consumption about 6%; 100° F. of superheat reduces
it about 10%; and 150° F. of superheat reduces it about 13f%.
The use of high superheat, however, produces expansion of
the rotor and the casing and may cause the blades to interfere;
as a result, the usual degree of superheat in steam-turbine
practice is 100° F., and seldom exceeds 150° F.

Exhaust-Steam Turbine. — The steam turbine shows better
economy than the steam engine when working with low-pressure
steam in connection with a high vacuum; but when working
with high-pressure steam and a vacuum of about 26 in., the
engine is the more economical. As a consequence, a combi-
nation of the steam engine and the steam turbine has been
adopted. The engine uses the high-pressure steam from the
boilers and expands it to about atmospheric pressure. This
exhaust steam then passes into the turbine, which exhausts
into a condenser carrying a high degree of vacuum, and the
expansion is carried to the extreme practicable limit. The
turbine thus used in connection with an engine is termed an
exhaust-steam turbine.

230 STEAM TURBINES

Maintenance of Vacuum. — As the economy of the steam
turbine is dependent so largely on the degree of vacuum carried,
it is necessary for the engineer to watch the vacuum gauge
closely. With reciprocating engines, the loss of 1 or 2 in. of
vacuum may not be of much consequence; but in a turbine
plant, where the vacuum is from 27 to 28 in., a loss of 1 or
2 in. will result in a considerable increase in the steam con-
sumption. Because of the high vacuum employed, the diffi-
culty of keeping pipes, valves, and glands from leaking is
greater in turbine practice than in engine practice, but the
greater economy obtained by keeping everything tight over-
balances the increased care and labor.

Shutting Down. — In shutting down a steam turbine, the
throttle valve should be closed partly before the load is reduced,
so as to prevent any possibility of racing when the load is
finally taken off. The load may then be used as a brake to
bring the rotor to a stop. When the throttle valve has been
closed and the steam supply has been shut off completely,
the auxiliary machinery may be stopped. If the load is taken
off before the throttle is wholly closed, the turbine may con-
tinue to rotate for half an hour, as the rotor is then running
in a vacuum and under no load. The speed may be reduced
by opening the drains and allowing air to enter the casing.
The oil supply to the bearings must be continued until the
turbine has come to rest, and the oil pump should be the last
auxiliary to be stopped.

Care of Gears in De Laval Turbines. — The De Laval Steam
Turbine Company in their directions for operating their tur-
bines state that in order to keep the gears in good condition
the teeth should be cleaned occasionally when the turbine is
not in service. They recommend that a wire brush and
kerosene be employed for this purpose. At the same time the
gear-case should also be thoroughly cleaned, and after the
cleaning the gears should be well lubricated.

Should an engineer for any reason desire to take the gears
out of the case, it is recommended that he secure special
directions relating to their removal from the manufacturers.
The same statement also applies to the adjustment of the
gears, which need to be kept in perfect adjustment.

PROPULSION OF VESSELS 231

PROPULSION OF VESSELS

SLIP

True Slip. — In considering the speed of a stream projected
by a propelling instrument from a ship or other vessel in
motion, it must be borne in mind that while the stream is
propelled astern the vessel is advancing. Since the stream
must move astern faster than the vessel advances, the rear-
ward speed of the stream in relation to a fixed point of the
water some distance astern of the ship, as a floating piece of
wood, will be the difference between the speed of the vessel
in relation to the piece of wood and the rearward speed of
the stream in relation to the vessel. When the propeller
works in a wake, which has a forward motion, the speed with
which water is fed to the propelling instrument is reduced
thereby and it becomes equal to the difference between the
forward speed of the vessel in relation to a fixed point of the
water clear of the wake and the wake velocity. Thus, if the
speed of the ship is 15 mi. per hr. and a wake that has a forward
velocity of 3 mi. per hr. collects at the stern, the speed with
which the water is fed to a screw propeller is 15 — 3 = 12 mi.
per hr. The difference between the speed with which water
is fed to the propelling instrument and the speed with which
it is projected astern, both speeds being measured in relation
to the vessel, is called the true slip, and also the real slip, of
the stream.

Apparent Slip. — In practice, it is very inconvenient and
exceedingly difficult to measure either the wake velocity or
the speed of the ship in relation to the wake, but it is a very
simple matter to measure the speed of the vessel in relation
to a fixed point in the water clear of the wake by means of
an instrument called a log. The difference between the speed
of the stream projected by the propelling instrument and
the speed of the ship thus found is taken as the slip. When
calculated in this manner it obviously is not the same as the
true slip; it is called the apparent slip.

232 PROPULSION OF VESSELS

Formulas for Slip. — It is customary to express slip in per
cent, of the velocity of the stream projected by the propelling
instrument.

Let 5t = true slip in per cent., expressed decimally;

Sa = apparent slip in reference to the ship's motion
through the water, expressed decimally and
in per cent.;
V — velocity of stream projected by propelling instru-

ment, in relation to vessel;

Vi = velocity of water fed to propelling instrument;
that is, speed of vessel in relation to the sur-
rounding water diminished by the wake velocity
at the point where the propelling instrument
is located, for a vessel under way.
Vt = speed of vessel in relation to the water, as shown

by the log.
Then, the true slip is given by the formula

and the apparent slip by the formula
V-Vt

S^~T (2)

It is customary among writers on marine propulsion to
refer to apparent slip simply as slip; when the true slip is meant,
it is usually called distinctly the true slip.

SCREW PROPELLERS

Definitions. — If a point is caused to rotate at a uniform dis-
tance from and about an axis, and if the point at the same time
is caused to advance at a uniform rate in the direction of axis,
its path will be a helix. If the point, when moving away from
the observer, moves in the direction of the hands of a watch,
the helix will be right-handed; if in an opposite direction, left-
handed. The distance that the point advances in one complete
revolution is known as the pitch. If a line passing through
the axis is caused to rotate about the axis, and to pass along

PROPULSION OF VESSELS 233

the path of the point mentioned above, its path will be the
surface of a true screw, provided the angle that the line makes
with the axis remains constant. From this, it follows that
a true screw is one in which the advance of any point, in the
direction of the axis, at any distance from it, for any part
of a revolution, but the same in each case, is the same. By
causing lines making equal angles with each other and the
axis to rotate about the axis in a helical path, a multiple-
threaded true screw will be generated, having the same pitch
as a single-threaded true screw generated by a line following
the same helical path.

Consider a four-threaded, right-handed screw, generated
by the lines 0 A , OB, O C, and O D, in the accompanying
illustration. These lines represent the intersections of the
four helical surfaces with a
plane E F perpendicular to the
axis. Assume the helical sur-
faces to be cut by a plane, asGH,
parallel to the first and inter-
secting the axis at another point. i^^^-^it^^^ M /* \~°'
Then, O A A' O', O B B' O', D^ A ^~IB'\D W

OCC' O', and O D D' O' will be

the helical surf aces of the blades ^_^ .^. . .

<5f a four-bladed. right-handed C^' c CJHC

screw propeller. If pieces of
metal are shaped to conform to these helical surfaces and
if these pieces of metal, which are called blades, are fas-
tened to a hub, which in turn is keyed to a shaft rotated
by an engine, the screw propeller in its simplest form is
obtained. It the screw propeller is revolving in the direc-
tion of the arrow, the portion of the blade that strikes the
water first, which will be near the plane G H, is known
as the anterior portion of the blade; and the portion that
is near the plane E F, as the posterior portion. That part
of the blade that is near the periphery A A' is known as
the tip. In practice, screw propellers are hardly ever made
of the shape shown. Generally the anterior portion of the
blade is rounded off toward the tip, as shown by the dotted
line on the blade O A A' O'. The posterior portion is also

234 PROPULSION OF VESSELS

slightly rounded. Very often part of the anterior portion
near the hub is also cut away.

Radially Expanded Pitch. — Sometimes the surfaces of the
blades are not truly helical; as usually found, the pitch near
the tip is greater than the pitch near the hub. Such a propeller
is said to have a radially expanded pitch. The reason for
constructing the blade in this manner is this: Since the part of
the blade near the hub strikes the water at nearly a right angle,
it acts chiefly to churn the water, and since the water near the
periphery is thereby disturbed, the tip of the blade acts on
water in motion. By increasing the pitch at the tip, it is
supposed that the resistance at all parts of the blade is more
nearly equalized.

Axially Expanded Pitch. — The blades are sometimes con-
structed in such a manner that the anterior portion of the blade
has a finer pitch than the posterior portion. Such a blade is
said to have an expanding or axially expanded pitch. The
object to be attained by it is as follows: The anterior por-
tion of the blade, striking on water at rest and encountering
the resistance due to a solid body moving through water at
rest, sets the water in motion, driving it astern. Therefore,
the posterior portion acts on water in motion. By expand-
ing the pitch to the same extent, further motion is given to
the water by the posterior portion, and it is supposed that the
resistance at all parts of the blade is thereby equalized, the
same as with radially expanded pitch blades.

Surface Areas. — The actual area of the surface on the
driving side of a propeller blade is known by various names,
as the developed blade area, the helicoidal blade area, or simply
the blade area. When referring to the total blade area, it is
usually spoken of as the developed propeller area, the helicoidal
propeller area, or simply, the propeller area. The area of a
blade projected on a plane at right angles to the propeller shaft
is called its projected area; the projected area of all the blades
is the projected propeller area. The area of the circle described
by the tips of the blades is the disk area of the propeller. The
pitch ratio is the ratio of the pitch of the propeller to its diameter.

Measurement of Pitch.— In practice, the pitch of a pro-
peller may be found quite closely in the manner shown in the

PROPULSION OF VESSELS

235

illustration. Take a piece of joist or lath D, which should be
as straight as possible and place it so as to touch one of the
blades at any distance, as b, from the axis A B, taking care to
hold it parallel to the axis. Next take a carpenter's square,
shown at E, and place it on the lath and against the blade, so
that the point at which the square touches the blade will be
the same distance from the axis as is the lath. Measure the
distances a, b, and c; a is the distance from the square to the
point at which the lath touches the blade, and c the distance
from the point at which the square touches the blade to the
lath. The distances a and c may be obtained in a different

manner, if considered more convenient, thus: Place the screw
propeller so that one blade is horizontal. To a piece of string
about 10 ft., or more, in length tie two nuts; place the string
over the blade, with the nuts hanging down, at the distance
from the shaft axis at which it is desired to find the pitch,
taking care to place the string so that both parts hanging down
are the same distance from the axis. The distance the two
parts are apart is the distance a. To find c, hold a lath against
the blade and both vertical parts of the string; while holding
the lath parallel to the shaft axis the distance c can be measured.
The pitch of the propeller may then be calculated by the
6.2832 ba

formula

236 PROPULSION OF VESSELS

in which P- pitch of screw propeller;
a = depth of blade;
b = distance from center of shaft where width and

depth of blade is measured;
c = width of blade.

The distances a, b, and c should all be taken in inches, and
the measurements for pitch should always be taken on the side
of the blade that strikes the water when propelling the vessel
ahead.

EXAMPLE. — If a screw propeller blade 6 ft. from the center
of the shaft is 22 in. deep and 41 in. in width, at right angles
to the shaft, what is the pitch?
SOLUTION. — Applying the formula,

6.2832 X 12 X 6 X 22
P = — — = 242.75 in. = 20 ft. 2J in.

Determining the Kind of Pitch. — To determine whether a
screw propeller is a true screw, two or more measurements
of the pitch should be taken on different parts of the blade at
the same distance from the axis. Another set of measure-
ments should be taken at some other distance from the axis.
If the pitches calculated from these measurements agree closely,
the propeller is a true screw.

To determine whether the pitch of the screw is radially
expanded, calculate the pitch at two or more distances from
the axis; if the pitch increases toward the tip of the blade,
the screw propeller is of radially expanded" pitch.

To determine whether the screw has an expanding pitch,
the pitch must be calculated for the anterior and posterior
portions of the blade. The pitch for the posterior portion
should be the coarser; and, if calculated for any distance
from the axis, the pitches of the anterior portion, as well
as those of the posterior portion of the blade, should agree,
provided that the axial measurements arc taken in the same
planes passing through the axis.

Required Pitch of Propeller. — The pitch required for a
screw propeller may be found by the formula

PROPULSION OF VESSELS 237

in which P = pitch, in feet;

Fj = speed of ship, in feet per minute;

Sa = apparent slip, in per cent., expressed decimally;

N = revolutions per minute;

Required Diameter of Propeller. — For the diameter of a
screw propeller, Seaton gives the formula:

in which D = diameter of screw propeller, in feet;
H = indicated horsepower;
P = pitch of screw propeller, in feet;
N = revolutions per minute;

C = a constant ranging from 17,000 for slow freight
steamers to 25,000 for fast-running light
steamers, as torpedo boats and fast steam
launches.

EXAMPLE. — Find the diameter of a screw propeller for a
steam launch with an engine of 10 H. P., the screw having
a pitch of 4 ft. and making 200 R. P. M.
SOLUTION. — Applying the formula,

25,000X-^ = 3.5 ft.

When the rule gives a diameter that is impossible for the
conditions, either P or N, or both, must be varied. Making
either or both of these values larger will give a smaller diameter
of screw; conversely, making either or both of these values
smaller gives a larger diameter of screw. The rule is intended
for screw propellers: with four blades; if three blades are to
be used, the diameter should be increased about 10%; and if
two blades are to be used, about 20%. The pitch ratio varies
in practice between 1.1 and 1.6.

Blade Area. — The total blade area of four-bladed propellers
ranges from 35 to 45% of the disk area; in three-bladed pro-
pellers, it ranges between 27 and 33%, and in two-bladed
propellers, between 20 and 25%. The value to be chosen
should vary with the pitch ratio, using a low total blade area
for a low pitch ratio and increasing the value as the pitch ratio
is made greater.
17

PROPULSION OF VESSELS

SPEED OF VESSELS

Powering of Vessels. — The exact power required to propel
a vessel at a given speed cannot be found very readily by
the principles of mechanics. Instead, empirical rules based
on the actual performance of vessels are usually relied on.
The conditions that influence the relation between power
and speed are many, but only a few of the more important
ones will be enumerated here. For instance, the area of the
blades of the screw propeller may not be sufficient for high
speed, owing to a churning of the water when the propeller
is revolved beyond a certain speed; and, although the power
expended in revolving the propeller faster may be considerable,
the increase of the speed of the vessel may be very slight.
A similar state of affairs may occur if the area of the buckets
of a paddle wheel is too small. It may be amply sufficient for
a low rate of speed, and still be entirely too small for a higher
rate, thus showing, probably, a high efficiency of the propelling
instrument at a low speed, and a very poor one at a higher
rate. Again, the efficiency of the engine may vary greatly
for different powers developed by the same engine. There-
fore, no hard-and-fast rule that will express the relation
between power and speed under all conditions can be laid
down.

Admiralty Rule. — The PJ!C most frequently used in the pow-
ering of vessels is known as the A dmiralty rule. It involves the
selection of a proper constant based on actual experience, when
this constant, a number of which are given in the accompany-
ing table, is properly selected, the results of the rule will be
found to agree very closely with the actual performance of
vessels powered by the rule, at least under ordinary conditions
and for ordinary efficiencies of the propelling apparatus. The
formula is

in which H = indicated horsepower;

TV = displacement of vessel, in tons of 2,240 lb.;
k =a constant taken from the table;
5 = speed, in knots.

PROPULSION OF VESSELS

239

Determining Fineness of Vessel. — To determine whether
a vessel is fair or fine, its displacement, in cubic feet, is usually
compared with the volume of a rectangular box having a length
equal to the length of the vessel on the water-line, a width
equal to the beam, and a depth equal to the mean draft of the
vessel diminished by the depth of the keel. If the displacement
is .55 of the volume of the box, or less, the vessel is fine; if
above .55 and less than .70, fair. The quotient obtained by
dividing the displacement by the contents of the imaginary
box is called the coefficient of fineness.

VALUES OF * IN ADMIRALTY RULE

Description of Vessel

Speed
Knots

ft

Under 200 ft., fair. .
Under 200 ft fine

9 to 10
9 to 10
10 to 11
11 to 12
9 to 11
9 to 11
11 to 12
9 to 11
11 to 13
9 to 11
11 to 13
13 to 15
9 to 11
11 to 13
11 to 13
13 to 15
15 to 17
15 to 17

200
230
210
200
220
240
220
250
220
260
240
200
260
240
260
240
190
240

Under 200 ft., fine..

Under 200 ft., fine..
From 200 to 250 ft.,
From 200 to 250 ft.,

fair

fine

From 200 to 250 ft.,
From 250 to 300 ft.,
From 250 to 300 ft.,
From 250 to 300 ft.,
From 250 to 300 ft.,
From 250 to 300 ft.,
From 300 to 400 ft.,

fine

fair

fair

fine

fine
fine

fair

From 300 to 400 ft.,
From 300 to 400 ft.,
From 300 to 400 ft.,
From 300 to 400 ft.,
Above 400 ft., fine..

fair . ..

fine

fine

fine

Selecting Constant in Admiralty Rule. — The selection of
a proper value of k calls for the exercise of considerable judg-
ment, based on personal knowledge of the actual performance
of similar vessels. Generally speaking, the value of k is influ-
enced by the length, speed, and shape of the vessel. The
value of k should be greater with an increased length of the
vessel in proportion to the width, and also with a finer under-
water body; conversely, its value should be less as the ratio of
length to width becomes smaller, and as the form becomes

240 PROPULSION OF VESSELS

fuller. Furthermore, the value of k should be smaller for
relatively high speeds than for low speeds, for vessels of the
same form and displacement. Prof. W. F. Durand states that
-a speed may be considered as relatively high or low if the
speed exceeds the numerical value of the square root of the
length of the vessel in feet, or falls below it. Thus, if a vessel
is 64 ft. long, V64 = 8, a speed of 10 knots would be considered
as relatively high, while a speed of 5 knots would be considered
as relatively low. For small boats, if the speed is given in
statute miles per hour, the values of k range between 150 and
225, and for speeds given in knots, between 100 and 150,
according to Prof. W. F. Durand.

Relation of Horsepower and Revolutions. — The speed of a
ship fully under way is about directly proportional to the
number of revolutions made by the engine. But the power
required to turn the propelling instrument varies as the cube
of the number of revolutions, or, what is the same thing, as
the cube of the speed. Hence, it is possible to find, approx-
imately, the power developed by an engine for any given
number of revolutions per minute, any other horsepower and
the corresponding revolutions per minute being known by the
use of the formula

in which Hi = required indicated horsepower;

Ri = revolutions per minute at required power;

H = given indicated horsepower;

R = revolutions corresponding to the horsepower H.
In practice, the horsepower calculated by this formula will
not always correspond to that actually used, as found by the
indicator diagram. This is due to the fact that the efficiency
of the machinery is not necessarily the same at all speeds.
As a general rule, the engine will be at its maximum efficiency
at some certain speed, and will have a lower efficiency at a
higher or lower speed. The speed at which the engine is at
its best efficiency can be found only by actual trial.

Reduction of Horsepower When Towing. — It is a well-known
fact among marine engineers that an engine will develop a lower
horsepower with a given boiler pressure, throttle position,

PROPULSION OF VESSELS 241

and cut-off when towing or having the resistance of the vessel
increased by other means, than will be developed under the
same engine conditions but running free. The reason for this
is explained in the following discussion, in which for the sake
of simplicity two convenient assumptions have been made
that are not absolutely correct in practice. These assumptions
are that the horsepower of an engine varies directly as the
number of revolutions, the mean effective pressure remaining
the same, and that the speed of the vessel varies directly as"
the number of revolutions.

Consider a paddle-wheel steamer running free, with its
engine developing its greatest horsepower possible. Since
the turning effort of the engine depends on only the mean
effective pressure in the cylinders, it is independent of the
revolution so long as the throttle position, boiler pressure,
and cut-off remain the same. This turning effort, when
exerted at the circumference of the effective diameter circle
tangentially to the same parallel to the surface of the water,
is the total force tending to propel the vessel forwards, and
is resisted by an opposing force, which is the resistance of
the vessel. Let the engine be started and assume that it is
making its greatest turning effort. The resistance being less
than the forward force, the vessel moves forwards under the
influence of a forward accelerating force equal to the differ-
ence between the total forward force and the resistance. As
the vessel gathers headway, the resistance increases; this
means that the difference between the forward and the resist-
ing force, that is, the accelerating force, decreases until the
total forward force and total resistance have become equal,
when the vessel continues at a uniform speed. Let the resist-
ance be increased either by the vessel picking up a tow, by a
head-wind or head-sea, by encountering an adverse current,
or by a combination of these circumstances. The conditions
remaining the same as before at the engine, the turning effort,
that is, the total forward force, is the same; but, as the initial
resistance is increased, the initial difference between the total
forward force and the total resistance is smaller than in the /
first case. This means that a smaller accelerating force is
available with an increased resistance, and consequently the

242 PROPULSION OF VESSELS .

total forward force and total resistance become equal at a
lower speed of the vessel, which then continues under way
at a uniform, but lower speed. Now, the horsepower of an
erigine varies (theoretically) directly as the number of revolu-
tions, the mean effective pressure remaining constant. It has
been shown that the speed of the vessel has been lowered; from
this it follows that the revolutions and consequently the horse-
power must be less when the resistance has been increased.
By adding to the resistance of the vessel, a condition is finally
reached similar to that of a vessel moored to a dock; the
forward force and resistance are equal and the vessel, as no
accelerating force is available, remains stationary. In this
condition, the number of revolutions, and, hence, the horse-
power, has dropped to the lowest limit.

Relation of Coal Consumption to Speed. — The fuel con-
sumption may be said to vary directly as the horsepower
developed (this is not exactly true, but only approximately).
The horsepower varies about directly as the cube of the speed,
whence it follows that the fuel consumption will also vary as
the cube of the speed, approximately. Hence, to find the
probable coal consumption for a speed different from a known
speed, use the formula

«-£ »

in which c = coal consumption, in tons, at the new speed;
5 = new speed;
5 = known speed;

C = coal consumption, in tons, at the known speed.
To find approximately the speed of steaming for a new coal
consumption, use may be made of the formula

c

At sea, owing to an accident, it is often desired to know what
speed to maintain in order to reach a given port with the
amount of coal on hand. This problem is readily solved by
trial and by. application of formula 1. In practice, a good
margin of coal should be shown by the calculations as left
over, for the reason that the actual coal consumption at the

PROPULSION OF VESSELS 243

reduced speed will, as a general rule, be in excess of the cal-
culated consumption, by reason of the decrease in economy of
the engine induced by reducing the developed horsepower.

EXAMPLE. — A steamer consumes 20 T. of coal per day at
a normal speed of 10 knots; the distance to the nearest port
where coal can be had is 600 mi., and the estimated quantity
of coal in the bunkers is but 35 T. Find what speed should
be maintained in order to reach the coaling station with the
coal supply on hand.

SOLUTION. — The best way to proceed in a case of this kind
is to assume a lower speed, as 8 knots, and calculate the new coal

consumption for that speed; thus, c = 3 — = 10.24 T. per

da., or .43 T. per hr. The time required to cover a distance
of 600 mi. at a speed of 8 knots is 600-^8 = 75 hr., and at a
coal consumption of .43 T. per hr. the total quantity of coal
required at that speed is 75 X. 43 = 32.25 T. Hence, if a speed
of 8 knots is maintained, the supply of coal on hand, or 35 T.,
will suffice to reach the coaling station under ordinary weather
conditions.

Relation Between Engine Speed and Ship's Speed. — On
taking charge, the number of revolutions to produce a given
speed is often desired. In that case the pitch of the screw, or
the effective diameter of the paddle wheel (taking the effective
diameter for this purpose from center to center of buckets)
must be measured and a fair slip value assumed. Then, to
find the revolutions per minute, multiply the pitch of the
screw in feet, or the circumference in feet of the effective
diameter circle of a paddle wheel, by 60, and by the difference
between 1 and the assumed apparent slip expressed decimally.
Divide the speed of the ship in feet per hour by this product.

EXAMPLE. — The pitch of a screw propeller is 16 ft.; how
many revolutions per minute must it make to drive the ship
at the rate of 10 knots, the apparent slip being estimated
at 10%?

SOLUTION. — Applying the rule and taking the knot at
6,080ft. 10X6,080

244 ENGINEERS' LICENSE LAWS

ENGINEERS' LICENSE LAWS

STATES AND CITIES HAVING LICENSE
LAWS

Engineers' license laws, on January 1, 1913, are in force
in the following states and cities in the United States of America :

States. — Massachusetts, Minnesota, Montana, Ohio, Penn-
sylvania, and Tennessee.

Cities.— Alleghany, Pa.; Atlanta (Pulton County), Ga.;
Baltimore, Md.; Buffalo, N. Y.; Chicago, 111.; Denver, Colo.;
Detroit, Mich.; Elgin, 111.; Goshen, Ind.; Hoboken, N. J.;
Huntington, W. Va.; Jersey City, N. J.; Kansas City,
Mo.; Lincoln, Neb.; Los Angeles, Cal.; Memphis, Tenn.; Mil-
waukee, Wis.; Mobile, Ala.; New Haven, Conn.; New York,
N. Y.; Niagara Falls, N. Y.; Omaha, Neb.; Peoria, 111.; Phila-
delphia, Pa.; Pittsburg, Pa.; Rochester, N. Y.; Saginaw, Mich.;
Santa Barbara, Cal.; St. Joseph, Mo.; St. Louis, Mo. ; Scranton,
Pa.; Sioux City, la.; Spokane, Wash.; Tacoma, Wash.; Terre
Haute, Ind.; Washington (District of Columbia) ; and Yonkers,
N. Y.

LICENSE LAWS FOR STATIONARY
ENGINEERS

ABSTRACTS OF STATE LAWS

Following are abstracts of the license laws and ordinances
of the different states and most of the cities just named.
Abstracts of license ordinances of some cities are omitted
because copies of the ordinances of these places were not
available at the time of going to press.

Massachusetts. — In Massachusetts, the engineers' and fire-
men's license law is under the supervision of the District
Police, Boiler-Inspection Department, State House, Boston.

Section 78, chapter 102, of the revised laws, acts of 1907,
and amendments, which took effect January 1, 1912, reads:

ENGINEERS' LICENSE LAWS . 245

"No person shall have charge of or operate a steam boiler
or engine in this commonwealth, except boilers and engines
upon locomotives, motor road- vehicles, boilers in private resi-
dences, boilers in apartment houses of less than five flats,
boilers under the jurisdiction of the United States, boilers for
agricultural purposes exclusively, boilers of less than 9 H. P.,
and boilers used for heating purposes exclusively, which are
provided with a device approved by the chief of the district
police limiting the pressure carried to 15 Ib. per sq. in., unless.
he holds a license as hereinafter provided."

A steam boiler or engine may not be operated for more than
1 wk., unless the person in charge of and operating it is duly
licensed.

"Section 80. — The words have charge or in charge, used in the
foregoing section, shall designate the person under whose
supervision a boiler or engine is operated. The person oper-
ating shall be understood to mean any and all persons who
are actually engaged in generating steam in a power boiler."
This section of the Massachusetts laws has been amended so-
as to include a designation of the terms operator, operated, or
'operating, where used in the law, as applying to any person
who, under the supervision of the licensed person in charge,,
operates any appurtenances of a boiler or engine, provided
that there is not more than one such person employed for every
licensed person, and that any such operating must be in the
presence of and under the personal supervision of the latter
person.

Section 81 provides that whoever desires to act as engineer
or fireman shall apply for a license therefor to the state inspc-c-
tor of boilers for the city or town in which he resides. The
application blanks are to be obtained from the boiler-inspection
department of the district police.

To be eligible for a first-class fireman's license, a person
must have been employed as a steam engineer or fireman in
charge of or operating boilers for not less than 1 yr., or he
must have held and used a second-class fireman's license for
not less than 6 mo. To be eligible for examination for a
third-class engineer's license, a person must have been employed
as a steam engineer or fireman in charge of or operating boilers-

246 . ENGINEERS' LICENSE LAWS

for not less than 1J yr., or he must have held a first-class
fireman's license for not less than 1 yr. To be eligible for
examination for a second-class engineer's license, a person must
have been employed as a steam engineer in charge of a steam
plant or plants having at least one engine of over 50 H. P.,
for not less than 2 yr.; or he must have held and used a third-
class engineer's license for not less than 1 yr., or have held and
used a special license to operate a first-class plant for not less
than 2 yr.; except that any person who has served 3 yr. as
apprentice to the machinist in charge or boilermaking trade
in stationary, marine, or locomotive engine or boiler works,
and who has been employed for 1 yr. in connection with the
operation of a steam plant, or any person graduated as a
mechanical engineer from a duly recognized school of tech-
nology, who has been employed for 1 yr. in connection with
the operation of a steam plant, shall be eligible for examination
for a second-class engineers' license.

To be eligible for examination for a first-class engineer's
license, a person must have been employed for not less than
3 yr. as a steam engineer in charge of a steam plant or plants
having at least one engine of over 150 H. P., or he must have
held and used a second-class engineer's license, in a second-
class or first-class plant, for not less than 3J yr. The appli-
cant shall make oath to the statements contained in his
application.

Section 82 provides that licenses shall be granted according
to the competence of the applicant and shall be distributed
in the following classes:

Engineers' licenses: First class, to have charge of and
operate any steam plant; second class, to have charge of and
operate a boiler or boilers, and to have charge of and operate
engines, no one of which shall exceed 150 H. P., or to operate
a first-class plant under the engineer in direct charge of the
plant; third class, to have charge of and operate a boiler or
boilers not exceeding in the aggregate 150 H. P., and an engine
not exceeding 50 H. P., or to operate a second-class plant
under the engineer in direct charge of the plant; fourth class,
to have charge of and operate hoisting and portable engines
and boilers.

ENGINEERS' LICENSE LAWS 247

Under the beading of classification of licenses, two new classes
have recently been added, namely, a portable class and a
steam fire-engine class. The former applies to a person having
charge of or operating portable boilers and engines, except
hoisting engines and steam fire-engines, and the latter applies
to a person who has charge of or operates a steam fire-engine
or boiler.

Minnesota. — The engineers' license and boiler-inspection
laws of the state of Minnesota are administered by a board
of inspectors, one of whom shall reside in each senatorial dis-
trict. This board is appointed biennially by the governor of
the state. It also has jurisdiction over the vessels on the inland
waters of the state, in relation to masters and pilots, as well
as to engineers and the machinery of such vessels.

The laws state that engineers shall be divided into four
classes, namely, chief engineers, first-class engineers, second-
class engineers, and special engineers.

1. No license shall be granted to any person under 21 yr.
of age, except to special engineers. No license shall be granted
to any person to perform the duties of chief engineer who has
not taken and subscribed an oath that he has had actual
experience of at least 5 yr. in operating steam boilers and
steam machinery, or whose knowledge, experience, and habits
of life are not such as to justify the belief that he is compe-
tent to take charge of all classes of steam boilers and steam
machinery.

2. No license shall be granted to any person to act as
first-class engineer who has not had actual experience of at
least 3 yr. in operating steam boilers and steam machinery,
and whose experience and habits of life are not such as to
warrant the belief that he is competent to take charge of all
classes of steam boilers and steam machinery not exceeding
300 H. P.

3. No license shall be granted to any person to act as
second-class engineer who has not had at least 1 yr. of actual
experience in operating steam boilers and steam machinery,
or whose experience and habits of life are not such as to warrant
the belief that he is competent to take charge of all classes of
steam boilers and steam machinery not to exceed 100 H. P.

248 ENGINEERS' LICENSE LAWS

4. No license shall be granted to any person to act as special
engineer unless he is found on examination to be sufficiently
acquainted with the duties of an engineer to warrant the belief
that he can be safely entrusted with steam boilers and steam
machinery not to exceed 30 H. P.

The fee for the examination of an applicant for an engineer's
license shall be $1; for the biennial renewal of certificates of
license, the fee shall be $1, which fee shall accompany the appli-
cation. Applicants must subscribe oath as to their experience
period.

Montana. — In Montana, the license laws are administered
by an inspector of boilers, who is appointed by the governor
of the state. The inspector has an assistant, and they must,
as often as is convenient, publish in some suitable newspaper
a notice stating on what days they will be in certain specified
localities. This notice must also state that they will, at the
time and place specified in such notice, receive applications and
make examination for the purpose of granting engineers' cer-
tificates and examine boilers subject to inspection.

In Montana, engineers entrusted with the care and manage-
ment of steam machinery are divided into three classes, namely,
first-class engineers, second-class engineers, and third-class
engineers. A candidate for a first-class license must have had
.at least 3 yr. of actual experience in the operation of steam
boilers and steam machinery, or his knowledge and experience
must be such as to justify the belief that he is competent to
take charge of all classes of steam boilers and steam machinery.
A candidate for a second-class license must have had at least
2 yr. of experience in the operation of steam boilers and sceam
machinery, and must on examination be found competent to
take charge of all classes of steam boilers and steam machinery
not exceeding 100 H. P. A candidate for a third-class license
must have served at least 1 yr. as fireman under a competent
engineer, and must be, on examination, found competent to
be entrusted with the duties pertaining to the operation of
steam boilers and steam machinery not exceeding 20 H. P.

All firemen who have charge of steam boilers, as to the regu-
lation of feed water and fuel, where the boilers are so situated
as not at all times to be under the eye of the engineer in charge.

ENGINEERS' LICENSE LAWS 249

are required to pass a third-class engineer's examination and
procure the same kind of license. Engineers holding licenses
of any of the preceding classes, and who are entrusted with
the care and management of traction engines, or engines or
boilers on wheels, other than locomotives, are required to pass
an examination as to their competency to operate such class of
machinery, and to procure a license known as a traction license.
Such traction license shall not entitle the holder thereof to
operate any other class of machinery.

All certificates of license to engineers of all classes shall be
renewed yearly. The fee for renewal is $1 in all cases. The
fee for the examination of applicants for engineers' license?
is $7.50 for first-class engineers, $5 for second-class engineers,
$3 for third-class engineers, and $3 for traction engineers.
Fees must be paid at the time of application for license. In
case of the failure of any applicant co pass a successful exami-
nation, 90 da. must elapse before he can again be examined
as an applicant for license in the class for which he was exam-
ined. *But the inspector may grant to the applicant a lower
grade of license than applied for on such examination.

Ohio. — In the state of Ohio, the license laws are administered
by the chief examiner of steam engineers and a number of
district examiners. The chief examiner is appointed by the
governor of the state, and the district examiners are appointed
by the chief examiner, with the approval of the governor.

The laws state that any person who desires to act as a
steam engineer shall make application to the district examiner
of steam engineers for a license so to act, on a blank furnished
by the examiner, and shall successfully pass an examination
on the construction and operation of steam boilers, steam
engines, and steam pumps, and also hydraulics, under such
rules and regulations as may be adopted by the chief examiner,
which rules and regulations and standards of examination,
however, shall be uniform throughout the state. If, on such
examination, the applicant is found to be proficient in the
prescribed subjects, a license shall be granted him to have
charge of and operate stationary steam boilers and engines.
It shall be unlawful for any person to operate a stationary
steam boiler or engine of more than 30 H. P. without having

250 ENGINEERS' LICENSE LAWS

been licensed to do so. Boilers and engines under the jurisdic-
tion of the United States and locomotive boilers and engines
are excepted.

Licenses continue in force for 1 yr. from the date of their
issue, unless something occurs to render the holder unfit to
discharge the duties of steam engineer, in which case the license
may be revoked. Renewals of licenses are granted on appli-
cation at the expiration of 1 yr. from the date of issue. The
fee for examination of applicants for license is $2, which must
be paid at the time of application for examination; each renewal
of license costs $2.

Pennsylvania. — In the state of Pennsylvania there are license
laws relating to steam engineers and the inspection of steam
boilers in cities of the second and third classes. The adminis-
tration of these laws is in the hands of the boiler inspector? of
the several cities involved. The councils of the cities provide
for the creation of the office of boiler inspector. No steam
boiler or steam engine of over 10 H. P. may be operated by
any person who is not over 21 yr. of age and who does not
hold a license, except in the following cases: locomotive boilers
used in transportation and steam boilers and engines carrying
pressures of less than 15 Ib. per sq. in.

Every person desiring authority to perform the duties of
an engineer shall apply to the boiler inspector of such cities,
who shall examine the applicant as to to his knowledge of steam
machinery and his experience in operating it, and also the
proofs he produces in support of his claim. If the inspector
is satisfied that the applicant's character, habits of life, knowl-
edge and experience in the duties of an engineer are such as to
authorize the belief that he is a suitable and safe person to be
entrusted with the powers and duties of such station, he shall
be granted a license on the payment of $3. Licenses are to
be renewed annually on the payment of $1 and within 10 da.
after the expiration of date of such license.

Licenses arc of two classes, namely, those entitling the holders
to have charge of or to operate stationary steam boilers and
steam engines only, and those entitling the holders to have
charge of or to operate portable steam boilers and steam
engines only. Transferring from one grade to the other can

6

nes

ENGINEERS' LICENSE LAWS 251

be done only through a reexamination, but without cost to the
licensee.

No person shall be eligible to examination for license unless
he furnishes proof that he has been employed about a steam
boiler or a steam engine for a period of not less than 2 yr.,
prior to the date of application, which proof must be certified
by at least one employer and two licensed engineers. It shall
be the duty of every licensed engineer when he vacates a posi-
tion as engineer to notify the boiler inspector of such fact.
Failure to do so is punishable by suspension of license for such
a period of time as the boiler inspector may determine.

Tennessee. — In Tennessee, the license laws are administered
by a board of inspectors appointed by the mayor or the presi-
dent of cities having a population of 30,000 or over. The
duties of the board are to examine into the qualifications of
applicants for license to act as engineers of steam plants, The
board holds sessions at least twice each month for the purpose
of receiving applications for license. The laws state that the
board shall grant certificates of license for 1 yr., to all appli-
cants who, on examination, shall have the skill, experience,
and habits of sobriety requisite to perform the duties of an
engineer. Any owner or user of steam boilers of a capacity
of not over 75 sq. ft. of heating surface and a pressure of not
over 25 Ib. per sq. in., and of all boilers of a pressure less than
15 Ib. per sq. in. used for heating purposes only, may obtain
a permit from the board to employ a careful and trustworthy
person instead of a licensed engineer, such person to be recom-
mended by two citizens, one of whom shall be a steam user or
a licensed engineer. When boilers are used for engines run day
and night, the owner or user of them may employ some trust-
worthy person in place of a licensed engineer, not exceeding
12 hr. at a time, under the instructions of a licensed engineer-
in-charge.

In case an owner may be deprived of the services of a
licensed engineer, he may put a careful and trustworthy per-
son in charge for a time not exceeding 6 da. In places where
there are steam boilers or steam-generating apparatus of over
10 H. P., and when such apparatus is in use, there must b«>
employed at least one licensed engineer.

252 ENGINEERS' LICENSE LAWS

Applicants for engineer's license must make application on
a blank furnished by the board for that purpose. Applicants
must have experience of at least 2 yr. at mechanical or steam
engineering, and must state their experience on the blanks.
All applications must be signed by two citizens, one of whom
must be a steam user or a licensed engineer, who shall go before
the board and make oath that the statements set forth in the
application are true. In taking charge of a plant, and when
leaving a plant to assume charge of another, engineers must
notify the board immediately in the first instance and 10 da.
previous in the second instance. The fee for each license or
renewal is $5.

ABSTRACTS OF CITY ENGINEERS' LICENSE
ORDINANCES

Allegheny, Pa. — See Pennsylvania state law, on page 250.

Atlanta, Fulton County, Ga. — The license laws for Atlanta,
which is in Fulton County, Ga., are, in part, as follows:

Any person desiring to be examined for a license to run and
operate steam boilers and stationary engines in Fulton County
shall make application 'in writing to the Board of Examiners
of Engineers of Fulton County. Such application must be
indorsed by three reputable citizens of this county, one of
whom shall be a licensed engineer. The three citizens must
certify to the good character and sober habits of the appli-
cant and that he has had experience of not less than 1 yr.
as an engineer, or experience of 1 yr. as an apprentice under a
licensed engineer. No license shall be issued by the board of
examiners to any one until after a full compliance with this
rule.

A license shall be granted to only such engineers as, after
a careful examination, the board of examiners shall be satisfied
are competent to have full charge of the class of engines and
boilers covered by the license issued to them.

The board of examiners shall classify all licenses in accord-
ance with the character of the engines run by stationary
engineers, from the plain slide-valve engine to that employing
the most difficult and complicated machinery. The license
must show on its face the character or class of same.

ENGINEERS' LICENSE LAWS 253

The board of examiners shall have the authority to issue
licenses to assistant engineers, classifying them as above pro-
vided, and issue to the same only such license as may cover
the character of the engine, which in their judgment such
assistant engineer is competent to have charge of, and then
only when the chief engineer in charge of the same engine has
a full license covering the class to which it belongs.

Whenever any engineer or assistant engineer has received
a license of one class, and desires to be licensed in a higher
class, or, in the case of an assistant engineer, to be licensed as
chief engineer, he may make application to the board of exam-
iners for that purpose. After a reexamination the engineer
or the assistant engineer may be granted such higher license
if, in the opinion of said board of examiners, he is competent
to take charge of such engine as may be covered thereby.

When any person shall, after written notification from the
board of examiners, continue to run or operate any stationary
engine or boiler in Fulton County without a license from
them covering the class of engine that he has in charge, or when-
ever any person shall knowingly employ or cause to be employed
any person to run or operate a stationary engine or boiler in
Fulton County who has not been licensed by the board of
examiners, such person shall be prosecuted by the board of
examiners under the criminal laws of this state.

Each license issued by the board is issued and accepted
subject to the rules of examiners.

The board of examiners shall receive a fee from each person
examined for a license as either engineer or assistant engineer
of $5 in each case, which fee shall be required to be paid prior
to the examination of the applicant and whether the license
is issued to him or not.

Baltimore, Md. — In the city of Baltimore there is a board
of examining engineers appointed biennially by the governor
of the state. The law states that this board shall have general
supervision of all stationary engineers within the state of
Maryland, except as hereinafter provided. It shall be the
duty of the board to examine all engineers of the age of 21 yr.
and upwards who shall apply to them for examination. Those
who pass the examination and receive a certificate shall pay
18

254 ENGINEERS' LICENSE LAWS

the board the sum of $3 for each certificate so issued, and tor
all renewals of all grades the sum of $1.50.

The certificates shall be of three grades. A certificate of the
first grade will permit the holder to take charge of any plant
of machinery; one of the second grade, to take charge of any
plant of machinery from 1 to 500 H. P.; and one of the third
grade, to take charge of any plant of machinery from 1 to
30 H. P. The said certificate shall run for the term of 1 yr.
and shall be renewed annually.

All persons desiring to fill a position as a stationary engineer
must make application to the board of examining engineers,
with the following exceptions: Persons who are running
•engines and boilers in sparsely settled country places, where
not more than twenty persons are engaged in work about such
engines and boilers; engineers running country saw mills and
grist mills, threshing machines, and other machinery of a
similar character; marine engineers engaged in steamboats or
any vessel run by steam; and persons engaged as locomotive
engineers of any steam railway company.

The law also states that the headquarters of the board shall
be in Baltimore and that it shall meet at least once in every
-week, and at a specified hour and day shall sit until all applicants
shall be examined. If there are too many applicants to examine
on the regular day for the purpose, the board shall continue
its sessions until all applicants have been examined.

Buffalo, N. Y. -Every person within the city limits of the
city of Buffalo in charge of or operating any steam engine or
steam boiler (excepting persons operating locomotive steam
engines or marine engines, or persons licensed as engineers by
the authorities of the United States, or persons in charge of
any steam engine or boiler in any of the public-school build-
ings, or any engineer while in the employ of the fire depart-
ment of the city) shall appear in person before the examiner
of stationary engineers for examination as to his qualifications
as a stationary engineer, and if found qualified, shall be duly
licensed, as the ordinance provides. But such persons who
have charge of any steam boiler or steam engine in public-
school buildings of the city shall be examined as to their
qualifications to have charge of same.

ENGINEERS' LICENSE LAWS 255

No person shall be granted a license unless he be an actual
resident of the city of Buffalo, and shall be a citizen, or shall,
have declared his intention to become a citizen, of the United
States. All licenses must be renewed annually, and no person,
shall have charge of or operate more than one steam plant.
A fee of $3 shall be collected by the examiner upon issuing a
license, and $2 for each annual renewal.

The classification and grades are as follows: Chief engineer f
first-class engineer, second-class engineer, and special engineer.
The grades are according to the capacity and horsepower of a
steam engine, steam boiler, or steam plant of which such
engineers are found competent to take charge. Chief engineers
are qualified to take charge of and operate any size of steam
plant; first-class engineers, to take charge of any steam plant
not exceeding 150 H. P.; second-class engineers, to take charge
of and operate any size plant not exceeding 75 H. P. ; and special
engineers, to take charge of only a certain steam engine or boiler
to be stated in the license, such steam engine or boiler not to-
exceed 10 H. P. and such license not to be used for a longer
term than 1 yr.

Chicago, 111. — In Chicago a board of examiners deals with
the licensing of engineers. This board holds in quarters pro-
vided by the commissioner of Public Works, daily sessions for
the purpose of examining and determining the qualifications of
applicants for licenses for engineers. Every application for a.
license must be made on printed blanks furnished by the board
of examiners; that for an engineer must be accompanied by a
fee of $2, and that for a boiler or water tender must be accom-
panied by a fee of $1.

An applicant for an engineer's license must be a machinist
or an engineer having a practice of at least 2 yr. in the man-
agement, operation, or construction of steam boilers and engines
An applicant for a boiler tender's license must be a person who
has a thorough knowledge of the construction and manage-
ment, and operation of steam boilers. Each applicant must state
upon the blank the extent of his experience; must be at least
21 yr. of age, a citizen of the United States, or have declared
his intention to become such; and must be of good character;
all of which must be vouched for in writing by at least

256 ENGINEERS' LICENSE LA ITS'

two citizens of Chicago, or may be verified under oath by the
applicant when required by the board of examiners.

It shall be the duty of the board to see that each boiler plant
in the city of Chi ,ago shall have a licensed engineer, or boiler
or water tender, or both as the case may be, in charge at all
times when working under pressure; certificates must be dis-
played in a conspicuous place in the engine or boiler room.
Each engine and boiler tender shall devote his entire time,
while boilers are working under pressure, to the duties of the
plant under his charge, Any person having charge of a steam
boiler whose duty it is to keep up the water in such boiler
shall be deemed a boiler or water tender within the meaning
of the ordinance, but the provisions for the examination, licen-
sing, and regulation of boiler or water tenders shall apply only
to boiler or water tenders who ~re in charge of a steam boiler
or boilers, that are detached from the engine room or so far
removed therefrom or otherwise located as to render it difficult
for the engineer in charge of the plant to give it or them his
personal attention and supervision.

The following are exempt from the provisions of the ordi-
nance: engineers in charge of locomotives and all boilers used
for heating private dwellings, hothouses, conservatories, and
other boilers carrying a pressure of not more than 10 Ib. per
sq. in. and the persons operating them.

Denver, Colo. — In Denver the mayor appoints a board of
examiners consisting of the city boiler inspector and two
practical engineers, whose duty it is to examine applicants for
licenses as engineers and boiler or water tenders, in accordance
with the rules and regulations of the ordinance, and to issue cer-
tificates of qualification. The law states that each certificate
issued by the board shall expire 1 yr. from the date of issue,
and that the board shall hold weekly sessions of such duration
as may be deemed requisite for the purpose of examining and
•determining the qualifications of applicants for licenses as
engineers or as boiler or water tenders.

Every application for a license must be made on printed
blanks furnished by the board of examiners, and must set forth
the name, age, and citizenship of the applicant and the extent
of his experience. An application for an engineer's license

ENGINEERS' LICENSE LAWS 257

must be accompanied by a fee of $2, and that for a boiler or
water tender's license, by a fee of $1.

According to the ordinance, an applicant for an engineer's
license shall be a machinist or engineer, having a practice of
at least 2 yr. in the management, operation, or construction
of steam engines and boilers, and an applicant for a boiler ten-
der's license shall be a person who has a thorough "knowledge
of the construction, management, and operation of steam
boilers. Each engineer and boiler or water tender so to be
licensed shall be at least 21 yr. of age and of good character,
all of which shall be vouched for in writing by at least two
citizens of Denver, or shall be verified under oath by the appli-
cant when required by the board of examiners.

All such licenses may be renewed from year to year upon
payment of the license fee before specified and without further
examination, unless the applicant applies for a different class
or grade of license.

Engineers in charge of locomotives and engineers or boiler
or water tenders in charge of boilers carrying a steam presssure
of not more than 10 Ib. per sq. in. are exempt from the pro-
visions of the ordinance.

Detroit, Mich. — In Detroit the city boiler inspector examines
candidates as to their fitness to perform the duties of the
stationary engineer. Any person claiming to be qualified to
operate a boiler must apply in writing on blanks provided for
the purpose for a license. The inspector shall examine him
and consider the proof offered in support of his claims. If the
inspector is satisfied that the applicant's knowledge, experience,
and character render him competent to handle boilers with
safety, he shall issue a license certificate to that effect, design-
ating the class in which the engineer is authorized to operate.

There shall be three grades of engineers' license. First-
class engineers' licenses shall be unlimited as to the number
of boilers and pressure, and shall be granted to any citizen
having an experience of 5 yr. in the care of steam boilers, pro-
vided he can pass a satisfactory examination. Second-class
licenses shall be limited to 75 H. P. and shall be granted to
any citizen having an experience of 3 yr. in the care of steam
boilers, provided he can pass a satisfactory examination.

258 ENGINEERS' LICENSE LAWS

Third class licenses shall be limited to 25 H. P. and shall be
granted to any citizen having experience in firing steam boilers
for 2 yr., provided he can pass a satisfactory examination.

If any person makes application for a certain class of license
and fails to procure it for any cause, the inspector can assign
him to the class to which his examination entitles him, and he
cannot make application again for a period of less than 3 mo.
Any person having a second-class or a third-class license can
act as assistant to a first-class engineer.

The fee for licenses shall be $1, payable before examination,
but one-half of the amount paid shall be refunded if the license
is refused. The provisions of the ordinance do not apply to
locomotive boilers used on railroads, boilers under the jurisdic-
tion of the United States, boilers in the fire department of the
city, and boilers used in private residences for heating purposes.

Elgin, 111. — The engineers' license laws for Elgin, 111., are,
in part, as follows:

There shall be and there is hereby authorized to be appointed
by the mayor, by and with the consent of the city council, a
board of examining engineers. The said board shall consist
of three practical engineers. The duties of the board shall be
to examine into the qualifications of applicants for engineer's
license; to license those found qualified, and, for cause, to
suspend or revoke the same.

The examination may be written or oral and shall be entirely
practical. Applications for license shall be made on a printed
blank furnished by a board of examiners and shall set lorth
the name, age, citizenship, residence, experience, etc., of the
applicant, together with the location of the plant for which a
license is desired. Each application for license shall be accom-
panied with $1, which fee shall be returned in case of failure
to secure a license.

The board of examiners may suspend the license of any
engineer for carelessly permitting the water to get too low and
burning the boiler; for carrying the steam pressure higher than
allowed by law; for absence from his post of duty; for neg-
lect, incapacity, or intoxication while on duty; provided that
no license be suspended or revoked without first giving the
accused person an opportunity to be heard in his own defense.

ENGINEERS' LICENSE LAWS 259

The license will be suspended not to exceed 30 da. for the first
offense, not to exceed 90 da. for the second offense, and not to
exceed 6 mo. for an offense after that.

Engineers' licenses will be good for 1 yr. from date of issue
and must be renewed annually. Engineers who change from
one plant to another must secure permission from the board
of examiners, who will either authorize the change or reexamine
the applicant, at their discretion, without additional cost to
applicant. Engineers' licenses must be framed under glass
and kept in a conspicuous place in engine room or boiler room.

All applicants for an engineer's license shall have a practi-
cal experience of at least 1 yr. in the management of steam
engines and boilers. Each applicant shall be at least 20 yr. of
age (except that by unanimous consent of the board a younger
man may be licensed) and must be of temperate habits and
good character, all of which must be vouched for in writing
by two freeholders of Elgin, or verified under oath by the
applicant when required by the examiners.

It shall be unlawful for any unlicensed person to take charge
of or operate any steam power or boiler plant within the city
of Elgin, excepting engineers in charge of locomotives, steam-
road carriages, and those in charge of boilers carrying a steam
pressure of less than 15 Ib. per sq. in. Any person who shall
take charge of or operate any steam power or boiler plant for
a longer time than to the next meeting of the board of examiners,
shall be guilty of a misdeameanor and subject to a fine of
not more than $20 nor less than $5. Any person, company,
or corporation controlling any steam power or boiler plant
who shall authorize or permit any person, without proper and
valid license, to take charge of or operate the same for a longer
period than above stated, shall be guilty of a misdemeanor
and subject to a fine of not more than $50, nor less than $20,
for each offense, and each day's violation of this ordinance
shall constitute a separate offense.

Any engineer whose license has expired for a period of 10 da.
must give satisfactory explanation to the board of examining
engineers why such a condition exists, and any engineer whose
license has expired for a period of 1 yr. or more shall be sub-
jected to a reexamination.

2CO ENGINEERS' LICENSE LAWS

Any engineer or water tender changing his position from
one plant to another shall within 5 da. have his license trans-
ferred to the plant he is to operate.

Goshen, Ind. — In the city of Goshen, Ind., there is appointed
by the mayor, with the consent of the common council, an
examining engineer who has charge of matters pertaining to
the licensing of stationary engineers.

Any person desiring to act as an engineer shall make appli-
cation to the examiner, upon blanks furnished by the examiner,
and if, upon examination, the applicant is found to be trust-
worthy and competent, a license shall be granted to said
applicant; such license shall continue in force for 1 yr., unless
for cause it may be revoked.

License shall be granted according to competency of the
applicant, and shall be divided into classes as follows: Class 1,
the engineer's license for which shall be unlimited as to horse-
power; class 2, the license for which shall be limited to 150 H. P.;
and class 3, the license for which shall be limited to 50 H. P.
Engineers holding second- or third-class licenses may act as
assistant engineers in a plant of any capacity, provided the
man in charge holds a first-class license.

The fee for examination of applicants shall be $1, to be paid
at the time of the application for examination, and $1 for
each renewal of license. Locomotive boilers and engines,
boilers of private residences, or boilers of less than 8 H. P.
do not require a licensed engineer to operate them.

Hoboken, N. J. — License laws in Hoboken, N. J. are admin-

and enforced by a board of examining engineers,

consisting of five members appointed by the council. The

mayor and the council of the city of Hoboken do ordain as

follows:

No person shall be the engineer of, or shall have charge of,
or operate any steam boiler, or steam engine in the city of
Hoboken, for a period exceeding 2 da., who shall not have a
license certificate or shall have made application for the same
authorizing him to have charge of, or to operate such engine,
or boiler, from the board of examining engineers, and no such
license shall be granted unless the applicant therefor be a
citizen of the United States.

ENGINEERS' LICENSE LAWS 2G1

Before any person shall be employed as an engineer of any
such steam boiler or engine, or shall have charge of or operate
any such boiler or engine, he shall make a written application
on blanks furnished by the city to said board of examining
engineers, for the license heretofore mentioned, which appli-
cation shall be accompanied by references as to the character
and ability of the applicant, and the filing of such references
with said board shall be considered as a compliance with the
provisions of this ordinance for 30 da. thereafter or until the
said application shall have been passed upon by said board,
and said applicant after the riling of said reference shall have the
right to operate and have charge of any such engine, boiler
or plant until his application shall have been passed upon by
said board.

Every person who shall satisfy said board of examining
engineers that he is a safe and competent person to operate
and have charge of such steam boiler, engine or plant specified
in his application, shall, upon payment of $2 to the city clerk
as his fee, receive a license permitting him to operate the same
for 1 yr., unless such license shall be sooner revoked. For an
annual renewal of such license the licensee shall pay to the
city clerk as his fee the sum of $1 therefor; additional hearing
shall not be required, unless in the judgment of the said board
the same may be necessary. Such licenses must be framed and
hung in a conspicuous place in the plant, or upon, or near the
engine or boiler, in charge of such licensee.

Said board may at any time after proper hearing revoke
any license issued on account of inebriety, incompetency, or
negligence of the holder of any such license, or for any other
good cause, and no license shall be issued to any licensee
whose license shall have been revoked for a period of 6 mo.,
after which the license revoked may be renewed, if in the
judgment of the board the cause of its revocation no longer
exists.

If said board shall refuse to grant to any applicant a license,
no license shall be issued to him for the next 6 mo. following
the refusal of said application, but after said period said appli-
cant may make another application, and, if qualified, may be
granted a license.

262 ENGINEERS' LICENSE LAWS

This ordinance shall not apply to locomotive engineers or
to engineers on steam vessels coming under the jurisdiction
of the United States Board of Supervising Inspectors, nor shall
it apply to boilers in private residences for heating purposes,
unless, in the opinion of said board, such boiler is so equipped
and run as to endanger public safety unless operated by a
licensed engineer.

Any engineer in charge of any steam engine or boiler who
shall abandon it while in operation without leaving a person
in charge of same, who shall, in the opinion of the board of
examining engineers, be competent to take charge of same,
shall be fined the sum of $10.

Huntington, W. Va. — License laws in the city of Huntington,
W. Va., are administered and enforced by a board of engineers
consisting of four members. Candidates for examination must
have had at least 1 yr. of experience in operating steam engines
and boilers. The law states that it shall be the duty of the
board of engineers, upon the payment of $3 by the applicant,
to examine persons touching their qualifications as engineers,
who desire to act as engineers and take charge of steam boilers,
engines, and pumps. If the applicant passes a satisfactory
examination, the board shall grant and issue to him a certi-
ficate of qualification. If the applicant fails to pass a satis-
factory examination, he shall not be allowed to apply again
for certificate for 2 mo. thereafter. All certificates granted
shall be in force for 1 yr, from the date thereof and no longer,
and any person holding a certificate from the board may have
the same renewed at its expiration for a period of 1 yr. by the
applicant for such renewal paying the sum of $2, provided,
however, that the person applying for such renewal is entitled
thereto, and such application for renewal is made on or before the
last regular meeting of the board before the expiration of the
applicant's certificate. Unless the above provision is complied
with, the board may, at its discretion, order a new examination.

The board shall have the right to adopt rules and regulations
as they deem necessary and proper, not inconsistent with this
ordinance. The full board, by an unanimous vote, shall have
power and may revoke any engineer's certificate upon cau.se
being shown therefor.

ENGINEERS' LICENSE LAWS 263

It shall be the duty of each engineer holding a certificate
from the board to display the same in some prominent place
near the boiler or boilers in his charge. The board may revoke
the certificate of any engineer who shall fail or refuse to comply
with this section.

It shall be unlawful for any person to operate or cause to be
operated any steam boiler used to furnish steam at a pressure
to exceed 25 Ib. per sq. in., unless there be in charge of such
boiler an experienced person having a certificate from the board
of engineers, and any person found in charge and operating
a boiler not having a certificate from the board of engineers
shall be deemed guilty of a misdemeanor and, upon conviction
thereof, shall be fined in the sum of not less than $5, nor more
than $50 for each offense; provided, however, that any owner
or user of any boiler in use which shall for any cause be deprived
of the service of a person holding such certificate may procure
an experienced and careful person to take charge of such boiler
for a period not to exceed 10 da.

Jersey City, N. J. — Engineers* license laws are administered
by a board of examiners in Jersey City, N. J. The laws, in
part, are as follows:

No person shall be the engineer of, or shall have charge of
or operate any steam boiler or steam engine, in the city of
Jersey City, for a period exceeding 1 wk., who shall not have a
license certificate authorizing him to have charge of or operate
such engine or boiler, from the board of examiners.

Before any person shall be employed as an engineer of any such
steam boiler or engine, or shall have charge of or operate any
such boiler or engine, he shall make a written application to
the board of examiners for the license, and shall specify in such
application the particular engine, boiler, or plant that he
desires to operate, or have charge of, which application shall
be accompanied by references as to his character and ability,
and the filing of such reference with such said board shall be
considered as a compliance with the provisions of this ordinance
for 30 da. thereafter, or until his said application shall have been
passed upon by said board, and said applicant, after the filing
of said references, shall have the right to operate until his
application shall have been passed upon by said board.

264 ENGINEERS' LICENSE LAWS

Every person who shall satisfy said board of examiners that
he is a safe and competent person to operate and have charge
of the steam plant, boiler, or engine specified in his application,
shall, on payment of $1 to the city clerk, for the benefit of the
city, receive a license permitting him to operate the same for
1 yr., unless sooner revoked. Said license shall apply only to the
plant, boiler, or engine for which it is issued, and before taking
charge of another plant the licensee shall apply for another
license for such other plant, for which other license, if the
application be made within a year, no charge shall be made.
For annual renewals of such licenses a fee of $1 shall be
paid. For the renewals above mentioned, no additional hear-
ing shall be required, unless in the judgment of said board
it shall be necessary. Said licenses must be framed and
hung in a conspicuous place in the plant, or upon or near the
engine for which is is issued.

If the board shall refuse to grant to any applicant a license,
oo license shall be issued to him for the next 6 mo. following
the refusal of his application, but after said period said appli-
cant may make another application, and if found qualified,
may be granted a license.

Whenever said board shall refuse to grant any application,
or shall revoke any license, they shall give immediate notice
of such refusal or revocation to the applicant or licensee, and
such applicant or licensee may appeal from the decision of such
board to the board of aldermen, in which case said applicant
or licensee shall file his appeal with the board of aldermen
within 10 da. after receiving notice of the decision of said
board, and the board of aldermen may confirm or reverse the
decision of said board, and issue such license.

The ordinance shall not apply to railway locomotives, nor
to engineers employed thereon, nor to steam vessels coming
under the jurisdiction of the United States Board of Super-
vising Inspectors, when employed upon the vessel to which
said license applies. Nor shall it apply to boilers in private
residences or buildings for heating purposes, unless, in the
opinion of said board, such boiler is so equipped and run
aj> to endanger public safety unless operated by a licensed

ENGINEERS' LICENSE LAWS 265

Kansas City, Mo. — In Kansas City, Mo., a board of engineers
appointed by the mayor, with the consent of the council,
administers the license laws. The board convenes for business
once each month, to examine into the qualifications of appli-
cants for engineers' licenses. According to the laws, the board
shall grant certificates of license, charging $5 to each applicant
for the first certificate, $3 of which is to be deposited at once.
Each applicant is to be allowed three trials, and if he then fails
to pass a satisfactory examination, the applicant shall forfeit
the money deposited (namely, $3) with the clerk of the board.
But if the applicant has the capacity, skill, experience, and
habits of sobriety requisite to perform the duties of an engineer,
and shall pass the examination, the board shall grant him a
license for the term of 1 yr. upon the payment of an additional
$2. Any person so qualified shall not be refused a license.

Renewal of license will be granted to applicants, upon
payment of $2.50, if renewed on or before the next regular
meeting of the board of engineers after its expiration. All
engineers, engines, and boilers of the fire department of Kansas
City, the locomotive boilers used on railroads, and steam
boilers supplied with water automatically, when used only for
heating dwelling houses and not carrying a pressure over
10 lb- per sq. in., are exempt from the provisions of this
ordinance.

Every applicant for a license who fails to pass the exami-
nation of the board is required to wait 4 wk. before again
making application for license, and the board shall then give
him another examination. Applicants failing to pass the
examination after the third trial shall not be permitted to
appear again before the board for 6 mo.

Every engineer licensed by the board and under control
of the board is required to notify the boiler inspector — who is
a member of the examining board referred to — when he accepts
employment, and within 3 da. thereafter, the name of his
employer, and the location of the boilers in his charge. Any
engineer who shall neglect or refuse to comply with this rule
shall be deemed guilty of a misdemeanor. Engineers shall
report semiannually to the boiler inspector, during the first
3 da. of the months of January and July, the condition of the

266 ENGINEERS' LICENSE LAWS

boilers, pumps, and connections under their charge. Failure
to comply with the rule shall be deemed a misdemeanor.

Lincoln, Neb. — License laws in Lincoln, Neb., are adminis-
tered by a board of engineers, which consists of three members
appointed by the mayor with the consent of the city council.

The law states that it shall be the duty of the board of
engineers, on the payment of $3 by the applicant, to examine
persons, touching their qualifications as engineers, who desire
to act as engineers and take charge of steam boilers. All
certificates granted shall be in force for 1 yr. from the date
thereof and no longer; and at the end of 1 yr. certificates may
be renewed for another year by the applicant paying the
sum of $2, provided the person applying for such renewal
is entitled thereto and such application is made on or before the
last regular meeting of the board, before the expiration of the
applicant's certificate.

It shall be the duty of every person holding a certificate
from the board to make a semiannual report to the board, during
the months of January and July of each year, of the condition
of every boiler, pump, and connection under his charge.
Failure to make such report is sufficient cause for the board
to revoke the certificate of the person involved. Heating
apparatus in private dwellings are exempt from inspection,
as provided by the ordinance in this city, also those boilers
kept insured in any reputable and legitimate insurance com-
pany requiring inspection.

Four grades of certificates, namely, first-, second-, and
third-grade certificates and a certificate specified low pressure,
are issued by the board. First-grade certificates are granted
to applicants who, on examination, are found qualified to take
charge of and operate any steam plant; second-grade certificates
are granted to applicants who, on examination, are found qual-
ified to take charge of and operate any steam plant up to
75 H. P. only; and third-grade certificates are granted. to
applicants who, on examination, are found qualified to take
charge of and operate any steam plant up to 25 H. P. only.
Certificates specified low pressure are granted to applicants
who, on examination, are found qualified only to take charge of
and operate low-pressure boilers for heating purposes.

ENGINEERS' LICENSE LAWS 267

Los Angeles, Cal. — The license laws in Los Angeles are admin-
istered by the city boiler inspector and an assistant inspector
appointed by the city council, together with a board of examin-
ing engineers, of which there are three in number.

The board, so the law states, shall hold one meeting on the
first and third Wednesday in each month for the purpose of
examining applicants for engineer's license, and shall hold the
meeting on the second and fourth Tuesday of each month for
the purpose of examining applicants for elevator license. The
board shall make a careful and thorough examination as to the
qualifications of all applicants for engineer's license, and shall
grant certificates of license to all persons found qualified; it
shall charge and collect from each applicant for a chief, or first-
class, license, the sum of $5, and from each applicant for a
second or a third-class license, the sum of $3. Such licenses are
good for the term of 1 yr., unless revoked for cause.

In case any owner or user of any boiler shall for any cause be
deprived of the services of a licensed engineer, he muct notify
the boiler inspector at once, and may place an experienced per-
son in charge, for a time not beyond the date of the next regular
meeting of the board of engineers. When boilers are used and
engines run night and day, the owner or user of them must
employ at least two licensed engineers, who shall stand watch
alternately. No person shall use or operate any steam boiler
or steam-generating apparatus in the city of Los Angeles with-
out obtaining a certificate of license as provided for; this applies
to apparatus of over 5 H. P.

Applicants for license who fail to pass the examination of the
board of engineers, shall be required to wait for 4 wk. before
making another application. Applicants who fail to pass after
a third trial shall not be permitted to again appear before
the board for 6 mo. An engineer must notify the boiler
inspector of any employment that he may enter into as an engi-
neer, and within 3 da. after, the name of his employer and the
location of the plant in his charge. Engineers must also report
semiannually to the boiler inspector, during the first 3 da. of
the months of January and July of each year, the condition of
the boiler or other apparatus and their connections under or
in his charge.

268 ENGINEERS' LICENSE LAWS

Applicants for renewal of licenses shall pay to the board of
engineers the sum of $1 for each yearly renewal.

Any person violating any of the provisions of this ordinance
shall be deemed guilty of a misdemeanor, and upon conviction
shall be punished.

Memphis, Tenn. — In the city of Memphis, Tenn., there is
a board of examiners appointed by the legislative council. This
board consists of the city boiler inspector and four practical
steam engineers, and is created for the purpose of examining
and licensing engineers having charge of or operating boilers
and steam engines in the city of Memphis.

The Jaws of this city state that the board of examiners shall
hold at least two sessions each month, on the first and third
Mondays, for the purpose of receiving and acting on applica-
tions for license. The board shall grant certificates of license
for 1 yr. to applicants who, on examination, shall have the
skill, experience, and habits requisite to perform the duties
of an engineer. Licenses shall be renewed without examination
upon payment of the required fee. Applicants for license must
not be less than 21 yr. of age, and must be citizens of the United
States or have declared their intention to become citizens. Appli-
cations must be made upon blanks furnished by the board for
such purpose. Applicant? must have an experience of at least
3 yr. at mechanical or steam engineering, and so state it on the
blanks. All applications must be signed by two citizens of the
United States, one of whom must be an engineer or steam user,
and both of whom must make affidavit before an officer, quali-
fied to administer an oath, that the statements set forth in
such applications are true. When an applicant fails to pass an
examination three times, he will not be eligible to take another
examination until 60 da. has passed from the time of his last
appearance before the board.

Licenses shall be of three grades, namely, first, second, and
third. A first-grade license shall entitle its rightful holder to
operate or to have charge of steam plants of unlimited capacity
as to horsepower of boilers. A second-grade license shall
entitle its rightful holder to assist a first-grade-license engineer
in any steam plant where such services are required under the
instructions of first-grade engineer in charge of steam plant;

ENGINEERS' LICENSE LAWS 269

or he may have charge of and operate steam plants limited to
75 H. P. of boilers. A third-grade license shall entitle its right-
ful holder to assist first- or second-grade engineers where such
services are required, under the instructions of engineer in
charge of steam plant; or he may have charge of or operate
steam plants limited to 25 H. P. of boiler.

The fee for each license or yearly renewal shall be $2.
The provisions of this ordinance shall apply to all steam plants or
boilers operated within the city limits, except locomotive boilers
used on railroads. If any owner or user of any boiler or boilers
or steam-generating apparatus is deprived of the services of the
licensed engineer or engineers employed by him, for any reason
over which he has not control, he may employ an unlicensed
engineer for 30 da., in which time he must secure a licensed
engineer.

No person shall receive a license who is not able to determine
the weight necessary to be placed on the lever of a safety valve
(the various data to work the problem being given) to with-
stand any given pressure of steam in the boiler. Applicants
must also be able to figure and determine the strain brought on
the braces of a boiler with a given pressure of steam, the position
and distance apart being known. They must be able to figure
and determine the safe working pressure of a boiler, such
knowledge to be determined by an examination in writing.
No license, except third grade, shall be granted to any engineer
who does not possess the foregoing qualifications. No license
shall be granted to any engineer who cannot read and write
and does not understand the plain rules of arithmetic. The
examination questions asked an applicant for license shall be
practical ones pertaining to boiler and engine care and
management; correct answers to 80% of such questions shall
qualify the applicant to receive his license.

Milwaukee, Wis. — The engineers' license laws in the city of
Milwaukee are administered and enforced by a board of exam-
ining engineers, consisting of two persons.

No person may operate or have control of any stationary or
portable steam boiler, engine, or any portion of a steam plant,
over 10 H. P., when working under pressure, except a duly
licensed engineer.
19

270 ENGINEERS' LICENSE LAWS

The board of examiners shall hold daily sessions for the pur-
pose of examining and determining the qualifications of appli-
cants for licenses for engineers and for persons having charge
of steam boilers or engines, as provided in the ordinance.

All persons desiring to perform the duties of a stationary or
portable-boiler engineer shall make application therefor to the
board of examiners, and shall present therewith a receipt from
the city treasurer for a fee of $3. The board shall have the
power to examine applicants, to grant licenses, and to revoke
or suspend the same for cause. Applications must be made on
printed blanks furnished by the board.

Licenses shall be in force for 1 yr. from date of issuance, and
at the expiration of 1 yr. and on the payment of $1 licenses may
be renewed without further examination. An applicant for
engineer's license must be a machinist, engineer, oiler, or fire-
man having an experience of at least 2 yr. in the management,
operation, or construction of steam boilers and engines. Each
applicant must state the extent of his experience, be at least
21 yr. of age, and of good character, all of which must be
vouched for in writing by at least two citizens of the city of
Milwaukee.

If the applicant, on examination, be found qualified as an
engineer of a stationary or a portable steam boiler or engine,
he shall be granted a license according to class, as provided for.
Licenses so granted shall be graded into three classes: (1) Per-
sons holding first-class licenses may take charge of and operate
any steam- or motive-power plant; (2) persons holding second-
class licenses may take charge of and operate any steam- or
motive power plant not exceeding 300 H. P.; (3) persons hold
ing third-class licenses may take charge of and operate ar
steam- or motive-power plant not exceeding 75 H. P. Twelv*.
sq. ft. of boiler heating surface shall be equivalent to 1 H. P.

The holder of a second-class license may act as an assistant
engineer to an engineer in charge of a plant under a first-class
license; and the holder of a third-class license may act as an
assistant engineer to an engineer in charge of a plant under a
second-class license.

It shall be unlawful to carry a higher pressure of steam than
that fixed by the board. Engineers' licenses must be displayed

ENGINEERS' LICENSE LAWS 271

under glass, in a conspicuous place in the boiler or engine room.
It shall be the duty of every licensed engineer to report to the
board of examiners any defects in any steam boiler, engine, or
appurtenance belonging thereto under his charge.

This ordinance does not apply to engineers in charge of loco-
motives or to those in charge of engines or steam-boiler machin-
ery under the civil service of the city, county, state, or federal
government, or to engines or steam boilers used for heating
private dwellings, and other engines or steam-boilers carrying
a pressure of less than 15 Ib. per sq. in.

Mobile, Ala. — A board of examiners of engineers, consisting
of three members and elected by the general council, admin-
isters the license laws in the city of Mobile. The board must
meet at least twice each month for the despatch of such business
as may come before it.

According to the laws of this city, no person shall be entrusted
with, or have charge of, the management or operation of any
steam boiler having more than 200 sq. ft. of heo.ting surface, or
carrying a pressure greater than 20 Ib. per sq. in., until such
person has been duly examined by the board of examining
engineers.

Whenever any person makes application, or is called before
the board for examination, he shall be thoroughly examined as
to his competency to manage and operate steam boilers, feed
pumps, and injectors. If the applicant is found competent by
the board, a license certificate shall be issued to him. Such
license shall be in force for 1 yr. from the date of issuance.
A new license may be issued to the said holder at the expiration
of each year thereafter without further examination, as long
as the holder continues in operating steam-engineering occupa-
tion. Should an engineer abandon his occupation as an operator
for more than 1 yr., his license certificate shall become null and
void, and it shall be necessary for said person to be reexamined
by the board to obtain a new license certificate, before again
undertaking to manage and operate steam boilers, feed pumps,
and injectors.

Engineers are required to report in writing to the board of
examining engineers, during the months of January and June
of each year, the condition of the boiler or boilers under their

272 ENGINEERS' LICENSE LAW'S

charge; this also applies to those engineers who have charge of
elevators. All reports mtist contain full detailed and accurate
information, and must be made on blank forms to be obtained
from the board.

For each original certificate of license issued by the board,
a sum of $2 shall be paid by the person to whom the license is
issued; and for each renewal of license the sum of SI shall be
paid. These fee shall be collected by the board of examining
engineers.

New Haven, Conn. — A board of examiners, appointed by
the mayor and consisting of three members, administers the
license laws in the city of New Haven.

No person shall be engineer of, or shall have charge of, or
operate any steam boiler or steam engine in the city of New
Haven, for a period exceeding 1 wk. who shall not have a license
certificate from the board of examiners, authorizing him to
have charge of and operate such boiler or engine. This ordi-
nance shall not apply to railway locomotives nor engineers
employed thereon, nor to steam vessels coming under the juris-
diction of the United States inspectors, nor to boilers in private
residences or buildings for heating purposes, unless, in the
opinion of the board, such boiler is so equipped and run as to
•endanger public safety, unless operated by a licensed engineer.

Before any person shall be employed as an engineer of any
steam boiler or engine he shall make written application to
the board for a license. He shall specify in the application
the particular engine, boiler, or plant that he desires to operate
or have charge of, and the application shall be accompanied
by references as to his character and ability. After filing
such references, he may operate a plant for 30 da. thereafter
or until his application shall have been passed upon by the
board.

Every person who shall satisfy the board of examiners that
he is a safe and competent person to operate and have charge
of the steam plant, boiler, or engine specified in his applica-
tion, shall on the payment of $1 receive a license permitting
him to operate the same for 1 yr. unless sooner revoked for cause.
Said license shall apply only to the plant for which it is issued.
Before taking charge of another plant, the licensee shall apply

ENGINEERS' LICENSE LAWS 273

for another license for such other plant, for which other license
if application be made within a year, no charge shall be
made. For annual renewals of such licenses, a fee of $1 shall
be paid.

The board may at any time revoke any license for cause,
such as incompetency, neglect, or inebriety. In case a license
is revoked, application may be made for a new license 6 mo.
after, and on examination, provided the applicant is found
qualified, the board may grant a license to him.

New York, N. Y. — The engineer's license laws for the city
of New York are, in part, as follows:

No owner, or agent of such owner, or lessee of any steam
boiler to generate steam shall employ any person as engineer
or to operate such boiler unless such person shall first obtain
a certificate as to qualification therefor from a board of prac-
tical engineers detailed as such by the police department, such
certificate to be countersigned by the officer in command of
the sanitary company of the police department of the city of
New York. In order to be qualified to be examined for and
to receive such certificate of qualification as an engineer, a
person must comply, to the satisfaction of said board, with the
f ol lowing requirements :

1. He must be a citizen of the United States and over 21
yr. of age.

2. He must, on his first application for examination, fill
out, in his own handwriting, a blank application to be prepared
and supplied by the said board of examiners, and which shall
contain the name, age, and place of residence of the applicant,
the place or places where employed and the nature of his
employment for 5 yr. prior to the date of his application, and
a statement that he is a citizen of the United States. »The appli-
cation shall be verified by him, and shall, after the verification,
contain a certificate signed by three engineers, employed in
New York City and registered on the books of said board of
examiners as engineers working at their trade, certifying that
the statements contained in such application are true. Such
application shall be filed with said board.

3. The following persons, who have first complied with the
provisions of subdivisions one and two of this section, and no

274 ENGINEERS' LICENSE LAWS

other persons may make application to be examined for a
license to act as engineer:

(a) Any person who has been employed as a fireman, as
an oiler, or a as general assistant under the instructions of a
licensed engineer in any building or buildings in the city of
New York, for a period of not less than 5 yr.

(&) Any person who has served as a fireman, oiler, or gen-
eral assistant t.o the engineer on any steamship, steamboat,
or on any locomotive engine for the period of 5 yr. and shall
have been employed for 2 yr. under a licensed engineer in a
building in the city of New York.

(c) Any person who has learned the trade of machinist,
or boilermaker, or steam fitter and worked at such trade for
3 yr. exclusive of time served as apprentice, or while learning
such trade, and also any person who has graduated as a
mechanical engineer from a duly established school of tech-
nology, after such person has had an experience of 2 yr. in the
engineering department of any building or buildings in charge
of a licensed engineer, in the city of New York.

(d) Any person who holds a certificate as engineer issued
to him by any duly qualified board of examining engineers exist-
ing pursuant to law in any state or territory of the United
States and who shall file with his application a copy of such cer-
tificate and an affidavit that he is the identical person to whom
said certificate was issued. If the board of examiners of engi-
neers shall determine the applicant has complied with the
requirements of this section, he shall be examined as to his
qualifications to have charge of, and operate steam boilers and
steam engines in the city of New York, and if found qualified
said board shall issue to him a certificate of the third class.
After the applicant has worked for a period of 2 yr. under his
certificate of the third class, he may be again examined by
said board for a certificate of the second class, and if found
worthy the said board may issue to him such certificate of the
second class. After he has worked for a period of 1 yr. under
said certificate of the second class he may be examined for a
certificate of the first class, and when it shall be made to appear
to the satisfaction of said board of examiners that the appli-
cant for either of said grades lacks mechanical skill, is a person

ENGINEERS' LICENSE LAWS 275

of bad habits, or is addicted to the use of intoxicating beverages,
he shall not be entitled to receive such grades of license and shall
not be reexamined for the same until after the expiration of 1 yr.

Every owner or lessee, or the agent of the owner or lessee,
of any steam boiler, steam generator, or steam engine afore-
said, and every person acting for such owner or agent is hereby
forbidden to delegate or transfer to any person or persons
other than the licensed engineer the responsibility and liabil-
ity of keeping and maintaining in good order and condition
any such steam boiler, steam generator, or steam engine, nor
shall any such owner, lessee, or agent enter into a contract for
the operation or management of a steam boiler, steam gen-
erator, or steam engine, whereby said owner, lessee, or agent
shall be relieved of the responsibility or liability for injury
tbat may be caused to person or property by such steam boiler,
steam generator, or steam engine. Every engineer holding a
certificate of qualification from said board of examiners shall
be responsible to the owner, lessee, or agent employing him
for the good care, repair, good order and management of the
steam boiler, steam generator, or steam engine in charge of,
or run, or operated by such engineer.

Niagara Falls, N. Y. — A board of examiners of stationary
engineers, consisting of three members, administers the license
laws in the city of Niagara Falls. Any person desiring a license
to act as a stationary engineer or fireman in this city, may file
with the city clerk an application, together with the required
fee for a license, provided one is granted, which fee is returned
to the applicant in case a license is not granted to him. The
application is to be submitted to the board of examiners by
the city clerk, when such board shall examine the applicant at
a time and place named by the board.

It shall be unlawful for any person to have charge of or oper-
ate any steam plant, steam engine, or steam boiler within this
city, excepting locomotive steam engines, or marine engines,
or engines used by the fire department of the city of Niagara
Falls, without having procured a license from the board of
examiners.

The board of examiners shall issue licenses of the following
classes :

276 ENGINEERS' LICENSE LAWS

(a) A license as chief engineer to any person found quali-
fied to take charge of and operate any steam plant.

(&) A license as first-class engineer to any person found
qualified to take charge of a steam plant or engine not exceed-
ing 300 H. P.

(c) A license as first-class fireman to any person found
qualified to take charge of a steam boiler not to exceed 300
H. P.

(d) A license as second-class engineer to any person found
qualified to take charge of and operate any steam plant or
engine not exceeding 75 H. P.

(e) A license as second-class fireman to any person found
qualified to take charge of and operate any steam boiler not
exceeding 75 H. P.

(/) A license as special engineer or fireman to any person
found qualified to take charge of and operate a certain steam
engine or steam boiler of a certain horsepower capacity, to be
designated in the license.

(g) A license to the owner of a steam engine or boiler
using not to exceed 10 H. P., and used by him in his own
business.

Licenses are granted for 1 yr. and the fees for them are as
follows: For any license, save the license provided for in
subdivision (g), $3. For a license issued under subdivision
(g), $1. Licenses are to be renewed annually and the fee for
each renewal is $2.

It shall be unlawful for any person to take charge of a
steam engine, a steam boiler, or a steam plant of greater
capacity and horsepower than that authorized by his license;
and it shall also be unlawful tor any person to have charge
of or operate more than one plant at the same time. It
shall be unlawful for any engineer or fireman to be absent
from the steam boiler or the steam engine operated by him
for more than 20 min. nor to be farther distant from such
plant than 100 ft., while wo^ng under pressure.

It shall not be necessary to psocure a license to take charge
of or to operate a steam boiler used in private residences in
cases where the water returns automatically to the boiler and
the pressure does not exceed 10 Ib. per sq. in.

ENGINEERS' LICENSE LAWS 277

Omaha, Neb. — In the city of Omaha a board of engineers
administers and enforces the engineers' license laws. This
board consists of the city boiler inspector and two practical
and mechanical engineers, all of whom, are appointed by the
mayor, with the consent of the city council. The board con-
venes once in each month to examine into the qualifications
of applicants for engineers' certificates.

Every applicant for a certificate who fails to pass the exam-
ination of the board is required to wait 3 mo. before again
making application for a certificate. At the expiration of that
time, the board will give him another examination. Appli-
cants for examination will be furnished with a blank for the
purpose by the board. Applicants must have an experience
of at least 2 yr. at mechanical or steam engineering, and must
write and state their experience in the blank. All applica-
tions must be signed by two citizens, one of whom must be a
steam user or engineer. Each applicant is required to make
oath before the board as to the truth of the statements in the
blank. Engineers holding certificates granted by the board are
required to notify the board when accepting or leaving employ-
ment; also to state the name of the new employer and the
location of the boiler in their charge. This must be done
immediately.

Engineers holding certificates granted by the board are
required to make out a report as to the condition of all boilers
and apparatus under their charge and to send it to the board;
this must be done during the first 10 da. of January and July
of each year.

The board shall issue three grades of certificates, as follows: —
First-grade certificates shall entitle tha holder to take charge
of and run any plant; second-grade certificates shall entitle the
holder to take charge of and run any steam plant under 100
H. P., and third-grade certificates shall entitle the holder to
take charge of and run any steam plant under 50 H. P. The
board of engineers may grant to persons operating low-
pressure, gravity steam-heating plants, carrying a pressure
not to exceed 20 Ib. per sq. in., a special third-grade certifi-
cate to be valid for one particular specified plant and no
other.

278 ENGINEERS' LICENSE LAWS

A fee of $5 shall be charged for each examination of an
engineer for license by the board. Applicants must be at least
21 yr. of age. Certificates are valid for 1 yr. and no longer,
but may be renewed each year upon the payment of $1 to the
city treasurer and then presenting his receipt for the same to
the city boiler inspector; where boilers are used and engines run
night and day, the owners or users of steam power must employ
two certified engineers, who may stand watch alternately.

Peoria, 111. — A board of engineers consisting of three mem-
bers, including the city boiler inspector, appointed by the
Mayor and approved by the council administers and enforces
the license laws in the city of Peoria.

According to the laws, the board shall hold sessions twice
each month for the purpose of examining and determining the
qualifications of applicants for engineers' licenses. The certi-
ficates of license shall be of two grades — first and second — and
the requirements for each grade shall be determined by the
board of examiners.

Every application for a license must be made on the printed
blank furnished by the board for that purpose; that for an
engineer must be accompanied by a fee of $5, and that for a
boiler or a water tender must be accompanied by a fee of $2.
Licenses are in force for 1 yr. only from date of issue. Reissues
are made upon the payment of a fee of $2 for an engineer's
license and a fee of $1 for a boiler tender's license.

An applicant for license must have had a practice of at least
3 yr. under the supervision of a practical engineer. An appli-
cant for a boiler tender's license must be a person who has
a thorough knowledge of the construction, management, and
operation of steam boilers. Each applicant must state upon
the blank the extent of his experience, he must be at least 21 yr.
of age and a citizen of the United States, or have declared his
intention to become such, and he must be of good character.
All of this information must be vouched for in writing by at
least three first-class engineers of Peoria, or it may be verified
under oath by an applicant when required by the board.

It shall be the duty of the board of examiners to see that each
boiler plant in the city shall have a licensed engineer or boiler
or water tender, or both, in charge at all times when working

ENGINEERS' LICENSE LAWS 279

under pressure. Any person who has charge of a steam boiler,
whose duty it is to keep up the water in such boiler, shall be
deemed a boiler or water tender within the meaning of this
ordinance, but the provisions for the examining and licensing
of a boiler or water tender shall apply only to boiler or water
tenders who are in charge of a steam boiler or boilers that are
detached from the engine room or so far removed therefrom as
to render it difficult for the engineer in charge of the plant to-
give it or them his personal attention or supervision.

Every engineer licensed under this ordinance shall within
the first 10 da. of January and July, respectively, of each year,
make a written report to the board of examiners of the condition
of the engine, boilers, and steam apparatus under his charge,
and every boiler or water tender shall at the same time make a
similar report of the condition of the boiler or boilers under
his charge.

Engineers in charge of locomotives are exempt from the
provisions of this ordinance, as are also all boilers used for
heating private dwellings and hothouses and other boilers
carrying a pressure of not more than 10 Ib. per sq. in., and the
persons operating them.

Philadelphia, Pa. — It is unlawful for any person or persons
to have charge of or to operate a steam boiler or steam .engine
over 10 H. P. in cities of the first class of the commonwealth
of Pennsylvania, except locomotive boilers used in transporta-
tion and steam engines and steam boilers carrying a pressure
of less than 15 Ib. per sq. in., unless said person or persons are
upward of 21 yr. of age and hold a license as provided for by
the laws.

The laws state that all persons desiring authority to perform
the duties of an engineer shall apply to the boiler inspector of
such cities, who shall examine the applicant as to his knowledge
of steam machinery and his experience in operating the same,
also the proofs he produces in support of his claim; and if the
inspector is satisfied that the applicant's character, knowledge,
and experience in the duties of an engineer are such as to
authorize the belief that he is a suitable person to be entrusted
with the powers and duties of such station, he shall grant him
a license, on the payment of $3, authorizing him to be employed

280 ENGINEERS' LICENSE LAWS

in such duties for the term of 1 yr., and such license shall be
annually renewed, without examination, upon the payment
of $1, provided it is presented for renewal within 10 da. after
its expiration.

Licenses so granted shall be graded into two classes, one of
which shall entitle the licensee to have charge of or to operate
stationary steam boilers and steam engines only, and the other
of which shall entitle the licensee to have charge of or to operate
portable steam boilers and steam engines only. Such licenses
shall not be transferred from one grade to the other without a
reexamination, said reexamination to be conducted without
cost to the licensee.

No person shall be eligible for examination for license unless
he furnishes proof that he has been employed about a steam
boiler or steam engine for a period of not less than 2 yr. prior
to the date of application, which must be certified to by at
least one employer and two licensed engineers.

The inspector shall have authority to suspend or revoke
licenses upon proof of negligence or incompetency of the holders
of licenses. Licenses must be framed under glass and placed
in a conspicuous place about the engine or boiler rooms. When
a licensed engineer vacates a position, he must notify the boiler
inspector of that fact.

Pittsburg, Pa. — See Pennsylvania state laws, on page 250.

Rochester, N. Y. — The ordinance governing the granting of
engineers' licenses in Rochester, N. Y., is in part as follows:
No person shall operate any boiler to generate steam within
the city of Rochester, except for railroad locomotive engines
and for heating purposes in private dwellings, unless he be 21 yr.
of age and shall have been duly examined and licensed for that
purpose as required by the terms of this ordinance.

The common council of the city shall appoint a committee
of three competent persons to examine all applicants for license
to operate steam boilers and to issue licenses to such applicants
as shall be found qualified.

Applications for examinations shall be made in writing to
the city clerk, and must state the location and capacity of the
boiler plant that the applicant intends to operate. Every appli-
cation must be accompanied by a certificate of two reputable

ENGINEERS' LICENSE LAWS 281

persons to the effect that the applicant is of good character.

The examining committee shall hold meetings at least twice
each month for the transaction of business and the conduct of
examinations of engineers. In case an applicant upon his first
examination shall fail to satisfy the committee of his ability to
operate the boiler plant mentioned in his application, a tem-
porary permit may be granted to him to operate the plant for
a period not exceeding 20 da., at which time the applicant
must again present himself for examination. Such temporary
permit shall not be granted more than once to the same person.

Every person found qualified by the committee to operate
a steam boiler shall be entitled to receive a license for that
purpose. The fee for such license is $2, to be paid to the city
treasurer. Licenses expire at the end of the year from the date
of issuance, and may be renewed for a term of 1 yr. on the pay-
ment to the city treasurer of $1. In case of a change of position,
licensed engineers, under this act, shall notify the city clerk
within 1 wk. of such change and present themselves for exami-
nation for the new position. If found qualified for the new posi-
tion, a license to operate the new plant for the unexpired part
of the year covered by the original license shall be issued with-
out further fee.

The common council of the city of Rochester has the power
to suspend or revoke a license at any time upon proof of negli-
gence or incompetency.

Santa Barbara, Cal. — A board of examining engineers, con-
sisting of three members appointed by the mayor, administers
and enforces the license laws in the city of Santa Barbara, Cal.
It is the duty of the board to examine all applicants for engi-
neer's license. The board shall hold one meeting a month —
on the second Tuesday — for the purpose of examining appli-
cants for license.

Licenses are granted for a term of 1 yr. upon a payment of $3
from each applicant. They may be revoked by the board upon
proof of incompetency or neglect on the part of the licensee.
Where boilers are used and engines are run night and day, the
owner or the us'er must employ at least two licensed engineers,
who may stand watch alternately. Boilers or steam -generating
apparatus of 5 H. P. or over must be operated by a competent

282 ENGINEERS' LICENSE LAWS

engineer who has secured a license. Automobiles are exempt
from the provisions of this ordinance, as are also all engines
and boilers of locomotives used on railroads.

Every applicant for a license who fails to pass the examina-
tion of the board shall be required to wait 4 wk. before making
another application. Any applicant who fails to pass after the
third trial shall not be permitted to appear again before the
board for 4 mo.

Engineers shall notify the boiler inspector when they enter
any employment as an engineer, and within 3 da. after give the
name of the employer and the location of the boiler or other
apparatus in charge. They also shall report the condition of
the apparatus under their charge semiannually, during the
first 3 da. of January and July of each year. Licenses must
be framed under glass and placed in a conspicuous place near
the boilers or engines.

St. Joseph, Mo. — A board of engineers consisting of the city
boiler inspector and two mechanical engineers, all of whom are
appointed by the mayor, with the consent of the common coun-
cil, administers and enforces the license laws in St. Joseph, Mo.

The board convenes for business twice each month to examine
into the qualifications of applicants for engineer's license. The
law states that the board shall grant licenses, charging each
applicant the sum of $10 for engineer's license, $3 to be depos-
ited with the clerk of the board when application is made.
Each applicant is to be allowed three trials. If he then fails to
pass a satisfactory examination, the applicant shall then forfeit
the money deposited with the clerk of the board; but if the
applicant successfully passes the examination, the board shall
grant him a license for the term of 1 yr. upon the paymert of
an additional $7. The fee for each annual renewal of license
shall be $2.50.

Any person taking charge of a steam boiler or steam boilers,
for heating purposes only, shall be examined by the board of
engineers, and if found qualified the board shall grant him a
license to that effect on the payment of $5, said license to be in
force for 1 yr. from the date of issue. Such licenses may be
reissued upon the payment of a fee of $2. The board has the
power to revoke licenses upon proof of incompetency or neglect.

ENGINEERS' LICENSE LAWS 283

When boilers are used and engines run night and day, two
licensed engineers must be employed and must stand watch
alternately.

All engineers, engines, and boilers of the fire department of
St. Joseph and all steam rollers, steam automobiles, and portable
boilers used on the streets of the city are subject to the provi-
sions of this ordinance, except that there shall be no fee charged
for the inspection of boilers of fire engines; but all locomotive
boilers used on railroads and steam boilers supplied with water
automatically, when used for heating dwellings and not carrying
a pressure of over 10 Ib. per sq. in., are exempt from the provi-
sions of this ordinance.

Every applicant for license who fails to pass the examination
is required to wait 2 wk. before again making application for
license. If applicants fail to pass after the third trial, they may
not make application again for 6 mo.

Engineers must notify the boiler inspector upon accepting
employment as an engineer; and, within 3 da. after, he must
give the name of his employer and the location of the boiler or
boilers under his care. Renewals for license shall be made not
later than the first regular meeting of the board next following
the expiration of the license. Unless this provision is complied
with, it shall be necessary for the applicant to be reexamined,
to take out a new license, and to pay the regular fee before
referred to.

St. Louis, Mo. — In the city of St. Louis the engineers' license
laws are administered and enforced by a board of engineers
consisting of the city inspector of boilers and elevators and two
other members, all of whom are appointed by the mayor, with
the consent of the council. This board convenes for business
once in each week to examine applicants for engineers' license.

According to the laws, the board shall giant certificates of
license for 1 yr. from the date thereof to all applicants who pass
the required examination and satisfy the board as to their
fitness. Each applicant for license shall at the time of filing
his application, pay to the inspector of boilers and elevators
a fee of $2, for each examination, but no charge is made for
renewals. Licenses may be revoked by the board, upon proof
of incompetency or neglect on the part of the licensee.

284 ENGINEERS' LICENSE LAWS

The owners or users of steam boilers or engines of a capacity
of not over 75 sq. ft. of heating surface, and a steam pressure
of not over 25 Ib. per sq. in., used for power only, and all boilers
under a pressure of 15 Ib. per sq. in. used for heating purposes
only, shall apply for a permit to employ a competent, careful,
and trustworthy person, instead of a licensed engineer; such
person to be recommended by two citizens, one of whom shall
be a steam user or a licensed engineer, and if found competent
by the inspector of boilers and elevators, said permit shall be
granted. The inspector of boilers and elevators may revoke
such permit for cause.

At all times when boilers are in use and engines run there
shall be in charge an engineer having a certificate of license
from the board of engineers, such certificate to be displayed
in some prominent place where the boilers or engines are in
use.

The engineers, engines, and boilers of the fire department,
locomotive boilers used on railroads, and steam boilers sup-
plied with water automatically, and having no pumps or injec-
tors and used only for heating dwellings, not carrying a steam
pressure of more than 8 Ib. per sq. in., are exempt from the pro-
visions of this ordinance.

Every applicant for license who fails to pass the examina-
tion of the board is required to wait 4 wk. before again making
application for license. Applications for license must be made
upon blanks furnished by the inspector of boilers and eleva-
tors. The applicant must have had an experience of at least
2 yr. at mechanical or steam engineering, and must write and
state his experience on said blank. He shall go before the
inspector of boilers and elevators and make oath that his
statements are true.

Licensed engineers must give to the inspector of boilers and
elevators notice of changes of employment when he accepts
or leaves his position, and within 24 hr. thereafter he must
give the name of his employer and the location of the boilers
in his charge. Licensed engineers must make semiannual
reports of the condition of all apparatus under their charge to
the inspector of boilers and elevators during the first 10 da.
of January and July.

ENGINEERS' LICENSE LAWS 285-

Scranton, Pa. — See Pennsylvania state laws, on page 250.

Sioux City, la. — A board of examining engineers consisting
of three persons, all of whom are appointed by the mayor,
with the consent of the city council, administers and enforces
the license laws in Sioux City, la.

It is the duty of the board of examining engineers to grant
licenses of the first, second, and third grade to persons examined
and found qualified. A first-class license qualifies the holder
to take charge of boilers of 125 H. P. or over; a second-class
license, to take charge of boilers of 25 H. P. or over, up to 125
H. P.: and a third-class license, to take charge of all boilers
of less than 25 H. P., 12 sq. ft. of heating surface to constitute
1 H. P. The certificates so granted shall run for 1 yr., at which
time they shall be renewed. The board of examiners has the
power to revoke licenses upon proof of incompetency or negli-
gence on the part of licensees.

Steam boilers or engines of a capacity of not over 75 sq. ft.
of heating surface with a pressure of not over 25 Ib. per
sq. in., and all boilers not exceeding 75 sq. ft. of heating
surface under a pressure of 15 Ib. per sq. in. used for heating
only, require a person with a permit only, instead of an engi-
neer holding a license. Such person must be recommended
by two citizens of Sioux City, one of whom shall be an engi-
neer holding a license from the board of engineers. Permits
are granted by the board to the proper persons.

When any boiler or engine requiring the services of an
engineer holding a first-class license is run day and night, the
owner or user may employ an engineer holding a second-class
license, not exceeding 12 hr. at a time, under the instructions
of an engineer in charge, holding a first-class license.

Applications for license must be made on blanks furnished
by the board of examining engineers. Licensed engineers
must notify the board when they accept or leave employment,
and within 10 da. after, the name of employer and the location
of the boilers must be given. Applications for renewals of
license or permits shall be made not later than the third week
preceding their expiration.

In case of the failure of any applicant for a license to pass-
the examination, he may within 10 da. after receiving notice
20

286 ENGINEERS' LICENSE LAWS

of such failure make written application to the mayor of the
city and also to the board of examining engineers for a second
examination, which shall be granted by the board within 10
da. after such application is made. Failure to comply with
the foregoing requirements as to a second examination neces-
sitates the applicant waiting the pleasure of the board as to
when he may be again examined, such time, however, must
not exceed G mo.

No person shall be granted a first-class license until he gives
satisfactory proof that he has had an experience of 5 yr. in
steam engineering. No person shall be granted a second-class
license until he gives satisfactory proof that he has had an
experience of 3 yr. in steam engineering. No person shall be
granted a third-class license until he gives satisfactory proof
that he has had an experience of 2 yr, in steam engineering.
For all the grades of licenses, the sum of $3 each shall be charged
and for each annual renewal of licenses the sum of $1 shall
be charged by the board of examining engineers. The provi-
sions of this ordinance shall not apply, and shall not be con-
strued to be applicable to, boilers or steam generators of any
kind used for heating private residences only, nor to persons
in charge of them.

Spokane, Wash. — The board of public works administers
and enforces the license laws in the city of Spokane.

Every engineer must appear before the examiner appointed
by the board of public works for examination as to qualifi-
cations to act as engineer in the city of Spokane. Applicants
for examination as engineer shall pay the examiner a fee of
50c. Every person receiving a permit from the board of
public works to run or operate a steam engine or boiler, before
acting as such, shall pay to the city treasurer a semiannual
license fee of $1, and no license shall be granted for a shorter
period. Upon presenting the treasurer's receipt for the fee
and the permit from the board of public works to the comp-
troller, that officer shall issue a license for a period of 6 mo.

All engineers shall instruct all night watchmen, or other
persons whose duty it may be to get up steam, as to their duty
and the practical mode of procedure, but no night watchmen
or other person not a licensed engineer shall be permitted by

ENGINEERS' LICENSE LAWS 287

reason of this clause to operate continuously any steam engine
or boiler to which this ordinance applies. Applications for
license must be made in writing to the board of public works.
Nothing in this ordinance shall apply to locomotive engines
or boilers.

Tacoma, Wash. — In the city ot Tacoma a board of examiners
consisting of the city boiler inspector and two other persons
all of whom are appointed by the mayor, administers and
enforces the engineers' license laws.

Any person desiring to procure a license as a stationary
engineer may apply for it to the boiler inspector upon an appli-
tion blank furnished by the inspector. He shall then be exam-
ined as to his qualifications as a stationary engineer by the
examiners. At the conclusion of the examination, the board
of examiners shall transmit to the city council all papers used
in the examination, including all questions and answers given,
together with the recommendation of the board as to its find-
ings. The city council decides as to whether or not a license
shall be granted the applicant.

Licenses are for a period of 1 yr. and the fee for a license
is $2, payable to the city treasurer. Upon the expiration of
a license and upon the payment of a fee of $1 to the city treas-
urer, the board of examiners may recommend a renewal of
the same, without further examination of the applicant, for a
period of 1 yr.

The licenses granted are classified as follows: First-class
or chief engineer's license which entitles the holder to take
charge of and control the operation of any steam plant in the
city of Tacoma; second-class, or assistant engineer's license,
which entitles the holder to take charge of and control the
operation of any steam plant in the city not exceeding 150 boiler
H. P., or to act as assistant engineer to the chief engineer of
any steam plant in the city; third-class engineer's license,
which entitles the holder to take charge of and control the
operation of any steam plant in the city not exceeding 50 boiler
H. P., or to act as ar assistant engineer to an engineer of the
second class or as a second assistant engineer to an engineer of
the first class; fourth-class, or special-engineer's license, which
entitles the holder to take entire charge and control of a

288 ENGINEERS' LICENSE LAWS

particular steam plant for which the same license is granted,
as stated upon its face.

This ordinance does not apply to locomotive or marine
engineers, nor to persons having charge of steam boilers, or
apparatus used in private dwellings for heating purposes only,
in which the steam pressure does not exceed 10 Ib. per sq. in.
while in operation.

Terre Haute, Ind. — A board of examining engineers con-
sisting of three members appointed by the mayor, subject to
confirmation by the common council, administers and enforces
the license laws in the city of Terre Haute.

Any person desiring to operate or to have charge of any
steam boiler or steam-generating apparatus under steam pres-
sure within the meaning of this act shall make a verified appli-
cation to the board of examiners for a license to do so. The
application shall be in writing, giving particulars as to expe-
rience, and attached thereto shall be a certificate of at least
two freeholders or householders to the effect that the appli-
cant for license is known to be a fit person to have charge of
steam-generating apparatus. The applicant must pay $3
to the board of examiners before the examination is entered
upon. If the applicant is found qualified, a license is issued
to him.

Applicants must be American citizens at least 21 yr. of age
and must have had at least 2 yr. experience in firing stationary
steam boilers or steam-generating apparatus, or must have an
actual experience of at least 1 yr. in the operation, management,
and control of steam engines or boilers or steam-generating
apparatus.

Examinations shall be made in writing, except by agreement
between the applicant and the board. All grading of such
examinations shall be upon the percentage basis. Three
grades of licenses — namely, first-class, second-class, and third-
class — are issued. Third-class licenses authorize the holder
only to operate a steam engine, engines, or other steam-gen-
erating apparatus under the direct supervision of a person
•or persons holding a first-class or a second-class license.

An applicant who has had 5 yr. or more of actual experi-
ence as an engineer, and who is otherwise qualified, and who,

ENGINEERS' LICENSE LAWS 289

on examination, makes a grade of 90% or more, shall be
entitled to a first-class license. An applicant who is ocher-
wise qualified, and who makes 75% or more, and less than
90%, shall be entitled to a second-class license. An applicant
who is otherwise qualified, and who makes 60% or more, and
less than 75%, shall be entitled to a third-class license. The
board has the power to suspend or revoke licenses upon proof
of incompetency or neglect.

All licenses must be renewed 1 yr. from date of issue, and
the fee for such renewal is $2. If any licenses are not renewed,
within 10 da. after the expiration of such, the fee for renewal
shall be $3.

Engineers in charge of locomotives are exempt from the
provisions of this ordinance, as are also persons who operate
boilers used for heating purposes only, not carrying more than
15 Ib. of steam pressure per square inch.

Washington and District of Columbia. — In the District of
Columbia, which includes the city of Washington, all persons
applying for a steam engineer's license shall be examined by a
board of examiners composed of the boiler inspector of the
District of Columbia and two practical engineers, to be
appointed by the district commissioner.

Applicants for license must be at least 21 yr. of age and of
good character, and certified to by at least three citizens of the
District of Columbia, themselves of good character. Applica-
tion must be made in writing. The fee for a license as steam
engineer is $3. Licenses may be revoked upon proof of negli-
gence on the part of licensee.

It is unlawful for any person to act as a steam engineer who
is not regularly licensed to do so by the commissioners of the
District of Columbia. Boilers, and operators of same used for
heating purposes, where the water returns to the boiler without
the use of a pump, injector, or inspirator, are exempt from the
provisions of this act. Engineers licensed by the United States
government are also exempt.

Yonkers, N. Y. — In the city of Yonkers, N. Y., a board of
examiners consisting of three members appointed by the mayor,
with the consent of the common council, administers and
enforces the license laws.

290 ENGINEERS' LICENSE LAWS

According to the law, it shall be the duty of the board of
examiners to examine all persons proposing to operate, manage,
or run steam boilers or engines, and to certify the qualifications
of such as are found competent as either first- or second-class
engineers. Persons desiring examination shall apply to that
member of the board officially known as the inspector of engi-
neers and of steam boilers in the city of Yonkers. Application
must be in writing, specifying in full the experience of the appli-
cant and stating where, how and by whom employed; also, the
application must contain the names of at least three residents
of the city who can vouch for the good character of the appli-
cant. Upon receiving such application, the inspector notifies
the board of examiners, who in turn notifies the applicant as
to the time and place of examination.

There shall be two classes of licenses issued — one to first-
class engineers and one to second-class engineers.

A license for a second-class engineer shall authorize the
person to whom it is issued to have charge of a steam boiler
only when not connected with any engine, or when the engine
connected therewith shall not be running or in operation. All
licenses shall be for 1 yr. from the date of issue. Licenses
may be renewed by the board for a period of 1 yr.

No license will be issued by the board to any person who
lacks ability, knowledge or experience, and who has not a good
character.

Licenses may be revoked by the board upon proof of neglect
or incompetency.

For the examination of engineers, the sum of $2 must be
paid by each applicant, and for each renewal of same, 50c.

This ordinance does not apply to railroad locomotives used
as such, nor to boilers actually used for propelling steam vessels
navigating the Hudson River, when the same shall have been
inspected and licensed according to the United States laws;
nor does it apply to steam boilers used solely for heating pur-
poses, or the persons operating them.

ENGINEERS' LICENSE LAWS 291

EXTRACTS FROM UNITED STATES LAWS

Following is a true copy of certain sections from the United
States Marine Laws, the sections relating to the licensing of
marine engineers:

''1. Before an original license is issued to any person to
act as a master, pilot, or engineer, he must personally appear
before some local board or a supervising inspector for examina-
tion; but upon the renewal of such license, when the distance
from any local board or supervising inspector is such as to put
the person holding the same to great inconvenience and expense
to appear in person, he may, upon taking oath of office before
any person authorized to administer oaths, and forwarding
the same, together with the license to be renewed, to the local
board or supervising inspector of the district in which he
resides or is employed, have the same renewed by the said
inspectors, if no valid reason to the contrary be known to them;
and they shall attach such oath to the stub end of the license
which is to be retained on file in their office: Provided, how-
ever, That any officer holding a license, and who is engaged
in a service which necessitates his continuous absence from
the United States, may make application in writing for one
renewal and transmit the same to the board of local inspect-
ors with a statement of the applicant, verified before a consul
or other officer of the United States authorized to administer
an oath, setting forth the reasons for not appearing in person,
and upon receiving the same the board of local inspectors
that originally issued such license shall renew the same for
one additional term of such license, and shall notify the
applicant of such renewal.

" The first license issued to any person by a United States
inspector shall be considered an original license, where the
United States records shows no previous issue to such appli-
cant."

'' No original license shall be issued to any naturalized
citizen on less experience in any grade than would have been
required of an American by birth.

" 2. All licenses hereafter issued to masters, mates, pilots,
and engineers shall be filled out on the face with pen and ink

292 ENGINEERS' LICENSE LAWS

instead of typewritten. Inspectors are directed, when licenses
are completed, to draw a broad pen and black ink mark
through all unused spaces in the body thereof, so as to prevent
as far as possible, illegal interpolation after issue.

"3. Licensed officers serving under 5 yr. license, entitled by
license and service to raise of grade, shall have issued to them
new licenses for the grade for which they are qualified, the
local inspectors to forward to the Supervising Inspector-General
the old license when surrendered, with the report of the cir-
cumstances of the case.

"But the grade of no license shall be raised, except as herein-
after provided, unless the applicant can show 1 yr. actual
experience in the capacity for which he has been licensed.

"4. In case of loss of license, of any class, from any cause,
the inspectors, upon receiving satisfactory evidence of such loss,
shall issue a certificate to the owner thereof, which shall have
the authority of the lost license for the unexpired term, unless
in the meantime the holder thereof shall have the grade of his
license raised after due examination; in which case a license
in due form for such grade may be issued.

"5. Inspectors shall, before granting an original license to
any person to act as an officer of a vessel, require the applicant
to make his written application upon the blank form author-
ized by the Board of Supervising Inspectors, which application
shall be filed in the records of the Inspectors' office. Inspectors
shall also, when practicable, require applicants for pilot's
license to have the written indorsement of the master and engi-
neer of a vessel upon which he has served, and of one licensed
pilot, as to his qualifications. In case of applicants for original
engineer's license, they shall also, when practicable, have the
indorsement of the master and engineer of a vessel on which
they have served, together with one other licensed engineer.

''6. No original master's, mate's, pilot's, or engineer's
license shall be issued hereafter or grade increased except upon
written examination, which written examination shall be
placed on file as records of the office of the inspectors issuing
said license; and, before granting or renewing a license, inspec-
tors shall satisfy themselves that the applicants can properly
hear the bell and whistle signals.

ENGINEERS' LICENSE LAWS 293

"7. Any applicant for license who has been duly examined
and refused may come before any local board for reexamination
after 1 yr. has expired.

"8. When any person makes application for license it shall
be the duty of the local inspectors to give the applicant the
required examination as soon as practicable.

"9. Any person who has served at least 1 yr. as master,
commander, pilot, or engineer of any steam vessel of the United
States in any service in which a license as master, mate, pilot,
or engineer was not required at the time of such service, shall
be entitled to license as master, mate, pilot, or engineer, if the
inspectors, upon written examination, as required for appli-
cants for original license, may find him qualified: Provided,
That the experience of any such applicant within 3 yr. of making
application has been such as to qualify him to serve in the
capacity for which he makes application to be licensed.

"Any officer of the Naval Militia who is an applicant for
license as chief engineer or assistant engineer of steam vessels
of the Naval Militia may be examined by inspectors and
granted a special license as such, and for no other purpose, if,
in the judgment of the inspectors, he is qualified. And the
inspectors shall state on the license the name of the vessel on
which such master, mate, pilot, or engineer is authorized to act
in the capacity for which he is licensed.

"All licenses issued to officers of the Naval Militia provided
for in the preceding paragraph of this section shall be surren-
dered upon the party holding it becoming disconnected from the
Naval Militia by resignation or dismissal from such service;
and no license shall be issued as above except upon the official
recommendation of the chief officer in command of the Naval
Militia station of the State in which the applicant is serving.

"10. No person holding special license (Form 878) shall be
eligible for examination for a higher grade of license until such-
person has actually served two full seasons under the authority
of his license and one additional full season in a subordinate
capacity upon steamers requiring regularly licensed officers.

"11. Whenever an officer shall apply for a renewal of his
license for the same grade the presentation of the old certificate
shall be considered sufficient evidence of his litle to renewal,

294 ENGINEERS' LICENSE LAWS

which certificate shall be retained by the inspectors upon their
official files as the evidence upon which the license was renewed:
Provided, That it is presented within 12 mo. after the date of
its expiration, unless such title has been forfeited or facts shall
have come to the knowledge of the inspectors which would
render a renewal improper; nor shall any license be renewed
in advance of the date of the expiration thereof, unless there are
extraordinary circumstances that shall justify a renewal before-
hand, in which case the reasons therefor must appear in detail
upon the records of the inspectors renewing the license.

"12. When the license of any master, mate, pilot, or engineer
is revoked such license expires with such revocation, and any
license subsequently granted to such person shall be considered
in the light of an original license. And upon the revocation or
suspension of the license of any such officer said license shall be
surrendered to the local inspectors ordering such suspension or
revocation.

"13. The suspension or revocation of a joint license shall
debar the person holding the same from the exercise of any of
the privileges therein granted, so long as such suspension or
revocation shall remain in force.

"14. When the license of any master, mate, pilot, or engineer
is suspended, the inspectors making such suspension shall
determine the term of its duration, except that such suspension
cannot extend beyond the time for which the license was issued.

CLASSIFICATION OF ENGINEERS

"20. Chief engineer of ocean steamers.

"Chief engineer of condensing lake, bay, and sound steamers.

"Chief engineer of non-condensing lake, bay, and sound
steamers.

"Chief engineer of condensing river steamers.

"Chief engineer of non-condensing river steamers.

"Any person holding chief engineer's license shall be per-
mitted to act as first assistant on any steamer of double the
tonnage of same class named in said chief's license.

"Engineers of all classifications may be allowed to pursue
their profession upon all waters of the United States in the
class for which they are licensed.

ENGINEERS' LICENSE LAWS 295

FIRST ASSISTANT

"First assistant engineer of ocean steamers.

"First assistant engineer of condensing lake, bay, and sound
steamers.

"First assistant engineer of non-condensing lake, bay, and
sound steamers.

"First assistant engineer of condensing river steamers.

"First assistant engineer of non-condensing river steamers.

" Engineers of lake, bay, and sound steamers, who have actu-
ally performed the duties of engineer for a period of 3 yr., shall
be entitled to examination for engineer of ocean steamers, appli-
cant to be examined in the use of salt water, method employed
in regulating the density of the water in boilers, the application
of the hydrometer in determining the density of sea water, and
the principle of constructing the instrument; and shall be
granted such grade as the inspectors having jurisdiction on the
Great Lakes and seaboard may find him competent to fill.

"Any assistant engineer of ocean steamers of 1,500 gr. T.
and over, having had actual service in that position for 1 yr.
may, if the local inspectors, in their judgment, deem it advis-
able, have his license indorsed to act as chief engineer on lake,
bay, sound or river steamers of 750 gr. T. or under.

"Any person having had a first assistant engineer's license
for 2 yr. and having had 2 yr. experience as second assistant
engineer, shall be eligible for examination for chief engineer's
license.

SECOND ASSISTANT

"Second assistant engineer of ocean steamers.

"Second assistant engineer of condensing lake, bay, and
sound steamers.

"Second assistant engineer of non-condensing lake, bay, and
sound steamers.

"Second assistant engineer of condensing river steamers.

"Any person having had a second assistant engineer's
license for 2 yr., and having had 2 yr. experience as third
assistant engineer, shall be eligible for examination for first
assistant engineer's license.

THIRD ASSISTANT

"Third assistant engineer of ocean steamers.

296 ENGINEERS' LICENSE LAWS

"Third assistant engineer of condensing lake, bay, and sound
steamers.

"First, second, and third assistant engineers may act as such
on any steamer of the grade of which they hold license, or as
such assistant engineer on any steamer of a lower grade than
those to which they hold a license.

"Any person having a third assistant engineer's license for
2 yr., and having had 2 yr. experience as oiler or water tender
since receiving said license, shall be eligible for examination for
second assistant engineer's license.

"Inspectors may designate upon the certificate of any chief
or assistant engineer the tonnage of the vessel on which he may
act.

"Any assistant engineer may act as engineer in charge on
steamers of 100 T. and under. In all cases where an assistant
engineer is permitted to act as engineer in charge, the inspectors
shall so state on the face of his certificate of license without
further examination.

"21. It shall be the duty of an engineer when he assumes
charge of the boilers and machinery of a steamer to forthwith
thoroughly examine the same, and if he finds any part thereof
in bad condition, caused by neglect or inattention on the part
of his predecessor, he shall immediately report the facts to the
master, owner, or agent, and to the local inspectors of the dis-
trict, who shall thereupon investigate the matter, and if the
former engineer has been culpably derelict of his duty, they
shall suspend or revoke his license.

"22. Before making general repairs to a boiler of a steam
vessel the engineer in charge of such steamer shall report, in
writing, the nature of such repairs to the local inspector of the
district wherein such repairs are to be made.

"And it shall be the duty of all engineers when an accident
occurs to the boilers or machinery in their charge tending to
render the further use of such boilers or machinery unsafe until
repairs are made, or when, by reason of ordinary wear, such
boilers or machinery have become unsafe, to report the same to
the local inspectors immediately upon the arrival of the vessel
at the first port reached subsequent to the accident, or after the
discovery of such unsafe condition by said engineer.

ENGINEERS' LICENSE LAWS 297

"23. Whenever a steamer meets with an accident involving
loss of life or damage to property it shall be the duty of the
licensed officers of any such steamer to report the same in
writing and in person without delay to the nearest board.
Provided, That when from distance it may be inconvenient
to report in person it may be done in writing only and the report
sworn to before any person authorized to administer oaths.

"24. No person shall receive an original license as engineer
or assistant engineer (except for special license on small pleasure
steamers and ferryboats of 10 T. and under, sawmill boats,
pile drivers, boats exclusively engaged as fishing boats, and
other similar small vessels), who has not served at least 3 yr.
in the engineer's department of a steam vessel, a portion of
which experience must have been obtained within the 3 yr.
next preceding the application.

"Provided, That any person who has served 3 yr. as appren-
tice to the machinist trade in a marine, stationary, or locomotive
engine works, and any person who has served for a period of not
less than 3 yr. as a locomotive or stationary engineer, and any
person graduated as a mechanical engineer from a duly recog-
nized school of technology, may be licensed to serve as an
engineer of steam vessels after having had not less than 1 yr.
experience in the engine department of steam vessels, a portion
of which experience must have been obtained within the 3 yr.
preceding his application; which fact must be verified by the
certificate in writing, of the licensed engineer or master under
whom the applicant has served, said certificate to be filed with
the application of the candidate; and no person shall receive
license as above, except for special license, who is not able to
determine the weight necessary to be placed' on the lever of a
safety valve (the diameter of valve, length of lever, distance
from center of valve to fulcrum, weight of lever, and weight of
valve and stem being known) , to withstand any given pressure
of steam in a boiler, or who is not able to figure and determine
the strain brought on the braces of a boiler with a given pressure
of steam, the position and distance apart of braces being known,
such knowledge to be determined by an examination in writing,
and the report of examination filed with the application in
the office of the local inspectors, and no engineer or assistant

298 ENGINEERS' LICENSE LAWS

engineer holding a license shall have the grade of the same
raised without possessing the above qualifications. No original
license shall be granted any engineer or assistant engineer who
cannot read and write and does not understand the plain rules
of arithmetic.

"25. Any person may be licensed as engineer (on Form
2130J) (New Form 880) on vessels propelled by gas, fluid,
naphtha, or electric motors, of 15 gr. T. or over, engaged in
commerce, if in the judgment of the inspectors, after due
examination in writing, he be found duly qualified to take charge
of the machinery of vessels so propelled.

"Any person holding a license as engineer of steam vessels,
desiring to act as engineer of motor vessels, must appear before
a board of local inspectors for examination as to his knowledge
of the machinery of such motor vessels, and if found qualified
shall be licensed as engineer of motor vessels. Form 878,
special license to engineers, shall be issued only to engineers in
charge of vessels of 10 T. and under. All other licenses to
engineers shall be issued on Forms 876 and 877, according to
grades specified in this section."

MEMORANDA

MEMORANDA

Promotion
Advancement in Salary

and

Business Success

Secured
Through the

STEAM

Steam-Electric

Engine Running

Stationary Firemen's

Engine and Dynamo Running

Locomotive Running

COURSES OF INSTRUCTION
OF THE

International
Correspondence Schools

International Textbook
Company, Proprietors

SCRANTON, PA., U. S. A.

^-^" SEE FOLLOWING PAGES ^S^

21

Salary Increased 450
Per Cent.

For several years I had charge of small steam
plants which paid me about $20 a month.
An I. C. S. Representative put the correspond-
ence school question up to me in such a way
I felt it plainly marked "Opportunity." I
subscribed for the Engine Running Course, and
began studying in my spare moments. Night
after night, when the little ones were in dream-
land, I was digging into the technicalities of
steam engineering.

My reward is being gathered each week as I
receive my pay envelope, increased- by 450 per
cent, over what it was when I bought the Course.

I now have charge of a new steam-electric
plant of about 850 horsepower, having from
five to eight men in my department. The
position I fill was won only by the preparation
the I. C. S. gave me. I know of no other way
I could have prepared myself for this position.
I have my diploma from the I. C. S., and I prize
it more highly than any mark of honor I have
received.

To all ambitious men I say, "To succeed you
need only pluck, push, perseverance, and a
Course in the I. C. S."

J. EDGAR WILLIAMS,
315 Cable St., Indianapolis, Ind.

IGNORANCE HINDERS; THE I. C. S. HELPS

S. T. RICHARDSON, Grosse lie, Mich., found himself stuck
fast in a night engineer's position, unable to advance because
of a defective education. Knowing nothing of fractions, nor
even of division, he took up our Complete Steam Engineering
Course. By so doing he fitted himself for the position which
he now holds as chief engineer at a salary of $125 a month.

150 PER CENT. INCREASE

That it pays an engineer to acquire a first-class knowledge of
everything connected with his work is proved by the case of
C. W. FELLOWS, First National Bank Building, Houston, Tex.
He was earning $70 a month when he enrolled for the Station-
ary Engineers' Course. He is now general superintendent of
a large office building, having 20 men at work under his direc-
tion. His salary has increased 150 per cent.

CHOSEN AHEAD OF MANY OTHERS

ELVIN THOMPSON, Afount Vernon, Ohio, had only a little
education and was working as a fireman when he enrolled for
the Stationary Engineers' Course. After graduating from the
Course, he made application for the position of engineer in the
State Sanitarium. Although there were hundreds of appli-
cants, he was chosen. He is now considered an authority on
steam engineering and his salary is 200 per cent, larger than
when he enrolled.

ONE THOUSAND DOLLARS A YEAR LARGER

W. A. BERGER, Hotel Rome, Omaha, Neb., was working in
a factory when he enrolled for the Stationary Engineers' Course.
He praises the I.C.S. because they have advanced him to the
position of chief engineer of the Hotel Rome and Hotel Millard,
increasing his salary about one thousand dollars a year.

EARNS $150 A MONTH

• CLARENCE GRETTUM, Innisfail, Alberta, Can., had obtained
so little education that he could barely read and write when he
enrolled for the Complete Steam Engineers' Course. At the
time he was earning $60 a month working twelve hours a day
as a fireman. He has now taken charge of the Municipal
Electric Light Plant of his city at a salary of $150 a month.

500 PER CENT. LARGER

When ARNOLD W. RIDLEY, 3256 Madison St., Denver, Colo.,
enrolled with the I.C.S. for the Steam Engineering Course he
was employed as a helper. He declares that a fireman's
practical experience combined with the I.C.S. training will make
an efficient engineer. He is now plant superintendent for the
Denver Gas & Electric Co. His salary has increased about
500 per cent.

300 Per Cent. Increase

Because of the death of his father, leaving
his mother on her own resources, R. J. BISSETT,
814-16 Columbia Building, Cleveland, Ohio,
was obliged to leave school and compelled to go
to work at the age of 13. While he was earn-
ing $2.75 a day as an engineer at the age of 34,
he enrolled with the I. C. S. for the Stationary
Engineers' Course. One year later he was
made superintendent of the Chamberlain &
Target Company, and his salary increased.
This position he held for about 10 years. For
the past 8 years he has been the president of
the R. J. Bissett Company, handling steam
appliances, having now 20 agents under his
direct supervision. His income has increased
300 per cent., and sometimes rises even higher.

PRAISES THE SCHOOLS

C. S. COUPLAND, Box -17, Maricopa, Calif., says that he can-
not praise the Schools too highly, since his Steam-Electric
Course has advanced him from a position as steamfitter's
apprentice to the position of chief engineer, increasing his sal-
ary from $50 to $125 a month.

SALARY INCREASED 266 PER CENT.

P. J. GRACE, 602 Atlantic St., Bridgeport, Conn., was a fire-
man working 12 hours a day in an electric light works when he
enrolled with the I.C.S. for the Stationary Engineers' Course.
He is now the chief engineer of the plant of the Locomobile
Company, having 22 men under his charge. His salary has
increased 260 per cent.

EARNS $1,800 A YEAR

C. M. IRWIN, 429 Walnut St., San Francisco, Calif., is now
chief engineer of the Head Building. Before he had a tech-
nical knowledge of engineering he was a machinist at $3 a day.
His I.C.S. Course has raised his salary to $150 a month.

GRADUATE BECOMES CHIEF ENGINEER

ED. BURROW, Box 175, San Angelo, Tex., is proud of his
diploma, because it has taken him from a position in the engine
room where he worked all night for $24 a month to the place
of chief engineer at a salary of $150 a month. He says: "I
cannot see how a boy with ambition can keep from enrolling."

145 PER CENT. LARGER

E. E. HUNTER, 1520 N. Broadway, Oklahoma City, Okla.,
was earning $85 a month at the time of his enrolment for the
Steam-Electric Course. He declares that this Course was
largely instrumental in securing his advancement to the posi-
ti9n of chief engineer at the Oklahoma Gas & Electric Company,
with an increase in salary of 145 per cent.

NOW CHIEF ENGINEER

GEO. W. DRENNON, 879 Mead Ave., Oakland, Calif., declares
that he has derived much benefit from his Marine Engineers'
Course for which he enrolled with the I.C.S. When he began
to study he was employed as an assistant engineer. He is now
chief engineer on the steamer "Frances" for the A., T. & S. F.
R. R. He holds an engineer's license for ocean steamers of any
tonnage as the result of spare-time study.

800 Per Cent. Increase

At the time of enrolling in the I. C. S. for the
Stationary Engineers' Course I had received
very little schooling — anything beyond long
division was a mystery to me. When I sub-
scribed I sold my watch to make the first two
payments. My wages at that time were $8.75
a week. I am now engineer and selling agent
for the Westinghouse Company at an increase
in salary of 800 per cent. There is not the
slightest doubt that the I. C. S. Course was the
tidal wave that carried my little boat into a
port not dreamed of in the beginning. All
men have not the same kind of a boat, but they
have some kind of boat, nevertheless. It is
up to each individual which chart to use.

JOHN M. NICHOLSON,
165 Broadway, New York, N. Y.

DOUBLED HIS PAY

CLARK DULEY, Allenswqrth, Tulare County, Calif., was
earning $GO a month at the time of his enrolment for the Steam-
Electric Course. Although he had never seen a dynamo, at
the time he took charge of the electric lighting plant of Bandcn,
Ore., he was able to make a record of keeping the lights burn-
ing for 3 months with only 10 seconds' trouble. His salary has
been increased to $130 a month.

ONCE A LABORER

IRA G. WHIFFLE, 1801 Kentucky St., Lawrence, Kans., was
a laborer 27 years old when he enrolled for the Steam-Electric
Course. He says that his work with the Schools helped him
to get his present position as assistant engineer at the Kansas
State University.

NOW CHIEF ENGINEER

JOHN M. MORRISON, Glace Bay, N. S., Canada, was run-
ning an air compressor for the Dominion Coal Company when
he enrolled with the I.C.S. for the Steam-Electric Course.
He recommends our system of teaching wh'ch enabled him to
become chief engineer for the No. 4 Colliery, one of the lead-
ing collieries of the company, with an increase in salary of
25 per cent.

SALARY NEARLY DOUBLED

When H. L. FULLER, Rossford, Ohio, enrolled for the Steam-
Electric Course, he was working as general utility man around
a plate glass works. Today he is first assistant engineer for
the Edward Ford Plate Glass Company, in charge of a modern
turbine plant at a salary of $100 a month.

FROM $660 TO $1,500 A YEAR

GARRETT BURGESS, 269 Stanford Ave., Detroit, Mich., was
working as a helper, earning $660 a year at the time he enrolled
for the Engine Running Course. Since obtaining his diploma
he has been advanced to the position of assistant chief engi-
neer for the Morgan & Wright Rubber Company at a salary
of $1,500 a year.

300 PER CENT. LARGER

EARNEST LEWIS, 5 Mott Ave., Burlington, N. J., was em-
ployed as a fireman by the Thomas Devlin Mfg. Company at
the time of his enrolment for the Complete Steam Engineering
Course. Sixteen months later, through faithful study of his
Course, he was advanced to the position of chief engineer, with
an increase in salary of 300 per cent. He declares positively
that he could never hold his present position if it had not been
for the I.C.S.

Salary Quadrupled

When I enrolled with the I. C. S. for the
Stationary Engineers' Course, I was a machin-
ist earning $13 a week. When a boy at school
I could see no need of an education, and quit
as soon as the law allowed, having learned very
little while I did attend school. For a few
years I was satisfied, and then I began to wish
that I had something better, but soon found out
that I was not qualified for advancement, as
I had wasted my time in school. I then got
out the old arithmetic, but could not get any
satisfaction out of it, so I threw it up and de-
cided that I was a hopeless case. Some time
afterward, one of my shop mates told me that
he had taken out the Stationary Engineers'
Course with the I. C. S. and invited me to his
home to see his books. I then enrol. ed, and,
although I have not made any very wonderful
strides, I have gained steadily until on May 1,
1910, I was appointed chief engineer of the
Springfield Street Railway Power Station at a
salary four times what I earned in the iron
works. My enrolment with the Schools was
the best move I ever made.

\V. C. TRACY.
791 Main St.. Springfield, Mass.

SALARY MORE THAN DOUBLED

R. F. SHANK, 22 Florence Ave., Rosedale, Kans., was work-
ing as an oiler for $50 a month when he enrolled for our Steam-
Electric Course. He had only obtained a fifth grade common
school education, and was obliged to work 12 hours a day.
Largely through the study of the Bound Volumes, he advanced
himself to the position of chief engineer for the Kimball Cereal
Company, of Kansas City, Mo., at a salary of $21 a week.

250 PER CENT. INCREASE

When C. F. RASMUSSEN, Clay Center, Kans., enrolled with
the I. C. S. for the Stationary Engineers' Course, he was work-
ing in a creamery at $30 a month. Having graduated from
our Stationary Engineers' Course, and also from our Steam-
Electric Course, he has been able to command a better position,
and hence has been advanced from time to time until he now
draws 250 per cent, larger salary, as superintendent of the City
Light and Water Works plant.

NOW CHIEF ENGINEER

J. G. BLYTHEWOOD, Voth, Tex., was trying to learn the engi-
neer's profession when he enrolled for our Stationary Engi-
neers' Course. At that time he was working wherever he
could, earning $1 a day. He says that our system is the best
way for a laboring man to acquire an education, since it has
promoted him to the position of chief engineer for the Beau-
mont Irrigating Company at a salary of $150 a month.

GRADUATE GAINS 150 PER CENT.

JOHN W. HILFRANK, White Plains, N. Y., is now chief engi-
neer at the New York Orthopaedic Dispensary and Hospital.
When he enrolled for our Stationary Engineers' Course, he
was working for $12 a week. He recommends the Cpurse,
from which he has graduated, because it has increased his sal-
ary 150 per cent.

NOW FOREMAN

GEORGE KORNEGOE, Van Meter, Iowa, had only a common
school education when he enrolled for our Steam-JElectric
Course. He is now foreman for the Platt Company, brick and
tile manufacturers, drawing $100 a month.

NOW EARNS $196 A MONTH

ARCHIE F. HUBBARD, Rich Grove, Tulare County, Cal.t
was running a harvester when he began to study our Engine
Running Course. He now runs a 130-horsepower traction
engine, earning $196 a month and board during the harvesting
months, and $130 a month during the plowing months.

9

Now Superintendent

When I enrolled with the International
Correspondence Schools for the Complete
Steam Engineering Course I was working on a
farm earning $20 a month. I had had a public
school education, and not being able to go to
the high school, decided to try the I. C. S.
method. After completing my Course with
very little difficulty, I became interested in the
mines. I am now superintendent of the Peter-
son Lake Mining Company at a salary of about
$160 a month. I am now working on your
Metal Mining Course. The large increase in
my earning capacity is due almost entirely to
your splendid Courses, which are worth their
cost 10 times over.

HENRY SANKEY,
Cobalt, Ontario, Canada

10

WORKING AGAINST ODDS

CARL SIMPSON, Newark, Ohio, had only a little education
and was working 13 hours a day 7 days in a week, trying to
support his family when he enrolled for our Engine Running
Course. Although his own people thought that he was spend-
ing his time and money for nothing, he struggled on alone until
he obtained his diploma. He is now chief engineer at the
Municipal Water Works for the city of Newark at a salary of
$100 a month, nearly double what he received at the time of
enrolment.

INCREASED HIS SALARY 100 PER CENT.

C. W. SINGER was earning $12 a week when he subscribed for
pur Advanced Engine Running Course. He is now super-
intendent of the Optimo Mining Company's mines at Linden,
Wis., having 35 men at work for him, and earning $25 a week. '

HAD NO EDUCATION

JOHN G. SCHAFNITZKY, 206 State St., Hudson, N. Y., had
never seen the inside of an American school house, and had
only been to a German school for 3 years. After picking up a
little English from his younger sisters, who were sent to school,
he became ambitious to learn and enrolled for our Engine
Running Course. At that time he was earning $1.30 for 12
hours' work. He is now master mechanic for the James
Stewart Construction Company at a salary of $25 a week
straight time.

NOW SUPERINTENDENT

M. C. REYNOLDS, Box 48, Carey, Ohio, was working as a
fireman in a small pumping station, earning $35 a month when
he telephoned our Representative to come to the works to
enroll him for the Engine Running Course. Today he is
superintendent of the electric lighting and water works plant
of Carey, Ohio, making three times his former salary.

SALARY NEARLY DOUBLED

Forced to leave school at an early age to go to work in the
mines, JOHN PARKS, 319 Highland Ave., Lexington, Mo.,
found himself at the age of IS with a knowledge of only simple

Eroblems in addition. While working as a fireman, he enrolled
ar the Engine Running Course. He is now engineer at a
salary 90 per cent, greater than he received at the time of his
enrolment.

HIS COURSE WORTH $50 A MONTH MORE TO HIM

MAYNARD JOSEPH, Collinsville, 111., was earning $50 a month
as a fireman when he took out our Engine Running Course.
This enabled him to pass the state examination and to obtain
a first-grade certificate of competency as a hoisting engineer.
He now has charge of the plant of the Donk Brothers Coal
Company, a plant having a capacity of 3,000 tons of coal a
day, and his salary has increased $50 a month.

11

Salary Increased 500
Per Cent.

I was employed as a farm hand at $15 a
month when I enrolled with the Schools for
the Stationary Engineers' Course. This en-
abled me to become an engineer for the Booth-
Kelly Lumber Company, increasing my salary
$50 a month. I studied your volumes on elec-
tricity, of which I had no previous knowledge,
and they enabled me to erect about 75 miles
of telephone lines and to install a central office.
I am now doing construction work for the
Oregon Power Company of this place, at a
salary 500 per cent, larger than what I re< ^
at the time of enrolment.

PHILIP A. JOHNSON,

Springfield, Ore.

12

NOW GENERAL MANAGER

JOHN J. PRICE, Cement City, Mich., had only a common
school education before he enrolled with the International
Correspondence Schools for the Stationary Engineers' Course.
He did his studying at night, running an engine during the day.
After working for the Peninsular Portland Cement Company in
a subordinate position, he was given charge of their power house,
and then of their dredges, until he was made general manager
of the entire works at a salary of $2,000 a year, the works
employing 150 men. Mr. Price earned $50 a month when he
enrolled.

NOW CHIEF ENGINEER

D. S. KENNEDY, 19 Wetmore St., Warren, Pa., was earning
$65 a month as an electrician when he began to study our
Stationary Engineers' Course. He recommends this Course
to young men because it has enabled him to become chief engi-
neer of the Warren Electrical Company with an increase of
50 per cent, in salary.

NO LONGER BLUNDERS ALONG

CHARLES H. WAINNER, Itox 353, Pratt, Kans., had no reg-
ular position, and was working wherever he could at $1.25 a
day when he enrolled for our Stationary Engineers' Course.
Until he had mastered this, no one wanted to have him blunder-
ing around an engine room. He is now a successful engineer
in charge of the power plant for the Pratt Milling Company,
at a salary 150 per cent, larger than when he first enrolled.

NOW PROPRIETOR

OTIS MORRIS, Warren, Idaho, was making $1.25 a day when
he enrolfed with the I. C. S. for the Stationary Engineers'
C9urse. He is now in business for himself, leasing several
mines, and taking charge of all machinery.

NOW GENERAL MANAGER

JOHN HARRIS, Lilly, Pa., was firing boilers at night when
,he enrolled for our Engine Running Course. This, he says,
proved a great help to him, enabling him to become the gen-
eral manager of the James Harris & Sons Bituminous Coal
Mines.

233 PER CENT. INCREASE

Gus LUNDGREN, Cherokee, Iowa, was a fireman in a small
electric lighting plant earning but $30 a month when he enrolled
with the I. C. S. for the Stationary Engineers' Course. With-
out this, he says, he could never have reached his present posi-
tion as manager of the Cherokee Electric Company. His
income has increased 233 per cent.

13

Now Foreman of Engines

I had been working for the Chesapeake &
Ohio Railroad Company as an engineman
for several years, and had always been con-
sidered an A No. 1 engineer, which made me
a little conceited. I imagined that I needed
no further training, but since completing my
Locomotive Running Course with the I. C. S.,
I am forced to change my mind, and must now
admit that my former knowledge was very
limited and ordinary. I would not exchange
the benefits I have received from the Course
for $1,000 in cash. On October 1, 1911, I was
promoted to the position of road foreman of
engines, which position I now hold, with head-
quarters at Covington, Ky.

D. F. EVANS,
1220 Madison St.,

Covington, Ky.

14

THREE TIMES HIS FORMER SALARY

J. C. WHITTEN, t6 Danforth St., Providence, R. I., while
working as a fireman for $12 a week, enrolled for our Loco-
motive Running Course. Having been a poor boy, he had no
chance for an education, needing a dictionary to define common
words. His Course enabled him to secure promotion at his
first examination. He is now an engineer, earning three times
what he received at the time of enrolment.

GRADUATE WORKS FOR THE GOVERNMENT

HUGH L. RUSSELL, Keams Canon, Ariz., was earning $12
a week in a roller mills when he subscribed for our Complete
Steam Engineering Course 9 years ago. Since- graduating,
he was able to pass the Civil Service examination with a grade
of 98.3, receiving immediate appointment. He has since
enrolled for the Complete Electrical Engineering Course.
He is now a steam and electrical engineer in the service of the
government, Interior Department, with a salary which has
increased about 300 per cent.

GRADUATE RECEIVES PROMOTION

M. J. McKiNNEY, 916 S. Fell Ave., Normal. 111., finished
our Locomotive Running Course and was able to pass the
State examination, receiving immediate promotion. He now
holds a profitable place as engineer on the Chicago & Alton
Railroad.

SALARY MORE THAN DOUBLED

HANS C. BROWN, 14 E. Linden St., Wilkes-Barre, Pa., was
a railroad fireman, earning $2.20 a day when he enrolled for
our Complete Locomotive Running Course. Although he had
received only a common school education in his native land,
Denmark, he was able to pass an examination and receive
promotion as engineer for the Lehigh Valley Railroad Company,
where he now earns more than double his former salary.

SALARY INCREASED $95 A MONTH
When NICHOLAS COLILAR, R. F. D. 31, Costello, Potter
County, Pa., enrolled for the Complete Locomotive Running
Course, he was earning $45 a month as a fireman. His Course
has helped him beyond his expectation. He is now a loco-
motive engineer, for the Emporium Lumber Company, earn-
ing $95 a month more than when he enrolled.

OFTEN EARNS $150 A WEEK

W. R. HAY, Gulfport, Miss., was straw boss of a ditch gang
repairing streets, earning $12.25 a week, when he enrolled with
the I. C. S. for the Complete Steam Engineering Course.
He also studied our Marine Engineering Course and Mechan-
ical Drawing. He is now chief engineer and manager of the
tug "Beaver," earning from $90 to $150 a week.

15

Bettered His Position

When I enrolled with the I. C. S. for the
Complete Locomotive Running Course, I was
employed as an engine wiper at a salary of
$54 a month. Since then I have become fire-
man, and was later promoted to the position
of engineer. I believe that my work with the
Schools on the above course helped me a great
deal in my examinations enabling me to pass
with great success. I am now employed by the
Northwestern Pacific Railway Co. as an engi-
neer, averaging from $125 to $160 a month.
G. F. BRADLEY, Jr.,
310 3rd St.,

San Rafael, Cal.

10

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