Google
This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project
to make the world's books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject
to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books
are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover.
Marks, notations and other maiginalia present in the original volume will appear in this file - a reminder of this book's long journey from the
publisher to a library and finally to you.
Usage guidelines
Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the
public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing tliis resource, we liave taken steps to
prevent abuse by commercial parties, including placing technical restrictions on automated querying.
We also ask that you:
+ Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for
personal, non-commercial purposes.
+ Refrain fivm automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine
translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the
use of public domain materials for these purposes and may be able to help.
+ Maintain attributionTht GoogXt "watermark" you see on each file is essential for in forming people about this project and helping them find
additional materials through Google Book Search. Please do not remove it.
+ Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just
because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other
countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of
any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner
anywhere in the world. Copyright infringement liabili^ can be quite severe.
About Google Book Search
Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers
discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web
at |http: //books .google .com/I
'>^^lm'ff■B^.f
HARVARD UNIVERSITY
DEPARTMENT OF
GEOLOGY AND GEOGRAPHY
From die Libnuy of
JAY BACKUS WOODWORTH
TEACHER OF GEMjOGY AT HARVARD
FROM 1894 TO 192;
The Gift of
G. S. HOLDEN R. W. SAYLBS
R. A. F. PENROSE B. WIGGLBSWORIH
HARVARD]
lib:
'J '. r
. / '
WILLIAMS'
BOSTON
.f.:-
The Coal Miner's
Handbook
A HANDY REFERENCE BOOK
FOR
Coal Miners, Pit Bosses, Fire Bosses, Foremen,
Superintendents, Managers, Engineers,
and All Persons Interested in the
Subject of Coal Mining
BY
International Correspondence Schools
SCRANTON, PA.
ist Edition, 6th Thousand, 1st Impression
scranton, pa.
International Textbook Company
t -VN^< Mf^. li.l
/■'
TRAHSFHUKEO TO
HARVARD COLLEGE LWf ART
copyright. 1913, by
International Textbook Company
Copyright in Great Britain
All Rights Reserved
24566
PREFACE
This Handbook is intended for all who are
interested in coal mining and for all who are
employed in and about the coal mines. While
the treatment of some of the subjects included
is necessarily brief, we have striven to anticipate
the daily wants of the user and to give him, in
the manner best suited to his needs, the informa-
tion he desires. The breaker boy, the driver, the
helper will find many useful hints to help him
in his work and to assist him in securing advance-
ment.
From a vast number of reference tables and
formulas only the best have been selected and
incorporated, and these have been thoroughly
explained. This feature in itself should result
in a great saving of time and in preventing the
selection of the wrong table or formula. The
subjects of surveying, use and care of wire ropes
in connection with hoisting and haulage, electric-
ity, opening of mines, timbering, methods of
working, and of ventilation have received special
attention. Safety appliances, which include elec-
tric signaling devices and safety lamps, are
treated in detail^ as is also the care and use of
■ • •
in
iv PREFACE
explosives. Considerable space is also devoted to
the treatment of persons injured in and about the
mines and those overcome with mine gases.
The man employed on the surface will find
recorded many useful facts dealing with surface
plants, considerable space being devoted to dams,
pumping, steam, preparation of coal, etc.
This little book should satisfy a want long
existing in the coal-mining industry for a ready
pocket reference containing information that any-
once can use in making calculations and settling
questions.
International Correspondence Schools
March 1, 1913
INDEX
Acetylene mine lamps, 256.
Acid waters, Pumps for, 129.
Afterdamp, 253.
Air brattice, 288.
bridge, 288.
coltmm. Calculation of mo-
tive coltmm or, 281.
Composition and measure-
ment of, 247.
Compressed, 144.
•current. Natural division
of, 271.
-current. Proportional divi-
sion of, 272.
-current, Splitting of, 270.
•current, Velocity of, 260.
currents. Conducting, 287.
Equal splits of, 271.
in mine ventilation. Dis-
tribution of, 270.
in pipes, Transmission of,
144.
Proportionate division of,
277.
required for ventilation.
Quantity of, 259.
Alabama methods, 222.
Alternating-current drctiits.
Power in, 158.
•current generators, 149.
-current motors, 149.
Aluminum wire, 162.
American coals, Analyses and
heating values of, 134.
Analyses and heating values
of American coals, 134.
Aneroid barometer, 248.
Angles or arcs, Measure of, 2.
Anthracite coal, 130.
Handling of, 313.
Methods of mining, 229.
Anthracite or hard coal, 130.
Revolving screen mesh for,
311.
screens. Duty of, 311.
will nin. Table of pitch at
which, 314.
Arc for any radius. To bend
rails to proper, 300.
lamps, 165.
Arcs, Measure of angles or, 2.
Area of cut timber. Table for,
9.
of round timber. Table for,
8.
of tract of land. Determin-
ing, 84.
Atmospheric pressure, Calcu-
lation of. 249.
Avoirdupois weight, 2.
Axle, Wheel and, 93.
Azimuth course, 83.
Barometer, Aneroid, 248.
Mercurial, 248.
Bars, Platform, 309.
Batteries, 165.
Battery, Double-chute, 235.
Single-chute, 234.
woricing. 232.
Beam, Breaking strength of a,
102.
Beams, Tables for bending
moment and deflection
of, 100.
Bell wiring. 166.
Bending moment and deflec-
tion of beams, Table for,
100.
Biram ventilator. 284.
Bituminous, or soft coal, 130.
Blackdamp, 251.
VI
INDEX
Blasting by electricity, 244.
Blowers, Force fans and, 283.
Board measure, Timber and, 8.
Boiler incrustation, 139.
Boilers, Horsepower of, 137.
Steam. 137.
Bord-and-pillar method of
mining, 202.
Box regulator, 272.
regulator, Calculation of
pressure for, 273.
Brattice. Air. 288.
Breaking strength of a beam,
102.
strength of columns, 102.
Breasts. Buggy, 215.
Chute, 216.
Bridge, Air, 288.
Briquetting, 315.
British thermal unit, 133.
Brown coal, or lignite, 131.
Bucket, Sinking, 177.
Buggy breasts, 215.
Calculation of atmospheric
pressure, 249.
of mine resistance. 263.
of motive column or air
column, 281.
of power, or units of work
per minute, 264.
of pressure for box reg-
ulator, 273.
of tension of haulage rope,
295.
of ventilating pressure in
furnace ventilation, 280.
Cannel coal, 131.
Canvas doors, 288.
Capacity, Metric measures
of, 4.
of pumps and horsepower
required to raise water,
127.
Capell fan, 287.
Centrifugal fans, 282.
fans. Types of, 284.
Chain, 78.
cables. Resistance and
proof tests of wrought-
iron, 117.
Chains, 115.
Charge, Firing a. 242.
Tamping a, 242.
Charging explosives, 241.
Chokedamp, 251.
Chute breasts, 216.
Circuit, Series, 150.
Circuits, Electric, 150.
Electric-haulage, 153.
Parallel, 151.
Power in alternating-cur-
rent, 158.
Power in direct-current,
158.
Protection of. 153.
Classifying apparatus, Sizing
and, 309.
Cleaning safety lamps, 256.
Clearfield region method of
mining, 220.
Clinometer, 79.
Closed work method of mi-
ning. 201.
Coal, Anthracite, 130.
Bitimiinous, 130.
Cannel. 131.
-crushing machinery, 307.
Formations likely to con-
tain, 168.
Methods of working, 200.
or bedded materials, 170.
Removal of sulphur from,
313.
seam. Determining con-
tents of, 84.
Semibituminous, 130.
Splint, 131.
storage, 214.
Systems of working, 202.
The preparation of, 307.
Coals, Classification of, 130.
Cokinsr. 131.
Composition of, 131.
Table of si>ace occupied by
2,000 pounds of various,
315.
Coefficient of elasticity. Table
for, 100.
of friction, 97.
Coking coals, 131.
Columns, Brei^dng strength
of, 102.
INDEX
Vll
Columns, Constant used in
formula for, 103.
Combustion, Spontaneous,
214.
Common logarithms of num-
bers. Table for, 33.
Compass, The, 76.
Comi>osition and measure-
ment of air, 247.
of coals, 131.
of fuels. Table of. 136.
Compressed air, 144.
-air locomotive, 298.
Conducting air currents, 287.
Connellsviile region method
of mining, 218.
Construction of dams in
mines, 120.
Contents of coal seam, De-
termining, 84.
Control of roof pressure,
207.
Conversion table for English
measures into metric, 6.
table for metric measures
into English, 7.
tables. Metric, 5.
Copper wire. Properties of,
161.
Cornish pumps, 126.
Cribs, 207.
Crushers, Selection of, 307.
Crushing machinery. Coal,
307.
Cubic measure, 2.
Culm, Flushing of, 239.
Current, Defimtion of, 155.
Horsepower or power of,
260.
Velocity of air, 260.
Currents, Conducting air,
287.
Measurement of ventila-
ting, 261.
Curves. 300.
in a mine. Laying out, 90.
Cuttimber.Tablef or area of, 9.
D
Dams, 120.
Debris, 125.
Earth, 124.
Dams in mines. Construction
of, 120.
Masonry, 125.
Stone, 124.
Wooden, 124..
Data, Wire, 159.
Debris dams, 125.
Decimal equivalents, 12.
equivalents of parts of 1
inch, Table for, 9.
Decimals of a foot for each
A-inch, Table for, 10.
Depth of shafts, Finding, 249.
Detaching hooks, 294.
Determimng area of tract of
land, 84.
contents of coal seam, 84.
Direct-current circuits. Power
in, 158.
-current generators, 147.
-ctirrent motors, 147.
-current motors. Efficien-
cies of, 162.
Disk fan, 282.
Distance between centers of
breasts or chambers,
Table of, 212.
Distribution of air in mine
ventilation, 270.
Door regtilator, 272.
regtilator. Side opening for,
274.
Doors, Canvas, 288.
Double-chute battery, 235.
Drainage and ventilation
during sinking, 178.
Drawing pillars, 211.
Drill holes. Arrangement of,
245.
Driving the gangway, 179.
Drums on life of wire ropes.
Effects of sheaves or,
110.
Dry measure, 2.
Dunn's tables of size of room
pillars for various depths,
211.
Duplex pumps. Simple and,
126.
Duty of anthracite screens,
311.
Dynamite, Thawing, 245.
vui
INDEX
E
Earth dams. 124.
Effects of sheaves or drums on
life of wire ropes, 110.
Efficiency of steam at various
pressures, 138.
Elasticity, Table for coeffi-
cient of, 100.
Electric apparatus in fire-
damp, 154.
circuits, 150.
exploder, 243.
generators and motors, 147.
-haulage circuits, 153.
mine lamps, 257.
-mining locomotive, 298.
signaling, 165.
Electrical calculations, 155.
units, 155.
units. Mechanical equiv-
alents of, 156.
Electricity, 147.
Blasting by, 244.
Electromotive force. Defini-
tion of, 155.
Elevators, Miscellaneous
forms of water. 128.
Elongation and shortening
under stress, 102.
Endless-rope haulage. Deter-
mination of friction pull
on, 296.
-rope system, 296.
Engine, Sinking. 178.
Engines, Steam, 142.
English, Conversion table for
metric measure into, 7.
measures into metric, Con-
version table for, 6.
Entries, Number of, 208.
Equal splits of air, 271.
Equivalent orifice, Tlie, 264.
Examples in solutions of tri-
angles, 60.
Exhaust fans. 283.
Exploder. Electric, 243.
Exploration by drilling or
bore holes. 171.
Explosives, 240.
Charging. 241.
Permissible, 240.
' '^sions. Mine, 258.
Factors of safety. Table for,
99.
Pan, C'apcll, 287.
Disk, 282.
Nasmyth, 284.
Position of. 283.
Fans and blowers. Force,
283.
Centrifugal. 282.
Exhaust. 283.
Types of centrifugal, 284.
Fastenings, Wire-rope, 113.
Faults, Schmidt's law of,
171.
Firedamp, 252.
Electric apparatus in, 154.
Firing a charge, 242.
Flattened-strand ropes, 104.
Flow of air in pipes. Table of
loss of pressure by, 146.
of water through pipes,
119.
Flushing of culm, 239.
Force fans and blowers,
283.
Formations likely to contain
coal, 168.
Formula, Rankine-Gordon,
27.
Formulas, 25.
for lamp wirin^^, 163.
for primary splits. Table of
ventilating, 275.
for secondary spUts, Table
of ventilating, 276.
Heating, 133.
Splitting, 275.
Table of ventilation, 267.
Wire, 162.
Friction and lubrication, 97.
Coefficient of, 97.
pull on endless^rope hatil-
age. Determination of,
296.
Fuels. 130.
Table of composition of,
136.
Furnace ventilation, 280.
ventilation. Calculation of
ventilating pressure in,
280.
INDEX
O
Gangway, Driving the, 179.
Gas by lamp flame. Testing
for. 253.
Treatment of persons over-
come by, 318.
Gases found in mines, 250.
Table of mine, 254.
Gathering locomotives, 297.
Gatige of track, 300.
^re. 160.
Generators, Alternating-cur-
rent, 149.
and motors. Electric, 147.
Direct-current, 147.
Geometry. 52.
George Creek District, Md.,
method of mining, 223.
Grades, 299.
Gravity planes, 294.
Guibal ventilator, 286.
H
Hard, or anthracite coal, 130.
Haulage, 294.
and transmission ropes.
Table of hoisting, 106.
Motor, 297.
Rope, 295.
rope, Calculation of ten-
sion of, 295.
Speed of, 299.
Head-frames, 293.
-frames or head-gears. Tim-
ber, 200.
-frames, Sinking, 177.
Head-gears, Timber head-
frames or, 200.
Head-sheaves, 293.
Heating formulas, 133.
values of American coals,
Analyses and, 134.
High-pressure steam, 138.
Hoistmg, 288.
haulage and transmission
ropes, Table of, 106.
Koepe system of, 289.
Power used for, 291.
Problems in, 291.
ropes, Starting strain on,
108.
Whiting system of, 290.
Horsepower of boilers, 137.
of manila rope, 117.
or power of current, 260.
Hydrogen sulphide, 252.
Hydromechanics, 118.
Hydrostatics, 118.
I
Illuminating power of safety
lamps, 256.
Incandescent-lamp ratings,
163.
Inclined planes, 95.
roads, 297.
Incrustation, Boiler, 139.
Prevention of, 140.
remedies, 140.
Indiana coal-mining method,
223.
Induction motors. Efficien-
cies of, 163.
Injured persons. Treatment
of, 316.
Instruments, Surveying, 76.
Iowa coal-mining method,
- 223.
Iron and steel supports, 195.
J
Jigs, 312.
K
Keeping surveying notes, 87.
Koepe system of hoisting,
289.
L
Landings, 193.
Lamp wiring, Formulas for,
163.
Lamps, Acetylene mine, 256.
Arc, 165.
Cleaning safety, 256.
Electric mine, 257.
Illuminating power of
safety, 256.
Locking safety, 256.
Oil for safety, 255.
Safety, 254.
Table of light given by
safety, 257.
Types of safety, 266.
Wiring calculations for,,
163.
INDEX
Laws, Mine ventilation, 270.
Lay of rope, 104.
Laying out curves in a mine,
90.
Length, Metric measure of, 4«
Levers, 92.
Light given by safety lamps.
Table of, 257.
Lignite, or brown coa^ 131.
Linear measure, 1.
Liquid measure, 3.
Ix)cking safety lamps, 256.
Locomotive, Compressed-air,
298.
Electric-mining, 298.
Locomotives, Gathering, 297.
Logarithms, 28.
of numbers, Table of com-
mon, 33.
Longwall face, Timbering,
207.
method. Modifications of,
229.
method of mining, 204.
Long-ton table, 2.
Lubricants for different pur-
poses. Best, 97.
Lubrication, Friction and, 97.
of ropes, 112.
M
Machine mining, 246.
Machinery , Coal crushing,
307.
Manila rope. Horsepower of,
117.
Masonry dams, 125.
Material required for 1,000 ft.
and for 1 M. of single
track, 302.
required for single-track
road, Table of, 305.
Materials, Strength of, 98.
Meandering, Definition of,
81.
Measure, Cubic, 2.
Dry, 2.
Linear, 1.
Liquid, 3.
of angles or arcs, 2.
of length, Metric, 4.
Square, 1.
Measurement of air, Com-
Ix>sition and, 247.
of ventilating currents, 261.
of pressure, 261.
of temperature, 263.
of velocity, 261.
Measures and weights, 1.
of capacity. Metric, 4.
of surface. Metric, 4.
of volume. Metric, 4.
of weight. Metric, 5.
Mechanical equivalents of
electrical units, 156.
ventilators, 281.
Mechanics, Elements of, 92.
Mensuration, 54.
M. E. P., Determination of,
143.
Mercurial barometer, 24$.
Mercury column. Water col-
imin corresponding to
any, 249.
Mesh for anthracite. Revolv-
ing screen, 311.
for shaking screens. Table
of, 310.
Methane, 250.
Methods of mining anthra-
cite, 229.
of working coal, 200.
Metric, Conversion table for
English measures into, 6.
measures into English, Con-
version table for, 7.
system, 3.
Mine corps, 90.
explosions, 258.
gases, Table of, 254.
lamps. Acetylene, 256.
lamps, Electric, 257.
Opening a, 172.
Potential factor of a, 264.
resistance, 260.
resistance, Calctdation of,
263.
roads and tracks, 299.
timber and timbering, 180.
timbering and tmderground
supports, Forms of, 183.
timbering. Joints in, 182.
ventilation. Distribution of
air in, 270.
INDEX
XI
Mine ventilation laws, 270.
Mines, Gases found in, 250.
Ventilation of, 247.
Mining,Bord-and-pillar meth-
od of, 202.
locomotive, Electric, 298.
Longwall method of, 204.
Machine, 246.
Pillar-and-chamber meth-
od of, 202.
Rock-chute, 237.
Motive coltunn or air column,
Calculation of, 281.
Motor haulage, 297.
troubles, 148.
Motors, Alternating-current,
149.
Direct-current, 147.
Efficiencies of direct-cur-
rent, 162.
Efficiencies of induction,
163.
Electric generators and.
147.
Murphy ventilator, 286.
N
Nasmyth fan, 284.
Natural division of air-cur-
rent, 271.
ventilation, 279.
New Castle, Colo., mining
method, 227.
Notes, Keeping surveying,
87.
Number of board feet in mine
ties. Table of, 306.
O
Ohm's law, 157.
Oil for safety lamps, 255. ,
Open work method of mining,
201.
Opening a mine, 172.
Orifice, The equivalent, 264.
Overcast, 288.
Overcome by gas. Treatment
of persons, 318.
P
Pack walls, 207.
Parallel circuits, 151.
Percentage, 25.
Permissible explosives, 240.
Pillar -and -chamber method
of mining, 202.
-and-stall method of mi-
ning, 217.
Pillars. 209.
Drawing, 211.
Room, 210.
Pins, 78.
Piping coefficients. Table of,
145.
Pitch at which anthracite will
run. Table of, 314.
Pittsburg region method of
mining, 220.
Plane trigonometry, 58.
Planes, Gravity, 294.
Inclined, 95.
Platform bars, 309.
Plats, 193.
Plotting, 81.
Plumb-bob, 78.
Position of fan, 283.
Potential factor of a mine
264.
Power calculations, 158.
Definition of, 157.
in alternating-current cir<^
cuits, 158.
in direct -current circuits,
158.
of current. Horsepower or»
260.
or units of work per min-
ute. Calculation of, 264.
pressure and velocity. Re-
lation of. 260.
used for hoisting, 291.
Preparation of coal. The, 307.
Pressure and velocity. Rela-
tion of power, 260.
for box regulator. Calcu-
lation of. 273.
Measurement of, 261.
Primary splits, 276.
sphts. Table of ventilating
formulas for, 275.
Problems in hoisting, 291.
Properties of copper wire,
161.
of various sections, Table
for. 101.
xu
INDEX
Proportion, or single rule of
three, Simple, 24.
Proportional division of air-
current, 272.
Proportionate division of air,
277.
Props, Undersetting of, 183.
Prospecting, 168.
Underground, 170.
Pulleys, 95,
Pulsometer, 128.
Pump machinery, 126.
Pumps and horsepower re-
?uired to raise water,
'apacity of, 127.
Cornish, 126.
for acid waters, 129.
Simple and duplex, 126.
Rail elevation, 300.
Weight of, 299.
Rails, Table of standard size
of, 304.
to proper arc for any radius.
To bend, 300.
Rankine-Gordon formula, 27.
Ratings, Incandescent lamp,
163.
Regulator, Box, 272.
Calculation of pressure for
box, 273.
Door, 272.
Side opening for door, 274.
Relation of power, pressure,
and velocity, 260.
Relighting stations, 256.
Removal of sulphur from
coal, 313.
Reservoirs, 125.
Resistance, Calculation of
mine, 263.
Definition of, 157.
Mine. 260.
Revolving screen mesh for
anthracite, 311.
screens or trommels, 311.
Reynoldsville region method
of mining, ^1.
Roads and tracks. Mine, 299.
Rock-chute mining. 237.
Rollers. 301.
Roof pressure. Control of,
207.
Room-and-pillar methods.
Modifications of, 215.
-and-pillar system, 202.
pillars, 210.
Rope calculations. Wire, 110.
haulage, 295.
Lay of, 104.
Ropes, Effects of sheaves or
drums on life of wire,
110.
Flattened-strand, 104.
Lubrication of, 112.
Table of hoisting, haulage,
and transmission, 106.
Wire, 103.
Round timber. Table for area
of, 8.
Rule of three. Simple propor-
tion, or single, 24.
S
Safety catches, 293.
lamps, 254.
lamps, Cleaning, 256.
lamps. Illuminating power
of, 256.
lamps. Locking, 256.
lamps. Oil for, 255.
lamps. Table of light given
by, 257.
lamps. Types of, 255.
Schiele ventilator, 286.
Speed of, 311.
Schmidt's l^w of faults, 171.
Screen mesh for anthracite.
Revolving, 311.
Screens, Duty of anthracite,
311.
or trommels. Revolving,
311.
Shaking, 309.
Table of mesh for shaking,
310.
Screws, 95.
Secondary splits, 277.
splits. Table of ventilat-
ing formulas for, 276.
Semibituminous coal, 130.
Series circuit, 150.
Shaft compartments, 174.
INDEX
zui
Shaft pillars. 209.
X>illars, Size of. 210.
sinking[, 174.
timbering, 188.
Shafts, 173.
Finding depth of, 249.
Size of, 174.
Shaking screens, 309.
screens. Table of mesh for.
310.
Shearing, 247.
Sheaves, 109.
or drums on life of wire
ropes. Effects of, 110.
Sheet-metal gauges. Table of
wire and. 111.
Shortening under stress, Elon-
gation and. 102.
Shtmt, 152.
Side opening for door reg-
ulator, 274.
Signaling, Electric, 165.
Simple and duplex pumps, 126.
proportion, or single rule
of three, 24.
Single-chute battery, 234.
-track road, Table of mate-
rial required for, 305.
Sinking bucket, 177.
Drainage and ventilation
during, 178.
engines, 178.
head-frames, 177.
tools, 178.
Siphons, 120.
Size of shaft pillars, 210.
Sizing and classifymg appa-
ratus, 309.
Slope bottoms, 302.
smking, 178.
Soft, or bituminous coal, 130.
Speed of haulage, 299.
of screen, 311.
Spikes required for ties,
Table of, 305.
Splicing a win rope, 113.
Splint coal, 131.
Splits of air, Equal, 271.
Primary, 275.
Secondary, 277.
Table of ventilating for-
mulas for primary, 275.
Splits, Table of ventilating
formulas for secondary,
276.
Splitting formulas, 275.
of air-current, 270.
Spontaneous combustion, 214.
Square measure, 1.
sets, 192.
Starting strain on hoisting
ropes, 108.
Stations, 193.
Rifflighting, 256.
Steam, 130.
at various pressures, Effi-
ciency of, 138.
boilers, 137.
engine, Requirements of a
good, 142.
engines, 142.
High-pressure, 138.
Steel supports. Iron and. 195.
Stinkdamp, 252.
Stone dams, 124.
Storage, Coal, 214.
Stowings, 207.
Strength of a beam, Break-
ing, 102.
of columns. Breaking. 102.
of materials, 98.
Strengths of materials. Table
for ultimate, 100.
Stress in hoisting ropes on in-
clined planes, 105.
Sulphur from coal, Removal
of, 313.
Sump, The, 179.
Supports, Iron and steel, 195.
Special forms of, 194.
Surface, Metric measures of.
4.
Survey, Traversing a. 83.
Surveying, 76.
instruments, 76.
Transit, 79.
Underground, 85.
Switches, 301.
Systems of working coal, 202.
Table for bending moment
and deflection of beams,
100.
ZIV
INDEX
Table for decimal equivalents
of parts of 1 in., 9.
for decimals of a foot for
each A-in., 10.
for factors of safety, 99.
for metric measures into
English, Conversion, 7.
for properties of various
sections, 101.
for stress in hoisting ropes
* on inclined planes, 105.
Long-ton, 2.
of composition of fuels, 136.
of distance between cen-
ters of breasts or cham-
bers, 212.
of effects of sheaves or
drums on life of wire
ropes, 110.
of heating values of Amer-
ican coals, 134.
of hoisting, haulage, and
transmission ropes, 106.
of light given by safety
lamp, 257.
of loss of pressure by flow
of air in pipes, 146.
of materials required for
single-track road, 305.
of mechanical ecLuivalents
of electrical units, 156.
of mesh for shaking screens,
310.
of mine gases, 254.
of number of board feet in
mine ties, 306.
of piping coefficients, 145.
of pitch at which anthra-
cite will run, 314.
of properties oi copper
wire, 161.
of space occupied by 2,000
pounds of various coals,
315.
of ^ikes required for ties,
of standard size of rails,304.
of ties per thousand feet
and per mile of track,
307.
of trigonometric functions,
64.
Table of ventilation formulas,
267.
of ventilating formulas for
primary splits, 275.
of ventilating formulas for
secondary splits, 276.
of wire and sheet -metal
gauges. 111.
Tables, Metric conversion, 5.
of logarithms, 33.
Traverse, 12.
Tail-rope system, 295.
Tamping a charge, 242.
Tape, 78.
Telescopes, Transit, 78.
Tem];>erature, Measurement
of, 263.
Tension of haulage rope, Cal-
culation of, 295.
Tesla, Cal., mining method,
225.
Testing for gas by lamp flame,
253.
Thawing dynamite, 245.
Thermal unit, British, 133.
Ties, 299.
per thousand feet and per
mile of track, Table of,
307.
Timber and board measure, 8.
and timbering. Mine, 180.
Choice of, 180.
head-frames or head-gears,
200.
Placing of, 181.
Table for area of cut, 9.
Table for area of round, 8.
Timbering a longwall face,
207.
and tmdergrotmd supports.
Forms <x mine, 1S3.
Shaft, 188.
Timbers, Preservation of, 180.
Tools, Sinking, 178.
Track, Gauge of, 300.
Material required for 1,000
ft. and for 1 M. of single,
302.
Table of ties per thousand
feet and per mile of, 307.
Tracks, Mine roads and, 299.
Transformers, 150.
INDEX
XV
Transit surveying. 79.
telescopes, 78.
The, 77.
Transmission ropes. Table of
hoisting, haulage, and,
106.
Traverse tables, 12.
Traversing a survey, 83.
Treatment of injured persons,
316.
of persons overcome by gas,
318.
Trestles,' 195.
Trianp;les, Examples in solu-
tions of, 60.
Trigonometric functions,
Table of, 64.
Trigonometry, Plane, 58.
Trommels, Revolving screens
or, 311.
Turnouts, 302.
Ttmnels, 180.
Types of centrifugal fans,
284.
U
Ultimate strengths "^f mate-
rials, Table for, 100.
Undercast, 288.
Undercutting, 202.
Underground prospecting,
170.
supports, Forms of mine
tunbenng and, 183.
surveying, 85.
Undersetting of props, 183.
Unit, British thermal, 133.
Units, Electrical, 155.
Mechanical equivalents of
electrical, 156.
of work per minute, Calcu-
lation of power or, 264,
V
Measurement
of.
Velocity,
261.
of air-current, 260.
Relation of power, pres-
sure, and, 260.
Ventilating currents, Meas-
urement of, 261.
formulas for primary splits,
Table of, 275.
Ventilating formulas for sec-
ondary splits. Table oft
276.
methods and appliances*
279.
pressure in furnace ventila-
tion. Calculation of, 280.
Ventilation, Distribution of
air in mine, 270.
during sinking, Drainage
and. 178.
Elements of, 260.
formulas. Table of, 267.
Furnace, 280.
laws, Mine, 270.
Natural, 279.
of mines, 247.
Quantity of air required
for, 259.
Ventilator, Biram, 284.
Guibal, 286.
Murphy, 286.
Schiele, 286.
Waddle, 284.
Ventilators, Mechanical, 281.
Volume, Metric measures of,
4.
W
Waddle ventilator, 284.
Water colimin corresx>onding
to any mercury column,
249.
elevators. Miscellaneous
forms of, 128.
through pipes. Flow of, 119.
Wedge. 95.
Weight, Avoirdupois, 2.
Metric measures of, 5.
Weights and measures, 1.
West Virginia method of mi-
ning, 221.
Wheel and axle, 93.
Whitedamp, 250.
Whitinar system of hoisting.
Wire, Aluminum, 162.
and sheet-metal gauges.
Table of. 111.
data. 159.
formulas, 162.
fauge, 160.
'roperties of copper, 161.
XVI
INDEX
Wire-rope calculations, 110.
-rope fastenings, 113.
rope, Splicing a, 113.
ropes, 103.
ropes, Effects of sheaves or
drums on life of, 110.
Wires, Estimation of cross-
section of, 159.
Estimation of resistance of,
150.
Wiring, Bell, 166.
calculations for lamps, 163.
Formulas for lamp, 163.
Wooden dams, 124.
Work, Definition of, 167.
Wrought-iron chain cables,
Resistance and proof
tests of, 117.
The Coal Miner's
Handbook
USEFUL TABLES
WEIGHTS AND MEASURES
LINEAR MEASURE
12 inches (in.) =1 foot ft.
3 feet =1 yard yd.
5 J yards =1 rod rd.
40 rods =1 furlong fur.
8 furlongs =1 mile mi.
in.
ft.
yd. rd. fur. mi.
36 =
3 =
1
198 =
16.6 =
5.5= 1
7,920 =
660 =
220= 40=1
63,360 = 6,280 = 1 ,760 = 320 = 8 = 1
SQUARE MEASURE
144 square inches (sq. in.).. . . = 1 square foot sq. ft.
9 square feet =1 square yard sq. yd.
30} 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
2
2 USEFUL TABLES
MEASURE OF ANGLES OR ARCS
60 seconds ("') * 1 minute
60 minutes =1 degree **
90 degrees »> 1 rt. angle or quadrant. . . . D
360 degrees =1 circle cir.
1 cir. =-360° = 21,600' =1,296,000'
CUBIC MEASURE
1,728 cubic inches (cu. in.) =1 cubic foot cu. ft.
27 cubic feet =1 cubic yard cu. yd.
128 cubic feet =1 cord cd.
24f cubic feet = 1 perch P.
cu. yd. cu. ft. cu. in.
1 = 27 = 46.656
AVOIRDUPOIS WEIGHT
437i grains (gr.) =1 ounce oz.
16 ounces =1 pound lb,
lOC^MJunds =1 hundredweight cwt.
20cwt., or 2,000 1b =1 ton .T.
T. cwt. lb. oz. gr.
1 = 20 = 2,000 = 32,000 = 14.000,000
The avoirdupois pound contains 7,000 gr.
LONG-TON TABLE
16 ounces =1 pound lb.
112 pounds =1 hundredweight cwt.
20 cwt., or 2,240 lb = 1 ton T.
DRY MEASURE
2 pints (pt.) =1 quart qt.
8 quarts = 1 peck pk.
4 pecks =1 bushel bu.
bu. pk. qt. pt.
1 = 4 = 32 = 64
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 i in.
in diameter and 8 in. deep. The heaped bushel is equal to
1| struck bu., the cone being 6 in. high. For approximations.
USEFUL TABLES 3
the bushel may be taken at IJ cu. ft. or 1 cu. ft. may be con-
sidefed I bu.
The British bushel contains 2,218.19 cu. in. = 1.2837 cu. ft.
= 1.032 U. S. bu.
The dry gallon contains 268.8 cu. in., or i struck bu.
LIQXnD MEASURE
4 gills (gi.) =1 pint pt.
2 pints = 1 quart qt.
4 quarts =1 gallon gal.
31i gallons =1 barrel bbl.
2 barrels, or 63 gallons « 1 hogshead hhd.
hhd. bbl. gal. qt. pt. gi.
1 = 2 = 63 = 262 = 504 = 2,016
The U. S. gallon contains 231 cu. in, = .134 cu. ft., nearly;
or 1 cu. ft. contains 7.481 gal. The following cylinders con-
tain the given measures very closely:
Diam. Height Diam. Height
Inches Inches Inches Inches
Gill H 3 Gallon 7 6
Pint 3J 3 8 gal 14 12
Quart 3§ 6 10 gal 14 15
When water is at its maximum density, 1 cu. ft. weighs
62.425 lb. and 1 gal. weighs 8.345 lb.
For approximations, 1 cu. ft. of water is considered equal
to 7i gal., and 1 gal. as weighing 8^ lb.
The British imperial gallon, both liquid and dry, contains
277.274 cu. in. =». 16046 cu. ft., and is equivalent to the volume
of 10 lb. of pure water at 62° P.
To reduce British to U. S. liquid gallons, multiply by 1.2.
Conversely, to convert U. S. into British liquid gallons, divide
by l.i\ or, increase the number of gallons one-fifth.
METRIC SYSTEM
The metric system is based on the meter, which, according to
the U. S. Coast and Geodetic Survey report of 1884, is equal
to 39.370432 in. The value commonly used is 39.37 in., and
is authorized by the U. S. government. The meter is defined
4 USEFUL TABLES
-as one ten-millionth the distance from the pole to the equator
measured on a meridian passing near Paris.
There are three principal imits — the meter, the liter (pro-
nounced lee-ter), and the gram, the units of length, capacity,
■and weight, respectively. Multiples of these units are obtained
by prefixing to the names of the principal units the Greek
words deca (10), hecto (100), and kilo (1,000); the submulti-
ples, or divisions, are obtained by prefixing the Latin words
deci (Ar). centi (lir), and milli (toW)- These prefixes form
the key to the entire system. In the following tables, the
abbreviations of the principal units of these submultiples begin
with a small letter, while those of the multiples begin with a
•capital letter; they should always be written as here printed.
MEASURE OF LENGTH
10 millimeters (nim.) =1 centimeter cm.
10 centimeters =1 decimeter dm.
10 decimeters =1 meter m.
10 meters =1 decameter Dm.
10 decameters =1 hectometer Hm.
10 hectometers =1 kilometer Km.
BfEASURES OF SURFACE (NOT LAND)
100squaremillimeters(sq.mm.)>sl square centimeter., .sq. cm.
100 square centimeters =1 square decimeter... .sq. dm.
100 square decimeters =1 square meter sq. m.
MEASURES OF VOLUME
1,000 cubic millimeters =1 cubic centimeter
(cu. mm.) c. c. or cu. cm.
1,000 cubic centimeters =1 cubic decimeter cu. dm.
1,000 cubic decimeters =1 cubic meter cu. m.
MEASURES OF CAPACITY
10 milliliters (ml.) =1 centiliter cl.
10 centiliters = 1 deciliter dl.
10 deciliters =■ 1 liter 1.
,10 liters =1 decaliter Dl.
10 decaliters =1 heooliters HI.
10 hecoliters =1 kiloliters Kl.
The liter is equal to the volume occupied by 1 cu. dm.
USEFUL TABLES 5
MEASURES OF WEIGHT
10 milligrams (mg.) » 1 centigram eg.
10 centigrams =1 decigram dg.
10 decigrams =1 gram g.
10 grams =1 decagram Dg.
10 decagrams <- 1 hectogram Hg.
10 hectograms = 1 kilogram Kg.
1,000 kilograms =1 ton T.
The gram is the weight of 1 c. c. of pure distilled water at
a tem];>erature of 39.2° P.; the kilogram is the weight of 1 1.
of water; the ton is the weight of 1 cu. m. of water.
CONVERSION TABLES
By means of the accompanying tables, metric measures
can be converted into English and vice versa, by simple addi-
tion. All the figures of the values given are not required
except in very exact calculations; as a rule, 4 or 5 digits only
are used. To change 6,471.8 ft. into meters, con- ^ „
sider 6,471.8 as 6,000+400+70-fH- .8; also, 6,000 i2192
-1,000X6; 400=100X4. etc. Hence, looking in 21336
the first column of the table entitled English Meas- ^oia
races Into Metric, for 6 (the first figure of the given oaoq
number), opposite it in the column headed Peet to '
Meters, is found the number 1.8287838. Using but _ ^^
five digits and increasing the fifth digit by 1 (as '
the next is greater than 5), gives 1.8288. In other words,
6 ft. -1.8288 m.; hence, 6.000 ft. = 1.000X1.8288 -1,828.8,
simply moving the decimal point three places to the right.
Likewise, it is found that 400 ft. = 121.92 m.; 70 ft. = 21.336 m.;
1 ft. -.3048 m., and .8 ft. -.2438m. Adding as
shown, gives 1.972.6046 m. as the value of 6.471.8 ft. 22.046
As another example, convert 19.635 kg. into 19.8416
pounds. Working according to the explanation 1.3228
just given, it is found that 19.635 kg. =43.2875 lb. .0661
The only difficulty in applying these tables lies .0110
in locating the decimal point; it may always be
found thus: If the figure considered lies to the left 43.2875
of the decimal point, count each figure in order,
beginning with units (but calling units' place zero), until the
6
USEFUL TABLES
desired figure is reached, then move the decimal point to the
right as many places as the figure being considered is to the
CONVERSION TABLE
English Measures Into Metric
Eng-
lish
Metric
Metric
Metric
Metric
1
Inches to
Meters
Feet to
Meters
Potmds to
Kilos
Gallons to
Liters
1
2
3
4
5
6
7
8
9
10
.0253998
.0507996
.0761993
.1015991
.1269989
.1523987
.1777984
.2031982
.2285980
.2539978
.3047973
.6095946
.9143919
1.2191892
1.5239865
1.8287838
2.1335811
2.4383784
2.7431757
3.0479730
.4535925
.9071850
1.3607775
1.8143700
2.2679625
2.7215550
3.1751475
3.6287400
4.0823325
4.5359250
3.7853122
7.5706244
11.3559366
15.1412488
18.9265610
22.7118732
26.4971854
30.2824976
34.0678098
37.8531220
Metric
Metric
Metric
Metric
Eng-
lish
Square
Inches
to
Square
MjBters
Square
Feet
to
Square
Meters
Cubic
Feet
to
Cubic
Meters
Pounds per
Square Inch
to Kilo per
Square
» Meter
1
2
3
4
5
6
7
8
9
10
.000645150
.001290300
.001935450
.002580600
.003225750
.003870900
.004516050
.005161200
.005806350
.006451500
.092901394
.185802788
.278704182
.371605576
.464506970
.557408364
.650309758
.743211152
.836112546
.929013940
.028316094
.056632188
.084948282
.113264376
.141580470
.169896564
.198212658
.226528752
.254844846
.283160940
703.08241
1.406.16482
2.109.24723
2.812.32964
3.515.41205
4.218.49446
4,921.57687
5,624.65928
6.327.74169
7,030.82410
left of the unit figure. Thus, in the first example, 6 lies three
places to the left of 1. which is in units' place; hence, the deci-
mal point is moved three places to the right. By exchanging
USEFUL TABLES
the words right and left, the statement will also apply to deci-
mals. Thusr in the second case above, the 6 lies three places
CONVERSION TABLE
Metric Measures Into English
English
English
English
English
Metric
Meters to
Inches
Meters to
Feet
Kilos to
Pounds
Liters to
Gallons
1
2
3
4
6
6
7
8
9
10
39.370432
78.740864
118.111296
167.481728
196.852160
236.222592
275.593024
314.963456
354.333888
393.704320
3.2808693
6.6617386
9.8426079
13.1234772
16.4043465
19.6862158
22.9660851
26.2469544
29.5278237
32.8086930
2.2046223
4.4092447
6.6138670
8.8184894
11.0231117
13.2277340
16.4323664
17.6369787
19.8416011
22.0462234
.2641790
.6283580
.7926371
1.0667161
1.3208961
1.5850741
1.8492631
2.1134322
2.3776112
2.6417902
English
English
EngUsh
English
Metric
Square
Meters
to
Square
Inches
Square
\Ieters
to
Square
Feet
Cubic
Meters
to
Cubic
Feet
Kilos per
Square
Meter to
Pounds per
Square
Inch
1
2
3
4
6
6
7
8
9
10
1,550.03092
3,100.06184
4,650.09276
6,200.12368
7,750.15460
9,300.18552
10,860.21644
12,400.24736
13,950.27828
15,600.30920
10.7641034
21.5282068
32.2923102
43.0664136
63.8206170
64.6846204
76.3487238
86.1128272
96.8769306
107.6410340
35.3156163
70.6312326
105.9468489
141.2624652
176.5780816
211.8936978
247.2093141
282.5249304
317.8405467
353.1561630
.001422310
.002844620
.004266930
.005689240
.007111560
.008533860
.009956170
.011378480
.012800790
.014223100
to the right of units' place; hence, the decimal point in the
number taken from the table is moved three places to the left.
8
USEFUL TABLES
TIMBER AND BOARD MEASURE
TIMBER MEASURE
Volume of Round Timber. — ^The voluxne of round timber, in
cubic feet, equals the length multiplied by one-fourth the prod-
uct of mean girth and diameter, all dimensions being in feet.
If length is given in feet and girth and diameter in inches,
divide by 144; if all dimensions are in inches, divide by 1,728.
AREA OF ROUJMD TIMBER
i Girths
Area
i Girths
Area
\ Girths
Area
Inches
Square
Feet
Inches
Square
Feet
Inches
Square
Feet
6
.250
12i
12}
1.04
19
2.50
6i
6i
.272
1.08
19i
2.64
.294
12J
1.12
20
2.77
6i
.317
13
1.17
20J
2.91
7
.340
13J
1.21
21
3.06
?l
.364
13i
1.26
2U
3.20
.390
13i
1.31
22
3.36
7i
.417
14
1.36
22 i
3.51
8
.444
14i
1.41
23
3.67
si
.472
14§
1.46
23i
3.83
.501
14 i
1.51
24
4.00
81
.531
15
1.56
24 J
4.16
9
.562
15i
1.61
25
4.34
^\
.594
15§
1.66
25§
4.51
9
.626
151
1.72
26
4.69
9!
.659
16
1.77
26i
4.87
10
.694
16i
1.83
27
5.06
lOi
10}
.730
16
1.89
27J
5.25
.766
16!
1.94
28
5.44
lOf
.803
17
2.00
28}
5.64
11
.840
17J
2.09
29
5.84
lU
.878
17*
17i
2.12
29i
6.04
111
.918
2.18
30
6.25
.959
18
2.25
12
1.000
18J
2.37
In the accompanying table is given the area of round timber.
The area corresponding to J girth (mean), in inches, multiplied
by the length, in feet, equals the solidity, in feet and decimal
USEFUL TABLES
AREA OF CUT TIMBER
9
Breadth
Inches
i
1
U
II
2
2J
24
2i
3
if
31
4
Area of
Breadth
1 Lin. Ft.
Inches
.021
4i
.042
4
.063
4^
.083
5
.104
5;
5
.125
.146
5
.167
6
.188
6i
.208
64
.229
6|
.250
7
.271
7:
.292
7
.313
7
.333
8
Area of
Breadth
1 Lin. Pt.
Inches
.354
8i
8
.375
.396
8:
.417
9
.438
9
.458
9
.479
9
.500
10
.521
10
.542
104
.563
10
.583
11
.604
Hi
.625
Hi
.646
Hi
.667
12
Area of
1 Lin. Ft.
.688
.708
.729
.750
.771
.792
.813
.833
.854
.875
.896
.917
.938
.958
.979
1.000
DECIMAL EQUIVALENTS OF PARTS OF 1 IN.
Part of
Inch
g
1
Part of
Inch
a
(U
>
Part of
Inch
1
Part of
Inch
4J
•3
(^
W
W
(^
A
.015625
H
.265625
H
.615625
4£
.765625
^
.031250
g
.281250
f
.531250
.781250
A
.046875
.296875
f
.546875
.796875
^
■ .062500
A
.312500
W
.562500
.812500
^
.078125
.328125
1
.578125
■
.828125
A
.093750
.343750
.593750
.843750
^
.109376
.359376
|-
.609375
. •-
.859375
.125000
i
.375000
f
.625000
i
.875000
.140625
.156250
. J,
*
.390625
.406250
II
.640625
.656250
1
.890625
.906250
44
.171875
.421875
■
.671875
.921875
A
.187500
i
.437500
.687500
.937500
H
.203125
.453125
: J .
1 4
,703125
■ 4
.953125
f
.218750
44
.468750
.718750
.968750
.234375
14
.484375
:
.734375
.984375
i
.250000
4
.500000
I
.750000
1
1
10 USEFUL TABLES
DECI2CALS OF A FOOT FOR EACH 1-32 IN.
Tn.
0"
1"
2"
3"
4"
6"
.0833
.1667
.2500
.3333
.4167
^
.0026
.0859
.1693
.2526
.3359
.4193
.0052
.0885
.1719
.2552
.3385
.4219
"it
.0078
.0911
.1745
.2578
.3411
.4245
I
.0104
.0937
.1771
.2604
.3437
.4271
~fm
.0130
.0964
.1797
.2630
.3464
.4297
-^
.0156
.0990
.1823
.2656
.3490
.4323
-Jg
.0182
.1016
.1849
.2682
.3516
.4349
4
.0208
.1042
.1875
.2708
.3542
.4376
Sf
.0234
.1068
.1901
.2734
.3568
.4401
jC
.0260
.1094
.1927
.2760
.3594
.4427
il
.0286
.1120
.1953
.2786
.3620
.4453
1
.0312
.1146
.1979
.2812
.3646
.4479
A
.0339
.1172
.2005
.2839
.3672
.4505
X
.0365
.1198
.2031
.2865
.3698
.4531
ll
.0391
.1224
.2057
.2891
.3724
.4557
^
.0417
.1250
.2083
.2917
.3750
.4583
.0443
.1276
.2109
.2943
.3776
.4609
jl
.0469
.1302
.2135
.2969
.3802
.4635
u
.0496
.1328
.2161
.2995
.3828
.4661
1
.0521
.1354
.2188
.3021
.3854
.4688
^
.0547
.1380
.2214
.3047
.3880
.4714
'1
.0573
.1406
.2240
.3073
.3906
.4740
1
.0599
.1432
.2266
.3099
.3932
.4766
■
.0625
.1458
.2292
.3125
.3958
.4792
• ' '
.0651
.1484
.2318
.3151
.3984
.4818
.0677
.1510
.2344
.3177
.4010
.4844
.0703
.1536
.2370
.3203
.4036
.4870
1
.0729
.1562
.2396
.3229
.4062
.4896
.0755
.1589
.2422
.3255
.4089
.4922
^
.0781
.1615
.2448
.3281
.4115
.4948
.0807
.1641
.2474
.3307
.4141
.4974
Volume of Square Timber. — ^When all dimensions are in feet:
Rule. — Multiply the breadth by the depth and that product by
the length, and the product will give the volume, in cubic feei.
When either of the dimensions is in inches:
Rule. — Multiply as before and divide by IB.
When any two of the dimensions are in inches:
Rule. — Multiply as before and divide by 144.
USEFUL TABLES
Table — {Continued)
11
In.
6"
7"
8"
9"
10"
.5000
.5833
.6667
.7500
.8333
.5026
.5859
.6693
.7526
.8359
.5052
• .5885
.6719
7552
.8385
.5078
.5911
.6745
.7578
.8411
.5104
.5937
.6771
.7604
.8437
.6130
.5964
.6797
.7630
.8464
.6156
.5990
.6823
.7656
.8490
.5182
.6016
.6849
.7682
.8516
.5208
.6042
.6875
.7708
.8542
.5234
.6068
.6901
.7734
.8568
.5260
.6094
.6927
.7760
.8594
.5286
.6120
.6953
.7786
.8620
.5312
.6146
.6979
.7812
.8646
.5339
.6172
.7005
.7839
.8672
.5365
.6198
.7031
.7865
.8698
.5391
.6224
.7057
.7891
.8724
.5417
.6250
.7083
.7917
.8750
.5443
.6276
.7109
.7943
.8776
.5469
.6302
.7135
.7969
.8802
.5495
.6328
.7161
.7995
.8828
.5521
.6354
.7188
.8021
.8854
.5547
.6380
.7214
.8047
.8880
.5573
.6406
.7240
.8073
.8906
.5599
.6432
.7266
.8099
.8932
.5625
.6458
.7292
.8125
.8958
.5651
.6484
.7318
.8151
.8984
.5677
.6510
.7344
.8177
.9010
.5703
.6536
.7370
.8203
.9036
.5729
.6562
.7396
.8229
.9062
.5755
.6589
.7422
.8255
.9089
.5781
.6615
.7448
.8281
.9115
.5807
.6641
.7474
.8307
.9141
11
//
.9167
.9193
.9219
.9245
.9271
.9297
.9323
.9349
.9375
.9401
.9427
.9453
.9479
.9505
.9531
.9557
.9583
.9609
.9635
.9661
.9688
.9714
.9740
.9766
.9792
.9818
.9844
.9870
.9896
.9922
.9948
.9974
BOARD MEASURE
In measttring, boards are assumed to be 1 in. thick. The
number of feet, board measure (B. M.), in a given board or
stick of timber, equals the length, in feet, multiplied by the
breadth, in feet, multiplied by the thickness, in inches.
Area of 1 lin. ft. multiplied by length, in fe^t, will give super-
ficial contents, in square feet.
12 USEFUL TABLES
DECIMAL EQUIVALENTS
In many cases of taking measurements, it is desirable to
change a fraction of an inch or foot to decimals, or getting the
nearest fraction of an inch or foot from a calculation in
which a large decimal appears. The preceding tables give the
decimal equivalents of each lAr in. and the decimal equivalents
of 1 ft. for each ^ in.
TRAVERSE TABLES
To use the traverse tables, find the number of degrees in the
left-hand column if the angle is less than 45^, and in the right-
hand column if greater than 45°. The numbers on the same
line running across the page are the latitudes and departures
for that angle and for the respective distances, 1, 2, 3, 4, 5,
6, 7, 8, 9, which appear at the top of the pages. Thus, if the
bearing of a line is 10° and the distance is 4, the latitude will be
3.939 and the departure .695; with the same bearing, and the
distance 8, the latitude will be 7.878 and the departure 1.389.
The latitude and departure for 80 is 10 times the latitude
and departure for 8, and is found by moving the decimal point
one place to the right; that for 500 is 100 times the latitude and
departure for 5, and is found by moving the decimal point two
places to the right and so on. By moving the decimal point
one, two, or more places to the right, the latitude and departure
may be fotmd for any multiple of any number given in the
table. In finding the latitude and departure for any nimiber
fiuch as 453, the number is resolved into three numbers, viz.
400, 50, 3, and the latitude and departure for each is taken
from the table and then added together.
Rule. — Write dawn the latitude and departure, neglecting the
decimal points, for the first figure of the given distance; write
under them the latitude and departure for the second figure, setting
ihem one place farther to the right; under these, place the latitude
and departure for the third figure, setting them one place still
farther to the right, and so continue until all the figures of the given
distance have been used; add these latitudes and departures, and
point off on the right of their sums a number of decimal places
USEFUL TABLES 13
equal to the number of decimal places to which the tables being
used are carried; the resulting numbers vriU be the latitude and
departure of the given distance in feet, links, chains, or whatever
unit of measurement is adopted. Should the departure or latitude
consist only of a decimal, a cipher should be inserted before the
decimal, as in the departures of example 1.
Example 1. — ^A bearing is 16° and the distance 725 ft.;
what is the latitude and departure?
Solution. — Applying the rule just given:
Distances Latitudes Departures
700 6729 1929
20 1923 0551
5 4806 1378
72 5 6 9 6.936 199.788
Taking the nearest whole numbers and rejecting the decimals,
the latitude and departure are 697 and 200.
When a occurs in the given number, the next figure must
be set two places to the right as in the following example:
Example 2. — The bearing is 22° and the distance 907 ft.;
required, the latitude and departure.
Solution. — Applying the rule just given:
{stances
Latitudes
Departures
900
8345
3371
7
6490
8 4 0.9 9
2622
907
3 3 9.7 2 2
Here the place of both in the distance column and in the
latitude and departure columns is occupied by a dash — .
Rejecting the. decimals, the latitude is 841 ft. and the depart-
ure 340 ft.
When the bearing is more than 45°, the names of the columns
must be read from the bottom of the page. The latitude of
any bearing, as 60°, is the departure of its complement, 30°;
and the departure of any bearing, as 30°, is the latitude of its
complement, 60°. Where the bearings are given in smaller
fractions of degrees than is found in the table, the latitudes
and departures can be found by interpolation.
14-
USEFUL TABLES
earing
egrees
1
2
3
4
5
2 &
n Q
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
.000
Lat.
Dep.
Lat.
n Q
1.000
.000
2.000
.000
3.000
4.000
.000
5.000
90
1.000
.004
2.000
.009
3.000
.013
4.000
.017
5.000
891
'
1.000
.009
2.000
.017
3.000
.026
4.000
.035
5.000
89
1.000
.013
2.000
.026
3.000
.039
4.000
.052
5.000
89i
1
1.000
.017
2.000
.035
3.000
.052
3.999
.070
4.999
89
1}
1.000
.022
2.000
.044
2.999
.065
3.999
.087
4.999
881
88
1.000
.026
1.999
.052
2.999
.079
3.999
.105
4.998
li
1.000
.031
1.999
.061
2.999
.092
3.998
.122
4.998
S8
2
.999
.035
1.999
.070
2.998
.105
3.998
.140
4.997
88
2i
.999
.039
1.998
.079
2.998
.118
3.997
.157
4.996
87 i
2i
.999
.044
1.998
.087
2.997
.131
3.996
.174
4.995
87
2i
.999
.048
1.998
.096
2.997
.144
3.995
.192
4.994
87:
3
.999
.052
1.997
.105
2.996
.157
3.995
.209
4.993
87
3i
.998
.057
1.997
.113
2.995
.170
3.994
.227
4.992
86f
3|
3i
.998
.061
1.996
.122
2.994
.183
3.993
.244
4.991
86
.998
.065
1.996
.131
2.994
.196
3.991
.262
4.989
86;
4
.998
.070
1.995
.140
2.993
.209
3.990
.279
4.988
86
4|
.997
.074
1.995
.148
2.992
.222
3.989
.296
4.986
85f
.997
.078
1.994
.157
2.991
.235
3.988
.314
4.985
85
4i
.997
.083
1.993
.166
2.990
.248
3.986
.331
4.983
85:
5
.996
.087
1.992
.174
2.989
.261
3.985
.349
4.981
86
^i
.996
.092
1.992
.183
2.987
.275
3.983
.366
4.979
841
5
.995
.096
1.991
.192
2.986
.288
3.982
.383
4.977
84
84
51
.995
.100
1.990
.200
2.985
.301
3.980
.401
4.975
6
.995
.105
1.989
.209
2.984
.314
3.978
.418
4.973
84
6}
.994
.109
1.988
.218
2.982
.327
3.976
.435
4.970
83f
.994
.113
1.987
.226
2.981
.340
3.974
.453
4.968
83
6}
.993
.118
1.986
.235
2.979
.353
3.972
.470
4.965
83
7
.993
.122
1.985
.244
2.978
.366
3.970
.487
4.963
83
7i
.992
.126
1.984
.252
2.976
.379
3.968
.505
4.960
821
74
71
.991
.131
1.983
.261
2.974
.392
3.966
.522
4.957
82
.991
.135
1.982
.270
2.973
.405
3.963
.539
4.954
82
8
.990
.139
1.981
.278
2.971
.418
3.961
.657
4.951
82
8}
.990
.143
1.979
.287
2.969
.430
3.959
.674
4.948
81f
8
.989
.148
1.978
.296
2.967
.443
3.956
.691
4.945
81
81
.988
.152
1.977
.304
2.965
.456
3.953
.608
4.942
81
9
.988
Dep.
.156
1.975
.313
Lat.
2.963
.469
3.951
.626
4.938
81
M s
Lat.
Dep.
Dep.
Lat.
Dep.
Lat.
Dep.
5
||
la
1
4
I
J
4
nQ
USEFUL TABLES
15
Bearing
Degrees
5
6
7
8
9
9 8
'5 £
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
9 9
.000
6.000
.000
7.000
.000
8.000
.000
9.000
.000
90
.022
6.000
.026
7.000
.031
8.000
.035
9.000
.039
89f
.
.044
6.000
.052
7.000
.061
8.000
.070
9.000
.079
89
.065
5.999
.079
6.999
.092
7.999
.105
8.999
.118
89
1
.087
5.999
.105
6.999
.122
7.999
.140
8.999
.157
89
U
l|
.109
5.999
.131
6.998
.163
7.998
.175
o.99o
.196
88i
.131
5.998
.157
6.998
.183
7.997
.209
8.997
.236
88
88;
1}
.153
5.997
.183
6.997
.214
7.996
.244
r».99o
.276
2
.174
5.996
.209
0.996
.244
7.996
.279
8.995
.314
88
2i
.196
5.995
.236
6.995
.276
7.994
.314
8.993
.353
871
2i
.218
5.994
.262
6.993
.305
7.992
.349
8.991
.393
87
2i
.240
5.993
.288
6.992
.336
7.991
.384
8.990
.432
87
3
.262
5.992
.314
8.990
.366
7.989
.419
8.988
.471
87
3i
.283
5.990
.340
6.989
.397
7.987
.464
8.986
.510
86}
3
.305
5.989
.366
6.987
.427
7.986
.488
8.983
.549
86
3}
.327
5.987
.392
6.985
.468
7.983
.523
8.981
.589
86
4
.349
5.985
.419
6.983
.488
7.981
.558
8.978
.628
86
^i
.371
5.984
.445
8.981
.519
7.978
.593
8.976
.667
85f
4
.392
5.982
.471
6.978
.649
7.975
.628
8.972
.706
85
4}
.414
5.979
.497
6.976
.680
".973
.662
8.969
.745
85
5
.436
5.977
.523
8.973
.610
7.970
.697
8.966
.784
85
Si
.458
5.975
.549
6.971
.641
7.966
.732
8.962
.824
84i
5
.479
5.972
.575
6.968
.671
7.963
.767
8.959
.863
844
51
.501
5.970
.601
8.965
.701
7.960
.802
8.955
.902
84i
6
.523
5.967
.627
6.962
.732
7.966
.836
8.961
.941
84
6i
.544
5.964
.653
6.958
.762
7.962
.871
8.947
.980
83}
6
.566
5.961
.679
6.966
.792
7.949
.906
8.942
1.019
83
83
6}
.688
5.958
.705
6.951
.823
7.945
.940
8.938
1.068
7
.609
5.955
.731
6.948
.863
7.940
.976
8.933
1.097
83
7i
.631
5.952
.757
6.944
.883
7.936
1.010
8.928
1.136
82}
7
.653
5.949
.783
6.940
.914
7.932
1.044
8.923
1.176
82
7|
.674
5.945
.809
6.936
.944
7.927
1.079
8.918
1.214
82
8
.696
5.942
.835
6.932
.974
7.922
1.113
8.912 1.2631
82
8i
.717
6.938
.861
6.928
1.004
7.917
1.148
8.907
1.291
81}
84
8}
.739
5.934
.887
6.923
1.035
7.912
1.182
8.901
1.330
81
.761
5.930
.913
6.919
1.066
7.907
1.217
8.896
1.369
81
9
.782
Lat.
6.926
.939
6.914
Dep
1.096
7.902
Dep
1.251
Lat.
8.889
1.408
81
2»8
Dep
Lat.
Lat.
Dep
Lat.
a*!
earii
egre
'
PQQ
5
6
7
8
9
m Q
16
USEFUL TABLES
■
ring
rees
1
2
3
4
5
c 8
2 S?
c4 bO
4) V
a P
Lat.
Dep.
.166
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
9
.988
1.975
.313
2.963
.469
3.951
.626
4.938
81
9i
.987
.161
1.974
.321
2.961
.482
3.948
.643
4.935
801
9i
.986
.165
1.973
.330
2.959
.495
3.945
.660
4.931
80
9*
.986
.169
1.971
.339
2.957
.508
3.942
.677
4.928
80
10
.985
.174
1.970
.347
2.954
.521
3.939
.695
4.924
80
lOi
.984
.178
1.968
.356
2.952
.534
3.936
.712
4.920
79i
lOi
.983
.182
1.967
.364
2.950
.547
3.933
.729
4.916
79
lOi
.982
.187
1.965
.373
2.947
.560
3.930
.746
4.912
79
11
.982
.191
1.963
.382
2.945
.572
3.927
.763
4.908
79
Hi
.981
.195
1.962
.390
2.942
.585
3.923
.780
4.904
78}
7si
Hi
.980
.199
1.960
.399
2.940
.598
3.920
.797
4.900
m
.979
.204
1.958
.407
2.937
.611
3.916
.815
4.895
78i
12
.978
.208
1.956
.416
2.934
.624
3.913
.832
4.891
78
12i
.977
.212
1.954
.424
2.932
.637
3.909
.849
4.886
77}
12i
.976
.216
1.953
.433
2.929
.649
3.905
.866
4.881
774
12}
.975
.221
1.951
.441
2.926
.662
3.901
.883
4.877
77}
13
.974
.225
1.949
.450
2.923
.675
3.897
.900
4.872
77
13i
13}
.973
.229
1.947
.458
2.920
.688
3.894
.917
4.867
76}
.972
.233
1.945
.467
2.917
.700
3.889
.934
4.862
76
76
13}
.971
.238
1.943
.475
2.914
.713
3.885
.951
4.857
14
.970
.242
1.941
.484
2.911
.726
3.881
.968
4.851
76
14}
14i
.969
.246
1.938
.492
2.908
.738
3.877
.985
4.846
75}
.968
.250
1.936
.501
2.904
.751
3.873
1.002
4.841
764
14}
.967
.255
1.934
.509
2.901
.764
3.868
1.018
4.835
75i
15
.966
.259
1.932
.518
2.898
.776
3.864
1.035
4.830
75
15i
15}
.965
.263
1.930
.526
2.894
.789
3.859
1.052
4.824
74i
.964
.267
1.927
.534
2.89f
.802
3.855
1.069
4.818
74
74
15}
.962
.271
1.925
.543
2.887
.814
3.850
1.086
4.812
16
.961
.276
1.923
.551
2.884
.827
3.845
1.103
4.806
74
16}
.960
.280
1.920
.560
2.880
.839
3.840
1.119
4.800
73}
16i
.959
.284
1.918
.568
2.876
.852
3.835
1.136
4.794
73
16}
.958
.288
1.915
.576
2.873
.865
3.830
1.153
4.788
73
17
.956
.292
1.913
.585
2.869
.877
3.825
1.169
4.782
73
17}
17}
.955
.297
1.910
.593
2.865
.890
3.820
1.186
4.775
72}
.954
.301
1.907
.601
2.861
.902
3.815
1.203
4.769
72
17}
.952
.305
1.905
.610
2.857
.915
3.810
1.220
4.762
72
18
.951
.309
1.902
.618
Lat.
2.853
Dep.
.927
3.804
1.236
Lat.
4.755
Dep.
72
91
Dep.
Lat.
Dep.
Lat.
Dep.
i 1
•d S
S «
flC Q
1
2
3
4
[
5
PQ Q
USEFUL TABLES
17
ring
:rees
5
6
t
7
8
9
jaring
sgrees
g 2?
Dep.
.732
Lat.
Dep.
.939
Lat.
Dep.
Lat.
7.902
Dep.
Lat.
8.889
Dep.
9
5.926
6.914
1.095
1.251
1.408
81
n
.804
5.922
.964
6.909
1.125
7.896
1.286
8.883
1.447
80}
9*
.825
5.918
.990
6.904
1.155
7.890
1.320
8.877
1.485
80
9f
.847
5.913
1.016
6.899
1.185
7.884
1.355
8.870
1.524
80
10
.868
5.909
1.042
6.894
1.216
7.878
1.389
8.863
1.563
80
lOi
.890
5.904
1.068
6.888
1.246
7.872
1.424
8.856
1.601
79i
10*
.911
5.900
1.093
6.883
1.276
7.866
1.458
8.849
1.640
79*
lOf
.933
5.895
1.119
6.877
1.306
7.860
1.492
8.842
1.679
79i
11
.954
5.890
1.145
6.871
1.336
7.853
1.526
8.835
1.717
79
Hi
.975
5.885
1.171
6.866
1.366
7.846
1.561
8.827
1.756
78i
11*
.997
5.880
1.196
6.859
1.396
7.839
1.595
8.819
1.794
78*
Hi
1.018
5.874
1.222
6.853
1.425
7.832
1.629
8.811
1.833
78i
12
1.040
5.869
1.247
6.847
1.455
7.825
1.663
8.803
1.871
78
12i
1.061
5.863
1.273
6.841
1.485
7.818
1.697
8.795
1.910
77 i
12*
1.082
5.868
1.299
6.834
1.515
7.810
1.732
8.787
1.948
77
12i
1.103
5.852
1.324
6.827
1.545
7.803
1.766
8.778
1.986
77;
13
1.125
5.846
1.350
6.821
1.575
7.795
1.800
8.769
2.025
77
13i
1.146
5.840
1.375
6.814
1.604
7.787
1.834
8.760
2.063
761
13*
1.167
5.834
1.401
6.807
1.634
7.779
1.868
8.751
2.101
76
13i
1.188
5.828
1.426
6.799
1.664
7.771
1.902
8.742
2.139
76 ;
14
1.210
5.822
1.452
6.792
1.693
7.762
1.935
8.733
2.177
76
14i
1.231
5.815
1.477
6.785
1.723
7.754
1.969
8.723
2.215
75i
14*
1.252
5.809
1.502
6.777
1.753
7.745
2.003
8.713
2.253
75
14i
1.273
5.802
1.528
6.769
1.782
7.736
2.037
8.703
2.291
75
15
1.294
5.796
1.553
6.761
1.812
7.727
2.071
8.693
2.329
75
15i
1.315
5.789
1.578
6.754
1.841
7.718
2.104
8.683
2.367
74 i
15*
1.336
5.782
1.603
6.745
1.871
7.709
2.138
8.673
2.405
74*
15i
1.357
5.775
1.629
6.737
1.900
7.700
2.172
8.662
2.443
74i
16
1.378
6.768
1.654
6.729
1.929
7.690
2.205
8.651
2.481
74
16i
1.399
5.760
1.679
6.720
1.959
7.680
2.239
8.640
2.518
73 i
16*
1.420
5.753
1.704
6.712
1.988
7.671
2.272
8.629
2.556
73
16i
1.441
5.745
1.729
6.703
2.017
7.661
2.306
8.618
2.594
73;
17
1.462
5.738
1.754
6.694
2.047
7.650
2.339
8.607
2.631
73
17i
1.483
5.730
1.779
6.685
2.076
7.640
2.372
8.595
2.669
72*
72*
17*
1.504
5.722
1.804
6.676
2.105
7.630
2.406
8.583
2.706
17i
1.524
5.714
1.829
6.667
2.134
7.619
2.439
8.572
2.744
72*
18
1.545
5.706
1.854
6.657
2.163
7.608
2.472
8.560
2.781
72
•^1
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
c I
^ qF
g !»
n Q
5
6
7
8'
9
a Q
3
18
»
USEFUL TABLES
Bearing
Degrees
1
2
3
4
5
CA SR
Lat. Dep.
Lat.
1.902
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
&S
18
.951
.<j09
.618
2.853
.927
3.804
1.236
4.755
72
18i
.950
.313
1.899
.626
2.849
.939
3.799
1.263
4.748
71|
18i
.948
.317
1.897
.636
2.845
.952
3.793
1.269
4.742
71
18i
.947
.321
1.894
.643
2.841
.964
3.788
1.286
4.735
71
19
.946
.326
1.891
.651
2.837
.977
3.782
1.302
4.728
71
19i
.944
.330
1.888
.659
2.832
.989
3.776
1.319
4.720
70|
194
19}
.943
.334
1.885
.668
2.828
1.001
3.771
1.335
4.713
70
.941
.338
1.882
.676
2.824
1.014
3.765
1.352
4.706
70
20
.940
.342
1.879
.684
2.819
1.026
3.759
1.368
4.698
70
20i
.938
.346
1.876
.692
2.815
1.038
3.753
1.384
4.691
69i
201
.937
.350
1.873
.700
2.810
1.051
3.747
1.401
4.683
69
69
20}
.935
.354
1.870
.709
2.805
1.063
3.741
1.417
4.676
21
.934
.358
1.867
.717
2.801
1.075
3.734
1.433
4.668
69
21}
.932
.362
1.864
.725
2.796
1.087
3.728
1.450
4.660
68}
21|
21}
.930
.367
1.861
.733
2.791
1.100
3.722
1.466
4.652
68
.929
.371
1.858
.741
2.786
1.112
3.715
1.482
4.644
68
22
.927
.375
1.854
.749
2.782
1.124
3.709
1.498
4.636
68
22}
22}
.926
.379
1.851
.757
2.777
1.136
3.702
1.615
4.628
67}
.924
.383
1.848
.765
2.772
1.148
3.696
1.631
4.619
67
67
23}
.922
.387
1.844
.773
2.767
1.160
3.689
1.547
4.611
23
.921
.391
1.841
.781
2.762
1.172
3.682
1.663
4.603
67
23}
23 i
.919
.395
1.838
.789
2.756
1.184
3.675
1.679
4.594
66}
66
.917
.399
1.834
.797
2.751
1.196
3.668
1.696
4.585
23}
.915
.403
1.831
.805
2.746
1.208
3.661
1.611
4.577
66}
24
.914
.407
1.827
.813
2.741
1.220
3.654
1.627
4.668
66
24}
.912 .411
1.824
.821
2.735
1.232
3.647
1.643
4.569
65f
24 k
24 1
.910
.415
1.820
.829
2.730
1.244
3.640
1.659
4.550
66
.908
.419
1.816
.837
2.724
1.256
3.633
1.675
4.641
66
25
.906
.423
1.813
.845
2.719
1.268
3.625
1.690
4.532
66
25}
.904
.427
1.809
.853
2.713
1.280
3.618
1.706
4.522
64}
25i
.903
.431
1.805
.861
2.708
1.292
3.610
1.722
4.513
64
64
251
.901
.434
1.801
.869
2.702
1.303
3.603
1.738
4.503
26
.899
.438
1.798
.877
2.696
1.315
3.595
1.753
4.494
64
26}
26}
.897
.442
1.794
.885
2.691
1.327
3.687
1.769
4.484
63}
.895
.446
1.790
.892
2.685
1.339
3.680
1.785
4.475
63
26}
.893
.450
1.786
.900
2.679
1.350
3.572
1.800
4.465
63
27
.891
.454
1.782
Dep.
.908
2.673
1.362
3.564
1.816
4.465
63
ring
rees
Dep.
Lat.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
11
^ »>
3 §0
4) «.
0) Q
1
S
I
3
4
5
&S
USEFUL TABLES
20
USEFUL TABLES
ring
rees
1
2
3
4
5
Bea:
Deg
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
27
.891
.454
1.782
.908 2.673
1.362
3.564
1.816
4.455
63
27 J
.889
.458
1.778
.916 2.667
1.374
3.556
1.831
4.445
62f
274
.887
.462
1.774
.923
2.661
1.385
3.548
1.847
4.435
62
27i
.885
.466
1.770
.931
2.655
1.397
3.540
1.862
4.425
62:
28
.883
.469
1.766
.939
2.649
1.408
3.532
1.878
4.415
62
28i
.881
.473
1.762
.947
2.643
1.420
3.524
1.893
4.404
61f
284
.879
.477
1.758
.954
2.636
1.431
3.515
1.909
4.394
61
28i
.877
.481
1.753
.962
2.630
1.443
3.507
1.924
4.384
61
29
.875
.485
1.749
.970
2.624
1.454
3.498
1.939
4.373
61
294
294
.872
.489
1.745
.977
2.617
1.466
3.490
1.954
4.362
60i
.870
.492
1.741
.985
2.611
1.477
3.481
1.970
4.352
60
29!
.868
.496
1.736
.992
2.605
1.489
3.473
1.985
4.341
60
30
.866
.500
1.732
1.000
2.598
1.500
3.464
2.000
4.330
60
304
.864
.504
1.728
1.008
2.592
1.511
3.455
2.015
4.319
591
304
20!
.862
.508
1.723
1.015
2.585
1.523
3.447
2.030
4.308
59
59
.859
.511
1.719
1.023
2.578
1.534
3.438
2.045
4.297
31
.857
.515
1.714
1.030
2.572
1.545
3.429
2.060
4.286
50
314
.855
.519
1.710
1.038
2.565
1.556
3.420
2.075
4.275
58f
314
31!
.853
.522
1.705
1.045
2.558
1.567
3.411
2.090
4.263
58
.850
.526
1.701
1.052
2.551
1.579
3.401
2.105
4.252
58
32
.848
.530
1.696
1.060
2.544
1.590
3.392
2.120
4.240
58
324
324
.846
.534
1.691
1.067
2.537
1.601
3.383
2.134
4.229
67!
67
.843
.537
1.687
1.075
2.530
1.612
3.374
2.149
4.217
32!
.841
.541
1.682
1.082
2.523
1.623
3.364
2.164
4.205
67
33
.839
.545
1.677
1.089
2.516
1.634
3.355
2.179
4.193
57
334
.836
.548
1.673
1.097
2.509
1.645
3.345
2.193
4.181
561
334
33!
.834
.552
1.668
1.104
2.502
1.656
3.336
2.208
4.169
56
56}
.831
.556
1.663
1.111
2.494
1.667
3.326
2.222
4.157
34
.829
.559
1.658
L118
2.487
1.678
3.316
2.237
4.145
56
344
.827
.563
1.653
1.126
2.480
1.688
3.306
2.251
4.133
661
34
34
.824
.566
1.648
1.133
2.472
1.699
3.297
2.266
4.121
65
.822
.570
1.643
1.140
2.465
1.710
3.287
2.280
4.108
66
35
.819
.574
1.638
1.147
2.457
1.721
3.277
2.294
4.096
66
354
.817
.577
1.633
1.154
2.450
1.731
3.267
2.309
4.083
64f
35
.814
.581
1.628
1.161
2.442
1.742
3.257
2.323
4.071
54
35
.812
.584
1.623
1.168
2.435
1.753
3.246
2.337
4.058
54
36
.809
.588
Lat.
1.618
1.176
2.427
1.763
3.236
2.351
4.045
54
II
Dep
Dep
Lat.
Dep
Lat.
Dep
Lat.
Dep
M s
'
i 1
flQQ
1
2
3
4 5
n Q
USEFUL TABLES
21
<S or
n P
27
27i
271
271
28
28i
28}
28i
29
29i
294
291
30
30i
30i
30i
31
3U
3U
3U
32
32i
32i
32i
33
33i
33i
33i
34
34J
34|
34!
35
35
35
35
36
60
S
a Q
Dep.
2.270
2.289
2.309
2.328
2.347
2.367
2.386
2.405
2.424
2.443
2.462
2.481
2.500
2.519
2.538
2.556
2.575
2.594
2.612
2.631
2.650
2.668
^686
^705
2.723
2.741
2.
2.778
2.796
2.814
2.832
2.850
2.868
2.886
2.904
2.921
2.939
760 5
Lat.
6
Lat.
5.346
5.334
5.322
5.310
5.298
5.285
5.273
5.260
5.248
5.235
5.222
5.209
5.196
5.183
6.170
5.156
5.143
5.129
5.116
5.102
5.088
5.074
5.060
5.046
5.032
5.018
.003
4.989
4.974
4.960
4.945
4.930
4.915
4.900
4.885
4.869
4.854
Dep.
Dep
2.724
2.747
2.770
2.794
2.817
2.840
2.863
2.886
2.909
2.932
2.955
2.977
3.000
3.023
3.045
3.068
3.090
3.113
3.135
3.157
3.180
3.202
3.224
3.246
3.268
3.290
3.312
3.333
3.355
3.377
3.398
3.420
3.441
3.463
3.484
3.505
3.527
Lat.
6
Lat.
Dep.
6.237
6.223
6.209
6.195
6.181
6.166
6.152
6.137
6.122
6.107
6.093
6.077
6.062
6.047
6.031
6.016
6.000
5.984
5.968
5.952
5.936
5.920
5.904
5.887
5.871
5.854
5.837
5.820
5.803
5.786
5.769
5.752
5.734
5.716
5.699
5.681
5.663
Dep.
.178 7
.232 7
3.
3.2051
3.
3.259
3.286
3.313
3.340 7
3.367 7
3.394 6
3.420 6
3.44716
3
3
3
579 6
474
500
526
3.553
3.
3.605
3.631
3.657
3.683
3.709
3.735
3.761
3.
3.
3.838
3.864
3.889
3.914
3.940
3.965
3.990
4.015
4.040
4.
4.090
787 6
812 6
065 6
4.115 6
Lat.
8
Lat.
.128
7.112
096
7.080
7.064
7.047
.031
.014
.997
.980
.963
6.946
6.928
6.911
6.893
875
6.857
6.839
6.821
6.803
6.784
6.766
6,747
.728
709
6.690
6.671
6.652
6.632
6.613
6.593
6.573
6.553
6.533
.513
6.493
.472
Dep.
Dep,
.848 7
3.632
3.663
3.694
3.72517
3.756r
3.787
3.817
3
3.878r7
3.909
3.939 r
3.970
4.000(7
4.03017
4.060
4.090
4.120
4.150
180
210
239
269
,298 7
,328 7
4.357 7
4.386 7
4.416(7
4.4
4.47417
4.502
4.531
4.56017
4.589 r
4.617
4.64617
4.674 7
4.702 7
Lat.
8
9
Lat.
8.019
8.001
7.983
.965
.947
7.928
7.909
.891
.872
7.852
833
7.814
.794
.775
7.755
7.735
7.715
7.694
7.674
7.653
7.632
7.612
.591
.569
.548
527
505
.483
.461
f7.439
.417
.395
.372
.350
.327
.304
.281
Dep.
Dep.
4.086
4.121
4.156
4.190
4.225
4.260
4.294
4.329
4.363
4.398
4.432
4.466
4.500
4.534
4.668
4.602
4.635
4.669
4.702
4.736
4.769
4.802
4.836
4.869
4.902
4.935
4.967
5.000
5.033
5.065
5.098
5.130
5.162
5.194
5.226
5.258
5.290
Lat.
9
63
62
62
62
62
61
61
61
61
60
60
60
60
59
59
59
59
58f
58{
58i
58
57
57
57
57
56}
56i
56i
56
55}
55^
55}
55
54
54
54}
54
22
USEFUL TABLES
36
36i
36i
36}
37
37J
37 i
37 i
38
38}
38}
38}
3g
39i
39i
39}
40
40i
40}
40}
41
4U
411
41}
42
42
42
42}
43
43i
43
43
44
44i
44}
44}
45
u
9 S9
A Q
Lat.
.809
.806
.804
.801
.799
.796
.793
.791
.788
.785
.783
.780
.777
.774
.772
.769
.766
.763
.760
.758
.755
.752
.749
.746
.743
.740
.737
.734
.731
.728
.725
.722
.719
.716
.713
.710
.707
Dep.
Dep.
.588
.591
.595
.598
.602
.605
.609
.612
.616
.619
.623
.626
.629
.633
.636
.639
.643
.646
.649
.653
.656
.659
.663
.666
.669
.672
.676
.679
.682
.685
.688
.692
.695
.698
.701
.704
.707
Lat.
Lat.
1.618
1.613
1.608
1.603
1.597
1.592
1.687
1.581
1.576
1.571
1.565
1.560
1.554
1.549
1.543
1.538
1.532
1.526
1.521
1.515
1.509
1.504
1.498
1.492
1.486
1.480
1.475
1.469
1.463
1.457
1.451
1.445
1.439
1.433
1.427
1.420
1.414
Dep.
Dep.
176 2
190 2
197 2
1.
1.183
1.
1.
1.204
1.211
1.218
1.224
1.231
1.
1
1
1.259
1.
1.272
1.279
1.286
1.292
1.299
1.306
1.312
1.319
1.
1.332
1.338
1.345
1.351
1.358
1.364
1.370
1.377
1.383
1.389
1
1.402
1
1.414
238 2
245 2
252 2
259 2
265 2
2.
2.
2.
2.
326 2
2.
2.
2.
2.
396 2
408 2
Lat.
Lat.
427
12.419
.412
.404
2.396
2.388
2.380
2.372
2.364
356
348
340
331
323
315
307
298
290
2.281
2.273
2.264
2.256
247
238
229
221
212
2.203
2.194
2.185
2.176
2.167
2.158
.149
P2.140
.131
^.121
Dep.
763 3
Lat.
1.
1.774
1.78413
1.795 3
1.805 3
1.816 3
1.826 13
1.837
1.847
1.85713
.868 3
.878 3
.888 3
1
1
1
1.89813
1.908 3
1.918|3
1.928
1.93813
1.948|3
1.958
1.968
1.978
1.988
1.998
2.007
2.01712
2.027
2.036
2.04612
2.056 2
2.065 2
2.075 P
2.084
2.09312
2.103 2
2.112^
2.121
.236
3.226
.215
.205
.195
.184
.173
3.163
3.152
.141
.130
120
.109
.098
086
075
3.064
.053
042
3.030
3.019
3.007
2.996
2.984
2.973
.961
2.949
2.937
925
913
901
889
12.877
865
.853
.841
12.828
Dep.
Lat.
2.476 3.927
2.490 3.913
2.504 3.899
2.517 3.886
2.558 3.844
Dep.
2.351
Lat.
4.045
2.365 4.032
2.379 4.019
2.393
2.407 3.993
2.421
2.435 3.967
2.449
2.463
2.531
2.544
2.571
2.584
2.598 3.802
2.611
2.624
2.637
2.650 3.745
2.664
2.677
2.741
2.791
Dep.' Lat.
4.006
3.980
3.953
3.940
3.872
3.858
3.830
3.816
3.788
3.774
3.759
3.730
3.716
2.689 3.701
2.702 3.686
2.715 3.672
2.728 3.657
3.642
2.753 3.627
2.766 3.612
2.779 3.597
3.582
2.804 3.566
2.816 3.551
2.828 3.536
Dep.
54
531
53j
53i
53
52}
521
52i
52
51i
51 i
51 i
51
50|
50
50i
50
49}
49|
49}
49
48]
48
481
48
47 i
47 j
47
47
46]
46
461
46
45]
45
45]
45
II
USEFUL TABLES
23
ring
rees
5
6
7
8
9
earing
egiees
SI
n Q
Dep.
2.939
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
5.290
PQQ
36
4.854
3.527
5.663
4.115
6.472
4.702 7.281
54
36i
2.957
4.839
3.548
5.645
4.139
6.452
4.730 7.258
5.322
53}
36
361
2.974
4.823
3.569
5.627
4.164
6.431
4.759 7.235
5.353
53}
2.992
4.808
3.590
5.609
4.188
6.410
4.78717.211
5.385
53}
37
3.009
4.792
3.611
5.590
4.213
6.389
4.815
7.188
5.416
53
37}
3.026
4.776
3.632
5.572
4.237
6.368
4.84217.164
5.448
52}
37}
3.044
4.760
3.653
5.554
4.261
6.347
4.870
7.140
5.479
52
37}
3.061
4.744
3 673
5.535
4.286
6.326
4.898
7.116
5.510
52;
38
3.078
4.728
3.694
5.516
4.310
6.304
4.925
7.092
5.541
52
38}
3.095
4.712
3.715
5.497
4.334
6.283
4.953
7.068
5.572
51}
38}
38}
3.113
4.696
3.735
5.478
4.358
6.261
4.980
7.043
5.603
51
51
3.130
4.679
3.756
5.459
4.381
6.239
5.007
7.019
5.663
39
3.147
4.663
3.776
5.440
4.405
6.217
5.035
6.994
5.664
51
39}
3.164
4.646
3.796
5.421
4.429
6.195
5.062
6.970
5.694
50}
39
3.180
4.630
3.816
5.401
4.453
6.173
5.089
6.945
5.725
50
50
39}
3.197
4.613
3.837
5.382
4.476
6.151
5.116
6.920
5.755
40
3.214
4.596
3.857
5.362
4.500
6.128
5.142
6.894
5.785
50
40}
3.231
4.579
3.877
5.343
4.523
6.106
5.169
6.869
5.815
49}
40}
40}
3.247
4.562
3.897
5.323
4.546
6.083
5.196
6.844
5.845
49
49
3.264
4.545
3.917
5.303
4.569
6.061
5.222
6.818
5.875
41
3.280
4.528
3.936
5.283
4.592
6.038
5.248
6.792
5.905
49
41}
3.297
4.511
3.956
5.263
4.615
6.015
5.275
6.767
5.934
48}
41}
41}
3.313
4.494
3.976
5.243
4.638
5.992
5.301
6.741
5.964
48
48
3.329
4.476
3.995
5.222
4.661
5.968
5.327
6.715
5.993
42
3.346
4.459
4.015
5.202
4.684
5.945
5.353
6.688
6.022
48
42}
3.362
4.441
4.034
5.182
4.707
5.922
5.379
6.662
6.051
47}
42
3.378
4.424
4.054
5.161
4.729
5.898
5.405
6.635
6.080
47}
42}
3.394
4.406
4.073
5.140
4.752
5.875
5.430
6.609
6.109
47}
43
3.410
4.388
4.092
5.119
4.774
5.851
5.456
6.582
6.138
47
43}
43}
3.426
4.370
4.111
5.099
4.796
5.827
5.481
6.555
6.167
46}
3.442
4.352
4.130
5.078
4.818
5.803
5.507
6.528
6.195
46
43}
3 458
4.334
4.149
5.057
4.841
5.779
5.532
6.501
6.224
46
44
3.473
4.316
4.168
5.035
4.863
5.755
5.557
6.474
6.252
46
44}
44}
3.489
4.298
4.187
5.014
4.885
5.730 5.582
6.447
6.280
45}
3.505
4.280
4.206
4.993
4.906
5.706 5.607
6.419
6.308
45}
44}
3.520
4.261
4.224
4.971
4.928
5.681 5.632
6.392
6.336
45}
45
3.536
Lat.
4.243
4.243
4.950
4.950
Lat.
5.6575.657
1
6.364
6.364
45
II
Dep.
Lat.
Dep.
Dep.
Lat.
Dep.
Lat.
•si
a Q
5
6
7
8
9
2 &
24 MA THEM A TICS
MATHEMATICS
SIMPLE PROPORTION, OR SINGLE RULE
OF THREE
A proportion is an expression of equality between equal
ratios; thus, the ratio of 10 to 5 = the ratio of 4 to 2, and is
expressed thus : 10 : 5 = 4 :2. There are four terms in proportion ;
the first and last are the extremes and the second and third are
the means.
Quantities are in proportion by alternation when antecedent
is compared with antecedent and consequent with consequent;
thus, if 10:5 = 4:2, then 10:4 = 5:2. Quantities are in propor-
tion by inversion when the antecedents are made consequents
and the consequents antecedents; thus, if 10:5 = 4:2, then
5:10 = 2:4. In any proportion, the product of the means will
equal the product of the extremes, thus, if 10:5 = 4:2, then
6X4 = 10X2.
A mean proportional between two quantities equals the
square root of their product; thus, a mean proportional between
12 and 3= the square root of 12X3, or 6.
If the two means and one extreme of a proportion are given,
the other extreme may be found by dividing the product of
the means by the given extreme. Thus, 10:5 = 4:(), then
(4X5) -MO = 2, and the proportion is 10:5 = 4:2. If the two
extremes and one mean are given, the other mean may be found
by dividing the product of the extremes by the given mean.
Thus, 10:() = 4:2, then (10X2)4-4 = 5, and the proportion is
10:5 = 4:2.
Example. — If 6 men load 30 wagons of coal in a day, how
many wagons will 10 men load?
Solution. — They will evidently load more, so the second
tenn of the proportion must be greater than the first.
6:10- 30: ( ); then, (10X30) -i- 6 -50.
MATHEMATICS 26
PERCENTAGE
Percentage means by or on the hundred. Thus, 1%»t^
-.01, 3%-Tfir^.03.
To Find the Percentage, Having the Rate and the Base.
Multiply the base by the rate expressed in hundredths; thus,
6% of 1.930 is 1, 930 X. 06 =115.80.
To Find the Amount, Having the Base and the Rate. — Mul-
tiply the base by 1 plus the rate; thus, the amount of $1,930
for 1 yr. at 6% is $1,930X1.06 = $2,045.80.
To VinA the Base, Having the Rate and the Percentage.
Divide the percentage by the rate; thus, if the rate is 6% and
the percentage is 115.80. the base is 115.80^.06=1,930.
To Find the Rate, Having the Percentage and the Base.
Divide the percentage by the base; thus, if the percentage is
115.80 and the base 1,930, the rate is 1 15.80 -s- 1,930= .06, or 6%.
FORMULAS
The term formula, as used in mathematics and in technical
books, may be defined as a rule in which symbols are used
instead of words; in fact, a formula may be regarded as a
shorthand method of expressing a rule. The signs used are
the ordinary signs indicative of operations and the signs of
aggr^ation; all of which are used in arithmetic.
The use of formulas can best be shown by means of an
example; therefore, the well-known rule for finding the horse-
power of a steam engine will be taken. This rtde may be stated
as follows:
Rule. — Divide the continued product of the mean effective
Pressure, in pounds per square inch, the length of the stroke, in
feet, the area of the piston, in square inches, and the number of
strokes per minute by SS,000: the result wUl be the horsepaiver.
An examination of the rule will show that four quantities
(viz., the mean effective pressure, the length of the stroke,
the area of the piston, and the number of strokes) are multi-
plied together, and the result is divided by 33,000. Hence, the
rule might be express^ as follows:
26 MATHEMATICS
-_ mean effective pressure . ^ stroke
Horsepower =,. - • i.\X,. ^ .v
(in pounds per square inch) (in feet)
area of piston number of strokes^- -.^
(in square inches) (per minute) ' '
This expression can be greatly shortened by representing
each quantity by a single letter, thus representing horsepower
by the letter H, the mean effective pressure, in pounds per
square inch, by P, the length of the stroke in feet, by L, the
area of the piston, in square inches, by A , the nimiber of strokes
per minute by N, and substituting these letters for the quan-
tities that they represent, the following formula is obtained,
PXLXAX N
33.(KX)
The formula just given shows that a formula is really a
shorthand method of expressing a rule. It is customary.
however, to omit the sign of multiplication between two or
more quantities when they are to be multiplied together, or
between a number and a letter representing a quantity, it
being always tmderstood that when two letters are adjacent
with no sign between them, the quantities represented by these
letters are to be multiplied. Bearing this fact in mind, the
formula just given can be further simplified to
PLAN
H =
33.0(X)
The sign of multiplication, evidently, cannot be omitted
between two or more numbers, as it would then be impossible
to distinguish the numbers.
Use of Formulas. — The area of any segment of a circle that
is less than (or equal to) a semicircle is expressed by the
formula irr^E c
A^ (r-h),
360 2
in which A — area of segment;
x=3.1416;
y — radius;
E>* angle obtained by drawing lines from center to
extremities of arc of segment;
c " chord of segment ;
h ~ height of segment.
MATHEMATICS 27
Example. — What is the area of a segment whose chord is
10 in. long, angle subtended by chord is 83.46°, radius, is
7.5 in., and height of segment is 1.91 in.?
Solution. — ^Applying the formula just given,
3.1416X7.5»X83.46 10
""-—^ JX (7.5- 1.91)
= 40.968-27.95=13.018 sq. in., nearly
The area of any triangle may be found by means of the
following formula.
i4=-
2
in which i4=area;
a, b, and <;= lengths of 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,
2 \ \ 2X50 /
v»-('^^^^s^)'-»V"-e)"
A = —
2
50
" 2
= 25 V44I - 8.25» - 25. ^441- 68.0625 = 25 V372.9375
= 25X19.312 = 482.8 sq. ft., nearly
These operations have been extended much further than was
necessary; this was done in order to show the reader every
step of the process.
Rankme-Gordon Formula. — The Ranldne-Gordon formula
for determining the least load in pounds that will cause a long
column to break is
SA
P = .
l+<?-
in which P = load (pressure), in potmds;
5= ultimate strength of material composing column,
in potinds per square inch;
28 MATHEMATICS
A =area of cross-section of column, in square inches;
(7 = a factor (multiplier) whose value depends on
shape of ends of column and on material com-
posing column;
/ = length of column, in inches;
G= least radius of gyration of cross-section of column.
ExAMPLE.^-What is the least load that will break a hollow
steel column whose outside diameter is 14 in., inside diameter
11 in., length 20 ft., and whose ends are flat?
Solution. — ^Por steel, 5=150,000, and g- for flat-
25.000
ended steel columns; A = .7854(di2— di"), di and Js being the
outside and inside diameters, respectively; / = 20X12 = 240 in.;
and (? = . Substituting these values in the formula,
150,000X.7854(14«-llg) 150.000X58.905
1 240« " 1+.1163
1+ X
25,000 14«-|-11»
16
8,835.750
1.1163
= 7.915,211 lb.
LOGARITHMS
Logarithms are designed to diminish the labor of multiplica-
tion and division, by substituting in their stead addition and
subtraction. A logarithm is the exponent of the power to
which a fixed number, called the base, must be raised to pro-
duce a given number. The base of the common system is 10,
and, as a logarithm is the exponent of the power to which the
base must be raised in order to be equal to a given number,
all numbers are to be regarded as powers of 10; hence,
10*= 1, therefore logarithm of 1=0
l(fi = 10, therefore logarithm of 10 = 1
10«- 100, therefore logarithm of 100=2
10» - 1 ,000. therefore logarithm of 1 ,000 - 3
10*= 10,000, therefore logarithm of 10,000=4
MATHEMATICS 29
The logarithms of numbers between 1 and 10 are less than
unity, and are expressed as decimals. The logarithm of any
number between 10 and 100 is more than 1 and less than 2,
hence it is equal to 1 plus a decimal. Between 100 and 1,000
it is equal to 2 plus a decimal, etc.
The integral part of a logarithm is its characteristic, the deci-
mal part is its mantissa. For example, the log of 67.7 is
1.83059; the characteristic of this logarithm is 1 and the man-
tissa is .83059. The characteristic of a logarithm is always
1 less than the number of whole figures expressing that ntim-
ber, and may be either negative or positive. The character-
istic of the logarithm of 7 is 0; of 17 is 1; of 717 is 2; etc. The
mantissa is always considered positive.
To Find Logaritiim of Any Number Between 1 and 100.
Look on the first page of the table, along the column marked
No., for the given number; opposite it will be found the loga-
rithm with its characteristic.
To Ffaid Logarithm of Any Number of Three Figures. — Find
the decimal in the first column to the right of the number;
prefix to this the characteristic 2. Thus, the logarithm of
327 is 2.51455. As the first two figures of the decimal are the
same for several successive figures, they are only given where
they change. Thus, the decimal part of the logarithm of 302
is .48001. The first two figures remain the same up to 310,
and are therefore to be supplied.
To Find Logarithm of kaj Number of Four Figures. — Look
in the column headed No. for the first three figures, and then
along the top of the page for the fourth figure. Down the
column headed by the fourth figure, and opposite the first
three, will be found the decimal part. To this prefix the char-
acteristic 3.
To Find Logarithm of Any Number of More Than Four
Figures. — Place a decimal point after the fourth figure from
the left, thus changing the number into an integer and a deci-
mal. If the decimal part contains more than two figures, and
its second figure is 5 or greater, add 1 to the first figure in the
decimal. Find the mantissa of the first four figures, and sub-
tract it from the next greater mantissa in the table. Under
the heading P. P., find a column headed by the difference first
30 MATHEMATICS
found. Find in this column the number opposite the number
corresponding to the first figure of the decimal, or the first
figure increased by one, and add it to the mantissa already
found for the first four figures of the given number.
Example. — ^What is the logarithm of 234,567?
Solution. — ^Placing a decimal point after the fourth figure
from the left gives 2,345.67. The mantissa of 2,345 is .37014;
the difference between .37014 and the next higher logarithm
.37033 is 19. Add 1 to the first figure of the decimal 6, and
in the column headed 19, under P. P., opposite 7, is found 13.3.
which, added to the portion of the mantissa already found,
.37014, gives .37027. The characteristic is 5, hence the loga-
rithm is 5.37027.
To Find Logarithm of Decimal Fraction. — ^Proceed according
to the rules just given, except in regard to the characteristic.
Where the number consists of a whole number and a decimal,
the characteristic is 1 less than the whole number. Where it
is a simple decimal, or when there are no ciphers between the
decimal point and the first numerator, the characteristic is
negative, and is expressed by 1, with a minus sign over it.
Where there is one cipher between the decimal point and first
numerator, the characteristic is 2, with a minus sign over it.
Where there are 2 ciphers, the characteristic is 3, with a minus
sign over it. Thus:
The logarithm of 67.7 = 1.83059
The logarithm of 6.77 =0.83059
The logarithm of .677 =1.83059
The logarithm of .0677 =2.83059
The logarithm of .00677 = 3.83059
The characteristic only is negative; the decimal part is
positive.
To Find Logarithm of Vulgar Fraction. — Subtract the loga-
rithm of the denominator from the logarithm of the numerator;
the difference is the logarithm of the fraction.
Example. — ^Find logarithm of A-
Solution. — Log 4=0.60206
Log 10= L
1.60206
1.60206 is the logarithm of .4.
MATHEMATICS 31
To Find Natural Number Corresponding to Any Logarithm.
Look in the column headed for the first two figures of the
decimal part : the other four figures are to be looked for in the
same or in one of the nine following columns. If they are
exactly found, the number must be made to correspond with
the characteristic by pointing off decimals or annexing ciphers.
If the decimal portion cannot be found exactly, find the next
lower logarithm, subtract it from the given logarithm, divide
the difference by the difference between the next lower and the
next higher logarithm, and annex the quotient to the nattiral
number found opposite the lower logarithm.
To Multiply by Logarithms. — ^Add the logarithms of the
factors together; the sum will be the logarithm of their product.
Example.— 67.7 X .677 = ?
SoLunoN.— Log 67.7 = 1.83059
Log .677 = 1.830 59
1.66118
1.66118 is the logarithm of 45.833
To Divide by Logarithms. — Subtract the logarithm of the
divisor from the logarithm of the dividend; the difference will
be the logarithm of the quotient.
Example. — Divide 67.7 by .0677.
Solution. — Log 67.7 = 1.83059
Log .0677 = 2.83059
3.00000
3 is the logarithm of 1,000
To Square a Number by Logarithms. — Multiply the loga-
rithm of the number by 2; the product will be the logarithm of
the square of the number.
Example. — Square .677.
Solution.— Log .677 = 1.83059
2
1.66118
1.66118 is the logarithm of .45833
To Cube a Number by Logarithms. — Multiply the logarithm
of the ntunber by 3; the product will be the logarithm of the
cube of the number.
32 MATHEMATICS
To Raise a Number to Any Power by Logarithms. — Multi-
ply the logsirithm of the number by 4, 5, 6, or 7, and the results
will be the logarithms of the 4th, 5th, 6th> or 7th powers,
respectively; thus, a number can readily be raised to any power
required.
To Extract Any Root of a Number by Logaritimis. — Divide
the logarithm of the number by the index of the root required;
the quotient will be the logarithm of the required root.
ExABtPLB. — Find the square root of 625.
Solution. — Logarithm of 625 = 2.79588
2.795884-2 =1.39794
1.39794 = logarithm of 25
Therefore, the square root of 625 is 25.
To Divide a Logarithm Having a Negative Characteristic.
If the characteristic is evenly divisible by the divisor, divide
in the usual manner and retain the negative sign of the char-
acteristic in the quotient. If the negative characteristic is
less than, or is not evenly divisible by, the divisor, add such
a negative number to it as will make it evenly divisible, and
prefix an equal positive number to the decimal part of the
logarithm; then divide the increased negative characteristic
by the divisor, to obtain the characteristic of the quotient
desired. To obtain the decimal part of the quotient, divide
the decimal part of the logarithm, with the positive number
prefixed, in the usual manner. To this quotient prefix the
negative characteristic already found, and this will be the
quotient desired. Logarithms are particularly useful in those
cases where the imknown quantity is an exponent, or when
the exponent is a decimal.
Example 1. — DJvide 6.3246846 by 3.
Solution.— 6-3246846 -J- 3 = 2. 1582282
Example 2.— Divide 14.3268472 by 9. _
Solution.— 14.326 8472 -j- 9 = (14+4 = 18) + (4 +.3268472)
X 18+4.3268472-5-9= '^2.4807608
Example 3.— Find "^77.
Solution. —
<f.677-log .677-*- 6-1.830578-1-5; 5 -i- 5+4.830589-4-6
-1.9661178 -.9249+
MATHEMATICS
33
TABLE
OF
COMMON LOGARITHMS
OF NUMBERS
FROM 1 TO 10,000
No.
Log
No.
20
21
Log
No.
40
41
Log
No.
60
61
Log
No.
80
81
Log
— 00
30
103
60
206
77 815
90 309
1
00 000
32
222
61
278
78 533
90 849
2
30 103
22
34
242
42
62
325
62
79 239
82
91 381
3
47 712
23
36
173
43
63
347
63
79 934
83
91 908
4
60 206
24
38 021
44
64
345
64
80 618
84
92 428
5
69 897
25
39
794
45
65
321
65
81 291
85
92 942
6
77 815
26
41
497
46
66
276
66
81 954
«6
93 450
7
84 510
27
43
136
47
67
210
67
82 607
87
93 952
8
90 309
28
44
716
48
68
124
68
83 251
88
94 448
9
95 424
29
30
31
46
240
49
50
51
69
020
69
70
71
83 885
89
90
91
94 939
10
00 000
47
712
69
897
84 510
95 424
11
04 139
49
136
70
757
85 126
95 904
12
07 918
32
50
515
52
71
600
72
85 733
92
96 379
13
11 394
33
51
851
53
72
428
73
86 332
93
96 848
14
14 613
34
53
148
54
73
239
74
86 923
94
97 313
15
17 609
35
54
407
55
74
036
75
87 506
95
97 772
16
20 412
36
55
630
56
74
819
76
88 081
96
98 227
17
23 045
37
56
820
57
75
587
77
88 649
97
98 677
18
25 527
38
57
978
58
76 343
78
89 209
98
99 123
19
27 875
39
40
59
106
59
60
77
085
79
80
89 763
99
100
99 564
20
30 103
60 206
77
815
90 309
00 000-
MATHEMATICS
COMMON LOOARITHMS.
MATHEMATICS
T« BL«— ( OonHnaed).
MATHEMATICS
TI.BLB— ( Continued) .
MA THEM A TICS
Table— ( Continutd) .
MATHEMATICS
T ABLE— ( ConHntied ).
MATHEMATICS
TiBLE— ( Centtaueli.
MATHEMATICS
Table— ( CotHirnitd).
MATHEMATICS
Tablk— ( Qmltnued),
MATHEMATICS
TlBUt— ( ConOtuird).
UATHEMATICS
TiW.B-< Continued) .
ifATffEMATICS
T A BLE— { Coaiin tttdj.
UATSEMATI
UATBEMATICS
Table— < CtmttHwd).
MATHEUATSCS
Ta bls— ( ConUaued ).
MATHEMATICS
Ti BLE— ( Continued).
MATHEMATICS
Table— ( CbnMniMrf) .
UATBEMATICS
Table— ( Coniintied).
MATHEMATICS
TiBLE— ( Continaed).
52 MATHEMATICS
GEOMETRY
1. The sum of all the angles formed on one side of a straig^ht
line equals two right angles, or 180°.
2. The sum of all the angles formed around a point equals
four right angles, or 360**.
3. When two straight lines intersect each other, the oppo-
site or vertical angles are equal.
4. If two angles have their sides parallel, they are equal.
5. If two triangles have two sides and the included angle
of the one equal to two sides and the included angle of the
other, they are equal in all their parts.
6. If two triangles have two angles and the included side
of the one equal to two angles and the included side of the other,
they are equal in all their parts.
7. In any triangle, the greater side is opposite the greater
angle, and the greater angle is opposite the greater side.
8. The sum of the lengths of any two sides of a triangle
is greater than the length of the third side.
9. In an isosceles triangle, the angles opposite the equal
sides are equal.
10. In any triangle, the sum of the three angles is equal to
two right angles, or 180°.
11. If two angles of a triangle are given, the third may be
found by subtracting their sum from two right angles, or 180°.
12. A triangle must have at least two acute angles, and can
have but one obtuse or one right angle.
13. In any triangle, a perpendicular let fall from the apex
to the base is shorter than either of the two other sides.
14. In any parallelogram, the opposite sides and angles are
equal each to each.
15. The diagonals divide any parallelogram into two equal
triangles.
16. The diagonals of a parallelogram bisect each other; that
is, they divide each other into equal parts.
17. If the sides of a polygon are produced in the same direc-
tion, the sum of the exterior angles will equal four right angles.
18. The simi of the interior angles of a polygon is equal
to twice as many right angles as the polygon has sides, less
MATHEMATICS 53
four right angles. For example, the stun of the interior angles
of a quadrilateral is (2X4) —4 » 4 right angles; the sum of the
interior angles of a pentagon is (2X5)— 4»'6 right angles;
the sum of the interior angles of a hexagon is (2 X 6) —4 » 8 right
angles.
19. In equiangular polygons, each interior angle equals
the sum divided by the number of sides.
20. The square described on the hypotenuse of a right-
angled triangle is equal to the sum of the squares described on
the other two sides. Thus, in a right-angled triangle whose
base is 20 ft. and altitude 10 ft., the square of the hypotenuse
equals the square of 20 + the square of 10, or 500; then the
hypotenuse equals the sqtiare root of 500, or 22.3607 ft.
21. Having the hypotenuse and one side of a right-angled
triangle, the other side may be found by subtracting from the
square of the hypotenuse the square of the other known side;
the remainder will be the square of the required side.
22. Triangles that have an angle in each equal, are to each
other as the product of the sides including those equal angles.
23. Similar triangles are to each other as the squares of
their corresponding sides.
24. The perimeters of similar polygons are to each other
as any two corresponding sides, and their areas are to each
other as the squares of those sides.
25. The diameter of a circle is gfreater than any chord.
26. Any radius that is perpendicular to a chord, bisects
the chord and the arc subtended by the chord.
27. Through three jxjints not in the same line, a circum-
ference may be made to pass. For example, draw two lines
connecting the three points and erect perpendiculars from the
centers of each of these two lines; the point of intersection of
the perpendiculars will be the center of the circle.
28. The circumferences of circles are to each other as their
radii, and their areas are to each other as the sqtiares of their
radii.
Example 1. — If the circumference of a circle is 62.83 in.
and its radius is 10 in., what is the circumference of a circle
whose radius is 15 in.?
64 MATHEMATICS
Solution. — ^Applying the principle just given, the circum-
ference is
10: 15»62.83: 94.245 in.
Example 2. — If a circle 6 in. in diameter has an area of
28.274 sq. in., what is the area of a circle 12 in. in diameter?
Solution. — ^Applidng the principle just given, the area is
3* : 6«- 28.274 : 113.096 sq. in.
MENSURATION
In the following formulas, the letters have the meanings
here given, xmless otherwise stated.
D= larger diameter;
d SB smaller diameter;
R» radius corresponding to D;
r» radius corresponding to d;
^■= perimeter of circumference;
C» area of convex surface, that is the area of flat surface that
can be rolled into the shape shown;
.5" area of entire surface ends = C4- area of the end or ends;
A »area of plane figure;
T» 3.1416, nearly, that is the ratio of any circumference to
its diameter;
V = volume of solid.
The other letters used will be found on the cuts.
cmcLB
p^'rd=-'3.UlQd
/>«2irr = 6.2832r
#-2V;S = 3.6449VI
2A 4A
. p p
3.1416
.3183^
4.
<«-2\/-- 1.1284 V4
^ --.1592/>
2ir 6.2832
MATHEMATICS
ii- — -.7854d*
4
A-wr»-3.1416r»
"2^4
65
TRIANGLES
D = B+C B +B-\-C-' 180«
B - D-C E'+B+C- ISO*
£'- E B'-B
' The above letters refer to angles.
For a right-angled triangle, c being the
hypotenuse, c= Va«+S
£» length of side opposite an acute angle
of an oblique-angled triangle.
c= Va«+y -26g
c ~ length of side opposite an obtuse angle
of an oblique-angled triangle.
c- Va«+fr»+26tf
A-
For a triangle inscribed in a semicircle; i. e., any right-
angled triangle, c -.h^a : h
ab ce
c a
a : fr+e— e : a— A : c
For any triangle,
h
.4=-
2
2
56
MATHEMATICS
-/ RECTANGLE AND PARALLELOGRAM
/ A'=ab
TRAPEZOID \*-»-*\
A-i/i(a+6)
TRAPEZIUM
Divide into two triangles and a trapezoid.
or, A'=i[bh'+ch-\-aih'+h)]
Or, divide into two triangles by drawing
a diagonal. Consider the diagonal as the
base of both triangles, call its length <;
call the altitudes of the triangles hi and ht; then
A-J/(*i+/ij)
p*'Tyj
ELLIPSE
D»-|-rf« {D-d)*
8.8
-Dd^JSS^Dd
4
SECTOR
A = i/r
A = = .008727r«E
360
/= length of arc
SEGMENT
A=h[ir-c(r-h)]
irr^E c
A -(f-A)
I
360
■wrE
180 "
\m_
xr
2
.0175r£
/
» 57.2956 -
f
* The perimeter of an ellipse cannot be exactly determined
without a very elaborate calculation, and this formula is
merely an approximation giving fairly close results.
MATHEMATICS
67
RING
4
CHORD
C"i length of chord
8h 2h
c^2'^2hr-h*
8e-c
» — , approximately
CONE
C'kTdl'jMrl
I 5-»r/+»r«=irr->/r«+/i«+irr«
x^ * .7854<i»/t ^
" 4^3" 3 "l2i
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
Name No. Sides Multiplier
Triangle 3 .433
Square 4 1.000
Pentagon 5 1.720
Hexagon 6 2.598 ^_\(^ ''
Heptagon 7 3.634
Octagon 8 4.828
finV Nonagon 9 6.182
Decagon 10 7.694
IRREGULAR AREAS
Divide the area into trapezoids, triangles, parts
inl of circles, etc., and find the sum of the partial areas,
-j-w If the figure is very irregular, the approximate area
may be found as follows: Divide the figure into
trapesoids by equidistant parallel lines b, c, d, etc. The lengths
68 MATHEMATICS
of these lines being measured, then, calling a the first and n
the last length, and y the width of strips,
y
(-^+6+c+etc.+mj
PLANE TRIGONOMETRY
DEFINITIONS
Plane trigonometry treats of the solution of plane triangles.
Every triangle consists of six parts, three sides and three angles.
These parts are so related that when three are given, one being
a side, the other parts may be found.
An angle is measured by the arc included between its sides,
the center of the circumference being at the vertex of the angle.
For measuring angles, the circumference is divided into 360
equal parts, called degrees; each degree is divided into 60 equal
parts called minutes.
A quadrant is one-fourth the circum-
ference of a circle, or 90**.
The complement of an arc is 90^
minus the arc; in Fig. 1, D C is the
complement of B C, and the angle DOC
is the complement of BO C.
The supplement of an arc is 180^
Pig. 1 minus the arc; in Fig. 1, A E is the
supplement of the arc B D E, and the
angle A O Eis the supplement of the angle BO E.
In trigonometry, instead of comparing the angles of triangles
or the arcs that measure them, the trigonometric functions
known as the sine, cosine, tangent, cotangent, secant, and
cosecant are compared.
The sine, or sin, of an arc is the perpendicular let fall from
one extremity of the arc on the diameter that passes through
the other extremity; in Fig. 2, C Z> is the sine of the arc A C.
The cosine, or cos. of an arc is the sine of its complement; or
it is the distance from the foot of the sine to the center of the
circle; in Fig. 2, C E or O D equals the cosine of arc A C.
MATHEMATICS
59
The tangent, or tan, of an arc is a line perpendicular to the
radius at one extremity of an arc and limited by a line passing
through the center of the circle and the other extremity; in
Fig. 2, A r is the tangent of A C.
The cotangent, or cot, of an arc is equal to the tangent of the
complement of the arc; in Fig. 2, B T' is the cotangent of A C.
The secant, or sec, of
an arc is a line drawn
from the center of the
circle through one ex-
tremity of the arc, and
limited by a tangent at
the other extremity; in
Fig. 2, r is the secant
of AC.
The cosecant, or cosec,
of an arc is the secant
of the complement of
the arc; in Fig. 2, the line O 7^ is the cosecant of the arc A C.
The versed sine of an arc is that part of the diameter included
between the extremity of the arc and the foot of the sine; in
Fig. 2, Z> A is the versed sine of A C.
The cooersed sine is the versed sine of the complement of the
arc; in Fig. 2, J3 £ is the coversed sine of A C.
From the above definitions, we derive the following simple
principles:
1. The sine of an arc equals the sine of its supplement, and
the cosine of an arc equals the cosine of its supplement.
2. The tangent of an arc equals the tangent of its supple-
m^it, and the cotangent of an arc equals the cotangent of its
supplement.
3. The secant of an arc equals the secant of its supplement,
and the cosecant equals the cosecant of its supplement. Thus,
Fig. 2
sin 70" = sin 110"
tan 70" = tan 110"
sec 70"= sec 110"
cos 70"= cos 110"
cot 70" -cot 110"
cosec 70" = cosec 110"
Thus, to find the sin 120" 30*, look for the sin 180- 120" 30'.
or 59" 30', etc.
60 MATHEMATICS
In the 1
right-angled triangle, xy%. Fig. 3, the following relations
hold:
/
t
b
sin c = -
h
a
cos c = ^
/
b
b
tan c=-
a
a
cot c«-
X 1
y
sec c=«
a
h
cosec c = -
6
Fig.
3
The functions of the sum and difference of two angles are:
sin (A-\-B)'=sm A cos S+cos A sin B
cos (yl+JB) = cos A cos JB— sin A sin B
sin (A — B) = sin A cos JB— cos A sin B
cos (A —5) =cos A cos B+sin A sin B
Natural sines, tangents, etc. are calculated for a circle having
a radius of unity, and logarithmic sines, tangents, etc. are cal-
culated for a circle whose radius is 10,000,000,000.
EXAMPLES IN SOLUTION OF TRIANGLES
To Determine Height of Vertical Object Standing on Hori-
zontal Plane. — Measure from the foot of the object any con-
venient horizontal distance A B, Fig. 1; at the point A, take
the angle of elevation JBA C. Then, as B is known to be a
right angle, two angles and the included side of a triangle are
known. Assuming that the line A B is 300 ft. and the angle
BAC = 40°, the angle C=180°-(90°+40'')-50^ Then,
sin C: A B = sin A : B C. or, .766044: 300 - .642788: ( ) or, 251.73
+ft. Or, by logarithms:
Log 300= 2.4 77 12 1
Log sin 40"= 9.8 08 06 7
12.2 8 5 18 8
Log sin 50"= 9.8 8 4 2 5 4
2.4 9 3 4 or log of 251.73 +ft.
Hence, B C=251.73+ ft.
To Find Distance of Vertical Object Whose Height is Known.
At a point A, Fig. 2, take the angle of elevation to the top of the
object. Knowing that the angle B is a right angle, the angles
" "^ A and the side B C of a triangle are known. Assuming
MATHEMATICS
61
that the side B C=200 ft. and the angle A =30**, the triangle
is: Angle A = 30^ B=90^ C-60^ and the side B C-200 ft.
c
A
1 1
/
/
/
/
/
/
/
/
/
f *
-D
c
/
B
1
1
1
/
1
/
/
r I
/
1
/
1 1
, /
1
A/
.1 L
Fig. 1
Pig. 2
200 =.866025:, or
Then, ^n A . B C =sin C : A B, or .6
346.4 1 ft. By logarithms :
Log 200= 2.30103
Log sin 60**= 9.937531
1 2.2 3 8 5 6 1
Log sin 30^= 9.6 9 89 7
2.5 3 9 6 9 1 or log of 346.41 ft.
To Find Distance of Inaccessible Object. — Measure a hori-
zontal base line A B, Fig. 3, and take the afigles formed by the
lines BAC and ABC; this
gives the two angles and the
included side. Assuming the
angle A = 60*, the angle B = 50*.
and the side A B = 500 ft.,
angle C = 180* - (60* + 50*)
-70*. Then,
sin70*:i4 B = smA:BC,
and
sin70*: A5 = sinB: AC;
or, .939693 : 500 = .866025
and .939693 : 500 = .766044
By logarithms:
Log 500 = 2.6 9 89 7
Log sin 60*= 9.937531
Fig. 3
B Cor 460.8 +,
A C. or 407.6+ .
Log sin 70*
1 2.6 3 6 5 1
9.9 7 2 9 8 6
2.6 6 3 5 1 5 = log of 460.8+
62
MATHEMATICS
Log500>
LogsinSO"'
Log sin 70**'
2.6 9 8 9 7
9.8 84 2 54
1 2.5 8 3 2 2 4
9.9 729 86
2.6 1 2 3 8 » log of 407.6+
To Find Distance Between Two Objects Separated by an
Impassable Baxrier. — Select any convenient station, as C,
Fig. 4, measure the lines C A and
B CB, and the angle included between
these sides; this gives the two sides
and the included angle. Assuming
angle C = 60*. the side C A »= 600 ft.,
and side CB»500 ft.,
CA-fCS :CA-CB-tan
A+B B~A
Then,
Then,
A-fB 180*»-60''
2 2
1.100 : 100-tan 60° : tan
tan
, or60«»
B-A
or, 1,100 : 100-1.732060
B-A
.157450. or tangent of »
or 8*» 57'.
Then,60*+8* 57' -68*' 57', or angle B, and 60*'-8*» 57'-61»
03', or angle A. Having found the angles, find the third side
by the method given in connection with Pig. 1.
The foregoing formula, worked out by logarithms, is as fol-
lows: Log 100- 2.0 0000
Log Tan 60''-10.23856 1
12.238561
Log 1,100- 3.04 13 93
9.19 71 6 8-logtanof
B-A
or S' 57'
Then. 60''+8'' 57'-68'» 57', or angle B, and 60''-8'' 57'-51«»
03', or angle A.
Note. — The greater angle is always opposite the greater
side.
MATHEMATICS
63
To Find Height of Vertical Object Standing Upon Inclined
Plane. — Measure any convenient distance D C, Fig. 6, on a
line from the foot of the object, and, at the point D, measure
the angles of elevation EDA and E D B to foot and top of
tower. This gives two triangles, both of which may be solved
by the method given in connection with Fig. 1, and the height
above D of both the foot and top will be known. The difference
between them is the height of the tower.
To Find Height of Inaccessible Object Above a Horizontal
Plane. — First Method. — Measure any convenient horizontal
line A £, Fig. 6, directly toward the object, and take the angles
Fig. 6
of elevation at A and B. Assuming the line A £« 1,200 ft.,
the angle A s25o. and the angle DBC'^40°; then angle ABC
- 180** - 40** - 140*». Then, having the side B C, and the angle
D B C=40**, and the angle B D C-QO**, we find the side CD
by the same method given in connection with Fig. 1.
Second Method. — If it is not convenient to measure a horizon-
tal base line toward the object, measure any line A B, Fig. 7,
and also measure the horizontal angles B A D, A B D, and the
angle of elevation D BC. Then, by means of the two triangles
ABD and CBD, the height C i> can be found. With the
line A B and the angles BAD and ABD known, two angles
and the included side are known. The third angle is then readily
found and the side B D can be found. In the triangle BDC
the angle B is known; by measurement, Ds90°, and the side
BD va known. Then, the side C D, or the vertical height, can
be found by the method given in coimection with Pig. 1.
64
MATHEMATICS
To Find Distance Between Two Inaccessible Objects When
Points Can Be Found From Which Both Objects Can Be Seen.
Wishing to know the horizontal distance between a tree and a
house on the opposite side of a river, measure the line A B,
Fig. 8, and, at point A , take the angles D A C, and DAB, and,
at the point B, take the angles C B A and C B D, Assume the
length of A B=400 ft.; angle DA C = 56** 30'; angle DAB
= 42*' 24'; angle C B A =44*' 36'; angle C B Z> = 68'» 50'. In
the triangle A B D, A B»400 ft., angle D A Bb42*' 24', angle
A B Z>= (44* 36'+68* 60') = 113«» 26'. and angle A D B- ISO**
.1 "jS
Pig. 7
- (42*> 24' + lis** 26') - 24** 10'. Then, according to the method
given in connection with Fig. 1, find the side D B\ this gives
three angles and two sides of the triangle A D B. The third
side A Z> is f otmd by the same method. In the triangle ABC
the angles ABC and B AC, and the distance A B are known,
so that the side A C may be fotmd. Then, in the triangle
ADC, the sides A D and A C, and the angle D AC, are known
and the side C D may be found by the method given in con-
nection with Fig. 4.
TABLE OF TRIGONOMETRIC FUNCTIONS
The following table contains the natural sines, cosines, tan-
gents, and cotangents of angles from 0° to 90°. Angles less
than 45° are given in the first column and the names of the
functions are given at the top; angles greater than 45" appear at
the right-hand side of the page, and the names of the functions
•tre given at the bottom. Thus, the second column contains
MATHEMATICS 65
the sines of angles less than 45° and the cosines of angles
greater than 45°; the sixth column contains the cotangents of
angles less than 45° and the tangents of angles greater than 45°.
To find the function of an angle less than 45°, look in the
first column for the angle, and at the top of the page for the
name of the function; to find a function of an angle greater
than 45°, look in the column at the right of the page for the
angle and at the bottom of the page for the name of the f unc-
tion. The successive angles differ by an interval of IC; they
increase downwards in the left-hand column and upwards in the
right-hand column. Thus, for angles less than 45° read down
from top of page, and for angles greater than 45° read up from,
bottom of page.
The columns headed d contain the differences between the
successive functions. For example, the sine of 32° 10' is .5324
and the sine of 32° 2(/ is .5348; the difference is .5348 -.5324
» .0024, so that 24 is written on the third column, just opposite
the space between .5324 and .5348. In like manner the differ-
ences between the successive tabular values of the tangents are
given in the fifth column, those between the cotangents in the
seventh colxmin, and those for the cosines in the ninth column.
These differences in the functions correspond to a difference of
IC in the angle; thus, when the angle 32° lO' is increased by
lO', that is, to 32° 20', the increase of the sine is .0024, or, as
given in the table, 24. In the tabular difference, no attention
is paid to the decimal point, as the difference is merely the
number obtained by subtracting the last two or three figures
of the smaller ftmction from those of the larger.
These differences are used to obtain the sines, cosines, etc.,
of angles not given in the table. For example, suppose that the
tangent of 27° 34' is required. Looking in the table, it is
found that the tangent of 27° 34' is .5206, and (column 5) the
difference for 10' is 37, or when written in full .0037. As the
difference for 1' is .0037 -MO = .00037, the difference for 4' is
.00037 X 4 ». 00148. Adding this difference to the value of the
tan 27° 30' gives
tan 27° 30' -.5206
difference for 4' = .00148
tan 27° 34' = .52208 or .5221, to 4 places
6
66 MATHEMATICS
Because only 4 decixnal places are retained, the 8 in the fifth
place is dropped and the fourth figure is increased by 1, as 8 is
greater than 5.
Column of Pir op orticmal Parts. — To avoid multiplication,
the colximn of proportional parts, headed P. P., is used. At
the head of each table in this column is the difference for IC/,
and below are the differences for any intermediate number
of minutes from 1' to 9'; these differences are written as whole
numbers and decimal parts of same. In the example the
difference for lO' was 37; looking in the table with 37 at the
head, the difference opposite 4 is 14.8; that opposite 7 is 25.9;
and so on. For want of space, the differences for the cotangents
for angles less than 45^ (or the tangents of angles greater than
46**) have been omitted from the tables of proportional parts.
The use of these functions should be avoided, if possible, for
the differences change so rapidly that computation is likely to
be inexact.
The method to be employed when dealing with these func-
tions is shown in the following example, in which the tangent
of 76° 34' is required. Because this angle is greater than 45^
it is found in the column at the right, which is to be read
upwards. Opposite 76** 3(y, in the sixth column, is found the
number 4.1653; and corresponding to it, in the seventh column,
is found the difference 540. As 540 is the difference for 10', the
difference for 4' is 540XA = 216. Putting this ntmiber in its
true form and adding gives
tan76*»30'=4.1653
difference for 4'= .0216
tan 76** 34' = 4. 1869
Angles Containing Seconds. — ^When the angle contains a
certain number of seconds, divide the number by 6, and take the
whole number nearest to the quotient. Find this number in the
table of proportional parts (under the proper difference), and
take out the number that is opposite to it. Shift the decimal
point one place to the left, and then add it to the partial function
already found. The following examples represent the methods
of using the tables of proportional i>arts for the different
-'is: For example, find the sine of 34 *» 26' 44".
MATHEMATICS 67
sin 34*> 20' = .5640 Difference for lO' = 24, or .0024
difference for 6' = .00144
difference for 44'' = .00017 V = 7i. In the P.P. table, the
^ sin 34** 26' 44" = .5656 number under 24 and opposite
7 is fotind to be 16.8. Shift-
ing the decimal point one place
to the left gives 1.68, or, 1.7,
which when put in its decimal
form is .00017.
The tangent is found in the same way as the sine.
As the angle increases the value of the cosine decreases, there-
fore, to find the cosine of an angle, instead of adding the values
corresponding to 6' and 44" to the function already found, sub-
tract them from it. Thus, find the cosine of 34*' 26' 44".
cos 34<' 20' - .8258 Difference for 10' = 17, or .0017.
difference for 6' = .00102
difference tor 44" = .00012 The number tmder the 17 and
total difference =.001 14 opposite the 7. in the P. P.
-- _ table, is 11.9. Therefore take
1.19, or, say, 1.2, which may
be written .00012.
Therefore, cos 34*> 26' 44" = .8258 -.0011 = .8247. Only 4
decimal places are kept; therefore, the figure of the difference
following the decimal point is dropped before subtracting.
The cotangent is found in the same manner.
To show the method when the angle is greater than 45°,
suppose that it is required to find the sine of 68° 47' 22". In
obtaining the difference, it must be remembered to choose the
one between the sine of 68° 40' and the next angle above it,
namely, 68° 50'.
sin 68° 40' = .9315 Difference for 10' = 10, or .0010.
difference for 7' = .0007
difference for 19" = . 00004 V = 3J, say 4. Under the 10
sin 68° 47' 22" = .9322 *^^ opposite the 4 is the
number 4.0; shifting the deci-
mal point, gives .4, or .00004.
As usual, only 4 decimal places are kept.
The tangent is found in a similar manner to the method just
given.
.3618
«8 MATHEMATICS
As before, the cosine decreases as the angle increases; there-
fore, to find the cosine of 68° 47' 22", subtract the successive
sine values corresponding to the increments in the angle.
cos 68" 4(y = .3638 Difference for 10' = 27, or, .0027.
difference for 7' = .00189
difference for 22" = .00011 Under the 27 and opposite the
total difference = .0020 * is the number 10.8; there-
fore, take 1.08 in this case,
or, say, 1.1, which may be
written .00011.
Therefore, cos 68" 47' 22" - .3638- .002 = .3618.
The cotangent is found in the same way.
Applying Proporti(mal Differences. — In finding the functions
of an angle, the only difficulty likely to be encountered is to
determine whether the difference obtained from the table of
proportional parts is to be added or subtracted. This can be
told by observing whether the ftmction is increasing or decreas-
ing as the angle increases. For example, take the angle 21"; its
45ine is .3584, and the following sines, reading downwards,
are .3611, .3638, etc. Therefore, the sine of say 21" 6' is greater
than that of 21" and the difference for 6' must be added. On
the other hand, the cosine of 21" is .9336, and the following
cosines, reading downwards, are .9325, .9315, etc.; that is, as
the angle grows larger the cosine decreases. The cosine of an
angle between 21° and 21° 10'. say 21" 6', must therefore lie
between .9325 and .9315; that is. it must be smaller than .9325,
which shows that the difference for 6' must be subtracted from
the cosine of 21".
Finding the Angle. — Find the angle whose sine is .4943.
The operation in this case may be arranged as follows:
.4943 Difference for 10' = 26. or .0026.
.4924 -sin 29" 30'.
1st remainder .0019
. 00182 «differencefor7'.
2d remainder .00008
As .78 is the difference for .3' or 18", .4943 -sin. 29" 37' 18".
Looking down the second column, the sine next smaller than
.4943 is found to be .4924. and the difference for 10' to be 26.
MATHEMATICS 69
The angle corresponding to .4924 is 29** 30'. Subtracting
the .4924 from 4943, the first remainder is 19. Looking in the
table of proportional parts, the part next lower than this differ-
ence is 18.2, opposite which is 7'. Subtracting this difference
from the remainder gives .8, and, looking in the table, it is
found that 7.8 with its decimal point moved one place to the
left is nearest to the second difference. This is the difference
for .3' or 18". Hence, the angle is 29°30'+7'+18"»29**37' 18".
Find the angle whose tangent is .8824.
.8824 Difference for IC - 61, or .0051.
.8796 =tan41'»20'.
1st remainder .0028
.00255 = difference for 5'.
2d remainder .00025
As 2.55 is the difference for .5' or 30", .8824 = tan 41<* 25' 30".
In the examples just given, the minutes and seconds corre-
sponding to the 1st and 2d remainders are added to the angle
taken from the table. Thus, in the first example, an inspection
of the table shows that the angle increases as the sine increases;
hence, the angle whose sine is .4943 must be greater than 29° 30',
whose sine is .4924. For this reason the correction must be
added to 29° 30'. The same reasoning applies to the second
example.
Find the angle whose cosine is .7742.
.7742 Difference for 10' = 18, or .0018.
.7735 =cos39°20'.
1st remainder .0007
.00054 = difference for 3'.
2d remainder .00016
As 1.62 is the difference for .9' or 54", 39° 20' -3' 54" =
39° 16' 6", which is the angle whose cosine is .7742.
Looking down the column, headed cos, the next smaller
cosine is .7735, to which corresponds the angle 39° 20'. The
difference for 10' is 18. Subtracting, the remainder is 7, and
the next lower number in the table of proportional parts is
6.4, which is the difference for 3'. Subtracting this from first
remainder, the second remainder is 1.6, which is nearest 16.2
of table of proportional parts, if the decimal point of the latter
70 MATHEMATICS
is moved to the left one place. As 16.2 corresponds to a differ-
ence of 9', 1.62 corresponds to a difference of .9', or 64". Hence,
the correction for the angle 39° 20' is 3' 64". From the table,
it api)ears that, as the cosine increases, the angle grows smaller;
therefore, the angle whose cosine is .7742 must be smaller than
the angle whose cosine is .7736, and the correction for the angle
must be subtracted.
Find the angle whose cotangent is .9847.
.9847 Difference for 10' = 57, or .0067.
.9827 =cos45°30'.
1st remainder .0020
.00171 = difference for 3'.
2d remainder .00029
As 2.85 is the difference for .5' or 30", 45** 30' -3' 30"-
46° 26' 30", the angle whose cotangent is .9847.
In finding the angle corresponding to a function, as in
the foregoing examples, the angles obtained may vary from the
true angle by 2 or 3 sec; in order to obtain the number of
seconds accurately, the functions should contain 6 or 7 decimal
places.
76 SURVEYING
SURVEYING
INSTRUMENTS USED
THE COBIPASS
Surveying is an extension of mensuration, and, as ordinarily
practiced, may be divided into surface work, or ordinary sur-
veying, and undei^rround work, or mine surveying. With slight
modifications, the instruments employed in both are the same.
The compass used may be either a pocket compass, or a
surveyor's compass; it may be held in the hand, or on a tripod.
The Jacob's staff is convenient for use on the surface, but is
frequently useless in the mine. The compass is not accurate
enough for the construction of a general map of the mine.
It may be used to secure an approximate idea of the shape
of the workings, so as to plan an approximate course on which
to drive an opening designed to connect two or more given
points. If the opening is one that will be expensive to drive,
and should be straight, the compass survey should never be
relied on.
Using the Compass. — In using the compass, the surveyor
should keep the south end toward his person, and read the
bearings from the north end of the needle, care being taken
always to keep the compass level. In the surveyor's compass,
the position of the letters E and W are reversed from their
natural position, in order that the direction of the sight may
be correctly read. As the circle is graduated to J°, a little prac-
tice will enable the surveyor to read the bearings to quarters,
estimating with his eye the space bisected by the point of the
needle.
The compass is usually divided into quadrants, and is
placed at the north and south ends; 90° is placed at the E and
W marks, and the graduations run right and left from the
to 90°. In reading the bearing, if the sights are pointed in a
N W direction, the north end of the needle, which always points
approximately north, is to the right of the front sight or front
SURVEYING
77
end of the telescope, and, as the number of d^^rees is read
from it, the letters marking the cardinal points of the compass
read correctly. If the E, or east, mark were on the right side
of the circle, a N W course would read N E. This same
fact applies to all four quadrants.
THE TRANSIT
The transit is the only instrument that should be used for
measuring angles in any survey where great accuracy is desired.
Its advantages over a vernier compass are mainly due to the
use of a telescope. With it angles can be measured either
vertically or horizontally, and, as the vernier is used through-
out, extreme accuracy is secured. In mine work all screws
and movable parts should be covered, so as to keep out acid,
water, and dust; if this is not done, the instrument will soon
be destroyed. The vertical circle on the transit may be a
full circle or a segment; the former is preferred, as it is always
ready without intermediate clamp screws.
Transit Verniers. — ^The verniers on a transit differ from those
on a compass in detail only; the principle is the same. The
transit vernier is so divided that 30 spaces on it equal in length
29 on the limb of the instrument. It is read practically the
same as a comx>ass vernier, except that on the transit the vernier
is made with all of the 30 divisions on one side of the mark.
Each division of the vernier is, therefore, -^, or, in other
words, 1' shorter than the i° graduations on the limb. In
the fignire the reading is 20° 10'. If the on the vernier should
be beyond 20^° on the limb of the transit, and the line 10 should
78 SURVEYING
coincide with a line on the limb, the reading would be 20° 40'.
In case the 12th line from should coincide with a line on the
limb, the reading would be 20° 42', etc.
In some transits, the graduated limb has two sets of con-
centric graduations, the in both being the same. While
the outside set is marked from 0° each way to 90°, and thence
to 0° on the opposite side of the circle, the other set is marked
from 0° to 360° to the right, as a clock face. The inside set
has the N, S, E, and W points marked, the 0° of the inside
set being taken as north.
Transit Telescopes. — The interior of the telescope is fitted
with a diaphragm, or cross-wire ring, to which cross -wires
are attached. These cross-wires are either platinum or strands
of spider web. For inside work, platinum should be used, as
spider web is translucent and cannot readily be seen. These
wires are set at right angles to each other and are so arranged
that one can be adjusted so as to be vertical and the other
horizontal. This diaphragm is suspended in the telescope
by four capstan-headed screws, and can be moved in either
direction by working the screws with an ordinary adjusting pin.
The intersection of the wires forms a very minute point, that,
when adjusted, determines the optical axis of the telescoi>e,
and enables the sxurveyor to fix it upon an object with the
greatest i>recision.
The imaginary line passing through the optical axis of the
telescope is termed the line of coUimation, and the operation
of bringing the intersection of the wires into the optical axis
is called the adjustment of the line of coUinuUion.
The transit should not be subjected to sudden changes in
temi>erature that may break the cross-hairs. In case of a
break, the cross-hair diaphragm must be removed and the
broken wire replaced.
CHAIN, TAPE, PINS, AND PLUMB-BOB
The chain, which is generally 50 or 100 ft. long, should be
made of annealed steel wire, each link being ocactly 1 ft. in
length.
The steel tape is simply a ribbon of steel, on which are marked,
by etching, or other means, the different graduations; these
SURVEYING 79
may be inches or tenths of a foot, or every foot. It is wound
on a reel, and may be any desired length up to 600 ft. When
distances do not come at even feet, the fractional part of the
foot should always be noted in tenths. Thus, 53 ft. 6 in. should
always be noted as 53.5 ft.
For the most exact work steel tapes are now almost exclusively
used by the leading mining engineers, on account of their greater
accuracy as compared with chains.
Pins should be from 15 to 18 in. long, made of tempered-
steel wire, and should be pointed at one end and turned with
a ring for a handle.
The plumb-bob takes the place of the transit rod in under-
ground work, as the stations are usually in the roof, and strings
are hung from them to furnish foresights and backsights.
Plumb-bobs vary in weight and shape. T\^e cord is best
illiuninated by placing white paper or cardboard behind it
and holding the lamp in front and to one side. The string
shows as a dark line against a white ground, and there is less
difficulty in finding it than when the light is placed exactly
behind it.
The clinometer, or slope level, is a valuable instrument for
side-note work, but it is not accurate enough for a survey;
its place has been taken by the vertical circle on the transit.
Clinometers are of two styles, one showing the inclination by
means of a bubble and the other, by means of a pendulum.
The latter is the old-fashioned and more accurate German
Gradbogen.
TRANSIT SURVEYING
READING ANGLES
The angle read may be included or de-
flected. If the transit is set up at O with
backsight at B and foresight at C, there
are two angles made by the line C O with
the line BOA, namely the included angle
B O C, and the deflected angle C O A.
To read the included angle set the zeros of the vernier and
graduated limb together accurately, and clamp the plates.
80 SURVEYING
Turn the telescope on the backsight, with the level bubble
down, and, when set, fasten the lower clamp so as to fix both
clamped plates to the tripod head. Loosen the upper clamp,
turn the telescope to C, and set accurately. The vernier will
read, for example, 45° left angle.
To read the deflected angle arrange the verniers as before,
being careful to turn the telescope over on its axis tmtil the
bubble tube is up, and then take the backsight and fix lower
clamp. Turn the telescope back (this is called plunging the
telescope) and then sight to foresight and fix as before; the
vernier will then read a right angle of 135°. The sum of
included and deflected angles must always be 180°.
Note. — In making a survey by included angles it is neces-
sary to add or subtract 180° at each reading to have the vernier
and compass agree; by deflected angles they will agree without
the above addition or subtraction, therefore the latter method
is generally used.
If the dip of a sight is to be taken the tape must be held
at the transit head and stretched in the line of sight. If the
pitch of the ground is to be taken the point of foresight must
be at the same height as the axis of the transit and the sight
will then be parallel to the surface. The angle of dip is read
"plus" or "minus " as it is above or below the horizontal
plane. If we have the dip of a sight and the distance between
the transit head and the point of sight we can get the vertical
and horizontal components of that distance from the table of
sines and cosines.
BfAKING SURVEY WITH TRANSIT
Surveying by Means of Individual An^^es. — To survey by
means of individual angles, set the vernier at of limb, plunge
the telescope, and, when set on the backsight, loosen the needle
and read the bearing of the line from backsight to set-up.
Plunge the telescope back and set on the foresight and read
both the needle and the vernier. The difference in the needle
readings should agree with the vernier reading within 15', as
local attraction will affect the needle equally on both sights.
NoTK._ — As the moving of any mass of iron or steel diuing
the readings of the needle will affect the same and destroy the
value of the needle as a check, the tape and other iron mate-
rials should not be moved during the taking of angles.
Surveying by Means of Continuous Vernier. — To survey by
means of continuous angles, set the vernier at 0, undamp the
SURVEYING 81
compass needle, and, when stationary, turn the north point of
the compass limb so as to coincide with the north point of the
needle. Fix the lower clamp, plunge the telescope, and take
a backsight by loosening the upper clamp. The vernier and
the needle should agree in giving the magnetic bearing of the
line from backsight to set-up. Record this in the notebook;
plunge the telescope, and take a foresight; the needle and
the vernier should agree as before. After making the record,
set up over the foresight and take a sight to the station just
left with the telescope plunged, having first seen that the
vernier reads exactly as it did on the last foresight, as a slip in
carrying the transit from one station to another, which is not
detected at the time, can never be checked afterwards when
the final work is found to be in error. The foresight is taken
as before; on every sight the needle and the vernier should
agree if there is no local attraction of the needle.
If all the comers of a field that is to be surveyed can be seen,
from a central point, the survey can be made by setting up
the transit at that point, and, with one comer as a backsight,
taking all the other comers as foresights with but one set-up,
and measuring from this point to all of the comers; or the transit
can be set up at any comer and a line run around the field.
This latter method is called meandering. Both methods will
give the same result when plotted.
PLOTTING
A pled is a map drawn to a given scale, and showing all of
the natural features. Plotting is the making of such a map
from notes of a survey, and may or may not require the per-
manent placing on it of the stations, by which the survey
is made. In underground work, the exact location and the
retention of those stations is of the first importance, and is
secondary only to the exact plotting of the side notes. The
scale of the plot is generally as large as will show the points of
interest in the property; but in Pennsylvania, the maps for
coal mines must be drawn to a scale of 100 ft. = 1 in. There
are two methods of plotting: by protractor, and by coordi-
nates. When the scale is sufficiently large, it makes little
difference which method is used, if the work be carefully done
7
82 SURVEYING
with exact instruments; but with small scales, 100 ft. ■>! in.,
or smaller, the method by coordinates should be used. When
the scale is from 1 to 25 ft. to 1 in., the errors are small enough
to make little chances of variation in a close of ten or twelve
stations; when the sturvey is of short sights from a main line
to points where no further work is to be done, the protractor
will afford a quick method of plotting.
To Calculate Vertical Distances. — ^When making the survey,
read the vertical angles to all stations. If the angle is one of
depression, place a minus sign (— ) before it; if it is an angle
of elevation, place a plus sign (+) before it. These will show
whether the vertical distance is to be added to, or subtracted
from the height of the preceding station.
Having the horizontal distance and the vertical angle:
Distance X tangent of vertical angle — vertical distance.
Having the pitch distance and vertical angle:
Distance X sine of vertical angle >■ vertical distance.
To Calculate Horizontal Distance, or Latitude. — Pitch dis-
tance X cosine of vertical angle = horizontal distance.
Vertical height or departure -r- tangent of vertical angle
» horizontal distance.
To Calculate Pitch Distance. — Horizontal distance -f- cosine
of bearing, or multiplied by secant of bearing ■> pitch distance.
Vertical distance 4- sine of vertical angle, or multiplied by
cosecant of bearings pitch distance.
To Calculate Vertical Axigle. — Horizontal distance -s- the
pitch distance = cosine of vertical angle.
Vertical distance -s- pitch distance — sine of vertical angle.
Vertical distance -(-horizontal distance — tangent of vertical
angle.
Note. — ^Whenever sines, cosines, tangents, etc., are here
named, they mean the natural sines, etc. of the angle.
Plotting by Coordinates. — In the establishment of a meridian
and a fixed point, the latter should be a stone post, or iron plug
sunk in solid rock; this point is called the origin of coordinates
Have the principal meridian passing through this point in an
exact north-and-south direction, and a secondary meridian or
base line passing through this point at right angles to the first,
or in an exact east-and-west line. Any point on the map will
SURVEYING 85
then be a certain distance north or south, and east or west of
the origin. The lines drawn from this point at right angles
to the two base Unes just given are called the coordinates of
that point, and the point can be plotted when they are given.
For example, the coordinates of a station are N 345.67, and
£ 890.12. Measure 890.12 ft. east of the origin on the second-
ary meridian and, from this point, 345.67 ft. north to the point
desired. Or measure on the primary meridian to the north
and then turn off a right angle to the east and reach the same
point. In any event the position of each station may be plotted
independently of all the others, and any error in locating one
is not carried to the next. When two stations are plotted, the
distance between them on the map should be exactly what is
found for their horizontal distance on the ground. This check
shows whether the plotting is correct. This is also called
traversing a survey if the meridian is north and south, and in
books on surveying there are printed traverse tables, which are
accurate within certain hmits, but not so accurate as the tables of
coordinates published separately, as the latter are carried to a
greater number of decimals.
With a north-and-south meridian, the point from which the
measuring of the angles is begun, the zero point, is the north
point, and the angles are read for continuous vernier in
the direction of the hands of a watch. The sines of angles
are eastings and westings, and the cosines are northings and
southings.
TRAVERSING A SURVEY
To traverse a survey, means to determine by calculation
how far north or south and east or west any station may be
from another, the location of which is fixed. To do this,
all distances must be meastired horizontally, or calculated to
horizontal distances. The horizontal angles, or courses, must
be read as quadrant courses, or reduced from azimuth to quad-
rant courses. An azimuth course is one that is read on a transit
that is graduated from 0° to 360°. A quadrant course is one
read in the quadrant of the circle, as S 67° W, N 43° E, etc.
Latitude means distance north or south, and is determined
by the first initial of the recorded course; thus, if a course is
84 SURVEYING
S 67"* W. the latitude is south; if N 43'' E, the latitude is north.
The latitude » distance X cosine of bearing.
Departure means distance east or west, and is determined
by the last initial of the recorded course; thus, if a course is
S 67** W, tfie departure is west; if N 43** E, the departure is
east. The departure ■* distance X sine of bearing.
If the survey is a continuous one around a tract, and ending
at the place of beginning, the sum of the northings should equal
the sum of the southings, and the sum of the eastings should
equal the sum of the westings. The most accurate way to
construct a map is to traverse the survey and place all stations
on it by the traversed distances, or to at least put a number of
the principal stations on the map by the traversed distances,
and use the protractor to plot only the intermediate stations.
DETERMINING AREA OF TRACT OF LAND
If the tract of land is a regular polygon, find the area by
the rule given under the head of Mensiu'ation for polygons of
the same number of sides. If it is an irregular polygon, divide
it into triangles and calculate the area of each triangle; the
sum of these areas will be the area of the tract. If the tract
is an irregular polygon in shape, the map should be made on as
large a scale as possible, and the distances should be measured
with the greatest care, owing to liability to error through very
slight inaccuracies of measurement.
DETERMINING CONTENTS OF COAL SEAM
If the seam lies flat, multiply the area of the tract, in square
feet, by the thickness of the seam, in feet; the product will be
the cubic contents of the seam, in feet. If the seam is an
inclined one, find its area by measuring the width of the tract
on its Une of pitch, and find the distance on the pitch of the
seam by dividing the horizontal distance measured by the
cosine of the angle of inclination; this will give the pitch dis-
tance. Multiply the pitch distance by the length of the tract,
to find the area of the seam; this multiplied by its thickness
will give the contents.
cubic contents, in feetXsp. gr.X62.5
Tons of coal •
2,240
SURVEYING 85
UNDERGROUND SURVEYING
ESTABLISHMENT OF STATIONS
There are a number of variations in the foregoing practice
that are caused by the entirely different set of conditions in
underground work. As the establishment of stations is the
most important duty of an engineer in surface work, so it
takes the first place in work underground, as the accuracy
of the work depends on the location of the stations, while its
rapidity depends on using the least number consistent with
completeness. Also, the fewer the number of stations, the
less are the chances of error. In underground work, stations .
should be located under the conditions of permanence, freedom
from destroying agencies, and ease of access. Temporary
stations for a single sight need not fill all these requirements.
They are generally established in the roof of the mine, less
frequently in the floor. In the former case, a center must be
established before each set-up of the transit. Places are chosen
that will be least affected by subsequent work, and the stations
are put in collars, lids, or wedges of props, in the props themselves
when they have sufficient incline to allow the transit to be set
under them, or in the roof itself. Wherever set, they should
not project far from the surface, and thus be liable to be brushed
away in a low gangway by cars with topping higher than usual,
or knocked away by flying fragments from a shot, if near the
working faces. Top stations have a mark about them to call
attention to their location; it is generally a circle. When there
are other corps at work in the same mine, the stations of the
two surveys should be given distinguishing marks to avoid
confusion.
Kinds of Stations. — ^The simplest top station is called by
some a jigger station. It is a shallow conical hole, made with
the point of the foresight man's hatchet which is dug into the
top rock and rotated. The sights are given and the centers
set by putting the plummet cord in this groove, and placing
the end in the jigger hole in the roof. Common shingle nails
are sometimes driven into collars, or cracks in the roof, and
the end of the plummet line is noosed and put over the head.
86 SURVEYING
This causes an eccentric hanging of the plummet that may result
in an error in backsight and foresight of the width of the nail
head, which will be quite appreciable in a short sight.
A wooden plug is driven into a hole drilled in the roof, and
into this is driven the spad. The swelling wood clamps the
same and prevents it from coming out as readily as it was
put in.
A hole is bored in the roof with a A-iu* twist drill and a
piece of cord or a copper wire, placed across this and driven
into the hole by a hardwood shoe peg. The plummet is tied
to the lower end. A cord will soon rot, and, if in the gang-
way, will be pulled out by the drivers for whip lashes; while
the wire is more permanent, it may be pulled out by catching
in the topping of a car in a low place.
In the best form of station, however, the use of spads is
dispensed with and all the stations are put in rock roof where
possible, and consist of a vertical hole 1 in. deep made with
a A-in. twist drill. When a sight is to be taken, the foresight
man puts into this a steel clip with serrated edges; this clip is
made by bending upon itself a thin piece of steel A -in. wide.
When the ends are pressed together it will go into the hole,
and the spring of the sides and the serrated edges hold it in
place so that it is hard to pull out. The cord passes through a
hole in the center of the bend and is, therefore, in the center
of the hole, no matter how the clip is inserted. The clip is
removed by pressing together the ends. This is the easiest
and quickest way of working, as there is no eyehole to be freed
from dirt and no knot to be tied and tmtied. The hanging
of the plummet takes a fraction of a second, and the station will
remain as long as the roof keeps up. The disadvantages are
that holes may be bored inclined to the vertical by a careless
man, and many roofs are unfit for piercing with a twist drill.
Marking Stations. — ^There should be some regular way of
witnessing all stations. In general, a vertical line on the rib
calls attention to a station in the floor near the side marked.
A roof station has a mark aiotmd it, as has been described,
and is some geometric figure. Each station must be lettered
or numbered so that it can be readily recognized when tho
subsequent surveys are made.
SURVEYING 87
White lead, or Dutch white, thinned with Unseed oil, is
ordinarily used for marking stations. The top should be wiped
dean and dry with a piece of cotton waste before the paint is
applied, or the white will be so discolored as to be scarcely
visible, or the paint will flake off and the numbers will be lost.
Centers. — When the station is in the roof, there must be
something for the transit to set over, as it is easier to do so
than to set under a station, and much more accurate as instru-
ments are now made. The set-up is made over a center.
To avoid being displaced, centers are made as small and heavy
as possible; they are usually made of lead in the following
manner: A hole li in. in diameter and § in. deep is bored in
a thick plank, and a brad is set in its center with the head
down. The hole is filled with melted lead and the brad is
slightly raised to surrotmd the head with lead, and held with
pincers in a vertical position until the lead has set. The brad
is cut off i in. above the lead and pointed. This center com-
bines weight and small size,
KEEPING NOTES
Taking Notes. — Complete notes should be taken and recorded
neatly and systematically, so that a stranger can easily follow
them. Every physical characteristic and aU surface improve-
ments should be noted and located. Every ledge of rock
should be noted, its character, dip, and course of strike should
be taken. In a large company there should be a separate
book for transit notes and for side notes, and where many
collieries are operated, a separate set of books should be used
for each colliery. But however the notes are kept, the follow-
ing facts should be recorded: The numbers of the stations; the
needle readings to check the vernier; the vernier reading; the
dip of the sight; the distance measured, either flat or on the
dip; the height of the axis of the transit from the ground;
the height of the point sighted at from the ground; and all
other necessary remarks to make the work plain. It is custom-
ary to have series of vertical columns headed (to suit the above)
Sta., Needle F. S., Needle B. S., Vernier, Pitch, Dist., H. I.
(height of instrument), H. R. (height of rod, or point to which
sis^t was taken), and Remarks.
89
SURVEYING
At the tc^ of the page, in starting a survey, there should be
entered the name of the mine and of the bed where the
work is to be done; the names of the regular corps employed
for the work, and those that were taken from the mine to
point out work or assist; the instruments used; the date of
the work, and, in case it is the continuation of a i>revious
survey, the pages where such work was noted must be set
down. Such books are complete records, and can be used
as time books in paying the men, or- as proofs of the kind
of work done in case a lawsuit requires such testiniony, by
showing the number of men, the instruments used, and the
time employed.
Transit and Side Notes. — ^There are about as many methods
of keeping the transit and side notes as there are engineers.
These methods arrange themselves into groups; those in most
common use in the mines are:
The side notes of each sight follow the transit notes of that
sight, and on the same page.
The side notes are entered in the same book on opposite
pages.
The transit notes of the whole survey come first, and are
followed by the side notes in the same book.
Each set of notes has a sei>arate book.
Suppose that the transit is set up at b, with backsight at
a; foresight to c, deflected angle abc='85° 27' left, and that
the distance b cis 421.76 ft. measured on a pitch of +4^ 35'.
Then some such form of notes as the following can be used.
Other forms are used, but all are made to suit the ideas of the
person surve)dng.
Sta.
Needle
B. S.
Vernier
Needle
P. S.
Pitch
Dist.
Sta.
A
B
— a
b
S25°
30' W
L85«
27'
26'
S60°
O'E
+4*35'
421.76
c
SURVEYING
8»
-1-140
+110
+91 —J
+W — , 5
+30
+90
+16^^
+14
In every case the notes should convey to the man that plots
some idea of the fonn of the place surveyed. An accurate
sketch cannot be made unless the whole locality can be seen
at a glance; it is not necessary to go to the other extreme
and write down the notes without a sketch.
In the accompanying illustration, the red line in the
center of the page of the notebook is taken as the line of
survey, and the next parallel line on either side is taken
as the boundaries of the solid on either side. The only-
figures on each side of the red line
are the distances from the line to
the solid, while the pluses at which
they were taken are noted at the
side of the page, and the exact dis-
tance between the two stations is
enclosed in the parallelogram. This
method at the pluses 155 and 157
calls attention to a point where
practice varies greatly; namely, the
noting of the comer pillar and the
locating of the comer. One method
calls the comer that point where
the pillar begins to diverge from
the gangway line, as at a, where a
chamber, cross-cut, or counter
starts from the gangway; a second
method designates the comer as
the first or last solid part met with
in the line of survey, as at b. The
first is faulty, as there is no record
of the gradual divergence of the pillar from the gangway line,
and the words "comer of pillar" usually mean the end of the
same. The pillar should be called solid until the line at right
angles to the line of survey is tangent to the ends, no matter
whether that end is 10 or 100 ft. distant. Any one can plot
side notes if acctirately taken, and two persons accurately
plotting such notes will reach the same result.
49
19
t
;n
u
90 SURVEYING
MINE CORPS
The method of dividing the work in an underground survey
depends on the size of the corps, therefore the work of each
man is considered in order to get the right number for the coxps.
The chief of the party should be where he can do the most
good, and where he can plan the work for his subordinates.
The principal point of the stirvey is the setting of the stations
so as to do the work thoroughly with the fewest set-ups, and
thus diminish the chances of error in instrument work. The
-chief should locate the stations and add all the necessary signs
to show how the work is to be done. As the transitman
should not have his attention distracted from his particular
work by questions as to procedure, the chief should not run
the transit. Upon this basis, the ideal mine corps consists of at
least four, or better five, men from the office, and three from
the mine. It is divided into two sections. The chief takes
the men supplied by the mine — one or more of whom is
acquainted with the work done since the last survey — and
locates the stations; the transitman follows with the second
section, to measure angles and distances. By this time the
stations are set and the chief takes his men after the transit
party and gets the side notes, with a check-measurement of the
distances between stations.
The foresight man should be intelligent and active, as the
■amount of work done in a day depends on his ability to keep
ahead of the transitman. Some of the latter are fast enough
to keep two foresight men on the jump. His duty is to set
the center for the next set-up under the station, and also place
the trii)od if three are used in the work, to give the sight,
and. in some corps, to carry the front end of the tape and
assist in taking the distance.
The backsight man has little to do inside; for this reason, he
cleans and oils the tape, gets out new plummet strings, and
sees that the tools are ready for the next work, as soon as
the corps gets to the office.
lAYING OUT CTTRVES IN A MINB
Curves in a mine are usually so sharp that they are desig-
nated as curves of so many feet radius, instead of as curves
SURVEYING
91
of so many degrees. For example, supi>ose that it is required
to comiect the two headings A and B, in the accompanying
illustration, which are perpendicular to each other, with a
curve of 60 ft. radius. Prepare the device shown on the
right-hand side, by taking three small wires or inelastic
strings fg, gh, and gk, each 10 ft. long, and connecting
one end of each to a small ring, and the other end of two
to the ends of a piece of wood 1} ft. Umg. Form a neat
loop at the end / of the
third gf. To use this de-
vice, lay oflf on the center
line of the heading B, cd
and d e equal to 60 ft.
and 10 ft., respectively.
Place the loop / of the de-
vice over a small wire peg
driven into the floor at e,
and the ring g over a simi-
lar peg at d. Take hold
of the stick h k, pull the
strings g h and g k taut, and place the center mark on the piece of
wood hkon the center line of the heading B. Drive a small peg
in at m, located by the point k, which is on the curve. Move
the device forwards, place the loop / over the peg at (/, the ring
g over the peg at m, and take hold of the stick h k and pull
until the strings g h and g k are taut, and the strings / g and g h
are in a straight line. The point k will fall on the curve at n,,
which mark by driving in a peg. To locate other points »
proceed exactly as in the last step. The distance cd in. any
case is found by the formula
cd^Rtan \ 1
in which 12 ""radius of curve;
/-■intersection angle of center lines of headings.
«2 ELEMENTS OF MECHANICS
ELEMENTS OF MECHANICS
DEFINITIONS AND LAWS
All machinery, however complicated, is merely a comtnna-
tion of the six elementary forms: the lever, the wheel and axle,
the pulley, the inclined plane, the wedge, and the screw; and
these can be still further reduced to the lever and the inclined
plane. They are termed mechanical powers, but they do not
produce force; they are only methods of applying and direct-
ing it. The law of all mechanics is:
Law. — The power multiplied by the distance through which it
moves is equal to the weight multiplied by the distance through
which it moves.
Thus, 20 lb. of power moving through 5 ft. = 100 lb. of weight
moving through 1 ft. In the following discussion friction is
not considered, the idea being to give an elementary knowledge
of the principles of the elements of mechanics.
Levers. — There are three classes of levers. They are:
(1) power at one end, weight at the other, and fulcrum between;
(2) power at one end, fulcrum at the other, and weight between;
(3) weight at one end, fulcrum at the other, and power between.
A lever is in equilibrium when the arms balance each other.
The distances through which the i)ower and the weight move
depend on the comparative length of the arms. Let L repre-
sent power's distance from the fulcrum (C), I the weight's
distance, and a the distance between power and weight; then,
if Z. is twice /, the power will move twice as far as the weight,
Substituting these terms in the law of mechanics,
f§9
i
P:W'='l:L PL'Wl
^ Wl PL
L I
Pa Wa
"w+P "PT-fP
ELEMENTS OF MECHANICS
93
Wl
P- —
L
PL-'Wl
PL
L=
Wa
W-P
P'.W^UL
m
L
Wa
P=
1.=
P-W
I'
PL>
W
h
Pa
W-P
Wl
PL
I
Pa
P-W
In first- and second-class levers, as ordinarily used, power
is gained but time is lost; and in the third class, time is gained
but power is lost.
ExABCPLB. — Having to lift a weight of 2,000 lb. with a lever,
the short end of which is 2 ft. from the fulcrum and the long
end 10 ft., how much power will be required?
Solution. — Substituting in the formula L:l^P:W and
2.000X2
solving gives
10
«4001b.
Wheel and A^e. — ^The wheel and axle. Pig. 1, of which the
ordinary windlass is a common form, is a modification of the
lever. The power is applied to the handle, the bucket is the
weight, and the axis of the windlass is the ftdcrum. The
long arm of the lever is the handle, and the short arm is the
radius of the axle. Thus, F is the fulcrum,
F c the long arm, and F b the short arm.
The wheel and axle has the advantage
that it is a kind of perpetual lever; it is
not necessary, to prop up the weight and
readjust the lever, but both arms work
continuously.
By turning the handle or wheel around
once, the rope will be wound once around
the axle, and the weight will be lifted
that distance. Applying the law of mechanics, power X
circumference of wheel* weight X circumference of axle; or.
94
ELEMENTS OF MECHANICS
as the circumferences of circles are proi)ortional to their radii,
PiW^rdi PR^Wr
Wr
P= —
R
Tr=
RP
Wr
R^ —
P
RP
A train. Fig. 2, con-
sists of a series of wheels
and axles that act on
one another on the
^ principle of a compound
|-===*i lever. The driver is
/ IT I the wheel to which
/ I power is applied. The
^^^' * driven, or /(Mower, is the
one that receives motion from the driver. The pinion is the
small gear-wheel on the axle.
If the diameter of the wheel A is 16 in., and of the pinion B
4 in., a ptill of 1 lb. applied at P will exert a force of 4 lb. on
the wheel C If the diameter of C is 6 in., and of I> 3 in., a
force of 4 lb. on C will exert a force of 8 lb. on E. If E is 16 in.
in diameter, and F 4 in., a force of S lb. on E will raise a weight
of 32 lb. on P. In order, however, to lift this amount according
to the principle already named, the weight will only pass
through ih of the distance of the i)ower. Thus, power is
gained and speed lost. To reverse this, apply power to the
axle F, and, with a correspondingly heavy power, gain speed.
Referring to Fig. 3, and applying the law of mechanics, the
following formulas are obtained,
Wrr'r"
TF=
PRR'R"
RR'R'' rr'r"
n.re' '^r'r" \RR'
vvff --rr'r" \RR'R"
in which n, n' , n" « number of revolutions;
f, »' = velocity of speed of
rotation;
r,r',r", etc. « radii of the pinions;
R, R', R", etc. -radii of the wheels.
Fig. 3
ELEMENTS OF MECHANICS
95
Inclined Planes. — In the inclined plane, Pig. 4, the power
mtxst descend a distance equal to A C to elevate the weight
to the height BC; hence FX length of inclined plaaie—W
X height of inclined plane, or P :W
B height of inclined plane : length of
inclined plane; or,
Wh PI P
p = — W=— =
/ h sin a
Pig. 4
Wedge. — The wedge usually con-
sists of two inclined planes placed
back to back. In theory, the same formula applies to the
wedge as to the inclined plane.
P : PF= thickness of wedge : length of wedge
Screws. — The screw consists of an inclined plane wound
arotmd a cylinder. The inclined plane forms the thread, and
the cylinder, the body. It works in a nut that is fitted with
reverse threads to move on the thread of the screw. The nut
may run on the screw, or the screw in the nut. The power
may be applied to either, as desired, by means of a wrench or
a lever.
Pulleys. — The pulley is simply another form of the lever
that turns about a fixed axis or fulcrum. With a single fixed
pulley, shown in Pig. 6, there can
be no gain of power or speed, as the
force P must pull down as much
as the weight W, and both move
with the same velocity. It is sim-
ply a lever of the first class with
JmL equal arms, and is used to change
I »r 1 ■ the direction of the force. » = ve-
locity of W; 1/ = velocity of P;
Fig. 5
Pig. 6
In the movable pulley, shown in Pig. 6, one-half of the weight
is sustained by the hook, and the other half by the power. As
the power is only one-half the weight, it must move through
twice the space; in other words, by taking twice the time,
it is i>ossible to lift twice as much. Here power is gained and
time lost. P = § W; 1/ = 2v.
ELEMENTS OP MECHANICS
In the cambinaii
U suslaiiied by
puUey. shown in Fig. 7, tbe weigbt W
which ia Ati«tched by a
lb. of power will balance
P[G. S
Pic. 10
3 lb. of weight. In the combination shown in Fig. S. 1 lb. wi
sustain a weight W oli lb, but it must descend 4 in. to laii
the weight 1 in. Fig. 9 represents the nidiaaj-y tackle bloc
used by mechanics. The power applied foi balance can I
rd by the following general rule:
. — In any tombinatioH of pulleys whtttoiu an
rapt is used, a load on the free nid via balan.
I on llu nopalrle bUick as many limes as trf
u load on Ihi frte nd as llitre art patis of II
supportins tht toad, not counting the free eni
marked ', has a
n the weight W is le, W-ieP. If H- number of potleys.
In [he diffcrmlial PulUy. shown in Fig. 11. W-- —
ELEMENTS OF MECHANICS 97
FRICTION AND LUBRICATION
Friction. — Friction is the resistance to motion due to the
contact of surfaces; it is of two kinds, sliding and rolling.
If the surface of a body could be made perfectly smooth,
there would be no friction; but, in spite of the most perfect
polish, the microscope reveals minute projections and cavities.
As no surface can be made perfectly smooth, some separation
of the two bodies must, in all cases, take place in order to clear
such projections as exist on the surfaces. Therefore, friction
is always more or less affected by the amount of the perpen-
dicular pressure that tends to keep them together. The
ultimate friction is the greatest frictional resistance that one
body sliding over another is capable of opiK)sing to any sliding
force when at rest.
The coefficient of friction is the proportion that the ultimate
friction in a given case bears to the perpendicular pressure.
The coefficient of friction is usually expressed in decimals;
but sometimes, as in the case of cars and engines, it is expressed
in pjounds (of friction) per ton. The coefficient of friction
equals the ultimate friction divided by the perpendicular
pressure, and the ultimate friction equals the perpendicular
pressure multiplied by the coefficient of friction. Thus, if a
block weighing 100 lb., stands on another block, and it takes
a pressure of 35 lb. to slide it, the coefficient of friction = "f^-,
or .35.
Lubrication. — To diminish the friction, oil or grease is placed
on the surfaces of sliding bodies so as to fill the cavities and
spaces between the projections; this oil or grease is called a
lubricant. There is probably no factor that has a more direct
bearing on the cost of production per ton of coal and ores than
the lubrication of mine machinery, and yet it is doubtful if
there is another item connected with the operation of a mine
less understood by owners, managers, and engineers in charge.
BEST LUBRICANTS FOR DIFFERENT PURPOSES
Low temperatures, as in rockl
drills driven by compressed f Light mineral lubricating oils.
air J
8
98 STRENGTH OF MATERIALS
Very great pressures, slow f Graphite, soapstone, and
speed \ other solid lubricants.
Heavy pressures, with slow f The above, and lard, tallow,
speed \ and other greases.
Heavy pressures and high f Sperm oil, castor oil, and
speed \ heavy mineral oils.
T . , ^ J I.- 1. , /Sperm, refined petroleum.
Light pressures and high speed < ,. ^ ,
L ohve, rape, cottonseed.
fLard oil, tallow oil, heavy
Ordinary machinery \ mineral oils, and the heav-
ier vegetable oils.
Steam cylinders.
"Watches and other delicate
Heavy mineral oils, lard, tal-
low.
Clarified sperm, neat's foot.
mechanism i I«n>ois«, olive, and light
I mmeral lubncatmg oils.
For mixture with mineral oils, sperm is best; lard is much
used; olive and cottonseed are good.
STRENGTH OF MATERIALS
USEFUL FORMULAS
The ultimate strengths of different materials vary greatly
from the average values given in the following tables. In
actual practice, the safest procedure is to make a test of the
material for its ultimate strength and coefficient of elasticity,
or else specify in the contract that it shall not fall below certain
prescribed limits. In the following formulas,
A = area of cross-section of material, in square inches;
£ = coefficient of elasticity, in potmds per square inch;
6^ = square of least radius of gyration;
/ » moment of inertia about an axis passing through center
of gravity of cross-section;
if » maximum bending moment, in inch-pounds;
P« total stress, in pounds;
Rs moment of resistance;
STRENGTH OF MATERIALS
99
S« ultimate stress, in pounds per square inch of area of
section;
FT— weight placed on a beam, in pounds;
ft — breadth of cross-section of beam, in inches;
d » depth of beam (in.) » diam. of circ. section = altitude
of triangular section = length of vertical side;
e^amotmt of elongation or shortening, in inches;
/= factor of safety;
/» length, in inches;
^■B pressure, in pounds per square inch;
IT —ratio of circumference to diameter « 3.1416, nearly;
g« constant used in formula for columns;
r=s radius of circular section;
5 » elastic set or deflection of a beam tmder a transverse
(bending) stress, in inches;
t« thickness of shell or hollow section.
Tension, Compression, and Shear. — For tension, compres-
sion (where the piece does not exceed 10 times its least diameter)
and shear,
/
Breaking Stress. — To find the breaking stress. P, make
/= 1. For safe load, take the values for / and 5 from the accom-
FACTORS OF
SAFETY
Material
Steady
Stress
Varying
Stress
Shocks
(Machines)
Cast iron
6
4
5
8
15
15
6
7
10
25
20
Wrought iron
Steel
10
16
Wood
15
Brick and stone. . . .
30
panying tables of Factors of Safety and Ultimate Strengths,,
espectively.
100
STRENGTH OF MATERIALS
ULTIMATE STRENGTHS
Material
Cast iron ....
Wrought iron
Steel
Wood
Stone
Brick
Tension
Com-
pression
20.000
90,000
50,000
50.000
100.000
150,000
10.000
8,000
6,000
200
2,500
20,000
47,000
70.000
600 to 3,000
Flexure
36,000
50,000
120,000
9,000
2,000
COEFFICIENT OF ELASTICITY
Material
Coefficient
of Elasticity
Elastic Limit
for Tension
Cast iron
Wroueht iron
15.000.000
25,000,000
30,000,000
1.500,000
6,000
25,000
Steel
50,000
Wood
3,000
BENDING MOMENT AND DEFLECTION OF BEAMS
Kind of Beam and Manner of Loading
M ^
1
Cantilever, load at end
Wl i— -
Cantilever, uniformlv loaded
^EI
Simple beam, load at middle
' 1 *£/
Simple beam, uniformly loaded
Beam fixed at both ends, load at middle
Beam fixed at both ends, uniformly
loaded
iWl
"EI
"^Ei
»*'£ /
"*£/
STRENGTH OF MATERIALS
101
PROPERTIES OF VARIOUS SECTIONS
Section
SoUd
circular.
Hollow
circtilax. . .
Solid square
Hollow
square. . . .
Solid
rectangular
1-
4
Hollow ,i
rectangular T
Solid
triangular >^^^
Solid
elliptic .
Hollow
elliptic ... ^ I
I-beam ••..'f i^Q
Cross with T
equal arms 7
Angle with ]
equal arms "«
64
ir{d*-di*)
64
di
12
d*-di*
12
12
bd^—bidi*
12
6^
36
Tbd^
64
64
ibd^-bidi»)
bd^—bidi*
12
32
ir(d*-di^)
S2d
6
d*-di*
6d
b^
6
b<P — b\di*
6d
db^
24
irbdi
32
r(6i»-fridi»)
32J
ferf* — M l*
6d
G>
16
16
12
. 12
12
h^d-biHi
12(bd-bidi)
di_
18
16
6*J-6i'rfi
i6{bd-bidi)
6» rf-6i»Ji
12(6J-6idi)
22.5
25
102 STRENGTH OF MATERIALS
Elonsation or Shortening Under Stress. — ^The amotant of
elongation or of shortening oi a piece under a stress is given by
the formula
PI
AE
The coefficient of elasticity E must be taken from the accom-
panying table.
Breaking Strength of a Beam. — To find the breaking strength
of a beam, use the formula
M-'SR
Obtain M and R from the accompanjring tables according
to the kind of beam and nature of cross-section. A simple
beam is one merely supported at its ends. In the expression
for R, d is always understood to be the vertical side or depth;
hence, that beam is the stronger that always has its greatest
depth or longest side vertical. The moment of inertia / is
taken about an axis perpendicular to d, and lying in the same
plane.
The value of S for beams should be taken from the flexure
column of table of Ultimate Strengths.
Deflection in Beams Due to Loads. — ^To find the amount of
deflection in a beam due to a load, substitute the values of
W, I, E, and / in the different expressions for the deflection 5
in the table Bending Moment and Deflection of Beams. The
value of / is to be taken from the table Properties of Various
Sections.
Columns. — To find the breaking strength of a column, use
the formula:
SA
P
fi
1+,^
The values of these quantities are taken from the accompany-
ing tables.
Ropes and Chains. — ^Let D — diameter of rope, in inches
—diameter of iron from which link in chain is made;
TT-safe load, in tons of 2.000 lb.
For common hemp rope, TT* } D*.
STRENGTH OF MATERIALS
103
For iron-wire rope, W^% IP.
For sted-wire rope, W=^ IP.
CONSTANT USED IN FORMULA FOR COLUMNS
Material
Both Ends
Flat or Fixed
One End
Round
Both Ends
Round
Cast iron
1
5,000
1
1.78
5,000
1.78
36,000
1.78
25,000
1.78
3,000
4
Wrought iron
Steel . . ....
5,000
4
36,000
1
36.000
4
Wood
25,000
1
3,000
25,000
4
3,000
For close-link wrought-iron chain, PF=6 LP.
For stud-link wrought-iron chain, W=>9 IP.
WIRE ROPES
Wire ropes for mine use are made of either iron or steel, and
are generally round. Flat wire ropes are sometimes employed,
but the round rope is the one generally used in American prac-
tice, except in some of the deep metal mines having small com-
partment shafts. Steel ropes are in most respects superior to
iron ropes, and are therefore gaining favor every year. Their
principal advantage is their greater strength; consequently,
they can be made lighter and can pass around pulleys and drums
with less injury than an iron rope of equal strength.
Where great flexibility is required, such as in hoisting ropes,
the strands are usually made up of 19 wires each, while haulage
ropes have but 7 wires to the strand; yet, both kinds have 6
strands. A hemp core is generally used, and in some cases a
core is also placed in each strand, to further increase the flex-
ibility of the rope.
104
STRENGTH OF MATERIALS
The lay of the rope is the twist or pitch of the wires in the
strand, or of the strands in the rope. As the lay of the wires
is less than that of the strands, each wire is exposed to external
wear for short distances at intervals along the rope.
In the ordinary lay. Fig. 1 (a), the wires are twisted in the
opposite direction to the strands; this method prevents the
rope from untwisting when in use, and the wires from unravel-
ing when they are worn through or broken at the surface.
In the Lang lay, view (6), the wires are twisted in the same
direction as the strands, thus giving each wire a greater wearing
surface, while the rope is smoother and will wear longer. After
(a)
the wires begin to break, unraveling becomes troublesome, and
it is more difficult to splice a Lang-lay rope than an ordinary-
lay one. Hoisting ropes, especially those used to raise and
lower men, should not be spliced.
The locked-wire rope, a cross-section of which is shown in
(c), consists of wires of special cross-section formed in concen-
tric layers. The lay of the inner wires is opposite to that of
the outer ones, and somewhat
longer.
In fastening a rope to a drum,
a great error is often made. Men
who would not think of pas^ng a
rope around a pulley of too small
diameter will insert it in the drum rim in such a way as to make
a very sharp curve, as shown in Fig. 2 (a), and make a weak
point in the roi>e that would not otherwise exist. The right
way of passing the rope through the drum rim is shown in (6).
Flattened-Strand Ropes. — Many ropes have flattened strands,
as shown in Pig. 3; several wires thus take the wear of the rope
instead of a single one, as is the case with a round strand when
new. The manufacturers claim for these ropes longer life, more
(")
Pig. 2
(*>
STRENGTH OF MATERIALS
105
uniform wear, greater flexibility, less liability of wires becom-
ing brittle, and freedom from all tendency to spin or kink. It
Fig. 3
is also claimed that the smoother surface effects considerable
saving in the wear of pulleys and sheaves.
STRESS IN HOISTING ROPES ON INCLINED
PLANES
Rise per
100 Ft.
Hori-
zontal
Feet
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Angle
of
Incli-
nation
2*>52'
5*>43'
8° 32'
11° 10'
14*> 03'
16° 42'
19° 18'
21° 49'
24° 14'
26° 34'
28° 49'
30° 58'
33° 02'
35° 00'
36° 53'
38° 40'
40° 22'
42° 00'
43° 32'
45° 00'
Stress
Rise per
100 Ft.
per Ton
of 2.000
Hori-
Lb.
zontal
Pounds
Feet
140
105
240
110
336
115
432
120
527
125
613
130
700
135
782
140
860
145
933
150
1,003
155
1,067
160
1.128
165
1,185
170
1.238
175
1,287
180
1,332
185
1,375
190
1,415
195
1,450
200
Angle
of
Incli-
nation
46° 24'
47° 44'
49° 00'
50° 12'
51° 21'
52° 26'
53° 29'
54° 28'
55° 25'
56° 19'
57° 11'
58° 00'
58° 47'
59° 33'
60° 16'
60° 57'
61° 37'
62° 15'
62° 52'
63° 27'
Stress
per Ton
of 2,000
Lb.
Pounds
1,484
1,516
1.535
1,573
1,597
1.620
1,642
1,663
1,682
1,699
1,715
1,730
1,744
1,758
1,771
1,782
1,794
1,804
1,813
1,822
Wire-Rope Tables. — The accompanying wire-rope table is
a rearrangement of the standard tables published in the
106
STRENGTH OF MATERIALS
CO
o
:^93j 'SAcaqs JO
UlIUQ JO dZIg XddOJJ
•o
CO C4 ^ O) 00 00 1^ t«
SupiiOj^ Jddai j
oooSoSSoi' ■ ■
I"*"*
^Q^C0»ONO><DC0
suox
ai^BTzmojddv
8QQOOOOOO
^ q q q c q q q q
oubp«oc>ir-ia)oo<D
bOCO
83
•S3 -a
w
:t;co
^aaj 'SAcaqs JO
mnzQ JO azig jadoj j
•-•OOOOt^QOCOtOtO
suoj^ "pBoq
Sin3[jo^ jddoj J
c6»6«5
suox
aKjBmixojddy
oooooq
00 •^ •«»; 00 ■^ ©
oociosto-^^
C^ C^ rH rH rH ^H
88888888
o<
q<
«d(NCS
?O<NQ0
■^ e< t^ -^ csi 00
■^ »-f OJ 00 1^ wa
laajj 'dAsaqs jo
uiTUQ p azig jddoj J
2
SUOJ^ 'PBGI
^OOOOt^COCOtOtO
gooooooco
_q(Noq<NoqTj<Tijq
SUOT
s^^BuiixGjddy
qqqqqqqqq
C^ rH i-^ rH
c
o
0)
• mm
I :jaajj -aABaqg jo
. UITUQ JO azTg jadoj j
»owc>«»-io»««r^i^
suoj, "pBoq
SupiJOj^ jddoj j
o p o o d 6 o o ©"
oqqoTi«co-^(Nc^q
c^o6>oc4oo6t>^«d>o
SUOT
s^Buiixojddy
q q q q q q q q q
■^»oo6No6c>i«d<-«>o
spunoj
:ioo J jcamq jad )i{Si9)^
i75»QQp«j»i5«3q'5
qaqowoq<-j»oq'«ij
^oJoocd'^'^cococi
saqouj '93naj9i
-umojiQ ai^Buiixojddv
Mt^r^sotoio-^-***^
saqouj
iW» MW i » ii*ii M
ado-^ JO asQ
ja^uaa doiaq
'ajiM-5x *pirej^-9
'sadoj 8m^sto{2
STRENGTH OF MATERIALS
107
COiO^i^C0C0C>IC>IC«f-4
C40000OOOC>4t^C0O«0
• ••••••••••
«o i*( eo N >-• ^ >-•
• ••••••••••
8QQPQOOOM»oo
"^■•^COCOWMMiH^i-i
QOOXMOOCOQCOOO
• ••••••••••
ppp'<*;«oqooooq'<ij'^
<DIO^-«COCOC4C4C4^
■«^ CO N ^ »-i 1-1
• •••••
§«oS<NoS©C^lSo
^uSNoqqubeocowi-jrH
H* •^••^('••■•••pii |Hr*p5ll|M'"P5»^
*-400)OOCOCO>0<<|l-<^<<|lCOCOC>4C>4^
OQOQOOOOOQP^t^t^cO
• •••■■«••••••••
f>H rH rH rH
'0 0<OOC>QQQQOQ*OiO^O^O
OOOOOOOOOOOiOCOCO®
oot»t»co»0'«^'^eoeocoMwoii-«^
OoSwM-^*
U3C0^0»t^«O'^C0C0Ni-«'-i^
^pppppp'^^cot-»o»ooqw
O»o6«d«dt>lo6^o6ioc4ojt^»oc6co
00 1^ t* ® »0 •f'^ "WCO CO M CS| W i-ii-i
CO
• ••#•■•••••■•••
e0'-<o»x«O'^eococ^w^'H
1-4 rH
PPPPPP?O00M«O'«*««OM^«
o6QOo6pci<<t4o6>oeodo6cd-<^c6c4
^OOJM«0«0»0'^"^'^COeONNf-i
«ooooOMTi«M25eoooO«0"^cOcsi
«>»0-^-^SOW.H^r-lr-l
OOOOOOCOO>50COCSjeOil<t^-^
SO»^o«ON<»t^«o»0"^eoN^^
»oo'^o»o^j»t^«o»5coeoN»H'-<
COCONNt-f^
•^fi^-illCOCOMMNN^^iHiH^
•wiM-/, 'pirBJis-9 'sddoj
uoi88iixi8crej:( pu« 38HxnB{{
108
STRENGTH OF MATERIALS
catalogs of most of the American manufacturers of wire roi>e.
The proper working load given in this table is one-fifth of the
approximate breaking stress, that is, a factor of safety of 5 is
used, and when the values given in this table are used this factor
is supposed to allow for the bending stress. The sizes of sheaves
or drums given in this table are largely empirical, but they are
based on a long experience in the use of wire ropes, and in most
cases represent the minimtun diameter recommended by the
roi>e makers. The factor of safety of 5 assumes ordinary con-
ditions of working; where the conditions are extraordinary, and
particularly in cases where men are to be hoisted, a larger factor
than 5 is used, varying from 5 to 10.
Stress in Hoistiiig Ropes on Inclined Planes. — The accom-
panying table is based upon an allowance of 40 lb. per T. for
roUing friction, but there will be an additional stress due to the
weight of the rope and inclination of the plane.
STARTING STRAIN ON HOISTING ROPES
Experiment
Empty cage, lifted gently
Empty cage, started with 2i in. of slack rope. . .
Empty cage, started with 6 in. of slack rope. . . .
Empty cage, started with 12 in. of slack rope. . .
Cage and loaded cars, as weighed
Cage, and loaded cars, lifted slowly and gently . .
Cage and loaded cars, started with 3 in. of slack
rope
Cage and loaded cars, started with 6 in. of slack
rope
Cage and loaded cars, started with 9 in. of slack
rope
Strain in
Rope
Potmds
4,030
5,600
8,950
12.300
11,300
11,525
19.025
24,625
26.850
Starting Strain on Hoisting Rope. — In selecting a hoisting
rope, due allowance must be made for the shock and extra
strain imposed on the rope when the load is started from rest.
Exi>eriments made by placing a dynamometer between the
rope and the cage have shown that the starting stress may be
from two to three times the actual load.
STRENGTH OF MATERIALS
109
The following table shows the results of a number of tests
under different conditions, with slack chain, amount of load,
and speed in starting.
EXTRA STRAIN ON A HOISTING ROPE WITH A FEW
INCHES OF SLACK CHAIN
Dynamometer Tests
First Test
Empty cage lifted gently
Empty cage with 2^ in. slack chain
Empty cage with 6 in. slack chain
Empty cage with 12 in. slack chain
Second Test
Cage and 4 empty cars weighed by
machine
Cage and 4 empty cars lifted gently
Cage and 4 empty cars with 3 in. slack
chain
Cage and 4 empty cars with 6 in. slack
chain
Cage and 4 empty cars with 12 in. slack
chain
Third Set
Cage and full cars weighed by machine . .
No. 1, lifted gently
No. 2, lifted gently
No. 1, with 3 in. slack chain
No. 2, with 3 in. slack chain
No. 1, with 6 in. slack chain
No. 2, with 6 in. slack chain
No. 1, with 9 in. slack chain ,
No. 2, with 9 in. slack chain ,
Tons
1
2
4
5
2
3
Hundred-
weights
16
10
10
17
10
5
1
5
1
5
3
8
10
8
10
10
10
11
10
12
10
11
10
Sheaves. — To decrease the bending stresses the sheaves for
wire-rope transmissions are generally of as large diameter as is
practicable to give the required speed to the rope. Large
sheaves are also advantageous because with them the rope is
run at a high velocity allowing of a lower tension and permit-
ting a rope of smaller diameter to be used than would be p>ossible
with smaller sheaves, provided, of course, that the span is
of sufficient length to give the necessary weight.
no
STRENGTH OF MATERIALS
Sheaves are generally made of cast iron when not exceeding
12 ft. in diameter, and when larger than this they are usually
bmlt up with wrought-iron arms. Sheaves, upon which the
rope is to make but a single half-turn, are made with V-shaped
grooves in their circumference. The bottom part of the groove
is widened to receive the filling, which consists of some sub-
stance to give a bed for the roi)e to run on and protect it from
wear, and to increase the friction so that the rope will not slip.
This filling is made of blocks of wood, rubber, leather, or other
material Rubber and leather have been used separately,
but blocks of rubber separated by pieces of leather have been
found to give the best results.
In the accompanying table, the ropes are made of cast steel
and used on inclines. The ropes are composed of 6 strands
of 7 wires each and have hemp cores.
EFFECTS OF VARIOUS SIZE SHEAVES OR DRUMS ON
LIFE OF WIRE ROPES
Percentages of Life for Various Diameters
Diameter
of Rope i 100
Inches
90
80
75
60
50
25
Diameter of Sheaves or
Drums,
in Feel
*
IJ
16.00
14.00
12.00
11.00
9.00
7.00
4.75
14.00
12.00
10.00
8.50
7.00
6.00
4.50
1 ' '
12.00
10.00
8.00
7.25
6.00
6.50
4.25
1
10.00
8.50
7.75
7.00
6.00
6.00
4.00
8.50
7.75
6.75
6.00
5.00
4.50
3.75
7.75
7.00
6.25
5.75
4.50
3.75
3.25
•
7.00
6.25
• 5.50
5.00
4.25
3.50
2.75
6.00
5.25
4.50
4.00
3.25
3.00
2.50
'
5.00
4.50
4.00
3.50
2.75
2.25
1.75
Wire-Rope Calculatioiis. — The working load, also called the
proper working load, is the maximum load that a rope should
be permitted to support under working conditions. When a
load is attached, the stress on a rope bending over a sheave, is
STRENGTH OF MATERIALS
WIRE AITD SHEET-METAL GAUGES
111
U. S.
British
Amer-
Stand-
Im-
ican or
Trenton
ard
perial
Stand-
Birm-
Brown
Roeb-
Wire
Gauge
Sheet-
ingham
&
ling's
Co.'s
Number
Metal
ard
Gauge
Sharpe
Gauge
Wire
Gauge
Wire
Gauge
Gauge
Gauge
Inch
Mm.
Inch
Inch
Inch
Inch
0000000
.5
12.7
.49
000000
.469
11.78
.46
00000
.438
10.97
.43
.45
0000
.406
10.16
.454
.46
.393
.40
000
.375
9.45
.425
.40964
.362
.36
00
.344
8.84
.38
.3648
.331
.33
.313
8.23
.34
.32486
.307
.305
1
.281
7.62
.3
.2893
.283
.285
2
.266
7.01
.284
.25763
.263
.265
3
.25
6.4
.259
.22942
.244
.245
4
.234
5.89
.238
.20431
.225
.225
5
.219
5.38
.22
.18194
.207
.205
6
.203
4.88
.203
.16202
.192
.19
7,
.188
4.47
.18
.14428
.177
.175
8
.172
4.06
.165
.12849
.162
.16
9
.156
3.66
.148
.11443
.148
.145
10
.141
3.26
.134
.10189
.135
.13
11
.125
2.95
.12
.09074
.12
.1175
12
.109
2.64
.109
.08081
.105
.105
13
.094
2.34
.095
.07196
.092
.0925
14
.078
2.03
.083
.06408
.08
.08
15
.07
1.83
.072
.05707
.072
.07
16
.0625
1.63
.065
.05082
.063
.061
17
.0563
1.42
.058
.04526
.054
.0525
18
.05
1.22
.049
.0403
.047
.045
19
.0438
1.01
.042
.03589
.041
.04
20
.0375
.91
.035
.03196
.035
.035
22
.0313
.71
.028
.02535
.028
.028
24
.025
.56
.022
.0201
.023
.0225
26
.0188
.45
.018
.01594
.018
.018
28
.0156
.38
.014
.01264
.016
.016
30
.0125
.31
.012
.01002
.014
.014
32
.0101
.27
.009
.00795
.013
.012
34
.0086
.23
.007
.0063
.01
.01
36
.007
.19
.004
.005
.009
.009
38
.0063
.15
.00396
.008
.008
40
.12
.00314
.007
.007
112 STRENGTH OF MATERIALS
made up of two parts: (1) That due to the load on the rope,
known as the load stress; (2) that due to the bending of the rope
about a sheave or drum, known as the bending stress. That
is, if 5 is the total safe stress, St is the bending stress, Si is the
load stress, S^S^-j-Si and Si=S—Sd- The total stress must
not equal the elastic limit of the material composing the rope
and is usually taken as from one-third to one-fourth the approx-
imate breaking stress. The proper size of rope to use to hoist
a given weight may be taken directly from the tables just given,
but these tables do not take account of the bending stress,
except by allowing for it in the factor of safety assumed.
The general formula for the bending stress is
EaA
5* = —.
in which St = bending stress;
£ = modulus of elasticity;
o = diameter of each wire;
D = diameter of drum or sheave;
i4= total area of w.re cross-section, in inches.
Wear of Wire Ropes. — The deterioration of wire ropes may
be either external or internal, and may be due (1) to abrasion,
due to the rubbing of the outside surface of the rope against
other objects, or to the internal chafing of the wires composing
the strands against one another; (2) to injury from overloading,
to shock due to sudden starting of the load, or to repeated
bendings about too sharp angles or over sheaves or rollers of too
small a diameter for the size of the rope; (3) to rust or corrosion
of the wire from acid waters, or to decay of the hemp cores.
Lubrication of Ropes. — Mine water has a very corrosive
action on wire ropes, and a rope will soon be destroyed unless
the water is prevented from coming in contact with the metal
of the rope. To avoid this corrosive act'on tar, black oil, or
some lubricating preparation is applied to the rope, but any
lubricant used must be free from acids or other substances that
would corrode the wire. The lubricants to be used are generally
specified by the manufacturers of the ropes, a list of which can
be obtained from them when purchasing a rope.
STRENGTH OF MATERIALS 113
Wire-Rope Fastenings. — ^An ordinary form of ikinible-spliced
fastening is shown in Fig. 1 (a). In this method, the wires, after
being frayed out at the end and the rope bent around the
thimble, are laid snugly about the main ix>rtion of the rope and
securely fastened by wrapping with ^^^^^^
stout wire; the extreme ends that pro- ^^^^S^BSIJ^ISSSZ, (o)
ject below this wrapping are then folded ^s^^"^
back, as shown. Another style of
thimble splicing is shown in (6). In i((P ^ ^.iim..„,. „„^^^^^
this case the strands are interlocked ^^^^jjlillMlIM*^''?^^^ (6/
as in splicing, and the joint is wrapped
with wire as in the former method. .J'-r
The socket fastening is shown in (c); "(^^^pSSgSgSSZc ic)
the hole in which the rope end is fas- p j
tened is conical in shape. The rope is
generally secured by fraying out the wires at the end, the
interstices being filled up with spikes driven in tightly. The
whole is finally cemented by pouring in molten Babbitt metal.
A good fastening can be made if the wires, after being frayed
out at the end, are bent upon themselves in hook fashion, the
prongs of some being longer than others, so that the bunch will
conform to the conical aperture of a socket, and the melted
Babbitt metal finally run in as usual. This makes a much
neater fastening than either of those shown in (a) and (6),
but it does not possess nearly as much strength. The thimble
possesses a serious disadvantage; it is usually made of a piece
of curved metal bent around into an oval shape, as shown in
(o) and (6), with the groove, in which the rope lies, outside,
the ends coming together in a sharp point. When weight is
placed on the rope, the strain on the thimble is apt to cause
one end to wedge itself beyond or past the other, and with its
sharp edge cut the strands in the splice.
Splicing a Wire Rope. — To splice a wire rope the only tools
needed are a cold cutter and hammer for cutting and trimming
the strands, and two needles 12 in. long, made of good steel and
tapered ovally to a point. Cut off the ends of the ropes to be
spliced and unlay three adjacent strands of each back 15 ft.;
cut out the hemp center to this point and relay the strands for
7 ft. and cut them off. Pull the ropes by each other until they
114
STRENGTH OF MATERIALS
have the position shown in Fig. 2 (a), cut off a and d', b and c',
view (jb), making their lengths approximately 10 and 12| ft., ,
respectively, measxired from the point where the hemp centers
are cut. Place the ropes together, view (jb) ; unlay e, d, c, view
(a), keeping the strands together, and follow with ef, d\ d,
view (ft). Similarly, unlay /', a', b\ view (6), and follow with
/, a, 6, until the rope appears as in view (c). Next run the
strands into the middle of the rope. To do this, cut off the
end of the strand «', view (c), so that when it is put in place
it will just reach to the end x of the hemp core, and then push
(b)f
V:S
J" w^ d;^
:5:?§S^1
^s^^i
*
i^^'feSS
si*^^!i%s^!S:^ss5?fes^s^ss^!^5
•^KS^^EXS^'^J
d
.f^ ^c ^
^=Vl ^
^*
^=^
^^^ac
Fig. 2
one needle A through the rope from the under side, leaving
two strands at the front of the needle, as shown. Push the
other needle B through from the upper side and as close to the
first needle A as possible, leaving the strands e and «f between
them; place the first needle A on the knee and turn the other
needle B around with the coil of the roi>e, and force the strand
tf into the center of the rope. Repeat this operation with the
other ends and cut them off so that the ends coming together
in the center of the rope will butt against each other as nearly
as possible.
STRENGTH OF MATERIALS
115
Ordinary Long Splice. — The tools required to make a long
splice in wire rope are a pair wire nippers, for cutting off strands;
a pair pliers, for pulling through and straightening ends of
strands; two marline-spUces, one round and one oval, for open-
ing strands; a knife to cut hemp center; two clamps, to untwist
rope to insert ends of strands, or, in place of them, two short
hemp-rope slings, with a stick for each as a lever; a wooden
mallet, and some rope twine. Also, a bench and vise are handy.
The length of the spUce depends on the size of the rope. The
larger ropes require the longer splices. The splice of ropes
from I in. to i in. in diameter should not be less than 20 ft.;
from i in. to li in., 30 ft.; and from li in. up, 40 ft.
■VMbBSaBBBBillltBBBBe
6'
To splice a rope, tie each end with a piece of cord at a distance
equal to one-half the length of the splice, or 10 ft. back from
the end, for a } in. rope, after which tmlay each end as far as the
cord. Then cut out the hemp center, and bring the two ends
together as close as possible, placing the strands of the one end
between those of the other, as shown in Fig. 3 (a). Remove
the cord k from one end M of the rope, and unlay any strand a,
and follow it up with the strand of the other end M' of the rope
that corresponds to it, as a'. Leave out about 6 in. of a and
cut off a' about 6 in. from the rope, thus leaving two short ends,
as shown at P in view (6), which must be tied for the present
116 STRENGTH OP MATERIALS
by cords as shown. The cord k should again be woujid around
one end M of the rope, view (a), to prevent the unraveling of
the strands. Remove the cord kf on the other end if' of the
rope, and unlay the strand b; follow it up with the strand 1/,
leaving out the ends and tying them down, as at view (6).
Replace the cord k' for the same purpose as stated before.
Again remove the cord k and unlay the next strand c, view (a),
and follow it up with (f, stopping, however, this time within
4 ft. of the first set. Continue this operation with the remaining
6 strands, stopping 4 ft. short of the preceding set each time.
The strands are now in their proper places, with the ends pass-
ing each other at intervals of 4 ft., as shown in view (c). To
dispose of the loose ends, clamp the rope in a vise at the left of
the strands a and a', and fasten a clamp to the rope at the right
of these strands; then remove the cords tied around the rope
that holds these two strands down; after which turn the clamp
in the opposite direction to which the rope is twisted, thereby
untwisting the rope, as shown in view (d). The rope should be
untwisted enough to allow its hemp core to be pulled out with
a pair of nippers. Cut off 24 in. of the hemp core, 12 in. at
«ach side from the point of intersection of the strands a and a',
and push the ends of the strands in their place, as shown.
Then allow the rope to twist up to its natural shape, and remove
the clamps. After the rope has been allowed to twist up,, the
strands tucked in generally bulge out somewhat. This bulging
may be reduced by lightly tapping the bulged part of the strands
with a wooden mallet, which will force their ends farther into
the rope.
CHAINS
The links of iron chains are usually made as short as is con-
sistent with easy play, so as to make them less liable to kink,
and also to prevent bending when wound around drums, sheaves,
etc. The weight of close-link chain is about 3 times the weight
of the bar from which it is made, for equal lengths.
The strength of a chain link is less than twice that of a straight
bar of a sectional area equal to that of one side of the link. A
weld exists at one end and a bend at the other, each requiring
at least one heat, which produces a decrease in the strength.
STRENGTH OF MATERIALS
117
The report of the committee of the U. S. Testing Board, on
tests of wrotight-iron and chain cables, is shown in the accom-
pansring table.
ULTIMATE RESISTANCE AND PROOF TESTS OF
WROUGHT-mON CHAIN CABLES
Average
Average
Diam.
Resist. =
Proof
Diam.
Resist. •=
Proof
of Bar
163% of
Test
of Bar
163% of
Test
Bar
*
Bar
Inches
Pounds
Pounds
Inches
Potmds
Pounds
71,172
33,840
1*
162,283
77,169
lA
79,544
37,820
If
174.475
82.956
88.445
42,053
IH
187,075
88,947
In
97,731
46,468
1}
200,074
95,128
IJ
107,440
51,084
111
213,475
101,499
In
117.577
55,903
1|
227,271
108,058
1
128.129
60,920
IH
241.463
114.806
lA
139.103
66,138
2
256,040
121,737
li
150,485
71,550
HORSEPOWER OF MANILA ROPES
^&^&
f
i
1
n
ij
If
II
H
2
4,000
5.000
7.500
9,000
12,250
14,000
18.062
20,250
.82,25,000
1.08 30,250
1.27 36,000
.15
.18
.27
.33
.45
.50
.65
.73
121
151
227
272
371
424
547
613
1,000 Ft.
per Min.
2
2
4i
5
7
8
101
lU
760; 141
916 17
1,000 20i
to
2,000 Ft.
per Min.
90 I
110
170
200
280
320
410
460
4i
5i
81
10
13i
X5i
20
22
570 27!
680 ' 33]
810 40
«
1^
90
110
170
200
270
310
400
440
550
660
790
3,000 Ft.
per Min.
X
61
71
111
14
19
22
281
3l|
39 i
471
56i
80
100
160
180
250
290
370
420
520
630
740
5,000 Pt.
per Min;
X
8J
lOi
16
19
26
29 f
38 1
43 1
55i
641
77J
CO
70
90
130
150
210
240
310
350
448
520
620
118 HYDROMECHANICS
HYDROMECHANICS
HYDROSTATICS
Hydrostatics treats of liquids at rest under the action of
forces. If a liquid is acted on by a pressure, the pressure per
unit of area exerted anywhere on the mass of Uquid is trans-
mitted undiminished in all directions, and acts with the
same force on all surfaces, in a direction at right angles to
those surfaces.
Downward Pressure of Liquids. — The pressure on the bot-
tom of a vessel containing a liquid is independent of the shape of
the vessel, and is equal to the weight of a prism of the liquid
whose base is the same as the bottom of the vessel, and whose
altitude is the distance between the bottom and the upper sur-
face of the liquid, plus the pressure per unit of area upon the
upper surface of the liquid multiplied by the area of the bottom
of the vessel.
Upward Pressure of Liquids. — ^The upward pressure on any
submerged horizontal surface equals the weight of a prism of the
liquid whose base has an area equal to the area of the submerged
surface, and whose altitude is the distance between the sub-
merged surface and the upper surface of the liquid, plus the
pressure i>er unit of area on the upi>er surface of the liquid mul-
tiplied by the area of the submerged surface.
Lateral Pressure of Liquids. — The pressure on any vertical
surface due to the weight of the liquid is equal to the weight of
a prism of the liquid whose base has the same area as the ver-
tical surface, and whose altitude is the depth of the center of
gravity of the vertical surface below the level of the liquid.
Any additional pressure is to be added, as in the previous cases.
Pressure of Liquids on Oblique Surfaces. — The pressure
exerted by a liquid in any direction on a plane surface is equal
to the weight of a prism of the liquid whose base is the projection
of the surface at right angles to the given direction, and whose
height is the depth of the center of gravity of the surface below
the level of the liquid.
HYDROMECHANICS 119
If a cylinder is filled with water, and a pressure applied,
the total pressure on any half section of the cylinder is equal
to the projected area of the half cylinder (or diameter length of
cylinder) multiplied by the depth of the center of gravity of the
half cylinder, multiplied by the weight of 1 cu. in. of water,
plus the diameter of the shell, multiplied by the pressure per
square inch, multiplied by the length of the cylinder.
If d -* diameter, in inches, and I » length of cylinder, in inches,
the pressure due to the weight of the water when the cylinder
is vertical upon the half cylinder«dX/X- X weight of 1 cu. in.
of water •= dX - X weight of 1 cu. in. of water.
2
The pressure, in pounds per square inch, due to a head of
water is equal to the head in feet multiplied by .434. The head
equals the pressure, in pounds per square inch, multiplied by
2.304.
Flow of Water Through Pipes. — ^The following formulas for
the flow of water through pipes are those arranged by Gould,
in which
Q>- amount of water, in cubic feet per second;
f^U. S. gallons per minute;
D = diameter of pipe, in feet;
(/>« diameter of pipe, in inches;
IT ■■ total head, in feet;
A -head per 1,000 ft.;
V — velocity, in feet per second.
Pipes above 8 in. in diameter, rough inside surface,
Q- Vd^^Z^^VdA; V = \.27^Dh
For diameter, in inches.
dt jc
''288 \
\dh
Pipes between 3 and 8 in. in diameter, rough inside surface,
- 0.89 VZJ^A- 0.89 m^h\ V^-l.lsVoA
Large pipes, smooth inside surface,
0-1.4 Vd^-1.4 m'^Dh, V^lJS-^Dh
Small pipes, smooth inside surface,
0-0.89 '>/2D*A= 1.25 m^Dh\ F-I.oVdA
120 HYDROMECHANICS
It is best to calculate any pipe line by th« formula for pipes
having a roueh internal 3urface» because all pipea become more
Siphons.— When any part of the pipe line rises above the
source of aitpiriy, such a line is called a liplunt. U tins rise
is greater than the height of the water barometer (34 ft, at
thfough the siphon will be the same as tliat throueh any pipe
line 90 long as there is no accumulation of air at the highest
point <^ the line; but such an accumulation will decrease or
entirely stop the flow. All siphons should be provided at their
highest points with valves for dischaising the air and intro-
lowec end of the pipe so that air cannot enter it, and to enlarge
discharge end should be considerable, if the rise amo
much.
DAMS
ConsOuctioo of Dams in Mines. — Dams may be coni
HYDROMECHANICS 121
flowing into the workings. But in either case the dam should
have sufficient strength to resist any column of water that will
come against it. The dam should be arched toward the direc-
tion from which the pressure comes, and should be given a good
firm bearing in both walls and in the floor and roof. A brick
dam that was constructed to isolate a portion of the seam so
that it might be flooded to extinguish a mine fire is shown in
Fig. 1, (a) being the plan and (6) a cross-section. This dam
is composed of three brick arches, each 5 ft. thick, placed one
against the other so that they act as one solid structure. The
gangway at this point is about 20 ft. wide, and the distance
to the next upper level is about 119 ft. It was intended that
this should be the maximum head of water that the dam would
have to resist, though it was made sufficioitly strong to resist
a head of water reaching the surface. The separate walls were
constructed one at a time, and the cement allowed to set before
the next wall was placed. The back wall was carried to a
greater depth and height than the others, so as to make sure
that all slips or partings had been closed. The total pressure
upon the dam when the water was in the mine was about
70,000 lb. per sq. ft.
Dams constructed to permit the flooding of a mine usually
require no passages through them, but dams constructed to
confine the water to certain parts of the workings, and so
reduce pumping charges, usually have both manways and drain
pipes through them. Fig. 2 (a) shows the plan and (Jb) shows
the cross-section of such a dam constructed to keep the water
that came from some exploring drifts out of the mine work-
ings. As originally constructed, it consisted of a sandstone
dam 10 ft. thick and arched on the back face with a radius of
6 ft. A piece of 20-in. pipe provided a manway through the
masonry and was held in place by three sets of clamps and
bolts passing through the stone work. A 5-in. drain pipe was
also carried through the dam and secured by clamps. When
the pressure came upon the dam it was found to leak, so the
water was drained off and a 22-in. brick wall built 2 ft. 4 in.
back of the dam, the space between being filled with concrete,
and the manway and drain pipe extended through the brick
wall. Before closing the drain pipe, horse manure was fastened
I] by means of a plank p
:he dam waa found to Leal
HYDROMECHANICS 123
pressure against the dam was something over 800 T., which it
successfully resisted.
Reinforced concrete is largely used for mine dams, as these
dams are strong, impermeable, quickly made, and of reason-
able cost. Old rails, strap iron, etc. may be used for the rein-
forcing material.
In mine work, dams are used for retaining water in reser-
voirs, for diverting streams in placer mining, and for storing
debris coming from placer mines in caiions or ravines.
Fotmdations for dams must be solid to prevent settling,
and water-tight to prevent leakage under the base of the dam;
whenever possible, the foundation should be solid rock. Gravel
is better than earth, but when gravel is used sheet piling must
be driven under the upper toe of the dam, to prevent water
from seeping through the formation under the dam. Vegetable
soil should be avoided, and all porous material, such as sand,
gravel, etc. should be stripped off until hard pan or solid rock
is reached.
AbiUmerUs are timber, masonry, or dry stonework struc-
tures at the ends of a dam. If possible, they should have a
curved outline, and should be so placed that there is no pos-
sibility of the water overflowing them, or getting behind them
during floods.
If the regular discharge from a dam takes place from the
main face, the discharge gates may be arranged in connection
with one of the abutments, or by means of a ttmnel and cul-
vert through the dam. In either case, some structure should
be constructed above the outlet so as to prevent driftwood,
brush, and other material from stopping the gates. When
the discharge gates are placed at one side of the dam, they are
usually arranged outside of the regular abutment, between it
and another special abutment, the discharge being through a
series of gates into a flume, ditch, or pipe.
SjriUways or waste ways, are openings provided in a dam for
the discharge of water during floods or freshets, or for the dis-
charge of a portion not being used at any time. The spillway
may be over the crest of the dam, or, where the topography
favors such a construction, the main dam may be of sufficient
height to prevent water from ever passing its crest and the
124 HYDROMECHANICS
spillway arranged at another outlet over a lower dam. Waste
ways, proper, are openings through the dam, to provide for
the discharge of the large quantities of water that come down
during freshets or floods.
Wooden Dams. — Wooden dams are constructed of round,
sawed, or hewn logs. The timbers are usually at least 1 ft.
square, or, if round, from 18 to 24 in. in diameter. A series
of cribs from 8 to 10 ft. square are constructed by building up
the logs log-house fashion and securing them together with
treenails. The individual cribs are secured to one another
with treenails or by means of bolts. The cribs are usually
filled with loose rock to keep them in place, and in many cases
are secured to the foundation by means of bolts. The dam is
made water-tight by a layer of planking on the upper face and
if the spillway is over the crest of the dam it will be necessary
to plank the top of the cribs, and, in most cases, to provide
an apron for the water to fall on. The apron may be set on
small cribs, or on timbers projecting from the cribs of the
dam itself.
Stone Dams. — ^Where cement or lime is expensive, and suit-
able rubble stone can be obtained, dams are frequently con-
structed without the use of mortar. The upper and lower faces
of the dam should be of hammer-dressed stone, carefully
bonded; sometimes the stones in the lower face of the dam are
anchored by means of bolts. The dam can be made water-
tight by means of a skin of planking on the upper face. In
case water should pass over t^e crest of such a dam, much of it
would settle through the openings in the stone into the interior
of the dam, and thus subject the stones in the lower portion
of the face to a hydrostatic pressure; for this reason, culverts
or openings should be made through the lower portion of the
dam, to discharge any such water. When such dams as this
are constructed, the regular spillway is not placed over the face
of the dam, but at some other point, and usually over a timber
dam.
Earth Dams. — Earth dams are used for reservoirs of mod-
erate height. They should be at least 10 ft. wide on top, a
height of more than 60 ft. being unusual. When the material of
which the dam is composed is not water-tight, it is sometimes
HYDROMECHANICS 125
necessary to construct, in the center of the regular dam, a
narrow dam of clay mixed with a certain proportion of sand.
This puddle wall should not be less than from 6 to 8 ft. thick
at the top and should have a slight batter on each side. It is
constructed dtiring the building of the dam, and should be
protected from contact with the water by a considerable thick-
ness of earth on the upper face. The upper face of an earthen
dam is frequently protected by means of plank or a pavement
of stone. The lower face is frequently protected by means
of sod, or sod and willow trees. Sometimes earth dams are
provided with a masonry core in place of the puddle wall,
to render them water-tight.
Masonry Dams. — ^High masonry dams should always be
designed by a competent hydraulic engineer. Masonry dams
are not, as a rule, used for hydraulic mining, as the length of
time during which the dam is required rarely warrants the
expense of the construction of a masonry dam.
Debris Dams. — Dams or obstructions are sometimes placed
across the bed of the stream to hold back culm, etc., from mines,
and to prevent damage to the valleys below. Tliey are made
of stone, timber, or brush. No attempt is made to render
these d6brls dams water-tight, as their only object is to retard
the flow of the stream and to give it greater breadth of dis-
charge, so that the water naturally drops and deposits the
sediment that it is carrying. The sediment soon silts or fills
up against the face of the dam, the area above the dam becom-
ing a flat expanse or plain over which the water finds its way
to the dam.
RESERVOIRS
In selecting a site for a reservoir, the points to be observed
are:
A proper elevation above the point at which the water is
required.
The total supply available, including observations as to the
rainfall and snow fall.
TJhe formation and character of the ground, with reference
to the amount of absorption and evaporation.
126 HYDROMECHANICS
PUMP MACHINERY
Pumps are used for unwatering mines, handling water at
placer mines, irrigation, water-supply systems, boiler feeds,
etc. For unwatering mines, two general systems of pumping
are used: In one, the pump is placed in the mine and is oper-
ated by a motor on the surface, the power being transmitted
through a line of moving rods; in the other, both the motor
and the pump are placed in the mine, the motor being an engine
driven by steam, compressed air, hydrauUc motor, or an elec-
tric motor.
Cornish Pumps. — Any method of operating pumps by rods
is commonly called a Cornish system. This sjrstem requires
no steam line down the shaft and is independent of the depth
of water in the mine, so that the pump is not stopped by the
drowning of a mine, but the moving rods are a great incon-
venience in the shaft, and they absorb much of the power
through friction.
Simple and Duplex Pumps. — In the simple pump, a steam
cylinder is connected directly to a water cylinder, and the
steam valves are operated by tappets. Such a pump is more
or less dependent on inertia at certain points of the stroke to
insure the motion of the valves, hence will not start from any
place and is liable to become stalled at times. In the duplex
pump, two steam cylinders and two water cylinders are arranged
side by side, and the valves are so placed that when one piston
is at mid-stroke it throws the steam valve for the other cylin-
der, etc. With this arrangement, the pump will start from
any point, and can never be stalled for lack of steam, due to the
position of the valves. Ordinarily, duplex pumps are to be
preferred for mine work.
The packing for the water piston of a pump may be either
inside or outside. As a rule, inside-packed pumps should be
avoided in mines, because acid or gritty waters are liable to
cut the packing and make the pumps leak in a very short time.
For dipping work in single stopes or entries, small single or
duplex outside-packed pumps may be used. It is generally best
to operate such pumps by compressed air, for the exhaust will
then be beneficial to the mine air. If steam is used, it is
HYDROMECHANICS 127
frequently necessary to introduce a trap and remove entrained
water from the steam before it enters the pump, and dispose
of the exhaust by piping it out or condensing it. Such isolated
steam pumps are about the most wasteful form of steam-driven
motor in existence.
For sinking, center-packed single or duplex pumps are usu-
ally employed, the duplex style being the better. For station
work, where much water is to be handled, large compotmd,
or triple-expansion, condensing, duplex pumping engines are
employed. They may, or may not, be provided with cranks
and a flywheel; engineers differ greatly upon this point, but as a
rule, for very high lifts and great pressures, the flywheel is used.
Capacity of Pumps and Horsepower Required to Raise
Water. — To find the capacity of ptmips and the horsepower
required to raise water any distance.
Let = cubic feet of water per minute;
G = U. S. gallons per minute;
G'»=U. S. gallons per hour;
d« diameter of cylinder, in inches;
/ — stroke of piston, in inches;
JV = number of single strokes per minute;
»•= speed of piston, in feet per minute;
PV= weight moved, in pounds per minute;
P= pressure, in pounds per square feet — 62.5 X^;
/> = pressure, in pounds per square inch = . 433 XH;
H-s height of lift, in feet;
H. P. » horsepower.
^ ^ ic (P IN
Then, = -X- X - = .0004545iVrf'/
4 144 12
X N(Pl
G = -X = OOMNcPl. G' = .20^Nd*l
4 231
The diameter of piston required for a given capacity per
minute will be
<'-«-9\^- 17-15-\/|,. or d- 13.54 -y/^-4.95'^^
The actual capacity of a pump will vary from 60% to 95%
of the theoretical capacity, depending on the tightness of the
piston, valves, suction pipe, etc.
128 HYDROMECHANICS
QP 0HX144X.433 QH Gp
H. P.
33.000 33.000 529.2 1.714.5
The actual horsepower required will be considerably greater
than th^ theoretical, on account of the friction in the pump;
hence, at least 20% should be added to the i)ower for friction
and usually about 50% more is added to cover leaks, etc.,
so that the actual horsepower required by the pump is about
70% more than the theoretical.
Limit of Suction. — ^Theoretically, a perfect pump will raise
water to a height of nearly 34 ft. at the sea level; but owing to
the fact that a perfect vacuum can never be attained with the
pump, that the water always contains more or less air, and that
more or less watery vapor will form below the piston, it is never
possible to reach this theoretical limit, and, in practice, it is
not possible to draw water much, if any, over 30 ft. at the sea
level, even when the water is cold. Warm water cannot be
lifted as high as cold water, because a larger amount of watery
vapor forms. With boiler feed-pumps handUng hot water,
the water should flow to the pumps by gravity.
Power Pumps. — ^Where comparatively small amotmts • of
water are to be handled and power is available, belt-driven
power pumps are very much more efficient than small steam
pumps. Where water is to be delivered from isolated work-
ings to the sumps for the large station pumps, electrically
driven power pumps are far more efficient than steam pumps.
Miscellaneous Fonns of Water Elevators. — In the jet pump
the energy of the jet of water is utilized for raising a larger
volume through a small distance, or a mixture of water and solid
material through a short distance.
The pulsometer consists of two chambers in a large casting,
with suitable automatic valves arranged at the top and bot-
tom of the chambers. Steam is introduced into one of the
chambers, then the valve at the top closed. As this steam
condenses, it forms a vacuum that draws water from the suc-
tion into the chamber. When the chamber is filled with
water, steam is again introduced and forces the water out
through the discharge pipe. The operation is then repeated,
more water being drawn in by the condensation of the
-*-•^m.
HyOROMECHANICS 129
In ctnlrifugal pumps, the height 0/ lift depends on the tan-
gential velocity of the revolving disk of pump and the quan-
tity of water discharged, and is proportional to the area of the
discharge orifices at the drcumfeteace of the disk. The most
efficient total lift for the centrifugal punp is. approiimately.
17 ft., and for small HEls the centrifugal pump ig much more
efficient than any style of piston pump. For a given lift, the
total efficiency of a centrifugal pump increases with the size
of the pump- Centrifugal pumps are always designated by
nKaning a 2-in. or 4-in. discharge pipe. Under the most favor-
able circumstances, the efficiency of the centrifugal pump may
be practically 70%; that is. the pump may do an amount of
work upon the water that is theoretically equal to 70% of
Where only a limited amount of water coUecCs in the mine
butka or waiff ior during the hours that the hoisting engine
would otherwise be idle. Where very large amounts of water
ate to be removed, it
has also been found
of deep shafts.
WatefS.— Where mine
ally employed. The Fic 1 1
130 STEAM
employed, placed as shown in Fig. 1, which is a section of
the pipe with the lining complete. In Fig. 2 is shown a cross-
section of one of the individual boards used in the lining.
These boards are usually made of pine about f in. thick, and
are grooved on each end as shown. They are sprung in so as
to complete a circle on the inside of the pipe, and then long,
thin, wooden keys are driven into the grooves. When the
water is allowed to go into the pipes, the linings swell and make
all joints perfectly tight. Elbows and other crooked sections
are lined with sheet lead beaten in with a mallet.
STEAM
FUELS
Classification of Coals. — Coals may be broadly divided into
two classes: anthracite, or hard, coal, and bituminous, or soft,
coal. The subdivisions given, however, are entirely arbitrary,
as the different varieties of coal are found to shade insensibly
into one another.
Anthracite, or hard coal, which has a specific gravity of 1.30
to 1.70, i? the densest, hardest, and most lustrous of all varieties.
It bums with little flame and no smoke, but gives a great heat,
and contains very little volatile combustible matter. Its color
is deep black and shining; sometimes it is iridescent; its frac-
ture is conchoidal. Semianthracite coal is not so dense nor so
hard as the true anthracite; its percentage of volatile combus-
tible matter is somewhat g^^ater, and it ignites more readily.
Bituminous, or soft, coal, which has a specific gravity of 1.25
to 1.40, is generally brittle. It has a bright pitchy or greasy
luster, and is rather fragile as compared with anthracite. It
bums with a yellow smoky flame, and gives, on distillation,
hydrocarbon oils or tar. Under the term bituminous are
included a ntunber of varieties of coal that differ materially
under the action of heat, giving rise to the general classification
Coking or caking coals , and free-burning coals. Semibituminous
STEAM 131
coal has the same general characteristics as the bituminous,
although it is usually not so hard, and its fracture is more
cuboid. The percentage of volatile combustible matter is less.
It kindles readily, btu*ns quickly with a steady fire, and is much
valued as a steam coal.
Coking coals are those that become pasty or semiviscid in the
fire; and, when heated in a closed vessel, become partially fused
and agglomerate into a mass of coherent coke. This property
of coking may, however, become greatly impaired, if, indeed,
not entirely destroyed, by weathering. Free-burning coals have
the same general characteristics as the coking coals, but they
bum freely without softening, and do not fuse or cake together
in any sensible degree.
Splint coal has a dull black color, and is much harder and
less frangible than the coking coal. It is readily fissile, like
slate, but breaks with difficulty on cross-fracture. It ignites
less readily, but makes a hot fire, constituting a good house
coal.
Cannel coal differs from the ordinary bituminous coal in its
texture. It is compact, with little or no luster and without any
appearance of a banded structure. It breaks with a smooth
conchoidal fractui-e, kindles readily, and bums with a dense
smoky flame. It is rich in volatile matter, and makes an
excellent gas coal. Its color is dull black and grayish-black.
Lignite, or brown coal, often has a lamellar or woody structure;
is sometimes pitch black, but more often rather dull and brown-
ish black. It kindles readily and bums rather freely with a
yellow flame and comparatively little smoke, but it gives only a
moderate heat. It is generally non-coking. The percentage
• of moisture present is invariably high — from 10% to 30%.
Compositum of Coals. — A proximate analysis determines
the proportion of those products of a coal having the most
important bearing on its uses. These substances as usually
presented are: moisture, or water, volatile combustible matter,
fixed carbon, sulphur, and ash. In addition to these, the fol-
lowing physical properties are generally given: color of ash,
specific gravity and strength or hardness. The determination
of these eight factors gives a fair general idea of the adapta-
bilities of a coal.
132 STEAM
Moisture, or water, in coal, has no fuel value.
VoUUtle combustible matter is an important constituent of
coal, the amount and quality deciding whether a coal is suitable
for the manufacture of illuminating gas. The coking of coal
also is largely dependent on this constituent.
The fixed carbon is the principal combustible constituent in
coal, and, in bittiminous and semibitiuninous coals, the steaming
value is in proportion to the percentage of fixed carbon.
Sulphur will bum and develop heat and is not inert like
moisture and ash; but it corrodes grates and boilers. In the
blast furnace, it injures iron, and produces a hot short pig, and
is objectionable in coal for forge use. For gas making, the
sulphtu* must be removed.
Ash is an inert constituent, which means that 20 lb. of weight
must be handled and 20 lb. loss per T. of coal for each per cent,
of ash present. The color of the ash furnishes a rough estimate
of the amount of iron contained in a fuel. Iron in an ash makes
it more fusible, and inci eases its tendency to clinker.
The specific gravity is an important factor when there is
restriction of space, as on railway cars and in ship bunkers.
A given bulk of anthracite coal will weigh from 10% to 15%
more than the same bulk of bittmiinous coal, so that from 10%
to 15% more pounds of fuel can be carried in the same place.
Strength or hardness is valuable in preventing waste. A very
soft coal is shipped in lump. Strength is a requisite for the use
of raw coal in the blast fiutiace, and also to prevent excessive
loss of coal through the grates in ordinary furnaces.
Coke is the fixed carbon of a coal, a fused and porous product
produced by the distillation of the gaseous constituent. For
metallurgical use, it should be firm, tough, and bright, with a
sonorous ring, and should contain not over 1% of sulphur.
For blast-furnace use, a dense coke is objectionable, and the
best is the one with the largest cell structxire and the hardest
cell wall. A high percentage of volatile hydrocarbon is, as a
rule, necessary for a good coking coal.
The essentials of a good gas coal are a low i>ercentage of ash,
say 5%, and of sulphur, say § of 1%, a generous share, say
37% to 40% of volatile matter, charged with rich illiuninating
hydrocarbons. It should yield, under present retort practice.
STEAM 133
85 candle-feet to the pound carbonized. It should be suffi-
ciently dense to bear transix>rtation well, so that, when carried
long distances, it will not arrive at its destination largely
reduced to slack or fine coal of the consistency of sand; and it
should ix>ssess coking qualities that will bring from the retorts,
after carbonization, about 60% of clean, strong, bright coke.
A good coal for blacksmith purposes should have a high heating
X)ower, should contain a very small amount of sulphur, if any,
should coke sufficiently to form an arch on the forge, and shotdd
also be low in ash.
The analysis of a coal does not necessarily determine its
value or the uses to which it can be put. However, for examin-
ing the analyses given in the accompanying tables, certain
standards may be adopted as showing in a general way about
what the analysis of coal should be for certain purposes. For
steam purposes, the semibittuninous coals have established
reputations; for gas coals, that from Youghiogheny, Pa., is well
known; for blacksmiths. Broad Top and Tioga Cotuity, Pa.,
coals are standards; while for coking, Coimellsville is recog-
nized as the best.
Heating Formulas. — A British thermal unit (B. T. U.) is the
quantity of heat required to raise the temperatiu^ of 1 lb. of
water 1° F. at or near the temperature of maximum density,
39.1° F.
A calorie (cal.) is the quantity of heat required to raise the
temperature of 1 Kg. of water 1° C. at or about 4° C.
A pound calorie is the quantity of heat necessary to raise the
temperature of 1 lb. of water 1° C.
1 French cal. = 3.968 B. T. U.
1 B. T. U. = .252 cal.
1 lb. cal. =1 B. T. U. = .4536 cal.
The heating value of any coal may be calculated from its
ultimate analysis, with a probable error not exceeding 2%, by
Dulong's formula:
Heating value per potmd=» 146 C-i-620
{'-%
in which C, H, and O are, respectively, the percentages of
carbon, hydrogen, and oxygen.
134
STEAM
9iqi^snquicK)
ptmoj J9d ^ziZ
%'e pUB UIOJJ UOT!JBJ
-OdBAg lBDi:^3J09I(X
^1 ^1 ^1 ^Jl
§§
CO C< CSj CO CO csi
w o CO CO CO
•n 'x 'a
aiq^snqoioQ punOjj
•3
c3
8888 88 888888
OOiOiOi lO tQ 00 1>> b« 00 00 1^
aiqi^snquiOQ jo
uoqjBQ poxTj
95.00
96.56
95.64
95.15
91.14
89.02
82.40
76.40
77.29
79.63
80.21
77.50
aiqi^snqraoQ jo
5.00
3.44
4.36
4.85
8.86
10.98
17.60
24.60
22.71
20.37
19.79
22.50
•a 'X a
IBOQ puno J
J3d anjB^ Sui!(e9H
COM^CSI MO CSI»oSo8t^
eocociei eoeo tjJ-^^-^^io
rHi-li-lTH i-H^H ,-t ,-t ,-t r-t r-t fi
jniidps
r^io>cco COO) oo)t*wt^>o
• ••• ■■ ••••••
1-H vH vH
4«V
• ••• •• •••••■
oooooo co>o tocor^oot^co
l-H
uoqjBQ paxiji
M'^uDW «« eo 00 «-• «o i-< CO
■ ••• •• ••■••«
OOOOWOO 0000 t>- 1>- 1>- 1>- 1* t^
00WC4X OO i-HCIOCvlOQ
• ■•• •■ ••••••
■^COM'^ OOOS iOMO»©t^»H
f-H C^ 1-4 1-4 i-H N
■^t^i-io coco t^t^o)u5oo
• ••■ •• ••••••
COWWCO i-H iHi-trH
« d ^
i c3 >>C.S P S 5 8 s 9
CO CO
136 STEAM
Heat in pound calorie « 8,080 C+34
or- 8,080 C+34.462 I H-r I +2,250 S
.4e2(fl-2)
,462 (h-^J +24
.100 (fl-?)
Heat in B. T. U. = 14,650 C+62
in which C, O, H, and 5 represent the weights of carbon, oxygen,
hydrogen, and sulphtir in 1 lb. of the substance.
COMPOSITION OF FUELS
Description
Anthracite
France
Wales
Rhode Island
Pennsylvania
Semibituminous
Maryland
Wales
Bituminous
Pennsylvania
Indiana
Illinois
Virginia
Alabama
Kentucky
Cape Breton
Vancouver Island. .
Lancashire gas coal .
Boghead cannel
Lignite
California brown , . .
Australian brown. . .
Petroleum
Pennsylvania
(crude)
Caucasian (light) . . .
Caucasian (heavy) ,
Refuse
o S
|o
90.9
91.7
85.0
78.6
80.0
88.3
75.5
69.7
61.4
57.0
53.2
49.1
67.2
66.9
80.1
63.1
49.7
73.2
84.9
86.3
86.6
87.1
Hydrogen
Per Cent.
Oxygen
Per Cent.
_. •
1.47
1.53
1.00
3.78
1.30
1.00
3.71
2.39
1.00
2.50
1.70
.80
5.00
2.70
1.10
4.70
.60
1.40
4.93
12.35
1.12
5.10
19.17
1.23
4.87
35.42
1.41
4.96
26.44
1.70
4.81
32.37
1.62
4.95
41.13
1.70
4.26
20.16
1.07
5.32
8.76
1.02
5.50
8.10
2.10
8.90
7.00
.20
3.78
30.19
1.00
4.71
12.35
1.11
13.70
1.40
13.60
.10
12.30
1.10
11.70
1.20
.80
.72
.90
.40
1.20
1.80
1.10
1.30
1.20
1.50
1.30
1.40
1.21
2.20
1.50
1.00
1.53
.63
<
4.3
1.5
7.0
14.8
8.3
3.2
5.0
3.5
5.7
8.4
6.7
7.2
6.1
15.8
2.7
19.8
13.8
8.0
STEAM 137
STEAM BOILERS
The steam boiler that will be the most suitable for a certain
mine will depend on the nature of the feedwater, the cost of
fuel, and the amount of steam required. When the acid water
from the mine is used for feedwater and fuel is cheap, either the
plain cyUndrical or the flue boiler is used, because it is simple
in construction and can therefore be easily cleaned and cheaply
replaced when eaten by the mine water. The tubular or loco-
motive type is used where good water can be obtained, except
in the best-equipped plants, where the water-tube boiler is used.
Feedwater taken from the mine, or containing acid, should be
neutrah'zed by lime or soda before being used. In case it con-
tains minerals in solution, a feedwater separator should be
employed to precipitate the mineral substance before the water
is allowed to enter the boiler.
The heating surface of a boiler is the portion of the surface
exposed to the action of flames and hot gases. This includes,
in the case of the multi-tubular boiler, the portions of the shell
below the line of brickwork, the exposed heads of the shell, and
the interior surface of the tubes. In the case of a water-tube
boiler, the heating surface comprises the portion of the shell
below the brickwork, the outer surface of the headers, and outer
surface of tubes.
Horsepower of Boilers. — The horsepower of a boiler is a
measure of its capacity for generating steam. Boilermakers
usually rate the horsepower of their boilers as a certain fraction
of the heating surface; but this is a very indefinite method, for
with the same heating surface, different boilers of the same type
may, under different circimistances, generate different quan-
tities of steam.
In order to have an accurate standard of boiler power, the
American Society of Mechanical Engineers has adopted as a
standard horsepower an evaporation of 30 lb. of water per hour
from a feedwater temperature of 100° F. into steam at 70 lb.
gauge pressure, which is considered equivalent to 34.5 units of
evaporation; that is, to 34.5 lb. of water evaporated from
a feedwater temperature of 212** F. into steam at the same
temperature.
138
STEAM
High-Pressure Steam. — ^A calculation of the power that
coal possesses, compared with the useful work which steam
engines exert, shows that probably in the very best engines
not one-tenth of the power is converted into useful work, and
in some very bad engines, probably not one one-hundredth.
Whatever pressure may be available at the steam boiler, a cer-
tain amount is absorbed in overcoming the resistance of the
engine and without doing any useful work. Then, again, the
amount of work that it is possible to get out of a given quantity
of steam depends on the difference between the temperature
at the commencement of the stroke and the temperature at the
end of the stroke.
There is a limit as to how low the temperature can be at the
end, therefore, as the commencing temperature is raised the
available difference is increased. The advantages of high-
pressure steam may be shown by taking a fixed temperature
in the condenser of say, 100° F., then initial temperatures
when the steam enters the cylinder, the temperature of varying
amounts, and the theoretic efficiency of that steam can be deter-
mined. At atmospheric pressure, there is an efficiency of
16.6%.
EFFICIENCT OF STEAM AT VARIOUS PRESSXTRES
Steam
'Pressure
Efficiency
Steam
Pressure
Efficiency
Pounds
Per Cent.
Pounds
Per Cent.
10
20.0
100
29.8
20
22.1
125
31.1
30
23.7
150
32.2
40
25.0
200
33.9
50
26.1
250
35.3
60
27.0
300
36.5
80
28.6
In practice, only a certain proportion of the theoretic power
of steam can be obtained, and that proportion varies with the
pressure of the steam. The advantages of high-pressure steam
are not yet sufficiently appreciated. It is not merely the
difference between 60 lb. and 120 lb. Suppose we use steam
STEAM 139
at 60 lb.; probably we shall get 50 lb. ac engine, and resist-
ances of engine will absorb 10 lb., leaving 40 lb. Now, sup-
X>08e we use 120 lb., we can get at engine 110 lb., and if
resistances of engine absorb 10 lb., we shall have 100 lb. as
against 40 lb.
By expansion cf steam is meant that at a certain point of the
stroke, tiie steam supply from the boiler to the cylinder is shut
off and the steam already within the cylinder performs the
remainder of the stroke unaided.
Incmstatioii. — Nearly all waters contain foreign substances
in a greater or less degree, and though this may be a small
amount in each gallon, it becomes of importance where large
quantities are evaporated. For instance, a 100-H. P. boiler
evaporates 30,000 lb. of water in 10 hr. or 390 T. pec mo.; in
comparatively pure water there should be 88 lb. of solid matter
in that quantity, and in many kinds of spring water as much as
2.000 lb.
The nature and hardness of ih.e scale formed will depend
on the kind of substances held in solution and suspension.
Analyses of incrustations show that carbonate and sulphate of
lime form the larger part of all ordinary scale, that from car-
bonate being soft and granular, and that from sulphate, hard
and crystalline. Organic substances in connection with carbon-
ate of lime will also make a hard and troublesome scale. The
causes of incrustation are:
1. Deposition of suspended matter.
2. Deposition of salts from concentration.
3. Deposition of carbonates of lime and magnesia, by boiling
off carbonic acid, which holds them in solution.
4. Deposition of sulphates of lime, because sulphate of lime
is soluble in cold water, less soluble in hot water, insoluble
above 270° P.
5. Deposit of magnesia, because magnesium salts decompose
at high temperatures.
6. Deposition of lime soap, iron soap, etc. formed by sapon-
ification of grease.
Incrustation may be prevented by the following methods:
1. Filtration.
2. Blowing off.
140
STEAM
3. Use of internal collecting apparatus, or devices, for
directing the circulation.
4. Heating feedwater.
5. Chemical or other treatment of water in boiler.
6. Introduction of zinc in boiler.
7. Chemical treatment of water outside of boiler.
INCRUSTATION REMBDIES
Troublesome Substances
Sediment, mud, clay, etc.
Readily soluble salts. . . .
Bicarbonate of lime,
magnesia, and iron
Sulphate of lime
Chloride and sulphate of
magnesium
Carbonate of soda in
large amotmts
Acid in mine water
Dissolved carbonic acid
and oxygen
Grease, from condensed
water
Organic matter, sewage.
Organic matter
Trouble
Incrustation
Incrustation
Incrustation
Incrustation
Corrosion
Priming
Corrosion
Corrosion
Corrosion
Priming
Corrosion
Remedy or Palliation
Filtration; blowing off
Blowing oSL
Heating feed; addition
of caustic soda, Ume,
or magnesia, etc.
Addition of carbonate
of soda, barium chlo-
ride, etc.
Addition of carbonate
soda, etc.
Addition of barium
chloride, etc.
Alkali
Heating feed; addi-
tion of caustic soda,
slaked lime, etc.
Slaked lime and filter-
ing: substitute min-
eral oil
Precipitate with alum
or ferric chloride,
and filter
Precipitate with alum
or ferric chloride,
and filter
Prevention of Incrustation. — The incrustation of boilers may
be prevented by adding various substances to the feedwater.
Oak, hemlock, sumac, catechu, logwood, and other barks and
STEAM 141
woods, are effective in waters containing carbonates of lime
or magnesia, by reason of their tannic acid, but are injurious
to the iron and not to be recommended.
Molasses, cane juice, vinegar, fruits, distillery slops, etc., have
been used, but the acetic add that they contain is even more
injurious to the iron than tannic acid, while the organic matter
forms a scale with sulphate of lime when it is present.
Milk of lime and metallic zinc have been used with success in
waters charged with bicarbonate of lime, reducing the bicar-
bonate to the insoluble carbonate.
Barium chloride and milk of lime are said to be used, with
good effect at Krupp's works, in Prussia, for waters impregnated
with gypsum.
Soda ash and other alkalies are very useful in waters con-
taining sulphate of lime, by converting it into a carbonate, and
so forming a soft scale that is easily cleaned. But when used
in excess they cause foaming, particularly where there is oil
coming from the engine, with which they form soap. All soapy
substances are objectionable for the same reason.
Petroleum has been much used of late years; it acts best in
waters in which sulphate of lime predominates. Sulphate of
lime is the injurious substance in nearly all mine waters, and
petroleum, when properly prepared, is a good preventive of
scale and pitting. Crude petroleum should not be used, as
it sometimes helps to form a very injurious scale. Refined
petroleum, on the other hand, is useless, as it vaporizes at
a temperature below that of boiling water. Therefore, only
such preparations should be used as will not vaporize below
500° P.
Tannate of soda is a good preparation for general use, but in
waters containing much sulphate, it should be supplemented by
a portion of carbonate of soda or soda ash.
A decoction from the leaves of the eucalyptus is found to work
well in some waters in California.
For muddy water, particularly if it contain salts of lime, no
preventive of incrustation will prevail except filtration, and in
almost every instance the use of a filter, either alone or in con-
nection with some means of precipitating the solid matter from
solution, will be found very desirable.
142 STEAM
In all cases where impure or hard waters are used, frequent
blowing from the mud-drum is necessary to carry off the accu-
mulated matter, which if allowed to remain would form scale.
When boilers are coated with a hard scale, diffcult to remove,
the addition of \ lb. caustic soda per horsepower, and steaming
for some hours, according to the thickness of the scale, will
greatly facilitate the cleaning, rendering the scale soft and loose.
This should be done, if possible, when the boilers are not other-
wise in use.
STEAM ENGINES
Requirements of a Good Steam Engine. — ^A good steam
engine should be as direct acting as possible; that is, the con-
necting parts between the piston and the crank-shaft should
be few in number, as each part wastes some power. Formerly,
beam engines were in general use and were suitable for pump-
ing when the pump was at one end of the beam and the piston
at the other. Pew of modem colliery engines, however, are
thus equipped. The moving parts of an engine should be
strong, to resist strains, and light, so as to offer no undue resist-
ance to motion; parts moving ux>on each other should be well
finished, to reduce resistances to a minimum; the steam should
get into the cylinder easily at the proper time, and the exhaust
should leave the cylinder as exactly and as easily. The steam
pipes supplying steam should have an area one-tenth the com-
bined areas of the cylinders they supply, and exhaust pipes
should be somewhat larger. The cylinder, steam pipes and
boiler should be well protected. The engine should be capable
of being started and stopped and reversed easily and quickly.
Rule. — To find the indicated horsepower developed by an engine,
multiply the mean effective pressure per square inch, the area of
the piston, the length of stroke, and the number of strokes per
minute; this gives the work per minute in foot-pounds. Divide
the product by 33,000.
Let I. H. P. s 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;
i\^" number of strokes per minute.
STEAM
143
Then,
I. H. P.=
PLAN
33.000
The number of strokes per minute is twice the number of
revolutions per minute. For example, if an engine runs at a
speed of 210 rev. per min., it makes 420 strokes per minute. A
few types of engines, however, are single acting; that is, the
steam acts on only one side of the piston, then the number of
strokes per minute equals the number of revolutions per minute.
Approximate Determination of M. E. P. — To approximately
determine the mean effective pressure, M. B. P., of an engine,
when the point of apparent cut-off is known and the boiler
pressure, or the pressure per square inch in the boiler from
which the supply of steam is obtained, is given:
Rule. — To find the M. E. P. of good, simple, non-condensing
engines, add 14'7tothe gauge pressure, and multiply the result by
the number opposite the fraction indicating the point of cut-off
in the accompanying table. Subtract 17 from the product, and
multiply by .9.
Let P = gauge pressure ;
k'^a. constant;
M. E. P. =»mean effective pressure.
Then. M. E. P. = .9 X [*(/>+ 14.7) -17]
TABLE OF CONSTANTS
Cut-Off
Constant
Cut-Off
Constant
Cut-Off
Constant
i
.566
i
.771
}
.917
\
.603
i
.789
1^
.926
.659
.847
}
.937
A
.708
^
.895
t
.944
i
.743
*
.904
.951
If the engine is a simple condensing one, subtract the pressure
in the condenser instead of 17. 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. For a | cut-off, and 92 lb. gauge pres-
sure in the boiler, the M.E. P. is, by the formula just given,
.9X[.917X(92+14.7)-17] = 72.7 lb. per sq. in.
144 COUPKESSBD AIR
COMPRESSED AIR
An Mr compressor consists essentially of a cytinder in
atm ospheric air is compressed by a piston, the driving power
hetng steam or water. Steam-driven co mp ressors in ordinary
ose may be classed as follows:
(1) StraiiffiAine type, in which a sinc^ honsontal air
cylinder is set tandem with its steam csdinder. and provided
with two flywheels; this pattern is generafly adapted for com-
pressors of small size.
(2) Duplex type, in which there are two steam cyUndefs.
each driving an air cylinder, and coupled at 90^ to a crank-
shaft carrying a flywheeL
(3.) HoritowUd, cross-compound engines, each steam cyl-
inder set tandem with an air cylinder.
(4.) Vertical, simple or compound engines, with the air
cylinders set above the steam cylinders.
{h.) Compound or stage compressors, in viiiich the air cyl-
inders themselves are compotmded. The compression is car-
ried to a certain point in one cylinder and successively raised
and finally completed to the desired pressore in the others.
They may be either of the straight-line or duplex form, with
simple or compound steam cylinders.
The first three and the last classes are those commonly used
for mine service. The principle of compound, or two-stage.
air compression is recognized as applicable for even the moder-
ate pressures required in mining, and the compressors of
class 5 are frequently employed.
Transmission of Air in Pipes. — The actual discharge capacity
of piping is not proix>rtional to the cross-sectional area alone.
that is, to the square of the diameter. Although the periphery
is directly proportional to the diameter, the interior siuface
resistance is much greater in a small pipe than in a large
one, because, as the pipe becomes smaller, the ratio of
perimeter to area increases. Among the formulas in com-
mon use, perhaps the most satisfactory is that of D'Arcy.
As adopted for compressed-air transmission, it takes the
form:
COMPRESSED AIR
145
D^cyj-
Wll
in which D = volume of compressed air, in cubic feet per min-
ute, discharged at final pressure;
c>s coefficient varying with diameter of pipe, as
determined by experiment;
d= diameter of pipe, in inches (the actual diameters
of li in. and li in. pipe are 1.38 in. and 1.61
in., resi>ectively; the nominal diameters of all
other sizes may be taken for calculations) ;
Z= length of pipe, in feet;
;^» initial gauge pressure, in potinds per square inch;
^s final gauge pressure, in pounds per square inch;
i«)i = density of air, or its weight, in potmds per cubic
foot, at initial presstire Pi.
The values of the coefficients c for piping up to 12 in. in
diameter are given in the accompanying table. Some appar-
ent discrepancies exist for sizes larger than 9 in. but they cause
no very material differences in the result.
PIPING COEFFICIENTS
Size of
Pipe
Inches
Coeffi-
cient c
Size of
Pipe
Inches
Coeffi-
cient c
Size of
Pipe
Inches
Coeffi-
cient c
1
2
3
4
45.3
52.6
56.5
58.0
5
6
7
8
69.0
59.8
60.3
60.7
9
10
11
12
61.0
61.2
61.8
62.0
Loss of Pressure in Transmission. — In the accompanying
table is given the loss of pressure in the transmission of com-
pressed air, calculated for pipes 1,000 ft. long. For other
lengths the loss varies directly as the leng^th. The resistance
is not varied by the presstu'e, only so far as changes in x>res-
sure vary the velocity. It increases about as the square of
the velocity, and directly as the length. Elbows, short turns,
and leaks in pipes tend to reduce the pressure in addition to
the losses given in the table.
11
146
COMPRESSED AIR
CO
B
fin
O
O
€0
€0
fin
O
€0
i
a
I
CO
I
I
CI
PI
I
*qq 08 o;^ psssajd
s«^
%99^ oiqnQ
'qq 09 o;^ pdssdJd
00 CO ^ 00 i-i O) CO Q
^O)'^O>^0000O0
•HfHdC^CO^
spnnoj
ajTissdjj JO ssoq
CO N O »-i © O »0 !*"
C) '^ 00 CO 00 CO C4
^.HCOIO
a
d
ob
^^ COCO ^^
COCOOCOb*
^sg
^ 00 CO t» i-i ^ ^ ob
» a^ * » •■ »
i-< i-< N C« CO '^
C0t*»O CO t*»
^Q0c'5K^3^S
coSocob^Ob^-^
C0N»0^OO«0C^
t^«00^»-<00»0'^
^t^00^O»b»»O«D
OO^CO^CONOS
%99^ oiqno
*cn 08 o* psssajd
-uioQ •uij\[ jad Jiy
i-i C5 ■^ U3 1* t^ O CO
"^00N«Op^C0»H
1-nH c5 c« CO "'jt
193^ ojqno
'^1 09 ^ passaid
-uioQ •aij\[ J9d jty
W»Ot*OCO»OQCO
CO CO o) CO CO a> S c)
1-1 1-1 »-• e^ CO
spimO({
Qjnssaj j JO sscyj
^csooooooowcj
t^COi-^^COL
>O>OQQ^r^C0<
ooi«3oioi-i<
«o
N
'•-JiHci^co
6
^ go CO t* iH © ^ CO
^00C2t*(NCO»O">*
w^cooJW'fjj^OJ'^
1^1-1 1-1 e^
CO CD a> C4 >0 GO <<f« KH
a)oor«r^«o>o^co
^C0tOt*0S?H»OO&
=^«^5g!
CO^TrOtop^cOiO
NO"^i-i55Qt^C5
P ^ N "'Jt CO O « CO
IHC^
^aaj otqno
'9,1 08 <^) passajd
-U103 •aij\[ jad jjy
O) a> QQ t^ CO to <«t« '
CI 10 06 iH ^ t* eo (
1-1 »H»HC|(
^aaj oiqnQ
•qq 09 o* passajd
-U103 "uip^ jad jiy
CO CO a> CO CO o >s CI
CI '^ CO o» *-i CO 00 CO
i-(i-(i-iCI
sptmoj
aanssajj jo ssoq
^OCOCOCIP^QO
O) >0 ^ O '^ CI CO CO
t^ o CI 10 CO ^ CI »o
O CO t^ CI 0> t* O 00
• •••••«•
i-< i-< CI »o »>•
04
d
0)0) AOO'
CO coot*'
i-ici»oco(
It^t^CO
i^»0 0&
)OC0CO
•^WCIt^iHiOCON
COCOOOOt^Pt^o^i
i-ici^u5cooooco
t>«i-iO»"^OJiO«OCO
53 CI g .^ « ob 5» Tt«
o 1-1 CI 10 1* 00 1-4
iHCICO
%99^ otqno
'<n 08 o^ passajduioQ
•uij^ jad Jiy
t* "3 CI OS t* ^ 0> "^
1-4 CI CI CO ^ »o t*
'91 09 o* passajduioQ
•uip^ jad jiy
CO CI 00 ^ o) to r* o)
^ i-< CI CI CO Tf< »o
spuno^i
ajnssaj({ jo ssoq
10 U3 U3 O "3 "3 O O
CO O -^ CI ^ CI « 00
^ -^ «0 CO CO CI ■^ CO
»-• CO "^ »o oa ^ cn^
• •••••••
i-<cico»oo«o
Oh
St>.«oco-
1-1 C^ CO'
1-4CIC0^I
> 1-1 00
)r«o6
'OOP
o CI CO CO g» U3 1* o>
OOt^tQ'^Cl^QOtO
i-< CI CO Tf »o O 00
t* »0 « C0 1-< Q CI '
Tf< d O « CI CO (
B
kO CO CI 00 to 1-1
i-i CO CO o» CO «o Oi
• •■■•••
tHNCO
pnooag lad :^a j
00 CO '^ N O 00 T(| P
citoob^tjjScjoo
CO CO O) CO CO oi CO ci
»Hi-4»-ICIC0
pno^ag Jad sja^aj^
i-< CI CO ^ »0 CO « o
00 CO :* CI o 00 ^ o
ci»5<».-H^cpcioq
cocoa>cocda>coci
1-4 1-4THCICO
fHd 00^ to CO OOP
ELECTRICITY 147
ELECTRICITY
ELECTRIC GENERATORS AND MOTORS
An electric generator is a machine for converting mechanical
energy into electrical energy. An electric motor is a machine
for converting electrical energy into mechanical energy. Either
a generator or a motor may be called a dynamo; but this word
IS commonly used to denote generators only. Generators and
motors may be divided into two general classes: those used
with direct current and those used with alternating current.
Direct-Current Generators. — Direct-current generators are
those that furnish a current always in the same direction.
They have three essential parts: the field magnet, often called
the field, the armature, and the commutator; the field is sta-
tionary but the armature revolves. The coils of wire on the
field are called the field coils, and when properly connected
make up the field winding. The individual coils on the arma-
ture are called the armature coils, and when properly connected
make up the armature winding. The commutator consists
of copper bars arranged in the form of a cylinder and revolves
with the armature. Stationary brushes, usually of carbon,
collect the current from the commutator; these brushes are
held in brush holders.
Direct-Current Motors. — Direct-current motors are in gen-
eral almost identical, so far as construction goes, with direct-
current generators. Motors are often required to operate
under very trying conditions, as for example, in mine haulage
or pumping plants or on the ordinary street car. For this
reason, their mechanical construction often differs from that
of the generator so that the working parts will be enclosed as
completely as possible, and thus protect them from dirt and
injury. Practically all of the motors in use are operated
from constant-pressure mains; i. e., the pressure at the terminals
of the motor is practically constant, no matter what load it
may be carrying. The various principal parts of a direct-
current motor and a generator are similarly named.
148 ELECTRICITY
None but very small motors or motors of special design
should be started without some form of resistance in series
with it to cut down the electric pressure of the line until the
motor is up to speed. Such a resistance is called a starting
rheostat, or starting box.
Motor Troubles. — If a motor fails to start when the con-
trolling switch is closed, the trouble may be due to any one of
several causes. There may be an open circuit, a short circuit,
a wrong connection, the power may be ofiE the line, or the
trouble may be purely mechanical. If there is no power on
the Une, the lamps on the same line will be out. If the x>ower
is on the line, but there is no flash at the starting box when
the handle is moved on and then off, the trouble is due to an
open circuit. Open circuits that may be located by inspec-
tion are: defective switches, broken wires, loose or open con-
nections, something under one of the brushes, brush stuck
in the holder, brush dropped out of holder, or a blown fuse.
With the exception of crosses in the wiring, short circttits are
usually in the motor itself and require the attention of a
skilled electrician.
Mechanical troubles that may interfere with the starting of
a motor are sometimes overlooked. The more common are:
too much load, bearings worn until the armature rubs the field
magnet, spnuig armature shaft, hot-box, tight belt or some-
thing in the gearing, lack of end play in the armature.
Excessive flashing at the brushes of a motor is called spark-
ing. When a motor sparks badly the attention of an electri-
cian should be caUed to it. The following are some of the com-
mon causes of sparking: Too much load, brushes improperly
set, commutator rough or eccentric, dirty brushes or commu-
tator, loose brushes, spnmg armature shaft, low bearings, worn
commutator, vibration, belt slipping. There are other causes,
but they cannot be located readily except by an electrician.
Heating of a motor is usually due to overload. If a person
cannot hold his hand firmly on any part of a motor, the machine
is rtmning too hot. Most modem motors will run continu-
ously under an overload of 25% without serious heating and
will run for 2 hr. under 50% overload without damage due to
heating. These limits should not be exceeded.
ELECTRICITY 149
Altematiiig-Ctirreiit Generators. — ^An alternating-current
generator, commonly called an alternator, is one that estab-
lishes a current which periodically reverses its direction.
Alternators are now largely used for both lighting and power
transmission, especially when the transmission is over long
distances. Alternating current is specially suitable for long-
distance work because it may be readily transformed from one
pressure to another. In order to keep down the amount of
copper in the line, a high line pressure must be used. Pressures
much over 500 or 600 volts cannot be readily generated with
direct-current machines, owing to the troubles likely to arise
due to sparking at the commutator. An alternator requires
no commutator; usually the armature is made stationary and
the field revolving. Alternators are now built that generate
as high as 8,000 or 10,000 volts directly. If a still higher pres-
sure is required on the line, it can be easily obtained by the
use of transformers.
Alternators may be divided into two classes: Single- phase
and xx)lyphase alternators. Single-phase alternators are so
called because they set up a single alternating current. Poly-
phase alternators are so called because they deliver two or
more alternating currents that differ in phase; that is, currents
that do not reach their maximum nor their zero values of the
same direction at the same instant.
Polyphase alternators are well adapted for power and light-
ing purposes in mines, especially for the operation of pumping
and hoisting machinery, because the motors operated by them
are simple in construction and not liable to get out of order.
Altemating-Current Motors. — ^Alternating-current motors
may be divided into two classes: synchronous and induction
motors. Synchronous motors are almost identical, so far as
construction goes, with the corresponding alternator. Induc-
tion motors are so called because the current is induced in the
armature instead of being led into it from some outside source.
The stationary part of an induction motor is usually called
the stator and the revolving part, the rotor.
Induction motors possess many advantages for mine work.
One is the absence of the commutator or any kind of sliding
contacts whatever. Such motors can therefore operate with
150 ELECTRICITY
absolutely no sparkiiig — a desirable feattire for mine work.
The motors are also very simple in construction, and are not
liable to get out of order, but, like direct-current motors,
they should not be overloaded
Tranaformers. — Transformers are used to change an alter-
nating current from a higher to a lower pressure, or vice versa,
with a corresponding change in current. Transformers used
for raising the voltage are known as step^up transformers;
those used for lowering the pressure are known as step-doum
transformers. The transformer consists of a laminated iron
core upon which are wound two coils of wire that have no
connection with each other. One of these coils, called the
primary, is connected to the mains; the other coil, called the
secondary, is connected to the circuit to which current is deliv-
ered. The core and coils are contained in an iron case usually
fiUed with oil.
ELECTRIC CIRCUITS
The path through which a current flows is generally spoken
of as an electric circuit. This path may be made up of a num-
ber of parts. For example, the line wires may constitute
part of the circuit, and the remainder may be composed of
lamps, motors, resistances, etc. In practice, the two kinds
of circuits most commonly met with are those in which the
different parts of the circuit are connected in series and those
in which the different parts of the circuit are connected in
multiple or parallel.
Series Circuits. — In the series circttits any two adjacent
parts are connected in tandem, so that the current passing
through one part also passes through the other parts. Pig. 1
(a) represents such a circuit in which the current passes from
the generator D at the + side through the arc lamps a, through
the incandescent lamps I, through the motor m and the resist-
ance r, back to the generator D. The most common use of
this system is in connection with arc lamps.
The objections to this system of distribution for general
work are that the breaking of the circuit at any point cuts
off the current from all parts of the circuit; also, the pressure
ELECTRICITY
151
generated by the dynamo has to be very high if many pieces
of apparatus are connected in series. In such a system, the
dynamo is provided with an automatic regulator that increases
or decreases the voltage of the machine, so that the current
in the circuit is kept constant, no matter how many lamps
or other devices are in operation. For this reason, such
circuits are often spoken of as constant-current circuits.
A series circuit should never be opened at any point unless
it is known that there is no current in the line. If it is desired
^TRTC^T-
-1 — ' yuou ^— r
Pig. 1
to disconnect an arc lamp, for instance, from a series circuit,
one end of a short wire, called a jumper, should be connected
to the line wire on each side of the lamp, so that the cur-
rent may pass through the jumper. Then the lamp may be
disconnected.
Parallel Circuits. — In parallel circuits, the different pieces of
apparatus are connected side by side, or in parallel, across
the main wires, as shown in Fig. 1 (6). In this case, the
generator D suppUes current through the mains to the arc
152 ELECTRICITY
lamps a, incandescent lamps I, and motor m. This system is
more widely used as the breaking of the circuit through any
one piece of apparatus will not stop the current through the
other parts. Incandescent lamps are connected in this way
almost entirely. Street cars and mining locomotives are oper-
ated in the same way, the trolley wire constituting one main
and the track the other, as shown in Fig. 1 {c). By adopting
this system, any car can move independently of the others,
and the current may be turned ofiE and on at will. In all these
sjrstems of parallel distribution, the pressure of the generator
is maintained constant no matter what current the generator
may be delivering. In mine-hatilage plants, the pressure is
usually 250 or 500 volts, the former being generally preferred
as being less dangerous. Lamps may also be connected in
series-multiple, as shown in Fig. 1 {c). Here the two 125-volt
lamps / are connected in series across the 250-volt circuit. Such
an arrangement is frequently used in mines when lamps are
operated from the haulage circuit. Parallel circuits are called
constant-potential circuits, to distingtiish them from the constant-
current circuit mentioned previously.
Shunt. — When one circuit B, Fig. 1 (d), is connected across
another A, so as to form, as it were, a by-pass, or side-track,
Fig. 2
for the current, such a circuit is called a shunt , or it is said to
be in shunt with the other circuit.
Distribution Systems. — Electric circuits may also be clas-
sified as direct-current circuits or alternating-current circuits,
depending on the kind of current carried. The system of
conductors, or wires, leading from a power station is called a
distribution system: it is a direct-current system if direct current
is used, an alternating-current system if alternating current is
used.
ELECTRICITY
IbZ
Direct-current is usually distributed by either the two-wire
system, shown in Fig. 2, or the three-wire system, shown in Fig. 3.
Alternating current may be distributed by the single-phase
system, the two-phase system, or the three-phase system. The
single-phase system usually employs two wires, as in Fig. 2;
the two-phase system, four wires; and the three-phase system,
three wires. The three-phase system is similar to the direct-
current three-wire system in the number of wires only. The
single-phase system is rarely used for mines.
Fig. 3
Protectioii of Circuits. — It is necessary to protect electrical
apparatus from the danger of bum-outs due to heavier currents
than those for which they are designed. This is accomplished
by means of cut-outs, which automatically open a circuit when
the current exceeds a certain value. A cut-out may be either
a fuse or a circuit-breaker.
Electric-Haulage Circuits. — ^In electric-haulage circuits, the
rails take the place of one of the conductors, so that, in cal-
culating the size of feeders required, only the overhead con-
ductors are taken into account. It is difficult to assign any
definite value to the resistance of the track circuit, as this
resistance depends very largely on the quality of the rail
bonding at the joints. If this bonding is well done, the resist-
ance of the return circuit should be very low, because the
cross-section of the rails is comparatively large. The follow-
ing example will serve to illustrate how calculations for haul-
age circuits are made.
154
ELECTRICITY
Example. — In Fig. 4 a 6 represents a section of track 4,000 ft.
long. From the dynamo c to the beginning of the section, the
distance is 1,200 ft. The trolley wire is No. 00 B. &. S., and
is fed from the feeder at regular intervals. Two mining loco-
motives are operated, each of which takes an average current
of 75 amp. The total allowable drop to the end of the line is
to be 5% of the terminal voltage, which is 500 volts. Calculate
the size of feeder required, assuming that the constant 14, in
the formula, takes account of the resistance of the return circuit.
Solution. — ^As the locomotives are moving from place to
place, the center of distribution for the load may be taken
at the center of the 4,000 ft. The distance L will then be
1,200+2,000 = 3,200 ft. The total cxirrent will be 150 amp.;
14X3,200X150X100
hence, = 268,800 cir. mis.
500X500
-1200
4000
■ik— A-
FiG. 4
This would require either a stranded cable or the use of two
No. 00 wires in parallel from c to a. Prom a to b, the No. 00
trolley wire is in parallel with the feeder; hence, the section
of feeder a b may be a single No. 00 wire.
In many cases, the drop is allowed to run as high as 10%,
because the loads are usually heavier, and the distances longer,
than in the example just given.
ELECTRIC APPARATUS IN FIREDAMP
If a fuse blows or a motor sparks in firedamp, the gas will be
ignited just as surely as though it came in contact with a naked
lamp. In any part of a mine where firedamp is apprehended,
a safety lamp should be provided for use with each electric
machine when working, and should the safety lamp give any
indication of gas, the person in charge should immediately
ELECTRICITY 156
stop the machine, cut off the current at the nearest switch,
and report the matter to the proper authority. This applies
especially to such apparatus as electrically driven coal cutters.
The operator of electric machinery should never leave the
machine running; that is, with the current on.
SIMPLE ELECTRICAL CALCULATIONS
PRACTICAL UNITS
In electrical work it is necessary to have units in terms of
which to express the different quantities entering into calcula-
tions. The four most important of these are used to express
current, electrical pressure, or electromotive force, resistance,
and power.
Current. — The current in a wire may be indicated in sev-
eral ways. If a compass needle is held under or over a wire,
it will be deflected and will tend to stand at right angles to
the wire. The stronger the current, the greater will be the
deflection of the needle. The unit used to express current
is called the ampere. The expression of current through a wire
as so many amperes is analogous to the expression of the flow
of water through a pipe as so many gallons per second.
Electromotiye Force. — In order that a current may pass
through a wire, there must be an electrical pressure of some
kind to cause the flow, just as in hydraulics there must alw^ays
be a head or pressure before water can be made to flow through
a pipe. However, there may be a pressure or head without
there being an^ flow of water, because the opening in the
pipe might be closed, though as soon as the valve closing the
pipe is opened, the current will start. In the same way,
an electrical pressure or electromotive force (usually written
E. M. P.) may exist in a circuit, but no current can pass tmtil
the circuit is closed or until the wire is connected so that there
will be a path for the current. The practical tmit of electro-
motive force is the volt. It is the ^tinit of electrical pressure,
and fulfills somewhat the same purpose as pounds per square
inch in hydraulic and steam engineering. "
156
ELECTRICITY
s
1-3
o-g
P
^
.■♦J lI •Y "^^ ..4fc>
■^ flCOffi Q C ?
- <
*—».—' V^w^i*
• -14
"♦-I
««-<
s^ bfi
o
O
°^f,2
<*.<
>»
>»
>.-3og
o
.ti
•- M
•t^'C 6-G
vr^
~
-•->
.M^
•♦J +» ..
G
§^
uan
elec
orce
in a
W
a p
d ^
O^
a
O fe
•
In
■«.>
'
5
(U
g* ^
p
1
w
1 2*
< o
i-<
1-1
.H H
^-t m
•
..si
er sec.
per min.
•
c
lica
ent
1 amp. at 1 volt
.7373 ft.-lb. per s
44.238 ft.-lb. per
2,654.28 ft.-lb. p.
.00134 H. P.
rinH.P.
^S-
Mechan
Equival
3 ft.-lb. p
38 ft.-lb.
H. P.
ft.-lb. per
00 ft.-lb.
mi. -lb. pe
watts
K. W.
737.
44,2
1.34
wS ec r^ -^tt iT
»oeorot* .
bo
4^
(>0
SP
•Tn
c
c
a
(3
.s
• *4
• >4
P
o
o
o
"ts
U-, u
**-• b
«4^
o
og
o 2
o
•o
a, ^
« ^
(a^
c
4-»
+*
*» u
cd
CD
a o
W
0^
Pf^
rt^
^
M
ELECTRICITY 167
Resistance. — ^All conductors offer more or less resistance
to a ctirrent of electricity, just as water encounters friction
in passing through a pipe. The amount of this resistance
depends on the length of the wire, the diameter of the wire,
and the material of which the wire is composed. The resist-
ance of all metals also increases with the temperature. The
practical unit of resistance is the ohm. A conductor has a resist-
ance of 1 ohm when the pressure required to set up 1 ampere
through it is 1 volt. In other words, the drop, or fall, in pressure
through a resistance of 1 ohm, when a current of 1 amp. is pas-
sing, is 1 volt. 1,000 ft. of copper wire .1 in. in diameter has
a resistance of nearly 1 ohm at ordinary temperatures.
Power. — The electrical unit of jxjwer" is the watt. It is
equal to the power developed by a current of 1 amp. under a
pressure of 1 volt. The watt is equal to ^ H. P. The watt
is too small a unit for convenient use in many cases, so that
the kilowatt, equal to 1,000 watts, is frequently used. The
word kilowatt is sometimes abbreviated to kw. or K. W.
Work.^-The electrical imit of work is the watt-hour. This
is the total work done at the rate of 1 watt for 1 hr. A kilo-
watt hour is 1,000 watt-hours. It is equivalent to -V^* or
about IJ H. P.-hr. ^»,„.« , .«,
OHM'S LAW
Ohm's law may be briefly stated as follows:
Law. — The strength of the current in any circuit is directly
proportional to the E, M. F. in the circuit, and inversely pro-
portional to the resistance of the circuit.
This means that if the resistance of a circuit is fixed, and
the E. M. F. varied, the current will be doubled if the E. M. F.
is doubled. Also, if the E. M. F. is fixed, and the resistance
doubled, the current will be halved.
Let E = E. M. F., in volts;
/{=: resistance, in ohms;
/ = current, in amperes.
Then, I = -, or R = -, or E = IR
R I
The last two forms are useful in many cases where the usual
E
form / = — is not directly applicable.
158 ELECTRICITY
Example 1. — In the accompanying figure, a dynamo D
that generates 110 volts, is connected to a coil or wire C,
which has a resistance of 20 ohms;
what current will pass, supposing the
resistance of the rest of the circtiit to be
\E-110VolU jg5 negligible?
Solution. — Here, £ = 110 volts; R
110
= 20 ohms; hence, / = — = 5.5 amp.
20
Example 2. — If the resistance of the coil C is 6 ohms, what
E. M. F. must the dynamo generate in order to set up a current
of 15 amp. through it?
Solution. — The third form of the law given is more con-
venient in this case. _ ,^^,« ^^
£ = 15X6 = 90 volts
In case the current and E. M. F. are known, the resistance
of the circuit may be calculated by using the second form of
the law given above. For example, if the current in the
example just given were 8 amp. and the E. M. F. of the dynamo
110 volts, the resistance of the circuit must be
110
/? = — = 13.75 ohms
8
POWER CALCULATIONS
Power in Direct-Current Circuits. — The power in any direct-
current circuit may be found by multiplying the current by
the pressure required to maintain the current in the circuit.
Let W= power, in watts;
H. P. = horsepower.
Then, watts = volts X amperes, or
PF=£/
Tr=/2/?
W
H. P. =
746
Power in Altematiiig-Current Circuits. — Owing to the nature
of alternating currents the formula Pr=£/ cannot always
be used for alternating-current calculations. It may be used
for single-phase circuits to which nothing but incandescent
ELECTRICITY 159
lamps are connected. On single-phase circuits operating
motors only the formula becomes approximately W^ .8 E I,
and on single-phase circuits containing both lamps and motors
the formula PF* .85 JS / may be used. For two-phase circuits
the foregoing expressions will give the power for one phase,
so that to obtain the total power for both phases multiply
by 2. On three-phase circuits, the expressions for power are
W= 1.732 E /, W= 1.386 E /, and PF- 1.472 E /. respectively,
for the three conditions mentioned.
WIRE DATA
Estimatioii <rf Cross-Section of Wires. — The diameter of
round wires is usually given in the tables in decimals of an
inch, and the area of cross-section is given in terms of a unit
called circtilar mil. This is done simply for convenience in
calctilation, as it makes calculations of the cross-section
much simpler than if the square inch were used as the unit
area. A mil is ^^ in., or .001 in. A circular mil is the area
of a circle, the diameter of which is ttAtv in., or 1 mil, or
.0000007854 sq. in.
If the diameter of the conductor were 1 in., its area wotild
be .7854 sq. in., and the number of circular mils in its area
would be .7854^- .0000007854 = 1,000,000; but 1 in. = 1,000
mils, and (1,000)««= 1,000.000; hence, the following is true:
C. M, — tP\ or the area of cross-section of a wire, in circular
mils, is equal to the square of its diameter expressed in mils.
Example. — If a wire has a diameter of .101 in., what is its
area in circular mils?
Solution. — .101 in. = 101 mils; hence, C, Af. = (101)*
= 10,201.
Estimation of Resistance. — The resistance of any conductor
is directly proportional to its length, and inversely proportional
to its area of cross-section, or
L
i? = /C-,
A
in which R = resistance ;
L= length;
A =area of cross-section;
K = constant.
leo ELECTRICITY
If L is expressed in feet and A is expressed in circular mils,
the constant K must be the resistance of 1 ft. of the wire in
question of 1 cir. mil cross-section. The resistance of 1 mil-ft. of
coi)per wire at 75° P. is about 10.8 ohms. Hence, for copper
10.8L
wire, /?= ; but A — d* when d is the diameter in mils;
A
10.8L
hence, ic = — — -
This formula is easily remembered, and is very convenient
for estimating the resistance of any length of wire of given
diameter when a wire table is not at hand, or when the diameter
of the given wire does not correspond to anything given in
the table.
Example. — Find the resistance of 1 mL of copper wire
.20 in. in diameter.
Solution. — 1 mi. » 5,280 ft., .20 in. = 200 mils. Area of
cross-section = (200)» = 40,000 dr. mils. Hence,
„ 10.8X6,280 ,
R= -1.42 ohms
40,000
Wire Gauge. — ^The gauge most generally used in America
to designate the difiFerent sizes of copper wire is the American,
or Brown & Sharpe (B. &. S.). The sizes given by this gauge
range from No. 0000. the largest, .460 in. diameter, to No. 40,
the finest, .003 in. diameter. Wire drawn to the sizes given
by this gauge is always more readily obtained than sizes
according to other gauges; hence, in selecting line wire for
any purpose it is always desirable, if possible, to give the size
required as a wire of the B. &. S. gauge. A wire can usually
be selected from this gauge, which will be suited to ordinary
wiring requirements in and about mines.
In the accompanying table, the common sizes of wire are
listed. Wires smaller than No. 14 are not given, because
No. 14 is the smallest size ordinarily used for light wiring.
Trolley wires are usually made of either No. 00 or No. 0000.
Conductors larger than No. 0000 are stranded and have no
gauge number. Stranded conductors, called^codZes, are speci-
fied by their area in circular mils.
ELECTRICITY
161
The table gives the dimensions, weight, and resistance of
pure copper wire. The weights given are for bare wire. The
first coltunn gives the B. &. S. gauge number, the second the
diameter in mils; the diameter in inches is the number qyvea.
PROPERTIES OF COPPER WIRE
V
^ u
u
(d b
4)
Oxi
% »
• 6
p4 *^
CO §
S:^
^'Z
Q
n
0000
460.0
000
409.6
00
364.8
324.0
1
280.3
2
267.6
3
229.4
4
204.3
5
181.9
6
162.0
7
144.3
8
128.5
114.4
10
101.8
11
90.7
12
80.8
13
71.9
14
64.1
211,600.0
167,805.0
133,079.4
105.534.5
83,694.2
66,373.0
52.634.0
41.742.0
33,102.0
26,250.5
20,816.0
16.509.0
13.094.0
10.381.0
8,234.0
6,529.9
5,178.4
4,106.8
•M
1^
4)
Q
T7X
g
^ «,
* 01
to
u C
0.1
0) rj
** d
O4
"S
•?
V
^
^
640.50
3,381.4
608.00
2,682.2
402.80
2,126.8
319.60
1,686.9
253.30
1,337.2
200.90
1,060.6
159.30
841.1
126.40
667.4
100.20
529.1
79.46
419.5
63.02
332.7
49.98
263.9
39.63
209.2
31.43
165.9
24.93
131.6
19.77
104.4
15.68
82.8
12.43
76.2
. CO
5.gO
. O
.0489
.0617
.0778
.0981
.1237
.1560
.1967
.2480
.3128
.3044
.4973
.6271
.7908
.9972
1.2570
1.5860
1.9990
2.5210
Current
Capacity
Nations^
Board
Fire
Under-
writers
(Amperes)
Vim
'^ 2
■M O
^^
312
262
220
185
156
131
110
92
77
65
46
32
23
16
I*
210
177
150
127
107
90
76
65
54
46
33
24
17
12
in this column, divided by 1,000. The third column gives the
area in circular mils, the numbers in this column being equal
to the squares of those in the second column. The safe car-
rying capacity is also given.
12
182
ELECTRICITY
APPROXIMATE EFFI-
CIENCIES OF DIRECT-
CTJKRENT MOTORS
fiiiiiMMwiw Wire. — ^The resistance of alnmiiiitm wire is prac-
tically If times that of copper wixe. For insulated (covered)
almninam wire, the safe-canyiog capacity may be taken as
84% that of copper wire with the same kind of insulation.
To estimate the resistance of aluminum wire use the formula
for copper and multiply the result by If . To obtain the resist-
ances per 1.000 ft. of the various
sizes. B. &. S. gauge, of alumi-
num wire multiply the values
given in the sixth column of
the table by If. To obtain
the carrying capacities of alu-
minum wires, multiply the
values in the seventh or eighth
column or by .84. By divi-
ding the values of the fourth
or fifth column of the table by
2 the approximate weights per
1,000 ft. or per mi. of the
various sizes of aluminum wire
will be obtained.
Wire Fcvmulas. — The size of wire for a direct-current motor
may be calculated by means of the formula
20.470 H. P. L
Een
in which A —the size of wire, in circular mils;
H. P. = output of motor, in horsepower;
L <- distance from the motor to feeding point, in feet;
E s voltage on nameplate of motor;
e « allowable drop from feeding point to motor;
n "= efficiency of motor.
This formula allows for 25% overload. The value of ff is
rarely known, but may be taken from the accompanying
table:
The size of wire for induction motor circuits may be found
by using the formtda
A
Size of
of Motor
Horsepower
EflBciency
of Motor
Per Cent.
1 to 3
3 to 5
5to20
Over 20
80
82
85
90
KR.V.L
in which
K>
Een
-constant;
ELECTRICITY
163
and the remaining symbols have the same significance as
in 'the formula for direct-current motors. For single-phase
motors, the value of K may be taken as 47,560; for two- and
three-phase motors as 23,780. Single-phase motors are rarely
used in mines. The value of n for pol3rphase motors may be
taken from the accompanying table of efficiencies.
The amperes per terminal
of an induction motor is often
given on the name plate, in
which case the following formula
may be used:
25.6CL
APPROXIMATE EFFI-
CIENCIES OF INDUC-
TION MOTORS
Size of
Motor
Horsepower
Efficiency
of Motor
Per Cent.
Under 6 •
5 to 20
20 to 100
Over 100
80
85
88
90
in which C » current rating;
and the other letters have the
meanings given before.
It is important that induc-
tion motors be operated at the
voltage given on the name plate;
therefore, in order to obtain
the most accurate results, the value of e in the foregoing formu-
las should be estimated as closely as possible.
WIRING CALCULATIONS FOR LAMPS
Incandescent-Lamp Ratings. — There are two classes of
incandescent lamps in common use; the carbon lamp and the
Mazda, or tungsten, lamp. Before the advent of the Mazda
lamp, it was the practice to specify lamps by their candle-
powers; as, for instance, a 16-candle power lamp or a 32-candle-
IKJwer lamp, abbreviated to 16-c.p. or 32-c.p. Now, however^
lamps are rated according to the watts required to oi>erate them.
A 16-c.p. carbon lamp is now known as a 50-watt lamp; a
32-c.p. lamp becomes a 100-watt lamp. The Mazda lamps
most commonly used are the 25-, 40-, 60-, and 100-watt sizes.
Most incandescent lamps are made for voltages ranging from
100 to 130, although lamps designed for other voltages may be
obtained.
Fonnulas for Lamp Wiring. — Because, with slight modifica-
tions, it may be adapted to any of the common distribution
164 ELECTRICITY
systems, the most convenient formula for lamp-wiring cal-
culations is
KWL
Ee *
in which A «size of wire, in circular mils;
X = constant;
py= power required by all lamps of group to which
wiring is run, in watts;
L = distance from feeding point to lamps, in feet;
£ = voltage of circuit at lamps;
e = allowable drop in circuit.
For direct-current, two-wire and three- wire circuits and for
single-phase, alternating current, two-wire and three-wire cir-
cuits, the value of K is 22. For two-phase four-wire, and
three-phase three- wire circuits, the value of K is 11. On a
two-phase or three-phase circuit, the lamps shotdd be, as far
as possible, distributed equally; that is, each phase should
have the same number of lamps connected to it.
If all the lamps are of equal size, W=Nw, where N is the
number of lamps and w is the watts per lamp. The formula
just given then becomes
KNwL
Ee
If a certain size of wire is at hand and it is desired to know
the number of lamps that the given size of wire will feed with
a certain drop, the last formula may be used in this manner:
AEe
KwL
The length to be used in the wiring formula is the average
distance traversed by the current in the conductor. For
example, if, as in view (a) the lamps were all grouped or bunched
at the end of the line, the length used in the formula would be
that from G to A. In case the load is tiniformly distributed
all along the line, as shown in view (Jb), the current decreases
step by step from the dynamo to the end. In such a case,
the length or distance to be used in the formula is one-half
that used in the former case, or one-half the distance from the
dynamo to the end.
ELECTRICITY 165
Arc Lamps. — ^Arc lamps are frequently run on constant-
potential circuits, and usually consume from 400 to 500 watts.
There are so many types of these lamps that it is difficult to
qL 1, ^A
4
6
mmm
give any current estimates that will be generally applicable.
Enclosed-arc lamps usually take from 3 to 5 amp. when xim
on 110-volt circuits.
ELECTRIC SIGNALING
BATTERIES
Batteries are used for various purposes in connection with
mining work, principally for the operation of bells and signals.
The unit of a battery is called a ceU, a battery consisting of
several cells properly connected together. An ordinary cell
consists, fundamentally, of two pieces of solid conducting
substances in a liquid that acts chemically upon one more than
upon the other. The liquid is called the electrolyte; the solid
substances, electrodes. The electrode at which the current
leaves the cell is called the cathode; the electrode at which the
current enters is called the anode. The anode is usually made
of zinc; the cathode of carbon, copper or iron. Most cells use
a chemical depolarizer to remove the objectional hydrogen
gas that is formed by the chemical action of the electrolyte
on the anode. An open-circuit cell is one designed for work
where current is used only intermittently and the circuit is
usually open. A closed-circuit cell is one designed for circuits
that are usually closed and the current passes continuously.
166
ELECTRICITY
For operating electric bells, any good type of open-circuit
battery may be used. The Ledanch^ cell is largely used for
this purpose, also several types of dry cells.
BELL WIRING
The simple bell circuit is shown in Pig. 1, where p is the
push button, b the bell, and c the cells of the battery connected
il
m
Fig. 1
up in series. When two or more bells are to be rung from one
push button, they may be joined up in parallel across the
f¥
§1
Fig. 2
battery wires, as at a and 6, Pig. 2, or they may be arranged
in series, as in Pig. 3. The battery B is indicated in each dia-
f¥
¥1
H^
4
Pig. 3
gram by short parallel lines, this being the conventional method.
In the parallel arrangement, the bells are independent of each
ELECTRICITY
167
other, and the failure of one to ring would not affect the other;
but in the series grouping, all but one bell must be changed
to a single-stroke action,
so that each impulse of
current will produce only
one movement of the ham-
mer. The current is then
interrupted by the vibrator
in the remaining bell, the
result being that each bell
will ring with full xx>wer.
The only change necessary
to produce this effect is to
cut out the circuit-breaker
on all but one bell by con-
necting the ends of the mag-
3
Pig. 4
net wires directly to the terminals of the bells in the circuit.
When it is desired to ring a bell from one of two places
some distance apart, the wires may be run as shown in Fig. 4.
The pushes p are located at the required points, and the battery
and bell are put in series with each other across the wires
joining the pushes.
A single wire may be used to ring signal bells at each end of
a line, the connections then being as shown in Pig. 5. Two
batteries B and B\ and a key and bell at each station are
required. The keys are of the double-contact type, making
connections normally between the bell and line wire L. When
one key is depressed, a ctirrent from the battery B passes along
l¥ir
^TSl
G
Pig. 5
the wire through the upper contact of key V to bell 1/ and back
through ground plates G' and G,
168
PROSPECTING
Q^
When a bell is intended for use as an alarm apparattts, a
constant-ringing attachment may be introduced, which closes
the bell circuit through an extra wire as soon as the trip at
door or window is disturbed. In the diagram, Fig. 6, the
main circuit, when the
push p is depressed, is
through the automatic
drop d by way of the
JL terminals a and b to the
"^ bell and battery. This
current releases a piv-
oted arm which, on fall-
ing, completes the cir-
cuit between b and c.
81
Pig. 6
establishing a new path for the current by way of c, indepen-
dent of the push p.
The failure of a bell to operate is usually due to one of the
following causes: Break in the circuit, crossed wires, wrong
connections, weak battery, wrong adjustment of the vibrator.
Inspection is necessary to locate the fault. If the bell rings
weakly, it is usually due to poor insulation somewhere on the
circuit or to a weak battery. Probably the most convenient
way to test a battery for weakness is to connect a good bell
directly across the battery terminals.
PROSPECTING
Formatioiis Likely to Contain Coal. — No coal beds of impor-
tance have ay yet been found below the Carboniferous period.
Though coal may be looked for in any later stratified or sedi-
mentary rocks the bulk of the best coal has been found in depos-
its made during this period. As a rule, highly metamorphic
regions and regions composed of volcanic or igneous rocks
contain no coal. The rocks most common in coal measures
are sandstones, limestones, shale, conglomerates, fireclays, and,
in some localities, beds of iron ore.
An examination of the fossils contained in the rocks of any
locality will usually determine whether the rocks belong to a
PROSPECTING
170 PROSPECTING
period below or above the Carboniferous, and hence whether
there is a probability of the formations containing coal. There-
fore, the prospector should familiarize himself with the geo-
logical periods, and with the most common fossils of the various
periods. The accompanying table gives the American and
foreign names of the various geological periods, together with
the name of the principal form of life during each period to
and including the Devonian, which is the one below the Car-
boniferous or coal-forming period.
Coal or Bedded Materials. — ^The presence of the outcrop of
any bed may often be located by a terrace caused by the dif-
ference in the hardness of the strata, though any soft material
overlaying a hard material will form a terrace. Usually, the
outcrop of a coal terrace is accompanied by springs carrying
iron in solution, which is deposited as ochery films upon
the stones and vegetable matter over which the water flows.
Sometimes the outcrop is characterized by a marked difference
in the vegetation, for instance, the outcrop of a coal bed con-
tained between very hard rocks will have more luxtuiant
vegetation than the stirrounding country.
Some indication as to the dip and strike of the material
composing the bed may be obtained by examining the terrace
and noting the deflections from a straight line caused by the
changes in contour of the ground. Where a bed or seam is
faulted, its continuation can frequently be found by breaking
through into the measures beyond, when an examination of
the formation will indicate whether the rocks are those that
usually occur above or below the desired seam.
Underground ProBpecting. — ^Frequently a seam or deposit
becomes faulted or pinched out underground, so that it is
necessary to continue the search by means of underground
prospecting. This work is, to a large extent, similar to surface
prospecting, the underground exx)OSures being simply additional
faces for the guidance of the engineer. In the case of coal
beds or similar seams, the manner of carrying on the search
win depend on the character of the fault. Where sand fatdts
or washouts are encountered, the drift or entry should be
driven forwards at the angle of the seam until the continuation
of the formation is encountered, when a little examination of
PROSPECTING
171
the rack, will indk
ate whether they are the
In the case of dislocatio
na or throw..
Ltion of the bed may be looked for by SchmiiCs
Ian, ,rf faults
, which
Ltw.—Ah
■.t ongU.
vered that, in the maiority
of caaea. the
. of Che fault has moved doi
ra, and there-
fore .uoh fi
lultB ai
■e commonly called twmwl /oiju. For
a b were being worked from
fault, upon .
Bncount.
:^iing the fault, nark would
farther
side of the fault toward d.
until the con-
tinuationofi
oward * wa» encountered. I
hHd the wor
k b«o proceeding from 6, the eipL
oration would
Kiploration by Drilll
or Bore Holes.— When te
much used in searching
y form that has been universally
direction through hard. soft, or
le use of the diamond drill, many
I, and demand careful study In
172 MINING
adapting the form of apparatus to the work in hand, and in
rightly interpreting the restilts obtained from any set of obser-
vations. The diamond drill is used very extensively and gives
the best results of any kind of drilling for exploration. Tlie
work is best done by firms that do this special work and
the surveying of the bore holes must be done by the mining
engineer.
MINING
OPENING A MINE
CHOOSING THE LOCATION
The location of the surface plant and the mine opening
depend on the formation of the deposit and on the facilities for
transporting the product to market. It is impossible for one
not on the ground, and unfamiliar with natural or railroad
transportation facilities in the neighborhood, to give an idea
regarding the second consideration. In regard to the first con-
sideration, the following points should be observed:
When the seam or vein outcrops within the limits of the
property and is flat, a water-level drift is the best method of
opening it. If the vein has any considerable inclination, it
should be opened by a slope, or by a tunnel driven across the
intervening measures. Where the dei)Osit has an inclination
of but from 1° to 1.26°, the water-level drift is generally used,
and the main-haul^e entry is opened at the lowest accessible
point on the outcrop, which insures free drainage and a favor-
able grade for haulage. Water-level drifts, however, are only
profitable where the inclined seam is exjKJsed in ravines or
gorges eroded across the strike of the measiu'e, or where the
vein can be reached by a short tunnel from the surface to the
seam across the measures. This is often the case when the
seam dips with the hill, but when the dip is against the hill,
the tunnel is generally a long one. While the expense of oper-
ating a mine opened by a long tunnel is less than one opened
by a sloi>e or shaft, owing to cheaper drainage and haulage,
MINING 173
when the coal above the water level is exhausted the ttuinel
is almost worthless.
When the outcrop dips into the hill, the drift is usually
commenced a few feet below the outcrop terrace, and is driven
on a slight up grade until the normal dip is reached. When the
inward dip is too strong, the better plan is to sink a shaft in the
center of the basin, provided the depth is not too great and the
amount of water to be pumped is comparatively small. If the
inward dip to the center of the basin does not exceed a total of
25 ft. difference in level, a drift may be used and drainage
effected by a siphon.
When the seam is inclined and is accessible at no xx>int along
its outcrop low enough to furnish sufficient lift or breast length, it
should be opened by a slope or shaft. Or, if the seam is flat and
does not crop on the tract, a shaft is the only method of working
it, unless it lies so near the surface that it can be stripped.
Where a seam has a dip of 20° or more, and is brought close
to the surface by an anticlinal axis or saddle, a rock slope, or,
in other words, a tunnel dipping the same as the seam may be
started from the surface, and, when the seam is reached, may
be continued to the desired depth in the seam.
In sinking slopes for coal mines, it is customary to sink an
airway alongside of and parallel with the slope, with a pillar
of about 10 yd. between. The slope for coal mines is usually
sunk so that there is a lift of from 100 to 110 yd., and then
gangways are turned off on each side. The lift is the length on
pitch that breasts or rooms, driven at right angles to the gang<
way, can be driven in good coal. Subsequent lifts are usually
from 80 to 100 yd. long.
SHAFTS
Shafts and tunnels may be temporary, or those that are
simply driven for exploration purposes, and are not to be used
for any great length of time; or they may be permanent, or those
that are driven for a specific purpose and usually have a definite
predetermined capacity. In the United States, shafts are
usually square or rectangular in form, as timber is used in
lining them. In Europe, round or oval shafts are frequently
tised; these have a lining of brick, iron, concrete, or masonry.
174 MINING
CompAitmente. — The number of compartments in a shaft
and their arrangement depends largely on the use to which the
shaft is to be put; also on the number of shafts at the property,
and the depth of the shaft. Where the material is to be
removed is comparatively near the surface, it is usually cheaper
to sink a ntunber of two- or three-compartment shafts than it is
to tram all the ore to one large shaft; while, in the case of very
deep mines, large four- or six-compartment shafts are sunk, and
the underground haulage extended over a greater area. When
the shafts are lined with timber, a strong construction can be
obtained by placing the compartments side by side, as shown
in Pig. 1. When a body of mate-
rial comparatively near the surface
is being removed through a number
of shafts, two-compartment shafts
Pig. 1 are frequently built, both compart-
ments being used for hoisting, and
separate shafts being provided for the pump column and lad-
derways. This reduces both the size of the shaft and the
timbering necessary, and also does away with the special dan-
ger from fire that always exists when there is a ladderway in
the shaft, for it is always difficult to fight fire in these special
compartments.
Size of Shafts. — Shafts vary greatly in size, depending on
the number of compartments desired and the size of the com-
partments. Por coal mines, they are generally from 10 to 12
ft. wide inside of timbers, and each compartment is from 6 to 7
ft. wide inside the guides. This would make the outside
dimensions of a double-compartment shaft about 13 to 15 ft.
wide, 17 to 18 ft. long, and a triple-compartment shaft frdm
24 to 25 ft. long.
Shaft Sinking. — As a general thing, the loose material or
wash above bed rock is not thick enough to cause any serious
trouble, and ordinary cribbing of heavy timber or a masonry
curbing is sufficient. But when the surface is very thick or
loose, and runs like quicksand, considerable difficulty is expe-
rienced. The general method of overcoming this difficulty in
the past was to at once divide the shaft into the required number
of compartments by heavy timbers alternating or placed skin
Quicksand.
MINING 176
to skin, which had the effect of bracing the cribbing against
the lateral pressure of the loose material. This method is
effectual where the wash will remain solid or stand long enough
to allow the timbering and cribbing to be put in. But when the
surface is thick, loose, or watery, or of quicksand, some one of
the following special methods of sinking must be adopted:
Forepoling
Metal linings, forced down with-
out use of compressed air
Pneumatic method, limited to
about 100 ft. in depth
. Poetsch process, freezing method
Rock, hard or soft, but very
wet . , Kind-Chaudron method
Rock, hard or soft, but not
very wet Continuous, or long-hole, method
When the ground is so bad that it will not stand for several
days between excavation and the completion of the lining, it
becomes necessary to carry the timber to the bottom of the
work. This may be accomplished by using square-set shaft
timbering and driving laths, or forepoling behind the timber so
as to keep the soft material from running into the opening.
The advantages of forepoling are that, if the shaft is being lined
with square sets, forepoling can be commenced at any point,
and, if the ground is not too bad, the work can be continued
by this means until solid material is encountered. When the
ground is particularly bad, it may become necessary to use
breast boards, which are simply boards braced against the bottom
of the shaft so as to keep the material from rising into the open-
ing, only one board at a time being removed while the material
behind it is excavated.
The pneumatic method of shaft sinking was developed from the
system in use for putting down foundations for bridge piers.
At the bottom of the shaft there is a small chamber called a
caisson, in which a sufficient air pressure is maintained to
exclude the water at all times. The shaft lining is built on
above this chamber, and gradually forced down into the soil.
Men enter the chamber and excavate the material from under
the caisson as it descends.
By this method the sinldng conunences at ooce uid ia contin-
ued without interruption until the Uning Is completed to bed
Tock, to which the lining is joined, a£ sliown in Fi^. 2. An air
compressor, which is subsequently used, is the only auxiliary
In the (HKBmalfc process, the fine material is aspirated out
depth of about 100 ft., as it is impossible for men W work under
a greater air pressure than that which coiresponds to about 100
ft, of hydrostatic pressure.
By the freeziii^ process.
pipes are sunk in the ground
about the area to be frozen.
ends of the pipes are sealed
introduced so that a freezing
Fig. 3
rdinary refTrgeratiTig machine. The circulation js maintained
n the pipes until the ground between them is frozen solid,
iter which the work may be continued as though the forma-
ion were sohd rock, the materia] being blasted and hoisted
a buckets. The freezing process may be applied to any
■rocess is applicable only to soft fonnations. The free-
ing process may be carried to practically any deptb.
MINING 177
The Kind-Chaudron method is applicable only to round shafts,
and is suitable for shafts passing through very wet and at the
same time comparatively soft formations. The excavation is
carried on by means of a large set of boring tools armed with
steel teeth, and operated in a manner similar to that employed
in drilling wells by the percussive system.
The long-hole process consists in the drilling of a series of
diamond-drill holes over the area of the proposed shaft, then
filling the holes with sand. Afterwards 5 or 6 ft. of sand is
removed from the holes in the interior of the shaft, and these
holes are charged with explosives, and fired by electricity.
Next, the holes around the boundary of the shaft are charged
and fired in the same manner, and the process is continued until
the bottoms of the diamond-drill holes are reached. This
method is especially applicable to work in hard rock, where
great speed in sinking is desired, for all the drilling is accom-
plished at one operation, after which the sinking x>rogresses by
simply cleaning out the drill hole, blasting the material and
cleaning it away.
Sinking Head-Frames. — ^Head-frames of very simple form
are used for sinking. The skeleton of the frame is formed of
heavy squared timber 10 in. X 10 in. or 12 in. X 12 in. mortised
and pinned together, and braced by diagonal braces. A good
height from the surface to the center of the sheave is from 20 to
25 ft. The sheave should be from 6 to 8 ft. in diameter.
Sinking Bucket. — The sinking bucket should be of boiler
iron, or of heavy hardwood strengthened by iron bands, about
3 ft. in diameter at the top by from 2^ to 3 ft. deep. It should
be suspended by a handle pivoted a trifle below the center, and
it should have a pin on the rim of the bucket that will hold it in
an upright position when a loose ring on the handle is slipi>ed
over it. A chain fastened to the top of the head-frame, with
a hook on its loose end, is suspended so that, when hanging
pliunb, it is over a chute leading to the dump car. As the
bucket is hoisted out of the shaft, this chain is attached, and the
engine reversed. The bucket swings over the chute, the ring
holding it upright is knocked off the pin, and the rock is dropped
into the chute. Rocks too large for the bucket are suspended
in chains and are hoisted in that way, and removed on a truck
13
178 MINING
that runs on a track inside of the head-frame, the gauge of
which is sufficiently wide to give plenty of clearance for the
bucket.
Sinking Engines. — Most shafts and slopes are sunk with
old engines, or else by engines especially designed for such work,
and so constructed that they can easily be moved from place
to place.
Tools. — The old method of hand drilling is still adhered to
in many instances, but it is gradually giving way to machine
drilling, especially in deep shafts. When properly managed,
the work is done much more rapidly and economically by the
several excellent types of rock drills now on the market. They
are constructed in a variety of shapes by the makers, and there
are so many convenient accessories in the shape of fittings, etc.,
that all contractors prominent in the various coal fields i>ossess
one or more of their favorite type of drills. These drills are run
either by compressed air, steam, or electric power, and in large
shafts two are ustially employed, so that work may not be
delayed by a breakdown of one drill.
Drainage and Ventilation. — When only a small amount of
water is encotmtered while sinking, the best plan is to allow
it to collect in a depression and bail it from there into the bucket,
hoisting it the same as the rock. Where the water is excessive,
in quantity, a steam pump is necessary; all the leading pump
works make pumps especially designed for sinking purposes.
When the shaft is of moderate depth, a fire burning in one
comer will supply ample ventilation. To rapidly clear away
smoke, a good plan is to bum a bundle of straw or shavings in
one end of the shaft, and throw a couple of buckets of -water
down the other end. When the shaft is very deep, or when the
sectional area is small, ventilation is produced either by a steam
jet, or by a small fan turned either by steam or by hand. In
some cases, a fire is tised that draws into a board pipe.
Slope Sinking. — ^A slope is an inclined plane driven down on
the bed of the seam, and is generally through coal or ore, though
sometimes it is driven through rock across measures to cut the
seam that cannot be conveniently worked by a slope. In the
latter case, it is merely an inclined tunnel; in the former it
might be termed an inclined gangway. A slope and an inclined
MINING 179
plane, when mentioned hereafter, will mean an inclined opening
in coal used as a passageway for mine cars.
When the location of the slope has been decided on, a tem-
porary ynlfiiig plant is erected. For a short distance, varying
with the nature of the grotmd, but usually ranging from 10 to
20 ft. on the pitch, an open cut is made, and the earth, rock, or
crop coal is thrown out by hand. As soon as sufficient cover is
reached, the work of undermining and timbering is commenced,
and at the same time a double or single track is laid, so that the
material can be taken out in a car or self -dumping skip. When
the latter is used, the track is continued up a trestle some dis-
tance above the surface, and a head-sheave so placed as to draw
the skip up the required distance and dump the material in a
chute beneath the trestling.
The width of the slope depends on the size of the cars and the
number of compartments. The most common arrangement is
to divi'^e the slope into three compartments; two laxige ones
for hoistways, and a smaller one for pump rod, column pipe,
steam pii>e, and traveling way. Tb&a last is also used as an
airway while sinking is going on.
The Sump. — ^When the shaft or slope is ccnnpleted, among the
first things necessary is a sump in which to collect the drainage
of the mine. This is an opening lower in the vein, when it is
a pitching one, or in the rock when it is a flat seam reached by a
shaft. It should be large enotigh to hold any excess of water
that the pumps cannot handle; and the pumping machinery
should be powerful enough to handle the ordinary drainage by
rtmning not over 10 hr. per da. When this is the case, in
an emergency, the pumps can be rtm, continuously, and thus
handle the surplus water. ' ■
Driving the Gangway. — In bituminous coal seams, the height
of the gangway is governed by the thickness of the seam; this
is also true, in a certain sense, in the anthracite regions, thotigh
in anthracite mines they are very seldom less than 6 ft. in
height. In the larger seams they are from 6 ft. 6 in. to 7 ft.
6 in. high in the clear, and from 10 to 15 ft. wide. The gatige
of track varies from 24 to 48 in. The grade should rise at least
4 in. in 100 ft., and a gutter 3 ft. wide by 18 in. deep should be
cut in the coal on the low side.
180 MINING
tunhels
Mining tunnds are usually ci small cross-section compared
with those that occur in railroad work, it being rare that their
size is such that they cannot be driven in full section, and if the
ground is firm the operation of placing the lining may follow
behind the work of driving. They are generally lined with tim-
ber, and in case the ground is of a soft or treacherous nature,
bridged square sets and forepoling are employed, with or with-
out breast boards, as the neressity of the case demands. When
the material is firm rock, the tunnel is sometimes not lined, the
roof being given an arched form.
MINE TIMBER AND TIMBERING
Choice of Timber. — ^Timber used for underground supports
in mines should be long-grained and elastic, and, at the same
time, should not be too heavy. Oak, beech, and similar woods
are very strong, but are heavy to handle, and when set in place
are treacherous, because they are short-grained and not elastic,
so that they break without warning. Mine timber is placed,
not with the intention of ultimately resisting the great pressure
of the earth, but to keep any loose pieces in place and to give
warning to the workmen, thus enabling them to escape before
a fall occurs. For this reason, pine and fir are suitable for mine
timbering, as they combine a fair amount of strength with con-
siderable elasticity, and hence give warning long before they
break. Very elastic timbers, such as cypress, willow, etc., are
to be avoided, for they simply bend like a bow and do not offer
the necessary resistance to hold the material in place for a short
time.
Preservation of Timbers. — ^The character of the ventilation
in a mine has considerable effect on the life of any timber sup-
ports. Damp stagnant air will cause mold and fungus growth.
which will be followed by the destruction of the timber through
decay or dry rot. All timbered openings should be well venti-
lated, and provision made for the speedy removal of damp hot
air, such as commonly occurs around pump rooms and along
steam lines. Water is a good preservative, as it washes off the
MINING 181
spores of the fungi as fast as they are formed, and for this reason
shaft timbers are sometimes kept wet.
Timber may be also preserved: (1) by a solution of common
salt and water; (2) by impregnating the wood with such metallic
substances as sulphates of copper, iron, etc. ; (3) by impregna-
tion with the chloride of magnesium or zinc; (4) by creosoting;
(5) by coal tar; (6) by carbolineum.
A solution of 1 lb. of salt in 4 or 5 gal. of water gives a cheap
and easily applied preservative with which the timber should
be thoroughly soaked. Sulphate of iron is economical and
effective. In the zinc process, a solution of 1 gal. of liquid
chloride of zinc (sp. gr. 1.5) mixed with 35 gal. of water is
forced into the wood by presstire. Impregnation with crude
creosote oil is effective, for the creosote fills the pores and pre-
vents saturation by water; it destroys organic life; the carbolic
acid that it contains coagulates the albuminoids and i>revents
decay; but it has the disadvantage of making the timber very
inflammable. Painting with liquid tar is effective, but makes
the wood very inflammable. Painting with ordinary white-
wash is also said to give good results. Carbolinetun is said to
be effective, but is quite expensive. It is applied with a brush,
or by steeping in a tank; 1 gal. will cover 300 to 400 ft. of tim-
ber. It has been shown that preservatives decrease the strength
of timber from 8% to 20%, depending on the process used.
In selecting props, the principal points to be observed are:
Straightness, slowness of growth as indicated by narrow
annular rings, freedom from knots, indents, resin, gum, and sap.
They should also be well seasoned before use. With these
precautions and proper mine ventilation, fungus growth may
generally be obviated and durability insured.
Pladug of Timber. — The individual sticks should never be
weakened by cutting mortise and tenon joints. The pressure
should be evenly distributed over a number of sticks, and not
concentrated or centered at one point. Centers of revolution
should be avoided. The individual sticks should be placed in
the direction of the strain that they are to resist, so that they
will be subject to compression along their length rather than
to a transverse strain. The individual sticks should be so
' placed, and the joints so formed, that the pressure tends to
182 MINING
strengthen rather than weaken the structure up to the crushing
strength of the timber. In the case of large stopes, the timber-
ing should be done according to some regular system, while,
at the face of coal mines, single props or posts are usually better,
owing to the fact that their duty is only to support the loose
IKMtion of the roof for a limited time. Probably the most
important point is to timber in time, before the rock becomes
broken or begins to settle.
It seems generally agreed that the main weight in mines
comes nearly at right angles to the bedding, and that the proiM
should be mainly set in that direction. If .the deposit is hori-
zontal, the weight generally comes vertically; but if the deposit
is inclined, the weight comes at a right angle to the inclination.
Some authorities hold it as a principle that all props should be
set parallel with the main presstire. Others, in order to guard
against possible side thrusts and a tendency of the ordinary
weight to ride to the dip in inclined deposits, purposely cause
a sufficient ntmiber of props to be set with their tops sli^^htly
uphill.
Sawyer fixes a maximtun and minimtim slope for the props,
varying with the rate of dip. He makes this maximum slojie
of the props one-sixth that of the dip, and the minimum slope
one-third of the one-sixth.
Proi>s are usually set with the butt end downwards, but not
always. Placing the butt end upwards adds a trifle to the
weight on the lower end, but the larger size at the top lessens
the liability of its being split by a coupling resting on it, and
also gives more surface for abrasion in hammering up against
a rou^ roof.
Joints in Mine Timbering. — ^In all mine timbering, the object
is to so form the joints that no fastenings will be necessary and
that the pressure from the surrounding material will keep the
joints tight. The reason for this is that metal joints usually
corrode rapidly in mines, while the timbering can be replaced
with greater ease if the sticks are so framed that, by relieving
them temporarily of the pressure from the sides and top, they
can be sinaply lifted out of place and new ones substituted.
The use of a framing machine renders it possible to frame the
joints more exactly than with hand framing. With hand-framed
MINING 183
timbers, the joints axe always cut a little free to allow for
any tinevenness in the surface, but, if machine-framed, they
are sure to be of the same size. As timber does not shrink in
the dix?ection of its grain, if the caps shrink slightly, they will
become loose in the space between the shoulders; hence, if
timbers are cut green and framed to the exact size, subsequent
shrinking may open some of the joints. This may be obviated
by keeping the timber moist.
Undersetting of Props. — Props at the working face should
not be set at right angles to the inclined floor of the seam, but
should be underset, and the greater the inclination, the greater
the imderset. The amount of underset should vary with the
inclination of the seam, and should not be so great that the
props will fall out b^ore the roof has tightened them.
Forms of Mine Timbering and Underground Supports. — The
timbering of a mine may be divided into two heads: timbering
the working faces and timbering the roads. The roof may be
supported (1) by packing the waste places entirely where
sufficient material is obtainable for the purpose, and timbering
the face and roads; (2) by partially packing the waste, by
cribs or stone pillars with intervening spaces, and by tim-
bering the face and roads; (3) by timbering the face and roads
and supporting the roof in the waste places by wooden or stone
pillars, but without any packing; (4) by timbering alone with-
out any packs or walls whatever; (5) by supporting the
main roads with brick arching, or by steel or iron supi)orts.
The accompanying figures show a number of the common
forms of mine timbering and underground supports.
Fig. 1 shows a post a and breast cap b. The breast cap b is
also sometimes called cap, head-block, headboard, lid or bonnet.
Sometimes the posts are placed upon blocks of wood similar
to the head-blocks or headboards, the block being called a sole;
at other times, two or more posts may be set upon one long
block of timber called a siU. When posts are used in inclines,
they should not be set perpendicular to the foot and hanging
walls, but should be underset slightly, so that any tendency
of the hanging wall to settle will bring the posts nearer at right
angles to the walls, and so tighten them; the amount of under-
set should never be more than one-sixth the pitch of the deposit.
Fic. 1 Pig. 2
Fi£. 2 represents a sfuji d. which is used either to k^ep the
walls of perpendicular or al«ep]y mclined beds or veins apart,
to support plaoldng o> lagging as a working platform, or as a
platform upon which to pile ore or rock.
Pig. 3 represents OKkermeei. which are simply timber frames
used in coal mines for holding the face of the coal in place while
it ifi being nndercut. They are composed of a pole c extending
sJong the face and supported by short stulls or braces d, tfae
whole being tightened into place by the long stulls b.
timbers and filled with
: shanty built up of
Pic. 4 Fic. 5
is a cribbing framed from round tiinbera laid ddn to slcin, and
Gangway or Level Timbers. — Fig. 6 is a set used in the caAe o£
an extra-wide ffangway, there bdnif a center prist under the
middle of the cap. This form of set may be provided with a
Bill when the floor of the drift or gangway is soft. Pig. 7 shows-
by bridging and used whew
such bad ground is encountered
id the refuUr set throngb which the spilea or
: driven. Fig. S ahov& a form of drift aet sotue-
rery heavy or sweUing ground. This method
of frajning the thnbera shorten
Lii additional brace b is placed parallel
covered with plank Lag^ng a, so as to
m provide a passage above
I the regular drift, which
1 form of drift si
The cap is usually in
the cap c. The joaalo
hird the thickness of the cap.
. length that the posts t hsve
MINING
:Juiatioii or batt<r as shown in th« illuKtration. thui givi
DTC* of the drift, which may be necnsaiy for drai
^s, watH pip«, etc. at the sides of Ihe track. When 1
ia not composed of solid material, the poGta I may be i
a sill that is framed to fit the legs in a manner similar
bown for the cap. The joegle cut in the dl should nei
a than 1 in. nor more than one-third the thi^lm^^ of t
The sill is usually composed id lighter material than t
> flattened on one or both sides, and is soinetimes used
FiQ. 11
Pig. II ibows a ftl 1 and the cap or foUar e. used where one
wall is of firm material. On one end the cap is placed in a
hitch. When the collar is supported in a hitch, it is sometimea
said to be needled, the operation being called ruBlling. The
bottom of the post a is also sfcuthI b a bitch, in case there is
any side prenure. To keep the surrounding mateiial in place.
lauini is necenary, as shown behind the timbers in Pigs. 10
made from saved material and driven close together.
Fig. 13 aiustrates a method of spiliHg or foritoUnt; o are the
posta of the regular set, b the caps, and ( the to^i hridgiag. The
front ends of the spiles from any given set rest on the bridging
grouod, so as to provid*!
, room for the placing of
j^ theneit set, tail-titcis i
mn placed behiDd tbe
back end of th« spiles as
they an being drivpn.
Alter the spiles have
been driven forwards the
denred amount, another
boards b. which are held in place by props /, that rest against
the forward set. When breast boardi are used, it is ueually
□ecesury to employ foot and collar braces between tbe seta,
lo as to transfer the pressure of the breast back thioufch several
Pift' ISshowsamethodof placing drift sets in the CB$e of very
heavy or swelling ground; a are the posts, b the caps, c the silla,
d the coUat braces that bear
Shift Timberinc,— Fig.
The method of framing the different
Pig. 15 repnaenU cribbing sometimes used for ahAfta. It is
tons are let into the whII pUtes u
so placed that they will bieali ioint
of the wall plates, thus preventing i
(rom bulging into the shaft.
and wall plftt«a an halv«d together oa
us is oftep fonned at D. This consttuc-
cutting of a toion od the end of the post P
ta ehown; 5 is a 2 in.X2 in. strip nailed along the center ot
the back of the wall and end plates as a support for the laggine
that IB placed outaide of the sets. The i^'gr^g is usually com-
posed of 2 in.X3 in. plank.
Fig. 17 shows the use of haiiftri between the individual
square sets. The hangers are bolts provided with hooks on the
ends, and are used to support the sets as the norlc pngnnea.
the posts serving to keep the sets property spaced, while the
f hangers keep the sets tight agaitut
the posts. Hangers are not always
left in permanenlly. but may be
removed after a considerable sec-
tion of the shaft has been completed.
Pig. IS shows a method of apply-
ing mugh squan sets, made from
round timber, to the sinldDg of a
siDBll prospectbig shaft bf the use
_■ _ of forepolkig; A is the fiirt set erf
^■" timbers and J is the second. The
hangers are made from 2 in. X 4 in.
timbers Psiriked to the seta and to the supports G, The supports
G from which the seta are himg are placed over sills 8. which are
situated at a convenient distance from the collar of the shaft.
192 MINING
At D u thomi the lagging ot the first act that is usually spiked
to the set and at K the lorepoling. which becomes the Itieging
betweni the second and third sets, and C the tail-^ecei used
for forcing the tagging out into the ground. The hangers
between the next two seta would be spiked to the other two
timberaoftheseta. Where the bottom of the shaft is very bad,
it may be neceaauy to use breast boards, as ahown in Fig. 19,
in which the shaft is being put down by means of square sets
and forepoling with the use of breast boards-
PlO.
20
Square
Sol^— Fig.
20 illusti
rates
one method
1 of framing
material for use
liriesi
are the post
5. B the .
and silk, while C are the
sliUl/ii. The
; method
aming the joi
nta is dearly
lade-
jftl
are framed al
ike. Pig. 21
ethodoffr^
■beisforsqua;
re sets. The
s / and £ are
usually ;
made
., d. e. and i.
ach2
m the dia
T of the post
that is to be
Md;i
Uld
fcasageneral
rule is cu'
tdow
m to an angle
of about 45".
MINING
L«nding», Pliti, « Statiani.— Pic. 22 L
gtation. The ngulBr
shaft is coDIinued
■5 ~V
reduced to tlmt o
MINING
The height of t
the drift or level i
Fig. 23 shows i
a represents
n. the t
Fig. 25
of the formation
rs all being
^s or by Btulls. Here
stulls and c the tim-
iked to the stulls and
itnngen for the car tracks
. the car track from the level
Light across above the akip
naste material in the lev^
anbination of stone or brick walls with wooden caps
ind lagging for the roof. Fig. 27 illustrates the hning of a drift
ir level supported by means of iron or steel shapes bent into
lie form of an arch and used for the support of lagging.
or stull that lias been
It is composed of two
UINING
Fig. 29 illiutntca a masonry shaft lintng supported by <| '
nteani of casl-iron plates C set in bell-shaped cavities
in the walls of the shaft. As the masonry (^ that sect
from below is built np toward that above, the overha
ing portion D lb cut out a little at a time, and
masonry from below built up under the plate so t
It in the wans of the shaft. The blodo of arti- ^
e are provided with inclined bearings C, which
transmit a portion of the downward thrust of
in the direction of the arrow.
foture,™™^ "«=■=«
•xnr form of support.
Traaet.— Figs. 31 and 33
Illustrate the vaiious timbers
and methods of cutting the jointa
Pig. 29 Pta. 30
for ordinary railroad treaties. In Pig. 32 (a) is si
manner of framing a pile trestle, whil
ncf of placing timbers and cutting
196
MINING
trestle. Pig. 31 represents bents of a frame and pile trestle
and the side elevation dL a low pile trestle. Fig. 33 shows a bent
3
z-y-r ..*. jr
c — V : • ^
1 *' r
Pig. 31
of a framed trestle that is fastened together entirely by means of
drift bolts, no joints whatever being cut.
Pig. 32
The various parts of the trestles shown are numbered; their
names are as follows:
Gainjng, dapping, or notching
GuHrd-TAil I
Jack-etringer
19d MINING «
joints for receiving the batter brace and post. Fig. 38 shows
how a tenon is sometimes formed on the top of the pile to secure
the cap. When the cap is secured by a tenon, the two are
united by a wooden pin shown in the lower part of the figure,
known as a treenail.
Pig. 39 shows how the cap may be placed upon a pile trestle
by splitting the cap into two pieces, a and b with the tenon c
the full width of the pile between them. Fig. 40 shows how
Fig. 42 Fig. 43
the cap is sometimes secured to a pile by means of a drift bolt,
and Fig. 41 shows how the same thing may be accomplished
with the use of a dowel.
Figs. 42 and 43 show two methods of longitudinal bracing
between the bents of the trestles for inclined planes, such as are
used at breakers or concentrating mills. Fig. 44 is an elevation
of a high trestle, showing the cross-bracing and framing of the
structure.
uiniNC iw
f Ta. ■ I 3
' ™ Pig. 45
Timba Hsad-Pranu* or HMd-G«*n. — Pig. 45 is the sini-
pleat farm of bead-gear. This consists of & verticsl post, which
carries the weight of th« aheave. etc., and a dia£ona] post that
approximately bisects the angle between the rope from the
Pig. 48 shows am
the main upright leg is
there 13 also another ver-
tical member on the op-
posite side of the shaft.
[ The inclined leg is also
5 braced and connected to
aA to protect the m
which the timbers e
METHODS OF WOHKIMG
ind separate proposition,
le general principles here
m mine. Every system
a amount of the deposit
MINING 201
in the best marketable shape and at a minimum cost and
danger.
The elementary conditions affecting the extraction of coal
are: (1) weight of overlying strata or depth of deix)sit, (2)
strength and character of roof, (3) character of floor, (4)
tezttire of bedded material, (5) inclination and thickness of bed,
(6) presence of gas in seam or in adjoining strata.
Open Work. — Open work appHes to the working of all
deposits that have no overburden, or to those in which the
overburden or overlying material is stripped from the portion
of the deposit to be removed by hand, steam shovels, scrapers,
etc. It includes particularly all quarries and placer workings,
and can be applied to many mineral and coal deposits. Open
work may be divided into two general classes: Where the
whole or a greater part of the deposit is of value and has to be
removed, as in quarries and in ordinary mines; where the val-
uable portion is but a small part of the whole, as in placers or
fragmental deposits carrying gold, platinum, etc.
Closed Work. — ^Under the heading of closed work, it is
customary to divide the methods of mining into coal-mining
methods and metal-mining methods. This classification, how-
ever, is not entirely logical, for identical methods are applied
regardless of the mineral. A more logical classification is one
based on the position, character, and thickness of the deposit,
but the older classification has become so firmly established that
it is not advisable to disregard it entirely.
The typical and most extensive bedded mineral deposits
are of coal and iron ore, and of these the former is by far the
more extensively mined. A description of the several methods
of mining coal beds will therefore comprise not only all the
essential points in the mining of other bedded deposits, but will
include a ntmiber of points not usually considered. The chief
of these is the presence of explosive gas in such quantities as to
influence the choice of a method of mining.
The panel system divides a mine into districts or panels by
driving entries and cross-entries so as to intersect one another
at regular intervals of, usually, about 100 yd. Large pillars
are left siurounding the workings within each panel, and any
method of development may be used for each panel. This
202 MINING
system has the following advantages: Better control of the
ventilation, because the air in any panel may be temporarily
increased or decreased, as required; an explosicm occurring
in one panel is less liable to affect the other workings. Coal
may be extracted, pillars drawn, and the panels closed and
sealed off independently of each other. Greater security is
afforded against creep and squeeze. Coal that disintegrates
on standing can be quickly worked out.
Bearing In, or Undercuttiiig. — In any method of mining
where the coal is undermined, advantage should be taken of
the roof pressure to assist in breaking down the coal and in
bearing in. The fact is often overlooked that the roof pressure
upon the face coal makes it brittle and more susceptible to the
pick, and the good miner starts a shallow mining in the under
clay, or lower coal, and carries it the entire width of the face.
Such a gradual system of mining throws the pressure on the
coal face gradually, and the coal breaks in larger pieces. The
depth of the tmdercut depends on the thickness of the seam and
the other conditions.
SYSTEMS OF WORKING COAL
There are two general systems of working coal seams, the
room-and-pillar, and the longwall. There are, however, a
great number of modifications of each so that it is often difficult
to exactly classify a given method.
Room-and-Pillar System. — The room-4ind-piUar system, also
known as the pillar-and-chatnber or bord-and-pillar, is the oldest
system, and the one very generally used in the mines of the
United States. The coal is first mined from a number of com-
paratively small places called rooms, chambers, stalls, bords, etc.,
which are driven either square from or at an angle to the haul-
ageway. These openings may be wide or narrow, and may be
a roadway, incline, or chute, according to existing conditions.
The pillars that are left between the openings in the original
workings support the roof, and usually are subsequently
removed. All forms of room-and-pillar workings become
impracticable when the thickness of the pillars necessary to
support the roof pressure much exceeds double the width of the
breast openings.
Fig. t ^owi a typical room-tuid-[nUar method for irorkiDg
1 appiaiiiOBtelr hoiiniiltHl aetun ot coal of moderate thkloua*
to 10 rt.), and with a fairly good roof and b
Fic. 1
The typical room-and-pillar plan, Fic- 1. ihowg the main
heodingi and the roonu driven paralld to the direction of the
dip, and the crofla-headingi parallel to the strike, but in moit
coal seams there are vertical cleavages, called dtati, which
croaa the coal in two directions about at right angles to each
other, Pau dtaU are the more pronounced, while the end, or
btiU. iltali are the shorter, less pronounced joints. The direc-
tion of the face with respect to the cleata is of prime importance
t* greatly facilitating, or retarding the m i n i n g of the coal.
204 MHJINC
Pig. 2 shows the different podtions that the face may occupy
with reaped to the direction of the cleats. The angle of the
breast dependa on the hardness of the coal and freedom of the
cleats, and each method has its peculiar adaptation to the vary-
ing conditions o( the coal seam. WTien the face cleats are work-
end on. The md-oii
I maftod is best adapted
Fic 2 breaks readily along
ably hard, the Itms-Aorn method is adopted, for when the coal is
iU weight must be thrown somewhat upon The end cleats.
Pati on is adopted when the face cleats are not as free or numer-
The shorl-korn mtlliod is adapted to heavy roof pressure and
wide room pillais, as the face cleats are here quite pronounced,
and the pillajs between the rooms thereby weakened to a large
extent; hence, wide pillars are moie often employed when
Loncwall HeUiad of Mining. — In the loitgwatt lysicm, no
ily of the shaft. The method depends on produang a uniform
shaft itself, the coal being taken out all around and its place
filled with solid paclo, leaving only space for the roadways; or
a pillar of soUd coal cut only by the roadways, may be left to
support the shaft. The longwal! work may then be started
uniformly all around this pillar.
L^ngwall may he advancing or retreating. In loHgwaU
"' itti, mining begins at or near the foot: of the shaft and
MINING 205
advances outwards, forming a gradually widening and increas-
ing length of face to the boundary. The passages are made
through the excavated portions of the mine, and are maintained
by pack walls built either of the refuse secured in mining or
from material brought in from the stuface. Pack walls are
built on each side of the roadways, and at regular intervals in
the gob or waste area, and the roof settles firmly on these packs,
pressing them into the bottom, or compressing them imtil the
roof subsidence is complete. The height of the main roadway
is maintained by brushing the roof or lifting the bottom. Long-
wall advancing is better suited to thin seams than to thick ones,
to flat rather than pitching, and to good roofs and hard floors.
In longwall retreating, entries, gangways, or headings are driven
to the boundary or to other convenient distances inbye, and
the pillars between these entries are then drawn back toward
the shaft; this is also called working home. Longwall retreating
is adapted to thick beds; to those liable to gob fires; to seams
of hard coal having a considerable pitch; to pockety, or irregu-
lar seams; and to a soft and treacherous top. The air-course
is also less broken along the face, and better haulage installa-
tions can be made. Its chief disadvantage is the large amotmt
of dead work necessitated before returns are received. There is
no expense in keeping up the haulage road so far as creep or
falling roof is concerned, as the roads are all in solid coal, nor
is there any trouble fron; gob fires or water; and little detri-
ment to the working face is caused by the mine having to stand
idle for a time. If 'the seam is high enough for the mules or
horses, no rock whatever will need to be taken down. The
coal seam will be proved before 10% of it is extracted. The
ventilation in the retreating plan is as near perfect as it is pos-
sible to get it in practice. All the airways are tight, a thing
impossible to get in the advancing plan; and it is a compara-
tively easy matter to shut ofif fire or to allow a portion of the
working face to remain idle.
Longwall retreating is frequently used for working quite
limited sections of a mine in which the seam of coal is 16 to 20
ft. thick, and, inclined not more than 10°. A series of 8 or 10
pairs of headings are turned off the butt entry and driven a
distance, dependent on local conditions, where the working face
209 MINING
is foimed by drivizig noss-cute from one to the otber. Tliis
Face b carried bock on the retreating plan, allowing the roof
to cave in or setUe on the gob aa the work approachea the butt
snliy. In this way, any eittra weiglit, that would crush and
ruia the adjacent coal ii avoided. Thu method la alao used in
ond'pillar ayatcm. SometiiD
headinfiB at considerable distances apart, a no:
headings are drivoi compaiatively close together.
MINING 2m
by cross-cuts from 10 to 20 yd. apart. When the limit of the
section is reached, the working face is formed and carried back,
as in the other plan. This latter method is more suitable for
tender roof, or a coal in which the face and butt cleats are not
prominent.
Pig. 3 shows a plan of combined longwall advancing and
retreating. In the upper arrangement, or Scotch longwall,
the face is semicircular and the roads are turned o£E at angles
of 45^. This plan is suitable for seams up to 3 ft. thick with
a weak top, which pitch less than 20^ and is situated at almost
any depth. It is the one from which most of the longwall prac-
tice in the central coal basins of the United States is taken.
In the lower arrangement headings from 200 to 300 ft. apart are
driven in pairs to the boundary. Such a combination of long-
wall advancing and retreating insures an unvarying supply of
coal, for while one side continually leaves the shaft, the other
approaches it.
Timbering a LongwaJl Face. — The method of timbering the
working face depends on the nature of the roof, floor, coal,
etc. The action of the roof on the coal face is regulated almost
entirely by timber; consequently, when the coal is of such a
nature as to require little weight to make it mine easily, the
roof must be timbered with rows of chocks and, if necessary, a
few props.
Cribs, Pack Walls, and Stowings. — Pack walls should be
built large enough at first and kept well up to the face, to pre-
vent the weight coming upon the timber and also to permit the
roof to settle rapidly when the timber is taken out of the face.
Often the roof will not stand this second movement without
breaking, and possibly closing in the entire face. The face
should therefore be kept in shape, and just as soon as there is
room for a prop or chock, it should be put in immediately, and
the pack walls likewise should be extended after each cut or
web is loaded out. No waste material, except such as will
hasten spontaneous combustion, should be taken out of the
mine to the surface.
Control of Roof Pressure. — ^The working face of a longwall
working should advance up grade, but this face cannot always
be kept parallel with the strike. When the angle at the line of
208
MINING
face, made with the line of strike, is less than 90^, the greater
pressure of the covering rocks is thrown on the gob; when this
angle is more than 90*^, the greater i>ressure comes on the coal.
The angle made by the working face with the line of pitch varies
inversely as the vertical angle of pitch, or for a high pitch this
angle is small and for a low pitch it is large. Where longwall is
worked in adjacent sections, care must be taken to prevent the
advancing of one section throwing
a crushing weight on any of the
others, and thus producing a crush
or an uncontrollable cave. Where
the rocks are pitching, and a greater
portion of the cracks that cut them
rtm in lines parallel to the strike,
neither stone nor timber can effi-
ciently support the roof, which fre-
quently breaks off close to the working face.
The ends of all stone packs nearest the face of the coal should
be in line, and the ends of these pack walls should form a line
parallel to the face of the coal. Timbers set at equal distances
and in line along a longwall face are much more efficient in
supporting the roof than irregularly set timbers. Pig. 4 shows
the proper way of locating the pack walls and the face timber.
Fig. 4
NUMBER OF ENTRIES
The entries in a mine nay be driven single, double, triple, etc.
The single-entry system is only advisable under certain condi-
tions and for short distances because the ventilation must be
maintained along the face of the rooms, and there is but one
haulage way, which may easily be closed by a fall or creep.
Rooms are turned off on one or both sides of the entry. The
double-entry system is most commonly used. Two parallel
entries are driven, separated by an entry pillar whose thickness
varies with the depth of the seam, and connected at intervals
of about 20 yd. by cross-cuts or breakthroughs to maintain
ventilation. The triple-entry system is used particularly in very
gaseous seams requiring separate return airways; or, at times,
in mines where the large output reqtiires ample haulage roads.
It is usually applied to the main entries only, but sometimes.
MINING 209
also, to the cross-entries. In gaseous mines, the middle entry-
is usually made the haulage road and intake airway, and the
outside entries the retxim air-courses for either side of the mine,
respectively. A still larger number of entries even has been
suggested for deep workings where it is difficult to keep open
broad passages, but these have not been generally adopted or
tried experimentally to any great extent.
PILLARS
It is impossible to give exact rules or formulas for determining
the proi>er size of pillars. Each case in practice requires special
consideration, and in laying out the pillars in a virgin field it is
well to find out what the current practice is in similar fields.
In general, the thicker the seam and the greater its depth from
the surface, the greater should be the thickness of the pillar.
Shaft Pillars. — ^Various formulas have been given to deter-
mine the size of shaft pillars, and the results given by these
several formidas are very diverse.
Vfo
MerivaU's Formula,— 5 - \/— X 22,
\50
in which 5 » length of side of pillar, in yards; D depth of shaft,
in fathoms.
Andre's Formula. — Up to 150 yd. depth, have the pillar 35
yd. square, and for greater depths increase 5 yd. on each side
for every 25 yd. of increased depth.
Dron's Formula. — Draw lines enclosing all surface buildings
that it is necessary to erect about the head of the shaft, and
make the shaft pUlar so that solid coal will be left outside these
lines all around for a distance equal to one-third the depth of
the shaft.
Wardle's Formula. — Shaft pillars should not be less than 40
yd. square down to a depth of 60 fath. and should increase 10
yd. on a side for every 20 fath. increase in depth.
Hughes' Formula. — Leave 1 yd, in width of pillar for every
yard in depth of shaft.
Pamely's Formula. — Allow a pillar 40 yd. square for any
depth up to 100 yd.; for greater depths, increase the pillar
5 yd. for every 20 yd. in depth.
15
210
MINING
Calculating the sue ci pillar from each ci these authorities
gives the results shown in the accompaniring table.
8IZB OF SHAFT FUIARS
Authority
For Shaft
300 Ft. Deep
For Shaft
600 Ft. Deep
Merivale
22 yd. square
35 yd. square
40 yd. square
40 yd. square
33 i yd. square*
100 3rd. diameter
31 3rd. square
Andre
45 yd. square
Waxdle
60 yd. square
Pamely
65 yd. square
Dron
66f yd. square*
200 yd. diameter
Hugheff -
•
*Outside of buildings.
None of these formulas takes account of the thickness of the
seam, and the following fonnula, which takes account of this
very important element, was suggested by Mr. R. J. Foster,
in Mines and Minerals:
Radius of pillar -3 V5x7.
in which Z>» depth of shaft;
/ » thickness of seam.
Pitching seams require smaller pillars on the low side than
on the rising side of the shaft.
Room PiUars. — ^The relative width of pillar and breast is
dependent on the weight of cover, as compared with the char-
acter of the roof and floor, and the crushing strength of the
coal. These relative widths are determined largely by prac-
tice. Speaking generally, the narrower the rooms or chambers,
the higher is the cost in yardage, the greater the production of
slack and nut coal, the greater the consumption of powder,
track iron, ties, etc., and the greater the cost of dead work.
For bituminous coal of medium hardness and good roof and
floor, a rule often used is to make the thickness of room pillars
equal to 1% of the depth of cover for each foot of thickness of
the seam, according to the expression
MINING
211
in which PF^— pillar width;
t<" thickness of seam;
D «■ depth of cover.
Then the width of breast or opening is made equal to the
depth of cover divided by the width of pillar thus found,
according to the expression
D
in which TT^— width of room.
The accompanying table is for first working, with the design
of afterwards taking out the pillars, the width of the principal
workings being 5 yd., and cross-holings 2 yd.
DUNNS' TABLES OF SIZE OF ROOM PILLARS FOR
VARIOUS DEPTHS
Size of
Pro-
Size of
Pro-
Depth
Pillars
portion
Depth
Pillars
portion
Feet
Yards
m
Pillars
Feet
Yards
m
Pillars
120
20X 6
.41
1,080
26X14
.69
240
20X 6
.50
1,200
26X16
.71
360
22X 7
.62
1.320
28X18
.73
480
22X 8
.67
1,440
28X20
.75
600 ,
22X 9
.69
1,560
30X21
.77
720 '
22X12
.61
1.680
30X224
.78
840
26X16
.63
1.800
30X24
.79
960
28X16
.66
Extremely large pillars must often be left as a precautionary
measure to protect permanent haulage ways and surface
buildings, or to avoid any possibility of a break in the roof that
would cause an inflow of water.
Drawing PiUars. — Drawing pillars is about the most danger-
ous work the miner has to perform,, but the fact of its being
so is no doubt the reason why, comparatively si>eaking, so
few serious accidents happen in it. It is not so much that the
best, most skilled workmen are chosen to perform i>illar drawing,
as that the men, being alive to the dangers, are more on the
alert and careful to protect themselves. Methods of drawing
212
MINING
o
«0
s
to
to
to
o
»o
CO
o
eo
to
o
OC0OC0C^»^^^0>0>C«'^OQ0«-<N'^00
toto«pr^o»«-<too>'^«-i^cooe50'^'^"3
O«0(0C0«0t^t^t^000>O<-iC0t00»t0t^'«
,-i,-i,-i(-i,-4C4COt»
oc^a»^a)e^cococoa)'<4<coootoa»coto
QOOc^cococ»eooo^eo^Ocs;torHto
cocococo(«t^ooa&oc4-^t^co-^(
i-i i-i i-i i-i d CO <
o<-<coe^'-4^«oo>^cocooo^a)xeoto
• ••••••••••••■•••a
QQQi-iCOtOl^QtOOt^t^OOOtOWr^W
lO to to to to to to O (O »^ t^ 00 O •-< ^ O) QOt^
I-I I-I I-I I-I C4 to
oc^t^coo>«ooo>»^cootootO(Oo>e^co
• •••••••••••••••••
iOiOtOCOtoO>C4<^GOCOOXOCP^COO>«0
^•^■^^•^•*»ototo«5i^i^o>ocor^toi-i
^HrH 1-4 e^lO
0<-itOe^e^cp-<44t>;t>;tqtOOOQO-^COCO«0-
tototd«ot^odQcsitoo>"^«-5ocsicit6i-;pH
cocoeoeococo9^^-«>o«ot^ooocooo
i-if-iW"^
o^Hto^at^cococ^-^t^cooot^Oiooe^
• ••••••••••••■••••
cocococococoeococO'^"^to©i^oo»-"t^'^
^^co
p'-4'^a»cqcoo>to(0'^o^copcs;i-40oo>
totototocot^ooocJtOQOcoQoiectd'^cd
WWWNC^NWCOCOCOCO'^tOtOt'-Oi'^OO
i-^C4
OOCOt'-CSJOO'^OON'-'OSOCOtO'^NtO
OOOO^C»CO'^tOOO«-«'^Ot«-CiOt*tO»
W (N <N M CSJ N N C^ CSJ C^ CO CO ^ ^ to b- •-< W
OtOQtOOtQQtOQtOOtOOtOptOOtO
O>a000t<>t<>«O«tOw3^^C0C0CSCl*HiH
MINING
213
pillars vary according to the inclinations of the seams, the
nature of the roof and floor, and the character of the coal;
Pigs. 1 and 2 show the common methods. In Fig. 1, at A,
B, and C, the drawing begins by cross-cutting the fast ends
II
II
11
Pig. 1
of the pillars to obtain a retreating face. At A is shown a
method for soft coal and narrowing pillars; at B, a method for
wide pillars, the end being taken in two lifts; while the method
at C is for harder coal and shows it taken in three lifts. At
D and E the pillars are cut into stocks to be drawn by side or
end lifts, according to the character of the coal, the inclination
Pig. 2
of the seam, thickness of the cover, and the strength or weak-
ness of the roof and floor.
Pig. 2 shows some of the methods used in robbing the pillars
in steep pitching, thick beds of anthracite. To get the coal
214 MINING
out oi the pillar at the left of A , a skip is taken off the side, as
shown. Successive skips are thus taken off until the whole' is
removed, the miner keeping the manway open to the heading
below as a means of retreat. The pillar between A and B
is similarly worked. To remove that between B and C, a nar-
row chute or heading is driven up the middle, and cross-cuts
put to the right and left a few yards from the upper end.
Shots are placed in the four blocks of coal thus formed, as
shovnit and they are fired simultaneotisly by battery. This
operation is repeated in each descending portion unless the
pillar begins to run. A pillar from which the coal has started
to run is shown to the right of C.
SPONTAIVEOnS COMBUSTION
The cause of the spontaneous ignition of coal, chiefly, is the
condensation and absorption of oxygen from the air by the
coal, which of itself causes heating, and this promotes the
chemical combination of the volatile hydrocarbons in the coal
and some of the carbon itself with the condensed oxygen.
Another cause is moisture acting on sulphur in the form of
iron pyrites. The heating effect of this cause is very small,
and it acts rather by breaking the coal and presenting fresh
surfaces for the absorption of oxygen.
Gob fires are due to the spontaneous ignition of coal, and
are most likely to occur in pack waUs and gobs where there
is an insufficiency of air. Ample ventilation is the best
preventive.
COAL STORAGE
The coal store should be well roofed in, and have an iron
floor bedded in cement. AH supports passing through and in
contact with the coal should be of iron or brick; if hollow iron
supports are used, they should be cast solid with cement.
The coal must never be loaded or stored during wet weather,
and the depth of coal in the store should not exceed 8 ft. . and
diould only be 6 ft. where possible. Under no condition must
a steam or exhaust pipe or flue be allowed in or near any wall
of the store, nor must the store be within 20 ft. of any boiler,
furnace, or bench of retorts. No coal should be stored or
shipped to distant ports until at least 1 mo. has elapsed since
MINING 215
it was broufi^t to the surface. Every care should be taken
during loading or storing to prevent breaking or crushing of
the coal, and on no account must a large accumulation oi small
coal be allowed. These precautions* if properly carried out,
would amply suffice to entirely do away with spontaneous
ignition in stored coal on land.
When the coal pile has ignited, the best way to extinguish
tiie fire is to remove the coal, spread it out, and then use water
on the burned part. The incandescent portion is invariably
in the interior, and when the fire has gained any headway
usually forms a crust that effectually prevents the water from
acting efficiently.
MODIFICATIONS OF ROOM-AND-FILLAR METHODS
Some modifications of the room-and-pillar plan shown in
Pig. 1 can usually be applied to seams whose dip does not exceed
3**. When the pitch is greater, rooms are often turned off
toward the rise only, and the cross-entries driven correspond-
ingly closer together. When the pitch is from 6° to 10®,
the cars may still be taken to the face if the rooms are driven
across the pitch, thus making an oblique angle with an entry
or gangway, the rooms being known as room breasts.
Buggy Breasts. — For inclinations between 10** and 18®, that
is, after mule haulage becomes impossible and until the coal
will slide in chutes, buggies are often used. Fig. 1 shows a
buggy breast, in plan and section. Coal is loaded into a small
car or buggy c, which runs to the lower end of the breast and
there delivers the coal upon a platform /, from which it is loaded
into the mine car. The refuse irora. the seam is used in building
up the track, and if there is not sufficient refuse for this, a
timber trestle is used.
Another form of buggy breast is shown in Fig. 2. Here
the coal is dtmiped directly into the mine car from the buggy.
If the breast pitches less than 6°, the buggy can be pushed to
the face by hand, but in rooms of a greater pitch, a windlass
is permanently fastened to timbers at the bottom of the breast,
while the pulleys at the face are temporarily attached to the
proiM by chains, so that they can be advanced as the face
advances. The rope used is from | to | in. in diameter, and
tS UIIflJTG
ay form of ordinary horizontal windlass can be used. With
IB windlass pn>p«ly geaiKd, one man can easily haul a
UBSy to the fac« of a breast in a few minutes. Tie baggy
ins upon 20-lb. T rails spiked with 3} in. X } io. spilus upon
in-X4 in. hemlock studding sawed into lengths of 14 ft.
Chute BroBiti. — Seams pitching more than 15^ aie usually
orked by chutes, or self-acting inclines. When the pitch is
ing surface tor the coal.
On incUni
itiona of
less than IS*
toZO'
arytopnahl
bhe coal di
]wn the chute.
Sheet
1 on pitches
above 30'
'. It must be
nbered that these pii
Iches are only fair avci
of the ooal.
To
mis from a
.. the slope' or
shaft
the basin, ai
test gangways
"^1«
■els first driven to tli
le property limits, and
the coal then
itmiNG 217
worked retreating toward the slope or shaft. Practice is.
however, usually contrary to this, and the upper levels or
gBjiEways are lumed off firat. mui-worldTis places opened otit
as rapidly oa the gangway is'drivea. Pig. 3 ahows a coethod
□f grouping moms that may be used where the pitch is from
8° to 20*. the straight heading beini-. driven on the atiilco
and the other heailings at such angles as w
for haulage putposes.
IHlUl-knd-StiiU Method.— The pillar-ai
modification of the room-anrJ-piUar, to w
breasts. ' TTie stalls are usually opened r
inude, according to o
1& yd. 1
Fic. 3
ai« oftfl] drivfln from J
m method carried I
cool fields of America:
ConDoUnille Regioii. — Pig. 5 shows '
in ConnellavillE. Pa ' '
The face and butt headinga
anglea to each other on
the face and the butt
of the coal. The face i
piUaii about Che aame
width. Pig.4,Aand£.
ahowB sin^e and double
ataUa- Thta ayitem !a
ad^ited to treak nwf
and floot. or stioiie roof
add aoft bottom, to a
fragile coal, or wherovtr
ample anppoct ia re-
quired, and ia paiticu-
laily useful in deep
Beams with great rooC
piessuie. DoubleaUdls
UININC
te coal. The hcAdin^ htq
I faces the diitHuv between
leaving a aolid rib of £2 ft.
1 the aide of each n
220 MINING
When necessary to protect the top or bottom, 4 to 6 in. of
coal are left covering the soft material.
The method just given is often applied to a whole series of
butts (4 or 5) at once instead of to each butt in turn. In this
case, work is started at the upper end of the uppermost butt
and progresses, as shown; but^ after cutting across the butt
heading from which the rooms were driven, the butt head-
ing itself and the upper rooms from the second butt, or that
just before, are drawn back by removing continuous slices
irom the rooms of the upper butt, and on across the next
lower butt, etc., all on an angle to the butts, until another
butt is reached, etc. This gradually makes a longer line of
fracture, which is only limited by the number of butts it is
desired to include at one time in the section thus mined.
Pittsburg Region. — ^The coal is worked in much the same way
as in the Connellsville region, except that a different system
of drawing ribs is used. The coal is worked on the room-and-
pillar system, with double entries, with cut-troughs between
for air, and on face and butt. Entries are about 9 ft. wide,
and the rooms 21 ft. wide and about 250 ft. long; narrow (or
neck) part of room, 21 ft. long by 9 ft. wide. Room pillars
are 15 to 20 ft. wide, depending on depth of strata over the coal,
which is from a few feet to several hundred feet. The mining
is done largely by machines of various types. Coal is hard,
of course, and, in many places, the roof immediately over the
coal is also quite hard. There are about 4 ft. of alternate
layers of hard slate and coal above the coal seam. Rooms
are mined from lower end of butt as fast as butt is driven,
the ribs being drawn as minings progresses. As the coal is
harder than in the Connellsville region, thickness of coal pillar
between parallel entries is somewhat less.
Clearfield Region. — The butt and face are not strongly
marked in the B or Miller seam, the one chiefly worked in the
Clearfield region. Where possible, these cleavages are followed
in laying out the workings, but the rule is to drive to the great-
est rise or dip and run headings at right angles to the right
and left, regardless of anything else. The main dip or rise
heading is usually driven straight, and is raised out of swamps
or cut down through rolls — ^very common here — unless they
MINING 221
are too pronounced, when the heading is ctirved around them.
The same is true of room headings, except that they are more
usually crooked, not being graded except over very minor
disturbances.
Reynoldsville Regicm. — ^The average thickness of the prin-
cipal seam is 6 § ft. and the pitch is 3^ to 4^. The coal is hard
and firm, and contains no gas; the cover is light, and on the
top of the coal there are 3 or 4 ft. of bony coal; the bottom is
fireclay. Drift openings and the double-entry system are
used. Both main and cross entries are 10 ft. wide, with a
24-ft. pillar between. The cross-entries are 600 ft. apart, and
a 24 ft. chain pillar is left along the main headings. The
rooms are about 24 ft. wide and open inbye, the necks being
9 ft. wide and 18 ft. long. The pillars are from 18 to 30 ft.
thick.
West Virgiiiia. — In the northern part of West Virginia, the
coal measures vary from 7 to 8 ft. in thickness, and have a
covering varying from 50 to 500 ft. The coal does not dip at
any place over 5%. In most places the coal is practically level,
or has just sufficient dip to afford drainage. The usual method
of exploitation is to advance two parallel headings, 30 ft. apart,
on the face of the coal. At intervals of 500 to 600 ft., cross-
headings are turned to right and left, and from these headings
rooms are turned off. These cross-headings are driven in pairs
about 20 or 30 ft. apart. Between the main headings and the
first room is left a block of coal about 100 ft., and on the cross-
headings there is often left a barrier pillar of 100 ft. after every
tenth room.
Theiheadings are driven from 8 to 12 ft. wide, and the roomsl
are made 24 ft. wide and 260 to 3Gb'ft.' long.* "A pillarls'left"
between the rooms about 15 to 20 ft. wide. These pillars are
withdrawn as soon as the panel of rooms has been finished.
The rooms are driven in from the entry about 10 ft. wide for a
distance of 20 ft., and then the width is increased on one side.
The track usually follows near the rib of the room. Cross-cuts
on the main and cross headings are made every 75 to 100 ft.,
and in rooms about every 100 ft. for ventilation.
The double heading system of mining and ventilation is in
vogue. Overcasts are largely used, but a great many doors are
222 MINING
used ID some of the mines. Rooma on worked in both dii
tioUp whea the gradea are slight, but when the coal dips 01
I%i th« locnns are driTCO in one diRction only; in thia e«
they ue made as much u 3S0 ft. long. It ia the custom Ct
to breolc about every third room into the croBB-beading abo
The floor of thb bed of coal, being composed of shale and fi
'day. olCen heaves, eapedslly »hen it is made wet. Soi
trouble is al timea eiperienced by having the floor heave by
reason of the pillara being too amall for the weight they support.
Alalianu Uethoda.— Pig. e shows the common methods uied
in working the Alabama coals. The seams now wcrking vary
from 2 to 6 ft. thick, and they pitch from 2° to 40°. Where the
seams are thin, tbe coal is hard, and pillars of about 20 to 30 (t.
are used to support tbe roof. The rooms are worked acroia the
pitch OB an angle of about 6° on the roil, Fie. 0- A, when the
MINING aa
coal does not pitch gnaXa than 20°; vhen the pitch ifl greater,
ehuta ate worked and the rooms an diiveo straicbt np tha
pitch, ai in Pi(. 6. B. In a few casea, where the pitch ia DM
Smter than 16", double moms an woclced with two loadwayi
in each coom, ai in Pig. e. C.
Omcic'b Cnak District, Hd. — Kg. 7 ihowi the metbod lued
in the George's Crsek Geld, Md. The coal shows no indicstion
of cleats, and the butu and headings can be driven in any
dinction. The main heading ia driven to secure a light grade
for hauling toward the mouth, Crosa-hefidings Tnal d n g on
angle of 35° to 40° aie usually driven diieetly to the rise, and of
dimensions shown.
Indiana Coal IColllg.— Pig. S shows the method as used
in Indiana. The entries are generally a ft. high, S ft. broad,
the minimum height required by law being 4 ft. in. The
rooms are from 21 to 40 ft. in width. The mines are generally
shallow. The room^ in Pig. S are shown as widened on both
ribs, but a more usual method in this locality is to widen tbe
room on the inbye rib, leaving one straight rib for the protection
of the road in the room.
Iowa Coal Mining. — Tbc entry i»llara along the main roadi
■re S to S yd. thick, for the cross entries 6 to fl yd., and foi the
rooms 3 to 5 yd. Room pillars are drawn in whoi approaching
a cross-cut. Both room-and-pillar and longwall methods ore
ID use, with modifications of each. In the room4nd-piUar
method, the double-entry system is almost invariably used in
the larger mines. Rooms are driven off each entry of each pair
of cniss^ntriea at distances of 30 to 40 ft., center la center. The
rooms are S to 10 yd. in width, and pillars 3 to 4 yd. The
Toomsarenauowforadistanceof 3 yd., and then widened inbr«
at an angle of 45° to their full width. They vary fiom 60 to
100 yd. in length, and the road is carried along the atraight rib.
When double nwma are driven, the mouths of the looms are
40 to 50 ft. apart, and they are driven aarrow from the entry
a distance of 4 or 5 yd. A crosscut is then made connecting
them, and a breast 16 yd. wide is driven up 50 to 00 yd. The
at of the shaft, and on both
irned at an angle of 45^. or
These are spaced 10 yd.
MINING
225
diasonal road. Panel breaala
are used where th
lecot
ditions
:ze. Rooms
med
off «ntri« and are anansed i
in seU of 6 1
o 12
kwitli
a pillar 10 to 20 yd. wide bet
neen the sets
, of IT>
When
n the
entry,
they ore connected by cross.
It. Packs ar.
i built
and the root
allowed to settle, as in loncwall. The wid
epiUa
out aftff the roof has settled.
Teria, Cal.— The Tesla.
Col., method is shown in Pig. 9
lie coal seam averages 7
ft. of clear coal, and pitches 60'
•his system was adopted i
ipidly; for, at this point, :
1 short-grained, slate cap rock cami
floor is a close blue slate and has a decided heaving tendency,
the roof is an eicellent sandstone. There is a small but
troublesome amount of gas. Two double chates are driven up
the pitch at a distance of 30 ft. apart, connected every 40 ft, by
320 iilNWC
croB-cuti. One &de of each chut« k D«ed for 4 coaI cfau
the ather for a nuuiny and air-coune. At a diitancs of
apart anull gangmye are driven psnUel with the nuii
^an^prays. TheiB are continued from each chute a dj
of 300 ft., if the conditions wuranl it. The top line i
altacked from the back end and the coal is worked i
cleava^ planes; the breast, or room, therefore amsiat
Ttc. 10
12-yd. face, including the drift or gangway through whicb tbc
coal u carried to (he chutes; a rib of coal (3 or 3 ft.) is left
between the breaats to keep Che rock from tallins on the bnait
below. Thus in each breast Che miners have a pforldng face of
about 16 or Ifl yd,, and aa the coal is directed to the car br a
light chute, moved along as the face advances, the coal is
btsa tbs falHiiB ooal. as s minimuin ol handling is thiu obtaine
Pig. 10 ehowB snotha ayatem used in No. 7 von at the ui
pUce. Tbe •enm averaaa 7 ft. of Goid. The roof in shelly «
brtaki qokkly. hence the coal mint be mined npidly.
Pig. 11
Hew C^MtiMf Colo. — The following method ia uaed At New
Cutle. Colo., for highly inclined bituminous teams. Thecoala
mined are only fairly bud, contain coniiderable gas. and make
much waste in mining. Pig. 11 abowa the method tued for
auactiog the Wheeta oc thicker vein to its full width of 4S ft..
MINING 229
and the E seaxn 18 ft. thick, excepting that left for pillars.
Rooms and pillars are laid out tinder each other in the two seams
whenever practicable. Entries are along the foot-wall; 30 ft.
up the pitch is an air-course. Rooms and breasts are laid out
as shown in B and C.
MODIFICATIONS OF LONGWALL METHOD
Pig. 12 shows a good arrangement of the main and temporary
haulageways in a flat seam. The chief object in any plan of
longwaU workings is to have the permanent roadways the
arteries of the system, providing the most direct route from all
sections of the mine to the shaft. The temporary roads or
working places are only maintained for a distance of 60 to 100
yd., until cut off by subroads branching at regular intervals from
the main roads. The full heavy lines indicate the permanent
haulageways, except only the main intake airway (12 ft. wide),
running west from the downcast shaft D. and the main return
air-course (12 ft. wide) leading from the face on the east side
to the manway around the upcast {/, which is the hoisting shaft.
The full light lines indicate the diagonal subroads, driven to
cut off the working places, shown by the dotted lines. The
stables are located as shown in the shaft pillar, between the two
shafts, where they will not contaminate the air going into the
mine, but will receive air fresh from the downcast and discharge
it at once into the ujx^ast current. This position also affords
ready access from either shaft in case of accident, and for the
handling of feed and refuse. The ptunps may be located in any
convenient position at the foot of the upcast, llie shaft
bottoms arl driven 14 ft. wide nearly through the shaft pillar,
and are continued 10 ft. wide north and south through the gob.
The width of all other roads and subroads is made 8 ft.
METHODS OF MINING ANTHRACITB
A i>erf ectly flat seam of anthracite is seldom found in America,
and even where a portion of the seam may be found lying com-
paratively flat, such sudden changes in dip must be expected
that a system adapted to working on a pitch is almost univer-
sally used. A breast may start on a low pitch and the pitch
may increase gradually until it becomes vertical, or the reverse
230 MINING
may be the case. The deat is usually lanVing in anthracite,
and the direction of driving the breasts is determined largely
by the pitch and by haulage considerations.
For pitches up to 30^, the methods already described are,
in general, applicable, with certain changes due to local con-
siderations. There is considerable difference in the methods of
opening rooms in anthracite and bituminous mines, owing to
variations in the characteristics of the coals and to the fact that
anthracite will slide on chutes of less inclination than bittuninous
coal. Where the pitch does not exceed 4^, the rooms are turned
off at right angles to the gangway. In moderately thick coal
seams, pitching between 4^ and 18**, the rooms are generally
driven across the pitch, forming room, breasts, thus securing a
grade that permits the haulage of the cars to the face.
There are two methods of mining thick .coal in breasts when
nearly flat: (1) The breasts are opened out and driven to the
limit in the lower bench of coal, and the top benches are blown
down afterwards, beginning at the face and working back.
(2) When the roctf is good and there is no danger of its falling
and closing up the workings, the upper benches may be worked
in the opposite direction, beginning at the gangway and driving
toward the limit of the lift, or the working of the upper bench
may follow up that of the lower bench. When the seam is less
than 12 ft., the top is supported by props; in thicker seams, the
ejcpense is so great for propping that but little attempt is made
to support the roof. In the thicker anthracite seams (notably
the Mammoth), the coal in the breasts is so worked as to make
an arch of the upper benches of coal, which acts as a temporary
support for the roof, the coal in the arch being exthicted when
the pillars are robbed.
When the inclination of anthracite seams is less than 30^, the
breasts may be opened with one chute in the center, which ends
in a platform projecting into the gangway, off which the coal
can be readily loaded into the mine car. When this method is
employed, the refuse is thrown to either side of the chute. If
the pillars are to be robbed by skipping or slabbing one rib
only, most of the refuse is kept on one side. Sometimes, when
the top is good, and the breasts are driven wide, two dmtes are
used, but the cost of making the second chute is considerable
•Dd u thenfOce oot ulviKble unlcH necadtBtad by ths method
at TcntiUtioa employed.
Pig. 1 ihowA A panel lyston thmt givei good renlti in thick
•eams pitching from lS°to4fi°, where Che top i« brittle, the cost
£ree, And the miBc giBeoua. Roome or bremjti ue tamed off
the gangway in pain, at intervali erf abont 80 yd. The breast*
are about 8 yd. wide, and the pillaT between about 5 yd. wide,
which 19 drawn back as soon as the bieaati reach the airway,
near the level above. In the middle of each large ptllar between
the several pairs ot breasts, chutes about 4 yd. pfide are driven
ftom the gangway up to the airway above. These are provided
with a travriing way on one side, giviim the miners free access
to the workings. Small headmgi are driven id the bottom
bench of coal, at right angles to these chutes, and about 10 or
20 yd. apart. These headings are continued on either aide of
the chutes until they intersect the breasts. When the chute
and hewlings are Gniahed, the work ol getting the coal in the
panel ia bef^un by going to the end of the uppermost heading and
and a wArldng face obliqoe to the heading is formed. This face
is then drawn back to the chute in the middle of the panel.
After the working face in the uppencost section has been drawn
back wme 10 or 12 yd., work in the next section bidow is bceiw.
and so on down to the gangway. Both sides of the pHloi are
worked similarly and at the same time toward the chute.
Soisllcw
1. or buKgies, are used i
loconv
ey then
»l from the
WMidogfac
s along the htadinfis t
hute, where it ia run
down to th«
gangway beh™ and loaded u
uto the regular mine
cars. This Systran affonls a great i
lsgr«c
rfasfety
toihework-
f a f all of roof or <Yal occur.
1 reach the heading in
every
few sec
iHidsandbe
perfectly safe. A great deal of r
work mi
list be done
The breasts
are driven ir
1 pairs and at intervals.
togetE
.fair qua
ntityoftoal
while the oa
rrow work is being don,
;,aadl
hey ate.
Ktanenen.
tial part of the sysl
cheapness with whii
Batlely Working.
einended up along tl
(ace, either by planki
a jugular manway.
™ in Fig. 3, (»:
UmtNG 233
plank, are made aa nearly air-tight as poflsible, to carry the air
from the heading o to the worldug face. Pig. 2 ahova a bicast
on a pitch too at«ep to enable the miner to keep up to the face.'
In Beams of leisa than Sfi°. the platform / shown neaf the face of
the breast is unneccessuy. and in seana thicker Chan 13 ft. it
caimot be built; hence, thia method of wttrldng is appUcahle
only to beds pitching more than 35°, and to thin seams.
The coal if separated from the refuse on the platform /, and
is ran down the nuuiway chutes and loaded into the cars from a
platform projecting into
platform to deaden the blow
from the falling coal. The
it. - This plao can also
employed in thick seai
having a heavy dip, if then
enough refuse to GH the ct
lars a. are used to form the .
manways b, aionG the sides of
the breast; and <« is a section ^"^- ^
through the same lii» when upright posts o are used to sup-
port the plank in fanning the mimwavs &- The refuse in these
cases only partiatty fills the gob.
In working very thick seams on heavy dips, where there is not
enough refuse to fill the middle of the breast, the miner has
nothing to stand on. the platform being inipracti[:able; there-
fore, it is necesaaiy to leave the loose coal in the breast. Loose
solid. This smpluB is drawn out through a central chute. If
the root is poor, the movement of the coal will not in this way
cause it to fall and mix with the coal; and if the floor is soft;
ty and bloddns the ventit^
[eATUig the looAe coal in the cefiter of the bieAit ondiiturbed.
until the limit is reached.
SiDcla^hDte BittMy. — To prevent the coal from lunninB
out thnjugh the chutea, the opening into the breast a closed by a
battery constructed by laying beavy logs acrosa the openings,
as shown at b. Fig. 4. or elM built on propa, as shown at b. Fig.
le coal may be drawE
Icp by a covering of plank,
4 is a plan and Kction of a breast opened up by a uuglo
The plan A is taken on the line m n ahovm on the
plan A. The pitch is great ai
MINING 23G
the furplu being drawn off >t th« battery b and run into th« cu
■tuidiiis on the Banswrny ( tbRngh the cbuM f. A maawsy w
is made jUont e&cb side of the bnast, for the purpoee of ventila-
tion and afiording a pamae for the men to reach the warldDg
face. The hesding a is luoi for an air-courai! between breaati.
Tlie main airway h 'a driven over the gangway (. where it iriU be
well protected.
Pig. B
through lide chutes, as the coal will move principally along the
diddle of Che bmut. When the breast is worked up to its
limit, all the looae coal la run out of the breaat and the drawing
back of the pillan ia conunenced, unlen for some purpose they
■re aUowed to stand for a time.
Dvoble-ChDM BatlUT.— Pig. 5 Bhowi a plan and section of
daabl»-dnite breasts used in very thick seams having a heavy
dip. The breasts are entered by two main coal chutes c, each
of wfakh is provided with a battery b. throu^ which the coal is
drawn. A maoway chute hi is driven np througfa the middle of
the pillar ior a few yaiis and is thea blanched in both directiaoa
until each branch (slant chute) intersecta the foot of a breast
opBT the battery b, aa ihown. The jugular manwaya n, are
started at this point and continued up each side of the breast.
The main airway h ia driven in the aolid thnjugh the atump A
above the gangway. By driving the main gangway g against
the roof, as shown, the pitch of the chute is lessened, and the
loading chute c is more readily controlled.
When the main gangway ia not driven against the roof, a gate
ia placed in the chute below the check-battery, which eiuiblea
the loader to p«>perly
chut«, from which it
loaded through an Hi
tight ebecli-battery.
ersect the airway. The
reaat is opened nut just above the
way. a battery being bui
t in the airway immediately above
riven from the gangway up throng
middle of the stump ur
ta it intersecta the airway, and a
P door is placed at this pi
int to confine the sir. This man'
>■ ia made about 4 ft.X
B ft., or smaller,. according to the
UmiNC 237
Pig. 8 shows B less oomplicated plan than Fig. fl. The main
cbutes n. are diiven op to th« headioe c. from which the brea3t
is opened out; a log battery is built at the tap at each chute at
the points marked a. The chutes are used for drawing the
used lor tiavelinB ways. A check-katl*ry b is placed in the
chute to prevent the air-current from taldng a short cut from
the gangway through the chute to tlie breast airways. Tliis
check-battery is of great assistance Itj the loader when the chute
has H very steep pitch, as he can readily control the flow of coal
Fig. 7
All these methoda aie open
to the object
lion that
in case
mt to the breast n
lanway. by wl
hich the
flow of
air, shown by the amiws, is ol
isolating the
breast in which
the accident
and the
beyond it is <
mtirely
stopped.
the pillsi A
in left-
hand breast,
in Fig. 8. is left
m each breas
It to pro
tect the
R«k-Chut
s Hinlng.— Pig. 7
showsasectu
inof twi
1 seams.
separated by
a few yards of t
oi-k. Chutes
from 4i
to 7 ft.
high and 7 to
kfromtl
way or level;
[to the level 1 in il
le seam above,
. at such .
an angle
Pig. B shows how one or more sauu are worked by cormectin^
them by « )kmt irifl. or (HHnrl, driven horiioDtBlly acKMs the
measures, through which the cod &om the Adjacent Beuns in
taken to the haulase-way leading to the landing at the foot of
the slope or shaft. Tunnels are Knnetimes driven ttoritontallir
throus^ ^^ taeaaures from the surface, t
TbiB lower seam of coal
level I. comkected by a tunne
BoncwILy t- in the thick seam. The stone drift may be
extended right and left to open seama above and bdow tlv
thick seam. This tunnel, or atonediift. is never driven under a
breast in the upper seam, but directly under the middle cf the
pillar.
len the coal is very hard,
le loose coal nearly all ntd
MINING 230
out through the chute 5 into the gangway g. The monkey
gangvMiy m is driven near the top as a return airway, and is
connected to the upper end of the chute 5 by a level heading n,
and to the main gangway £ by a heading v. These headings
are driven for the purpose of ventilation and to provide access
to the battery in case the chute s should be closed. In the
lower seam, the breast is still being worked upwards in the
CMrdinary way.
FLUSHING OF CULM
From 15% to 20% of the coal taken out of an anthracite
mine, according to the methods used in the past, became so fine
in the course of preparation through the breaker that it could
not be used or sold, and had to be piled away as refuse. Recently
the coarser portions of these culm piles have been screened
out and sold for use as steam sizes, while the finer part, together
with the fine material from the breaker, has been carried back
into the mines with water to fill the abandoned portions of the
underground workings.
This culm is carried through a system of conveyors to the
hopper, usually an old oil barrel, and the stream of water is
conducted into the same hopper by a 3-in. pipe. The culm is
then carried by the water through a pipe from 4 to 6 in. in
diameter, which passes into the mine through the shaft, bore
hole, or other opening, thence along the gangways to the cham-
bers through the cross-cuts, and to the point where it is desired
to deposit the culm. The bottoms or outlets of the diambers
to be filled are closed by board partitions fitted closely, or by
walls of slate or mine rubbish. The culm, as it issues from the
end of the pipe, takes a very flat slope, and it is carried a long
distance by the water, which ultimately filters through the
deposited c\ilm to the lower ];x>rtion of the mine, to be pumped
to the sturface. When the chamber is filled to the roof, the pipe
is withdrawn and extended to the next place to be filled, and
so on.
The amount of water used depends on the distance to which
the culm is carried and the slope of the pipe. From li to If
lb. of water is reqtiired to flush 1 lb. of culm to level and down-
hill places; 3 to 6 lb. of water to 1 lb. of culm to flush up-hill
240
MINING
for heights
varying fr
om 10
to 100 ft. •
ibovB the level of the
•baft botb
sm. Any
le amount
elevatii
f water
m of the
pipe very nutteriaily
Torew
re the pilla™ after
ling breasts have been
filled with
face of
along the gansway is
flttadied. and a road driven i
the pLllai. sidittiDg it.
asdiowQin
the accompanying
. This road may be the
full width a< the piUu,
.but in
general it is
necessary to leave the
stump of coal on either
sidetokeepap the fine flushed
breaata.
The thickneas of this
flushed
1 the condition of the
EXPLOSIVES
two genetal classea: Low
explosites or direct-exploding
msteriab, and high explraives
or indirect- exploding mate-
rials that require a detonator.
Tbe characteiistics of a good
blasting explosive are; suffi-
cient stability and strength, difficulty of detonating by mec han ical
shock, handy form, absence of injurious effects un the user.
Gunpowder or black powderis a low explosive; its compositiorx
depends on the purpose for which it is to be used, but the ingre-
dients commonly used ore saltpeter, sulphur, and charcoal. The
high explosives are a mixture of nitroglycerine with an absorb-
ing niatehal, the composition of which is such that, in addition
to thomughly and permaoently absorbing the nitroglycerine,
it is itself a gas-producing compoimd.
Saftly ixplosiirts, or as they are called, pirmissiblt iiflosaes.
are compounds intended for use in gaseous mines, and they are
so constituted that they will ignite wiWiout producing the
Lfen by ordinary extJoaives.
MINING 241
Fennissible explosives may be arranged in four classes, the clas-
sification being based on the natiire and proportions of the
substances used in the manufacture. These classes are hydratedt
ammonium-nitraU, organic nitrate^ and nitroglycerine explosives.
Permissible explosives are made by nearly all the manufacturers
of blasting ];x>wder and a list is publi^ed each year by the
United States Bureau of Mines giving the i)owders that have
passed the test for permissible explosives with full instructions
how they should be used and where manufactured.
Charging ExplosiYes. — No invariable rule can be laid down
as to the diameter and length of cartridges to be used tmder
any and all circtmistances, nor the amotmt or grade of i>owder
required for all kinds of work. Much depends on the good
sense and judgment of the persons using the explosives. In
blasting coal, slate, marble, granite, freestone, or any other
material that it is desirable to obtain in large blocks, cartridges
of small diameter should be used in wide bore holes, the charge
being rolled in several folds of paper, to prevent its touching
the sides of the bore holes. The intensity of action and the
crushing effect of the explosive are thtis lessened. ' The charge
must fit and fill the bottom of bore and be packed solid. If
holes are comparatively dry, slit the paper of the cartridges
lengthwise with a knife, and as each is dropped into the hole,
strike a wooden rammer on it with sufficient force to make the
powder completely fill the bottom and diameter of the bore.
Where water is not present, a more perfect loading is made by
taking i)owder out of cartridge and dropping it in loosely, ram
each 6 or 8 in. of the charge, using the paper of each cartridge
as a wad, to take down any i)owder that may have stuck to the
sides of the hole. If water is standing in the hole, do not break
the paper of the cartridges and avoid ramxning more than
enough to settle the charge on the bottom, using cartridges of
as large diameter as will readily run into the bore.
When cartridges are used, the last cartridge placed in the hole
should contain an electric exploder, or cap with fuse attached.
When loose i)owder is used, a piece of cartridge 2 or 3 in. in
length, with exploder or cap attached, should be pressed firmly
on top of charge. Some blasters put an exploder or cap in the
first cartridge used, placing remainder of charge on top.
17
242
MINING
If a seam is found in the rock, remove the powder from the
cartridges and push it into the seam and fire a cap beside it.
This will open the
seam so that a larger
quantity of explosive
can be used, and the
rock broken without
drilling.
Tamptng. — In deep
holes, water makes a
good tamping, but fine
sand, clay. etc. are gen-
erally used. Fill in for
the first 5 or 6 in. carefully, so as not to displace cap and
primer; then with a hardwood rammer pack balance of
material as sohd as possible, ramming with the hand alone.
Fig. 1
Fig. 2
and not using any form of hammer. Never use a metal
tamping rod.
Firing. — If the work is wet, or the charge used under water,
waterproof fuse must be used, and the end of the
fuse protected by applying bar soap, pitch, or
tallow around the edge of the cap. Water must
not be allowed to reach the i>owder in the fuse
or the fulminate in the cap. Exploding by elec-
tricity is best under water at great depth, as the
pressure of water is so great that the water is
forced through the fuse and it so prevents firing.
Nitroglycerine explosives always require deto-
nation by a cap or exploder in order to develop
their full force. Fig. 1 illustrates the method of
attaching such an exploder to the end of a fuse
and the placing of it in the cartridge. The explo-
ders are loaded with fulminate of mercury and are slipped over
the end of the fuse, after which the upper end is crimped tightly
Fig. 3
MINING
243
against the end of the fuse, as shown. (Miners sometimes bite
the caps on the fuse with their teeth; thisshould never be allowed,
for should one explode in a man's mouth it may prove fatal.)
In placing the cap or exploder into the dynamite or giant-
powder cartridge, care shotald be taken that only about two-thirds
of the cap is embedded
in the material of the
cartridge, for if the fuse
has to pass through a
I)ortion of the material
before reaching the cap,
it may ignite the mate-
rial, thus ca\asing defla-
gration of the cartridge
in place of detonation. The fumes given off by high explosives
are much worse in the case of deflagrating a cartridge.
The electric exploder. Fig. 2, consists of wires A and B that
carry the cturent to the exploder; cement D (usually sulphur)
that protects the explosive compound C (usually mercury ful-
minate), all of which is contained in a copper shell, and a
small platinum wire E is heated by the passage of a current and
ignites the explosive. Fig. 3 shows the method of placing a cap
or an electric exploder in a cartridge of ];x>wder. When a num-
ber of holes are exploded at one time, the electric exploders are
Fig. 4
Fig. 5
oonnected in series, as shown in Fig. 4, for a small number of
holes, and as in Fig. 6 for a larger number. The battery for
fumisdiing the current of electricity is a magneto machine that
is worked by pulling up or by depressing a handle or rack bar,
or else by turning a crank.
244 MINING
BUstmg by Electricity. — To blast by electricity, drill the
number of holes desired to be fired at one time; the depth and
spacing of the holes will depend on the character of rock, size
of drill holes, etc., the blaster, of course, using his judgment in
this matter. Load the hole in the usual manner, fitting one
cartridge with a fuse (electric exploder) instead of cap and fuse.
The fuse head is fitted into the bottom end of the cartridge, or
into the middle of one side of the cartridge, where a hole has been
punched with a pencil or small sharp stick to receive it; push
the powder close arotmd the fuse head. The fuse can then
be held in position by tying a string arotmd the cartridge and
the fuse wires, binding the wires to the cartridge, as shown in
Pig. 3, where A shows head of fuse, B the two fuse wires, C
string used to tie wires to cartridge. Hitches should never be
made in fuse wires, as the insulation of the wires may be
injured and the current of electricity pass from one wire to the
other, without passing through the cap, hazarding a misfire.
The cartridge containing the fuse is put in on top of the
charge by some blasters; by others, at bottom of the charge.
The best place for it is in the center of the charge. In tamping
the hole, great care must be taken not to cut the wires, injure
the cotton covering of fuse wires, or to pull the fuse out of the
cartridge. At least 8 in. of the fuse wire should project above
the hole, to make connections.
When all the holes to be fired at one time are tamped, separate
the ends of the two wires in each hole, and, by the use of con-
necting wire, join one wire of the first hole with one of the
second, the other or free wire of the second with one of the
third, and so on to the last hole, leaving a free wire at each end
hole. All connections of wires should be made by twisting
together the bare and clean ends; it is best to have the joined
parts bright. This may be done by scraping ofE the cotton
covering at the ends of the wires to be connected, say for 2 in.,
then rubbing the wire with a small hard stone. All connections
should be well twisted. Bare joints in wire should never be
allowed to touch the ground, particularly if the ground is wet.
This can be prevented by putting dry stones under the joints.
The charges having all been connected, the free wire of the
""^t hole should be joined to one of the leading wires, and the
MINING 246
free wire of the last hole to the other of the two leading wires.
The leading wires should be long enough to reach appoint. at
a safe distance from the blast, say 250 ft. at least. All being
ready, but not until the men are at a safe distance, connect the
leading wires, one to each of the projecting screws on the front
side or top of the battery, through each of which a hole is bored
for the purpose, and bring the nuts down firmly on the wires.
Take hold of the handle for the purpose, lift the rack bar (or
square rod, toothed on one side) to its ftill length, and press it
down, for the first inch of its stroke with moderate speed, but
finishing the stroke with all force, bringing rack bar to the
bottom of the box with a solid thud, and the blast will be made.
Do not chum rack bar up and down. It is unnecessary and is
harmful to the machine. One quick stroke of the rack bar is
sufficient to make the blast. Never use fuses (exploders) made
by different manufacturers in the same blast. G>nnecting
wire should be of same size as the fuse wire; leading wire
should be at least twice as large. Covering on wire should not
strip or come off easily.
Arrangement of Drill Holes.— The arrangement of drill holes
for driving and sinking should be such as to permit the easy
handling of the drills and also to minimize the number of holes
and the weight of the explosive. Two distinct systems are
in use: the center cut, by which a center core or key is first
removed, and after that concentric layers about this core; the
square cut, in which the lines of holes are parallel to the sides of
the excavation, the rock being removed in wedges instead of in
concentric circles.
Thawing Dynamite. — ^AU frozen cartridges should be thawed,
ks, when frozen, cartridges are very hard to explode, and even
if they do explode, the results are not nearly as satisfactory as
when proi)erly thawed. When cartridges are frozen, they
should not be exposed to a direct heat, but should be thawed
by one of the following methods: (1) Place the number of
cartridges needed for a day's work on shelves in a room heated
by steam pipes (not live steam) or a stove; where regular blast-
ing is done, a small house can be built for this purpose, fitted
with a small steam radiator. Exhatist steam through these
pipes gives all heat necessary. The house should be banked
246 MINING
around with earth, or, preferably, with fresh manure. (2) Use
two water-tight kettles, one smaller than the other, put cart-
ridges to be thawed in smaller kettle, and place it in larger
kettle, filling space between the kettles with hot water at, say,
130*' to 140** F., or so that it can be borne by the hand. To
keep water warm, do not try to heat it in the kettle, but add
fresh warm water. Gsver kettles to retain heat. In thawing
do not allow the temperature to get above 212° F. (3) Where
the number of cartridges to be thawed is small, they may be
placed about the x>erson of the blaster tmtil ready for use, the
heat of the body thawing the cartridges.
MACHINE MINING
There are four general types of mining machines in use; pick
machines, chain-cutter machines, cutter-bar machines, and
longwall machines. The first two are the types almost uni-
versally used in America. Cutter-bar machines have almost
entirely disappeared from use. Longwall mining machines have
not been very generally adopted in America, as the longwall
method of mining is not extensively used. Both compressed
air and electricity are used for operating mining machines.
Pick machines work very similarly to a rock drill. They can
be used wherever mining machines are applicable, and their
particular advantage is that they are more perfectly under the
control of the operator, who can cut around pyrites and similar
obstructions without cutting them with the machine. This
renders such a machine particularly applicable for seams of
coal having rolls in the bottom and containing pyrites or other
hard impurities. They are also applicable for working pillars
on which there is a squeeze, as they are light and can be easily
handled and readily removed.
A good pick machine will tmdercut 450 sq. ft. in 10 hr., while
an ordinary miner will undercut 120 sq. ft. in the same time.
In a seam varying from 4| to 6 ft. in thickness, the machine
will undercut from 50 to 100 T. of coal in 10 hr. The cost of
undercutting under these conditions has been given as approxi-
mately 10c. per T. Extraordinary records show 1,400 sq. ft.
MINING 247
to have been cut in 9 hr. in Western Pennsylvania, and in an
8 ft. seam, 240 T. have been undercut in a shift of 10 hr.
Chain-cutter machines consist of a low metal bed frame U];x>n
which is motmted a motor that rotates a chain to which suitable
cutting teeth are attached. To operate chain machines to the
best advantage, the coal should be comparatively free from
pyrites. They also require more room than pick machines,
and a space from 12 to 15 ft. in width is necessary along the
face to work them to advantage. A good chain cutter will make
from 30 to 45 cuts, 44 in. wide and 6 ft. deep, in 10 hr. under
moderately fair conditions, while in high seams two men hand-
ling the same machine tmder ordinary conditions can make 60
cuts per shift, and under particularly favorable conditions, 80
to 120 cuts per shift.
Shearing. — ^All the pick machines can be converted into
shearing machines and can be used for longwall work by using a
longer striking arm and a longer supply hose. The chain
machines are used to do shearing work by having the cutting
parts turned vertically.
VENTILATION OF MINES
COMPOSITION AND MEASUREMENT OF AIR
Air consists chiefly of oxygen and nitrogen, with small and
varying amounts of carbonic-acid gas, ammonia gas, and
aqueous vapor. These gases are not chemically combined,
but exist in a free state in uniform proportion of 79.3% nitrogen
and 20.7% oxygen by voliune and 77% nitrogen and 23% oxy-
gen by weight. Wherever air is fotmd, its composition is
practically the same. The weight of 1 cu. ft. of air at 32° F.
and under a barometric pressure of 30 in. is .080975 lb. Air
decreases in weight per cubic foot as its height above the sea
level increases and it increases in weight below that level.
The weight of 1 cu. ft. of dry air at any temperattire and
barometric pressure is found by the formula
1.3253 XB
tt? = .
459+/
248 MINING
in which wweight of 1 cu. ft. of dry air;
B * barometric pressiire, in inches of mercury;
f* temperature, in degrees F.
The constant 1.3253 is the weight in potmds avoirdupois of
459 cu. ft. of dry air at a temperatiu'e of 1° P. and 1 in. baro-
metric pressure.
Example. — Find the weight of 1 cu. ft. of dry ait at a tem-
perature of 60° F. and a barometric pressure of 30 in.
Solution. — ^Applying the formula
1.3253X30
-.07661b.
469+60
The atmospheric pressure is the pressure caused by the weight
of the atmosphere above a given point. It is measured by the
barometer, and this gives rise t6 the synonymous term baro-
metric pressure. Atmospheric pressure is usually stated in
I)otmds per square inch, while barometric pressure is stated
in inches of mercury. Thus, at sea level, the atmospheric
pressure tmder normal conditions of the atmosphere is 14.7 lb.
per sq. in., while the barometric pressure at the same level is
30 in. of mercury column, or simply 30 in.
Mercurial Barometer. — The mercurial barometer is often
called the cistern barometer; or, when the lower end of the tube
is bent upwards instead of the mouth of the tube being sub-
merged in a basin, it is known as the siphon barometer. The
instnmient is constructed by filling a glass tube 3 ft. long, and
having a bore of i in. diameter, with mercury, which is boiled
to drive off the air. The thumb is then placed tightly over
the open end, the tube inverted, and its mouth submerged in
a basin of mercury. When the thumb is withdrawn, the mer-
cury sinks in the tube, flowing out into the basin, tmtil the
top of the mercury column is about 30 in. above the surface
of the mercury in the basin, and after a few oscillations above
and below this point, comes to rest. The vacuum thus left
in the tube above the mercury column is as perfect a vacuum
as it is possible to form, and is called a Torricelli vacuum, after
its discoverer.
Aneroid Barometer. — The aneroid barometer is a more port-
able form than the mercurial barometer. It consists of a
MINING 249
brass box resembling a steam-pressure gauge, having a similar
dial and ];x>inter, the dial, however, being graduated to read
inches, corresponding to inches of mercury column, instead of
reading pounds, as in a pressure gauge. Within the outer case
is a delicate brass box having its upper and lower sides corru-
gated, which causes it to act as a bellows, moving in and out
as the atmospheric pressure on it changes. The air within
the box is partially exhausted, to render it sensitive to atmos-
pheric changes. The movement of the upper surface of the
box is communicated to the pointer by a series of levers,
and the dial is graduated to correspond with the mercurial
barometer.
Calculation of Atmospheric Pressure. — The weight of the
merctiry column of the barometer is the exact measure of the
pressure of the atmosphere, since it is the downward pressure
of the atmosphere that supports the merctiry column, area
for area; that is, the pressure of the atmosphere on 1 sq. in.
supports a coltmin of mercury having an area of 1 sq. in.,
and whose height is such that the weight of the mercury col-
umn is equal to the weight of the atmospheric column. Hence,
as 1 cu. in. of mercury weighs .49 lb., the atmospheric pressure
that supports 30 in. of mercury column is .49X30=14.7 lb.
per sq. in. In like manner, the atmospheric pressure corre-
sponding to any height of mercury column may be calculated.
The sectional size of the mercury column is not important
because it is supported by the atmospheric pressure on an
equal area, but the calculation of pressure is based on 1 sq. in.
Water Column Corresponding to Any Mercury Column. — The
density of mercury referred to water is practically 13.6; hence,
the height of a water column corresponding to a given mercury
column is 13.6 times the height of the mercury column. For
example, at sea level, where the average barometric pressure
is 30 in. of mercury, the height of water column that the
atmospheric pressure will support is 13.6XH = 34 ft. This is
the theoretical height to which it is possible to raise water by
means of a suction pump, but the length of the suction pipe
should not exceed 76% or 80% of the theoretical water coltmin.
Finding Depth of Shafts. — The barometer is often used to
determine the depth of a shaft or the depth of any point in a
250 MINING
X
mine below a corresponding point on the surface, llie aneroid
is used for this work, being more portable. Allowance must
always be made in such cases for the ventilating pressure of
the mine. A simple formula often used for such calculations
is the following:
H= 65,000 1
{->©■
jn which H = difference of level between two stations, in feet;
r » reading of barometer at higher station, in inches ;
J?": reading of barometer at lower station, in inches.
The most important use of the barometer in mining practice,
however, is found in the warning that it gives of the decrease
of atmospheric pressure, and the expansion of mine gases that
alwa3rs follows.
GASES FOUND IN MINES
Oxygen, O, is a colorless, odorless, tasteless, non-poisonous
gas. It is heavier than air, having a specific gravity of 1.1056.
It is the great supporter of life and combustion.
Nitrogen, N, is sl colorless, odorless, and tasteless gas; it is
neither combustible nor a supporter of combustion. It is
not poisonous, and is lighter than air, having a specific gravity
of .9713. Nitrogen is a particularly inert gas; it takes no active
part in any combustion, in the sense of causing such combustion.
Its province is to dilute oxygen of the atmosphere, on which
life depends.
Methane, CHi, often called light carbureted hydrogen, or
marsh ga&, is a chemical compound, consisting of 4 atoms of
hydrogen to 1 atom of carbon. It is one of the chief gases
occluded in coal seams, and results from the metamorphism
of the carbonaceous matter from which coal is formed, when
such metamorphism has taken place with the exclusion of
air, and in presence of water. Pure methane is colorless,
odorless, and tasteless, and is lighter than air. Its specific
gravity is .559, and it diffuses rapidly in the air, forming a
firedamp mixture. Marsh gas bums with a blue flame, but
it will not support combustion, and a lamp placed in it is
immediately extinguished
Carbon monoxide, CO, often called carbonic oxide gas, or tuhite-
damp, is a chemical compound consisting of 1 atom of carbon
MINING 251
united to 1 atom of oxygen. To a certain extent it occurs as
an occluded gas in coal. It is chiefly formed, however, in coal
mines, by the slow combustion of carbonaceous matter in the
gobs or waste places of the mine; where the supply of air is
limited. It is always the product of the slow combustion of
carbon in a limited supply of air, and is therefore one of the
chief products of gob fibres; it is also a product of the explosion
of powder in blasting. This gas often fills the crevice made
behind a standing shot, and causes the flash that takes place
when the miner puts his lamp behind such shot to examine the
same. This gas is formed in large quantities whenever the
flame of a blast or explosion is projected into an atmosphere
in which coal dust is suspended. The force of a blast often
blows the dust into the air, and the flame acting on it distils
t^arbon monoxide.
Carbon monoxide is lighter than air, having a specific gravity
of .967, and it therefore accumulates near the roof and in the
higher working places. It is colorless, odorless, and tasteless,
but is combustible, burning with a light-blue flame. It is the
flame often seen over a freshly fed anthracite fire. Carbon
monoxide is a very poisonous gas, and acts on the htmian
system as a narcotic, producing drowsiness or stupor, followed
by acute pains in the head, back, and limbs, and afterward
by delirium. When breathed into the lungs, it absorbs th^
oxygen from the blood, or, in other words, poisons the blood.
Carbon monoxide is detected in mine workings by its effect
on the flame of a lamp, which bums more brightly in the pres-
ence of the gas, and reaches upwards as a slim, quivering taper,
having often a pale-blue tip that, however, is not readily
observed.
Carbon dioxide^ C(h, often called carbonic-acid gas, black-
damp, or choke damp, is a chemical compound consisting of
1 atom of carbon united to 2 atoms of oxygen. It is heavier
than air, having a specific gravity of 1.529. It therefore
accumulates near the floor or in the low places of the mine
workings. It is always the result of the complete combustion
of carbon, in a plentiful supply of air, and is a product of the
breathing of men and animals, burning of lamps, or any other
complete combustion. It is always present in occluded gases.
262 MINING
Carbon dioxide is a colorless, odorless gas, but possesses a
peculiarly sweet taste, which may be detected in the mouth
when it is inhaled in laurgp quantities. It is not combustible,
nor is it a supporter of combustion. Lamps are at once extin-
guished by it. It diffuses slowly into the atmosphere, and is a
difficult gas to remove in ventilating. It is not poisonous, but
stiffocates by excluding oxygen from the lungs. Its effect,
when breathed for any length of time, is to cause headache and
nausea, followed by weakness and pains in the back and limbs;
when present in larger quantities, it causes death by suffoca-
tion. This gas, when present in the firedamp mixlnires, has
the opposite effect from that of carbon monoxide, inasmuch
as it narrows the explosive range of the firedamp, and ren-
ders such mixtures inexplosive, which would otherwise be
explosive.
Carbon dioxide is detected in the mine air by the dimness of
the lamps and by their extinguishment when the gas is present
in larger quantities. It should always be looked for at the
floor, and in low places of the mine workings.
Hydrogen sulphide, H»S, occurs at times as an occluded gas in
coal seams, but more often exudes from the strata immediately
underlying or overlying those seams. It is generally supposed
to be formed by the disintegration of pjrrites in the presence
of moisture. It is heavier than air, having a specific gravity
of 1.19^2. It is a colorless gas, having a very disagreeable
odor resembling that of rotten eggs, and is known to the miners
as stinkdamp. It is an exceedingly dangerous gas when
occurring in considerable quantities. When mixed with 7 times
its volimie of air, it is violently explosive. It is extremely
poisonous, acting to derange the system, when breathed in
small quantities, and, when inhaled in larger quantities, it pro-
duces unconsciousness and prostration. Its smell serves as
the best means for its detection.
The general term firedamp relates to any explosive mixture
of marsh sras and air, although in some localities this term is
understood as referring to any mixture of methane and air
whatever, whether explosive or otherwise. Many persona
speak of pure methane as firedamp. The first meaning given
however, is the general acceptance of the term.
The compositioQ of af-
terdamp is Bic«dinglv
no genera] analysis that
can be applied with cer-
Ij-th
The
oifold.
impossible to s;ive moic than a genera] analysis of afterdamp^
Outbunte of gas are frequent occurrences in some coal fleams-
They are caused by the occluded gas finding its way to a vertical
crevice or cleat in the coal seam, as illuitrated in Fig. 1 , and the
pressure of the gas thtis becomes distributed over a large area.
Teatinc for Ou by huajf Flame. — Methane and firedamp
are detected in mine workings by the small flame cap that envel-
h the flame. The pi
264
MINING
In Fig. 2, the heights of flame cap due to the presence of
different proportions of methane are shown. These heights,
as given, refer to the experimental heights of flame cap obtained
with pure methane. It should be observed, however, that the
presence of other gases in the firedamp will vary its explosive
character, and this fact very materially modifies the explosive-
ness of certain caps.
Constants for Jjime Gases. — ^The following table shows the
symbols, specific gravities, and relative velocities of diffusion
and transpiration of the principal mine gases, arranged in the
order of their specific gravities, air being taken as 1. The
values given in the next to the last column were obtained by
experimenting with the gases, and agree quite closely with
the calculated values given in the preceding column. This
column shows that 1,344 volumes of methane will diffuse in
the same time as 1,000 volumes of air, or 812 volumes of car-
bon dioxide.
TABLE OF MINE GASES
Name of Gas
Sym-
bol
Specific
Gravity
1
Relative
Velocity
of Dif-
fusion
(Air-1)
Relative
Velocity
of Trans-
piration
(Air=l)
"Vsp. gr.
Air
COi
H^S
CiHi
N
CO
CHa
H
1.00000
1.529
1.1912
1.1056
.978
.9713
.967
.6235
.559
.06926
1.0000
.8087
.9162
.9510
1.0112
1.0147
1.0169
1.2664
1.3375
3.7794
1.000
.812
.95
.9487
1.0191
1.0143
1.0149
1.344
3.83
•
1.0000
Carbon dioxide.. . ,
Hydrogen sulphide
Oxygen.
1.2371
.903
Olefuint
1.788
Nitroizen
1.0303
Carbon monoxide..
Steam
1.034
Methane
1.639
H vdrosren
2.066
SAFETY LAMPS
The safety lamp is designed to give light in gaseous workings
without the danger of igniting the gases present in the atmos-
phere. Its principle depends on the cooling effect that an
iron-wire gauze exerts on flame. It is well known that all
MINING 255
gases ignite at certain fixed temperatures, and if this tempera-
ture is decreased from any cause, the fiame is extinguished.
Safety lamps are also used for testing for gas.
The essential features of a lamp designed for general mine
work are: safety in strong currents, good illuminating power,
security for lock fastening, freedom from flaming, security
against accident, simplicity of construction. The essential
features of a lamp for testing purposes are: free admission of
air below the flame, no reflecting surface behind the flame,
ability to test for a thin layer of gas at the roof. The Davy
lamp in the hands of a careful person may be made to detect
the presence of gas in quantities as low as 3%. It is claimed
by some fire-bosses that 2% of gas may be detected with a
good Davy. For the detection of small quantities of gas,
esi)ecially constructed lamps have been used.
Types of Safety Lamps. — In the year 1815, Sir Htmiphrey
Davy and George Stevenson, the latter a poor miner, discov-
ered simultaneously, that flame would not pass through small
openings in a perforated iron plate. This led to the construc-
tion of what are known as the Davy and the Stevenson or
"Geoidy," lamps. The Davy lamp is still a great favorite
among fire-bosses for the detection of gas in mine air. Inas-
much as all safety lamps, of which there are a large ntmiber,
depend on the same principle, only such lamps as possess
essential features, and show important improvements and the
gradual developments in safety-lamp construction are here
mentioned. They are the Davy, Clanny, Mueseler, Marsant
Ashworth-Hepplewhite-Gray, and Wolf.
Oils for Safety Lamps. — Most safety lamps bum vegetable
oils, which are considered the safest for mining use; such oils
are rape-seed oil and colza oil, made from cabbage seed. Seal
oil is also largely used. Seal oil affords a better light than
vegetable oils, and in its use there is less charring of the wick.
A mixture of 1 part of coal oil to 2 parts of rape or seal oil is
often used and improves the light, but tbe smoke from the
flame is increased. The Ashworth-Hepplewhite-Gray lamp
is constructed to bum coal oil, or a mixture of coal and lard
oil. The Wolf lamp is especially designed for burning naphtha
or benzine. Special tests have been made to prove the safety
256 MINING
of using such a fluid in this lamp, and resulted in demonstrat-
ing the fact that the lamp was safe under any conditions that
might arise. A thorough test was made, the oil vessel of the
burning lamp being heated to 180** P., at which point the lamp
was extinguished without manifesting any dangerous results.
Locking Safety Lamps. — The ordinary lock consists of a
lead plug, which, when inserted in the lamp, will show the
least tampering on the part of the jniner. Other locks consist
of an ordinary tumbolt operated by a peculiar key. Magnetic
locks allow of the opening of the lamp only by means of a
strong magnet kept in the lamp room.
Cleaning Safety Lamps. — Safety lamps should be thoroughly
and regularly cleaned and filled between each shift. Each
lamp should then be lighted and inspected by a competent
person before being given to the miner. A careful inspection
of the gauze of the lamp is necessary, as well as of all the joints
by which air may enter the lamp. It should be known to a
certainty that each lamp is securely locked before it leaves the
lamp room.
Relighting Stations. — The relighting stations are located at
certain places ' in gaseous mines where they can be supplied
with a current of fresh air, and where there is no danger from
the gases of the mine. The lamp is apt to be overturned, or
to fall, and is often extinguished thereby; and if these stations
were not provided, the man would have to return with his
lamp to the surface in order to have it relighted. Such a
station is always located at the entrance of the gaseous portion
of a mine, in cases where the entire mine does not liberate gas.
A number of self -igniters have been invented and some are
used. If the lamp goes out all that is needed is to turn a screw
in the bottom of the lamp and a spark is made which relights
the lamp.
Illuminating Power of Safety Lamps. — The accompanying
table gives the illuminating power or candlepower of some of
the principal lamps. The light of a sperm candle is taken
as 1, or unity.
Acetylene Mine Lamps. — ^Acetylene gas is generated by
dropping water on to calcium carbide; as in the automobile
and bicycle acetylene lamps. The miner's lamps using
MINING
257
acetylene are small brass lamps consisting of two main parts,
the carbide container and the water tank; a regulator limits
the amount of water dropping on to the carbide. The gas
given off bums with a bright white flame. Besides givinfir
greater illumination, acetylene lamps bum practically without
generating soot, and are much less harmful to the miner's
respiratory organs than the constantly smoking oil lamps.
Ventilation is also facilitated, owing to the acetylene lamp
constuning less oxygen than any other. Acetylene illumination
is also cheaper than oil lighting.
Electric Mine Lamps. — Several forms of electric mine lamps
have been invented. Some of them^ are in use by miners, but
others are not extensively used, on account of their weight.
These heavier types may be used by mine rescue parties.
Electric mine lamps should have a battery that is not heavy,
a good tungsten lamp, and a good strong reflector. In the
Hirsch is an example which is carried by ike miner, the battery
is fastened on the miner's back to a belt passing around his
waist. An insulated copper wire transmits the current from
LIGHT GIVEN BY SAFETY LAMPS
Name of Lamp
Davy
Geordy ,.
Clanny
Mueseler
Evan Thomas
Marsaut, 3 gauzes
Marsaut, 2 gauzes
Marsaut, with Howat's deflector
Ashworth-Hepplewhite-Gray. . . .
Wolf
Illuminating Power
of Lamp
Candlepower
.16
.10
.20
.35
.45
.45
.55
.65
.65
.90
the battery to the lamp on the miner's cap. The battery is
charged by connecting it with the current in the lamp house
at night and is ready for use the next morning. A type of
electric lamps to carry in the hand and for use on locomotives
is the HubbeQ electric lantern
18
258 MINING
EXPLOSIVE CONDITIONS IN MINES
In the ventilation of gaseous seams, the air-corrent may be
rendered explosive by the sudden occturence of any one of a
nimiber of circumstances that cannot be anticipated. Hence,
the condition of the air-current should be maintained far
within the explosive limit. Amoilg these are the following:
(1) Derangement of the ventilating current; (2) sudden
increase of gas due to outbursts, falls of roof, feeders, fall of
barometric pressure, etc. ; (3) Presence of coal dust thrown into
suspension in the air, in the ordinary working of the mine, or
by the force of blasting at the working face, or by a blown-out,
or windy, shot; (4) Pressure due to a heavy blast, or any con-
cussion of the air caused by closing of doors, etc.; (5) rapid
succession of shots in close workings; (6) accidental dischaxge
of an explosive in a dirty atmosphere. The explosive condi-
tions vary considerably in different coal seams, as the nature
of the coal and its enclosing strata, its friability and inflam-
mability, together with the character of its occluded gases,
determine, to a large extent, the explosive conditions. A
great many of these conditions have been investigated by the
U. S. Bureau of Mines and the results published in pamphlet
form.
Mine Explosions. — The explosion of gas in a mine usually
arises from the ignition of an explosive mixture of gas and air
called firedamp, which has acctmiulated in some unused
chamber or cavity of the roof, or in the waste places of the
mine, and has been ignited by a naked light, by the flame of a
shot, or by a mine fire. The initial force of an explosion is
generally expended locally, but the flame continues to feed
upon the carbon monoxide generated by the incomplete com-
bustion of the firedamp mixture, and distilled also from the
coal dust thrown into the air by the agitation. Air is required
to bum this carbon monoxide; this causes the flame to travel
against the air-current, or in the direction in which fresh air is
found. In the other direction, or behind the explosion, the
flame is soon extinguished in its own trail when the initial
force of the explosion is expended. The explosion continues
to travel along the airways against the current as long as there
is sufficient gas or coal dust for it to feed upon, or until its
MINING 250
temperature is cooled below the point of ignition, by some
cause such as, for example, the rapid expansion of the area of
the workings. The chief factor in transmitting an explosion
is the presence of carbon monoxide, which lengthens the flame
and extends the effect.
The recoil of an explosion is the return of the flame along the
path that it has just traversed. In the recoil, the flame bums
more quietly, advances more slowly and travels close to the roof.
QUANTITT OF AK REQTJIRED FOR VENXILATION
The quantity of air required for the adequate ventilation
of a mine cannot be stated as a rule applicable in every case.
Regulations that would supply a proper amount of air for the
ventilation of a thick seam would cause great inconvenience
if applied without modification to the workings in a thin seam.
The quantity of air required by the laws of the several States
is generally specified as 100 cu. ft. per min. per man and in many
cases an additional amotmt of 500 cu. ft. per min. per animal
is stated. This quantity is in no case stated as the actual
amotmt of air required for the use of each man or animal,
but is only the result of experience, as showing the quantity
of air required for the proper ventilation of the average mine,
based on the number of men and animals employed. The
number of men employed in a mine is an indication of the
extent of the working face, while the number of animals
employed is an indication likewise of the extent of the haulage
roads, or the development of the mine. These amotmts refer
particularly to non-gaseous seams.
The Bituminous Mine Law of Pennsylvania specifies that
there shall be not less than 100 cu. ft. per min. per person in
any mine, while 150 cu. ft. is required in a mine where fire-
damp has been detected.
The Anthracite Mine Law of Pennsylvania specifies a mini-
mum quantity of 200 cu. ft. per min. per person. Each of
these laws contains modifying clauses, which specify that the
amount of air in circulation shall be sufficient to "dilute,
render harmless, and sweep away" smoke and noxious or
dangerous gases.
260 MINING
ELEMENTS OF VENTILATION
The elements in any circulation of air are (1) horsepower, or
power applied; (2) resistance of airways, or mine resistance,
which gives rise to the total pressure in the airway; (3) velocity
generated by the power applied against the mine resistance.
Horsepower or Power of Current. — The power applied is often
spoken of as the power upon the air. It is the effective power
of the ventilating motor, whatever this may be, including all
the ventilating agencies, whether natural or otherwise. The
power upon the air may be the power exerted by a motive
column due to natural causes, or to a furnace, or may be the
power of a mechanical motor. The power upon the air is
always measured in foot-pounds per minute, which expresses
the units of work accomplished in the circulation.
Mine Resistance. — ^The resistance offered by a mine to the
passage of an air-current, or the mine resistance, is due to the
friction of the air rubbing along the sides, top, and bottom of
the air passages. This friction causes the total ventilating
pressure in the airway, and is equal to it, or, the total x>ressure
is equal to the mine resistance or
R'^pa,
in which /?= resistance;
^«=vinit of ventilating pressure;
a = sectional area of airway.
Velocity of Air-Current. — ^Whenever a given power is applied
against a given resistance, a certain velocity results. For
example, if the power «, in foot-poimds per minute, is applied
against the resistance P a, a. velocity of v, in feet per minute,
is the result; and as the total pressure P a moves at the velocity
of V, the work performed each minute by the power applied is
the product of the total pressure by the space through which
it moves per minute, or the velocity. Thus, u = (P a)v.
Relation of Power, Pressure, and Velocity. — The relation
of power, presstire, and velocity is not a simple one. For
example, a given power applied to move air through an airway
establishes a certain resistance and velocity in the airway.
The resistance of the airway is not an independent factor; that
is, it does not exist as a factor of the airway independent of the
velocity, but bears a certain relation to the velocity. Power
MINING 261
always produces resistance and velocity, and these two factors
always sustain a fixed relation. .
This relation is expressed as follows: The total pressure or
resistance varies as the square of the velocity; i. e., if the power
is sufficient to double the velocity, the pressure will be increased
4 times; if the power is sufficient to multiply the velocity
3 times, the pressure will be increased 9 times. Thus, a change
of power applied to any airway means both a change of
pressure and a change of velocity.
Again, as the power is expressed by the equation m= (^ a)r,
and as ^ a, or the total pressure, varies as tfl, the work varies
as ifi. Therefore, if the velocity is multiplied by 2, and, conse-
quently, the total pressure by 4, the work performed ip a)v will
be multiplied by 2« = 8, or the power applied varies as the
cube of the velocity.
MEASUREMENT OF VENTILATING CURRENTS
The meastirement and calculation of any circulation in a
mine airway includes the measurement of: (1) the velocity
of the air-current, (2) of pressure, (3) of temperature, (4) cal-
culation of pressure, quantity, and horsepower of the circula-
tion. These meastirements should be made at a point on the
airway where the airway has a uniform section for some dis-
tance, and not far from the foot of the downcast shaft or the
fan drift.
Measurement of Velocity. — ^For the purpose of mine inspec-
tion, the velocity of the air-current should be measured at the
foot of the downcast, at the mouth of each split of the air-cur-
rent, and at each inside breakthrough, in each split. These
measurements are necessary in order to show that all the air
designed for each split passes around the face of the workings.
The measurement of the velocity of a current is best made by
means of the anemometer.
Rule. — To obtain the quantity of air passing in cubic feet per
minute, multiply the area of the airway, at the point where the
velocity is measured, by the velocity.
Measurement of Pressure. — The measurement of the ven-
tilating pressure is made by means of a water column in the
form of a water gauge, which is simply a glass U tube open at
both ends, as shows in Pig. 3. WB,ter ia placed in tbe bent
portion of the tube, and stands at the same height in both
anna of the tube when each end of the tube ia subjected to the
same pressure. If, however, one end ot the tube is subjected
to a greater pressoie than the other end, the water wOl be
farced down in that ana of the tube, and will riae a correapond- *
ing height in the other aim. the difference oS level in the two
arms of the tube repnaenting the water column balanced by
the excess of precaure to whicb the water in the first arm is
subjected. An adju<t*ble scale, graduated in inchei. m
Pics FiO. i
the height of the water column. The cero is adjusted to the
lower water level and the upper water level will then give the
reading of the water gauge. One end of the glass tube is
drawn to a narrow opening to exclude dust, while the other
end is bent to a right angle, and passing back through the
brass tube that passes through a hole in the partition or brat-
tice, when the water gauge is in use. The bend of the tube
ia contracted to reduce the tendency to oadllat ion in the height
MINING 263
When in use, the water gatige must be m a perpendicular
position. It is placed upon a brattice occupying a position
between two airways, as shown at A, Fig 4. The brass tube
forming one end of the water gauge is inserted in a cork, and
passes through a hole bored in the brattice. The water gauge
must not be subjected to the direct force of the air-current, as
in this case the true pressure will not be given. Pig. 4 shows
the instrument occupying a .position in the breakthrough,
between two entries. It will be observed that the water
gauge records a difference of pressure, each end of the water
gauge being subject to atmospheric pressure, but one end in
addition being subject to the ventilating pressure, which is the
difference of pressiu'e between the two entries. The water
gauge thus permits the measiu-ement of the resistance of the
mine inbye from its position between two airways. If placed
in the first breakthrough, at the foot of the shaft, it measures
the entire resistance of the mine, but if placed at the mouth
of a split, it measures only the resistance of that split. It
never measures the resistance outbye from its position in the
mine, but always inbye.
Measurement of Temperature. — ^It is important to measure
the temperature of the air-current at the point where the veloc-
ity is measured, as the temperature is an important factor of
the voltmie of air passii^.
Calculation of Mine Resistance. — ^The mine resistance is
•eqiial to the total pressure pa that it causes. This mine resist-
ance is dependent on three factors: (1) The resistance k
offered by 1 sq. ft. of rubbing surface to a current having a
velocity of 1 ft. per min. The coefficient of friction k, or the
unit of resistance, is the resistance offered by the unit of rubbing
surface to a current of a unit velocity. This tinit resistance
has been variously estimated by different authorities. The
value most universally accepted, however, is that known as the
Atkinson coefficient .0000000217. (2) The mine resistance,
which varies as the square of the velocity. (3) The rubbing
surface. Hence, if the unit resistance is multiplied by the
square of the velocity, and by the rubbing surface, the total
mine resistance as expressed by the formula pa^ksi^, will be
obtained.
264 MINING
Calculation of Power, or Units of Work per Minute. — If the
total pressure is multiplied by the velocity in feet per xninute,
with which it moves, the tmits of work per minute, or the power
upon the air, will be obtained. Hence, u^pavkstj^j which is
the fundamental expression for work per minute, or power .-
The Equivalent Orifice. — ^The term equivaUnt orifice, often
used in regard to ventilation, evaluates the mine resistance, or,
as will be seen from the equation given for its value, it expresses
the ratio that exists between the quantity of air passing in an
airway and the pressure or water gauge that is produced by the
circulation. This term refers to the flow of a fluid through an
orifice in a thin plate, under a given head. The formula
expressing the velocity of flow through such an orifice is v
« '\2gh; multiplying both members of this equation by A, and
substituting for the first member Av, its value q, after trans-
q
posing and correcting A = ; , in which .62 is the coefficient
.62V2«A
for the contracted vein of the flow. Reducing this to cubic feet
per minute and inches of water gauge represented by i, gives
q
the equation A = .0004X"~7=. By this formula, Murgue has
V*
suggested assimilating the flow of air through a mine to the flow
of a fluid through a thin plate, for in each case, the quantity
and the head or pressure vary in the same ratio. Thus, apply-
ing this formula to a mine, Murgue multiplies the ratio of the
quantity of air passing, in cubic feet per minute, and the square
root of the water gauge, in inches, by .0004, and obtains an
area A , which he calls the equivalent orifice of the mine.
Potential Factor of a Mine. — ^Ventilating formulas 8 and 27
page (267) give, respectively, the pressure and the power that will
circulate a given quantity of air per minute in a given airway.
These formulas may be written as equal ratios, expressed in f ac-
p ks
tors of the current and the airway, respectively; thus, — = — , and
u ks ,
— = — , which show that the ratio between the pressure and the
<p a'
""uare of the quantity it circulates in any given airway is equal
MINING 266
td the ratio between the power and the cube of the quantity it
circulates. Solving each of these formulas with respect to g:
With respect to pressure.
'- («%© ^
With respect to power,
- fe) «
Hence, in any airway, for a constant pressure, the quantity
\^
of air in circulation is proportional to the expression a\\ — ;
\ks
and for a constant power, the quantity is proportional to the
a
expression -— =, which terms are called the potentials of the
mine with respect to i>ressure and power, respectively; and their
q q
values — ^ and —= are the potentials of the current with respect
to presstire and power, respectively. These factors evaluate
the airway, as they determine the quantity of air a given pres-
sure or power will circulatfe in that airway, in cubic feet per
minute. By their use, the relative quantities of air any given
presstire or power will circulate in different airways are readily
determined. The rule may be stated as follows:
Rule. — For any given pressure or power, the quantity of air in
circulation is always proportional to the potential for pressure, or
the potential for power, as the case may be.
This rule finds important appUcation in splitting. In all
cases where the potential is used as a ratio, the relative potential
may be employed by omitting the factor k\ or- it may be
employed to obtain the pressure and power, in several splits
by multiplying the final result by ^, as in the spUtting form-
ulas 46 and 47, page 275.
The accompanying table will illustrate the use of the formulas
used in these calculations. There are several formulas for
quantity, velocity, and work or horsepower, but in each case
266
MINING
the several formulas are derived by simple transposition of the
terms of the original formulas p ^ — , Q^av, and u « qp.
a
To illustrate the use of the formulas, take an underground
road, 6 ft. wide by 4 ft. high, and 2,000 ft. in length, and calcu-
late the value of each symbol or letter, aMiimjng a velocity of
600 ft. per min.
Area of airway (5 ft.X4 ft.)
Horsepower*
Coefficient of frictionf
Lenjgth of airway
Perimeter of airway, 2 X (5 ft. +4 ft.)
Pressure, in pounds per sq. ft
Quantity of air, in cubic feet per
minute
Area of rubbing surface
Units of work per minute, power. . . .
Velocity, in feet per minute
Water gauge
Equivalent orifice of the mine
Potential for power
Potential for pressure
Weight of 1 cu. ft. of downcast air . .
Motive column, downcast air
Depth of furnace shaft
Average temperature of the upcast
column
Average temperature of the down-
cast column
Symbol
Value of
Symbol
a
20 sq. ft.
h
2.959 H. P.
k
.0000000217 lb.
I
2.000 ft.
o
18 ft.
P
9.766 lb.
Q
10,000 cu. ft.
s
36,000 sq. ft.
u
97.650 ft.-lb.
V
600 ft.
•
t
1.87788 in.
A
2,919 sq. ft.
Xu
217.16 units
Xp
3,200 units
w
.08098 lb.
M .
120.6 ft.
D
306.77 ft.
T
360'* P.
t
32*' F.
Note. — ^The water gauge is calculated to 6 decimal places
to enable all the other values to be accurately arrived at; in
practice, it is only read to 1 decimal place.
*A horsepower is equal to 33,000 units of work.
fThis coefficient of friction is an invariable quantity, and is
the same in every calculation relating to the friction of air
in mines.
MINING
VENTILATION FORMULAS
267
To Find
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
Formula
To Find
No.
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Formula
Rubbing
surface of
an airway
in sq. ft.
S'lo
Water
gauge in
mches.
''£
Area of
an airway,
in sq. ft.
V
Resistance
of an air-
way in lb.
pa = ksv*
Velocity
in ft. per
min.
a
u
'-pa
p"-"
Quantity
in cu. ft.
per min.
q^av
u
q'^^Xp^u
q=XpSp
Pressure
in lb. per
sq. ft.
-I
p'^Mw
i>»5.2«
Units of
work per
minute,
or power
on air, in
ft.-lb. per
min.
u^avp
u^qp
a"
M»/»33.000
268
MINING
Table — (Continued)
To Find
No.
Units of
work per
minute, or
29
power on
air, in ft.-
30
Ib. per min.
Horse-
31
power
Power
potential,
in units
32
33
34
Formula
X^
33,000
^"^''^ks
-\;?
^•"4fu-
To Find
Pressure
potential,
m units
Equiva-
lent orifice,
in sq. ft.
M o t i ve
column,
downcast
air, in ft.
Mot ive
column,
upcast air,
in ft.
No.
35
36
37
38
39
40
39
Formula
^'-'V^
""*'%
.0004g
M^DX
M
T-t
459 4- r
w
T—t
M^DXzF.-.
M
'459 + <
w
As specimen calculations, take a formula for pressure and one
for quantity. Taking the values from the table and formula 7,
ksi^ aju
p^ — for pressure and formula 20, q'^\j—Xa, gives —
.0000000217 X 36,000 X 500«
20
= 9.765 lb.
and
-4-
97.650
— X 20 =-10,000 cu. ft.
.0000000217X36,000
In this way any of these formulas may be worked out.
Variation of Elements. — In the foregoing table, fixed condi-
tions of motive column, as well as fixed conditions in the mine
airways, were asstuned. It is often convenient, however, to
MINING 269
know how the different elements, as velocity v, quantity q,
pressure p, power u, etc., will vary in different circulations; as,
by this means it is possible to compare the circulations in
different airways, or the results obtained by applying different
pressures and powers to the same airway. These laws of
variation must always be applied with great care. For example,
before it is possible to ascertain how the quantity in circulation
will vary in different airways, it is necessary to know whether
the pressure or the power is constant or the same for each
airway. The following rules may always be applied:
fa U
For a constant pressure: v vanes as \l~] Q varies as «\/~
(relative potential for pressure).
1 a
For a constant power: v vanes as — — r; q varies as — pr (relative
\lo \lo
potential for power).
lo
For a constant velocity: q varies as a; ^ varies as — ; m varies
as lo. ^
For a constant quantity: v varies inversely as a; ^ varies
inversely as Xu* (potential for power) ; u varies inversely as
X«' (potential for power) or directly as p.
For the same airway: The following terms vary as each other :
V, q, 'Sp, ^u.
Similar Airways: r = length of similar side, or similar
dimension.
For a constant pressure: v varies as \/-; q varies as r*
X '\j~\ f varies as lifl, or \l^.
For a constant power: v varies as -,,— ; q varies as rX '\j~"t
1
1 sr- ^^'
r varies as — , or 'V/g'.
Iv^ I
For a constant velocity: q varies as r'; ^ varies as -; « varies
as /r; r vanes as \g, -, or -.
P I
For a constant quantity: v varies inversely as r*; ^ and u vary
inversely as— ; r varies as —p, Vl , or V/_i.
>/» \p \lu
r — ^,'
270 MINING
Furnace VerUikUion. — p (motive column) varies as £>; <; varies
as Vd.
Fan Ventilation. — It has been customary in calculations per-
taining to the yield of centrifugal ventilators to assume as
follows: <7 varies as n; ^varies as n>; m varies as n*.
More recent investigation, however, shows that doubling the
speed does not double the quantity of air in circulation; or, in
other words, the quantity does not vary exactly as the ntunber
of revolutions of the fan. Investigation also shows that the
efficiency of centrifugal ventilators decreases as the speed
increases. To what extent this is the case has not been thor-
oughly established. The variation between the speed of a fan
and the quantity, pressture, power, and efficiency, as calculated
from a large number of reliable fan tests, may be stated as
follows:
For the same fan, discharging against a constant potential:
q varies as n •'^; p varies as n ^•^. Complement ci efficiency
a-K) varies as n •'*^.
The efficiency here referred to is the mechanical efficiency, or
the ratio between the effective work qp and the theoretical work
of the fan.
DISTRXBUTION OF AIR IN MINE VENTILATION
Legal Requirements. — The Anthracite Mine Law of Penn-
sylvania specifies that every mine employing more than 75
persons must be divided into two or more ventilating districts,
thus limiting the ntmiber that are allowed to work on one air-
current to 75 persons. The Bituminous Mine Law of Pennsyl-
vania limits the number allowed to work upon one ctirrent to
65 persons, except in special cases, where this number may be
increased to 100 persons at the discretion of the mine inspector.
Splitting of Air-Current. — ^When the air-cxurent is divided
into two or more branches, it is said to be split. The current
may be divided one or more times; when split or divided once,
the cturent is said to be traveling in two splitSt each branch
being termed a split. The number of splits in which a current
is made to travel is understood as the ntunber of separate ctar-
rents in the mine, and not as the number of divisions of the
current.
MINING 271
When the main air-current is divided into two or more splits,
each of these is called a primary split. Secondary splits are the
divisions of a primary spb't. Tertiary splits result from the
division of a secondary spUt.
Equal Splits <rf Air. — ^When a mine is spoken of as having
two or more equal splits, it is understood to mean that the
length and the size of the separate airways forming those splits
are equal in each case. It follows, of course, from this that the
ventilating ctirrent traveling in each split will be the same,
inasmuch as they are all subject to the same ventilating pres-
sure. When an equal circulation is obtained in two or more
splits by the use of regulators, these splits cannot be spoken of
as equal splits.
Natural Dividon of Air-Current. — ^By natural di^dsion of air
is meant any division of the air that is accomplished without
the use of regulators; or, in other words, such division of the
air-current as results from natural means. If the main air-
current at any given point in a mine is free to traverse two
separate airways in passing to the foot of the upcast shaft, and
each of these airways is free or an open split, i. e., contains no
regulator, the division of the air will be a natural division. In
such a case, the laiger quantity of air will always traverse
the shorter split of airway. In other words, an air-current
always seeks the shortest way out of a mine. A comparatively
small current, however, will always traverse the long split
or airway.
It is always assumed, in the calculation of the splitting of
air-currents, that the pressure at the mouth of each split,
starting from any given point, is the same. In order to find the
quantity of air passing in each of several splits starting from a
common point, the following rule may be applied.
Rule. — The ratio between the quantity of air Passing in any
split and the pressure potential of that split is the same for all splits
starting from a common Point. Also, the ratio between the entire
quantity of air in circulation in the several splits and the sum of
the pressure potentials of those splits is the same as the above ratio,
and is equal to the square root of the pressure.
Stated as a formula, indicating the sum of the pressure
potentials (-Yi-j-Xs-fetc.) by the expression l,Xp,
272 MINING
%Xp Xi
(? (?
Hence, P — and u « ezoress the pressure and
power respectiirdy, absorbed by the diculatiofli of tiie splits.
These are the basal formulas for flitting, from which any
of the factors may be calculated by transposition.
Proportional Divisioii of Alr-Cimeiit. — ^Different propor ti ons
of air are required in the several ^lits c^ a mine than would
be obtained by the natural division of the air-current. For
example, the longer splits employ a larger ntunber of men and
require a larger quantity of air to pass through them. They,
moreover, liberate a larger quantity of mine gases, for which
they reqttire a larger quantity of air than is passing in the
smaller splits. Hie natural division of the air-current would
give to these longer splits less air, and to the shorter ones a
larger amount of air, which is directly the reverse of what is
needed. On this account, recourse must be had to some means
of dividing this air proportionately, as required. This is
accomplished by the use of regulators, of which there are two
general types, the box regulator and the door r^ulator.
The box regulator is simply an obstruction placed in those
airways that would naturally take more air than the amount
required. It consists of a brattice or door placed in the entry,
and having a small shutter that can be opened a certain amount.
The shutter is so arranged as to allow the passage of more or
less air, according to the requirements.
The door regulator divides the air made at the mouth of the
split. It consists of a door hung from a point of the rib between
two entries, and swung into the current so as to ctft the air like
a knife. The door is provided with a set lock, so that it may
be secured in any position, to give more air to the one or the
other of the splits, as required. The position of this regulator
door, as well as the position of the shutter in the box regulator,
is always ascertained practically by trial. The door is set so as
to divide the area of the airway proportionate to the work
absorbed in the respective splits. The pressure in any split
is not increased, each split retaining its natural pressure.
MINING 273
Calcttlatioii of Pressure for Box Regulators. — ^When any
required division of the air-currerit is to be obtained by the use
of box regulators, these are placed in all the splits, save one.
This split is called the open, or JreCt split, and its pressure is
calculated in the usual way by the formula ^= . The
o'
natural pressure in this open split determines the pressure of the
entire mine, as all the splits are subject to the same pressure in
this form of splitting.
First, determine in which splits regulators will have to be
placed, in order to accomplish the required division of the air.
Calculate the natural pressure, or pressure due to the circulation
of the air-current, for each split, when passing its required
ksq*
amoxmt of air, using the formula P^ . The split showing
a*
the greatest natural pressure is taken as the free split. In each
of the other splits, box regulators must be placed, to increase
the pressure in those sph'ts; or, in other words, to increase the
resistance of those splits per unit of area.
The size of opening in a box regulator is calculated by the
formula for determining the flow of air through an orifice in a
thin plate under a certain head or pressure. The difference in
pressure between the two sides of a box regulator is the pressure
establishing the flow through the opening, which corresi>onds
to the head h in the formula »= yl2gh. This regulator is
usually placed at the end of a split or airway, and as the regula-
tor increases the pressure in the lesser split so as to make it
equal to the pressure in the other split, the pressure due to the
regulator will be equal to the ventilating pressure at the mouth
of the split, less the natural pressure or the pressure due to
friction in this split. Hence, when the position of the regulator
IS at the end of the split, the presstire due to friction in the split
ksqi
is first calculated by the formula P= , and this pressure is
a»
deducted from the ventilating pressure of the free or open split,
which gives the pressure due to the regulator. This is then
reduced to inches of water gauge, and substituted for i in the
19
274 MINING
.0004^7
formula A = -^ — p— . The value of A thus obtained is the area,
v»
in square feet, of the opemng in the regulator.
By the use of the box regulator, the pressure in all the splits
is made equal to the greatest natural pressure in any one.
This split is made the open or free split, and its natural pressure
becomes the pressure for all the splits, or the mine pressure.
This mine pressure, multiplied by the total quantity of air in
circulation (the siun of the quantities passing in the several
splits), and divided by 33,000, gives the horsepower upon the
air, or the horsepower of the drctilation.
Size of Opening for a Door Regulator. — ^The sectional area
at the regulator is divided proportionately to the work to be
perioTxned in the respective splits according to the i>roportion
All At^ui: It*. Or as Ai-\-At^a,Ai: a^ui: ui+«s, and i4i
til
= Xo. This furnishes a method of proportionate split-
ttl + Mt
ting in which each split is ventilated under its own natural
pressure. The same result would be obtained by the placing
of the box regulator at the intake of any split, thereby regulat-
ing the amount of air passing into that split, but the door
regulator presents less resistance to the flow of the air-current.
The practical difference between these two forms of regulators
is that in the use of the box regulator each ^lit is ventilated
under a pressture equal to the natural pressure of the open or
free split, which very largely increases the horsepower reqtiired
for the ventilation of the mine; while in the use of the door
regulator each spUt is ventilated under its own nattural pressure,
and the proportionate division of the air is accomplished with-
out any increase of horsepower.
In the use of the door regulator, each split is ventilated tmder
its own natural pressure, and hence, in the calculation of the
horsepower of such a circulation, the power of each split must
be calculated separately, and the siun of these several powers
will be the entire power of the circulation.
MINING
275
SPLITTING FORMULAS
Primary Splits. — In the accompanying table are given the
formulas used in the calculation of primary splits in the natural
division. The letters represent the same quantities they did
in the ventilating formulas already given.
VENTILATING FORMULAS FOR PRIMARY SPLITS
To Find
No.
Formula
Pressure, potential
35
Natural division
41
,^^^XQ
Pressure
42
y,- ^
Power
43
Quantity
44
45
= 2 XpV^"
(?-«(SA-p)»«
Increase of quantity due to
splitting the pressure be-
ing constant
46
Increase in Quantity due to
splitting, the power being
constant
47
^-\/(^)'
Example. — What is the pressure potential necessary to
ventilate a mine that has one primary split 4 ft. X 5 ft. X 800 ft.
and one 4 ft. X 5 ft. X 1 .200 ft?
276 MINING
SoLunoM. — Sabstituttng in formtila 35, the pressure potential
« 5.060; and for
of the first split is 20
20
.0000000217X14.400
the second split
it. 20 ^/_
\.(
20
4.131. There-
.0000000217X21.600
fore the pressure potential for the mine is 5,060+4.131 » 0.191
units.
VENTILATIlfG FORMULA FOR SECONDARY SPLITS
To Find
Relative potential
for pressure
Natural division
Pressure
Power
Quantity
No.
35
48
41
49
50
51
Formula
Xz-a-^
fl»*
Q
'+^W^+(XiTX0i
^-^f/^
p^k
Xi+
o*
p
MINING 277
Secondary Splits. — ^In the calculation of secondary splits
in the nattiral division, the work is often shortened, when many
splits are concerned, by using the relative potential, omitting
the factor k. But the final result must then be mtiltiplied by k
to obtain the pressure or power; or, these factors must be
divided by k, when finding the quantity, as in formulas 49 to 51.
Example. — ^How much air, in cubic feet per minute, is
required to ventilate each split, in the natural division, having
four secondary splits, as follows: one 4 ft.X5 ft. X 800 ft.;
one 4 ft.X5 ft.XSOO ft.; one, 4 ft.X 5 ft.X400 ft.; and one
4 ft. X 5 ft. X 300 ft?
Solution. — Substituting in formula 48, the amount of air
required in the first split is 10,000—5,388 — 4,612 cu. ft.; and in
the second split
10.000
■ i_r- 5,388 cu. ft.
1
\9,42
1 + .7471\/ +-
^''^,428* (1.054H-1.2172)«
The amount of air required in the third split, from formula 41,
is
1.0541
X 5,388 -2,500 cu. ft.;
(1.0541 + 1.2172)
and in the fourth split,
1.2172
-X 5,388 -2,888 cu. ft.
(1.0541 + 1.2172)
Proportionate Division of Air. — To accomplish the propor-
tionate division of air in primary splits, the pressure in one split
must be increased by means of a regulator to make it equal to
the pressure in the free or open split. Hence the pressure due
to the regulator is equal to the difference between the natural
pressures in these splits. The pressure due to the regulator
may, therefore, be found by the formula
in which P — pressure due to regulator;
/>2 = pressure in free split;
Pi — pressure in regulator split.
The pressure due to friction may be found by means of for-
mula 13 and the area of the opening in the regulator by formula
37.
278 MINING
Example. — What is the pressure due to friction if one split
is 4 ft. X 5 ft. X 800 ft. and has 3,500 cu. ft. per min. of air passing
through it and the other split is 4 ft. X 5 ft. X 1,200 ft. and has
6,500 cu. ft. per min. of air passing through it?
Solution. — Substituting in formula 13, the pressure due to
friction in the first split is 3.500«-t-5,060« = .47845 lb.; and in
the second spht, 6,5002-i-4,131>- 2.4757 lb.
When using the relative potential, in all calculations relating
to secondary splits, multiply the result by /; to obtain the pres-
sure or the power. To find the pressure due to friction, &ee
split, and secondary pressure, use formula 13; the areas of the
openings in the regulators may be fotmd by formula 37.
Example. — What is the pressure in each secondary split if
3,500 cu. ft. per min. of air passes through a split 4 ft.X5 ft.
X800 ft.; 6,500 cu. ft. per min. passes through a split 4 ft.
X5 ft. X 500 ft.; 4,000 cu. ft. per min. passes through a split
4 ft.X5 ft. X 400 ft.; and 2,500 cu. ft. per min. passes through
a split 4 ft.X 5 ft.X 300 ft., the constant /; in each case being
.0000000217?
Solution. — ^Applying formula 13 and multiplying by k gives
as the pressure
In the first split,
.0000000217 X (3,500-5- .7471)2 = .47848 lb.
In the second split,
.0000000217X (6,600-^.9428)2-1.0314 lb.
In the third split,
.0000000217X (4)000-5- 1.0541)2 = .31248 lb.
In the fourth split,
.0000000217 X (2,500 ^1.2172)2 = .091546 lb.
As the natural pressure in the third split is greater than that
in the fourth; the third is the free split and its natural pressure
is the pressure for the secondary splits. The pressure for the
primary splits is then found by first adding the pressures in
the second and third, and if their sum is greater than the natural
pressure for the first, it becomes the pressure for the primary
splits, or the mine pressure. If the natural pressure for the
first is the greater, this is made the free split, and its natural
nressure becomes the primary or mine pressure. In this case.
MINING 279
the secondary presstire must be increased by placing a regulator
in the third split.
If the primary or mine pressure is Pi-\-p», the pressure due to
the regulators is Pi — Pi, and (jpi+Pij — Pi.
VENTILATING METHODS AND APPLIANCES
There are, in general, three systems of ventilation, with
respect to the ventilating motor employed: natural ventila-
tion, furnace ventilation, and mechanical ventilation.
Natttral ventilation means such ventilation as is secured by
natural means, or without the intervention of artificial appli-
ances, such as the furnace, or any mechanical appliances by
which the circulation of air is maintained. In natural ventila-
tion, the ventilating motor or air motor is the air column that
exists in the downcast shaft by virtue of the greater weight of
the downcast air and forces the air through the airways of the
mine. An air column always exists where the intake and
return currents of air pass through a certain vertical height,
and have different temperattires.
In any ventilation, air columns are always established in
slopes and shafts, owing to the relative temperatures of the
outside and inside air. The temperature of the upcast, or
return column, may always be assumed to be the same as that
of the inside air. The temperature of the downcast, or intake
column, generally approximates the temperature of the outside
air, although, in deep shafts or long slopes, this temperattire
may change considerably before the bottom of the shaft or
slope is reached, and consequently the average temperature
of the downcast, or intake, is often different from that of the
outside air. The difference of temperatures will also vary with
the season of the year. In winter the outside temperature is
below that of the mine, and the circulation in shafts and slopes
is assisted, as the return coltunns are warmer and lighter than
the intake colunms for the same circulation. In the summer
season, however, the reverse of this is the case. The course
of the air-current will thus often be changed. "When the out-
side temperattire approaches the average temperature of the
mine, there wiU be no ventilation, except such as is caused by
accidental wind pressure.
280
MINING
In furnace ventilation the temperature of the upcast column
is increased above that of the downcast column by means of a
furnace. The chief points to be considered are the arrangement
and size of the furnace. Furnace ventilation should not be
applied to gaseous seams, and in some cases is prohibited by-
law; it is, however, in use in many mines liberating gas. In
such cases the furnace fire is fed by a current of air taken
directly from the air-course, sufficient to maintain the fire,
and the return current from the mines is conducted by means
of a diunb drift, or an inclined passageway, into the shaft, at a
point from 50 to 100 ft. above the seam. At this point, the
heat of the furnace gases is not sufficient for the ignition of the
mine gases. The presence of carbon dioxide in the furnace
gases also renders the mine gases inexplosive. In other cases
where the dumb drift is not used, a sufficient amount of fresh
air is allowed to pass into the return current to insure its dilu-
tion below the explosive point before it reaches the furnace.
In a slope opening, the air column
is inclined; it is none the less, how-
ever, an air column, and must be
calculated in the same manner as a
vertical column whose vertical
height corresponds to the amount
of dip of the slope. Fig. 1 shows a
vertical shaft and a slope, the air
column in each of these being the same for the same tempera-
tvue. The air column in all dips and rises mxist be estimated
in like manner, by ascertaining the vertical 'height of the dip.
Calculation of Ventilating Pressure in Furnace Ventilation.
The ventilating pressure in the mine airways, in natural or in
furnace ventilation, is caused by the difference of the weights
of the primary and secondary columns. Air always moves
from a point of higher pressure toward a point of lower pres-
sure, and this movement of the air is caused by the difference
between these two pressures. In this ceilculation each coluxnn
is supposed to have an area of base of 1 sq. ft. Hence, if the
weight of 1 cu. ft. of air at a given barometric pressure, and
having a temperature equal to the average temperature of the
column, is multiplied by the vertical height D of the column.
Pig. 1
iziar
MINING 281
not only is the weight of the coltmin obtained but the pressure
at its base due to its weight. Now, as the ventilating pressure
per square foot in the airway is equal to the difference of the
weights of the primary and secondary columns,
.3253 XB 1.3253 X5\
459+< 469+ r /
Calculation of Motive Colunm or Air Colunm. — It is often
convenient to express the ventilating pressure p pound per
square foot in terms of air column or motive column M, in feet.
The height of the air colunm M is equal to the pressure p
p
divided by the weight wofl cu. ft. of air, or Af « — . The expres-
w
sion for motive column may be written in terms of the upcast
air or of the downcast air, the former giving a higher motive
colunm than the latter for the same pressure, because the
upcast air is lighter than the downcast. As the surpltis weight
of the downcast column of air produces the ventilating pressure,
it is preferable to write the air column in terms of the downcast
air, or, in other words, to consider the air column as being
located in the downcast shaft, and pressing the air downwards,
and through the airways of the mine. If the expression for the
ventilating pressure is divided by the weight of 1 cu. ft. of
/ 1.3253 XB\
downcast an: 1 1 , after simplifying the motive
\ 459+< /
;) XD,
/ T-t
\459+r
column, Af = I ; — ) XD, which is the expression for motive
column in terms of the downcast air.
If, on the other hand, the expression for the ventilating pres-
sure is divided by the weight of 1 cu. ft. of upcast air
/1.3253XM / T-t \
I I , M = I I XD, which is the expression for
\ 459+ r / \459+</
motive column in terms of the upcast air.
Mechanical Ventilators. — ^A large nimiber of mechanical
ventilators have been invented and applied to the ventilation
of mines. Mechanical motors of the fan type present two
distinct modes of action in producing an air-current: (1) by
propulsion of the air; and (2) by establishing a pressure due
to the centrifugal force incident to the revolution of the fan.
282 MINING
Pans have been constructed to act wfaoOy on one or tlie other
of these principles, wfaile others have been contracted to act
on both of these princxides combined.
The action of the disk fan resembles that of a windmill,
except that in the latter the wind drives the mill, ^dule in the
former the fan propels liie air or pcoduces the wind. This type
of fan consists of a number of vanes radiating from a central
shaft, and TwHinAH to the plane of revolution. The fan is set
up in the passageway between the outer air and the mine air-
ways. Power being applied to the shaft, the revolution of the
vanes propels the air, and pcoduces a cuiient in the airwairs.
The fan may force the air through, or exhaust the air from, the
airways, according to the direction of its revolution. This
type of fan is most efficient under light pressures. It has found
an extensive application in mining jnuctice. but has been
replaced to a large degree in the ventilation of extensive mines;
this type of fan acts wholly by propulsion.
Centrifugal fans include all fans that act soldy on the centrif-
ugal principle, and those that combine the centrifugal and pro
XMilsion principles. The action of the fan depends on the form
of the fan blades, which are set at right angles to the plane of
revolution, and not inclined, as in the disk fan just described.
The blades may, however, be either radial, sometimes spoken
of as paddle blades^ or they may be inclined to the radius either
forwards in the direction of revolution, or backwards. When
the blades are radial, the action of the fan is centrifugal only.
The inclination of the blades backwards from the direction of
motion gives rise to an action of propulsion, in addition to the
centrifugal action of the fan. The blades in this position may
be either straight blades in an inclined position, as in the origi-
nal Guibal fan, or they may be curved backwards in the form
of a spiral, as in the Schiele and Waddle fans.
Centrifugal fans may be exhaust fans or force fans or blowers.
In each, the action of the fan is essentially the same; i. e., to
create a difference of pressure between its intake or central
opening, and its discharge at the circumference. The centrif-
ugal force developed by the revolution of the air between the
blades of the fan causes the air within the fan to crowd toward
the circiunference; as a result, a depression is caused at the
MINING 283
center and a compression at the circumference, giving rise to a
difference of pressure between the intake and the discharge of
the fan.
Exhaust Fans. — If the intake opening of the fan is placed
in connection with the mine airways, and the discharge is
open to the atmosphere, the fan will act to create a depression
in the fan drift leading to the mine, which will cause a flow of
air through the mine airways and into and through the fan.
In this case, the fan is exhausting, its position being ahead of
the current that it produces in the airway. The atmospheric
pressure at the intake of the mine forces the air or propels the
current toward the depression in the fan drift caused by the
fan's action.
Force Fans and Blowers. — If the discharge opening of the
fan is placed in connection with the mine airways, a compression
will result in the fan drift owing to the fan's action, and the air
will flow from this point of compression through the airways of
the mine, and be discharged into the upcast, and thence into
the atmosphere. The ventilating pressure in the case of either
the exhaust fan or the force fan is equal to the difference of pres-
sure created by the fan's action. In the former case, when the
fan is exhausting, the absolute pressure in the fan drift is equal
to the atmospheric pressure less the ventilating pressure, while
in the latter case, when a fan is forcing, the absolute pressure
in the fan drift is equal to the atmospheric pressure increased
by the ventilating presstire. This gives rise to two distinct
systems of ventilation, known as the vacutmi and the plenum
system. In the vacuum system, the ventilation of the mine
is accomplished by creating a depression in the return airway
of the mine. In the plenum system, the air-current is propelled
through the mine airways by means of the compression or ven-
tilating pressure created at the intake opening of the mine.
Position of Fan. — The position of the fan, whether used as
an exhaust or blower, should be sufficiently removed from the
fan shaft to avoid damage to the fan in case of explosion in the
mine. Even in non-gaseous mines, the fan should be located
a short distance back from the shaft mouth, to avoid damage
due to settlement. Connection should be made with the fan
shaft by means of an ample drift, which should be deflected
\e shock to the cu
mouth. The ventilator
should be arranged so
from an exhaust to a
1 notice. This is managed
i by housing the central
orifices or intake of the
hem directly with the fan
Tnwa of Ceotilcufil Fuu.— The Nasmyth fan, shown in
Pig. 2 is the original type of fan. It had straight paddle
blades radiating from the center, and was probably the earliest
attempt to apply the centrifugal principle to a mine ventilator.
at a considerable speed, but proved
very ineffirient. It depended more
on the effort of propulsion given to
the air than on the centriftigal prin-
ciple, as the depth of the blade was
as much too small as that of Na-
The discharge took place a
286
MINING
by having the discharge made into a spiral chamber surround-
ing the fan and leading to an expanding chimney.
The Guibal ventilator, shown in Fig. 6, embodied the feattares
of the Nasmyth ventilator, with the addition of a casing built
over the fan to protect its circumference. This casing was,
however, a tight-fitting casing, and as such, differed very
materially from the Schiele casing. In the Guibal fan the
blades were arranged ui>on a series of parallel bars passing upon
each side of the center and at some distance from it. By this
construction, the blades were not radial at their inner edge or
the throat of the fan. They were curved, however, as they
approached the circumference of the fan, so as to be normal or
radial at the circumference.
Fig. 7
The Murphy ventilator, shown in Fig. 7, consists of twin fans
supported on the same shaft and set a few feet apart. Each fan
receives its air on one side only, the openings being turned
toward each other. This ventilator is built with a small
diameter, and is run at a high speed. The blades are curved
backwards from the direction of motion. The intake opening
is considerably enlarged; a spiral casing generally surrotmds
the fan, and in every respect this fan makes an efficient high-
speed motor. It has received considerable favor in the United
States, where it has been introduced into a large number of
mines.
Perhaps no centrifugal ventilator has been as little understood
*n regard to its principle of action as the CapeU fan, shown in
HIKING 287
Pig. 8. Tlie fan is constnKrted along the lines of the SchicLe
body of the fan. A set of smaller Bupemuinerarf blades occupi'
inclined to the plane of levolution so as to asist in deflecting
the entering air through soibU ports or openings into the main
body of the fan, ivhere it is revolved and discharged at the
B ^Hml space lesembliag that sunounding
the Schieie fan. The larger blades of this fan are curved back-
wafdfl ai the Schieie blades, but are not tapered lonatd the
drrumference. The Can is capable (rf giving a high water gauge,
sad is efScient as B mine ventilator. The space surrounding
the fan is extended to form an expanding chimney. The
£an may be used either as an exhaust fan or a blower.
The best results in the United SUtes have been obtained by
blowers; in Geimany, where this fan is in gfoefal use. there are
288 MINING
Stoppings are used to close break-throughs that have been
made through two entries, or rooms, for the ptirpose of main-
taining the circulation as the workings advance; also to close
or seal off abandoned rooms or working places. Stoppings
must be air-tight and substantially built.
An air bridge is constructed for the passage of air across
another airway. When it crosses over, it is called an overcast;
when it passes tmder the airway, it is called an undercast. In
almost every instance, overcasts are preferable to undercasts.
An air brattice is any partition erected in an airway for the
purpose of deflecting the current. A thin board stopping is
sometimes spoken of as a brattice; but the term applies more
particularly to a thin board or canvas partition nmning the
length of an entry or room and dividing it into two airways,
so that the air will pass up one side of the partition and return
on the other side, thus sweeping the face of the heading or
chamber. Such a temporary brattice is often constructed by
nailing cloth to upright posts set from 4 to 6 ft. apart along one
side of the entry a short distance from the rib.
Curtains are sometimes called canvas doors; they are heavy
duck, or canvas, himg from the roof of the entry to divide
the air or deflect a portion of it into another chamber or entry.
Curtains are thus used very often previous to setting a perma-
nent door frame. They are of much use in longwall work, or
where there is a continued settlement of the roof, which would
prevent the construction of a permanent door; also, in tempo-
rary openings where a door is not required.
HOISTING AND HAULAGE
HOISTING
There are two general systems of hoisting in use: (1) Hoist
ing without attempting to balance the load, when the cage and
its load are hoisted by an engine and lowered by gravity; (2)
Hoisting in balance, when the descending cage or a special
counterbalance assists the engrine to hoist the loaded ascending
cage. Hoisting in balance is usually effected by the use of
MINING
289
double cylindrical drums, flat ropes winding on reels, conical
drums, the Koepe system, and the Whiting system.
Double cylindrical drums axe widely used. They consist
essentially of an engine coupled directly or else geared to the
common axis of the drums. The drtmis are usually provided
with friction or positive clutches, and brakes, so that they can
be nm singly if desired, or the load can be lowered by gravity
and the brake.
Flat ropes wound on reels are sometimes used either for
unbalanced hoisting with a single reel or for balanced hoisting
with a double reel. A flat rope has the advantage of prevent-
ing fleeting, but its first cost, extra weight, wear, and difficulty
of repairing have prevented its very general adoption.
Pig. 1
A conical drum. Pig. 1, equalizes the load on an engine just
as a flat rope on a reel. On account of the fleeting of the rope,
however, the drum must be set at a considerable distance from
the shaft to prevent the rope leaving the head-sheave. A tail-
rope gives the most perfect counterbalance, the weight of the
cage and rope on each side being exactly equal.
In the Koepe system. Pig. 2, one rope runs over and the other
under driving sheaves S. A tail-rope R is used, and the head-
sheaves X, vf are placed vertically and at such an angle to each
other that their grooves and the groove in the driving sheave
are in line. As the main driving shaft is short, the engines can
20
be placed close together, thus requiring a smaller toundatioD
and engine house than for a drum hoist. The objection to the
system is the liabilitj' of the rope to slipping about the driving
B. for which reason a hoisting indicator cannot be depended
The system is also
MuM the rope break, both
cages wiU fall to the bottom.
The WhiUns system. Pig. 3, uses two narrow.fiTooved dnims
placed tandem instead of a single-driving sheave as in tbe
^ Koepe system. The
- ■ rope passes from the
cage A over a head-
the sheaves M and F
the fleet sheave C. back
' under another guide
St coupled direct to
liaft. or geared. The
drums F and M are
rMipled together by b
a balance to the loads,
lest to incline the foUoT
possible to utilize all the
rope. A toil-rope is not
n. though oi
wr sheave F from the vertical an
the distance between the centers
adjacent grooves, the object being to eliminate chafing
ceu the ropes around the drums and to prevent them from
ing off by enabling the rope to run from each grwive in one
1 straight to the proper groove in the other. This throm
MINING
291
the shaft aod crankpina out of parallel with those of the main
dnun, but this difficulty is overcome by the eonoectiona la the
enda ot the parallel roda. The fleet sheave C is arranged to
travel backnarda and forwards, as shown by the dotted lines,
in order to change the worldne length of the tope, whereb/
holatins can be done from different levels in the shaft.
Power Uaed for Hoisting, — The power used for ht^ting la
generally ateom for the main boiats- Electricity la, however,
coming rapidly into use. particularly for acooller holata and
underground Inatallations, and Iot main hoista in localiona
292 MINING
top C, empty cage pltis rope at bottom D, small diameter of
drum X, and large diameter y; then,
Ax—By^Cy—Dx
To Find the Size of Hoisting Engine. — ^Let
D = diameter of cylinder;
P = mean effective steam pressure in cylinders;
r = ratio of stroke to diameter of cylinder;
w=work per revolution required to be done;
then, by making one cylinder capable of doing the work, n
s number of strokes, « = work per minute in foot-pounds.
^-l-97iy/^.orD='^-
.7854Pr»
To Find Actual Horsepower of Engine for Hoisting Any Load
Out of Shaft at Given Rate of Speed. — To the weight of the loaded
car add the weight of the rope and cage. This will give the
gross weight.
Then,
gross weight in lb. X speed in ft. per min.
H. P. ^ ~"~ ■
33,000
Add J for contingencies, friction, etc.
The following rules regarding winding engines are given by
Percy:
To Find Load That Given Pair of Direct-Acting Engines Will
Start. — Multiply the area of one cylinder by the average pres-
sure of the steam per square inch in the cylinder, and twice the
length of the stroke. Divide this by the circumference of the
drtun, and deduct J for friction, etc.
Knowing Load and Diameter of Cylindrical Drum, and Length
of Stroke, Cut-off and Pressure of Steam at Steam Gauge, to Find
Area and Diameter of Cylinders of Pair of Direct-Acting Engines,
Multiply the load by the circumference of the drum, and add i
for friction, etc. Divide this by the mean average steam pres-
sure, multiplied by twice the length of the stroke.
To Find Approximate Period of Winding on a Cylindrical
Drum With Pair of Direct-Acting Engines. — ^Asstime the piston
to travel at an average velocity of 400 ft. per min., and divide
this by twice the length of the stroke, and multiply by the cir-
cumference of the drum. This gives the speed of cage in feet
UWING
>f shaft by ttii>,uid the r
263
ps minute. Dinde the depth ol
will be the period of winding.
Head-Pnunca.— Head-frames are built of wood or rt«L
They vary in height from 30 to 100 ft., depeading □□ local cod-
dilions. The inclined leg of a hnd-fiHine should be placed so
the shaft and the pull of an engine.
Fig. 4 shows the graphic method of detmnir
mgihedireeti
and magnitude of this resultant force. Prod
i« the ditKti
umanddownt
distance GK
scale to represent the load hanging
sent the pull of the engine, complete
tion of the line GL represents the
this force. The inclined leg of the
head-frame should be placed as S
nearly as possible parallel to this
resultant line, and should be
strain equal to this resultant.
Htadskiavts are made of iron.
e used. The fori
but the latt
er are lighter and stronger, and therefore usually
better. Th
of the rope,
md the table giving this will be found on page 108.
Wmught-iron spokes should be staggered in the
placed radially.
Safay caic
Iits usually consist of a pair of toothed cams placed
on either Sid
of the cages and enclosing the guides. When the
hoisting rope, these cams are kept away tn^m the
guides by su
table springs; but if the rope breaks, the springs
294 MINING
come into acticm and throw the catches or dogs so that they
grip the guides, then the tendency to fall increases the grip on
the guides.
Detaching hooks are devices that automatically disconnect
the rope from the cage in case of overwinding.
HAULAGE
The magnitude of modem mines and the practice of loading
or of treating the coal or ore at a large central station makes the
underground haulage of the material one of the most important
problems in connection with mining. A good haulage system
is now essential to make most mines a commercial success.
Gravity Planes. — With gravity planes the loaded car or trip
hauls the empty car up the grade. Two ropes are fastened to a
drum so that the rope attached to the loaded car tinwinds from
the drum as the car descends, while the rope secured to the
empty car is wound on the dnun and the car thus hauled up the
plane. The following rule gives suggestions based on practice
that have been successful: For lengths not exceeding 500 ft.,
the minimum grade for the incline should be 5% when the
weight of the descending load is
JL ^® 8,000 lb. and that of the ascend-
C — — •-"•^^. — —^ D ing load 2,800 lb. Or the in-
clination should not be less than
5i% if the respective descending and ascending loads are one-
half of those just given. When the length of the-plane is from
500 to 2,000 ft., the grade should be increased from 5% to 10%,
according to the loads. A load of 4,000 lb. on a 10% grade
2.000 ft. long will hoist a weight of 1.400 lb.
The angle of inertia is that angle or inclination at which a car
will start to move down the slope or plane. The car, when it
has once started on this grade, will continue to accelerate its
speed as it descends the plane AB,m the accompanying illus-
tration. If the angle of inclination is decreased until the plane
AB occupies the position i4C, so that the moving car will con-
tinue to move at a uniform velocity instead of accelerating
its speed, the angle DC A will be the angle of roiling friction, and
the tangent of this angle will be the coefficient of rolling friction
for the car.
MINING 296
The upper portion of a plane is made steeper than the lower
portion so that the trip may start quicldy at the head and after-
wards maintain a tiniform velocity. With a good brake to
control the cars, the tmiform grade of a central portion of a
gravity plane should not fall much below 3*, which corresi)onds
practically to a 5i% grade.
Rope Haulage. — The tail-rope system of haulage uses two
ropes and a pair of drums on the same shaft. The main rope
passes from one drtmi directly to the front of the loaded trip,
and the tail-rope passes from the other drum to the large sheave
wheel at the end of the road, and back to the rear of the loaded
trip. While hauling the loaded trip, the drtun on which the
tail-rope is wound is allowed to turn freely on its journal by
throwing its clutch out, while the engine turns the other drum.
When the empty trip is being hauled, the clutch on the main-
rope drum is thrown out and the one on the tail-rope drum is
thrown in. The engine then turns the tail-rope drum and
allows the other one to pay out rope as the trip advances.
The tail-rope system is suitable for steep, circuitous, and
undulating roads. The trip can be kept stretched at all points,
and thus the cars will be prevented from bumping together or
from being jerked apart as the trip is passing over changes in
the grade. It is tindoubtedly the most satisfactory system of
rope haulage under the natural conditions of most haulage roads
in mines, and especially so where but one road is available for
haulage purposes.
Calculation of Tensioii of Haulage Rope. — The tension of
haulage ropes may be found by the formula,
r= W(sin a-f-ft cos a)-\-w(d-\-fi.l),
in which 7* »■ tension or pull upon rope, in pounds;
PFa- weight of loaded trip, in pounds;
w weight of rope per linear foot, in i>ounds;
/■-length of two ropes; equals 2 times the distance
from winding drum to tail-sheave, in feet;
d«« vertical drop of rope, in feet;
a « slope angle of maximum grade.
Example. — ^What size of steel wire rope will be required to
haul a trip of 20 mine cars, the weight of the loaded cars being
3,000 lb. each, the depth of the shaft 300 ft., and the distance
296 MINING
from the foot of the shaft to the tail-sheave 000 yd., the znaxi-
mum grade in this haulage being lO**, m " A? Assttming a | in.
rope, weighing .89 lb. per lin. ft.
Solution. — ^From the formula just given,
_ __ / ^ .9848\ / 6.000\
r=60,000X (.17365-f— — j -f.89X (SOO-f^ j
«say 12,300 lb., or somewhat over 6 T.
Referring to the tables for steel haulage ropes with 6 strands
of 7 wires each, the breaking strain of a } in. rope, weighing^ .89
lb. per lin. ft., is found to be 18.6 T. which will give a factor
of safety of about 3. However, a }-in. or even a l-in. rope,
should be used for a change of ropes would then be required less
often. Making the necessary corrections for l-in. rope weigh-
ing 1.58 lb. per lin. ft., r- 12,607 lb.
The endless-rope system uses an endless rope, which is kept
rtmning continuously by a pair of drums geared together and
set tandem. The drums are comparatively narrow and pro-
vided with grooves for the rope to run in. Two drtmis are
necessary to get sufficient friction to drive the rope when the
trip is attached to it. The rope is passed arotmd both drums
a ntmiber of times, depending on the amount of friction desired,
without completely encircling either. It then passes to a ten-
sion wheel at the rear of the drums and thence to the sheave
wheel at the far end of the road and back to the drums. To be
used to best advantage, the grade should be in one direction
and it should be necessary to haul cars from a number of places
en route. The cars are attached to the rope by friction grips
in a manner quite similar to the way in which street cars are
attached to cable lines. Therefore, any jerking due to the cars
bumping together or stretching the hitchings will seriously
injure the rope where the grip takes hold. A double road is an
essential feature of endless-rope haulage.
To Determine Friction Pull on an Endless-Rope Haolace.
Let 0= output in pounds per minute;
V — speed of winding, in feet per minute;
/« length of haulage road, in feet;
<; = capacity of mine car, in pounds;
zoi — weight of mine car, in po\mds;
tt»— weight of rope, in pounds;
MINING 297
r— load on the rope, in potinds;
fi -» coefficient of friction.
10
Then, — —weight of material in transit;
V
©
wi — weight of moving cars, loaded and empty;
2lw » weight of rope ;
(-t)
lO , ,
-f2wZ»« entire moving load.
V
And if the coefficient of friction equals ^,
X O (l+— j -f 2iw
H P —
* 33,000
Inclined Roads. — ^The calculation of power for incUned
roads is the same as that just given, except that the work due
to lifting the coal through a height h must be added to that
found by the previous formulas. If h equals the elevation due
to the grade of the incline, the additional work of the engine
due to hoisting the load from this elevation will be Oh and the
total work per minute u will be
; = ^/ O (l+-^) +2w» -\-0k
Motor Haulage. — ^Wire-rope hatdage is very efficient in
headings, on heavy grades, and against large loads, but in
crooked passages it entails great costs for renewals and repairs.
When the grades do not exceed 5% for short distances and
average 3% against, or for short distances 8% and 5% average
in favor of loads, locomotives have been found the most econom-
ical form of haulage. Gathering locomotives are used to take the
cars from the rooms. They are similar in their general cauf
struction to the ordinary traction locomotive but are ^hontet'
and lower.
f
In general, it costs from 6 to 10c. per T. to deliver coal from
face of workings to shaft, slope, or tipple, where the haul is 1
mi. and the tracks approximately level; yet there are mines-
that at present haul from parting with the trolley system, the
298 MINING
miner delivering from face of room, making an average rotuid
trip of 9,000 ft., at a total cost of Ic. per T. Since the advent
of the electric-mining locomotive, there has been a change in
the mine wagons universally tised. Formerly it was ctistomary
to find as much as 60 lb. i>er ton car resistance on the level,
while at present it is as low as 15 lb.
Compressed air locomotives are particularly useful in gaseous
mines, as they improve ventilation and are i>erfectly safe under
all conditions. Their great disadvantage is their size.
For a number of years gasoline motors have been used for
various purposes on the Pacific coast and in metal mines of the
west, this development being brought about by the high cost
of steam generation and, in many cases, scarcity of water in
arid regions. In shape and appearance the gasoline locomotive
resembles the electric locomotive. They are usually con-
structed to run on full and on half speed. Each motor is
equipped with a carbureter, which properly mixes the air and
the gasoline in the cylinder. Each locomotive is also equipped
with an electric igniting device, which oi>erates from a storage
battery when the motor is starting and thereafter from a
magneto. In some motoi*s, absorption chambers are used to
absorb the carbon dioxide generated and to cool the gases.
These chambers are also a protection against the ignition of
gas or coal dust when the engine back fires.
The advantages of the gasoline motor are: No power plant
is needed to oi>erate them, the power-generating apparatus
being a part of the motor. No transmission-wire lines or pipe
lines are needed. Humidification of the air is aided. The
disadvantages are: The use of gasoline in mines, as a mixture
of gasoline and air forms an explosive gas. Combustion of
gasoline extracts oxygen from the air. Carbon dioxide and
nitrogen are products of combustion, and if combustion is not
complete carbon monoxide is formed. The gasoline motor
costs 25 to 50% more than an electric motor of the same power.
The gasohhe motor will not start as large a trip or take an over-
load like an electric motor does.
The Bituminous Mine Laws of Pennsylvania say, *' No prod-
uct of i>etroleam or alcohol or any compound that in the
ooinion of the inspector will contaminate the air to such an
MINING 209
extent as to be injtuious to the health of the miner, shall be
used as motive power in any mine. " Modem gasoline motors
are eliminating this objection more and more as improvements
are made.
Speed of haulage depends on the system of haulage used and
on the condition of the haulage road. The law in Pennsylvania
provides for a speed of haulage not over 6 mi. per hr., and this
is the speed at which electric and compressed-air haulages are
usually calculated and at which loaded trips are usually run.
Empty trips are usually run at a slightly higher speed. It has
been found in general practice that the maximum pulling power
of a mule as well as a locomotive is, approximately, one-fifth of
its weight, or, in other words, a locomotive will pull as much as
the same weight of mules will pull, and at a speed about three
times as great.
MINE ROADS Ain> TRACKS
Underground or mine-car tracks should be solidly laid on
good sills, resting on the solid floor of the mine. They should
be well ballasted, and should have good clean gutters on the
lower side of the entry, so that the rails may be protected as
much as possible from the action of the mine water.
The grades depend entirely on circumstances, but, when
possible, the grade should be in favor of the load, and should
be at least 5 in. in 100 ft. to insure flow in the gutters alongside
the track.
Ties should be spaced about 2 ft. apart, center to center,
making 15 to a 30-ft. rail. The rail should be well spiked to the
ties with four spikes to each tie, the joint between two rails on
one side of the track being located about midway between two
joints on the opposite raU. On curves, ties should be laid
so as to form radii of the curves of the track.
The weight of rail to be chosen in any individual case depends
entirely on the weight of cars used, and the motive power. For
cars having a capacity of about 1^^ T., the weight of rail, when
the motive power is live stock, should not be less than 16 lb.
per yd., while for cars having a capacity of 2 T. or over, a 20-lb.
rail should be used. There is no economy in using a very light
rail, as the base is gradually eaten away by the mine water;
300 MINING
a heavy section of rail can be used much longer before the rails
become weakened. On main roads, where haulage machinery
of one kind or another is used, the weight of rail for 2-T. cars
should be from 25 lb. to 35 lb. per yd., and on steep slopes as
high as 40 lb. per yd. In the case of locomotive haulage,
authorities claim that the weight of rail should be regulated
by allowing 1 T. for each driver for each 10 lb. weight of rail
per yd.
The gauge of the track in coal mines should not be less than
30 in. nor more than 48 in. A mean between these two, or a
gauge of from 38 in. to 42 in. is desirable, because it com-
bines, to a certain extent, the advantages claimed for the
extremes.
Curves should be of as large a radius as permissible, and
never, if possible, of less radius than 25 ft. The resistance of
curves is considerable; and the smaller the radius of the curve,
and the greater the length of the curved track occupied by the
trip, or train, the greater is the resistance.
To Bend Rails to Proper Arc for Any Radius. — ^Rails are
usually 30 ft. long, and the most convenient chcnrd to use in
bending mine rails is 10 ft. Hien, having the radius and chord,
find the rise of middle ordinate by squaring the radius, and
from it take the square of one-half the chord. Extract the
square root of the remainder and subtract it from the radius;
the result will be the rise of the middle ordinate. Thus, having
a radius of 30 ft. and a chord of 10 ft. the middle ordinate will be,
30-V302-5*-.42ft.
Rail Elevation. — In elevating rails on curves, consider
whether the hauling is to be done by a rope, a locomotive, or an
electric motor. For either of the latter, elevate the rail on the
outside of the curve; but for the first, elevate the inner rail,
for as the power is applied by a long flexible rope', there is
always a tendency for both rope and cars to take the long chord
of the curve as soon as the point of curve is reached. On slope
haulages, operated by a single rope, when the weight of the cars
traveling on the grade of the slope is sufficient to draw the rope
off the hoisting dnmi, the rails on ctuves should be elevated on
the outside, the effect then being similar to that of a locomotive,
i. e., the centrifugal force tends to throw the car to the outside
MINING
301
of the track. In such cases, the elevation should be moderate
so as not to interfere with the trip when drawn out again by the
rope — ^the opposite effect being then experienced.
Rollers. — The rollers on level tracks should not be more
than about 20 ft. apart to properly carry the rope, and on gravity
slopes where the lower end of the slope gradually flattens off,
the distance between rollers should not be more than 12 to 15
ft., as this spacing allows the trip of cars to rtm much farther
by keeping the rope well off the ties, than if they are farther
apart, thereby not supporting the rope, and causing a great
amotmt of friction between the rope and the ties.
Switches. — The switch, or latch, most commonly used in
mines is shown in Pig. 1. When the branch or siding is in
constant use, an ordinary railway frog is substituted for the
cross-bar b. The latches a, are wedge-shaped bars of iron
(made as high as the rail) with an eye in the thick end.
A modification of this
switch is shown in Fig. 2, ^ ^
which represents a form of
double switch. These
latches are set by the
drivers, who kick them over
and drop a small square of
plate iron between them to
hold them in place. This
switch costs more than the
other style and is better
adapted to outside roads than to inside roads. The ordinary
movable rail switch in every-day use on all surface railways is
sometimes used in mine roads. It is commonly used in slopes
arranged as shown by Fig. 6, to replace latches set by the car,
and is also largely used in outside roads.
For crossings, ordinary railway frogs and grade crossings are
sometimes used, as is also a small ttuntable, which then answers
two purposes. More frequently the plan shown in Fig. 3, in
which four movable bars are thrown across the main track when-
ever the other road is to be used, is adopted. The subordinate
road is built from 1) to 2 in. higher than the main road, to
allow the bars to clear the main-track rails.
Fig. 1
302
MINING
Tunumts. — On gangways or headings used as main haul-
age roads, turnouts should be constructed at convenient
Fig. 2
Fig. 3
intervals to allow the loaded and empty trii>s to pass. These
turnouts should be long enough to accommodate £rom 5 or 6
up to 15 or 20 cars.
Slope Bottoms. — ^At the foot of a slope or at the landing on
any lift, the gangway is widened to accommodate at least two
tracks — one for the empty and one for the loaded cars. The
empty track should be on the upi>er side of the gangway, or
that side nearer the floor of
the seam, and the loaded track
on that side of the gangway
nearer the roof of the seam.
An arrangement of tracks often
used is shown in Pigs. 4 to 9.
Fig. 6
BCaterial Required for 1,000 Ft. and for 1 Mi. ol Sinde
Track. — For the quantity of wooden ties required for 1,000 ft.
MINING
303
and for 1 mi. of single track, see page 307. Weights of rails
are given in long tons of 2,240 lb.; hence .9 T. is equal to
W
ar CM
BOTTOm.
BOTTOM
orstop£
2,016 lb. and not to 1,800 lb. Each increase of 5 lb. per yd.
in the weight of the rail, increases by 1.488 T. and by 7.857 T.,
respectively, the tons required to lay 1,000 ft. or 1 mi. of track.
In measuring a rail, it will be found that the height of a rail is
equal to the width of its base.
Rule. — To find the weight, in long tons, of the rails necessary
to lay 1 mi. of single track, multiply the
weight per yard of the rail by ^, or by
1.5714.
Rule. — To find the weight of rails for
1,000 ft. of single track, multiply the
weight per yard by .29761.
Thus, the weight of 70-lb. steel for
1 mi. and for 1,000 ft. of single track
would be. respectively, 70X¥= 110 T.,
and 70 X .29761 = 20.833 T.
'Fig. 9
For lengths other than 1,000 ft., multiply the quantities for
1.000 ft. by the ratio the given length of track bears to 1,000.
304
MINING
Thus for the material for 600 ft.. 1.580 ft. or 4,000 ft., multiply
the quantities (rails, fish-plates, bolts, or spikes) by .6, 1.58 or
by 4 as may be.
Prices quoted for rails include the necessary splice bars
(fish-plates) and bolts, but not the spikes. If requested at the
time of placing the order, the mills will drill the holes necessary
for electric bonding, and, generally, without charge. While the
STANDARD SIZE OF RAILS
Amount
Amount
Weiffht
per Y ard
Height
Width
of Head
Required
per 1.000
Required
per Mile
Ponnds
Inches
Inches
ft. Tons
Tons
8
1
^
H
2.381
12.571
12
.
lA
3.571
18.857
16
2
.
4.762
25.144
20
2
.
1
5.952
31.429
25
21
■
1' '
7.441
39.286
30
3
8.929
47.143
35
3i
1
10.417
55.000
40
3}
3H
li
11.905
62.857
45
2
13.393
70.714
50
31
4^
2f
14.881
78.671
55
i
16.369
86.428
60
H
21
17.858
94.286
65
^Xf
2i}
19.346
102.143
70
4}
2t^
20.833
110.000
75
4H
2H
22.321
117.857
80
5
2A
23.809
125.714
85
5J^
25.298
133.671
90
5|
2f
26.786
141.429
95
5tt
2H
28.274
149.286
100
5f
2i
29.763
157.143
standard length of rails is 30 ft., the order is considered to
have been acceptably filled, if not to exceed 10% of the rails
are in shorter lengths, varying by even feet down to 24 ft. In
the accompanying table all sizes from 40 lb. to 100 lb., are of
the standard established by the American Society of Civil
Engineers. A certain quantity of these standard sizes are
"Uy in stock, insuring the prompt filling of small orders.
MINING 305
BCATERIALS REQUIRED FOR SINGLE-TRACK ROAD
Size of
Number
of 30-Ft.
Rails
Required
Number
of Splices
Required
Number of Bolts
Required
4 per Joint
6 per Joint
1,000 ft
1 mi
68
352
236
704
272
1.408
408
2,112
SIZES AND QUANTITIES OF SPIKES REQUIRED FOR
TIES 2 FT., CENTER TO CENTER, 4 SPIKES
PER TIE
Size
Average
Measured
Number
Under
per
Keg
Head
of 200
Lb.
Inches
2iXi
1,342
3 X
1,240
3iX
1,190
4 X
1,000
3iXA
900
4 XA
720
4iXA
680
4 X
600
4iX
530
5 X
450
5 XA
400
5iXA
5§X}
375
300
Quantity Required
per 1,000 Ft.
Track
per Mile of
Track
Lb.
300
324
340
360
445
550
590
670
750
880
980
1,112
1,334
Kegs
Lb.
1
1,575
1,710
1
1,780
1
2,090
2
2,350
2
2,910
3
3.110
3}
3,520
3}
3,960
4f
4,660
5
5.170
el
5,870
7,040
Kegs
7J
8*
9
lOi
11
14 i
15i
171
20
23i
26
29i
35i
Weight
of Rail
Used
Pounds
8 to
16 to
16 to
16 to
16 to
20 to
20 to
25 to
30 to
35 to
40 to
45 to
75 to
16
20
20
25
25
30
30
35
35
40
55
75
100
Note. — ^When ordering spikes, a reasonable allowance should
be made for waste. For ordinary mine track with 2 spikes to
the tie, divide the quantities given in "the table by 2. For
other spacing than 2 ft., proceed as follows: For 30 in.,
multiply the quantity of spikes by .8; for 28 in., by .858;
for 26 in., by .893; for 22 in., by 1.092; for 20 in., by 1.2; and
for 18 in., by 1.334.
21
306
MINING
00
,ooqocoo«qqco<
oc6cdc6o-^coo6e«ie«ir>Icio4o6'^eoQcp
c
SoSqqqSqS
S8S1
coiocDqt>>icoqe^(OqqqcoocoSe4»o
a»c4ic>oa6e^i-4c6ooooo>>oQO«Desi
vHi-ii-ii>4CICIC>9COCOOO^CO^iOiO>OQO
CO
V
o
PC4
d
t-i
CO
CO
PC4
-s
O
COQCO
jcooco
icicqtoco
Q6'H-^-^t>^«-HO-^o6o6e*jr^cdcit>^cDe«iQO
gw8<
C0»O(
coccr^(
uScooco
t«C0iOCD
a6ococ6c6oio6cj«d«do'<t^a>c6e«5a6'^
SCOCOQQQCQQCO
« i-H © O O 00 Q t-H
«-ioo>ooc4>oa»b-ub
t*ONe«<»ooot>-'-i'^-^ooN»-icooo»oo
o
o
I— I
(O
»0«0«0©Oi-tQOO<
»«DC0»0O»5 "
• COCg W(
Sow
lOec
•-)coc4 00
<oo)i-Hi-Heoco<oo)C4C^>oaoocot«coi-4i4
8eot^Q
co©o
tooeocot
cdo6dd(N>0'^t>^oooi5cocdocoeotN^i-H
I— I
CO
Soooo
«
00 O (N »C »H t^ CO
»or^o»o>»-<ooeo«o«*»H-^coi^OOcot>-
,_,,_(,_,,_,,_,_c>io<wwcocoeoco
o
g
'i'S^
•8
C3
ioioiO(OcD«ot^t»t^xxooa»afta»ooo
xxxxxxxxxxxxxxxxxx
CO ^ ic -^ o CO udcot* cot* oot* ooa» 0008 o
MINING 307
TIES PER 1,000 FT. AND PER MILE 6f TRACE!
Distance From Center to Center of Ties, in Inches
Length
Track
18
20
22
24
26
28
30
Number of Ties
1,000 ft...
Imi
667
3,520
600
3,168
546
2.880
640
2.640
462
2.437
429
2,267
400
2.112
Example. — How many feet, board measure, are there in the
ties required to lay 1,600 ft. of track; the ties are 6 ft. 6 in. long,
5 in. X 6 in. in cross-section, and spaced 22 in. between centers?
Solution. — 1.500 ft. = li thousands of feet. Prom the
accompanying tables, liX646X16i-13.308J. say, 13,500 ft.,
B. M.
THE PREPARATION OP COAL
CRUSHING MACHINERY
The object of crushing ore or coal is: first, to free the min-
eral or other valuable constituents from the gangue, slate,
pyrites (sulphur), or other worthless or objectionable constit-
uents so that they can be subsequently separated; or, second,
simply to reduce the size of the individual pieces and so get the
material into a more salable or convenient condition for use.
Selection of a Crusher. — The style of crusher employed is
influenced by: The amount of material to be crushed in a
given time. The size of the material as it goes to the crusher.
The physical characteristics of the material to be crushed;
that is, whether it is hard or soft, tough or brittle, clayey
or sticky. The object of the crushing. The character of
the product desired; that is. whether an approximately sized
product is desirable and whether dust or fine material is
objectionable.
308 MINING
The terta eroiking rciii is applied to rolls having te«th, which
are usually made separate and inserted. These rails. Pig. 1,
are used for hrealdng coal, phosphate rack, ett., the object being
possible production of very fine matfrial. The principle field
for cracldng rolls b in the prepsxs.tiDn of anlhrscitc. and the
exaft style or design of the roll depends largely on the physical
ere constructed with an iron cylinder having steel teeth inserted,
the size, spacing, and form of the teeth depending on the sze
ie nuterial to be broken. Cracldns
The form of the teeth varies areatly, but, as a rule, the larger
rolle have straight pointed teeth of the sparrow-bill or some
similar form. Pig. 2 a. The old curved, or bawk-bOled, teeth.
Fig. 2 fi. have now gone wholly out of use.
Disiniesrating rolls and pulverizers are sometimsi used to
reduce coking coal to the size of com or rice before intro-
dudng it into the ovens. One roll is driven at double the
speed of the other, the slower roll acting as a feed roll, and
MINING 300
For the reduction of coal. cruAhera employiDg hammtrs have
leen umA. Pig. 3. Th« cniahing chamber is usually of a cir-
ular or barrel form, and the crashing is done by meuis of
dmmers pivoted about a central shaft. These swing out by
entiifugal force and itrike blows upon the eoal to be broken.
• wflM
M mK'l ■■■■■"■
Pig 2 Fic. 3
When it is reduced suSiciently £ne. it is discharged through
rolls.
SIZmO AMD CLASSIFYDtG APPARATUS
natfonn Barm. — In the anthracite breakers, the terms plat-
form bars or head-bars are usually onplcyed ior the bars that
coarse will go to the crushers. These bars are made of 11-in.
(.pacing depending on the sise of coal it is desired to make in the
Sbakinc Screens. — Shaking screens have an advantage in
310
MINING
applicable where the coal is wet and has a tendency to stick
together. The principal disadvantage of the shaking screen
is that the reciprocating motion imparts a vibration to the
framing of the building. .
The capacities of shaking screens operating on anthracite
have been given as follows. The parties giving these figures
advise the use of 140 R. P. M. for the cam-shaft. For broken
and egg coal, \ sq. ft. per T. for 10 hr. For stove and chestnut
coal, i sq. ft. per T. for 10 hr. For pea and buckwheat coal
J sq. ft. per T. for 10 hr. For birdseye and rice, 1 J sq. ft. per T.
for 10 hr. For sizing bituminous coal, inclined shaking screens
are extensively used in certain sections, particularly in the
Middle Western States. These screens are given a shaking
motion by means of cams and connecting-rods, which make
from 60 to 100 strokes i>er minute, the speed varying according
to the amount of moisture in the coal.
Size of Mesh. — ^The perforations given in the accompanying
table have been adopted by two of the largest anthracite
companies as the dimensions for the holes in shaking screens
to produce sizes equivalent to those produced by revolving
screens.
MESH FOR SHAKING SCREENS
Kind of Coal
Lehigh
Valley
Coal Co.
Phila. & Reading
Coal & Iron Co.
Kind of Coal
Round
Inches
Round
Inches
Square
Inches
Steamboat . . .
Lump
Broken
Egg
It
1*
H
A
51
4^
3i
2i
li
i
A
5
4
2i
2
1}
Steamboat
Large broken
Small broken
Egg
Stove
Chestnut
Pea
Stove
Chestnut
Pea
Buckwheat . . .
Rice
Buckwheat
Rice
MINING 311
Revolying Screens, or Trommels. — The screen is placed
about the periphery of a cylinder or frustum of a cone. The
material to be sized is introduced at one end; the small size
passes through the screen, and the other size is discharged from
the other end. If the form is cylindrical, the supporting shaft
must be inclined so that the material will advance toward the
discharge end. The inclination determines the rapidity with
which the material will be carried through the screen. The
advantage of the conical screen is that the shaft is horizontal
and hence the bearings are simpler; this a very decided advan-
tage where the machinery must be crowded into a minimum
space, and is hard to get at.
Speed. — The periphery of a revolving screen should travel
about 200 ft. per min. In the case of very fine material,
screens are sometimes run faster than this. The following
have been adopted as standard speeds for screens by one of the
largest anthracite companies:
Speed of Screens
Rev. per Min. Rev, per Min.
Mud-6creens 8.87 Big screens 8.62
Coimter mud screens . . 15.49 Pony screens 10.87
Cast-iron screens 1 1.25 Buckwheat screens 15.30
Duty of Anthracite Screens.— The following list gives the
number of square feet of screen surface required for a given duty
in the case of revolving screens working upon anthracite:
Egg Coal 1 T. per 1 sq. ft. per 10 hr.
Stove coal IT. per 1} sq. ft. per 10 hr.
Chestnut coal IT. per if sq. ft. per 10 hr.
Pea coal IT. per 2 sq. ft. per 10 hr.
Buckwheat coal IT. per 2} sq. ft. per 10 hr.
Rice coal IT. per 3} sq. ft. per 10 hr.
Culm IT. per 5 sq. ft. per 10 hr.
These figures may be reduced from 20% to 30% for very
dry or wash coal.
Revolving Screen Mesh for Anthracite. — A standard mesh
for revolving screens for sizing anthracite was adopted some
years ago, but it is only approximately adhered to and a
considerable variation from the standard is found throughout
the anthracite region. The following are probably as nearly
standard meshes for revolving screens for sizing anthracite
coal as can be given:
2 MINING
Mbsh for Sizing Coal
Culm passes Ihrough A-in. mesh
BirdKye -..-. passes ova l-iTi- meah, and through
Buckwheat . . . psssea over l-in. mtsh, mid through
Pea pii5a« over l-in. mesh, and through
l-in. mesh
Chestnut passes over i-in. mesh, and through
U-in. mtsh
SCove ....... .passes over l|-in. mesh, and through
2-in. mesh
Grate passes over 2I-in. mesh, and out end
Special grate, .passes over a^n. mesh, and out end
Special steamboat passes over3-in. bars, and through
applied to that clas:
ruf ■
takes pUi
^ona
screen or h
micuirents
rofi
m<
■e used for,
>thF
ala-injigs,
. Some use plain
the
the same
to both the
1 up and the dowu
MINING 313:
of parts, which give a quick down stroke and' a slow up stroke,
thus allowing the water ample time to work its way back
through the bed without any sucking action from the piston.
This tends to make a better separation in some cases than the
use of the plain eccentrics.
Stationary screen jigs are illustrated by Fig. 4, which shows a
3-compartment jig. The separation takes place on screens
supported on wooden frames g, and is effected by moving the
water in each compartment so that it ascends through the
screen, lifting the mineral and allowing it to settle again, thus
giving the material an opportunity to arrange itself according
to the law of equally falling particles.
Removal of Sulphur from Coal. — The object of washing coal
is to remove the slate and pyrites, thus reducing the amount of
ash and sulphur. Many forms of washers easily and cheaply
reduce the slate from 20% in the coal to 8% of ash in the coke,
but it is much more difficult to reduce 4% of sulphur in the
coal to 1% or less of stilphur in the coke. Sulphur occurs in the
coal in three forms, as hydrogen sulphide, calcium sulphate,
and pyrite.
HANDLING OF MATERIAL
Anthracite. — The following may be taken as average figures
for the angle or grade of chutes for anthracite, to be used where
the chutes are lined with sheet steel: For broken or egg coal,
2i in. per ft.; for stove or chestnut coal, 3i in. per ft.; for pea
coal, 4 J in. per ft.; for buckwheat coal, 6 in. per ft.; for rice
coal, 7 in. per ft.; for culm, 8 in. per ft.
If the coal is to start on the chute, 1 in. per ft. shotald be
added to each of the foregoing figures; while if the chutes are
lined with manganese bronze in place of steel, the figures can be
reduced 1 in. per ft. for coal in motion, or wotild remain as in the
table to start the coal. When the run of mine is to be handled,
as in the main chute, at the head of the breaker, the angle
should be not less than 5 in. per ft., or practically 22J° from the
horizontal. If chutes for hard coal are lined with glass, the
angle can be reduced from 30% to 50%, depending somewhat
on the nature of the coal. In all cases, the flatter the coal, the
steeper the angle must be, on account of the large friction sur-
faces exposed, compared with the weight of the piece. If the
314
MINING
chutes are lined with cast iron, the angle should be about the
same as that employed for steel, though sometimes a slightly-
greater angle is allowed.
The accompanying table is printed through the courtesy of
the Link-Belt Engineering Co., Philadelphia, Pa.:
PITCH AT WmCH ANTHRACITE WILL RUN
Size of Coal
Brolqen slate
Dry egg slate. . . .
Dry stove slate. . .
Dry chestnut slate
Broken coal
Egg coal
Stove coal
Chestnut coal. . . .
Pea coal
Buckwheat No. 1 .
Buckwheat No. 2.
Buckwheat No. 3.
Buckwheat No. 4.
Dry Coal
Wet Coal
Glass Lining
Pitch of Chute, in Inches per Foot
a
O
51
51
51
5
31
4i
4i
6i
a
O
(2
41
41
4i
4i
3
41
41
5
c
O
CO
51
51
51
51
31
4f
4!
51
d
O
3
3
31
31
2f
21
3
3
31
3f
3!
4t
4J
c
O
a
§
3
3
3
3
21
21
21
21
21
31
i
41
8
1
03
21
21
3
3
31
31
4J
41
a
O
«
a
o
O
If
2
it
i
Bituminous Coal. — ^When the run of mine is to be handled,
the angle of the chutes should be from 35° to 45° from the hori-
zontal, or from 81 in. to 12 in. per ft. If the coal is wet, the
angle should always be steeper, as coarse coal will slide on a
flatter angle than slack or fine coal.
MINING
315
BRIQUETING
Fuel, fuel dust, and other products may be briqueted by a
number of different styles of machines, but all these may be
divided into two classes, briquet and eggetle machines. Fuel
briquets have not come into general use in the United States
on accotint of the great amount of cheap fuel available, which
has prevented the utilization of culm, coal dust, etc.; and on
accotmt of the lack of or high price of suitable bonding material.
This latter condition is now being removed by the introduction
of by-product coke ovens, from which supplies of coal tar can be
obtained.
SPACE OCCUPIED BT 2,000 LB. OF VARIOUS
COALS
Anthracite
Lackawanna . . . . .
Garfield red ash .
Lykens Valley. . .
Shamokin
Plymouth red ash
Wilkes-Barre
Lehigh
Lorberry
Scranton
Pittston
Broken
Egg
Stove
Chestnut
Cubic
Cubic
Cubic
Cubic
Feet
Feet
Feet
Feet
37.10
36.65
34.90
34.35
37.30
36.95
36.35
36.35
37.55
37.25
37.55
37.25
38.05
37.70
37.25
37.25
34.90
34.85
34.75
34.70
34.95
34.35
33.75
34.00
33.30
33.80
33.55
32.55
34.65
34.20
33.80
33.55
35.35
35.20
34.60
33.30
35.45
34.95
34.35
33.70
Pea
Cubic
Feet
37.25
37.50
38.50
38.50
36.90
36.90
33.05
35.20
34.95
35.50
Bituminous
Cumberland
Clearfield . . .
New River. .
Cubic
Feet
36.65
33.55
40.15
Bituminous
Pocahontas
American cannel
English cannel . .
Cubic
Feet
34.00
41.50
42.30
316 MINING
TREATMENT OF INJURED PERSONS
The dangers to be feared in case of wounds, are shock or
collapse, loss of blood, and tinnecessary suffering in the moving
of the patient. '
In shock, the injured person lies pale, faint, and cold, some-
times insensible, with feeble pulse and superficial breathing.
The cause of death in case of a shock is arrest of heart action,
produced by the suspendon of the functions of the brain and
spinal cord. In treatment, the two most important parts are:
the position of the injured person and the application of external
warmth.
The injured person should at once be placed in a recumbent
position, his head resting on a plane lower than that of his
trunk, legs, and feet. He shotild be well wrapped up and pro-
tected from the chilling influences of external air. Where there
is danger of immediate death, stimulants shotild be given; in
all other conditions of shock, stimulants are injurious.
Loss of Blood. — In case of loss of blood, two conditions
present themselves: (1) The bleeding is arrested spontaneously
or otherwise, but the injtured person presents all the symptoms
of loss of blood; (2) the injured person is actually bleeding,
and he is, or is not, suffering from loss of blood.
In the first condition, life is threatened by anemia of the
brain and spinal cord, and all the efforts of treatment should
be to direct the flow of whatever quantity of blood that may
still remain in the body to these vital centers. This is most
efficiently done by placing the injtured person in a recum-
bent position, with his head resting on a plane somewhat lower
than that of his trunk and legs. In graver cases, constricting
bands shotild be applied to both arms, as near the shoulders as
possible, and to both thighs, as near the abdomen as possible.
This last maneuver directs the entire quantity of blood in the
body to the suffering centers, the centers of life itself. Stimu-
lants may be sparingly administered.
If there is bleeding, do not try to stop it by binding up the
wound. The current of blood to the part must be checked.
To do this, find the artery, by its beating; lay a firm and even
compress or pad (made of cloth or rags rolled up, or a round
MINING
317
stone or piece of wood well wrapped) over the artery, as shown
in Fig. 1. Tie a handkerchief around the limb and compress;
put a bit of stick through the handkerchief and twist the latter
Fig. 1
Fig. 2
up until it is just tight enough to stop the bleeding; then put
one end of the stick tmder the handkerchief, to prevent untwist-
ing, as in Pig. 2.
The artery in the thigh runs along the inner side of the
muscle in front of the bone, as shown by dotted line in Fig. 3.
A little above the knee it passes to the back of the bone. In
injuries at or above the knee, apply the compress higher up, on
the inner side of the thigh, at the point P, Fig. 3, with the knot
on the outside of the thigh. When the leg is injtured below the
knee, apply the compress at the back of the thigh, just above
the knee, at P, Pig. 4, and the knot in front, as in Pigs. 1 and 2.
The artery in the arm rtms down the inner side
of the large muscle in front, quite close to the
bone, as shown by dotted line;
low down it is further for-
wards, toward the bend of the
elbow. It is most easily com-
pressed a little above the mid-
dle, at P, Fig. 6. Careshotaldbe
taken to examine the limb from
time to time, and to lessen the
compression if it becomes cold
or purple; tighten up the hand-
kerchief again if .the bleeding
b^ns afresh.
To Transport a Wounded Person Comfortably. — Make a
soft and even bed for the injured part, of straw, folded blankets,
quilts, or pillows, laid on a board with side pieces of board
nailed on, when this can be done. If possible, let the patient
Pig. 3
Fig. 4
318
MINING
be laid on a door, shutter, settee, or some firm support, properly
covered. Have sufficient force to lift him steadily, and let those
that bear him not keep step.
Shotild any important ar-
teries be opened, apply the
handkerchief, as recom-
/ 'jCr**^^""*''^i3£L mended. Secure the vessel by
a surgeon's dressing forceps,
or by a hook, then have a
^'G. 5 silk ligature put around the
vessel, and tighten. Should the bleeding be from arterial
vessels of small size, apply persulphate of iron, either in
tincture or in powder, by wetting a piece of lint or sponge
with the solution; then, after bleeding ceases, apply a compress
against the [parts, to sustain them during
the application of the persulphate of iron,
and to prevent further bleeding, shotild ip
occur. The persulphate of iron should be
kept in or about all working places.
Bleeding From Scalp Wounds. — ^A pad or
compress is placed immediately before the
ear, over the region marked by a dotted
Une, Fig. 6. The compress is firmly secured,
by a handkerchief. If this does not arrest
bleeding, a similar compress on the oppo-
site side shotild be appUed. Shotdd the
bleeding issue from a wound of the posterior or back part of
the head, a compress should be placed behind the ear, over the
region marked by the dotted line. Fig. 6, and firmly secured
by a handkerchief or bandage.
Fig. 6
TREATMENT OP PERSONS OVERCOME
BY GAS
Miners are exposed to asphyxia when the circulation of the
air is not sufficiently active, when the mine exhales a quantity
of deleterious gas, when they penetrate into old and abandoned
workings, and when there is an explosion. The symptoms
of asphyxia are sudden cessation of the respiration, of the
MINING 319
pulsations of the heart, and of the action of the senses; the
countenance is swollen and marked with reddish spots, the
eyes are protruded, the features are distorted, and the face is
often livid, etc. The best and first remedy to employ, and in
which the greatest confidence ought to be placed, is the renewal
of the air necessary for respiration. Proceed as follows:
1. Promptly withdraw the asphyxiated person from the
deleterious place and expose him to pure air.
2. Loosen the clothes round the neck and chest, and dash
cold water in the face and on the chest.
3. Attempts should be made to irritate the mucous mem-
brane with the feathered end of a quiU, which shotald be gently
moved in the nostrils of the insensible person, or to stimulate
it with a bottle of volatile alkali placed under the nose.
4. Keep up the warmth of the body, and apply mustard
plasters over the heart and around the ankles.
5. If these means fail to produce respiration, Docter Syl-
vester's method of producing artificial respiration shotild be
tried as follows: Place the patient on the back on a flat sur-
face, inclined a little upwards from the feet; raise and support
the head and shoulders on a small firm cushion or folded article
of dress placed tmder the shoulder blades. Draw forwards
the patient's tongue and keep it projecting beyond the lips; an
elastic band over the tongue and under the chin will answer
this purpose, or a piece of string or tape may be tied around
them, or by raising the lower jaw the teeth may be made to
retain the tongue in that position. Remove all tight clothing
from about the neck and chest, especially the suspenders.
Then standing at the patient's head, grasp the arms just above
the elbows, and draw the arms gently and steadily upwards
above the head, and keep them stretched upwards for 2 sec.
(by this means air is drawn into the lungs). Then turn down
the patient's arms and press them gently and firmly for 2 sec.
against the sides of the chest (by this means air is pressed
out of the lungs). Repeat these measures alternately, deliber-
ately, and perseveringly about 15 times in a minute, until a
spontaneous effort to respire is perceived, immediately upon
which cease to imitate the movements of breathing, and pn>
ceed to induce circtilation and warmth.
320 MINING
6. To promote warmth and circulation, rub the limbs
upwards with firm, grasping pressure and energy, using hand-
kerchiefs, flannels, etc. Apply hot flaxmels. bottles of hot
water, heated bricks, etc., to the pit of the stomach, the arm
pits, between the thighs, and to the soles of the feet.
7. On the restoration of life, a teaspoonful of warm water
should be given, and then, if the power of swallowing has
returned, small quantities of wine, warm brandy and water,
or coffee should be administered.
8. These remedies should be promptly applied, and as
death does not certainly appear for a long time, they ought
only to be discontinued when it is clearly confirmed. Absence
of the pulsation of the heart is not a sture sign of death, neither
is the want of respiration
Promotion
Advancement in Salar
and
I .
Business Success
Through the
COALMINING
Mine Foremen's
Fire Bosses'
Metal Mining
Metallurgy
Mining Engineering
COURSES OF INSTRUCTION
OF THE
International
Correspondence Schools
Inlernational Textbook
Company, Proprietors
SCRANTON, PA.. U- S. A.
SEE FOLLOWING PAGES
22
General Superintendent
Over 1,000 Men
When I enrolled in the Complete Coal Mining
Course of the International Correspondence
Schools, my education was confined to a knowl-
edge of how to read and write. Notwithstand-
ing the disadvantage of so poor an education,
your instruction carried me through and I
passed a creditable examination. I consider
that it is to your Schools that I owe my advance-
ment. When I enrolled I was a mine boss;
I am now General Superintendent for the
National and Parkdale Fuel Companies, of
Denver, Colo., and my salary has been in-
creased 125 per cent. There never was a time
in the history of the United States when good,
competent, and reliable mine foremen and
superintendents were so much in demand as
at fwesent; and any intelligent mine worker
who has the ambition can fit himself to assiune
the responsibility by taking a Course in Mining
with the I. C. S. and completing it in leisure
time that could not be spent in anything more
advantageous to himself.
Jos. Watson,
Louisville, Colo.
BEGilN WORKING WHEN 8 YEARS OLD
J. M. Baker, Woodland, Pa., had received but an imper-
fect education when he took up our Complete Coal Mining-
Course, having begun to work in the mine at the age of 8.
At the time of his enrolment his wages were so small that he
could with difficulty support himself. His Course has been
of the greatest benefit to him, enabling him to become mine
superintendent for the Harbison-Walker Refractories Com-
pany, having eight foremen and several hundred men at work
under Ms direction. His wages have been increased 500 per
cent.
BECAME GENERAL MANAGER
Wm. Hollis, Cordova, Ala., says that it was his Complete
Coal Mining Course with the I. C. S. which enabled him to
rise from the position of mine foreman to that of general man-
ager of the Alberta Coal, Mineral and Lumber Company.
His salary has been doubled since he enrolled with us.
DRAWS $300 A MONTH )
While working as top boss of a small mine, Gus Blair,
Murphysboro, 111., enrolled with the I. C. S. for the Complete
Coal Mining Course. As he had worked in the mines from the
age of 9, it was hard work for him to confine himself to study.
However, he pursued the Course until his education was
improved, and made a substantial advancement in position and
salary. • At the time of enrolment he was paid $50 a month.
He now draws $300 a month from the Gus Blair Big Muddy^
Coal Company, of which he is half owner and general manager
A GRADUATE'S SUCCESS
S. J. RouTLEDGE, KcUerman, Ala., holds I. C. S. Diplomas-
both in Coal Mining and in Stirveying and Mapping. When
he enrolled for the first Course he was earning about $75 a
month. He is now drawing a salary 150 per cent, larger as
the superintendent of coal mines for the Central Iron and Coal
Company. He says that his present position is due solely to-
the knowledge gained from his I. C. S. Course.
EMPLOYS 500 MEN
Chas. A. Sine, Johnson City, 111., left school before he
knew the multiplication table. When he enrolled for our Coal
Mining Course, he was driving a mule, earning $40 a month.
Before he received his diploma he was able to pass the exam-
ination for mine manager. He is now superintendent of the
Johnson City Coal Company, employing 600 men.
GRADUATE BECOMES SUPERINTENDENT
S. B. IsENBURG, Osceola Mills, Pa., was working as a laborer
when he enrolled with the I. C. S. for the Short Coal Mining
Course, from which he jp;raduated. This enabled him to pass
the state examination for mine foreman and to become the
mine superintendent of the Blair Brothers Coal Company^
with an mcrease in salary of 150 per cent.
Income Ten Times
As Lar^e
I used to feel that I was working hard enough
without having to devote my nights to study,
when employed as a clerk at $45 a month in the
mining department of the Cambria Steel Com-
pany. However, I stuck to the Complete
Coal Mining Course, which enabled me to gain
a first-class certificate of competency as fire
boss, and afterwards as mine foreman. I am
at present superintendent of the Johnstown
mines of the Cambria Steel Company, employ-
ing 2,000 men. In addition, I am a stock-
holder and director in several other companies,
consequently my income is at least 10 times
what it was when I enrolled.
Geo. T. Robinson,
143 Green St., Johnstown, Pa.
NOW PROPRIETOR
Jambs Nevin, Ottumwa, Iowa, while working as a hoisting
engineer enrolled with the I. C. S. for the Complete Coal
Mining Course. He gives the Schools the highest indorsement,
because they have enabled him to become superintendent of
the Trio Coal Company, of which he is also part owner.
ONCE A MULE DRIVER
While driving a mule in the mines at the age of 19, John
Clapperton, Jr., Minden, W. Va., enrolled for the Complete
Coal Mining Course. Through the knowledge he obtained
from this he has been able to pass two exanunations and to
become superintendent of the New River Coal Company,
largdy incre&dng his salary thereby.
A GOOD FRIEND OF THE SCHOOLS
A good friend of the Schools, Jos. Knapper, Philipsburg,
Pa., advises his friends to study I. C. S. Courses, because of
his experience since enrolment for our Complete Coal. Mining
Course. Mr. Knapper was earning $75 a month at the time
of enrolment. After {mrsuing his Course he rose step by step
tmtil he is now state mine inspector for the eighth district, at
a saUury of $3,000 a year.
CREDITS HIS SUCCESS TO THE L C. S.
D. J. Griffith, Trinidad, Colo., was earning only $20 a
month as a miner, at the age of 37, when he enrolled with us
for the Complete Coal Mining Course. After graduation
he served the state of Colorado for a time as chief inspector
of coal mines. He is now chief in8x>ector of mines for the
American-Victor Fuel Company, and he attributes all his
success to the I. C. S.
PAY INCREASED 233 PER CENT.
P. J. Moore, Carbondale, Pa., was employed as a fire boss
when he enrolled for the Complete Coal Mining Course. He
is now state mine inspector for the first anthracite district,
and pay days bring him 233 per cent, more than they did
at the time of enrolment.
DIRECTS 10,000 MEN
W. R. Cai.verley, Windber, Pa., was a miner when he en-
rolled for the Complete Coal Mining Course. By diligent
study he advanced to the position of general superintendent
of the Berwind- White Coal Mining Company, having the wel-
fare of 10,000 men committed to his charge. He has always
given great credit to the Schools.
Now State Mine
Inspector
When I enrolled in the Complete Coal
Mining Course of the International Corre-
spondence Schools, Scranton; Pa., I had had
about 20 months of schooling all told. I was
employed at the time as assistant foreman,
and was getting $55 a month. After enrolling
in the Schools, I was soon advanced to the
position of mine foreman at $75 a month,
which was voluntarily increased to $90 a
month. I am now Mine Inspector of the Fifth
Bituminous District, at a salary of $3,000 a
year.
Correspondence instruction, as conducted by
the I. C. S., is the finest and most complete
in the world today; every young man that
desires to advance or better his condition should
enroll at once. No one can enroll with you
and apply himself to his work, without being
greatly benefited.
I shall be glad to answer any inquiries regard-
ing the Schools and my Course with them.
Isaac G. Roby,
Inspector, Fifth Bituminous District, Union-
town, Pa.
6
STATE MINE INSPECTOR
By diligent study of the Complete Coal Mining Course, for
which he enrolled with the I. Cf. S., Jos. Williams, 245 Beale
Ave., Altoona, Pa., has risen from a position as miner to that
of inspector of mines, for the tenth bituminous district. State
of Pennsylvama. His salary has increased from $45 a month
to $3,000 a year, and he gives the I. C. S. all the credit.
NOW MANAGER
T. E. Moore. Eyremore, Alta., Can., was working as a
shift man for the Prairie Coal Company, when he enrolled
with the Schools for the Complete Coal Mining Course. He
is still working for the same company, and he has risen to the
position of manager of their mine on the Bow River at a salary
of $150 a month.
COULD HARDLY WRITE HIS NAME
A. W. Courtney, Princeton, B. C, was 25 years old and was
working as a laborer when he enrolled for the Short Coal
Mining Course. At the time he could hardly write his name.
Keeping diligently at his studies, he was able to pass the exam-
ination for mine foreman and now holds a foreman's position
at a salary of $150 a month.
THREE TIMES HIS FORMER SALARY
J. J. Clark, Sagamore, Pa., began to reap the benefits of his
study on the Complete Coal Mining Course 10 months after
enrolment. By devoting all his spare time to his Course, he
was able to obtain a mine foreman's certificate. He is now
assistant superintendent for the Buffalo & Susquehanna Coal
and Coke Company, and his wages are three times as great
as when he was loading coal.
IN CHARGE OF A LARGE PLANT
When H. L. Fisher, Kayford, W. Va., enrolled with the
I. C. S. for the Complete Coal Mining Course his knowledge
of mining was very hmited. By diligent study of his Course
he is now able to take charge of the largest plant of the Cabin
Creek Consolidated Coal Company, which includes eight of
their principal mines. His salary is $190 a month.
NOW SERVES THE STATE
F. J. Pearce, Rm. 120, State Capitol, Indianapolis, Ind.,
enrolled with the I. C. S. 12 years ago for the Complete Coal
Mining Course. He has now risen to the highest position in
his profession, deputy inspector of mines and mining for the
State of Indiana, at a salary of $2,000 a year. He had little
education before enrolment, but the secret of his advancement
lies in the fact that he has used his spare time and his I. C. S.
Course to obtain an education.
$540 to $3,000 a Tear
In reply to your letter, I beg leave to state
that my present position is Mine Inspector,
employed by the State of Pennsylvania. When
I enrolled in the PuU Mining (now the Mining
Engineering) Course, my salary was $45 a
month. I was employed as bratticeman, at
the Woodward Mines. After studying some
time, I passed the examination for mine fore-
man and was appointed assistant mine fore-
man — later foreman. Then I passed the Mine
Inspector's examination and was elected to that
position. My present salary is $250 a month.
I can conscientiously recommend the Interna-
tional Correspondence Schools to any young
man that has any desire to advance himself.
L. M. Evans,
Inspector Second Anthracite Inspection Dis-
trict, 10 Belmont Terrace, Scranton, Pa.
8
NOW A MINE OWNER
J. P. Davis, Coltunbia, Mo., was earning $75 a month as
mine foreman when he enrolled with the I. C S. for the Com-
plete Coal Mining Course. This has been so ];>rofitable to him
that he is now senior partner and manager of the Davis &
Watson Coal Company, employing 30 men.
NOW A FOREMAN
Howell John, Box 48, Meritt, B. C, declares that his
I. C. S. Mine Foremen's Course advanced him to the position
of foreman with the Pacific Coast Collieries. Mr. John began
working in the mines at 13 years of age and was a miner
when he enrolled. His Dresent position pays him $135 a
month
BARNS $200 A MONTH
While working as a timberman, John Prbnticb, Lund-
breck, Alta., Can., took up the Mine Foremen's Course with
the I. C. S. At the time he was earning $70 a month. He
is now mine manager for the Breckenridge & Lund Coal Com-
pany, earning $200 a month, and he says it was the I. C. S.
that made the difference.
WORTH $40 A MONTH TO HIM
His Mine Foremen's Course with the I. C. S., for which
Addison Shaw, Berryburg, W. Va., subscribed, was the means
of advancing him to the position of mine foreman for the Con-
solidated Coal Company, with an increase in scdary of $40 a
month.
NOW AN OFFICER OF THE COMPANY
R. S. BURCHINAL, Smithfield, Pa., says that the Mine Fore-
men's Course for which he enrolled with the I. C. S., was the
cause of his obtaining a foreman's certificate which enables him
to look after the mine, as well as the outside management of
his company. He is now treasurer and general manager of the
Smithfield Coal and Coke Company, receiving a salary of $125
a month.
A WORLD OF GOOD
The experience of Gus Champ, Cherokee, Kans., shows what
the I. C. S. Mine Foremen's Course will do for the man that
has the grit to go ahead. Mr. Champ says that his Course
did him a world of good, since it has advanced him to the posi-
tion of foreman for the Hamilton Coal Company, at a salary
of $100 a month.
9
Earning $3,000 a Tear
Howard M. Black,
Mining Engineer, Grass Valley, Cal.
International Correspondence Schools,
Scranton, Pa.
GENTi.EBfCEN: — At the time of enrolment as
a student of the I. C. S.. I was superintending
a small mine at a salary of $100 a month. I
have finished my Metal Mining Course, with
the exception of geometrical drawing. I still
hold the same position, but as this only occu-
pies part of my time, I make a specialty of
examining and reporting on mines, and do con-
siderable assaying and other work in the line
of mining engineering. For this outside work
I receive $12 a day and expenses. I can safely
say that my income since enrolment has been
increased from the original $1,200 a year to
$3,000 a year, due in great part to the technical
knowledge acquired through the I. C. S. Course.
Very truly yours,
Howard M. Black,
Grass Valley. Cal.
10
NOW PRESIDENT
G. W. WiLMOTT, Maryd. Pa., was earning about $60 a month
as chief repairman about the mines, when he enrolled for the
Mine Mechanical Course. After rising to the position of
superintendent, in charge of 450 men, he resigned to become
president and general manager of the Wilmott Engineering
Company, his present position.
LARGEST OF ITS KIND
E. E. Carter, Ouartzburg, Idaho, commenced studying the
Complete Metal Min'og Course soon after leaving grammar
school, while working tor $10 a week. Later he enrolled for the
Complete Metallurgy Course. He considers that his success
is largely due to the instruction he received from the I. C. S.
At present he is manager of the largest coal mines in Idaho.
FROM $2.50 A DAY TO $38.20 A WEEK
Henry Hoard, Selwood, Ore., feels that he owes to the
I. C. S. all his success. He was working around the mines as
a mucker, or at anything else he could get, when he enrolled
for the Metal Mining Course. His wages then averaged $2.50
a day. He is now assistant foreman for the John Clark Lead
Company, employing some 40 men, and his salary averages
$38.20 a week.
BECAME SUPERINTENDENT
E. A. Roberts, Entwistle, Alta., Can., was workixig as a
steam engineer for $80 a month when he enrolled with the
Schools for the Mining Engineering Course. He is now man-
ager of the shaft sinking work for me Pembina Coal Company,
at a salary of $150 a month.
EARNS $160 A MONTH
Geo. H. Shepherd, National, Nev., was earning $2 a day
as a millman and sampler, when he enrolled with the I. C. S.
for the Metal Mining Course. He now handles the retorting
of the huge mass of bullion dispatched from the camp, earning
$160 a month.
WHAT THE SCHOOLS DID FOR HIM
In 1909, Peter Kasavage. Johnson City, lU., could neither
read nor write and was earning $2.42 a day as a tracklayer.
He then enrolled with the I. C. S. for the Mine Foremen's
Course. In July, 1911, he passed the state examination for
mine examiner and the next day was appointed to the position
of mine examiner of the Illinois Hoclang Washed Co^ Com-
pany, at Marion, 111.
11
A Toun^ Man's Success
When I began with the Desoto Coal Mining
Development Company I counted cap boards.
The president advised me to study Mining
Engineering through your Schools. As a result
of this study i>roniotion and advancement
have been my lot, together with commensu-
rate compensation. My salary has increased
400 per cent, since taking up instruction by
mail. If one received the mental training
alone, the Course would be worth many times
its cost! Today I am Secretary and General
Manager of the company and a director and
stockholder. To have gone step by step from
a counter of cap boards, to the Secretary and
General Manager's chair has meant hours and
nights and weeks and months of study as well
as close application to my duty.
Jas. a. Worsham,
Morris, Ala.
12
SALARY DOUBLED
Nels Johnson, Zeigler, 111., was earning $60 a month when
he enrolled with the I. C. S. for the Short Coal Mining Course.
He afterward graduated from the Full Mining Course. He is
now mine manager of the Bell & Zoller Minmg Company's
plant, and his salary has be(m doubled.
EIGHT TIMES HIS FORMER SALARY
Henry Sankey, Box 766, Cobalt, Ont., was working on a
farm at $20 a month when he took up our Metal Mining Coiu^e.
This has enabled him to become superintendent of the Peter-
son Lake Mining Company, at a salary of $160 a month.
SIX TIMES HIS FORMER SALARY
E. P. BuFFi^T, Briceville, Tenn., was supporting a family
on the small salary of a bookkeeper when ne enrolled with
the I. C. S. for the Metal Mining Course. He is now super-
intendent of the Tennessee Coal Company's mine at Brice-
ville, employing about 200 men, at a salary six tunes what he
received at the time of enrolment.
EARNS $250 A MONTH
Lewis R. Smith, 314 Second Ave., Rome, Ga.,'was an assist-
ant chemist, earning $45 a month when he enrolled with the
Schools. His Course in Metallurgy has enabled him to be-
come superintendent of the Silver Creek Furnace Company
at a salary of $250 a month.
NOW SUPERINTENDENT
J. W. Powell, Tabet, Alta., was working as a fire boss,
when he enrolled with the Schools for the Complete Coal
Mining Course. Through the study of this Course he qualified
himself for a first-class certificate in the Pennsylvania anthra-
cite region, and afterward for the mine foreman's position in
Alberta. He is now superintendent of mines for the Canada
West Coal Company, Ltd.
WORKING AGAINST ODDS
D. R. Jones, Parrot, Va., had attended school only a few
months when he enrolled for our Complete Coal Mining Course.
In spite of obstacles he has advanced step by step until he is now
superintendent of the Pulaski Anthracite Coal Company, at a
salary of $150 a month.
13
Increased His Salary
500 Per Cent
I had learned the machinist's trade and was
prepared to enter Cornell University, when I
enrolled for yotir Coal Mining Course. I had
no knowledge of mine engineering or metal
mining at the time, but had worked in the coal
mines. In making the radical change from the
drift coal mines to the comparatively deep
lead mines of this section, I found that my
knowledge of metal mining was thorough.
I was able to make my work very successful
from the start. I found my Course very use-
ful in all my work, and have always been a
firm advocate of the I. C. S. At the time of
enrolment I was earning $600 a year. I am
now general superintendent of the Washburn
Lignite Coal Company, of this place, employ-
ing 300 men, and my salary has increased 500
per cent.
A. W Pollock,
Wilton, N. Dak.
14
NOW MANAGER
RoBT. Elminstok, Box 696, Panama, 111., had to start life
with a common school education; but with the help of our
Short Coal Mining Course, he was able to obtain a nrst-class
certificate in the State of Illinois. This advanced him from a
position as miner to that of manager of the Shoal Creek Coal
Company's mine No. 1.
NOW SUPERINTENDENT
Geo. E. Loughner, R. P. D. No. 4, Johnstown, Pa., went
into the mines at 11 years of aae to help support a large family.
While he was earning about $60 a month he enrolled for our
Short Coal Mining Course, and afterwards for the Conaplete
Coal Mining Course. He is superintendent for the Kelso
Smokeless Coal Company, employing 125 men, and his salary
has been increased $75 a month.
PASSED WITH 100 PER CENT.
While John Sanderson, Red Lodge, Mont., was working
as a miner, he enrolled with the I. C. S. for the Short Coal
Mining Course. When he came up for examination he was
able to pass with a percentage of 100, although his previous
education had been greatly limited, owing to the fact that he
began to work in the mines at 10 years of age. He is now
acting as foreman for the Northwestern Improvement Com-
pany, and his salary has increased 125 per cent.
BECAME FOREMAN
Wm. Fleming, Windber, Pa., was working in the coal mines
when he enro led with the I. C. S. for the Short Coal Mining
Course. What he learned enabled him to obtain a first-grade
mine foreman's certificate, and he now holds the position as
foreman of the Eureka No. 42 Mine of the Berwind- White
Coal Mining Company. His saUur has been increased 60 per
cent, since enrolment.
INCREASED HIS SALARY
Because he had studied the Short Coal Mining Course for
which he enrolled with the I. C. S., John H. Hauser, Mar-
guerite, Pa., was able to advance from the position of driver
to that of mine foreman, increasing his salary to $135 a month.
BflNER BECAME SUPERINTENDENT
J. C. Glancy, Pineville, Ky., was working as a miner when
he subscribed for the Mine Foremen's Course. Two jrears
ago he secured a state certificate and is now holding a position
as mine superintendent for the Pioneer Coal Company, at a
salary of $100 a month. He says that the I. C. S. have done
wonderful things for him.
15
State Mine Inspector
Salary $3,000
Since I had started to work In the mines
when only 9 years old, my education at the
time when I enrolled with the International
Correspondence Schools for the Short Coal
Mining Course, was principally what I had
picked up by observation in the school of
experience. Without question, your Course
offered the best advantage I had ever had,
and the farther I went with it the better I
liked it. I was so pleased with your treatment
of your scholars that I have recommended the
I. C. S. to other miners who are now holding
positions as foremen and assistant foremen
in my district, which should be sufficient guar-
antee that I have every faith in the I. C. S.
My work with the Schools was my best prei>-
aration to stand for an examination for State
Inspector of Mines, which, I am pleased to say,
I was successful in passing. I am now Inspec-
tor for the Seventeenth Anthracite Inspection
District. When I took up your Course I was
receiving a salary of $60 a month. My present
salary is $3,000 a year, therefore, you see I have
every reason to praise the bridge that carried
me over.
I recommend your Course to any one, young
or old, who has ambition. It matters not what
his previous schooling has been, the I. C. S.
will see him through.
Isaac M. Davibs,
Lansford. Pa.
16
A T^.-
J. • f
i
N
I
« ■
I
-•I
I
This book should be returned to
the Library on or before the last date
stamped below.
A fine is incurred by retaining it
beyond the specified time.
Please return promptly.
FEB 2
(^'fif-O
>tt*H******t
Ml \ D E /v
NOV 7 1983
►#*^###*^*^
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11