(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "The Coal Miner's Handbook ...: A Handy Reference Book for Coal Miners, Pit ..."

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 



►#*^###*^*^