\fdO'^ - Old Forge Coal Mines

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286 RAILROAD CONSTRUCTION. (859) First £^raviijf, i.e., the weight of the wall itself, and second friction produced by the weight of the wall upon its foundation and by the pressure of the backing against the wall. (860) The angle of wall friction is the angle at which a plane of masonry must be inclined in order that dry sand and earth may slide freely over it. (861) The base ^/, Fig. 74, of the triangle b d f is 12.73 feet, and the altitude ^ ^ is 16 feet. Hence, area of b d f is 12.73 X 8 = 101.84 square feet. Taking the weight of the backing at 120 pounds per cubic foot, we have the weight of bdf^ 101.84 X
RAILROAD CONSTRUCTION. 287 120 = 12,231 pounds. Multiplying this weight by -/ / = 8.56 feet, we have 12,221 X 8.50= 104,612 pounds, which, divided by o d, 16 feet, = 6,538 pounds = the pressure of the backing. This pressure to a scale of 4,000 pounds to the inch equals 1.63 inches. P, the center of pressure, is at ^ of the height of b d measured from d. At P erect a perpendicular to the back of the wall. Lay off on this perpendicular the distance /*//= 1.63 in. Draw /*/, making the angle ;//*/= 33° 41' = the angle of wall friction. At // draw a perpendicular to P n^ intersecting the line P t \n h. Draw h k, completing the parallelogram ;/ h k P\ h n, or its equal k J\ will represent the friction of the backing against the wall and the diagonal h P, which, to the same scale, = 7,857 pounds, will be the resultant of the pressure of the backing and the friction. Produce P // to 5. The section a b d c oi the wall is a trapezoid. Its area is 84 square feet, which, multiplied by 154 pounds, the weight of rubble per cubic foot, gives 12,936 pounds, as the weight of the wall, which, to a scale of 4,000 pounds to the inch, = 3.23 inches. Find the center of gravity g of the section a b d c, diS explained in Art. 1488. Through g draw the vertical line g ty intersecting the prolongation of P h in /. Lay off from /, on g i, the distance / z\ 3.23 inches = weight of the wall, and on Is, the distance I in = 1.96 inches, the length of the resultant P h\ complete the parallelogram I in u v. The diagonal / u is the resultant of the weight of the wall and the pressure. The distance c r from the toe c to the point where the resultant / u cuts this base is 3.6 feet, or nearly \ of the base c d. This guarantees abundant stability to the retaining wall. The distance o f\s obtained as follows : c d=S feet ; bat- ter of c a = 1 inch for each foot of length of ^ ^= 16 inches; hence, a o = S feet — 16 inches = 6 feet 8 inches; a b = 2. 5 feet; therefore, ^/= 12.73 — (6 feet 8 inches — 2. 5 feet) = 8 56 feet. (862) See Art. 1491. (863) See Art. 1491 and Figs. 409, 410, and 411
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( W v. 5 Copyright, 1897, by The Co
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Arithmetic, - CONTENTS Algebra, Log
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i ARITHMETIC. of tens. 1 + 8 + 7 +
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4 ARITHMETIC. and the difference (4
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ARITHMETIC. (c) 217 Multiply any tw
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8 ARITHMETIC. 72 in the dividend an
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10 ARITHMETIC. (70 X 50 X 24 X 20).
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12 ARITHMETIC, The 5 in the dividen
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14 ARITHMETIC. (22) (a) 576) 589824
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16 ARITHMETIC. (33) To reduce a fra
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18 ARITHMETIC. 3 3 (e) 15-r-7-43-=
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20 ARITHMETIC. (41) ,9| + 50i + 41+
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22 ARITHMETIC. (45) The man evident
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24 ARITHMETIC. • u s o e 3 2 o 93
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26 ARITHMETIC. {b) Here again the p
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28 ARITHMETIC. 64) 1.000000(. 01562
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30 ARITHMETIC. (66) In subtraction
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38 ARITHMETIC. (6) .875 — 5-=? Re
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84 ARITHMETIC. {c) First perform th
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36 ARITHMETIC. Reducing 387 387 to
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38 ARITHMETIC. nominator of the fra
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40 ARITHMETIC. (d) Base = percentag
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42 ARITHMETIC. Another method of so
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44 ARITHMETIC. (89) Here we have gi
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46 ARITHMETIC. 24 ) 13750 gr. 20 )
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48 ARITHMETIC. (98) Reduce the grai
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50 ARITHMETIC. contained times in 3
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gal.
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54 ARITHMETIC. (108) In multiplicat
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56 ARITHMETIC. Since there are 24 g
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58 ARITHMETIC. There are 100 lb. in
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60 ARITHMETIC. 62 is contained in 1
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63 ARITHMETIC. (121) (a) 106' = 106
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64 ARITHMETIC. (^) .4044* = .4044 X
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6G ARITHMETIC. Since there are 2 de
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68 ARITHMETIC. (128) {a) .0133' =.0
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70 ARITHMETIC (130^ (a) 1 1 20 _8 2
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72 ARITHMETIC. in the root. Write i
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74 ARITHMETIC. (^) 9 -/QO.OO'OO'OO
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76 ARITHMETIC. correction. This, mu
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78 ARITHMETIC. found by division sh
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80 ARITHMETIC. (137) {a) 1 1 f .0 6
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82 ARITHMETIC. (138^ {a) In this ex
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84 ARITHMETIC. (^)
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86 ARITHMETIC. {b) f 6 = VTa 2 4/G.
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88 8 8 ARITHMETIC.
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90 ARITHMETIC. 40,000 144)40000.0(2
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92 ARITHMETIC. (163) 2 ft. 5 in. =
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94 ARITHMETIC. (164) Taking the tim
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96 ALGEBRA. (171) See Arts. 352 and
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98 ALGEBRA. In this case, where we
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100 ALGEBRA. By Art. 482, the signs
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102 ALGEBRA. (189) Applying the met
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104 ALGEBRA. (196) {a) ^+_;/ + ^-(^
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106 ALGEBRA- (201 ) The subtraction
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108 ALGEBRA. Canceling the factors
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110 ALGEBRA. (208) (a) Writing the
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112 ALGEBRA. 20j^(4^+5)-12.r(3:r-7)
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ALGEBRA. (QUESTIONS 218-257.) (218)
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ALGEBRA. 117 Clearing of fractions,
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ALGEBRA. 119 Transposing, — A:X*
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Completing the square, ALGEBRA. 131
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Extracting ALGEBRA. 123
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(d) Completing the square, Extracti
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ALGEBRA. 127 (238) (a) i/| by Art.
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(242) ALGEBRA. 139 Let X = the whol
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(246) Then,-^ X ALGEBRA. 131 Let X
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ALGEBRA. 133 y+5-{x-o) = 6. (1) But
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ALGEBRA. 136 (266) Let X — the nu
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LOGARITHMS. (QUESTIONS 258-272.) (2
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l^OGARITHMS. 139 .6602 -3 — 1.980
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LOGARITHMS. 141 {l>) .76'"._ Log .7
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LOGARITHMS. 143 (271) Substituting
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140 GEOMETRY AND TRIGONOMETRY. in t
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148 GEOMETRY AND TRIGONOMETRY. 3 (2
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150 GEOMETRY AND TRIGONOMETRY. (302
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154 GEOMETRY AND TRIGONOMETRY. draw
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158 GEOMETRY AND TRIGONOMETRY. {d)
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1G4 GEOMETRY AND TRIGONOMETRY. (354
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166 ELEMENTARY MECHANICS. per min.
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168 ELEMENTARY MECHANICS. replaced,
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170 ELEMENTARY MECHANICS. (384) (a)
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172 ELEMENTARY MECHANICS. (389) See
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174 ELEMENTARY MECHANICS. (398) 1 h
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176 ELEMENTARY MECHANICS (412) Use
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180 ELEMENTARY MECHANICS. a distanc
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184 ELEMENTARY MECHANICS. (d) Using
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186 ELEMENTARY MECHANICS. (452) (a)
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188 HYDROMECHANICS. (457) (a) Area
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190 HYDROMECHANICS. Pressure due to
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192 HYDROMECHANICS. (47 1 ) (a) 36
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194 HYDROMECHANICS. 5' X 7854 (479)
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196 HYDROMECHANICS. (d) See Art. 10
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198 HYDROMECHANICS. Pressure per sq
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aOO HYDROMECHANICS. For z;„ = 4,/
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202 PNEUMATICS. (509) Substituting
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204 PNEUMATICS. (519) 8.47 = origin
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206 PNEUMATICS. (537) (a) 30 — 17
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208 PNE-aMATlCS. (548) CO' — 50'
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210 STRENGTH OF MATERIALS. P- p-^^.
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212 STRENGTH OF MATERIALS. Since 40
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214 STRENGTH OF MATERIALS. drawn. P
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21G STRENGTH OF MATERIALS. c \d of
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218 STRENGTH OF MATERIALS. n o. I//
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220 STRENGTH OF MATERIALS. Substitu
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222 STRENGTH OF MATERIALS. (589) Su
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224 STRENGTH OF MATERIALS. (597) {a
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226 STRENGTH OF MATERIALS. (d) In t
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228 STRENGTH OF MATERIALS. (604) Us
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230 STRENGTH OP MATERIALS. (609) Th
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232 STRENGTH OF MATERIALS. moments
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234 SURVEYING. adjacent sides of th
Page 248 and 249: 236 SURVEYING. (622) 1st. A B in Fi
Page 250 and 251: 238 SURVEYING. true bearing IS the
Page 252 and 253: 240 SURVEYING. A B, as the bearing
Page 254 and 255: Un SURVEYING. an angle of 15° 10'
Page 256 and 257: 244 SURVEYING. in dotted lines. In
Page 258 and 259: 246 SURVEYING. table of Radii and D
Page 260 and 261: 248 SURVEYING. ^^^ = 1.875'. The de
Page 262 and 263: . (690) 250 SURVEYING. sight to the
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Page 266 and 267: 254 SURVEYING. horizontal lines 1 f
Page 269 and 270: (706) LAND SURVEYING (QUESTIONS 706
Page 271 and 272: LAND SURVEYING. 259 ture of A B is
Page 273 and 274: LAND SURVEYING. 261 -{-, in the col
Page 275 and 276: LAND SURVEYING. 263 is +8.86 chains
Page 277 and 278: a a *• o « .i Q a V Q + • hJ *
Page 279 and 280: LAND SURVEYING. 2G7
Page 281 and 282: RAILROAD LOCATION. (756) (QUESTIONS
Page 283 and 284: RAILROAD LOCATION. 271 second curve
Page 285 and 286: RAILROAD LOCATION. 273 in which;!'
Page 287 and 288: RAILROAD LOCATION. 275 Whence, we h
Page 289 and 290: RAILROAD LOCATION. 277 4.0827 ft.,
Page 291: point so determined by RAILROAD LOC
Page 294 and 295: 282 RAILROAD CONSTRUCTION. (818) Th
Page 296 and 297: 884 RAILROAD CONSTRUCTION. (833) Ap
Page 300 and 301: 288 RAILROAD CONSTRUCTION. (864) (8
Page 303 and 304: RAILROAD CONSTRUCTION. (QUESTIONS 8
Page 305 and 306: RAILROAD CONSTRUCTION. 293 (896) Se
Page 307 and 308: RAILROAD CONSTRUCTION. 295 (a) The
Page 309: RAILROAD CONSTRUCTION. 207 (939) Se
Page 312 and 313: 300 TRACK WORK. (962) (963) (964) (
Page 314 and 315: 302 TRACK WORK. (994) See Art. 1687
Page 316 and 317: 304 TRACK WORK. (1008) 8 ft. G in.
Page 318 and 319: 306 RAILROAD STRUCTURES. (1039) See
Page 320 and 321: 308 RAILROAD STRUCTURES. (1060) Fro
Page 326 and 327: 3," ^ >;> :3 3>32> ^ >:> J> Oi?^ :>
Page 328: UNIVERSrTY OF ILLINOIS-URBANA 3 011
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