\fdO'^ - Old Forge Coal Mines

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208 PNE-aMATlCS. (548) CO' — 50' = 10'. Since the volumes are proper tional to the lengths of the spaces between the piston and the end of the stroke, we may apply formula 62, 14.7 iVÂZi, X GO ^ /. X 10 ' T r, ^^ 460 + 60 460 + 130* ^ 14.7 X COX 590 ,^^^^1, . . - _,, Therefore, p, = -— r = r^r 100. 07 lb. per sq. m. Ans. ''^' 520 r M X 10 (549) T = 127° + 460° = 587°. Using formula 60, p V= .37052 r, or p^^ -37052 X 587 ^ ^^^^ ^^ ^^ ^^^^ A/ I (550) T - 100° + 4C0° = 5C0°. Substituting in formula ei,/>V= .37052 W T, or rr .37052 W T .37052 X .5 X 560 p 4,000 144 = 3.735 cu. ft. Ans. (551) Use formula 64. PV=U^+^^T. r= 110° + 460° = 570°; T^ = 100° + 460° = 560°; T, = 130° + 460° = 590°. / 90 X 40 80 X 57 \^yQ Therefore, V= \-^ ^^^ / = 67.248 cu. ft. ^^^ Ans. (552) The pressure exerted by squeezing the bulb may be found from formula 53, in which / is 14.7, v, the orig- inal volume = 20 cu. in., and v^, the new volume, = 5 cu. in. pV 14.7X20 r,o o û n.u a ^ *u p,-=-— = = = 58.8 lb. The pressure due to the atmosphere must be deducted, since there is an equal pressure on the outside which balances it. 58.8 — 14.7 =44.1 lb. per sq. in. = pressure due to squeezing the bulb. 3'X .7854= 7.0686 sq. in. = area of bottom. 7-0686 X 44.1 = 311.725 lb. 7.0686 X .434= 3.068 lb. = pressure due to weight of water. 311.725 + 3.068 = 314.793 lb. Ans. (553) Use formula 58. Z//4C0 '4G0_+ + /A . . ,/460+115\ ,^ ,4C0 +
STRENGTH OF MATERIALS. (QUESTIONS 554-613.) (554) See Arts. 1094, 1097, and 1096. (555) See Arts. 1 1 02, 1 1 03, 1 1 1 0, and 1 1 1 2. (556) (557) See Art. 11 05. Use formula 67. E = -T— ; therefore, e = A =.7854 X 2'; /=10X 12; /*= 40 X 2,000; i5"= 25,000,000. Therefore, . ^ ,^^'7 Â", n ,1 = -l^^'- ^ns. ' .7854 X 4 X 25,000,000 (558) Using formula 67, E — -r- = ^^^/— ,.,., ^ PI 7,000 X 7i^ _- ^^_ o^_ - ,, = ^,,,, 29,708,853.2 lb. per sq. in. ' ' A e .78o4 X (i) X .009 ' , (559) Using formula 67, PI r, „ AeE 1^X2X .000 X 15,000,000 ^ = = :?7'^'^=—r- 2,500 lb. Ans. (560) By formula 67, 93o2 Ans. P /»/ , AeE .7854 X3'X.05X 1,500,000 __ ^^, ^=^.or/ = -^= Poo ' = = 265.07. Ans. (561) Using a factor of safety of 4 (see Table 24), formula 65 becomes
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c c c tec C €
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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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lÔGARITHMS. 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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Page 170 and 171: 158 GEOMETRY AND TRIGONOMETRY. {d)
Page 172 and 173: 160 GEOMETRY AND TRIGONOMETRY. (341
Page 174 and 175: 162 GEOMETRY AND TRIGONOMETRY. (348
Page 176 and 177: 1G4 GEOMETRY AND TRIGONOMETRY. (354
Page 178 and 179: 166 ELEMENTARY MECHANICS. per min.
Page 180 and 181: 168 ELEMENTARY MECHANICS. replaced,
Page 182 and 183: 170 ELEMENTARY MECHANICS. (384) (a)
Page 184 and 185: 172 ELEMENTARY MECHANICS. (389) See
Page 186 and 187: 174 ELEMENTARY MECHANICS. (398) 1 h
Page 188 and 189: 176 ELEMENTARY MECHANICS (412) Use
Page 192 and 193: 180 ELEMENTARY MECHANICS. a distanc
Page 196 and 197: 184 ELEMENTARY MECHANICS. (d) Using
Page 198 and 199: 186 ELEMENTARY MECHANICS. (452) (a)
Page 200 and 201: 188 HYDROMECHANICS. (457) (a) Area
Page 202 and 203: 190 HYDROMECHANICS. Pressure due to
Page 204 and 205: 192 HYDROMECHANICS. (47 1 ) (a) 36
Page 206 and 207: 194 HYDROMECHANICS. 5' X 7854 (479)
Page 208 and 209: 196 HYDROMECHANICS. (d) See Art. 10
Page 210 and 211: 198 HYDROMECHANICS. Pressure per sq
Page 212 and 213: aOO HYDROMECHANICS. For z;„ = 4,/
Page 214 and 215: 202 PNEUMATICS. (509) Substituting
Page 216 and 217: 204 PNEUMATICS. (519) 8.47 = origin
Page 218 and 219: 206 PNEUMATICS. (537) (a) 30 — 17
Page 222 and 223: 210 STRENGTH OF MATERIALS. P- p-^^.
Page 224 and 225: 212 STRENGTH OF MATERIALS. Since 40
Page 226 and 227: 214 STRENGTH OF MATERIALS. drawn. P
Page 228 and 229: 21G STRENGTH OF MATERIALS. c \d of
Page 230 and 231: 218 STRENGTH OF MATERIALS. n o. I//
Page 232 and 233: 220 STRENGTH OF MATERIALS. Substitu
Page 234 and 235: 222 STRENGTH OF MATERIALS. (589) Su
Page 236 and 237: 224 STRENGTH OF MATERIALS. (597) {a
Page 238 and 239: 226 STRENGTH OF MATERIALS. (d) In t
Page 240 and 241: 228 STRENGTH OF MATERIALS. (604) Us
Page 242 and 243: 230 STRENGTH OP MATERIALS. (609) Th
Page 244 and 245: 232 STRENGTH OF MATERIALS. moments
Page 246 and 247: 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
Page 264 and 265: 252 SURVEYING. and including that a
Page 266 and 267: 254 SURVEYING. horizontal lines 1 f
Page 269 and 270: (706) LAND SURVEYING (QUESTIONS 706
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LAND SURVEYING. 259 ture of A B is
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LAND SURVEYING. 261 -{-, in the col
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LAND SURVEYING. 263 is +8.86 chains
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a a *• o « .i Q a V Q + • hJ *
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LAND SURVEYING. 2G7
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RAILROAD LOCATION. (756) (QUESTIONS
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RAILROAD LOCATION. 271 second curve
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RAILROAD LOCATION. 273 in which;!'
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RAILROAD LOCATION. 275 Whence, we h
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RAILROAD LOCATION. 277 4.0827 ft.,
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point so determined by RAILROAD LOC
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282 RAILROAD CONSTRUCTION. (818) Th
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884 RAILROAD CONSTRUCTION. (833) Ap
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286 RAILROAD CONSTRUCTION. (859) Fi
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288 RAILROAD CONSTRUCTION. (864) (8
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RAILROAD CONSTRUCTION. (QUESTIONS 8
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RAILROAD CONSTRUCTION. 293 (896) Se
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RAILROAD CONSTRUCTION. 295 (a) The
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RAILROAD CONSTRUCTION. 207 (939) Se
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300 TRACK WORK. (962) (963) (964) (
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302 TRACK WORK. (994) See Art. 1687
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304 TRACK WORK. (1008) 8 ft. G in.
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306 RAILROAD STRUCTURES. (1039) See
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308 RAILROAD STRUCTURES. (1060) Fro
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3," ^ >;> :3 3>32> ^ >:> J> Oi?^ :>
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UNIVERSrTY OF ILLINOIS-URBANA 3 011
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