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TABLE II -'Continued <br />TRIGONOMETRIC FORMULAE (continued) <br />In, any triangle: <br />Given a, b, C; to find c, B, A. <br />Ude Law of Lines. <br />Given A. B, c; to find a, b, C. <br />Use Law of Lines. <br />Given a, b, c; to find A, B, C.'. <br />Leta+b+c_sI(s-a) (s -b) <br />2 ' wl e <br />coo 312 A = V . be <br />tan Y A = - <br />s -a <br />tau 3/ B = r <br />a r b <br />tan M C = <br />e=c• <br />Area of a triangle: <br />Area = y ab Sin C <br />Area = s (s - a) (s - b) (s - c) <br />PRISMOIDAL FORMULA, <br />Vol. = 6 (B+b+4M) <br />h = altitude; b, B = bases; M = midsection <br />TABLE III <br />INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A <br />FOOT <br />0 <br />0 <br />12 <br />3 <br />4 <br />5 <br />6 <br />7 <br />8- <br />'9 <br />10 <br />11 <br />X.0006 <br />�g <br />.0052.0 <br />Square inches X.007 <br />.1719.255 <br />a = 3.141592654 - I 1 = 0.564190 <br />.3385.4219.5052.5815.6719.755 <br />X.111 <br />= square yards <br />= 0.785398163 I = 1.240700982 <br />Square yards <br />X.0002067 <br />.8385.9219 <br />6 = 0.523598776 %' = 9.869604401 <br />119 <br />X4840 <br />.0104 <br />.0938.1771.260 <br />Cubic inches <br />X.00058 <br />.3438.4271.51 <br />.59 <br />.6771.7 <br />.8438.9271 <br />.YS <br />.0156.0990.1823.2656.3490.4323.5156.599( <br />.6823.7656-8490.9323 <br />34 <br />.0208.10 <br />.1875:2768.3542.4375.5208.604,' <br />.6875.770 <br />.8542.9375 <br />y <br />A <br />.0260.1094.1927.2760.3594.4427.5260.6094 <br />.692 <br />.7760.859 <br />.9427 <br />Y8 <br />.0313.11 <br />.1979.2813.3646.4479.5313.614 <br />.6979.7813:8646.9479 <br />A <br />.0365,1198.2031.2865.3698.4531.5365.6198.7031.7865' <br />- 8698.9531 <br />y78 <br />.0417.125 <br />.2083.291 <br />.3750.4583.5417.625 <br />.7083.7917.8750.9583 <br />Y2 <br />�g <br />.0469.130 <br />.2135.2969.3803.4635.5469.630 <br />.7135.7969.8802.9635 <br />ties <br />.0521.1354-2188.3021.3854.4698.5521.6354.7188.8021.8854.9688 <br />}} <br />.0573.140 <br />.224 <br />.307 <br />.390 <br />.4740.5573.640 <br />.72 <br />.8073.8906.9740 <br />11. <br />.0625.145 <br />.2292.3125.395 <br />.4792.5625.645 <br />.7292.8125.8958.9792 <br />1J <br />.0677.151 <br />.23 <br />.3177.4010.4844.5677.6510.73 <br />.8177.9010.9844 <br />* <br />Y, <br />.0729.15 <br />.239 <br />.3229.4063.4896.5729.6563.7396.8229.9063.9896 <br />YS <br />1f <br />.0781.161 <br />.244 <br />.3281.4115.4948.5781.6615.7448.8281.9115.0948 <br />* <br />I <br />.0833 <br />.1667 <br />.2500 <br />.3333 <br />.4167 <br />.5000.5833 <br />.6667 <br />.7500 <br />.8333 <br />.91671.000 <br />1. <br />0 <br />1 <br />2 <br />3 <br />4 <br />5 <br />6 <br />7 <br />8 <br />9 <br />10 <br />11 <br />0 <br />Cubic feet X.03704 = cubic yards <br />2" b <br />. TABLE IV <br />Links X.66 = feet <br />USEFUL RELATIONS. <br />Lineal feet <br />X.00019 <br />= miles <br />Lineal yards <br />X.0006 <br />= miles <br />1 L�� <br />Square inches X.007 <br />= square feet <br />a = 3.141592654 - I 1 = 0.564190 <br />Square feet <br />X.111 <br />= square yards <br />= 0.785398163 I = 1.240700982 <br />Square yards <br />X.0002067 <br />= acres <br />6 = 0.523598776 %' = 9.869604401 <br />Acres <br />X4840 <br />= square yards <br />Cubic inches <br />X.00058 <br />= cubic feet <br />Cubic feet X.03704 = cubic yards <br />2" b <br />Links X.22 = yards <br />Links X.66 = feet <br />Feet X1.5 = links <br />360° = 21600' = 1296000" . <br />Radius = arc of 57.2957790° <br />Are of 1° (radius = 1) = .017453292 <br />Are of V (radius = 1) = .000290888 <br />Arc of 1' (radius = 1) _ .000004848 <br />4- (' <br />a = 3.141592654 - I 1 = 0.564190 <br />v .a <br />= 0.785398163 I = 1.240700982 <br />L.2 <br />- ,6-� <br />4 <br />r <br />6 = 0.523598776 %' = 9.869604401 <br />`I = 1.1283791671-�, = 0.101321184 �r� Z <br />= 0.523598776 ,i = 1.77245385 <br />6 <br />43 = 4.188790205 1 = 0.3183099 <br />a i6z,z <br />Curvature of Earth's surface =about 0.7 feet in 1 mile <br />Curvature in feet = 0.667 (Dist. in miles)' C-'' ' Z` <br />Difference between are and chord length, 0.05 feet in 11 � miles 's , 9 <br />V, 61 -?Probable error of a single observation = 0.6754- I n - 1 <br />�JI z <br />3 rz,7 <br />�2L,g <br />�1 <br />Error in chaining of 0.01 feet in 100 feet: <br />Due to - <br />1. Length of tape error of 0.01 feet <br />2. Alignment. One end 1.4 feet out of line <br />3. Sag of tape at centre of 0.61 feet <br />4. Temperature difference of 15° <br />5. Difference of pull of 15 lbs <br />STADIA REDUCTION FORMULM <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance =.R M sin 2 a+C sin a <br />R = Reading distance from Object glass to cross hairs <br />distance between cross hairs <br />C = distance from Object glass to cross hairs + distance from Object <br />glass to center of instrument. <br />a = angle of elevation for mid Reading <br />