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TABLE II -Continued <br />TRIGONOMETRIC FORMULAE (continued) <br />In any triangle: <br />Given a, b, C; to fund c, B, A. <br />Use 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 />Let a+b+e _ s' V (s - a) (s - b) (s - c) <br />2 <br />e <br />cos YaA=� a) <br />be be <br />tan MA= <br />s -a <br />tau H 13 = <br />s <br />tan Y2 C = ' <br />s -c <br />Area of a triangle: <br />Area = �i ab Sin C <br />Area = s (s - a} (s --b) <br />PRISMOIDAL FORMULA. <br />Val. = 6 (B+b+4M) <br />h ._= altitude; b, B = bases;. M = midsection <br />=r <br />TABLE III <br />INCHES AND FRACTIONS OF AN INCH IN DECIMALS OF A <br />FOOT <br />TABLE IV <br />USEFUL RELATIONS, <br />Lineal feet X.00019 = miles <br />Lineal yards X.0006 = miles <br />Square inches X.007 = square feet <br />Square feet X.111 = square yards <br />Square yards X.0002067 = acres <br />Acres X4840 = square yards <br />Cubic inches X.00058 = cubic feet <br />I Cubic feet X.03704 = cubic yards <br />j Links X.22 =yards <br />Links X.66 Z feet <br />Feet X 1.5 = links <br />360° = 21600` = 1296000" <br />Radius = are of 57.2957790' <br />Are of 1' (radius = 1) = .017453292 <br />Are of 11 (radius = 1) = .000290888 <br />Are of 1" (radius = 1) = .000004848 <br />a = 3.141592654 I 1 = 0.564190 <br />4 = 0:785398163 = 1.240700982 <br />= 0.523598776 M2 = 9.869604401 <br />6 � <br />` - 1.128379167, = 0.101321184 <br />��( = 0.523598776 = 1.772453851 <br />s <br />4'� = 4.188790205 1 = 0.3183099 <br />3 W <br />Curvature of Earth's surface = about 0.7 feet in 1 mile <br />Curvature in feet = 0.667 (Dist. in miles)* <br />Difference between are and chord length, 0.05 feet in 11Y2 miles <br />Probable error of a single observation = 0.6754 Mv2 <br />n-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 />8. Difference of pull of 15 lbs <br />STADIA REDUCTION FORMULM <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance =.R A sin 2 a+C Bin 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 />IL = angle of elevation for mid Reading <br />0 <br />1 <br />2 <br />8 <br />4 <br />5 <br />6 <br />7 <br />8 <br />9 <br />10 <br />11 <br />11g <br />.0052.0 <br />1719 <br />255 <br />.3 <br />.4219.5052.5885.6719.755 <br />.9219 <br />.0104.09 <br />.1771.260 <br />.3438.4271.5104.59 <br />.6771.7 <br />.843 <br />.9271 <br />y <br />.0156. <br />.182 <br />.265 <br />.3490.4323.5156.59 <br />.682 <br />.765 <br />.849 <br />.9323 <br />.0208.10 <br />.1875.270 <br />.3 <br />.4375.520 <br />.6042.6875.770 <br />.9375 <br />f <br />* <br />.0260.109 <br />.1927.27 <br />.359 <br />.442 <br />,5260.6094.6927.7760.859 <br />.9427 <br />* <br />,0313.11 <br />.1979.281 <br />.364 <br />.4479.5313.6146.6979.781 <br />.884 <br />.9479 <br />�g <br />.031M.1198.2031-2865.3698.4531.5363.6108.7031.7865.869 <br />.9531 <br />7,Cj <br />0417.1250-2083.2917.375C.4583.5417,6250.7083.7917.875 <br />.9583 <br />�g <br />0469.1302.2135.2969.3803.4635-5469-6302.7135.7969.8802.9635 <br />s <br />0521.13 <br />.21$8.3021.3&5 <br />.4688.5521.635 <br />.7188.8021.8$ <br />.9688 <br />0573.140 <br />.3D73.3906.474 <br />.5573.6406.7240.807 <br />.890 <br />.9740 <br />} <br />.0625.1458,2292.3125-31358.4792-5625,6458.7292.8125,8958,9792 <br />1'8 <br />0677.151 <br />.2344.3177.4010.4844.5677.651 <br />.7344.8177.9010.9844 <br />Y4 <br />, 0729 <br />.1 <br />23W <br />3229 <br />.406 <br />.4896 <br />.5729 <br />.6563 <br />.7396 <br />.822 <br />.9063 <br />.9896 <br />1�0781.161 <br />.2448.3281.4115.4948.5781.661 <br />.7448.8281.9115 <br />.9948 <br />j1 <br />.0833.1667.2500.3333,4167.5000.5833.6667.7500.8333.91671.000 <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 />TABLE IV <br />USEFUL RELATIONS, <br />Lineal feet X.00019 = miles <br />Lineal yards X.0006 = miles <br />Square inches X.007 = square feet <br />Square feet X.111 = square yards <br />Square yards X.0002067 = acres <br />Acres X4840 = square yards <br />Cubic inches X.00058 = cubic feet <br />I Cubic feet X.03704 = cubic yards <br />j Links X.22 =yards <br />Links X.66 Z feet <br />Feet X 1.5 = links <br />360° = 21600` = 1296000" <br />Radius = are of 57.2957790' <br />Are of 1' (radius = 1) = .017453292 <br />Are of 11 (radius = 1) = .000290888 <br />Are of 1" (radius = 1) = .000004848 <br />a = 3.141592654 I 1 = 0.564190 <br />4 = 0:785398163 = 1.240700982 <br />= 0.523598776 M2 = 9.869604401 <br />6 � <br />` - 1.128379167, = 0.101321184 <br />��( = 0.523598776 = 1.772453851 <br />s <br />4'� = 4.188790205 1 = 0.3183099 <br />3 W <br />Curvature of Earth's surface = about 0.7 feet in 1 mile <br />Curvature in feet = 0.667 (Dist. in miles)* <br />Difference between are and chord length, 0.05 feet in 11Y2 miles <br />Probable error of a single observation = 0.6754 Mv2 <br />n-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 />8. Difference of pull of 15 lbs <br />STADIA REDUCTION FORMULM <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance =.R A sin 2 a+C Bin 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 />IL = angle of elevation for mid Reading <br />