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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 />Use Law of Tangents. <br />Given A. B. c; to find a, b, C. <br />Use Law of Sines. <br />Given a, b, c; to find A, B, C. <br />Let a+b+e _ s, I (s - a) (s - b) (s - c) _ r <br />2 �VI S <br />WE Y2 A <br />bo <br />tan Y2A= ` <br />e-a <br />tan % B = <br />r <br />s-b <br />tan %C= <br />r <br />s-o <br />Area of a triangle: <br />Area = Y2 ab Sin C <br />Area = -\/s (s - a) (s --b) (s - c) <br />PRISMOIDAL FORMULA. <br />Vol. _ 11 <br />_ (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 />IO <br />1 <br />2 <br />3 <br />4 <br />5 <br />i 6 <br />7 <br />g <br />10 <br />11 <br />0052.0885.1719.2552 <br />3385.4219.5052 <br />5885.6719.7552.8385 <br />9219 <br />Y <br />.0104.0938.1771.2604,3438.4271I.5104..5938.6771 <br />7604.8438.9271 <br />.0156.0990.1823.2656.3490.4323.5156.599 <br />.6823.7656.8490.9323 <br />.0208.1042.1875.2708.3542.4370.5208.6042.6875.7708 <br />8542.9375 <br />1/4 <br />.0260.1094.1927.2760.3594.4427.5260.6094,6927.7760.8594.9427 <br />.0313.1146.1979.2813 <br />3646 <br />4479" <br />5313.6146.6979' <br />7813 <br />* 8646 <br />9479 <br />y <br />.0365.1198.2031.2865.3698.4531.5365.6198.7031.7865.8698.9531 <br />.0417.1250.2083.2917.3750.4583.5417.6250.7083.7917.8750.9583 <br />.0469.1302.2135.2969 <br />.3803.4635.5469.6302.7135 <br />.7969.8802.9635 <br />.0521.1354.2188.3021.3554.4688.5521.6354.7188.8021.8854 <br />9688 <br />.0573.1406.2240.3073.3906.4740.5573.6406.7240.8073.8906.9740 <br />Y, <br />.0625 <br />.1458.2292.3125,3958.4792.5625.6458 <br />M92.8125.8958.9792 <br />JJ <br />.0677 <br />.1510.2344.3177.4010.4844.567 <br />.6510.7344.8177.9010.9844 <br />.0729.1563.2396,3229 <br />4063.4896.5729.6563.7396,8229.9063 <br />9896 <br />VS <br />Jg <br />.0781 <br />.1615.2448.3281 <br />.4115 <br />4948.5781 <br />6615 <br />74481 <br />8281 <br />.9115.9948 <br />iJ <br />1 <br />.0833 <br />.1667.2500.3333 <br />.4167 <br />.5000.5833.6667 <br />.7500.8333.91671.000 <br />1 <br />0 <br />1 <br />2 <br />3 <br />4 <br />5 <br />6 <br />7 <br />8 <br />9 <br />1u <br />11 <br />TABLE IV <br />USEFUL RELATIONS <br />Lineal feet X.00019 <br />= miles <br />Lineal yards X.0006 <br />= miles <br />Square inches X.007 <br />= square feet <br />Square feet X.111 <br />= square yards <br />Square yards X.0002067 <br />= acres <br />Acres X4840 <br />= square yards <br />Cubic inches X.00058 <br />= cubic feet <br />Cubic feet X.03704 <br />= cubic yards <br />Links X22 <br />= yards <br />Links X.66 <br />= feet <br />Feet X 1.5 <br />= links <br />360' = 21600' = 1296000' <br />Radius = are of 57.2957790' <br />Arc of V (radius = 1) = <br />.017453292 <br />Are of 1' (radius = 1) _ <br />.000290888 <br />Are of 1" (radius = 1) = <br />.000004848 <br />7c = 3.141592654 <br />- I 1 = 0.564190 <br />�I 7C <br />4 = 0.785398163 <br />I = 1.240700982 <br />_ <br />- = 0.523598776 <br />a' = 9.869604401 <br />6 <br />1.1283791672 <br />= 0.101321184 <br />77 = 0.523598776 <br />6 <br />-\/�=-1.772453851 <br />43 = 4.188790205 - = 0.3183099 <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 arc and chord length, 0.05 feet in 11% miles <br />Probable error of a single observation = 0.6754_ Iv2 <br />n-1 <br />Error in chaining of 0.01 feet in 100 feet: <br />Due to- <br />t. 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 sing a+C cos a <br />Vertical Distance = R Y2 sin 2 a+C sin a <br />R Reading X <br />distance from Object glass to cross hairs <br />= <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 />