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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 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+c_s I(s -a) (s - b) (s-c)_p <br />2 s <br />cosi A'= be <br />r <br />tan MA= <br />s -a <br />r <br />tau Y2 B _ - <br />tan Y2C= r <br />s=c <br />Area of a triangle: <br />Area = M ab Sin C <br />Area = Vs (s - a) (s - b) (s - e) <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 />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 />r Cubic feet X.03704 = cubic yards <br />1 Links X.22 = yards <br />Links X.66 = feet <br />Feet X 1.5 = 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 />Are of 1" (radius = 1) = .000004848 <br />a = 3.141592654 I 1 = 0.564190 <br />4 = 0.785398163 _ I = 1.240700982 <br />� v <br />6. = 0.523598776 'C' = 9.869604401 <br />i 4 1 <br />1.128379167 ; = 0.101321184 <br />r W <br />= 0.523598776 T = 1.772453851 <br />6 <br />4•,x = 4.188790205 1 = 0.3183099 <br />3 r <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 11'% miles <br />Probable error of a single observation = 0.6754_ f vR <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 />5. Difference of pull of 15 lbs. <br />STADIA REDUCTION FORMULM <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance = It y sin 2 a+C sin a <br />distance from Object glass to cross hairs <br />R = Reading 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 />0 <br />1 <br />2 <br />34 <br />5 <br />6 <br />7 <br />8 <br />9 <br />10, <br />11 <br />1X6 <br />.0052.0885.1719.255 <br />.3385.4219.5052.5885.6719.755 <br />.8385.9219 <br />�g <br />3/ <br />.0104.0938.1771.260 <br />.3438.4271.5104.5938.6771.7604.843 <br />.9271 <br />A <br />.0156.0 <br />.1823.265 <br />.3490.4323.5156.5990.6823.7656.849 <br />,9323 <br />� <br />Y <br />0208.1042.1875:2768.3542.4375.5208.6042.6875.7708.8542,9375 <br />y <br />7& <br />.0260.109 <br />.1927.2760.359 <br />.4427.5260.609 <br />.6927.776 <br />.8594.9427 <br />* <br />Yg <br />.0313.114 <br />..1979.2813.3646.4479.531 <br />.614 <br />.6979.7813.8646.9479 <br />�g <br />.0365.119 <br />.2031.2865.3698.4531.5365.619 <br />.7031.7865.8698.9531 <br />Ya <br />.0417.125 <br />.2083.2917.3750.4583.5417.625 <br />.7083.7917.8750.9583 <br />Y2 <br />19g <br />.0469.130 <br />.2135.2969.3803.4635.5469.6302.7135.7969.8802.9635 <br />% <br />.0521 <br />.13 <br />.2188.3021 <br />.385 <br />.4688.5521 <br />.63 <br />.7188.8021 <br />.88 <br />.9688 <br />Ji <br />.0573.-1406.2240.3073.31306.4740.5573.6406.7240.8073.9906,9740 <br />}J <br />Y4 <br />.0625.145 <br />.2292.3125.3958.4792.5625.6458.7292.8125.895 <br />.9792 <br />V4 <br />}} <br />.0677.151 <br />.23 <br />.3177.4010.4844.5677.651 <br />,7344.8177.9010.9844 <br />jU <br />Y8 <br />.0729.15 <br />.2396.3229.4063.4896.5729.6563.7396.8229.9063.9896 <br />}g <br />.0781.161 <br />.2448.3281.4115.4948.5781.6615.7448.8281.9115.9948 <br />1 <br />.0833 <br />.1667 <br />.2500 <br />.3333 <br />.4167 <br />.5000 <br />.5833 <br />.6667 <br />.7500 <br />.8333 <br />.9167 <br />1.000 <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 />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 />r Cubic feet X.03704 = cubic yards <br />1 Links X.22 = yards <br />Links X.66 = feet <br />Feet X 1.5 = 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 />Are of 1" (radius = 1) = .000004848 <br />a = 3.141592654 I 1 = 0.564190 <br />4 = 0.785398163 _ I = 1.240700982 <br />� v <br />6. = 0.523598776 'C' = 9.869604401 <br />i 4 1 <br />1.128379167 ; = 0.101321184 <br />r W <br />= 0.523598776 T = 1.772453851 <br />6 <br />4•,x = 4.188790205 1 = 0.3183099 <br />3 r <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 11'% miles <br />Probable error of a single observation = 0.6754_ f vR <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 />5. Difference of pull of 15 lbs. <br />STADIA REDUCTION FORMULM <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance = It y sin 2 a+C sin a <br />distance from Object glass to cross hairs <br />R = Reading 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 />