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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 f (s -a) (s - b) (s - c) n <br />2 ' s <br />9(8-a) <br />coo 1,/aA=+� be <br />tan Y, A = <br />r <br />s -a - <br />tau Y2B=srb <br />r <br />tan Y2 C = <br />s=e <br />Area of s triangle: <br />Area = Y2 ab Sin C <br />Area =1/s (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 />Linealfeet 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 />Cubic feet X.03704 = cubic yards <br />Links X.22= <br />yards <br />Links X.66 -feet <br />Feet X 1.5 = links <br />360° = 21600' -12()6000' <br />Radius = are of 57.2957790° <br />Are of 1° (radius = 1) = .017453292 <br />Are of 1' (radius = 1) = .000290888 <br />Are of 1" (radius = 1) = .000004848 <br />�[ = 3.141592654 1 1 = 0.564190 <br />r � <br />¢ = 0.785398163 ( = 1,240700982 <br />0523598776 >S' - 9.869604401 <br />3 <br />11 = 1.128379167 1 = 0.102321184 <br />= 0.523598776 = 1.772453851 <br />6 <br />4'-x = 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 arc and chord length, 0.05 feet in 11 Y2 miles <br />Probable error of a single observation = 0.6754 � 0 <br />�n-1 <br />Error in chaining of 0.01 feet in 100 feet.- <br />Due <br />eet:Due to -- <br />1. Length of tape error of 0.01 feet <br />d 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 150 <br />5. Difference of pull of 15 lbs. <br />STADIA REDUCTION FORMULA;, <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance = It Y2 sin 2 a+C sin a <br />distance from Object glass to cross hairs <br />R = ReadingX distance between cross hairs <br />C = distance from Ob]'ect 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 />3 <br />4 <br />5 <br />B <br />7. <br />.8 <br />9 <br />10_ <br />11 <br />A <br />.0052 <br />,0885.1719.255 <br />.336 <br />.4219 <br />.505 <br />.5885.6719.7552.8385 <br />:9219 <br />A <br />YS <br />.0104 <br />.N38.1771.260 <br />.343 <br />.4271.5104.593 <br />.6771,7604.8438.9271 <br />Y, <br />,0156.0990.1823.2656,3490.4323.5156-5990.6823.7656.8496.9323 <br />.0208 <br />.1042 <br />.1875 <br />:270 <br />:3542 <br />,4375 <br />.5208 <br />.6042 <br />.6875 <br />.7708 <br />.8542 <br />-9375 <br />�g <br />.0260.109 <br />.1927.276 <br />.359 <br />.4427.5260.6094.6927.7760.859 <br />.9427 <br />.0313 <br />,1146 <br />,1979.2813.3646.4479 <br />.5313.6146 <br />, 6979.781 <br />'8646,9479 <br />.0365.119 <br />.2031.2865.3698.4531.5365.6198.7031.7865.869 <br />,9531 <br />.2083 <br />.2917 <br />.375 <br />.4583.5417 <br />, 025 <br />.7083.7917 <br />.8750.9583 <br />Y2 <br />�q <br />.0469.1302.2135-2969-3803.4635.5469.6302.7135'7969.8902.9686 <br />-& <br />.0521.13 <br />,218 <br />.3021:385 <br />.4688.5521.63 <br />.7188.8021.885 <br />.9688 <br />f <br />} <br />0,%73,1406.2240.3073.3906.4740.5573.6406.7240.8073.8906.9740 <br />} <br />4 - <br />.0625 <br />.145 <br />.2292.3125 <br />, 3958.4792 <br />.5625 <br />.6458 <br />.7292 <br />.8125 <br />.8958.9792 <br />3/4 <br />} <br />.0677 <br />.151 <br />.2344 <br />.3177 <br />.4010 <br />.4844.5677 <br />.6510 <br />.7344 <br />.8177 <br />,9010 <br />.9844 <br />¢ <br />0729 <br />.156 <br />.2396.3229 <br />.4063.4896.5729.6563.7396.8229 <br />.9063.9896 <br />1 <br />.0781.161 <br />.2448.3281.4115.4948.,5781.6615.7448.8281,9115,9948 <br />'fie <br />1 <br />.0833.1667.2500.3333.4167.5000.5833.6667.7500.8333.91671.000 <br />1 <br />0 <br />1 <br />2 <br />3 <br />4 <br />5 <br />6 <br />7 <br />8 <br />9 <br />10 <br />11 <br />, <br />TABLE IV <br />USEFUL RELATIONS. <br />Linealfeet 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 />Cubic feet X.03704 = cubic yards <br />Links X.22= <br />yards <br />Links X.66 -feet <br />Feet X 1.5 = links <br />360° = 21600' -12()6000' <br />Radius = are of 57.2957790° <br />Are of 1° (radius = 1) = .017453292 <br />Are of 1' (radius = 1) = .000290888 <br />Are of 1" (radius = 1) = .000004848 <br />�[ = 3.141592654 1 1 = 0.564190 <br />r � <br />¢ = 0.785398163 ( = 1,240700982 <br />0523598776 >S' - 9.869604401 <br />3 <br />11 = 1.128379167 1 = 0.102321184 <br />= 0.523598776 = 1.772453851 <br />6 <br />4'-x = 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 arc and chord length, 0.05 feet in 11 Y2 miles <br />Probable error of a single observation = 0.6754 � 0 <br />�n-1 <br />Error in chaining of 0.01 feet in 100 feet.- <br />Due <br />eet:Due to -- <br />1. Length of tape error of 0.01 feet <br />d 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 150 <br />5. Difference of pull of 15 lbs. <br />STADIA REDUCTION FORMULA;, <br />Horizontal Distance = R - R sin' a+C cos a <br />Vertical Distance = It Y2 sin 2 a+C sin a <br />distance from Object glass to cross hairs <br />R = ReadingX distance between cross hairs <br />C = distance from Ob]'ect glass to cross hairs + distance from Object <br />glass to center of instrument. <br />a = angle of elevation for mid Reading <br />