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General Equations and Useful Data <br />Table I. -Minutes in Decimals of a Degree. <br />1' <br />Symbol <br />on Equation <br />Numerical <br />Value <br />Area of circle ................... <br />A d2 <br />.3500 <br />31' <br />.4 <br />41' <br />Area of Sector of Circle (Length 'of <br />51' <br />.8500 <br />are = 1) .....................: <br />1/21r <br />12 <br />Area of Segment of Parabola (app.) <br />'22 <br />.3667 <br />(c = chord; m = mid. ord.)..... <br />2/3 em <br />42. <br />Area of Segment of Circle ........ <br />2/3 cm <br />.8667 <br />Cubic Feet in 1 Cubic Meter...... <br />.0500 <br />35.3145 <br />Cubic Inches in 1 Imperial Gallon: <br />23 • <br />277.274 <br />Cubic Inches in 1 U.S. Gallon. . . . <br />.8500 <br />231 <br />Feet in 1 Meter................. <br />53 <br />3.2808 <br />Feet in 1 Mile .................. ... <br />• ' . <br />5280 <br />Gallons (Imperial) in 1. Cubic Foot. <br />24 <br />6.2321 <br />Gallons (U.S.) in 1 Cubic Foot ._ . <br />.5667 <br />7.48 <br />Miles in 1 Kilometer ............. <br />54 <br />0.6213 <br />Pounds (Av.) in 1 Kilogram ...... <br />.0833 <br />2.2046 <br />Ratio of Circumference to Diameter <br />a <br />3.14159 <br />Reciprocal of 7r .. - ......... a .... <br />.5333 <br />0.31831 <br />Square Feet in 1 Acre............ <br />55 <br />43,560 <br />Volume of Sphere ..:.:..:.......... <br />•4/3,rr3 <br />16 <br />Table I. -Minutes in Decimals of a Degree. <br />1' <br />.0167. <br />11' <br />.1833 <br />21' <br />.3500 <br />31' <br />.5167 <br />41' <br />6833 <br />51' <br />.8500 <br />2 <br />.0333 <br />12 <br />.2000 <br />'22 <br />.3667 <br />32 <br />.5333 <br />42. <br />:7000 <br />52 <br />.8667 <br />3 <br />.0500 <br />13 <br />.2167 <br />23 • <br />.3833 <br />33 <br />.8500 <br />43 <br />:7167 <br />53 <br />.8833' <br />4 <br />.0067 <br />14 <br />.2333 <br />24 <br />.4000. <br />34 <br />.5667 <br />44 <br />.7333 <br />54 <br />".9000 <br />5 <br />.0833 <br />15 <br />.2500 <br />25 <br />.4167 <br />36. <br />.5333 <br />45 <br />'.7500 <br />55 <br />.9167 <br />6 <br />.1000 <br />16 <br />.2667 <br />26 <br />.4333 <br />36 <br />.6000' <br />46 <br />.7667 <br />56 <br />.9333 <br />7 <br />.1167 <br />17 <br />.2833 <br />27 <br />.4500 <br />37 <br />'.6167 <br />47 <br />.7833 <br />57 <br />.9.500 <br />8 <br />.1333 <br />18 <br />.3000 <br />28 <br />.4607 <br />38 <br />.6333 <br />48 <br />.8000 <br />68 <br />.9667 <br />9 <br />..1500 <br />19 <br />.3167 <br />29 <br />•4833 <br />39 <br />.6500 <br />49 <br />.8167 <br />59 <br />.9833 <br />10 <br />.1667 <br />20 <br />.3333 <br />30. <br />.5000 11 <br />40 <br />1 .6667 it <br />50 <br />1 .8333 <br />60 <br />1 1.0000 <br />Table II. -Inches in Decimals of a Foot. <br />0052 0078 .0104 1 0156 1 .0208 I ,0260 I .0313 I .0417 .0521 0625 .0729 <br />0833 I2 4,1667 .2500 .3333. .4167 40600 .5833 .6667 .7500 .8333 .91167 d <br />2 <br />Tc1,1e TTT _R.tt.riii nrriinatAc anti nP.flPCtians <br />Deg. <br />Radius <br />Mid. <br />Ord. <br />Tan <br />Offset <br />Def. <br />for <br />1 Foot <br />Deg.. <br />Radius <br />Mid. <br />Ord. <br />Tan <br />Offset <br />Def. <br />for <br />1 Foot <br />0° 10' <br />•34377.5 <br />.036 <br />.145 <br />0.05' <br />7° <br />819.02 <br />1.528 <br />6.105 <br />2.10'. <br />20 <br />17188.8 <br />.073 <br />.291 <br />0.10 <br />20 <br />781.84 <br />1.600 <br />6.395 <br />2.20 <br />30 <br />11459.2 <br />.109 <br />.436 <br />0.15 <br />30 <br />764.49 <br />1.637 <br />6.540 <br />2.25 <br />40 <br />8594.42 <br />.145 <br />.582 <br />0.20 <br />40 <br />747.89 <br />1.673 <br />6.685 <br />2.30 <br />50 <br />6875.55 <br />.182 <br />.727 <br />0.25 <br />5° 08' <br />102.29 <br />44° <br />133.47 <br />2141, <br />3113, <br />4° 18' <br />5° 22' <br />102.53 <br />46° <br />8 <br />716.78 <br />1.748 <br />8.976 <br />2.90 <br />1 <br />5729.65 <br />.218 <br />.873 <br />0.30 <br />20 <br />688.16 <br />1.819 - <br />7.266 <br />2.50 <br />10 <br />4911.15 <br />.255 <br />1.018 <br />0.35 <br />30 <br />674.69 <br />1.855 <br />7.411 <br />2.55 <br />20 <br />4297.28 <br />.291 <br />1.164 <br />0.40 <br />40 <br />661.74 <br />1.892 <br />7.556 <br />2.60 <br />30 <br />3819.83 <br />.327 <br />1.309 <br />0.45 <br />104.14 <br />58° <br />103.14 <br />3° 29' <br />4° 10 <br />40 <br />3437.87 <br />.364 <br />1.454 <br />0.50 <br />9 <br />637.28 <br />1.965 <br />7.846 <br />2.70 <br />50 <br />3125.36 <br />.400 <br />1.600 <br />0.55 <br />20 <br />614.56 <br />2.037 <br />8.136 <br />2.80 <br />80 <br />603.80 <br />2.074 <br />8.281 <br />2.85 <br />2 <br />2864.93 <br />.430 <br />1.745 <br />0.60 <br />40 <br />593.42 <br />2.110 <br />8.425 <br />2.90 <br />10 <br />2644.58 <br />.473 <br />1.891 <br />0.65 <br />20 <br />2455.70 <br />.509 <br />2.036 <br />0.70 <br />10 <br />573.69 <br />2.183 <br />8.716 <br />3.00 <br />30 <br />2292.01 <br />.545 <br />2.181 <br />0.75 <br />30 <br />546.44 <br />2.292 <br />9.150 <br />3.15 <br />40 <br />2148.79 <br />.582 <br />2.327 <br />0.80 <br />11 <br />521.67 <br />2.402 <br />9.585 <br />3.30 <br />50 <br />2022.41 <br />.618 <br />2.472 <br />0.85 <br />30 <br />499.06 <br />2.511 <br />10.02 <br />3.45 <br />13 <br />478.34 <br />2.620 <br />10.45 <br />3.60 <br />3 <br />11 10.0855 <br />2.618 <br />0.90 <br />30 <br />459.28 <br />2.730 <br />10.89 <br />3.75 <br />l0 <br />1809.57 <br />.691 <br />2.763 <br />0.95 <br />13 <br />441.68 <br />2.839 <br />11.32 <br />3.90 <br />20 <br />1719.12 <br />2.908 <br />1.00. <br />30 <br />425.40 <br />2.949 <br />11.75 <br />4.05 <br />30 <br />1637.28 <br />.727 <br />.764 <br />3.054 <br />1.05 <br />14 <br />410.28 <br />3.058 <br />12.18 <br />4.20 <br />40' <br />1562.88 <br />.600 <br />3.199 <br />1.10 <br />30 <br />396.20 <br />.3.168 <br />12.62 <br />4.35 <br />50 <br />1494.95 <br />.836 <br />3.345 <br />1.15 <br />15 <br />383.07 <br />3.277 <br />13.05 <br />4.50 <br />4 <br />1432.69 <br />3.400 <br />1.20 <br />30 <br />370.78 <br />3.387 <br />13.49 <br />4.65 <br />10 <br />1375.40 <br />.873 <br />.909 <br />3.635 <br />1.25 <br />16 <br />359.27 <br />3.496 <br />13.92 <br />4.80 <br />20 <br />1322.53 <br />3.718 <br />1.30 <br />30 <br />348.45 <br />3.606 <br />14.35 <br />4.95 <br />30 <br />1273.57 <br />.945 <br />3.926 <br />1.35 <br />17 <br />338.27 <br />3.716 <br />14.78 <br />6.10 <br />40 <br />1228.11 <br />.982 <br />1.018 <br />4.071 <br />1.40 <br />18 <br />319.62 <br />3.935 <br />15.64 <br />5.40 <br />50 <br />1185.78 <br />1.055 <br />4.217 <br />1.45 <br />19 <br />302.94 <br />4.155 <br />18.51 <br />5.70 <br />1146.28 <br />1.091 <br />4.362 <br />1.50 <br />20 <br />287.94 <br />4.374 <br />17.37 <br />6.00. <br />10 <br />1109.33 <br />4.507 <br />1.55 <br />21 <br />274.37 <br />4.594 <br />18.22 <br />6.30 <br />20 <br />1074.68 <br />.1.127 <br />1.164 <br />4.653 <br />1.60 <br />22 <br />262.04 <br />4.814 <br />19.08 <br />6.60 <br />30 <br />1042.14 <br />1.200 <br />4.798 <br />1.65 <br />23 <br />250.79 <br />5.035 <br />19.94 <br />6.90 <br />40 <br />1011.51 <br />1.237 <br />4.943 <br />1.70 <br />24 <br />240.49 <br />5.255 <br />20.79 <br />• 7.20 <br />50 <br />982.64 <br />1.273 <br />5.088 <br />1.75 <br />25 <br />231.01 <br />5.475 <br />21.64 <br />7.50 <br />6 <br />955.37 <br />1.309 <br />5.234 <br />1.80 <br />26 <br />222.27 <br />5.697 <br />22.50 <br />7.80 <br />10 <br />929.57 <br />1.346 <br />5.379 <br />1.85 <br />27 <br />214.18 <br />5.918 <br />23.35 <br />8.10 <br />20 <br />905.13 <br />1.382 <br />5.524 <br />1.90 <br />2S <br />206.68 <br />6.139 <br />24.19 <br />8.40 <br />30 <br />881.95 <br />1.418 <br />5.669 <br />1.95 <br />29 <br />199.70 <br />8.360 <br />25.04 <br />8.70 <br />40 <br />859.92 <br />1.455 <br />5.814 <br />2.00' <br />30 <br />1 193.18 <br />6.583 <br />25.88 <br />L 9.00 <br />Noris. Chord Deflection=2 times tangent deflection. ' <br />Table IV. -Deflections for Sub Chords <br />far Shnrt Radius Curves <br />Degree <br />Curve <br />Radius <br />efleetion Angles or. <br />Sub Chords of Various Lengths <br />Len th of <br />Are for <br />100 Ft. Chord <br />12.5 Ft. <br />15 Ft. <br />20 Ft. <br />25 Ft. <br />301 <br />193.18 <br />1° 51' <br />2° 17' <br />2° 58' <br />3-431 <br />101.15 <br />32° <br />181.39 <br />1° 59' <br />2° 25' <br />3° 10' <br />31581- <br />101.33 <br />34° . <br />171.01 <br />2106' <br />2° 33' <br />3° 21' <br />4° 12' <br />101.48 <br />36° <br />161.80 <br />21 13' <br />2° 41' <br />3° 33' <br />4° 26' <br />101.66 <br />38° <br />153.58 <br />2120' <br />2° 49' <br />3° 44' <br />4° 40' <br />101.65 ' <br />40° <br />146.19 <br />2° 27' <br />2° 57' <br />3° 50' <br />4° 54' <br />102.06. <br />42° <br />139.52 <br />21 34' <br />3° 05' <br />4107' <br />5° 08' <br />102.29 <br />44° <br />133.47 <br />2141, <br />3113, <br />4° 18' <br />5° 22' <br />102.53 <br />46° <br />127.97 <br />2° 48' <br />30 21' <br />40 29' <br />P361 <br />102.76 <br />46° <br />122.92 <br />21 55' <br />30 29' <br />4140' <br />5° 50' <br />103.00 <br />50° <br />118.31 <br />31 02' <br />3° 38' <br />4° 51' <br />6° 04' <br />103.24 <br />62° <br />114.06 <br />31 09' <br />3° 46' <br />5° 02' <br />6° 17' <br />103.54 <br />54° <br />110.11 <br />3116, <br />3154' <br />5° 13' <br />6° 31' <br />103.84 <br />56° <br />106.50 <br />3122' <br />4102' <br />5° 23' <br />6'44' <br />104.14 <br />58° <br />103.14 <br />3° 29' <br />4° 10 <br />5° 34' <br />6° 57' <br />104.43 <br />60° . ` <br />100.00 <br />3° 35' <br />41 18' <br />5° 44' <br />7° I1' <br />1 104.72 <br />3 <br />