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IV TABLE I. - Tangents and Externals to a 1' Curve. <br />Chord =100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int <br />Angle <br />Tangent External <br />Int' <br />Angle <br />Ta agent <br />External <br />43' <br />2257.0 <br />428.5 <br />500 <br />2671.8 <br />592.8 <br />57° <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />600.0 <br />20 <br />3132.6 <br />600.4 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />605.8 <br />30 <br />3143.4 <br />605.6 <br />40 <br />2295.6 <br />442:8 <br />40 <br />2712.5 <br />609.6 <br />40 <br />3154,2 <br />810.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3105,1 <br />816.1 <br />44 <br />2314.9 <br />450.0 <br />51 <br />2732.9 <br />61,6.4 <br />fib <br />3176.0 <br />821.4 <br />10 <br />2324.8 <br />453.6 <br />10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />820.7 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />627.2 <br />20 <br />3197.8. <br />832.0 <br />30 <br />2344.1 <br />461.0 <br />30 <br />2763.7 <br />631.7 <br />20 <br />3208.8 <br />837.n <br />40 <br />2353:8 <br />464.6 <br />40 <br />2773.9 <br />636.2 <br />40 <br />3219.7 <br />842.7 <br />60 <br />2363.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />45 <br />2373.3 <br />472.1 <br />52 <br />2794.5 <br />645.2 <br />59 <br />3241.7 <br />853.5 <br />LO <br />2383.1 <br />475.8 <br />t0 <br />2804.9 <br />649.7 <br />10 <br />3252.7 <br />858.9 <br />20 <br />2392.8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />804.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2825.6 <br />658.8 <br />30 <br />3274.8 <br />869.8 <br />40 <br />2412.4 <br />487.2 <br />40 <br />2835.9 <br />663.4 <br />40 <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />668.0 <br />50 <br />3296.0 <br />880.8 <br />46 <br />2432,1 <br />494.,8 <br />53 <br />2856.7 <br />072.7 <br />60 <br />3308.0 <br />886.4 <br />10 <br />2441,9 <br />498:7 <br />10 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />20 <br />2451.8 <br />502.5 <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330,3 <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3341.4 <br />903.2 <br />40 <br />2471,5 <br />510.3 <br />40 <br />2898.4 <br />691.4 <br />40 <br />3352.6 <br />909.6 <br />50 <br />'2481.4 <br />514.3 <br />50 <br />2908.9 <br />896.I <br />50 <br />3363.8 <br />914.5 <br />47 <br />2491.3 <br />518.2 <br />54 <br />2919.4 <br />700.9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />2929.9 <br />705.7 <br />10 <br />3386.3 <br />925.9 <br />20 <br />2511.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />931.6 <br />30 <br />2521.1 <br />530.1 <br />30 <br />2951.0 <br />715.3 <br />30 <br />3408.8 <br />937.3 <br />40 <br />2.531.1 <br />534.2 <br />40 <br />2961.5 <br />720.1 <br />40 <br />3420,1 <br />943.1 <br />50 <br />2541.0 <br />538.2 <br />50 <br />2972.1 <br />725.0 <br />50 <br />3431.4 <br />948.9 <br />48 <br />2551.0 <br />542.2 <br />55 <br />2982,7 <br />729.9 <br />62 <br />3442,7 <br />954.8 <br />10 <br />2561,0 <br />546.3 <br />10 <br />2993.3 <br />734.8 <br />30 <br />3454.1 <br />950.6 <br />20 <br />2571.0 <br />550.4 <br />20 <br />3003.9 <br />739.7 <br />20 <br />3465.4 <br />966.5 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />3476,8 <br />972.4 <br />40 <br />2591.0 <br />558.6 <br />40 <br />3025.2 <br />749.0 <br />40 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3035.8 <br />754.0 <br />50 <br />3499.7 <br />984.3 <br />li <br />2611.2 <br />566.9 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <br />10 <br />2G21.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />10 <br />3522.6 <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />30G7.9 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />30 <br />3073.7 <br />774.7 <br />80 <br />3545.6 <br />1008.3 <br />40 <br />2651.5 <br />583.8 <br />40 <br />3089.4 <br />779.9 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661.6 <br />588.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added (T=Tangent. E=External) <br />Angie <br />Guru. 50 <br />10' <br />IS' <br />20' <br />25' <br />30' <br />35' <br />40' <br />45 <br />SO' <br />55' <br />60' <br />65° <br />79' <br />400 <br />T=.13 <br />.26 <br />.40 <br />.53 <br />.67 <br />.80 <br />.93 <br />.106 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 <br />1.94 <br />20 <br />E=.023 <br />.046 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.205 <br />.277 <br />.290 <br />.315 <br />.341 <br />45° <br />T=15 <br />.30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 <br />2.21 <br />50 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />.4455 <br />cam° <br />T=17 <br />.34 <br />.51 <br />.68 <br />.85 <br />1.02 <br />1.19 <br />1.36 <br />1.54 <br />1.72 <br />1.91 <br />2.10 <br />2.29 <br />2.48 <br />30 <br />E-.037 <br />.075 <br />.118 <br />.151 <br />.169 <br />.227 <br />.266 <br />.305 <br />.345 <br />.384 <br />.425 <br />.467 <br />.508 <br />.550 <br />° <br />T=.19 <br />.38 <br />.57 <br />.78 <br />.95 <br />'114 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 <br />2.58 <br />2.74" <br />73 <br />E=.040 <br />.093 <br />.142 <br />.188 <br />.236 <br />.283 <br />.332 <br />3.81 <br />.420 <br />.479 <br />.530 <br />.582 <br />.641 <br />.700 <br />60. <br />=.21 <br />.42 <br />.83 <br />.84 <br />1.05 <br />1.27 <br />1jIIIIL:4L17& <br />7 <br />.30 <br />2.17 <br />2.38 <br />2.60 <br />2.83 <br />3.07 <br />30 <br />=.050 <br />.112 <br />.188 <br />.225 <br />.233 <br />.390 <br />4291.5 <br />1429.0 <br />40 <br />.575 <br />.638 <br />.697 <br />..7T4 <br />851 <br />f5. <br />=.23 <br />j <br />.46 <br />.69 <br />.93 <br />1.18 <br />1.40 <br />12.88 <br />1141.4 <br />74 <br />4317.6 <br />2.63 <br />2.88 <br />3.13 <br />329 <br />10 <br />-.067 <br />.13 <br />.204 .273 <br />,343 <br />.412 <br />10 <br />,897 <br />.711 <br />.845 <br />.927 <br />1.01 <br />TABLE I. - Tangents and Externals to a 1° Curve. V <br />Chord =100 f t. <br />Int. <br />Angle <br />Tangent <br />g <br />External <br />Int. <br />AAgle <br />'Tangent <br />External <br />Int' <br />Angle <br />Tangent <br />Extemal <br />64' <br />35S0.3 <br />1025.6 <br />71' <br />4U86.9 <br />1308.2 <br />78° <br />4630.8 <br />1G43.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4653.6 <br />1051.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1560.5 <br />30 <br />3615.1 <br />1015.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1069.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4695.2 <br />1678.1 <br />50 <br />3039.5 <br />1057.7 <br />50 <br />4150.1 <br />1345.1 <br />50 <br />4709.2 <br />1686.9 <br />65 <br />3650.2 <br />1063.9 <br />72 <br />41G2.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />19 <br />3661.9 <br />1070.2 <br />10 <br />4175.6 <br />1360.1 <br />10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4188.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.0 <br />30 <br />4101.2 <br />'375.2 <br />30 <br />4765.3 <br />1722.7 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4214.0 <br />1382.8 <br />40 <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />4793,6 <br />1740.8 <br />66 <br />3720.9 <br />1102.2 <br />73 <br />4239.7 <br />1398.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />4822.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4265.6 <br />1413.5 <br />20 <br />4836.2 <br />1768.2 <br />.30 <br />3756.5 <br />1121.7 <br />30 <br />4278.5 <br />1421.2 <br />30 <br />4850.5 <br />1777.4 <br />40 <br />37458.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />4864.8 <br />1786,7 <br />50 <br />3780.4 <br />1134.8 <br />50 <br />4304.6 <br />1436.8 <br />50 <br />4879.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 <br />4317.6 <br />1444.6 <br />81 <br />4893.6 <br />1805.3 <br />10 <br />3804.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />3$16.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />4922.5 <br />1824.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4356.9 <br />1468.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />40 <br />4951.5 <br />1843.1 <br />50 <br />3852.6 <br />1174,8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4966.1. <br />1852.6 <br />68 <br />3864.7 <br />1181.6 <br />75 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4995.4 <br />1871.8 <br />20 <br />3889.0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />1881.5 <br />30 <br />3901.2 <br />1202,0 <br />30 <br />4436.4 <br />1516.7 <br />30 <br />5024.6 <br />1891.2 <br />40 <br />3913.4 <br />1208.9 <br />40 <br />4449.7 <br />1524.9 <br />40 <br />5039.5 <br />1900.9 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />1910,7 <br />69 <br />3937.0 <br />1222.7 <br />76 <br />4476.5 <br />1541.4 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4489.9 <br />1549.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4503:4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5113.0 <br />1950.3 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />3999.5 <br />1257.9 <br />50 <br />4544.0 <br />1583.1 <br />50 <br />5143.9 <br />1970.3 <br />76 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.G <br />84 <br />5159.0 <br />19S0.4 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.6 <br />20 <br />4036.8 <br />L279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4049.3 <br />1266.5 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5234.9 <br />2031,4 <br />Corrections to be Added (T =Tangent. E = External.) <br />Int. <br />Curve 5' <br />1 10' <br />15' <br />20° 25' 30° <br />350 <br />40' <br />45' Sr <br />55° 1 600 65° 70° <br />Angle <br />T-.21 <br />.42 <br />.63 <br />1.05 1.27 <br />1.49 <br />1.71 <br />1.94 2.17 <br />2.36 2.60 2.83 3.07 <br />60' <br />E =.056 <br />.112 <br />.168 <br />Ml .340 <br />.39S <br />.457 <br />.516 .575 <br />.636 .697 .774 .851 <br />T=.23 <br />.46 <br />.681.10 <br />I.40 <br />1.64 <br />1.88 <br />2.13 2.36 <br />2.63 2.88 8.I2 3.89 <br />65° <br />E=.007 <br />.135 <br />.204 <br />.343 .412 <br />.483 <br />.554 <br />.625 .697 <br />.711 .845 .922 1.01 <br />T=.25 <br />76 <br />[.273 <br />1.28 1.54 ,1.80 <br />2.08 <br />2.33 2.60 '2.88 <br />8.16 3.44 8.72 <br />70° <br />E =.080 <br />.51 <br />.159 <br />.240 <br />.403 .485 <br />.568 <br />.652 <br />.735 .819 <br />.906 .994 1.08 1.17 <br />T=.27 <br />1.40 169 <br />198 <br />2.27 <br />2.57 2.57 <br />3.16 8.47 3.76 4_09 <br />75° <br />E=.095 <br />.56 <br />L82 <br />.83 <br />.286 <br />.480 .578 <br />.876 <br />.777 <br />.877 .977 <br />1.07 1.18 1.29 139 <br />T=.30 <br />.81 <br />91 <br />1.22 1.53 1.64 <br />2.15 <br />2.48 <br />2.78 3.10 <br />3.44- 4.12 4.46 <br />8D° <br />F=110 <br />.220 <br />.332 <br />.445 .558 .671 <br />.787 <br />.903 <br />1.02 1.13 <br />1.25 1.38 1.50 1.62_ <br />85° <br />T=.33 <br />56 <br />1.00 1.33 1.68 2.02 <br />2.36 <br />2.70 <br />3.05 3.40 <br />3.77 4.14 4.55 4.89 <br />E =.128 <br />2.59 391 <br />524 .657 .790 <br />.920 <br />1.06 <br />1.20 134 <br />1.47 1.62 1.76 1.91 <br />