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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 <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />423.5 <br />50° <br />2671.S <br />592.3 <br />571 <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />2631.9 <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 />600.9 <br />20 <br />3132.6 <br />800.4 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />605.3 <br />30 <br />3143.4 <br />805.6 <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 />440.4 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3165.1 <br />816.1 <br />44 <br />2314.9 <br />450.0 <br />51 . <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />821.4 <br />10 <br />2324.6 <br />453.6 <br />10 <br />2743.1 <br />G22.8 <br />10 <br />318G.9 <br />826.7 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />627.2- <br />20 <br />3197.3 <br />832.0 <br />30 <br />2344.1 <br />461.0 <br />30 <br />2763.7 <br />631.7 <br />30 <br />3208.8 <br />&37.3 <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 />50 <br />2363.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />84S.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 />10 <br />2383.1 <br />475.8 <br />10 <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 />864.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2825.6 <br />658.8 <br />30 <br />3274.8 <br />809.8 <br />40 <br />241.2.4 <br />457.2 <br />40 <br />2935.9 <br />GQ. 4: <br />40 <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />GG8.0 <br />50 <br />3296.9 <br />880.5 <br />46 <br />2432.1 <br />494.8 <br />53 <br />2856.7 <br />672.7 <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 />2398.4 <br />691.4 <br />40 <br />3352.6 <br />908.8 <br />50 <br />2481.4' <br />514.3 <br />50 <br />2908.0 <br />696.1 <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 />2531.1 <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 />94S.9 <br />48 <br />2551.0 <br />542.2 <br />55 <br />29S2.7 <br />729.9 <br />62 <br />3442.7 <br />954.8 <br />10 <br />25G L 0 <br />546.3 <br />10 <br />'2993.3 <br />734.8 <br />10 <br />3454.1 <br />060.6 <br />20 <br />2571.0 <br />- 550.4 <br />20 <br />3003.9 <br />739.7 <br />20 <br />3465.4 <br />066.5 <br />.30 <br />2531.0 <br />5..5511.5 <br />30 <br />'3014.5 <br />741.6 <br />30 <br />3476.8 <br />972.4 <br />40 <br />2591.0 <br />558.G <br />40 <br />3025,2 <br />740.6 <br />40 <br />3488.3 <br />078.3 <br />50 <br />260 L 1 <br />562.5 <br />50 <br />3035.5 <br />. 754.6 <br />• 50 <br />3499.7 <br />9&l.3 <br />69, <br />2611.2 <br />566.0 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />090.2 <br />10 <br />2621.2 <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 />3067.0 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />30 <br />3078.7 <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />40 <br />2051.5 <br />553.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />20U1.6 <br />583.0 <br />50 <br />3100.2 <br />754.9 <br />50 <br />3565.7 <br />1020.5 <br />Corrections to be Added (T=Tangent. E=External.) <br />Int. <br />Angle <br />Curve 5° <br />10° 15° 20° <br />25° <br />30° <br />35° <br />40° 45° 50° 55° <br />60° 65° <br />70° <br />40° - - <br />T=.13 <br />.26 .40 .53 <br />.67 <br />.80.03 <br />1308.2 <br />.105 1.20 1.34 1.49 <br />1.64 1.79 <br />1.94 <br />10' <br />E=.023 <br />.046 .070 .003 <br />.117 <br />.141 <br />.172 <br />.203 .234 .265 .277 <br />.290 .315 <br />.341 <br />45° <br />T=.15 <br />30 .44 .GO <br />.76 <br />.91 <br />1.06 <br />1.21 1.37 1.52 1.70 <br />1.87 2.04 <br />2.21 <br />30 <br />E =.030 <br />.060 .093 .119 <br />.153 <br />.184 <br />.21G <br />.254 .289 .325 .351 <br />.378 .411 <br />'.445 <br />50° <br />T=.17 <br />.34 .51 .68 <br />.85 <br />1.02 <br />1.19 <br />1.36 1.54 1.72 1.91 <br />2.10 2.29 <br />2.48 <br />50 <br />E=.037 <br />.075 .116 :151 <br />.189 <br />.227 <br />.266 <br />.305 .345 .384 .425 <br />.467 .508 <br />.550 <br />55° <br />T=.19 <br />.38 .57 .76 <br />.95 <br />1.14 <br />1.32 <br />1.52 1.72 1.92 2.14 <br />2.35 2.56 <br />2.77 <br />10 <br />E =.046 <br />.093 .142 .188 <br />.236 <br />.283 <br />.332 <br />3.81 .420 A79 .530 <br />.582 .641 <br />.700 <br />60° <br />T=.21 <br />.42 .63 84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 1.94 2.17 2.38 <br />2.60 233 <br />3.07 <br />30 <br />E=.056 <br />.112 .168 .225 <br />.283 <br />.340 <br />.398 <br />.457 .516 .575 .636 <br />.697 .774 <br />.851 <br />65° <br />T=.23 <br />.46 6993 <br />1.16 <br />1.40 <br />1.64 <br />1.88 2.13 2.38 2.63 <br />2.88 3.13 <br />3.39 <br />50 <br />E =.067 <br />.135 .'1.04 .273 <br />.343 <br />.412 <br />.4.83 <br />.554 .625 .697 .711 <br />.845 .922 <br />1.01 <br />TABLE L - Tangents and Externals to a 1° Curve. q <br />C,hnrrl =100 ft: <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />64° <br />35SO.3 <br />1026.6 <br />71° <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4653.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.:; <br />30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1669.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />'4.0 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />1345.1 <br />50 <br />4709.2 <br />1686.9 <br />G5 <br />3650.2 <br />1063.9 <br />7Z <br />4162.8 <br />1352.6 <br />10 <br />4723.2 <br />1695.8 <br />10 <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 />3G73.7 <br />1076.6 <br />20 <br />4185.5 <br />1367.0 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.9 <br />30 <br />4201.2 <br />1375.2 <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 />4226.5 <br />1390.4 <br />50 <br />4793.6 <br />1740:8 <br />GG <br />3720.9 <br />1102.2 <br />73 <br />4239.7 <br />1395.0 <br />80 <br />4807:7 <br />1749.9 <br />10 <br />3732.7 <br />1108.G <br />10 <br />4252.G <br />.1405.7 <br />10 <br />4822.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4205.6 <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 />3768.5 <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 />5U <br />430..G <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 />1444.0 <br />81 <br />4893.6 <br />1805.3 <br />10 <br />"3&04.4 <br />1148.0 <br />10 <br />4336.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />3316.4 <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 />1533.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />90 <br />4951.5 <br />1843.1 <br />50 <br />3552.6 <br />117.1.8 <br />50 <br />4383.3 <br />1454.4 <br />50 <br />4966.1 <br />1852;6 <br />68 <br />3564.7 <br />1181.6 <br />75 <br />4306.5 <br />1492.4 <br />82 <br />4950.7 <br />1862.2 <br />10 <br />2876.8 <br />1158.4 <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 />5024.8 <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 />3937.9 <br />1222.7 <br />76 <br />44.76.5 <br />1541.4 <br />83 <br />5069.2 <br />1920:5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4459.9 <br />1549.7 <br />10 <br />5084.0 <br />1930.4 <br />2U <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 />5113.9 <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 />3909.5 <br />1257.9 <br />50 <br />4514.0 <br />1553.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.G <br />84 <br />5159.0 <br />1.980:4 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4584.8 <br />1668.6 <br />`20 <br />5189.3 <br />2000.6 <br />30 <br />4049.3 <br />12SG.5 <br />30 <br />4595.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4312.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />1 4626.0 <br />1634.4 <br />50 <br />5234.9 <br />2031.4 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int. Curve So <br />10° <br />15° <br />20° <br />25° <br />30° 1 <br />35° 1 40° 1 4a <br />50° <br />55° 1 60° 1 <br />65° 70° <br />Angle <br />T=.21 <br />.42 <br />.63 <br />.34 <br />1.05 <br />1 7 <br />1.49 1.71 1.94 <br />2.17 <br />2.38 2.60 <br />2.83 3.07. <br />�° <br />E=.056 <br />.112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 .457 .516 <br />.575 <br />.636 .697 <br />.774 .851 <br />T=.23 <br />.46 <br />.69 <br />.03 <br />1.16 <br />1.40 <br />1.64 1.88 2.13 <br />2.38 <br />2.63 2.88 <br />3.13 3.39 <br />65° E=.067 <br />.135 <br />.264 <br />273 <br />.343 <br />.412 <br />.483 .554 .625 <br />.697 <br />.711 .845 <br />.922 1.01 <br />T=.25 <br />.76 <br />1.02 <br />1 23 <br />1.54 <br />1.50 2.06 2.32 <br />2.60 <br />2.88 3.16 <br />3.44 3.72 <br />i0° E=.080 <br />.5l <br />.159 <br />.240 <br />..321 <br />.403 <br />.485 <br />.568 .652 .735 <br />.819 <br />.906 .994 <br />1.08 1.17 <br />T=.27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 2.27 2.57 <br />2.87 <br />3.16 3.47 <br />3.78 4.09 <br />75° E=.095 <br />.182 <br />.286 <br />383 <br />.480 <br />.578 <br />.678 .777 .877 <br />.977 <br />1.07 1.18 <br />1.29 1.39 <br />T=.30 <br />.61 <br />.91 <br />122 <br />1.53 <br />1.84 <br />2.15 2.46 2.78 <br />3.10 <br />3.44 3.78 <br />4.12 4.46 <br />80° E=.110 <br />.230 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 .903 1.02 <br />1_18 <br />1.25 1.38 <br />1.50 1.62 <br />T=.33 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 2.70 3.05 <br />-.92611:06 <br />3.40 <br />3.77 4.14 <br />4.55 4.89 <br />SS° E=.128 <br />.66 <br />.259 <br />.391 <br />.524 <br />.657 <br />.790 <br />1.20 <br />1.34 <br />1.x7 1.62 <br />1.76 1.91 <br />A <br />