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IV TABLE I. - Tangents and Externals to.a 1° Curve. <br />Chord=100 ft. <br />Angle <br />Tangent <br />External <br />Anngle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />430 <br />2257.0 <br />428.5. <br />501 <br />2671.8 <br />592.3 <br />570 <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />- 10' <br />2681.9 <br />. 596.6 <br />101 <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 />446.4 <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 />622.8 <br />10 <br />3186.9 <br />826.7 <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 />30 <br />3208.8 <br />837.3 <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 />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 />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 />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 />3296.9• <br />. 880.8 <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 />2898.4 <br />691.4. <br />40 <br />'3352.6 <br />908.8 <br />50 <br />2481.4 <br />514.3 <br />50 <br />2908.9 <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 />:948.9 <br />148 <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 />"10 <br />3454.1' <br />960.6 <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 .,3476.8 <br />5113.9 <br />972.4 <br />% <br />2591.0 <br />558.6 <br />40 <br />3025.2 <br />749.6 <br />40 <br />3488.3 <br />978.3 <br />50; <br />2601.1 <br />562.8' <br />50 <br />3035.5 <br />754:6 <br />50 <br />3499.7 <br />984.3 <br />•49 <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 />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 />306719 <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 />2651.5 <br />583.8 <br />40 <br />3089.4, <br />779.8 <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 />t <br />TABLE L - Tangents and.Externals to a 1°'Curve; V ' <br />Chord =100 ft. <br />Ink <br />Angle <br />Tangent <br />External <br />Int. <br />Angle • <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />640 ' <br />3580.3 <br />1026.6 <br />71° <br />4086.0 <br />1308.2 <br />780 <br />4639.8 <br />1643.0 <br />101 <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 />f'20 <br />4112.1 <br />1322.9 <br />20. <br />4667.4 <br />1660.5 <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 />40 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />S0 <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 />4162.8 <br />1352.6 <br />79 . <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 />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 />1082.9 <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 />4226.8 <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 />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 />.- 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 />30 <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 />3816.4 <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 it <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 />I 30 <br />5024.8 <br />1891.2 <br />40 <br />3913.4 <br />1208.9 <br />AO <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 />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 />5113.9 <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 />3999.5 <br />1257.9 <br />50 <br />4544.0 <br />'1583.1 <br />50 <br />5143.9 <br />1970.3 <br />r <br />70 <br />4011.9 <br />1265.0 <br />77 ' <br />4557.6 <br />1591.6 <br />84 <br />5159.0 <br />1980.4 <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 />1608.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4049.3 <br />1286.5 <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 />1 <br />Corrections to be Added (T = Tangent. E = External.) <br />Corrections to be Added (T = Tangent. E = External.) <br />t- <br />Curve 5' <br />100 15' 20o 25o 30o 35° 400 45° Soo 55° 60° 650 70o <br />Angle <br />Curve So <br />loo 15° 20° 25o 30° 35° 40o 45° 50° 550 60° 650 70o <br />�I <br />Angle <br />. <br />, <br />o <br />40_ <br />T=.13 <br />.26 .40 .53 .67 .80 .93 .106 1.20 1.34 1.49 1.64. 1.79 1.94. <br />o <br />T=.21 <br />.42 .83 .84 1.05 1.27 1:49 1.71 1.94 2.17 2.38 2.60 2.83 3.07 <br />E=,023 <br />.016 -.070 .093 .117 .141 .172 .203 .234 .265 .277 .290 .315 .341 <br />E=.056 <br />.112 .168 .225, .283 .340 .398 .457 .516 .575 .636 .697 .774 .851 <br />45° <br />E <br />.7.87 04 21 <br />1.216 1.254 1 1.325 1.351 1.378 ? <br />65° <br />3 .13 339 <br />.69 .931.343 1.412 1.483 1.554 2.625 2.697 2.711 2 <br />=,030 <br />.060 093 .6019. 153 '.184 289 411 .441' <br />E =.067 <br />.165 204 .273 845 922 1.01 <br />Soo <br />02 9,.31.345 1.384 1425 x.487 2 .29 <br />1.227 1.286 1 2.550 <br />700 <br />1.321 .02 1 .28 6 3.44 13.72 <br />1 1.568 .80 2.652 .06 2 33 2.819 ? 3.994 <br />E=.037 <br />.075 116 .151 .689 305 508 <br />E=.080 <br />.159 .240 403 485 735 906 1.08 11.17 <br />�i <br />r,So <br />T=.19 <br />E=.046 <br />.38 .57 .76 .95 1.14 1.31 1.52 1.72 1. 2.14 2.35 2.58' 2.77 <br />.093 .142 .183 .236 .283 .332 3.81 .420 .479 .b30 .582 .641 .700 <br />75o <br />T=.27 <br />E =.095 <br />.56 .83 1.12 1.40 1.69 1.98 2.27 2.57 2.87 3.16 3.47 3.78 4.09 <br />.182 .286 .383 .480 .578 .878 .777 .877 .977 1.07 1.18 1.29 1.39 <br />05 1340 .27 1.398 .49 1457 .71 1.516 .94 2.575 .17 2:31 <br />1 2.697 2.774 .83 2.851 <br />800 <br />1.445 .22 1 .53 1 <br />2.787 .15 2 <br />600 <br />.' E =.058 <br />112 .168 225 283 36 <br />E= 110 <br />.220 .332 558 .6711.84 <br />903 1.02 1.13 1.25 1.38 1.50 162 <br />fro <br />T=.23 <br />.46 69 93 1.16 1.40 1.64 1.88 2.13 2.38 2.63 2.88 3.13 3.39 ' <br />�o <br />T=33 <br />.68 1.00 1.33 1.88 2.02 2.36 2.70 3.05 3.0 3.77 4.14 4.55 4.89 <br />E=.087 <br />.135 .204 .273 .343 .412 .483 .554 .625 .697 .711 .84b .922 1.01 <br />E=.128 <br />.259 391 .524 .857 ;,79 .92 1.06 1.20 1.34 1.47 1.82 <br />l� <br />