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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 />Angle <br />Tangent <br />External_ <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <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 />600.9 <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 />46 <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 />48 <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 />706.91 <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 />1900.9 <br />:. 50 <br />2541.0 <br />538.2 <br />; 50 <br />'2972,1 <br />725.0 <br />50 <br />3431.4 <br />''943.1 <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 />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 <br />3476.8 <br />'972.4 <br />40 <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 />3035.8 <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 />3067.9 <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 />TABLn L = Tangents and Externals to a V Curve. <br />Chord=100 ft. <br />Angle <br />Corrections to be Added (T= Tangent. " E = External.) <br />Int. <br />Curve S. <br />10° 15° 1 20° 25° ' 30° <br />50° 55° 60°Ingle <br />External <br />Angle <br />Tangent <br />40° <br />T=.13 <br />.26 .40 .53 .67 . •.80 1.20 1.34 1.49 1.64 <br />1026.6 <br />E =.023 <br />kj.40-45° <br />.046 .070 .093 .117 .141 .234 .265 .277 290 <br />45° <br />T=.15 <br />.30 .44 .60 .76 .91 1.37 1.52 1.70 1.87 <br />1643.0 <br />E=.030 <br />.060 .093 .119 .153 .184 .289 .325 .351 .378 <br />50°T=.17 <br />10' <br />.34 : .51 . .68 ..85 1.02 1.54 1.72 1.91 2.10 <br />1315.6 <br />E=.037 <br />.075 .116 .151 .189 2275 .345 .384 .425 .467 <br />55° <br />T=.19 <br />.38 .57 .76 .95 1.14 1.32 1.52 1.72 1.92 2.14 2.35 <br />. <br />E=.046 <br />.093 .142 .188 .236 .283 .332 3.81 .420 .479 .530 .582 <br />600 <br />T=•21 <br />.42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 2.38 2.60 <br />1660,5 <br />E=.056 <br />.112 .168 .225 .283 340 .398 .457 .516 .575 .63G .697 <br />o <br />T=.23 <br />A 69 93 1.16 1.40 1.64 1.88 2.13 2.38 2.63 2.88 <br />1330.3 <br />E=-067 <br />.135 .204 .273 343 .412 .483 .554 .625 .697 .711 .845 <br />TABLn L = Tangents and Externals to a V Curve. <br />Chord=100 ft. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />Eatemal <br />04°. <br />3580.3 <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 />1660,5 <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 />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 />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 />3102.,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 />:,30 <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 />•30 <br />4265.6 <br />1413.5 <br />20 <br />4836.2, <br />1768.2 <br />30 <br />3756.5 <br />1121.7 <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 />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 />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 />_ <br />40 <br />.4370.1 <br />`1476.4 <br />�10 <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 />5024.8 <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 />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 />1533.1 <br />50 <br />6143.9 <br />1970.3 <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 />.1990.3 <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 />Corrections to be Added (T =Tangent. E = External.) <br />70° <br />Int. <br />Curve 50 <br />10" 15° 20° 25° 30° 35° 40° 45° 50° 55° 60° 65° 70° <br />Angle - - <br />- <br />_ <br />1.94 <br />60o <br />T=.21 <br />.42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 3.07 <br />.341 <br />E=.056 <br />.112 .168 .225 .283 .340 .398 .457 .516 .575 .636 .697 .774 .85 <br />2.21 <br />650• <br />1 .16 .64 1.554 88 2.625 13 2 <br />.38 2.711 .63 2 .88 3.922 <br />1.412 1. <br />E=.067 <br />..135 .204 .273 38 83 697 845 1.01 <br />2.48 <br />70o <br />T=.25 . <br />.51 , .76 1.02 1.28 1.54 1.80 2.06 2.33 2.60 2.88 3.16 3.44 3.72 <br />'159 <br />.550 <br />E =.080 <br />.240 .321 .403 .485 .568 .652 .735 .819 .906 .994 1.08 1.17 <br />2,77 <br />75° <br />T=.27 <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 />700 <br />E=.095 <br />-.182 .286 •.383 .480 .578 .678 .777 .877 .977 1.07 1.18 1.29 1.39 <br />3.07 <br />80o <br />T=.30 <br />61 .91 1.22 1.53 1.84 2.15 2.46 2.78 3.10 3.44 3.78 4.12 4.46 <br />.851 <br />E =.110 <br />220 .332 .445 .558 .671 .787 .903 1.02 1.13 1.25 1.38 1.50 1.62 <br />3.39 <br />S5o <br />T=.33 <br />36 2.70 3.05 3.40 3.77 4.14 4.55 4.89 <br />88 1.00 11.33 1.68 2.02 2:926,11 <br />1.01 <br />E=.128 <br />259 391 .524 .657 ,.7 .926 1.06 1.20 134 1.47 1.62 1.78 J1.91 <br />