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IN TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Wigle <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 />571 <br />3110.9 <br />790.1 <br />10'; <br />2266.6 <br />432.0 <br />X10' <br />2681.9 <br />590." <br />1e' <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 />500.4 <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 />2732.0 <br />G1S.4 <br />58 <br />3176.0 <br />821.4 <br />10 <br />2324.6 <br />453.6 <br />10 <br />2743.1 <br />022.8 <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 />532.0 <br />30 <br />2344.1 <br />461.0 <br />.30 <br />2763.7 <br />631.7 <br />30 <br />3208.8 <br />537.3 <br />40 <br />2353.8 <br />464.6 <br />40 <br />2773.9 <br />636.2 <br />4D <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 />843.1 <br />46 <br />2373.3 <br />472A <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 />858.0 <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 />G58.8 <br />30 <br />-3274.S <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 />2346.3 <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 />672.7 <br />60 <br />'3308.0 <br />886.4 <br />10 <br />2441.0 <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 />2401.7 <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 />3303.8 <br />914.5 <br />47 <br />2491.3 <br />518.2 <br />54 <br />2919.4 <br />700.9 <br />01 <br />3375.0 <br />920.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />2920.0 <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 />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 />566.0 <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 />553.8 <br />40 <br />3059.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />281.0 <br />588.0 <br />50 <br />3100.2 <br />754.9 <br />50 <br />3563.7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E = External.) <br />Angle <br />Ctirce 5° <br />10° <br />15° <br />20° <br />25° <br />1 30° <br />35° <br />40° <br />45°. <br />50°, <br />55° <br />1 60° <br />1 65° <br />70°. <br />40° <br />T=.13' <br />.26 <br />.40 <br />a3 <br />.57 <br />.80 <br />.93 <br />.106 <br />1.20 <br />1.34 <br />1.40 <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 />200 .315..341 <br />4081.3 <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 />1345.1 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.134 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />.445 <br />50° <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 />1713.7 <br />E=.037 <br />.075 <br />.116 <br />.151 <br />.189 <br />.227 <br />.266 <br />.305 <br />.345 <br />.384 <br />.425 <br />.467 <br />.508 <br />.550 <br />55° <br />T=.19 <br />.38 <br />.57 <br />.78 <br />95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 <br />2.50 <br />2.77 <br />1102.2 <br />E =.046 <br />.093 <br />.142 <br />.188 <br />.236 <br />.283 <br />.3321 <br />3.81 <br />.420 <br />.479 <br />.530 <br />.582 <br />.641 <br />.700 <br />60o <br />T=21 <br />.42 <br />.63 <br />.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 <br />IN <br />2.83 <br />3.07 <br />142t.2 <br />E=.056 <br />.112 <br />.18 <br />.225 <br />.283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 <br />.351 <br />650 <br />T=,23 <br />.46 <br />09 <br />93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 <br />1805.3, <br />E=.067 <br />.135 <br />.204 <br />273 <br />.343 .412 <br />.483 <br />.b54 .625 <br />.697 <br />.7t1 <br />.845 <br />.922 <br />1.01 <br />TABLE I. - Tangents and Externals to a V Curve. V <br />Chord =100 ft.: <br />Angle <br />Tangent <br />External <br />Aigje <br />Tangent <br />Extemal <br />Int <br />je <br />Tangent <br />External <br />64° <br />3580.3 <br />1026.6 <br />71° <br />4086.9 <br />1303.2 <br />780 <br />4039.8 <br />1643.0 <br />10' <br />3591.9 <br />103`2.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4053.G <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 />4081.3 <br />1669.2 <br />'40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4095.2 <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 />41SS.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 />421.1:0 <br />1382.8 <br />40 <br />4770.4 <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 />1749.0 <br />10 <br />3732.7 <br />1108.6 <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 />4265.6 <br />14t3.5 <br />20 <br />4836.2 <br />1768.2 <br />30 - <br />3756.5 <br />1121.7 <br />30 <br />4273.5 <br />142t.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 />37S0,4 <br />1134.8 <br />50. <br />4304.6' <br />1436.8 <br />50 <br />4870.2 <br />1796.0 <br />67 . <br />3702.4 <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 />a0 <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 />G8 - <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 />_ <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 />3937.9. <br />1222.7 <br />76 <br />4476.5 <br />1541.4 <br />83 <br />5069.2 <br />1920.5 <br />.69 <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 />3987.8 <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 />70 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.0 <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 />1900.5 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4554.8 <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 />40G1.8 <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 />,1G34.4 <br />50 <br />1 5234.9 <br />2031,4 <br />Corrections to be Added (T =Tangent. E=External.) <br />Iat. <br />Curve 5° <br />10 <br />15° <br />20° <br />25° 1 <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° 1 <br />65° <br />1 70° <br />Angle <br />60° <br />T=.21 <br />.42 <br />.63 <br />.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.33 <br />2.60 <br />2.83 <br />3.07 <br />E=.056 <br />.112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.630 <br />.697 <br />,774 <br />.851 <br />65° <br />T=.23 <br />.46 <br />.69 <br />.93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 { <br />E=.067 <br />.135 <br />.204 <br />.273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />1.321 .02 <br />1.403 .28 <br />1A85 .54 <br />1.568 .30 <br />2.652 .06 <br />2.735 <br />2.8109 <br />2 <br />3.994 <br />1 <br />17U° <br />E, <br />.159 <br />.240 <br />906 <br />1.08 <br />1.17 <br />75° <br />T=.27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98. <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />' <br />E=.095 <br />.182 <br />.286 <br />.383 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />80° <br />T=.30 <br />61 <br />.91 <br />1.22 <br />1.53 <br />1.842.15 <br />2.46 <br />2.78 <br />3.10 <br />344 <br />3.78 <br />4.12 <br />14.46 <br />E=.110 <br />.220 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1.02 <br />1.13 <br />1.25 <br />1.38 <br />11.50 <br />11.62 <br />SSo <br />T=.33 <br />66 <br />1.00 <br />1.33 <br />1.8 <br />12.02 <br />2.36 <br />12.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />E=.128 <br />.259 <br />.391 <br />.524 <br />.657 <br />.790 <br />926 <br />1.06 <br />1.20 <br />1.34 <br />1.47 <br />1.62 <br />1.76 <br />1.91 <br />