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IV TABLE L- Tangents and Externals to a 1° Curve. <br />Chord =100 It. <br />Angle <br />Tangent <br />External <br />Ang1e <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />43°- <br />2257.0 <br />428.5 <br />60° ' <br />2671.8 <br />592.3 <br />67° <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />d0' <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.G <br />453.0 <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 />G63,4 <br />40 <br />3255.8 <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 />2850.7 <br />672,7. <br />60 <br />3303.0 <br />SS6.4 <br />10 <br />2441.9 <br />498.7 <br />10 <br />2867.1 <br />677.3 <br />LO <br />3319.1 <br />892.0 <br />20 <br />2451.8 <br />502.5 <br />. 20 <br />2377.5. <br />682.0 <br />20 <br />3330.3 <br />597.5 <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 />G9611 <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 />3356.3 <br />025.9 <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 />340S.S <br />0.37.3 <br />40 <br />2531.1 <br />534.2 <br />40 <br />2961.5 <br />720,1 <br />40 <br />5420.1 <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 />943.9 <br />48 <br />2551.0 <br />542.2 <br />66 <br />2982.7 <br />729,9 <br />62 <br />3442.7 <br />95.1.8 <br />10 <br />2561.0 <br />5.16.3 <br />10 <br />2993.3 <br />734,8 <br />10 <br />3154.1 <br />960.6 <br />20 <br />2571.0 <br />550.4 <br />120 <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 />,3035.2 <br />749,6 <br />40 <br />3483.3 <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 />084.3 <br />49 <br />2611.2 <br />566:9 <br />56 <br />3046.5 <br />759.G <br />63 <br />3511.1 <br />990.2 <br />10 <br />2621.2 <br />671.1 <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 />3007.9 <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 />'1003.3 <br />40 <br />2651.5 <br />583.8 <br />40 <br />3039.4 <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 />35(38:7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E = External.) <br />Angle Curve 59 <br />10° <br />15° 20° 25° <br />30° <br />1 35° <br />1 40° <br />45° <br />50° <br />55° <br />60° 65° 70° <br />40° T=.13 <br />.26 <br />.40 .53 .67 <br />.80 <br />.93 <br />.106 <br />1.20 <br />1.34 <br />1.49 <br />1,64 1.79 1.94 <br />E =.023 <br />.046 <br />.070 .093 .117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 <br />.277 <br />290 .315 .341 <br />45° T=.15.30 <br />4112.1 <br />.44 .60 .70 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1,87 2.04 2.21 <br />E =.030 <br />.080 <br />.093 .119 .153 <br />.184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 .411 .445 <br />50° T=.17 <br />.34 <br />.51 .68 .85 <br />1.02 <br />1.19 <br />1.30 <br />1.54 <br />1.72 <br />1.91 <br />2,10 2.29 2.48 <br />E =.037 <br />.075 <br />.116 .151 .189 <br />.227 <br />.266 <br />.305 <br />.345 <br />.381 <br />.425 <br />.467 .508 .550 <br />55o T=.10 <br />.38 <br />.57 .78 .95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 2.56 2.77 <br />E=.046 , <br />.093 <br />.142 .188 .230 <br />.283 <br />.332 <br />3.81 <br />.420 <br />.479 <br />.530 <br />.582 .641 .700 <br />60° T =.21 <br />.42 <br />.63 .84 1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.3S <br />3.60 2.83 3.07 <br />F.=.058 <br />.112 <br />.168 .225 .283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.636 <br />.697 .774 .851 <br />'65° T=•23 <br />.46 <br />69 93 1:16 <br />1.40 <br />1.64. <br />1.88 <br />2 .13 <br />2.38 <br />2.63 <br />2.38 3.13 3.39 <br />E =.067 <br />.135 <br />.204 .273 .343 <br />.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 .922 1.01 <br />TABLE I. - Tangents and Externals to a P Curve. D <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 />64° <br />3550.3 <br />1026.6 <br />711 <br />4086.0 <br />1305.2 <br />781 <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 />4137A <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 />1656.9 <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 />4183.5 <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 />4214A <br />1352.8 <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 />1395.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6, <br />10 <br />4252.G <br />1405.7 <br />10 <br />4522.0 <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 />3750.4 <br />1134.8 <br />50 <br />4304.6 <br />1436.8 <br />50 <br />4870.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 • <br />4317A <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 />1465.4 <br />30 <br />4937.0 <br />M33.6 <br />40 <br />3S40.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />.40 <br />4951.5 <br />1843.1 <br />50 <br />3552.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4960.1 <br />1852.6 <br />68 <br />3864.7 <br />1181.6 <br />76 <br />4396.5 <br />1492.4 <br />82 <br />4950.7 <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 />4459:9 <br />1549.7 <br />10 <br />5034.0 <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 />6113.9 <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 />1257.0 <br />50 <br />4514.0 <br />I5S3.1 <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 />1090.5 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5139.3 <br />2000.6 <br />30 <br />4049.3 <br />1286.5 <br />30 <br />4595.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.5 <br />1293.6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5210.7 <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 />Curve 51 <br />101 <br />15° <br />20° <br />25° <br />30. <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />70° <br />Aagle <br />60. <br />T=.21 <br />.42 <br />.83.84 <br />1.05 <br />1.27 <br />1.4'9 <br />17! <br />1.94 <br />2.17 <br />2.38 <br />2.60 <br />2.83 <br />3.07 <br />F.=.056 <br />.112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 <br />'.457 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 <br />.851 <br />65° <br />T=.23 <br />.40 <br />.69.93 <br />1.16 <br />1.40 <br />1.64 <br />1.85 <br />2.13 <br />2.38 <br />2:63 <br />2.83 <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 />70. <br />T=.25- <br />.51 <br />.76 <br />1.02 <br />1.28 <br />1.54 <br />MO <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />3.16 <br />3.44 <br />3.72 <br />E =.080 <br />.159 <br />.240 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.994 <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 />2.572.87 <br />3.Ifi <br />3.47 <br />3.78 <br />4.00 <br />E =.095 <br />.182 <br />.286 <br />.383 <br />.430 <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 />1.84 <br />2.15 <br />2.46 <br />2.73 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />E =.IIO <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 />1.50 <br />1.62 <br />gSo <br />T=,33 <br />.66 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <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 />.534 <br />.657 <br />.7901.9201.06 <br />1.20 <br />1.34 <br />1.47 <br />1.62 <br />1.76 <br />I. <br />