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uua� <br />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 />In <br />Tangent <br />External <br />43° <br />2257.0 <br />428.5 <br />.50° <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 />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 />&L <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 />X40 <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 />Q5 <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 />2515.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />.2402.8 <br />483.4 <br />30 <br />2325.6 <br />G58.8 <br />30 <br />3274.8 <br />869.8 <br />40 <br />•2412.4 <br />487.2 <br />40 <br />'2835:9 <br />GG3.4 <br />40 <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />GGS.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 />905.8 <br />50 <br />2481.4 <br />514.3 <br />50 <br />2908.9 <br />600.1 <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 />3 75.0 <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 />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 />33488.3 <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 />30G7.9 <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 />5S8.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E = External.) <br />'Int. <br />Angle Curve S° <br />10° 15° 20° 1 25° 1 30° <br />35° 40° <br />45° <br />50° <br />55° 60° 65° 70° <br />40 o T=.13 <br />.26 .40 53 .67 .80 <br />.93 .106 <br />1.20 <br />1.34 <br />L49 1.64 1.79 1.94 <br />E =.023 <br />.046 X70 .093 .117 .141 <br />.172 .203 <br />.234 <br />.265 <br />.277 290 .315 .341 <br />45o - T=.15 <br />.30 .44 GO .76 .91 <br />1.06 121 <br />1.37 <br />1.52 <br />1.70 1.87 2.04 2.21 <br />E=.030 <br />.060 .093 .119 .153 .184 <br />.216 X54 <br />.289 <br />.32:5 <br />.351 .378 .411 .445 <br />50° T=.17 <br />.34 :51 .68 .65 1.02 <br />1.19 1.36 <br />1.54 <br />1.72 <br />1.91 2.10 2.29 2.48 <br />E =.037 <br />.075 '.116 .151 .189 .227 <br />.266 .305 <br />.345 <br />.384 <br />.425 .467 .508 •550 <br />55° T=.19 <br />.38 .57 .76 .95 1.14 <br />1.32 1.52 <br />1.72 <br />1.92 <br />E <br />2.14 2.35 2.56 2.779 <br />=.040 <br />.093 .142 .188 .236 .283 <br />.332 3.81 <br />.420 <br />.479 <br />.530 .552 .641 <br />60° T =.21 <br />.42 .63 84 1.05 1.27 <br />1.49 1.71 <br />1.04 <br />2.17, <br />2.38 2.60 2.83 3:08751 <br />E =.056 <br />.112 .168 .225 .283 .340 <br />.39S .457 <br />.516 <br />.575 <br />.636 .697 .774 <br />65o T=.23 <br />.46 69 93 1.16 1.40 <br />1.64 1.86 <br />2.13 <br />2.38 <br />2.63 2.88 3.13 3.39 <br />E =,067 <br />.135 .204 273 .343 .412 <br />.483 .554 <br />.625 <br />.697 <br />.711 .845 .922 1.01 <br />TABLE L --Tangents and Externals. to a 1° Curve. V. <br />° Chor'd =100 ft. <br />Angle <br />Tangent <br />External <br />Ang a <br />I <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />6}° <br />3580.3 <br />1028.6 <br />'71° <br />4056.9 <br />1308.21 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591:9 <br />1032.8 <br />10' <br />4099.5 <br />1315.0 <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 />4 150. 1 <br />13.15.1 <br />504709.2 <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.:e <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 />4252.0 <br />140:5:7 <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 />179 6. 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.&' <br />20 <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 />.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 />49S0.7 <br />1862.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1503.5 <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 />4430.4 <br />15163 <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 />1257.0 <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 />1591.6 <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 />Corrections to be Added (T =Tangent. E=External.) <br />Int, Curve 5° 10° 15°L20' <br />25° <br />30° 35° <br />40° <br />45° 50° <br />55° <br />60° <br />65° <br />70° <br />6v ..:631.05 <br />1.27 1.49 <br />1.71 <br />1.94 2.17 <br />2.38 <br />2.60 <br />2.83 <br />3.07 <br />.168 <br />.283 <br />.340 .398 <br />.457 <br />.516 .575 <br />.630 <br />.697 <br />,774 <br />,851 <br />�,...691.16 <br />1.40 1.64 <br />1.83 <br />2.13 2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 <br />.201 <br />.343 <br />,412 .483 <br />.554 <br />.625 .697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />70. T=.25 .51 ..76 <br />1.28 <br />1.54 1.80 <br />2.05' <br />2.33 2.60 <br />2.83 <br />3.16 <br />3.44 <br />3.72 <br />E=.080 .159 .240 <br />.403 <br />.485 .568 <br />.552 <br />.735 .819 <br />.906 <br />.994 <br />1.08 <br />1.17 <br />75° T=.27 .56 .83 <br />1.12 <br />1.40 <br />1.69 1.98 <br />2.27 <br />2.5? 2.87 <br />3.18 <br />3.47 <br />3.78 <br />4.09 <br />E=.095 .182 .286 <br />.383 <br />.480 <br />.578 .678 <br />.7 <br />.877 .977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />800 T=.30 .61 ,91 <br />'..220 <br />1.22 <br />1.53 <br />1.84 2.15 <br />2.48 <br />2.78 3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />E=.110 .332 <br />.445 <br />.558 <br />.671 .787 <br />.903 <br />1.02 1.13 <br />11.25 <br />1.38 <br />1.50 <br />1.62 <br />85o T=.33 .66 1.00 <br />1.33 <br />1.68 <br />2.02 2.36 <br />2.70 <br />3.05 3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />E=.128 .259 .391 <br />.524 <br />.657 <br />.790 .926 <br />IXG <br />1.20 1.34 <br />11.47 <br />1.62 <br />1.70 <br />1.91 <br />