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IV TABLE I. - Tangents and Externals to a P Curve. <br />Chord =100 ft. <br />Int. <br />Tangent <br />External <br />Angle-' <br />Tangent 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 />HY <br />3121:7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20, <br />2692:1 <br />600.9 <br />26 <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 />80 <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 />4b - <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 />433.4 <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 />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 />56 <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 />Corrections to be Added '(T '=Tangent. E = External.)` i <br />I <br />Curve 5° "10° 15° 20°. 25° 30° 35° 40° 45° 50° 1 55° 60°. 65° 1 706 <br />T=.13 26.40 .53 `.67 .80 .93 .106 1.20 1.34' 1A9 1.64 1.79 1.94 <br />E =.023 ..046 '.070 .093 -.117 .141 .172 .203 ..234 .265 .277 290 .315 .341 <br />T=.15 .30 :44 -.60 .76 .91 1.06 1.21 1.37 1.52 1.70 1.87 2:04 2.21 <br />E=.030 .060 .".093 .119 .153 .184 .216 .254 .289 .325 .351 .378 .411 .445 <br />T=.17 :34 .51 :68 .85 1.02 1.19 1.36 1.54 1.72 1.91 2.10 2.29 2.48 <br />E=.037 .075 ..116 .151 .189 .227 .266 .305".345 .384 .425 .467 .508 .550 <br />T=.19 .38. .57 76 .95 1.14 1.32 152 1.72 1.92 2.14 2.35 2.58 2.77 <br />-E=.046 :093 .142 .138 .236 '.283 ..332 3.51 .420 .479 .530 ..582 .641 .700 <br />T=.21 .42 .63 1 .84 11.05 11.27 11.49 1:71 1.94 2.17 2.38 12.60 12.83 3.07 <br />=.067 I :1351 .69 •2041 .93 •273 11.16 11.40 11.64 11.88 12.13 12.38 12.63 12.88 13.13 3.30 <br />=.067 ;135 .204 .273 .343 .412 .483 1 551I2.625I2.697I2.711I2 845I3.922I1 01 <br />TABLE I. Tangents and Externals to a-1° Curve. <br />V <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />'.Angle <br />Tangent <br />External <br />64° <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 />80 <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 />1063.0 <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 />10 <br />8804.4 <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 />1476.4.40 <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 />a8 <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 />4514.0 <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 />1591.6 <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. <br />Cure 5° <br />10° <br />IS- <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />70° <br />_Angle <br />- . <br />..- <br />60° <br />1 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 />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..516 <br />,.575 <br />.636 <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 />70° <br />T=.25 <br />.51 <br />.76 <br />1.02 <br />1.28 <br />1.54 <br />1.80 <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=.2� <br />56 <br />.83 <br />1.12 <br />1.40 <br />169 <br />1.98 <br />2:27-12:57 <br />' <br />2.87 <br />3.18 <br />3.47 <br />3.78 <br />4.09 <br />E. 495 <br />.182 <br />.286 <br />.383 <br />.480 <br />..578 <br />.678 <br />.777 <br />.577 <br />.977 <br />1.07 <br />1.18 <br />11.29 <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 />2.78 <br />3.10 <br />3.44 <br />3:78" <br />14.12 <br />14.46 <br />E =.110 <br />.220 <br />.332.445 <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 />° '.'T=.33 <br />66 .1:00 <br />1.33 <br />1.68 X2.02 <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 />.259'1 <br />.391 <br />.524 <br />.657 <br />.790''.926 <br />1.06 <br />1.20' <br />1.34 <br />1.47 <br />1:62 <br />1.76 <br />1.91 <br />