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Iv TABLE I..- Tangents and Externals to.a 1° Curve. <br />Chord =100 ft. <br />Int.. <br />Angle <br />Tangent <br />External <br />-Int. <br />Angle <br />Tangent External <br />Int: <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />'42j. 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 />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 />2324.6 <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 />.2753.4627.2 <br />4183.5 <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 />469.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />45 <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 />2304.9 <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 />2325.6 <br />658.8 <br />30 <br />3274.8 <br />869.8 <br />40 <br />2412.4 <br />487.2 <br />40 <br />2335.9 <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 />.500.4 <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 />2598.4 <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 />.906.5 <br />30 <br />2581.0 <br />'554.5 <br />30 <br />301415 <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 />5G2.8` <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 />533.8 <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.) <br />Angle Curve 5° 10° 15° •20° 25° 30° 35° 40° 45° 50° 55° 60°- 65° 70° <br />40° T=.13 26 .40 .53 .67 .80 .93 .106 1.20 1.34 1.49 1.64 1.79 1.94 <br />E =.023 .046 .070 .003 .117 .141 .172 .203 .234 .265 .277 290 .315 .341 j <br />45° 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 />50° T=.17 .34 .51 1 .68 .85 1.02 1.19 1.36. 1.54 1.72 1:91 2.10 2.29 2.48 I <br />E=.037 .075 .116 .151 .189 .227 .266 .305 .345 .384 '.425 .467 .508 .550 <br />55° T=.19. .38 .57 -.76 .95 1.14' 11.32 1.52 1.72 1.92 2.14 2.35 2.56 2.77 <br />E=.046 .093 ..142 .188 .236 .283 '.332 3.81 .420 .479 .530 '.582 .641 .700 i <br />60° T=.21 .42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 3.07 <br />E=.056 .112 .168 :223 .283 .340 .398 .457 .516 .575 .638 .697 .774 .851 <br />65° T=.23 .46 .69.93 1.16 1.40 1.64 1.88 2.13 238' 2.63 2.88 3.13 3.39 <br />E =.067 .135 .204 .273 .343 .412 .483 .554 .625 .697 .711 '.845 .922 1.01 <br />l <br />i <br />TA 3i, I. 'Tangents and Externals to a 1° Curve. 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 />1Y <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 />1060.5 <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 />3661.0 <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 />4214.0 <br />1382.8 <br />-40' <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />`1095.7 <br />; 50 <br />4220.8 <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 />1-. 20 <br />3744.6 <br />1115.1 <br />20 <br />4265.6 <br />,1413.-5 <br />20 <br />4536.2 <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 />! 1 .'50 <br />i4304.6 <br />1436.8 <br />-50, <br />4879.2 <br />• 1796.0 <br />167 <br />3792.4 <br />11411.4. <br />74 - <br />4317.6.:1444.6 <br />1.25 <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 />•'404370,.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 />98 <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 />4109.8 <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'i <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 />3608.6 <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 />e <br />Curve 5° <br />10° <br />15° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />70° <br />Angle : <br />_20° <br />60°T7•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 />656 <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=.27 <br />.58 <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 />•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 />=•30 <br />.61 <br />.91 <br />1.22 <br />1.53 <br />'.558 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />B-1 <br />'.220 <br />'.332 <br />.445 <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 />B5o <br />T=.33 <br />.66 <br />1.00 <br />1.33 <br />1.68 <br />12.02 <br />136 <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />B-.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 />1.78 <br />1.91 <br />e <br />