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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 />External <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 />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 />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 />30 <br />.2344:1 <br />461.0 <br />.30 <br />2763.7 <br />631.7 <br />1,30 <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 />45'1 <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 />16 <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 />32741v8 <br />869.8 <br />402412.4 <br />40 <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 />00 . <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 />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 />T '. <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 />•202511.2 <br />20 <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 />566.9 <br />563046.5 <br />.77 <br />759.6 <br />63 , <br />'3511.1 <br />990x2 <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 />TABLE I. - Tangents and Externals to a 1° Curve. V <br />Chord =100 f t:. <br />Int. <br />Angle <br />Coriections'to be Added (T = Tangent. E = External.) <br />Angle <br />Curve 5°: <br />10° 15° 20° '25° 30° 35° 40° 45° 50° 55° 60°- 65° 70- <br />40. <br />T=13 <br />.26 '.40 .53. .67 .80 :93 .106 1.20 1.34 1.49 1.64 1.79 1.94 <br />External <br />E=.023 <br />.046 ..070 .093 .117 _.141 :172 .203 .234 .265 .277 290 .315 .341 <br />45°T=15 <br />.30 .44 .60 .76 .91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 2.21 <br />'.060 <br />` <br />:IE -'.030 <br />_.093 .119 _.153 .184 .216 .254 .289 .325 .351 .378 .411 .445 <br />50' T=.17 <br />'.34 .51 '.68 .85 1.02 1.19 1.36 1.54 1.72 1:91 2.10 2.29 2.48 <br />10' <br />E=.037 <br />.075 _.118 .151 .189 .227 .266 .305 .345 .384 .425 .467 .508 .550 <br />55° <br />"T=:19 <br />38 .57 .76 s95 1.14 1.32 1.52 1.72 1.92 2.14 2.35 2.56 2.77 <br />10' <br />E =:046 <br />' .093 .142 .138 .236 .283 :332 3.81 .420 .479 .530 .532 .841 .700 <br />60° <br />T=.21 <br />.42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 3.07 <br />20 <br />E_.056 <br />.112 :168 .225 .283 .340 .393 .457 .516 .575 .636 .697 .774 .851 <br />65' <br />T=.23' <br />.46 .69 .93 1.18 1:40 1.64 1.88 2.13 2.38 2.63 2.88 '13 3. 3.39 <br />30 <br />E=.067 <br />.135 .204 .273 :343 .412 .483 .554 .625 •.697 .711 .845 .922 1.01 <br />TABLE I. - Tangents and Externals to a 1° Curve. V <br />Chord =100 f t:. <br />Int. <br />Angle <br />Tangent, <br />External <br />Int. <br />'Angie <br />Tangent <br />External <br />Int. <br />, Angle <br />Tangent <br />External <br />644 <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 />131516 <br />10' <br />4658.6 <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 />1660.2 <br />40 <br />3626.8 <br />1051.4 <br />40. <br />4137.4 <br />1337.7 <br />40 <br />469512 <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 />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 />8732.? <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 />4804.8. <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 />4317:0 <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 />3316.4 <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 />130 <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 />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 />.68 <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 />:Z0 <br />5054.3 <br />1910.7 <br />69 <br />3937.9 <br />12224 <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 />1549.4 <br />10 <br />5054.0 <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 />4011.0 <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 />J <br />Curve'S° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° <br />4-0 <br />50' <br />55° <br />60° <br />65° <br />10° <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 />_2.38 <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 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 <br />.851 <br />650 <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°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 />E.288 <br />.383 <br />..480 <br />.578 <br />.878 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18- <br />1.29 <br />1.39 <br />800 <br />=.30 <br />.81 <br />91 <br />1,22 <br />1.53 <br />1.84 <br />2.15 <br />2.48 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.40 <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 />1.50 <br />1.62, <br />r 85o <br />T=.33 . <br />88 - <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.38 <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 />-.524 <br />.657 <br />.790 <br />.92611.06" <br />1.20 <br />1:34' <br />1.47 <br />Y.62 <br />1.76 <br />1'.91 <br />J <br />