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i <br />TABLE I. - Tangents and Externals to a 1' Curve. <br />Chord =100 ft. <br />lilt. <br />Angle <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 />670 <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />IV <br />268I.9 <br />596.6 <br />1 101 <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.0 <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 />600.6 <br />40 <br />3154.2 <br />610.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2122.7 <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 />820.7 <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 />2703.7 <br />631.7 <br />30 <br />3208.8 <br />837.3 <br />40 <br />2353.8 <br />464.6 <br />40 <br />2773.0 <br />038.2 <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 <br />2373.3 <br />472.1 <br />52, <br />2794.5 <br />645.2 <br />69 • <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 />854.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />2402.0 <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 />863.4 <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 />3295.9 <br />880.8 <br />46 <br />2432.1 <br />494.8 <br />63. <br />2856.7 <br />672.7 <br />66 <br />3308.0 <br />886.4 <br />10 <br />2441.9 <br />498.710 <br />1148.0 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />20 <br />2151.8 <br />502.5 <br />1,20 <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 />008.8 <br />60 <br />2481.4 <br />514.3 <br />/ 50 <br />2908.9 <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />1852.6 <br />.68 <br />3864.7 <br />1181.6 <br />78 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />17 <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 />296t.5 <br />720.1 <br />40 <br />3420.1 <br />943.1 <br />50 <br />2.541.0 <br />538.2, <br />50 <br />2972.1 <br />725:0 <br />50 <br />3431.4 <br />948.9 <br />1920.5 <br />2551.0 <br />542.2 <br />65 <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 />960.5 <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 />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 />1286.5 <br />30G7.9 <br />7G9.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />.20 <br />30 <br />3073.7 <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 />z <br />�le <br />40- <br />45- <br />so. <br />0°45°50° <br />55° <br />60- <br />63. <br />Corrections to be Added (T =Tangent. E=External.) <br />Curve 5° 10° <br />I5° <br />20° 25° <br />30° 1 35° 1 40° 45° 50° 1 55° 1 60° 65° <br />70° <br />T-13 .28 <br />.40 <br />.53 .67 <br />.80 .93 .100 1.20 1.34 1.49 1.64 1.79 <br />1.94 <br />E�.023 .048 <br />.010 <br />.093 .117 <br />.141 .172 .203 '.234 .205 .277 .290 .315 <br />1 <br />.341 <br />T-.15 .30 <br />.44 <br />.60 .76 <br />.91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 <br />2.21 <br />-E-.030 -.060 <br />.093 <br />.119 .153 <br />,184 .216 .254 .289 .325 .351 .378 .411 <br />.445 <br />T =.17 .34 <br />.51 <br />.68 85 <br />1.02 1.19 1.36 ].54 1.72 1.91 2.10 2.29 <br />2.48 <br />R-,037 .075 <br />.115 <br />.151 .189 <br />.227 .266 .305 .345 .384 .425 AN .503 <br />.559 <br />T=.19 .38 <br />.57 <br />.76 .95 <br />1.14 1.32 1.52 1.72 1,92 2.14 2.35 2.56 <br />2..i <br />_E =.048 .093 <br />.142 <br />.188 .236 <br />.283 .332 3.81 .420 .479 .530 .592 .641 <br />.700 <br />.42 <br />.63 <br />.84 1.05 <br />1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 <br />3.07 <br />.112 <br />.168 <br />.225 .283 <br />.340 .393 .457 .516 .575 .G38 .697 .774 <br />.851 <br />L---OO=56.45 <br />.69 <br />.93 1.16 <br />1.40 1.64 1.88 2.13 2.38 2.63 2.88 3.13 <br />3.39 <br />.135 <br />.204 <br />.273 .343 <br />.412 .483 .554 .825 .897 .711 .$45 .922 <br />1.01 <br />TABLE I. - Tangents and Externals to a 1° Curve. V <br />Chord =100 ft. } <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />G4° <br />3580.3 <br />1026.6 <br />71° <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10': <br />4653.6 <br />1G51:7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.5 <br />30 <br />3615:1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30- <br />4081.3 <br />1669.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />1345.1 <br />50, <br />4709.2 <br />1686.9 <br />65 <br />3650.2 <br />]OG3.9 <br />72. <br />4162.8 <br />1352.G <br />79 <br />4723.2 <br />1695.8 <br />10 <br />36631.9 <br />1070.2 <br />10 <br />4175.43 <br />'1360.1. <br />10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4189.5 <br />1.367.G <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.0 <br />30 <br />4201.2 <br />1.375.2 <br />30 <br />4765.3 <br />1722.7 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4214.0 <br />1382.8 <br />40 <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226,8 <br />1390.4 <br />50 <br />4793.6 <br />1740.8 <br />66 <br />3720.9 <br />1102.2 <br />73 <br />4239.7 <br />1393.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3782.7 <br />1108.6 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />4822.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4265.6 <br />141$.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 />130 <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 />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 />3328.4 <br />1161.3 <br />30 <br />4356.9 <br />1.168.4 <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 />78 <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 />15500.5 <br />10 <br />4995.4 <br />1871.8 <br />20 <br />3880.0 <br />1195.2 <br />20. <br />4423.1 <br />1.508.6 <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 />189 1. 2 <br />40 <br />3913.4 <br />1208.0 <br />40 <br />4449.7 <br />1524.9 <br />40 <br />5039.5 <br />1000.9 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4463.1. <br />1533.1 <br />50 <br />5054.3 <br />1010.7 <br />69 <br />3937.9 <br />12227 <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 />320 <br />3962.6 <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 />15°.,3.1 <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.G <br />30 <br />4019.3 <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 />1525.7 <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 />Ink. <br />Curve 5° <br />10° <br />15° 20° <br />1 25° 30° <br />4D° <br />45° 50° <br />55° 60° 65° 76° <br />_4ngle <br />.35° <br />T=.21 <br />.42 <br />.63 <br />1.05 1.27 1.49 <br />1.71 <br />1.94 2.17 <br />2.38 2.60 2.83 3.07 <br />60' <br />E=.058 <br />.112 <br />.84 <br />.168 .225 <br />.283 .340 .393 <br />A57 <br />.516 .575 <br />.636 .697 ,774 •851 <br />T-.23 <br />.46 <br />69 .93 <br />1.16 1.40 1.04 <br />1.88 <br />2.13 2.38 <br />2.53 2.88 3.13 3.39 <br />66° <br />E-.067 <br />.135 <br />.204 .273 <br />.343 .412 '.483 <br />•554 <br />.625 .697 <br />.711 .845 .922 1.01 <br />70° <br />T-.25 <br />.51 <br />76 1.02 <br />1.28 1.54 1.60 <br />2.00 <br />2.33 2.60 <br />2.88 3.18 3.44 3.72 <br />E-.080 <br />.159 <br />.240 .321 <br />.403 .485 .508 <br />.652 <br />.735 .819 <br />.900 .994 1.08 .1..17 <br />TS° <br />T=.27 <br />.68 <br />.83 1.1'2 <br />1.40 1.09 1.98 <br />2.27 <br />2.57 2.87 <br />8.15 3.47 3.78 4.09 <br />_ <br />E =.095 <br />.182 <br />286 .383 <br />.480 .578 .678 <br />.777 <br />.877 .977 <br />1.07 1.18 1.29 1.89 <br />60° <br />91 1.22 <br />1.53 1.84 2.15 <br />2.48 <br />2.78 3.10 <br />3.44 3.78 4.12 4.45 <br />E=.110 <br />:6 <br />.220 <br />.332 .445 <br />.658 .071 .787 <br />.903 <br />1,p2 11.13 <br />11.25 1.38 1.50 1.62 <br />85° <br />T =.33 <br />86 <br />1.00 1.33 <br />1.68 2.02 2.36 2.70 <br />8.05 3.40 <br />3.77 4.14 4.55 4.89 <br />E =.128 <br />259 .391 .524 <br />.857 .790 .920 I. <br />].20 1 :34 <br />1.4 <br />LL 82 1.76 1.91 <br />