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i <br />TABLE I. - Tangents and Externallio a 1' Curve. <br />Chord= 100 ft. ° <br />Int. <br />Angle <br />Tangent <br />External <br />Inc. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />423:5 <br />501 <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.G <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 />14 <br />2314.0 <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 />31M A <br />826.7 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />.G27.2 <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 />-3205.8 <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 <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 />- 30 <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 />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 />665.0 <br />50 <br />3296.9 <br />'850.8 <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 />2807.1 <br />677.3 <br />10 <br />3319.1 <br />•592.0 <br />20 <br />2451.8 <br />502.5 <br />20 <br />2377.5 <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 />636.7 <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.G <br />30 <br />252(.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 />043.1 <br />.50 ' <br />2541.0 <br />533.2 <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 />2501.0 <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 />3003.0 <br />739.7 <br />20 <br />3465.4 <br />966.a- <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />3476:3 <br />972.4 <br />1 40 <br />2591.0 <br />558.6 <br />40 <br />3025.2 <br />749.6 <br />40 <br />348S.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 />7G4.6 <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.S <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 <br />Curve 5° 10° 15° 20° <br />25° <br />301 <br />35° <br />40° <br />1.45- <br />50° 55' 60° 65° <br />-70° <br />40° <br />T=.13 .26 .40 .53 <br />-67, <br />.80 <br />.93 <br />.106 <br />1.20 <br />1.34 1.49 1.64 1:79 <br />1.94 <br />10' <br />E=.023 .046 .070 .093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 277 .290 .315 <br />.341 <br />45° <br />T=.15 .30 .44 .60 <br />.76 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 1.70 1.87 204 <br />2.21 <br />.30 <br />E=.030 .060 .093 .l 10 <br />.153 <br />.184 <br />.216 <br />.254 <br />.239 <br />325 .351 .378 .411 <br />.445 <br />'50° <br />T=.17 .34 .51 GB <br />.85 <br />1.02 <br />1.19 <br />1.36 <br />1.54 <br />1.72 1.91 2.10 2.29 <br />2.48 <br />50 <br />E =.037 .075 .116 .151 <br />.189 <br />.227 <br />.266 <br />.305 <br />.345 <br />.384 .425 .467 .508 <br />.550 <br />55° <br />T=.19 .38 .57 .76 <br />.95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 2.14 2.35 2.56 <br />2.77 <br />,65 <br />E=.046 .093 .142 .183 <br />.236 <br />.283 <br />.332 <br />3.81 <br />.420 <br />.479 .530 .582 .641 <br />X700 <br />60' <br />T=.21 .42 .63 84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.04 <br />2.17 2.38 2.60 2.83 <br />3.07 <br />20 <br />E-.056 .112 .168 225 <br />.233 <br />340 <br />.398 <br />.457 <br />.618 <br />.575 .636 .697 .774 <br />.851 <br />65' <br />T=.23 .46 69 93 <br />1.16 <br />1.40 <br />1.64 <br />-i-.!!72:.13 <br />30 <br />238 2.63 2.88 3.13 <br />3.39 <br />40 <br />E=.067 .135 204 273 <br />.343 <br />.412 <br />.483 <br />.55.625 <br />40 <br />.697 .711 .845 -.922 <br />1.01 <br />�.4 <br />Corrections 'to be Added (T = Tangent. . E =External.) <br />TABLE L - 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 <br />g <br />External <br />Int.Tangent <br />Angle <br />g <br />External <br />•64° <br />3580.3 <br />1026.6 <br />710 <br />4080.9 <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 />16G0.5 <br />.30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />16G9.2 <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 />1630.9 <br />.273 <br />'S <br />.412 <br />.483 <br />.554 <br />.625 .697 <br />.711 <br />.845 .922 <br />1.01 <br />,65 <br />3650.2 <br />1063.9 <br />72 <br />4162.8 <br />1352.6 <br />70 <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 />4793.0 <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 />426.5.6 <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 />1134.5 <br />50 <br />4304.6 <br />1430.8 <br />50 <br />4879.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 <br />4317.6, <br />1441.6 <br />S1 <br />4893.6 <br />1805.3 <br />10 <br />3SO4.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4905.0 <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 />3S2S.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 />.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 />4960.1 <br />1852.6 <br />08 <br />3804.7 <br />1181:6 <br />75 <br />4396.5 <br />1492.4 <br />82 <br />4960.7 <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 />1503.6 <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 />70 <br />447G.5 <br />15.11.4 <br />S3 <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 />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 />19.10.3 <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 />5123.9 <br />1060.2 <br />50 <br />3999.5 <br />1257.9 <br />50 <br />4514.0 <br />1583.1 <br />50 <br />5143.9 <br />1070.3 <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 />30 <br />5174.1 <br />1990.5 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4534.8 <br />1603.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4049.3 <br />1230.5 <br />30 <br />4593.5 <br />1617.] <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />12A3.6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />b0 <br />4074.4 <br />1300.9 <br />50 <br />4G2G.0 <br />1034.4 <br />50 <br />5234.9 <br />2031.4 <br />Int. <br />Curve 5° <br />W. 15° <br />20° <br />25° <br />30° 1 <br />35° <br />40° <br />45° 50° <br />55° <br />60° 1 65° <br />70° <br />Angle <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.516 2.575 17 <br />38 <br />2.697 60 2.774 83 <br />3.07 <br />60° <br />E=.056 <br />.112 .168 <br />.225 <br />283 <br />340 <br />.398 <br />.457 <br />? 636 <br />851 <br />T=.23 <br />.46 69 <br />.93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 2.38 <br />2.63 <br />2.88 3.13 <br />3.39 <br />65° <br />E=.067 <br />.135 .204 <br />.273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 .697 <br />.711 <br />.845 .922 <br />1.01 <br />T=.25 <br />.51 .76 <br />1.0'2 <br />1.28 <br />1.54 <br />1.80 <br />MG <br />2.33 2.60 <br />2.88 <br />3,16 3.44 <br />3.72 <br />70° <br />E=.080 <br />.159 .240 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 .819 <br />.906 <br />.994 1.08 <br />1.17 <br />T=.27 <br />.56 .83 <br />11.12 <br />1.40 <br />1.69 <br />1.93 <br />2.27 <br />2.57 2.87 <br />3.16 <br />3.47 3.78 <br />4.09 <br />75° <br />E =.095 <br />.182 .286 <br />.353 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 .977 <br />1.07 <br />1.18 1.29 <br />1.39 <br />T=.30 <br />.61 .91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 3.10 <br />3.44 <br />3.78 4.12 <br />4.46 <br />80° <br />E =.110 <br />.220 .332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1.02 1.13 <br />1.25 <br />138 1.50 <br />1.62 <br />SS* <br />8a <br />T=.33 <br />.66 1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <br />3.05 3.40 <br />3.77 <br />4.14 4.55 <br />T89 <br />E=.128 <br />.259 .391 <br />.524 <br />.657 <br />.790 <br />.926 <br />1.06 <br />1.20 134 <br />1.a7 <br />1.82 1.76 <br />].91 <br />