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IV TAs1 E'I. _ Tangents and Externals to,a PCurve. <br />Chord =100. ft. <br />Angie <br />Tangent <br />External <br />Angle <br />Tangent <br />External. <br />Angle, <br />Tangent <br />External <br />430 <br />2257.0• <br />428.5 <br />50° <br />2671.8 <br />592.3' <br />-57° <br />3110.9 <br />790.1 <br />40' <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 />30 <br />3208.8 <br />'837.3 <br />40 <br />2353.8 <br />.404.6. <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 />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 />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 />48 • <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 />i <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 />749.640 <br />40 <br />3488.3 <br />978.3 <br />60- <br />2601.1 <br />562.8 <br />50 <br />'30 35.8 <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.) <br />Int.. <br />Angle <br />Curve 5° <br />10°' 15° 20° 1 25° 30° 35° 40° 1 45° 50° 55° 1 <br />60° 1 65° 70° <br />40° <br />T=.13 <br />.20.40 .53 .87 .80 .93 .106 1.20 1.34 1.49 <br />1.64 1.79 1.94 <br />External <br />E=.023 <br />.046 .070 .093 .117 .141 :172 .203 .234 .265 .277 <br />.290 .315 .341 <br />45° <br />T=.15 <br />.30 .44 .60.76 .91 1.06 1.21 1.37. 1.52 1.70 <br />1.87 2.04 2.21 <br />4639.8 <br />E=.030 <br />..060 .093 .119 .153 .184 -.216 .254 .289 .325 .351 <br />.378 .411 .44E <br />50° <br />T=.17 <br />.34 .51 .68 .85 1.02 1 IT 1.36 1.64 172 <br />2.10 2.29 2.48 <br />10', <br />E =.037 <br />.075 .116 .151 .189 .227 .266 .305 .345 .384 <br />.467 .508 .550 <br />55o <br />T=.19 <br />.38 .57 .76 .95 1.14 1.32 1.52 1.72 1.92 <br />2.35 2.56 2.77 <br />1322.9 <br />E=.046 <br />.093 .142 .188 .236 .283 .332 3.81 .420 .479 <br />.582 .641 .700 <br />60° <br />T=.21 <br />.42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 r2.38 <br />2.60 2.83 3.07 <br />4124.8- <br />E =.056 <br />.112 .168 .225 .283 .340 .398 .457 .516 .575 <br />.697 .774 .851 <br />Gro <br />T=.23 <br />.46 69 93 1.16 1.40 1.64 1.88 2.13 2.38,2.88 <br />3.13 3.39 <br />40 <br />E =.067 <br />.135 .204 .273 .343 .412 .483 .554 .625 .697 <br />.845 .922 1.01 <br />TABLE L = Tangents and Externals to a 1' Curve. <br />Chord =100 ft. <br />Int. <br />Angle .. <br />Tan Tangent <br />g - . <br />External <br />Int. <br />Angle <br />Tan ent_ <br />g <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />840 <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 />'8 <br />1045.2 <br />30 <br />4124.8- <br />.1330.3 <br />. <br />30 <br />4681.3 <br />1669.2 <br />40 <br />3626 <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 />. <br />50 <br />4709.2 <br />1686.9 <br />65 <br />3650:2 <br />3063.9 <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 />_ <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 />S <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 />+1141.4 <br />„ 50 , <br />;4304.6 <br />1436.8 <br />50 . <br />4879.2 <br />1796.0 <br />67, .r <br />3792.4 <br />'74 <br />14317.6 <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 />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 <br />.40 <br />4951.5 <br />1843.1 <br />50 <br />385,2:6 <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 />3876.5 <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 />8937.9 <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 />45084.0 <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 />4544.0 <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 />1990.8 <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 />12S6.5 <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 />Ingle <br />Curve 5° <br />10° 15° 20° 1 25° 1 30° 35° 1 40° 1 45° 1 500 55° 1 60° 1 65° 700 <br />60o <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 />E=.058 <br />.112 .168 .225 .283 .340 .398 .457 .518 .575 .636 ..697 .774 .85 <br />65- <br />'T=.23 <br />.48 .69 .93 1.16 1.40 1.64 1.88 2.13 2.38 2.63 2.88 3.13 3.39 <br />E=.06T <br />135 .204 .273 .343 .412 .483 .554 .625 .697 .711 .845 .922 1.01 <br />700 <br />T=.25.51 <br />.76 1.02 1.28 1.54 1.80 2.06 2.33 2.60 2.88 3.16 3.44' 3.72 <br />E=.080 <br />.159 .240 .321 .403 .485 .568 .652 .735 .819 .906 .994 1.08 1.17 <br />750 <br />T=.27 <br />.56 .83 1.12 1.40 1.69 1.98 2.27 2.57 2.87 3.18 3.47 3.78 4.09 <br />E =.095• <br />.182 .286 .383 .480 .578 .678 .777 .877 .977 1.07 1.18#4.55 <br />Soo <br />T=.30 <br />61 .91 1.22 1.53 1.84 2.15 2.46 2.78 3.10 3.44 3.78 <br />E=.110 <br />.220 .332 .445 .558 .671 .787 .903 1.02 1.13 1.25 1.38 <br />r4.8 <br />gro <br />T=.33 <br />66 1.00 1.33 1.68 2.02 2.36 2.70 3.05 3.40 3.77 4.14E=.128 <br />.259 .391 .524 .657 .79 .92 1.06 1.20 1.34 147 182 <br />