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IV TA13LE I.'.= Tangents and Externals tb-a-119 Curve. <br />Chord,=100- ft: <br />ngle <br />Angle. <br />Tangent <br />External <br />,Angle' <br />'Tangent <br />Eate;nalAInng.e <br />: <br />Tangent <br />External <br />43° <br />2257.0 <br />428.5 <br />50° , <br />2671.8 <br />592.3 <br />57° <br />31.10.9 <br />790.1 <br />10'-2266.1 <br />1.87 2.04 2,21 <br />432.0 <br />.10'. <br />2G81.9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />.120 <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 />3105.1 <br />816.1 <br />.697 .711 <br />2314.9 <br />450:0 <br />51 <br />2732.9 <br />613.4 <br />5S <br />3176.0 <br />821.4 <br />SO <br />2324:6' <br />-,453.6 <br />..10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />626.7 <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 />i- .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 />27n3"D <br />636.2 <br />40 <br />3219.7 <br />642.7 <br />1. ,-602363.5 <br />3709.0 <br />468,4. <br />50 <br />2784,2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />X46`- <br />10 <br />2373"3 <br />2383.1 <br />472.1 <br />475.8 <br />b2 <br />2794.5 <br />645.2 <br />" <br />59,. <br />3241.7 <br />853.5 <br />20- <br />2392.8 <br />479.6 <br />10 <br />20 <br />2804.'3 <br />2815:2 <br />649.7 <br />654.3 <br />10 <br />20 <br />3252.7 <br />3263.7 <br />858.9 <br />864.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2825.6 <br />655.8 <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 />2622:3 <br />491.0 <br />.50 <br />2846.3 <br />668.0 <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 />2367.1 <br />677.3 <br />.10 <br />3319.1 <br />892.0 <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 />2.161.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <br />30 <br />3311.4 <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 />2-181.4 <br />514.3 <br />50 <br />29.08 .9 <br />666.1 <br />50. <br />3363"8 <br />914.5 <br />47: <br />2491.3 <br />518.2 <br />54 <br />2019.4 <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 />1871.8 <br />30 <br />2521.1 <br />530.1 <br />30 <br />2951.0 <br />715:3 <br />1. 30. <br />3408.S <br />.931.6 <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 />60 <br />2541;0 <br />538.2 <br />50 <br />2972.1' <br />725.0 <br />50 <br />3431.4 <br />945.9 <br />48 <br />2551;0 <br />542.2 <br />55 <br />2082.7 <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 />900.6 <br />20 <br />2571:0 <br />550.4 <br />20 <br />3003:9 <br />739.7 <br />I .. 20 <br />3465.4 <br />DGM <br />30 <br />2581.0 <br />554.5 <br />30 <br />. 3014.5 <br />744.6 <br />80. <br />3476.8 <br />972.4 <br />40 <br />2591:0 <br />555.6 <br />'40 <br />3025.2 <br />749.6 <br />40 <br />3488.3 <br />D7S.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 1 <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 />3D57.2 <br />764.6 <br />10 <br />3522.0 <br />990.2 <br />202131.3 <br />4024.4 <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 />3;x45-0 <br />1008.3 <br />40 <br />2651.E <br />583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1.014.4 <br />50 1 <br />2661.6 <br />588.0 <br />59 <br />3100-2 1 <br />784.9 <br />:- 50. <br />3563.7 <br />1020.5 <br />Corrections to be Added- (T = Tangent. - E = External.) <br />Angle Curve 5° <br />10° 15°; 20° 25°' <br />30° 3a • 40° `45° <br />50°• 55° <br />60° 651 70° <br />740° T =.13 <br />=26.40 .53 :07 <br />.80 .93 106 1.20 <br />1.34 1.49, <br />1.64 1'.79 1.94 <br />E-.023 <br />.046 .070 .093 .117 <br />.141 .172 .303 .234 <br />.265 .277 <br />290 .315 .341 <br />d5°' T-.15 <br />AD ..44 .60 •.76 <br />.91 1.06 1.21 1.37 <br />1.52 1.70 <br />1.87 2.04 2,21 <br />E=.0'30 <br />.060 .093 .119 .153 <br />'.134 .21fi 254 .289 <br />.325 .351 <br />:.378 .411 .445 <br />50° T=•17 <br />.34 :51' .58 .85 <br />1.02. 1.19' 1-06 1.54 <br />1.72 1.91 <br />2.10 2.29 2.48 <br />E =.037 <br />.075 .116 .151 .189 <br />_227 .266 .305 .345 <br />.384 .425 <br />.467 .508 .550 <br />55° T-.19 <br />.38 .57 .76 .95 <br />1.14 132 L52 1.72 <br />1.92 2.14 <br />2.35 2..56 2.77 <br />E=•046 <br />.003 .142 :188 .236 <br />.283 332 3.81 .420 <br />.479 .530 <br />.582 .641 .700 <br />60. T=.21 <br />.42 .63 .84 1.05 <br />1.27 1.49 1.71. 1.94 <br />2:17 2.38 <br />2.60 2.83 3.07 <br />Ev.056 <br />_.112 .168 .225 ..283 <br />.340 308 .457 .516 <br />.575 .636 <br />.697 .774 .651 <br />6s° T-.23 <br />.46 69 03 1.16 <br />1.40 1.64 1.88' 2.13 <br />2.38 2.63 <br />2.88 3.13 3.39 <br />E -.067 <br />.135 :204 .273 .343 <br />'.412 A83 .554 .625 <br />.697 .711 <br />.845 .922 1.01 <br />io <br />TABLE I, - Tangents and Externals to a P Curve <br />Chord =.100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int.Int. <br />.�ngpe <br />Tangent <br />ExternalAng1e <br />30° <br />Tangent <br />External <br />641 <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 />1.0' <br />4653.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.4 <br />1322.0 <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 />4631.3 <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 />13.15.1 <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 />70 <br />4723.2 <br />1695.S <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 />1076-0 <br />20 <br />&.188.5 <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 />1300.4 <br />6.0 <br />4793.6 <br />1710.8 <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 />4265.0 <br />1413.5 <br />20 <br />4336.2 <br />1765.2 <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 />50 <br />4304.6 <br />1436.8 <br />50 <br />4879.2 <br />1796.0 <br />07. <br />3792.4 <br />1141.4 <br />74 <br />4317-6 <br />1444:6 <br />81 <br />4893.6 <br />1805.3 <br />16 <br />3504.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />3$16.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />4922.5 <br />1824.1 <br />• <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4350.9 <br />1468.4 <br />30 <br />.4937.0 <br />1833.6 <br />46 <br />.3540,5 <br />'1168.1 <br />40 <br />4370.1 <br />1476.4 <br />40 <br />4951.5 <br />1843.1 <br />50 <br />-3852.6 <br />1174.8 <br />.50 <br />4383.3 <br />1484.4 <br />50 <br />4966.1 <br />1852.0 <br />68 <br />3864,7 <br />1181.6 <br />75 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4995.4 <br />1871.8 <br />20 <br />3889:0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />1881.5 <br />30 <br />3901.2 <br />1202.0 <br />80 <br />4436.4 <br />1516.7 <br />30. <br />5024:8 <br />1891.2 <br />140 <br />3913.4 <br />1208.9 <br />40 <br />4449.7 <br />1524.9 <br />40 <br />5039.5 <br />1900.9 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />1910.7 <br />09 <br />3937.9 <br />1222.7 <br />76 <br />4476.5 <br />1541.4 <br />81 <br />5069.2 <br />1920.5 <br />'10 <br />3950.2 <br />1229.7 <br />10 <br />4189.9 <br />1549.7 <br />10. <br />5084.0 <br />1930.4 <br />20 <br />3962.5 <br />123G.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30: <br />5113.9 <br />1950.3 <br />40 <br />3987.2 <br />1250.$ <br />140 <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 />1593.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1265.0. <br />77 <br />4557:6 <br />1x91.0 <br />84 <br />5159.0 <br />1980.4 <br />1.0 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />. 10 <br />5174.1 <br />190015 <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 />4595.5 <br />1617.1 <br />30 <br />5204.4 <br />2D10.8 <br />40 <br />4061.8 <br />1293.0 <br />40 <br />4612.2 <br />1625-7 <br />40 <br />5219,7 <br />2021.1 <br />59 <br />4074.4 <br />1360.9 <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 />A <br />5°' <br />10° <br />15° <br />20° <br />2� <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />-60° <br />65° 70° <br />n"It- <br />60° <br />1 <br />2 <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 />2.63 3.07" <br />58 <br />.112 <br />.168 <br />.22 <br />.263 <br />.3ID <br />.398 <br />.457 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 .851 <br />Y ; '3 <br />65. <br />E=.2 <br />'.46 <br />69 <br />93 <br />1.10 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.36 <br />2.63 <br />2.88 <br />'.845 <br />3-13 3.39 <br />67 <br />,135 <br />.201 <br />.273 <br />.343 <br />,.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />-022 1.01 <br />70° <br />5 <br />.51 <br />.75 <br />1-02 <br />1.28 <br />1.54 <br />1.60 <br />2.06 <br />2.33 <br />2.60 <br />2.38 <br />3.16 <br />3.44 3-72 <br />80 <br />'.159 <br />.240 <br />:321 <br />.403 <br />.485 <br />.563 <br />:652 <br />.735 <br />.819 <br />.906 <br />.994 <br />1.08 1.17 <br />75° <br />112 <br />1.480 <br />1.578 <br />1.688 <br />2.777 <br />u.877 <br />2.977 <br />E=.005 <br />.182 <br />.?8G <br />.353 <br />1.07 <br />ITIS <br />1.29 1.30 <br />EO° <br />T=-30 <br />.61 <br />.9[ <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 4.40 <br />E=.110 <br />.220 <br />.332 <br />.445 <br />.558 <br />.071 <br />.787 <br />AM <br />1-02 <br />1.13 <br />.1.'25 <br />1.38 <br />180 1.62. <br />85° <br />T=.33 <br />.66 <br />1.00 <br />1.23 <br />1.6$ <br />2.02 <br />2.36 <br />2.70 <br />305 <br />3.40 <br />3.77 <br />4.14 <br />14.55 4.89 <br />E =.I28 <br />.259 <br />.301 <br />.524 <br />.651 <br />.700 <br />.926 <br />1.06 <br />1.20 <br />1.34 <br />1.47 <br />1.62 <br />11.76 1.91 <br />A <br />