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IV TABLE 1. Tangents and Externals to a V Curve. <br />Chord =.100 ft. <br />Angle <br />Tangent <br />External <br />In <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />43° <br />2257.0" <br />428.5 <br />50° <br />2671.5 <br />592.3 <br />57° <br />8110.0 <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 />3197.5 <br />832.0 <br />30 <br />2344.1 <br />461.030 <br />51 <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 />2773.9 <br />636.2 <br />40 <br />3219.7 <br />842.7 <br />50 <br />2363.5 <br />466.4 <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 />2504.9 <br />649.7 <br />10 <br />3252.7 <br />858.0 <br />20 <br />2392.8 <br />479.6 <br />• 20 <br />281.5.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />2402.6 <br />483.4 <br />30 <br />282.5.6 <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 />2422.3 <br />491.0 <br />50 <br />2846.3 <br />668.0 <br />50 <br />3296.9 <br />880.5 <br />48 <br />2432.1 <br />494.8 <br />53 <br />2356.7 <br />672.7 <br />60 <br />3308.0 <br />836.4 <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 />2877.5 <br />682.0 <br />20 <br />3330.3 <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2388.0 <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 />903.8 <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 />1518.2 <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 />9'25.9 <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 />3405.8 <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 />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 />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 />34G5.4 <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 />55S.6 <br />40 <br />3025.2 <br />749.6 <br />40 <br />3488.3 <br />•978.3 <br />50 <br />2601.1 <br />562.5 <br />50 <br />3035.8 <br />754.6 <br />50 <br />3499.7 <br />,984.3 <br />49 <br />2611.2 <br />566.0 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <br />30 <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 />3075.7 <br />774.7 <br />30 <br />3545.6 <br />1003.3 <br />40 <br />2651.5 <br />' 533.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661.6 <br />558.0 <br />50 <br />3100.2 <br />7S4.9 <br />50 <br />3565.7 <br />1020.5 <br />Corrections to be Added '(T =Tangent. E=External.) <br />Int. <br />Cunt 5° <br />10° <br />15° <br />20° 1 <br />25° <br />300 <br />35° <br />40° <br />45° <br />50° <br />55° <br />1 60° <br />65` <br />70° <br />Angle <br />4639.8 <br />1643.0 <br />101 <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />i0' <br />4653.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />40° <br />T=.13 <br />.26 <br />.40 <br />53 <br />.67 <br />.80 <br />.93 <br />.106 <br />MO <br />1.34 <br />1.49 <br />1.G4 <br />1.79 <br />1.94 <br />40 <br />E=.023 <br />.046 <br />X70 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 <br />.277 <br />290 <br />.315 <br />.341 <br />45° <br />T=.15 <br />.30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 <br />2.21 <br />10 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.215 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />.445 <br />50° <br />T=.17 <br />.34 <br />51 <br />.68 <br />.85 <br />1.02 <br />1.19 <br />1.36 <br />1.54 <br />1.72 <br />1.91 <br />2.10 <br />2.29 <br />2.48 <br />40 <br />E =.037 <br />675 <br />.116 <br />.151 <br />.189 <br />.227 <br />.266 <br />.305 <br />.345 <br />.384 <br />.425 <br />.467 <br />.508 <br />.550 <br />55° <br />T=.19 <br />.38 <br />.57 <br />.76 <br />95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 <br />MG <br />2.77 <br />20 <br />E=.040" <br />.093 <br />.142 <br />.188 <br />236 <br />.283 <br />.332 <br />3.81 <br />.420 <br />.479 <br />.530 <br />.582 <br />.641 <br />.700 <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 />50 <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 />.551 <br />65° <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 />20 <br />E =.067 <br />.135 <br />204 <br />273 <br />.343 <br />.412 <br />.483 .554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />i <br />TABLE I. - Tangents and Externals to a 10 Curve. V <br />Chord =100 ft: <br />Int. <br />Angle <br />Tangent <br />Externa] <br />Int' <br />Angle <br />Tangent <br />g <br />Externa] <br />Int. <br />Angle <br />Tangent <br />g <br />External <br />64° <br />35S0.3 <br />1026.6 <br />71° <br />40S6.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />101 <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />i0' <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 />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <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 />1063.9 <br />72. <br />4162.5 <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 />4138.5 <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 />1005.7 <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 />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 />48614.8 <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 />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 />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1454.4 <br />50 <br />4966.1 <br />18.52.6 <br />68 <br />3864.7 <br />1151.6 <br />75 <br />4300.5 <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 />151G.7 <br />30 <br />5024.8 <br />1891.2 <br />40 <br />3913.4 <br />120S.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 />76 <br />447G.5 <br />1541.4 <br />S3 <br />5069.2 <br />1920:5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />44S9.9 <br />1549.7 <br />10 <br />5084.0 <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 />1.574.7 <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 />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.0 <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 />4584.5 <br />1608.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4040.3 <br />1256.5 <br />SO <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 />10° 15° <br />20° <br />25° <br />30° 35° <br />40° <br />45° <br />50° <br />55° <br />601 <br />65° 70° <br />AngletE--OBO <br />60- <br />60° <br />168 <br />105 <br />1.27 1.49 <br />1.71 <br />94 <br />1 <br />2.575 .17 <br />2.38 <br />2.697 <br />2.33 3.07-- <br />112 <br />.225 <br />283 <br />.340 .398 <br />.457 <br />516 <br />636 <br />.774 <br />65° <br />.46 .60 <br />.93 <br />1.16 <br />1.40 1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.G3 <br />2.68 <br />3.13 3.39 <br />.135 .204 <br />273 <br />.343 <br />.412 .483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 1.01 <br />70° <br />.51 .76 <br />1.02 <br />1.28 <br />1.54 LSO <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />3.16 <br />3.44 3.72 <br />.159 .240 <br />.321 <br />.403 <br />AS5 .568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.994 <br />1.08 1.17 <br />75° T=.27 <br />.56 .33 <br />1.12 <br />1.40 <br />1.69 1.98 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 4.09 <br />E=.095 <br />.182 .286 <br />.383 <br />.480 <br />.578 .678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 1.39 <br />80° T=.30- <br />.61 .91 <br />1.22 <br />1.53 <br />1.84 2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 4.46 <br />E=.110 <br />.220 .332 <br />.445 <br />.558 <br />.671 .787 <br />.903 <br />1.02 <br />1.13 <br />1.25 <br />1.38 <br />1.50 1.62 <br />85° T=.33 <br />.66 1.00 <br />1.33 <br />1.G8 <br />2.02 2.36 <br />2.70 <br />M. <br />3.40 <br />3.77 <br />4.14 <br />11.62 <br />4.55 4.89 <br />E=.128 <br />.259 .391 <br />.524 <br />.G57 <br />.790 .926 <br />1.06 <br />11.20 <br />1.34 <br />11.47 <br />1.76 1.91 <br />