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I-V TABLE I. Tangents and Externals,to,a V Curve. <br />Chord =100. ft. <br />t. <br />Angle <br />Tangent <br />External <br />Int <br />Angle_ <br />Tangent External <br />Angje- <br />Tangent <br />External <br />439-, <br />2277._0' <br />428.5 <br />.50° <br />2671.8. <br />592.3' <br />57° <br />3110.9 <br />790.1 <br />:. 10', <br />'2266:6 <br />432.0 <br />101' <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 />2G92.1. <br />600.9,; <br />_ , 20 ' <br />3132:6 <br />800.4 <br />30 <br />'2285.9 <br />439.2: <br />{442.8. <br />30 <br />2702:3' <br />'605.3; <br />`30 <br />3143.4 <br />805.6 <br />40 <br />'2295:6' <br />T=.15 ' <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 />810.1 <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 />: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 />27947.5 <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 />2315.2; <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 />3.07 <br />3274.8 <br />869.8 <br />40 . <br />:2412.4 <br />''487.2 <br />40 <br />2S35:9' <br />663.4 <br />.30 <br />40 <br />3285.81 <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 />46. <br />2432.1' <br />494:8 <br />53 <br />2856.7. <br />672.7 <br />60 <br />3308.0 <br />880.4 <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 />42451:8 <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 />2908.0; <br />696.1. <br />'+: 50 <br />X3363.8` <br />'014.5 <br />47 <br />,2491.3. <br />518.2 <br />54 <br />2919.41 <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 />734.5. <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 6" <br />.40.3488.3; <br />-40 <br />978.3 <br />50 <br />2601.2 <br />502.8� <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 />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 />'553.8 <br />•40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661:6, <br />588:0"50 <br />1300.9 <br />3100.2 <br />784.9' <br />" 50 <br />3568.7 <br />1020.5 <br />CorrectionsAo.`be Added (T Tangent. E.=External.), <br />Int.Curve <br />Angle <br />5° <br />- <br />10° <br />15° <br />20° <br />25° <br />30° <br />-35° <br />40° <br />45° <br />.50° <br />55°. <br />.60°. <br />65° <br />70° <br />40° <br />E.046 <br />.164310 <br />10' <br />.53 <br />7 <br />10" <br />03 <br />.1315.6 <br />10' <br />1.265 .34 <br />1.277 <br />1290 <br />1.79 <br />.94 <br />1.341 <br />•• ',20' <br />4112:1 <br />1322.9 <br />.070 <br />:093 <br />.117 <br />.8414 <br />.172_ <br />:20311.234 <br />30 <br />4124:8 <br />:1330.3 <br />30 <br />.315 <br />1660.2 <br />45° <br />T=.15 ' <br />..30 <br />.44- <br />; .60 <br />.76 <br />".91 <br />1.06 <br />1.21 <br />'.254 <br />1.37 <br />1.52 <br />1.70 <br />1.87. <br />2.04 <br />- <br />50 <br />E=.030 <br />••,.060 <br />..093 <br />.119 <br />.153 <br />.184 <br />.216 <br />1352.6 <br />.289 <br />.325 <br />.351 <br />:378 <br />..411 <br />:445 <br />.445 <br />509 ?- <br />T=.17 " <br />" .34 <br />.51 <br />.68 <br />.85:1.02 <br />20 <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 />':30. <br />E-.037 <br />.075 <br />.116 <br />.151 <br />.189 <br />.227 <br />.266 <br />1305 <br />.3.45 <br />.334 <br />.425 <br />.467 <br />.503 <br />.550 <br />559 <br />T-.19 : <br />38' <br />".093 <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 />2.56 <br />2.77 <br />73 <br />E=.046 <br />1398:0 <br />.142 <br />.188 <br />.236 <br />.283 <br />.332 <br />3.81 <br />.420 <br />.479 <br />.530'.582 <br />10 <br />.641 <br />.700 <br />60° <br />tT=.21 <br />.42 <br />63 ' <br />'.84 <br />1.05 <br />127 <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 />30 <br />E=.056 <br />112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.638 <br />.697 <br />.774 <br />.851 <br />65° <br />TT -.2346 <br />1436.8 <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 />3.30 <br />'10• <br />t E-.067 <br />.135 <br />.204 ..273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />TkBLE••I. _ Tangents and -Externals to a 1° Curve. <br />Chord =100 ft. <br />V <br />Int 'V <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Int.- <br />Angle <br />Tangent <br />External <br />64' <br />3550.3 <br />1026:6. <br />71° <br />40S6.9 <br />)1303:2 <br />78°• ."4639.8 <br />._ <br />.164310 <br />10' <br />3591.0 <br />.1032.8 <br />10" <br />4099:5 <br />.1315.6 <br />10' <br />4653.6 <br />1651.7 <br />-20 <br />3G03.5 <br />' 10390 <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 />1660.2 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />413714" <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 />i 72 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1695:$ <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 />4793.6 <br />:1740.8 <br />66- " <br />3720:9 <br />1102.2 <br />73 <br />423957 <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 />-'403768.5 <br />1.22 <br />1.53 <br />40 <br />'4291:5 <br />:1429.0 <br />40 <br />4864.8 <br />1786.7 <br />60 . <br />3780,4 <br />.1128.2 <br />'1134.8 <br />`50'' <br />4304.6 <br />1436.8 <br />50' <br />4879.2 <br />- 1796.0 <br />167 <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 />380414 <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 />"1484.4 <br />50 <br />4966.1 <br />1852.6 <br />.68 <br />3864.7 <br />11 IA" <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 />1:500.5 <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 />11202.0 <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 />F69 i`• <br />3937.9 <br />122217 <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 />20• <br />3962.5 <br />' 1236.7 <br />.20 <br />4503::4 <br />.1558.0 <br />20 <br />5099.0 <br />1940.3 <br />1130 <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 />11250.8 <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 />i 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 />;1591.6 <br />' 84 - <br />5159.0 <br />1980-'4 <br />10 <br />1272.1 <br />10 <br />4571.2 <br />:1600.1 <br />10 <br />5174.1 <br />1990.5 <br />.20, <br />.4024.4 <br />+1279.3 <br />'.'20 <br />4584.8 <br />1608.6 <br />20 <br />5189:3 <br />2000.6 <br />30 <br />.'4036.8 <br />"4049:3 <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 />'1625.7 <br />'• 40• <br />15219.7 <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 />Ciave.5° <br />10° <br />20° <br />25° <br />30° <br />35° <br />40°_ <br />45° <br />50° <br />55° <br />60°- <br />65° <br />70° . <br />Angle" <br />._ <br />:, _ <br />.. <br />T-•21 <br />.42 <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 />60° <br />E=.056 <br />:112 <br />.225 <br />..283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.638 <br />.697 <br />.774" <br />;851 <br />.16 <br />1.412 <br />1.483 <br />1.554 .88 <br />2.625 .13 <br />38 <br />? <br />2;63 <br />88 <br />Z <br />3.922 <br />65° - <br />r=-.067.-.135 <br />[.883 <br />.273 <br />1.343 <br />697 <br />:711 <br />845 <br />1.01 " <br />T=.25. <br />.511.02 <br />1.28 <br />1.54 <br />1:80 <br />2.06 <br />2.33 <br />2:60. <br />2:88 <br />3.16 <br />3.44 <br />3:72 <br />7U'. <br />E=.080 <br />' .159 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.9941.08 <br />1.17. <br />T =.27 <br />.561.1'2 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />75 <br />E=.095 <br />.182 <br />.383 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 <br />.9771.07 <br />1:18 <br />1.29 <br />1.39 <br />=•30 <br />61 <br />.91 <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 <br />4:46 <br />80°. <br />E=:110 <br />220 <br />.332 <br />.445 <br />.558' <br />.671 <br />'.787 <br />.903 <br />1.02 <br />1.13 <br />1.25 <br />1.38" <br />1.50 <br />1.62 <br />T=.33 <br />66 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2:36 <br />2.70 <br />3.05 <br />3.40. <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />85' <br />E =.128 <br />259 <br />..391 <br />.524 <br />.657 <br />.790 <br />.926 <br />1.06 <br />1.20 <br />1.34 <br />1.47 <br />1:62 <br />1,78 <br />1.91 <br />