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II TABLE I. - Tangents and Externals. to a V Curve. <br />Chord= 100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Iul: <br />Angle <br />Tangent <br />External, <br />1° <br />50.00 <br />1-22 <br />8°, - <br />400. GG. <br />13.99 <br />15" <br />754.32 <br />49.44_' <br />10' <br />53.34 <br />30` <br />10' <br />409.03 <br />14,58 <br />10' <br />762.80 <br />50.55_ <br />20 <br />65.67 <br />.29 <br />20 <br />417.41 <br />15,18 <br />20 <br />771,29 <br />51.68 <br />30' <br />75.01 <br />.49'- <br />30 <br />,425:79-- <br />15,80 <br />`30. <br />779.77 <br />52.52 <br />40 <br />83.34 <br />G1 <br />40 <br />434.17 <br />16.43 <br />40 <br />788:26 <br />53.97 <br />50 <br />91.68 <br />.73 <br />50 <br />442.55 <br />17.07 <br />60 <br />796.75 <br />55.1:1 <br />2 <br />100.01 <br />,87 <br />0 <br />'450.93 <br />37.72 <br />16 <br />805.25 <br />56.31 <br />10' <br />108.35.. <br />1.02 <br />10 <br />-459.32 <br />,18.38 <br />-10- <br />813.75. <br />67.50 <br />20 <br />116.68 <br />.1.19 <br />20 <br />467.71 <br />19.06 <br />20 <br />822.25 <br />58.70 <br />00 <br />125.02 <br />1.36 <br />30 <br />476.10 <br />19.75' <br />30 <br />830.76 <br />59.91 <br />40 <br />133,86 <br />1.55 <br />40 <br />484.49 <br />20.45 <br />40 <br />839.27 <br />61.14 <br />'50 <br />141.70. <br />1.75 <br />50 <br />.492.88 <br />21.16 <br />50 <br />' 847:78, <br />62,38 <br />3'. <br />150.04 <br />1.96. <br />10 <br />501.28 <br />21.89 <br />17 - <br />856.30 <br />63.63 <br />10. <br />.158.38 <br />2.19• <br />10 <br />509.68 <br />22.62 <br />•10 <br />864.82 <br />64.90 <br />20 <br />1(36.72 <br />2.43 <br />20 <br />518.08 <br />23,38 <br />20 <br />873.35 <br />66.18 <br />30 <br />175.)G <br />2.07 <br />30 <br />526.48 <br />•24.14 <br />30' <br />881.88 <br />67.47 <br />40 <br />183.40 <br />2.93 <br />40 <br />534.89 <br />24.01 <br />40 <br />890.41 <br />68.77 <br />50 <br />191.74 <br />3.21 <br />50 <br />543.29 <br />25.70 <br />50 <br />898.95 <br />70.09 <br />4 <br />200.08 <br />`, 3.49 <br />11 <br />551.70 <br />.26.50- <br />18, <br />907.49 <br />7L.42 <br />10 <br />208.43 <br />"6.791 <br />10 <br />560.11 <br />27.31 <br />10 <br />916.03 <br />72,76 <br />•20 <br />216.77 <br />4.10' <br />20 <br />568.53 <br />28.14 <br />20 <br />924.58 <br />74.12 <br />30 <br />225.12 <br />4.42 <br />30 <br />576.95 <br />28.97 <br />30 <br />933.13 <br />75.49 <br />40 <br />233.47 <br />4.76 <br />40 <br />-585.30 <br />29.82 <br />40 <br />941.69 <br />70.86 <br />50 <br />241.81 <br />5.10 <br />50 <br />593.79 <br />30.68 <br />50 <br />950.25 <br />78.26 <br />5 <br />250.16 <br />5.46 <br />12 <br />602.21 <br />31.56 <br />10 ' <br />958.81 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10 <br />G10.64 <br />32.45 <br />10 <br />967.38 <br />81.09 <br />20 <br />266.86 <br />6.21 <br />20 <br />619.07 <br />33.35 <br />20 <br />975.96 <br />82.53 <br />30 <br />275.21 <br />6.61 <br />30 <br />627.50 <br />34.26- <br />30 <br />954.53 <br />83.97 <br />40 <br />233.57 <br />17.01 <br />40 <br />635.93' <br />35.18 <br />40 <br />993.12 <br />65.43 <br />50 <br />291:92 <br />7.43 <br />. <br />50 <br />644.37 <br />36.12 <br />50 <br />1001.7 <br />86.90 <br />0 , <br />3011.28 <br />7.86 <br />13 <br />G52.81 <br />37.07• <br />20 <br />1010.3 - <br />88.39 <br />-' 10 <br />308.6 4,- <br />8.31 <br />10 <br />GG1.25 <br />38.03 <br />30 <br />1018.9 <br />89.8 9 <br />20 <br />316.99 <br />8.76 <br />20 <br />669.70 <br />39.01 <br />20 <br />1027:5 <br />01.40 <br />30 <br />325.35 <br />9.23 <br />30 <br />G78.15 <br />39.99 <br />30 <br />1036.1 <br />02.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />G8G.G6. <br />40.99 <br />40 <br />1044.7 <br />94.40 <br />•'50 <br />342.08 <br />10.20 <br />50 <br />695.GG <br />42.00 <br />50 <br />1053.3 <br />96.01 <br />7 <br />350.44 <br />10.71 <br />14 <br />703.51 <br />43.03 <br />21 <br />1061.9 <br />97.57 <br />10 <br />35S.S1 <br />11.22 <br />10 <br />711.97 <br />44.07 <br />10 <br />1070.6 <br />99.15 <br />20 <br />367.17 <br />x'11.75 <br />20 <br />720.44 <br />45.12 <br />20 <br />1079.2 <br />100.75 <br />30 <br />375.54 <br />12.29 <br />30 <br />728.90 <br />46.18 <br />30 <br />1087.8 <br />102.35 <br />40 <br />'333:91 <br />12.85 <br />40 <br />737.37 <br />47.25 <br />40 <br />1096.4 <br />103.97 <br />50 <br />392.28 <br />13.41 <br />50 <br />745.85 <br />48.34' <br />50 <br />1105.1 <br />105.60 <br />Corrections to be Added (T =Tangent. E=External.) <br />Angle 30° <br />Int. Curve'S° 10° 15° 20°t.018.023 <br />35° 40° <br />.11 .13 <br />45° <br />.15 <br />50° 551 60° <br />_18 .18 .20 <br />65° <br />.21 <br />70`> <br />-- <br />`�, <br />5° T=.02 .03 .05 .05.10 <br />E=.000 .000 .001 .00.002 <br />.0021 <br />.22 .25 <br />.003 <br />.28 <br />.004 .004 .004 <br />.31 .34 38 <br />•005 <br />.42 <br />.48 <br />10° T=.03 .06 .09 .13.19 <br />E =.001 .003 .004 .00.008 <br />.009 .011 <br />.012 <br />.014 x15 .017 <br />.018 <br />1123.4 <br />16 ° = 04 10 .14 19.29 <br />.34 39 <br />A5 <br />.51 .53 .58 <br />-3 <br />•� <br />E -.003 _007 .010 .01.023 <br />T.46.13.1B28.39_45 <br />.027 .020 <br />.51 <br />.038 045 <br />.032 <br />.58 <br />.051 <br />.035 .039 .043 <br />.65 .72 .7B <br />.057 .083 .070 <br />.0471 <br />.84 <br />.076 <br />0120° <br />E=.008 _OlI.017 02.034 <br />20 <br />.68 67.7b <br />300.0 <br />.83 .00 ,99 <br />108 <br />T,.08 18 .24 33.49 <br />.30 <br />E=.409 'A18 .027 -.03.050 <br />.065 .0 <br />.083 <br />.093 .100 .120 <br />127 <br />40 <br />1148.4 <br />113.95 <br />- .40 <br />1517.4 <br />197.53 <br />m <br />TABLE I. ='Tangents and Externals to a 1° Curve. III <br />Chord -100 ft. <br />lot.Angle <br />Angle <br />Tangent <br />External, <br />. Int <br />Angle <br />Tangent <br />g <br />r�:xterna: <br />Int: <br />Angle <br />Tangent <br />g <br />External <br />22° <br />1113,7 <br />107.24: <br />291 " <br />1481.8 <br />188.51 <br />36°r. <br />1861.7 <br />294.9 <br />101 <br />1123.4 <br />103.00 <br />10' <br />1490.7 <br />190.74 <br />BY <br />1870.9 <br />297.7 <br />201.131.0 <br />T=,08 .18 <br />110.57 <br />20 <br />1499.6 <br />192.99 <br />20 <br />1880.1 <br />300.0 <br />20 <br />1,139.7 <br />112.25 <br />.30 <br />1508:5 <br />195.25 <br />30 <br />1889.4 <br />303.5 <br />40 <br />1148.4 <br />113.95 <br />- .40 <br />1517.4 <br />197.53 <br />40 <br />1808.6 <br />306.4 <br />50 <br />1157.0 <br />115.665p <br />..051 <br />1526.3 <br />199.82 <br />50 <br />-1907.0 <br />309.3 <br />23 <br />1105..7: <br />117.33 <br />30• <br />1535.3 <br />202.12 <br />37 <br />1917.1 <br />312:2 <br />10 <br />1174.4 <br />119.12 <br />10 <br />1544.2 <br />204.44 <br />10 <br />1920.4 <br />315.2 <br />20 <br />1183.1 <br />120.87 <br />- 20 - <br />1553.1 <br />208.77 <br />20 <br />1935.7 <br />318.1 <br />• .30 <br />1191.8 <br />122.63 <br />30 <br />1562.1. <br />209.12 <br />- 30 <br />1945.0 <br />321.1 <br />40 <br />1200.5 <br />124.41 <br />'40 <br />1571.0 <br />211-.48 <br />40 <br />1954.3 <br />324.1 <br />50 <br />1209,2 <br />126.20 <br />50 <br />1580.0 <br />213.86 <br />50 <br />1963.6 <br />327.1 <br />24 <br />1217.9 <br />128.00 <br />$1 <br />1589.0 <br />216,3 <br />38:• <br />1972.9 <br />330.2 <br />10 <br />1226.6 <br />129.82 <br />a10 <br />1598.0 <br />218,7 <br />10 <br />1982.2 <br />333.2 <br />20 <br />1235.3 <br />131.65 <br />20 <br />1606.9 <br />221.1 <br />20 <br />1991.,5 <br />336.3 <br />30 <br />1244.0 <br />133.50 <br />30 <br />1615:9 <br />223.5 <br />30 <br />2000.9 <br />339.3 <br />40 <br />1252.8 <br />135.35 <br />40 <br />1624.9 <br />226.0 <br />40 <br />2010.2 <br />342.4 <br />50 <br />1261.5 <br />137.23 <br />50 <br />1633.9 <br />228.4 <br />50 <br />2019.6 <br />345.5 <br />26 <br />1270.2 <br />139.11. <br />32 <br />1643.0 <br />230.9 <br />30� <br />2029.0 <br />348.6 <br />10 <br />1279.0 <br />141.01 <br />10 <br />1652.0 <br />233.4 <br />1�0 <br />2038.4 <br />351.8 <br />20 <br />1287.7 <br />142.93 <br />20' <br />1661.0 <br />235.9 <br />20 <br />2047.8 <br />354.9 <br />'30 <br />1295.5 <br />144.85 <br />30 <br />1070.0 <br />238.4 <br />30 <br />2057.2 <br />.358.1 <br />40 <br />1305.3 <br />140,79 <br />40 <br />1679.1• <br />241.0 <br />'40 <br />206G.6 <br />361.3 <br />50 <br />1314.0 <br />148.75 <br />50 <br />1688.1 <br />243.5 <br />50 <br />2076.0 <br />364.5 <br />E6. <br />1322.8 <br />150.71 <br />33 - <br />1597:2 <br />246.1 <br />40 <br />2085.4 <br />867.7 <br />10 <br />1331.6 <br />152.69 <br />•10 <br />1705.3 <br />248.7 <br />10 <br />2094.9 <br />371.0 <br />20 <br />1340.4 <br />154.69 <br />20 <br />1715.3 <br />251.3 <br />20 <br />2104:3 <br />374.2 <br />30 <br />1349.2 <br />156:70 <br />30 <br />1724.4 <br />253.9 <br />'30 <br />2113.8 <br />377.5 <br />40 <br />1358.0 <br />158.72 <br />40 <br />1733.5 <br />256.5 <br />.40 <br />2123.3 <br />380.8 <br />50 <br />1366.8 <br />160.76 <br />50 <br />1742.G <br />259.1 <br />50 <br />2132.7 <br />384.1 <br />27 <br />1375.6 <br />162.81 <br />34 <br />1751.7 <br />261.8 <br />41 <br />2142.2 <br />387.4 <br />10 <br />1384.4 <br />164.86 <br />10 <br />1760.8' <br />2G4.5 <br />.. 10 <br />2151.7 <br />•390.7 <br />20 <br />1393-2 <br />166.95 <br />20 <br />1770.0 <br />267.2 <br />20 <br />2161.2 <br />'394.1 <br />30 <br />1402.0 <br />169.04 <br />30 <br />1779.1 <br />269.9 <br />30 <br />2170.8 <br />397.4 <br />.40 <br />1410,9 <br />171.15 <br />40 <br />1788.2 <br />272.6 <br />40 <br />2180.3 <br />400.8 <br />50 <br />1419.7 <br />173.27 <br />50 <br />1797.4 <br />275.3 <br />50 <br />2189 9 <br />404.2 <br />28 <br />1428.6 <br />175.41 <br />35 <br />1804.6 <br />278.1; <br />42 <br />2199.4 <br />407.6 <br />10 <br />1437.4 <br />177.55 <br />10 <br />1815.7 <br />280,8 <br />10 <br />220910 <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />20 <br />1824.9 <br />283.0 <br />20 <br />2218.6 <br />414.5 <br />130 <br />1455.1 <br />181.89 <br />30 <br />1834.1 <br />286,4 <br />30 <br />2228:1 <br />418.0 <br />40' <br />1464.0 <br />184.08 <br />40 <br />1843.3 <br />289.2 <br />40 <br />2237.7 <br />421.4 <br />50 <br />1472.9 <br />186.29 <br />50 <br />1852.5 <br />292.0 <br />50 <br />2247.3 <br />425.0 <br />Corrections to be Added (T =Tangent. E ---External.), <br />o <br />all, <br />I.CurveS* 10° <br />15° <br />20° <br />.25'. 30° <br />35° 40° <br />45° <br />50° <br />W60° 65' 70° <br />!0. <br />T=.08 I3 <br />.19 <br />.28 <br />.32 .39..45 <br />51 <br />.58 <br />.05 <br />79 <br />E=.006 .011 <br />.017 <br />.022 <br />.028 .034 <br />.0381 .015 <br />.051 <br />.057 <br />.72 .84 .90 <br />.063 .070 .076 .083 <br />15° <br />T=,08 .18 <br />.24 <br />33: <br />.40 .49 <br />.58 ..67 <br />.75 <br />.83 <br />.90 .99 1.06 1.14 <br />E-.009 .018 <br />'.027 <br />.036 <br />.046 .056 <br />.005 .074 <br />.OS3 <br />:093 <br />.106 .120 .127 .135 <br />! o <br />T=.10 715 <br />.29 <br />.39 <br />.40 .59 <br />.69 .79 <br />.89 <br />.99 <br />1.09 1.20 1.29 1.30 <br />E=.013 _025 <br />..038 <br />..051 <br />.065 .078 <br />.090 -.103 <br />.115 <br />129 <br />-.149 :170 .179 .188 <br />5° <br />=.11 22 <br />34 <br />.47 <br />.58. _69 <br />80 A3 <br />1.05 <br />1.17 <br />1.29 1.0 1.54 1.66 <br />E=.018 .035 <br />x54 <br />.072 <br />.086 .109, <br />.131 .153 <br />.175 <br />.197 <br />.213 230 .247 .264 <br />p° <br />T=.13 _26 <br />.40 <br />.53 <br />.67 .80 <br />.93 1.08 <br />1.20 <br />1.34 <br />149 1.64 1.79 1.94 <br />E=.023 010 <br />-T-=15--.3-0-1 <br />' <br />.070 <br />.44 <br />.093 <br />.00...76 <br />.1I7 .141 <br />.172 _203 <br />.234 <br />285 <br />.277 .290 .315 ;341 <br />.91 <br />1.06 1.21 <br />1.37 <br />1.52 <br />1.70 1.87 2.04 2.21 <br />E=.630• .060 <br />,.093 <br />.119 <br />.153 .184 <br />.216 .254 <br />:289 <br />.325 <br />.3511 .3781 :4P1 .495 <br />