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II TABLE I. - Tangents and Externals to a V Curve. <br />Chord= 100 ft. <br />t <br />Angle <br />Tangent <br />External <br />Angl <br />Tangent <br />External <br />.rL�gle <br />Tangent <br />External <br />1° <br />-50.00 <br />22 <br />8": <br />400.66 <br />13.99 <br />15° <br />754.32 <br />43.44 <br />10' <br />55.34` <br />.30 <br />10' <br />409.03 <br />14.58 <br />10' <br />'762.80 <br />50.55 <br />20 <br />.GG.67 <br />.39 <br />20 <br />417.41 <br />15.18 <br />-, 20 <br />771.20 <br />- 51.68 <br />30 <br />75.01 <br />.49 <br />3U <br />425,79 <br />15.80 <br />30 <br />770.77 <br />52.82 <br />40 <br />`83.34 <br />.61 <br />40 <br />434,17 <br />16.43 <br />40 <br />788.26 <br />53.97 <br />r 50 , <br />91.68 <br />.73 <br />50 <br />442.55 <br />17.07 <br />50 <br />796.75 <br />-.55.13 <br />2 <br />100.01 <br />.87 <br />9 <br />450.93 <br />17.72 <br />16 <br />805.25 <br />.56.31 <br />10 <br />-109.35 <br />1.02 <br />10 ' <br />459.32 <br />18.38 <br />10 <br />813.75 <br />57.50 <br />20 <br />116.68 <br />1.19 <br />20 <br />467.71 <br />19:06 <br />20' <br />522.25 <br />55.70 <br />30 <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 />133.36 <br />1.55 <br />40 <br />484.49 <br />20.45 <br />40 <br />839.27 <br />G1'.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 />166.72 <br />2.43 <br />20 <br />518.08 <br />23.38 <br />20 <br />873.35' <br />336.3 <br />30 <br />175.06 <br />2.67 <br />30 <br />526.48 <br />24.14 <br />30 <br />881.88 <br />'67.47 <br />40 <br />18.3.40 <br />2.93 <br />40 <br />534.89 <br />24.91 <br />.40 <br />890.41 <br />CS.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 />71.42 <br />10 <br />208.43 <br />3.79 <br />10 <br />560.11 <br />27.31 <br />10 <br />916.03. <br />72.76 <br />20 <br />210.77 <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 />555.36 <br />29.82 <br />40 <br />041:69 <br />•76.86 <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 />19 • <br />058.81 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10 <br />610.64 <br />32.45 <br />10 <br />967.38 <br />81.00 <br />20 <br />266.86 <br />6.21 <br />20 <br />619 A7. <br />- 33.35 <br />20•. <br />075.96 <br />C' 82.53 <br />30 <br />275.21 <br />6.61 <br />30 <br />627.50 <br />34.26 <br />30 <br />984:53 <br />83.97 <br />40 <br />283.57 <br />7.01 <br />40- <br />635.93 <br />35.18 <br />-40 ' <br />993.12 <br />85.43 <br />50 <br />291.92 <br />7.43 <br />50 <br />644_.37 <br />. 30.12 <br />50 <br />1001:7 <br />86.90 <br />6 <br />300.28 <br />7.86 <br />13 <br />652.81 <br />37.07 <br />20 <br />1010.3 <br />88.39 <br />10 <br />305.64 <br />8.31 <br />`--10 <br />661.25. <br />38.03 <br />10 <br />1018.9 <br />89.89 <br />20 <br />316.99 <br />8.76 <br />20 <br />669.70 <br />39.01 <br />20 <br />1027.5 <br />91.40 <br />30 <br />325.35 <br />9.23 <br />30 <br />678.15 <br />39.99 <br />30' <br />1036.1 <br />92.92 <br />40 <br />333.71 <br />0.71 <br />40 <br />6861.60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 <br />342.08 <br />10.20 <br />50 <br />695.06 <br />42.00 <br />50 <br />1053.3 <br />96.01 <br />7 <br />350144 <br />10.71 <br />14 <br />703.51 <br />43.03 <br />21 ' <br />1061.9 <br />97.57 <br />10 <br />355.81 <br />11.22 <br />10 <br />..711.97 <br />44.07 <br />10 <br />1070.6 <br />99.16 <br />20 <br />367.17 <br />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 />725.90 <br />46.18 <br />'.30 <br />1087.8 <br />102.35 <br />40 <br />383.91 <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. GO <br />Corrections to be Added (T =Tangent. E=External.) <br />Int. <br />Angle <br />Curve 5° 10° 150 <br />20° <br />1 25-30° <br />Tangent <br />35° 40° <br />1 45° <br />506 <br />-55° <br />600 <br />651 <br />701 <br />5. <br />T=.02 .03 .05 <br />.06 <br />.08 <br />.10 <br />.11 .13 <br />.15.16 <br />1122.4 <br />.18 <br />.20 <br />.21 , <br />.23 <br />10' <br />E =.000 .000 .001 <br />.OU1 <br />.002 <br />.002 <br />.002 .003 <br />.003 <br />.004 <br />.004 <br />.004 <br />.005 <br />.005 <br />30 <br />T=.03 .05 .09 <br />.13. <br />.1G <br />.19 <br />.22 .25 <br />.28 <br />.31 <br />.34 <br />.38 ' <br />.42 <br />,.46 <br />10, <br />E =.001 .003 .004 <br />.006 <br />.007 <br />.008 <br />.009 .011 <br />.012 <br />.014 <br />.015 <br />.017 <br />.018 <br />,.020 <br />50 <br />T=.04 .10 .14 <br />.19 <br />.24 <br />.29 <br />.34 .30 <br />.45 <br />.51 <br />.53 <br />.58 <br />.63 <br />.63 <br />15o <br />E =.003 .007 .010 <br />.014 <br />.018 <br />.023 <br />.027 .029 <br />.032 <br />,035 <br />.039 <br />.013 <br />.047 <br />.051 <br />20o <br />T=.06 .13 .19 <br />a6 <br />.32 <br />.30 <br />.45 .51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84I <br />.90 <br />30 <br />E=.000 .011 .017 <br />.022 <br />.023 <br />.034 <br />.038 .015 <br />1 <br />.051 <br />.0..57 <br />.063 <br />.070 <br />.076 <br />083 <br />25° <br />T=.08 .16 .24 <br />.33 <br />.40 <br />.49 <br />.58 .67 <br />.75 <br />.53 <br />.90 <br />a9 <br />1.06 <br />1.14 <br />31. <br />.01S .027 <br />.030 <br />.046 <br />.O5G <br />.065 .074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 <br />.135 <br />Me <br />-TABlm I. --Tangents and Externals to a 1` Curve. <br />Chard =100 ft. <br />Int.Tangent <br />te Angle. <br />Curve 5° <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle- <br />Tangent <br />External <br />22° <br />1113:7 <br />107.24 <br />29° <br />'-1481.8 <br />188.51 <br />36° <br />-1861.7 <br />294.9 <br />101 <br />1122.4 <br />•108.90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />1870.9 <br />297.7 <br />20 <br />1131.0 <br />110.57 <br />20 <br />1499.6 <br />192.99 <br />20 <br />1880.1 <br />300.6 <br />30 <br />1139.7 <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 />1898.6 <br />306.4 <br />50 <br />1157.0 <br />115.GG <br />50 <br />1526.3 <br />199.82 <br />50 <br />1907.9 <br />309.3 <br />23 <br />1165.7 <br />117.38 <br />30. <br />1535.3 <br />202.12 1 <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 />1926.4 <br />315.2 <br />20 <br />1183.1 <br />.120.87 <br />-'20 <br />1553.1 <br />206.77 <br />20 <br />1935.7 <br />318.1 <br />30 ' <br />1'101.8 <br />-122.63 <br />30 <br />1502.1 <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 />213.8G . <br />50 <br />.1963:6 <br />327.1 <br />24 <br />1217.9 <br />128.00 <br />31. <br />1589.0 <br />216.3 <br />-38 <br />1972:9 <br />330.2 <br />10 <br />1226.6 <br />129.82 <br />- 10 '•1598.0 <br />.218.7 <br />10- <br />1992.2 <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 -.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 />34:.4 <br />50 <br />1261.5 <br />137.23 <br />50 <br />1633.9 <br />'228.4 <br />50 <br />2019.6 <br />3.15.5 <br />=e <br />-.25 <br />1270.2' <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />.39 <br />2029.034 <br />8.6 <br />10 <br />.1279.0 <br />141_01 <br />10 <br />1652.0 <br />233.4 <br />10 <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 />2647.8 <br />354.9 <br />30 <br />1296.5 <br />144.85 <br />30 <br />1670.0 <br />238.4 <br />30 <br />2057.2 <br />358.1 ' <br />40 <br />1305.3 <br />.146.79 <br />40 <br />4679.1 <br />241.0 <br />40 <br />2066.6 <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 />-,26.. <br />1322.5 <br />150:71 <br />33 <br />1697.2 <br />2x16.1 <br />40 <br />2085.4 <br />367.7 <br />10 ' <br />. 1,331.6 <br />152.69' <br />10 <br />-1706.3 <br />248.7 <br />t0 <br />209.1.9 <br />311.0 <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 />s '.• 50 <br />;-1366.8 <br />160.70 <br />50 <br />1742.6 <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 />161.56 <br />10 <br />1760.8 <br />264.5 <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 />r : 30 <br />1402.0 <br />169.01 ' <br />30 <br />17779.1 <br />269.9 <br />80 <br />2170.8 <br />397.4 <br />40 <br />1410.9 <br />171.15 <br />_ <br />4.0 <br />1738.2 <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 />142S.6 <br />17.5.41 <br />35 <br />1806.6 <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 />2209.0 <br />411.1 <br />^_0 <br />1446.3 <br />179.72 <br />20 <br />1824.9 <br />283.6 <br />20 <br />2218.6 <br />414.5 <br />• 30 <br />1450.1 <br />181.89 <br />30 <br />1.834.1 <br />286.4 <br />30 <br />2228.1 <br />418.0 <br />°"'40 <br />1464.0 <br />184.08 <br />40 <br />1343.3 <br />289.2 <br />40 <br />2237.7 <br />421.4 <br />'50 <br />;1472.9 <br />136.29 <br />50 <br />1852.5 <br />202.0 <br />50 <br />2247.3 <br />425.0 <br />Corrections to be Added (T=Tangent. E=External.) <br />•Int. <br />Angle <br />Curve 5° <br />10° <br />_15° 201 <br />25° <br />30° 35° 40° I 45° <br />50° <br />55° <br />1 60° 65° 70° <br />20° <br />T=.06 <br />-.13 <br />.19 .26 <br />.32 <br />.39 .45 .51 .58 <br />.65 <br />.72 <br />.79 .84 .00 <br />E=.006 <br />.011 <br />.017 .022 <br />.028 <br />.034 .038 .045 .051 <br />.057 <br />.063 <br />.070 .076 .083 <br />:25° <br />T =.03 <br />.16 <br />24 .33 <br />.40 <br />,49 .5S .67 .75 <br />.83 <br />.90 <br />.99 1.06 1.14 <br />E=.009 <br />.018 <br />.0--17 .036 <br />.046 <br />.056 .065 .074 .083 <br />.OU3 <br />.106 <br />.120 .127 .135 <br />30° <br />T=.10 <br />.19 <br />^9 .39" <br />.49 <br />.59 .69 .79 .80 <br />.99 <br />1.09 <br />1.20 1.29 1.39 <br />E=.013 <br />.025 <br />.038 .0.51 <br />.065 <br />.078 .090 .103 .116 <br />.129 <br />.149 <br />.170 .179 .188 <br />35°, <br />T=.11 <br />22 <br />.34 .47 <br />.53 <br />.69 .80 .93 1.05 <br />1.17 <br />1.29 <br />1.42 1.54 1.66 <br />E=.018 <br />.035 <br />.054 .072 <br />.036 <br />.109 .131 .153 .175 <br />.197 <br />13 <br />.230 .247 ?64 <br />40° <br />T=.13 <br />26 <br />1 .40 .53 <br />1 .67 <br />1 .80. .93 1.06 1.20 <br />1.34 <br />1.40 <br />1.64 1.79 1.94 <br />E=.023 <br />.046 <br />.070 .093 <br />.117 <br />.141 .172 .203 234 <br />.265 <br />.277 <br />.290 .315 .341 <br />qjo <br />T=.15 <br />.30- <br />.44 .GO <br />.i6 <br />.9 1 1.37 <br />91 LOG 1 <br />1.52 <br />1.70 <br />1.87 2.04 2.21 <br />E =.030 <br />.060 <br />.093 .119 <br />.153 <br />.184 .216 .254 289 <br />.3251 <br />.351 <br />.378 .411 .4.15 <br />