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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 />Int <br />Angle <br />Tangent <br />External <br />1. <br />50.00 <br />.22 <br />S. <br />400.60 <br />13,99 <br />15° <br />754.32 <br />49.44 <br />10' <br />58.34 <br />.30 <br />10' <br />409.03 <br />14.58 <br />10' <br />702.80 <br />50.55 <br />20 <br />66.67 <br />.39 <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 />52.82 <br />40 <br />83.34 <br />.61 <br />40 <br />434.17 <br />16.43 <br />40 <br />788.26 <br />53.97 <br />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 />,67 <br />9 <br />450.93 <br />17.72 <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 />57.50 <br />20 <br />110.68 <br />1.19 <br />20 <br />467,71 <br />19.06 <br />20 <br />822.25 <br />58.70 <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 />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 />509.6S <br />22.62 <br />10 <br />804.82 <br />04.90 <br />20 <br />166.72 <br />2.43 <br />20 <br />518.OS <br />23.38 <br />20 <br />873.35 <br />66.18 <br />30 <br />175.00 <br />2.67 <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 />24.91 <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 />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 />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 />576.05 <br />28.97 <br />130 <br />933.13 <br />75.49 <br />40 <br />233,47 <br />4.76 <br />40 <br />585.36 <br />29.82 <br />40 <br />941,69 <br />76.86 <br />50 <br />241,81 <br />5.10 <br />50 <br />593.79 <br />30.08 <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 />'958.81 <br />79.57 <br />10 <br />258.51 <br />5.83 <br />10 <br />610.64 <br />32.45 <br />10 <br />967.38 <br />81.09 <br />20 <br />206.8G <br />6.21 <br />20 <br />619.07 <br />33.35 <br />20 <br />975.96 <br />82,63 <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 />G35.93 <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 />36.12 <br />50 <br />1001.7 <br />86.90 <br />0 <br />3N.2$ <br />7.80 <br />12 <br />G52.81 <br />37.07 <br />20 <br />1010.3 <br />88.39 <br />10 <br />3 .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 />01.40 <br />30 <br />325.35 <br />9.23 <br />30 <br />678.15 <br />39.99 <br />30 <br />1030.1 <br />02.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />G8G.60 <br />40.99 <br />40 <br />.1044,7 <br />94.46 <br />50 <br />342.08 <br />10.20 <br />50 <br />695.OG <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 />338.81 <br />1 1. 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 />728.90 <br />46.18 <br />30 <br />1087.8 <br />102.33 <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 />Int Angie <br />Curve 5° <br />10° 15° 20° 25' 30° <br />351 40° 45° SO- 55° 60° <br />65° <br />70° <br />5. <br />T-.02 <br />.03 05 JA .08 .10 <br />_11 .13.15 .l6 .18 .20 <br />.21 <br />.23 <br />290 <br />F-.000 <br />.000 .001 .OD1 .002 .002 <br />.002 .003 .003' .004 .004 .004 <br />.22 .2528 3l .34 3B <br />.005 <br />-q2 <br />.005_ <br />.46 <br />10° =.03 <br />.06 .D9 .18 .10 .19 <br />'108.90 <br />H-001 <br />.003 .004 .000 .007 .008 <br />.009 .011 A1$ .014 .015 .017 <br />.018 <br />.020 <br />Ura <br />T =.04 <br />.10 .14 10 .24 .29 <br />.24 .89 45 .51 .58 .58 <br />J631 --.6f <br />1499.6 <br />192,99 <br />E =.003 <br />.007 .010 .014 .018 .023 <br />.027 .029 .032 .035 .039 .013 <br />.45 .51 .58 .65 .72 .79 <br />.D47 <br />.84 <br />.051 <br />.90 <br />20° T=.00 <br />.13 .19 .26 .32 .39 <br />1508.5 <br />E=.006 <br />.011 .017 .022 .028 .034 <br />.038 .045 .051 .057 .063 .070 <br />.1 <br />.083 <br />25° <br />T=.QB <br />.16 .24 33 .4d .49 <br />.68 87 .75 .83 .90 .99 <br />].06 <br />114 <br />1398.6 <br />E=.000 <br />.018 .027 .030 .048 .058 <br />.065 074 .083 .093 .108 .120 <br />.127 <br />.135 <br />TABLE I. - Tangents and Externals.to a P Curve. III <br />Chord =100 ft. <br />Int.Tangent <br />Angle <br />External <br />Int'• <br />Angle <br />Te <br />angnt <br />External <br />Int' <br />Angle <br />Tangent <br />External <br />22° <br />1113.7 <br />107.24 <br />290 <br />1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.0 <br />10' <br />1122,4 <br />'108.90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />1870.9 <br />297.7 <br />211 <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 />1398.6 <br />306.4 <br />50 <br />1157,0 <br />115.G6 <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 <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 />1191,8 <br />122,63 <br />30 <br />1562.1 <br />209.12 <br />30 <br />1945.0 <br />321.1 <br />4U <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 />1200.2 <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 />31 <br />1589.0 <br />216.3 <br />38 <br />1972,0 <br />330.2 <br />10 <br />1226.6 <br />129.82 <br />10 <br />1598.0 <br />218.7 <br />10 <br />1952.2 <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 />25 <br />1270.2 <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />39- <br />2029,0 <br />348.0 <br />10 <br />1270.0 <br />141.01 <br />10 <br />1652.0 <br />233,4 <br />10 <br />2038.4 <br />35118 <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 />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 />140.79 <br />40 <br />1679.1 <br />241.0 <br />40 <br />2066.0 <br />361.3 <br />5U <br />1314.0 <br />148.75 <br />50 <br />1688.1 <br />248.5 <br />50 <br />2076.0 <br />36415 <br />26 <br />1322.8 <br />150.71 <br />33 <br />1697.2 <br />246.1 <br />40 <br />2085.4 <br />367.7 <br />10 <br />1331.0 <br />152.69 <br />10 <br />1706.3 <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 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 />164.86 <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 />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 />275.8 <br />50 <br />2189 9 <br />404.2 <br />28 <br />1428.0 <br />175.41 <br />35 <br />2800,6 <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 />20 <br />1446.3 <br />179.72 <br />20 <br />1S24.9 <br />283.6 <br />20 <br />2218.6 <br />4.14.5 <br />30 <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 />Int. <br />Angle <br />Curve P 10° <br />15° <br />20° 25° 300 <br />35a <br />40° <br />1 45° <br />50° 55° 1 601 1 65° 70° <br />qp° <br />T =.OB 13 <br />.19 <br />.28 .32 .39 <br />.45 <br />.51 <br />.58 <br />.89 .90 <br />65 .73k".2230 <br />E =.Q08 .011 <br />.017 <br />.022 .028 .034 <br />.038 <br />.045 <br />.051 <br />.057 .063 .076 .083 <br />250 <br />TT=.08 .IB <br />.24 <br />.33 .40 _49 <br />.58 <br />.67 <br />.75 <br />.83 .901.00 1.14 <br />B=.009 .018 <br />.027 <br />.036 .048 _056 <br />.065 <br />.074 <br />.033 <br />.093 .106 .127 .135 <br />30° <br />=,10 .19 <br />.29 <br />.39 .49 .59 <br />.69 <br />.79 <br />.89 <br />.99 1.09 1.29 1.39 <br />E=.013 .025 <br />.038 <br />.051 .065 .078 <br />.090 <br />.103 <br />.118 <br />.129 .149 .I79 .188 <br />35° <br />=•11 .22 <br />.34 <br />.47 .58 .69 <br />.80 <br />.93 <br />1.05 <br />1.17 1.29 1.54 1.66 <br />E=.018 D35 <br />.054 <br />.072 .086 .109 <br />.131 <br />.153 <br />.175 <br />.197 .213 .247 .204 <br />401 <br />T =.13 .26 <br />.40 <br />.53 .67 .80 <br />.93 <br />1.06 <br />1.20 <br />1,34 1.49' 1.04 1.79 1.94 <br />E =.023 .048 <br />.070 <br />.093 .117 .141 <br />.172 <br />.203 <br />.234 <br />.265 .277 .290 .315 .391 <br />45° <br />T=.15 .30 <br />.44 <br />.60 .76 .01 <br />1.08 <br />121 <br />1.37 <br />1.52 ].70 1.B7 2.04 2.21 <br />E =.030 .000 <br />.093 <br />.119 .153 .184 <br />21fi <br />.254 <br />.289 <br />325 351 .378 .411 .445 <br />