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1I TABLE I. - Tangents and Externals to a V Curve. <br />Chord =100 "f t. <br />Int. <br />Angle <br />Tan ent <br />g <br />External <br />Int. <br />Angle <br />Tan ent <br />g <br />External <br />Int. <br />Angle <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 />49.44 <br />10' <br />58.34 <br />.30 <br />10' <br />400.03' <br />14.53- <br />: 10' <br />762.80 <br />50.55 <br />20 <br />66.67.. <br />.39 <br />20 <br />417.41 <br />15.15 <br />20 <br />771.29 <br />51.68 <br />30 <br />75.01 <br />:49 <br />30 <br />425.79 <br />15. g0" <br />'"30 ' <br />779.,77 <br />" 52.S2 <br />40 <br />53.34 <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 />79G.75. <br />55.13 <br />2 ` <br />100.01 <br />.87 <br />9 <br />450.93 <br />17.72 <br />-16 <br />505.25 <br />56.31- <br />10 <br />108:35 <br />1.02 <br />10 <br />.459.32 <br />IS.38 <br />10 <br />513:75 <br />'57.50" <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 />30 ` <br />125.02 <br />1.3G <br />30 <br />476:10 <br />19.75 <br />30: <br />.530.76 <br />59:91 <br />40 <br />-133.36 <br />1.55 <br />40 <br />48.1.49 <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.iG <br />50 " <br />547:78. <br />62.38 <br />3 <br />150.04 <br />1.96 <br />10 <br />501:28 <br />21.59 <br />17' " <br />856.30. <br />: 63.63 <br />_ <br />10 <br />158.38, <br />2.19 <br />10 <br />509.68 <br />22.62 <br />.10 <br />864.52 <br />, 64.90 <br />20 <br />166.72 <br />2.43 <br />20 <br />518.08 <br />23.38, <br />.20 <br />873.3.5 <br />66.IS <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 />183.40 <br />2.93 <br />40 <br />534.S9 <br />24.91 <br />40 <br />890.41 <br />GS. 77 <br />50 <br />191.74 <br />3.21 <br />50 <br />543.29 <br />25.70 <br />50 <br />895.95 <br />70.09 <br />4 <br />200.OS <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 />91G.03 <br />72.76 . <br />20 <br />216.77 <br />4.10 <br />20 <br />568.53 <br />25.14 <br />20 <br />924.58 <br />74.12. <br />30 <br />225.12 <br />4.42 <br />30 <br />570.95 <br />28.97 <br />30 <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 />241.61 <br />5.10 <br />50 <br />593.79 <br />30.68 <br />50 <br />950.25• <br />78.26 <br />b <br />250"16 <br />5.46 <br />12 <br />602.21 <br />31.56 <br />i9 <br />958.51 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10 <br />610.G4 <br />32.45 <br />10 <br />967.38 <br />51.09 <br />20 <br />266.86. <br />6.21. <br />20 <br />619.07 <br />33.35 <br />20 <br />975.96 <br />S2.53 <br />30 <br />275.21 <br />6:61 <br />30 <br />627.50 <br />34.26 <br />30 <br />934.53 <br />83.97 <br />40 <br />283"57 <br />7.01 <br />40 <br />635.93 <br />35.15- <br />' 40 <br />993.12 <br />55.43 <br />50 <br />291.92 <br />7.43. <br />50 <br />6144.37 <br />36.12 <br />50 <br />1001.7 <br />SG.90 <br />6 <br />300.28 <br />7.S6 <br />13 - <br />652.81 <br />37.07 <br />20 <br />1010.3 <br />89.39 <br />10 <br />30S.64 <br />8.31 <br />10 <br />661.25 <br />35.03' <br />10 <br />1018.9 <br />SO.S9 <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 />92.02 . <br />40 <br />333.71 <br />9.71 <br />40 <br />686.60 <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 />350.44 <br />10.71 <br />14 <br />703.51 <br />43.03 <br />21 <br />1061.9 <br />97.57 <br />10 <br />358.51 <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 />100.75.1 <br />30 <br />375"54 <br />12.29 <br />30 <br />728.90 <br />4G. 1S <br />30 <br />IOS7.8 <br />1G2.35;i <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 />105.60aj <br />Corrections to be Added (T =Tangent. E=External.) <br />Angle <br />Curve 5° <br />10° 15° 20° <br />25° <br />30° <br />35° <br />1 40° <br />45° <br />SO° <br />55° <br />60° 65° 70 <br />5o <br />T=.02 <br />.03 .05 .06 <br />.08 <br />.10 <br />.11 <br />.13 <br />.I5 <br />.16 <br />.18 <br />.20 .21' 2 <br />1490.7 <br />E =.000 <br />.0001 .001 .001 <br />.002 <br />.002 <br />.002 <br />.003 <br />.003 <br />.004 <br />.001 <br />..004 .005 .0 <br />10° <br />T=.03 <br />.06 .09 .13 <br />.16 <br />.19 <br />.22 <br />"25 <br />.28 <br />.31 <br />.34 <br />.38 .42 .4 <br />303.5 <br />E=.001 <br />.003 .001 .006 <br />•.007 <br />.008 <br />.009 <br />•011 <br />.012 <br />..014 <br />.015 <br />.017 .018 .0 <br />15o <br />T =.04 <br />.10 .14 .19 <br />24 <br />.29.34 <br />50 <br />.30 <br />"45 <br />.51 <br />:53 <br />.58 .63 A <br />30 <br />r.=.003 <br />.007 "010 .014 <br />.018 <br />.023 <br />.027 <br />.029 <br />.032 <br />.035 <br />.039 <br />.013 .047 .0 <br />20° <br />T =.06 <br />1 .13 1 lg .26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />G5 <br />.72 <br />.79 84 ` <br />1935.7 <br />E =.006 <br />Olt .017 .022 <br />.028 <br />.034 <br />.035 <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 .076 .0 <br />25° <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 />06 <br />1.1127 1.1 <br />126.20 <br />E=.009 <br />.018 .027 .030 <br />046 <br />.056 <br />.065 <br />.074 <br />.053 <br />093 <br />.106 <br />.120 <br />Q <br />TABLE L - Tangents and Externals to a 1° Curve. III <br />Chord =100 f t. <br />Int. <br />Angle <br />Tan ent <br />g <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 />30° <br />1861.7 <br />294.9 <br />10r <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 />1380.1 <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• <br />37 <br />1917.1 <br />.312:26 <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 />1153.1 <br />120.57 <br />'20 <br />1553.1 <br />206.77 <br />20. <br />1935.7 <br />318.1 <br />30 <br />.1191.5 <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 />31 <br />1589.0 <br />216.3 <br />38 <br />1972.0 <br />330.2 1 <br />10 <br />.1226.6 <br />129.82 <br />10 <br />1598.0 <br />218.7 <br />10 <br />19S2.2 <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 />12.14.0 <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 />1G43.0 <br />230.9 <br />39 <br />2029.0 <br />348.6 <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 />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 />146.79 <br />40 <br />'1679.1 <br />241.0 <br />40 <br />2066.6 <br />361.3 <br />5U <br />1314.0 <br />148.75 <br />50 <br />1688.1 <br />243.5 <br />50 <br />2076.0 <br />361.5 <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 />,1331.6 <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 />15G.70 <br />30 <br />1724.4 <br />253.9 <br />30 <br />2113.3 <br />377.5 <br />40 <br />1358.0 <br />153.72 <br />40 <br />1733.5 <br />256.5 <br />40 <br />2123.3 <br />3S0.8 <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 />2G1.8 <br />41 <br />2142.2 <br />357.4 <br />10 <br />1384.4 <br />•104.8610 <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 />1462.0 <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 />1428.0. <br />175.41, <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 />280.8'10 <br />2209.0 <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />20 <br />1524.9 <br />283.0 <br />'20 . <br />2218.6 <br />414.5 <br />30 <br />1455.1 <br />"151.89 <br />30 <br />1834.1 <br />2S6"4 <br />30 <br />2228.1 <br />413.0 <br />40 <br />1164,0 <br />IS4.08 <br />40 <br />1843.3 <br />289.2 <br />40 <br />2237.7 <br />421.4 <br />:i0 <br />1172.9 <br />IS6.29 <br />50 <br />1552.5 <br />292.0 <br />50 <br />2247.3 <br />425.0 <br />1 <br />Corrections to be Added (T = Tangent. E = External.) <br />ogle <br />' Curve 5° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° 70° <br />!p° <br />T=.08 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84 .90 <br />_ <br />E=.000 <br />.011 <br />.017 <br />.022 <br />.028 <br />.03.4 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 .083 <br />15° <br />T=.08 <br />.1G <br />.24 <br />.33 <br />.40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.06 1.14 <br />E =.009 <br />.018 <br />.027 <br />.036 <br />.046 <br />.050 <br />.065 <br />.074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 .135 <br />30° <br />-r= 1- <br />=.10 ' <br />.19 <br />• 29 <br />.39 <br />.49 <br />.59 <br />.69 <br />.79 . <br />.89 <br />.99 <br />1"09 <br />1.20 <br />1.29 1.39 <br />E=.013 <br />.025 <br />.038 <br />.051 <br />.085 <br />.078 <br />.090 <br />.103 <br />.116 <br />.129 <br />.149 <br />.170 <br />.179 .188 <br />35° <br />T=.11 <br />?2 <br />.34 <br />.47 <br />.53.69 <br />.80 <br />.93 <br />1.05 <br />1.17 <br />1.29 <br />1.42 <br />1.54 1.66 <br />E=.018 <br />.035 <br />.054 <br />.072 <br />.OSG <br />.109 <br />.131 <br />.153 <br />.175 <br />.197 <br />213 <br />.230 <br />247 .284 <br />401 <br />a0 <br />.53 <br />67 <br />EO <br />.93 <br />1,OG <br />1.20 <br />134 <br />1.49 <br />1.614 <br />1.94 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />234 <br />.265 <br />.277 <br />.290 <br />11.79 <br />.31b .341 <br />is. <br />ffl-,.3 <br />.44 <br />.60 <br />.7G <br />.91 <br />1.06 <br />121 <br />1.37 <br />1.53 <br />1.70 <br />1.87 <br />2.04 2.21 <br />.093 <br />.119 <br />.153 <br />.1-- <br />.--- <br />.254 <br />.289 <br />325 <br />.351 <br />378 <br />.411 .445 <br />a <br />