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II TABLE I. - Tangents and Externals to a P Curve. <br />Chord= 100 ft. <br />Int.Int: <br />Angle <br />Tar gent <br />ExEernal <br />Angle <br />Tangent <br />External <br />Int. z <br />.Angle <br />Tangent <br />External <br />1° <br />50.00 <br />.22 <br />S°- <br />400.66 <br />13.99 <br />16' <br />754.32 <br />49.44 <br />10` <br />51, <br />,30, <br />,. ,10! <br />-409.03. <br />14.58 <br />10' <br />762.80 <br />50.55 <br />20 <br />66.67 <br />.30 <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 />15.50 <br />30 <br />'779:77 <br />"52.52 <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 />91.08 <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 />108.35 <br />1.02. <br />.10 <br />459.32 <br />1S.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 />822.25 <br />58.70 <br />30 <br />125.02 <br />1.36 <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 />484.49 <br />20.45 <br />40 <br />S30.27 <br />61.14 <br />50 <br />141.70 <br />1.75 <br />50 <br />492.SS <br />21.16 <br />50 <br />547.75 <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 />153.38 <br />2.19 <br />10 <br />509.68 <br />22.62 <br />10 <br />'864:82 <br />64.90 <br />20 <br />1.661.72 <br />2.43 <br />20 <br />518.08 <br />23.3S <br />20. <br />.873.35 <br />66.18 <br />30 <br />175.06 <br />2.67 <br />30 <br />526.48 <br />24.14- <br />30 <br />881.58 <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 />-25 <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 />203.43 <br />3.79 <br />10 <br />.560.11 <br />27.31 <br />10 - <br />916.03 <br />72.70 <br />- 20 <br />216.77 <br />4.10 <br />20 <br />568.53 <br />28.14 <br />20 <br />''924.53 <br />74.12 <br />30 <br />225.12 <br />4.42 <br />30 <br />576.95 <br />28.97 <br />30 <br />033.13 <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 />241.51 <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 />958.81 <br />79.67 <br />10 <br />255.51 <br />5.83 <br />.10 <br />610.64 <br />32.45 <br />10 <br />1167538'. <br />81.09 <br />20 <br />266.56 <br />6.21 <br />•20 <br />619.07 <br />33.35 <br />20 <br />975.96 <br />52.53 <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 />36.12 <br />50 <br />1001.7 <br />8G.90 <br />6 <br />300.25 <br />7.86 <br />13 <br />652.81 <br />37.07 <br />20 <br />1010.3 <br />88.39 <br />10 <br />308.64 <br />-8.31 <br />10 <br />661.25 <br />38.03 <br />10• <br />1018.9 <br />39.59 <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 />678.16 <br />39.99 <br />30 <br />' 1036.1 <br />92.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />656:60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50. <br />342.06' <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 />358.81 <br />11.22 <br />10 <br />711.97 <br />44.07 <br />10 <br />Mr, 0.6 <br />99..10 <br />20 .-367.17 <br />1446.3 <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 />72S.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 />392.25 <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. <br />Tangent <br />External <br />Int' <br />Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tan gent <br />External <br />1113.7 <br />107.24 <br />Angle Curve 5o <br />10° <br />15° 20° <br />2'a° 30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />170° <br />5° T=.02 <br />.03 <br />.05 .06 <br />.08 .10 <br />.I1 <br />.13.15 <br />20 <br />.16 <br />.18 <br />20 <br />.21 <br />23 <br />E=.000 <br />.000 <br />.001 .001 <br />.002 .002 <br />.002 <br />.003 <br />.003 <br />.004 <br />.004 <br />.004 <br />.005 <br />.005 <br />10° T=.03 <br />.00 <br />.09 .13 <br />.16 .19 <br />.22 <br />.25 <br />.28 <br />.31 <br />.34 <br />.38 <br />.42 <br />,46 <br />E=.001 <br />.003 <br />.004 .005 <br />.007 .008 <br />.009 <br />.011 <br />.012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />15° T=.04 <br />.10 <br />.14 .19 <br />.24 .29' <br />.34 <br />.39 <br />.45' <br />.51 <br />.53 <br />.58 <br />.63 <br />.58 <br />F.=.003 <br />,.007 <br />.010 .014 <br />.018 .023 <br />..027 <br />.029 <br />.032 <br />'.035 <br />.039 <br />.043 <br />.047 <br />•051 <br />20° T=.06 <br />.13 <br />.19 .26 <br />.32 '.39 <br />.45 <br />'.51 <br />.58 <br />.65 <br />.72,79 <br />40 <br />.84 <br />'324.1 <br />B=.006 <br />.011 <br />.017 .022 <br />.028 .034 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 <br />'.070 <br />,076 <br />011 <br />83 <br />25o T=.08 <br />1 .16 <br />.24 .33 <br />.40 .49.58 <br />1972.9 <br />.67 <br />.75 <br />83 ' <br />.90 <br />.99 <br />1.00 <br />1.14 <br />E =.000 <br />.013 <br />.027 .036 <br />.046 .056 <br />.065 <br />.074 <br />.083 <br />:093106 <br />221,1 <br />.120 <br />.127 <br />.135 <br />TABLE I. - Tangents and Externals to a 1° Curve. III <br />Chord =100 ft. <br />t' <br />An <br />Tangent <br />External <br />Int' <br />Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tan gent <br />External <br />1113.7 <br />107.24 <br />29° <br />1481.8 <br />188.51 <br />361 <br />1861.7 <br />294.9 <br />101. <br />1122.4 <br />108.90 <br />161' <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 />'1130.7 <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 />115.60• <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 />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 />120.20 <br />50 <br />1580.0 <br />213.85 <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 <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 />1901.5 <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 />2019.0 <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 />364.9 <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 />50 <br />:1314:0 <br />148.75 <br />50 <br />1685.1 <br />243.5 <br />50 <br />2076.0 <br />304.5 <br />126 <br />1322:8 <br />150.71' <br />33 <br />1697.2 <br />246.1 <br />40 <br />2055.4 <br />367.7 <br />10 <br />1331:6 <br />152. G9 <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 />874.2 <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 />1.58.72 <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 />357.4 <br />10 <br />1384.4 <br />164.86 <br />10 <br />17610.8 <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 />1770.1 <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.G <br />40 <br />21S0.3 <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.G <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 <br />10 <br />2209.0 <br />411.1 <br />- 20 <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 />1455.1 <br />181.89 <br />30 <br />1834.1 <br />2S6.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />1464.0 <br />184.08 <br />40 <br />1843.3 <br />259.2 <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 />I❑t. <br />En[;le- <br />Curve 5° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° 45° <br />Sr <br />55° <br />1 60° <br />1 65° 70° <br />'0° <br />T=.06 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 .53 <br />.05 <br />.72 <br />.79 <br />.84 .90 <br />E=.000 <br />.011 <br />.017 <br />.022 <br />.028 <br />.034 <br />.038 <br />.045 .051 <br />.051 <br />.063 <br />,070 <br />.076 .083 <br />25°.-- <br />T=.08 <br />.16 <br />.24 <br />.33 <br />.40 <br />.40 <br />.58 <br />.67 .75 <br />.83 <br />.90 <br />.99 <br />1.Q6 1.14 <br />E =.009 <br />.018 <br />.027 <br />.036 <br />.046 <br />.056 <br />,065 <br />.074 ,083 <br />.093 <br />.106 <br />.120 <br />.127 .135 <br />30° <br />T=.10 <br />.19 <br />29.39 <br />49 " <br />.59 <br />.69 <br />.79 .89 <br />.99 <br />1.09 <br />1.20 <br />1.29 1.39 <br />r=.013 <br />.025 <br />.038 <br />.051 <br />.065 <br />.078 <br />.090 <br />.103 .116 <br />.129 <br />.149 <br />.170 <br />.170 .188 <br />35° <br />T=.11 <br />.22 <br />.34 <br />.47 <br />.58 <br />.69 <br />.80 <br />.93 1.05 <br />1.17 <br />1.20 <br />1.42 <br />1.54 1.66 <br />=.018 <br />.035 <br />.054 <br />.072 <br />.086 <br />.109 <br />-.131 <br />.153 ,175 <br />.197 <br />213 <br />.230 <br />.247 .264 <br />40° <br />T=.13 <br />96 <br />.40 <br />.53 <br />.67 <br />.80 <br />.93 <br />1.06 1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 1.94 <br />E=.023 <br />.046 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 .234 <br />265 <br />.277 <br />.290 <br />.315 341 <br />45° <br />T =.15 <br />.30 <br />,44 <br />.00 <br />.76 <br />.91 <br />LOG <br />1.21 1,37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 2.21 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />,153 <br />.184 <br />.210 <br />.254 289 <br />.325 <br />.351 <br />.378 <br />.411 .445 <br />