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II TABLE I. - Tangents and Externals to a P Curve. <br />Chord =100 ft. <br />Int, <br />Angle <br />'Tangent <br />g <br />External <br />lat` <br />Angle : <br />Tangent <br />8 <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 />40.44 <br />10' <br />58:34 <br />.30 <br />10' <br />409.03 <br />14.58 <br />10' <br />762.80 <br />50.55. <br />20 <br />66.67.39 <br />.018 .020 <br />20 <br />417.41 <br />15.18 <br />20 <br />771.29, <br />51.68 <br />30 <br />75:01 <br />.49 <br />36 <br />425.79 <br />15.80 <br />30 <br />779.77 <br />52.82 <br />40' <br />'33.34 <br />61 <br />•46 <br />434.17 <br />16.43 ' <br />40 <br />788.26 <br />53.97 <br />50 <br />91.GS <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 />SG.31 <br />30 <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 />116.68 <br />1:I9 <br />20 <br />4G7.71 <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 />'484.40 <br />20.45 <br />P 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 />S - <br />150.04 <br />1:96• <br />10. <br />501,2$ <br />21.80 <br />17--": <br />.856.30 <br />63.63 . <br />10 <br />158.38' <br />2.19 <br />10 <br />500.68 <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 />66.18 <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 />534.89 <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 />2G.50 <br />18 <br />947.49 <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 />576.95 <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 />241.81 <br />5.10 <br />50' <br />593.79 <br />30.68 <br />50 <br />950.25 <br />78.26 <br />6 <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 />25S.51 <br />5.S3 <br />10 <br />•610.64 <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 />984..53, <br />83.97 <br />40 <br />283:57 <br />7.01 <br />.40" <br />635.93 <br />35.15 <br />•30 <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 />6 <br />800.28 <br />7.83 <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 />89-89 <br />20 <br />316.99 <br />8.76 <br />20 <br />669.70 <br />39.01 " <br />20 <br />1027.5 <br />41.40 <br />80 <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 />9.71 <br />40 <br />6S6.60 <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 />06.01 <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 />1437.4' <br />11.22 <br />10 <br />711.97 <br />44.07 <br />10 <br />1070.6 <br />99.16 <br />.,358.81 <br />20 <br />367.17 <br />11.75 <br />• <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 />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.S5 <br />48.34 <br />50 <br />1105.1 <br />105.60 <br />Corrections to be Added (T = Tangent. E = External.) ' <br />lnt. <br />Angle <br />Curve S. IO° IS° 20° <br />25° 30° 35° 40° 45° <br />50° <br />55° 60° <br />65° 70° <br />5 o <br />T=.02 .03 .05 .06 <br />.08 .10 .11 .13 .15 <br />.16 <br />18 .20 <br />.2I .23 <br />29° <br />E=.000 .100 .001 .001 <br />.002 .002 .002 .003 .003 <br />.004 <br />.004 .004 <br />.005 .005 <br />loo <br />T=.03 .05 .09 .13 <br />.16 .19 .22. .25 •.28 <br />.31 <br />,34 .38 <br />.42 .46 <br />10' <br />E=.001 .003 .004 .005 <br />.007 .008 .009 .011 .012 <br />.014 <br />.015 .017 <br />.018 .020 <br />15o <br />T=.04 .10.- .14 .19 <br />.2-1 .29 ..34 <br />.51 <br />.53 .58 <br />.63 .63 <br />30 <br />'E =•003 .007 .010 .014 <br />.018 .023 .027 <br />.035 <br />.039 .043 <br />.047 .051 <br />20o <br />T =.OG '.13 .19 .25 <br />.32 .39 .45 <br />40 <br />.79 <br />.84 .90 <br />40 <br />E=,006 .011 .017 .022 <br />.028 .034 .038 <br />*.074. <br />.057 <br />AM .070 <br />.076 .083 <br />25° <br />T=.08 .16 .24 .33 <br />40 .49 .58 <br />.83 <br />.90 .99 <br />1.00 1.14 <br />50 <br />E=.009 .018 .027 .038 <br />.046 .056 .065 <br />.093 <br />.105 .120 <br />.127 .135 <br />TAsiE L: Tangents and Externals to''a-l�_Curve. TTI <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />_ <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 />lot <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 />1S80.i <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 />115.66- <br />50 <br />1520.3 <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 />1017,1 <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 />29 <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 />1502.•1 <br />209.12 <br />30 <br />1945,0', <br />321.1 <br />' 40" <br />1209.5 <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 />1560.0 <br />213.85 <br />50 <br />1963.6; <br />327.1 <br />84 ' <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 />122G,0 <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 />1991.5 <br />336.3 <br />30 <br />1244.0 <br />133.50 <br />30 <br />•1015.9 <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 />220.0 <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 />39- <br />'2029.0 <br />348.6 <br />10 <br />1279.0 <br />141.01 <br />10 <br />•1652.0- <br />233,4 <br />to <br />20`38.4 <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 />49 <br />2066.8 <br />361.3 <br />50 <br />1314.0 <br />148.75 <br />"- ,50• <br />-168S:I. <br />243.5 <br />--'50 <br />20"46.0 <br />364.5 <br />26 . <br />'1322.8 <br />150.71 <br />33' <br />1697.2 <br />24G:1 <br />40 <br />2035.4 <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 />00 <br />.1724.4 <br />253.0 <br />30 - <br />2113.8 <br />377.5 <br />40 <br />1358.0 <br />158.72 <br />40 <br />1733.5 ' <br />2515.5 <br />40 <br />2123.3 <br />380.8 <br />50 <br />.1360.3 <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 />2I42.2 <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 />272.0 <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 />1806.6 <br />' 275.1 <br />2 <br />2199.4 <br />407.6 <br />16 <br />1437.4' <br />177•.55 <br />10 <br />1815.7 <br />280.8 <br />.10 <br />2209.0 <br />4L1. 1 <br />20' <br />1446.3 <br />179.72 <br />20 <br />IS24:9 <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 />286.4 <br />••30 <br />12228.1 <br />41.8.0 <br />40 <br />1464.0 <br />184.08 <br />40 <br />1843.3 <br />239.2 <br />40 <br />2237.7 <br />421.4 <br />50. <br />1472.9 <br />18G.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 />Tnt. Carve 5° <br />Angle <br />10° 15° <br />29° , <br />25°• 30° 35° <br />40° <br />'45° 50° <br />55° <br />500 65° 70° <br />20° T=•06 <br />.13 .19 <br />'.20 <br />'.32 .39 .45 <br />•.5I <br />.5S .65 <br />.72 <br />.79 .84 .90 <br />E=.000 <br />.011 .017 <br />;022 <br />.028 .034 .038 <br />.045 <br />'.051 .057 <br />.063 <br />.0701 .076 .063 <br />25o T=.08 <br />.16 .24 <br />.23 <br />.40 .49 11.59 <br />.67 <br />.75 .83 <br />.90 <br />.99 1.06 1.14 <br />E=.009 <br />.018 .027 <br />.036 <br />.046 .050 .065 <br />.074 <br />.083 .093 <br />.106 <br />.120 .127 .135 <br />30° T=.10 <br />.19 .29 <br />.39 <br />.49' .59 .69 <br />.79 <br />.89' .99 <br />1.09 <br />1120 1.29 1.39 <br />E-.013 <br />.025 .038 <br />.Da`1 <br />.055 .678 .090 <br />.103 <br />.116 .129 <br />.1d9 <br />.]70 .179 .188 <br />35°' T=-11 <br />.22 .34 <br />.47 <br />.58.09 .80 <br />.93 <br />1.05 1.17 <br />1.29 <br />142 1.54 1.66 <br />E=.018 <br />.035 .054 <br />.072 <br />.086 109 .131 <br />.153 <br />.175 .107 <br />.213 <br />.230 .247 .264 <br />401 T=.13' <br />.26 .40 <br />.53 <br />.67 '.80 .93 <br />1.06 <br />1.20 1.34 <br />1.49 <br />1.64 1.79 1.94 <br />E =.023 <br />.046 .070 <br />.093 <br />.117 .141 .172 <br />.203 <br />.234 ,265 <br />.277 <br />.290 .315 .341 <br />45o T=.15 <br />.30 ,44 <br />.60 <br />.76 .91 1.06 <br />1.21 <br />1.37 1.52 <br />1.70 <br />1.87 2.94 2.21 <br />E x.030 <br />.060 .093 <br />.119 <br />.153 .184 .210 <br />.254 <br />.289 .325 <br />.351 <br />.378 .411 .445 <br />1 <br />A <br />