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II TABLE I. - Tangents and Externals to a P Curve. - - <br />Chord= 100 ft. <br />Angle <br />Tangent <br />External <br />' Angle <br />Tangent <br />External <br />: Angle <br />Tangent <br />External <br />1° <br />50.00: <br />".22 <br />8° .. <br />400. 66, <br />13.99• <br />" i6° <br />754.32 <br />49.44 <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- <br />.89 <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,._.91.68 <br />1157.0 <br />.73 <br />_ 50 <br />442.55 <br />17.07 <br />.50•. <br />,796.75 <br />•55.13 <br />8 <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 />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 ''822:25 <br />1935.7 <br />58.70 <br />80 <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 />_ <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 />1T <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 />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 />1624.9 <br />24.91 <br />40 <br />890.41 <br />68.77 <br />50 <br />191.74 <br />3.21 <br />50 <br />_534.89' <br />543.29 <br />25.70 <br />-50 <br />898.95 <br />70.09 <br />{ <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 />1670.0 <br />28.97 <br />30 <br />933.13 <br />75.49 <br />40 <br />233.47 <br />4.76 <br />- <br />40 <br />,576.95 <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 />d <br />250.16 <br />5.46 <br />12 <br />'602.21. <br />31.56 <br />19 <br />M.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 />81.09 <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 />35:18 <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 />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 />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 />91.40 <br />30 <br />325.35 <br />9.23 <br />80 <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 />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 />358.81 <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 />728.90 <br />46:18. <br />_ <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 />1 13.41 <br />1 50 <br />745.85. <br />48.34 <br />50 <br />11105.1 <br />105.60 <br />Corrections to be Added (T =Tangent. E = External.) <br />Int <br />Angle <br />Curve S. <br />10° 15° 20° <br />25° '30° 35° 40° 450 500 55° 600 65° 70° <br />5o <br />T=.02 <br />.03 .05 .06 <br />.08. .10 'Al .13. _.15 .16 .18 .20 21 '23 <br />Extemal <br />E =.000 <br />.000 .001 .001 <br />.002 .002 .:002 .003 '.003 .004 .004 .004 .005 .005 <br />10° <br />T=.03 <br />.06 .09 ,:13- <br />.16- .19 .22 .25 '.28 -=.31 :34 .38 .42 A6 <br />-:014 <br />1861.7 <br />E=.001 <br />.003 .004 -.006 <br />.007 .008 ..009 .011 .012 .015 .017 .018 .020 <br />IV <br />T=.04 <br />.10 .14 .19 <br />.24 .29 .34 .39 .45 .51 :'53 .58 .63 .68 <br />10' <br />E=.003 <br />.007 .010 .014 <br />.018 .023 .027 .029 .032 .035 .039 .043 .047 .051 <br />20o <br />T=.06. <br />.13 .19 .26 <br />.32 .39 .45 .51 .58 .85 :.72 .79. .84 .90 <br />192.99 <br />E =.006 <br />.011 .017 .022 <br />.028 .034 .038 .045 .051 .057 .063 .070 .078 .083 <br />25° <br />T=.08 <br />.18 .24' .33 <br />.40 .49 .58 67 .75 .83 .90 .99 1.06 1A.14. <br />.1508.5 <br />E=.009 <br />.018 .027 .038 <br />.046 .058 .065 ..074 .083 .093 .106 .120 .127 .135 <br />I <br />r <br />i; <br />•T. sLm L Tangents and Externals to a 1° Curve. IIY <br />Chord =100 f t. <br />t. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />Extemal <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 />115.66 <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 />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 />1972.9 <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 />11991.5 <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 />348.6 <br />10 <br />1279.0 <br />141.01 <br />16 <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 />50 <br />1314.0 <br />148.75 <br />50 <br />1688.1 <br />243.5 <br />50 <br />2076.01 <br />364.5 <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 />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 />880.8 <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 />341751.7 <br />261.8 <br />41 <br />2142.2 <br />387.4 <br />10 <br />1384:4 <br />164.86 <br />110 <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 />80 <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 />275.3 <br />50 <br />.2189.9 <br />404.2 <br />28= <br />1428.6 <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 />4455.1 <br />181.89 <br />30 <br />1834.1 <br />286.4 <br />30 <br />2228.1 <br />'418.0 <br />:740, <br />4464:0, <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 Curve S° 10° <br />15° <br />20° 25° <br />30° <br />1 35° <br />40° <br />1 45° 50° <br />'SS' 60° 65° 70° <br />.20" T=.06 .13 <br />.19 <br />26 ..32 <br />.39 <br />.45 <br />.51 <br />.58 .65 <br />.72 .79 .84 .90 <br />E=.006 .011 <br />.017 <br />.022 .028 <br />..034 <br />.038 <br />.045 <br />.051 .057 <br />.063 .070 .076 .083 <br />25° T=.08 .16 <br />.24 <br />.33 .40 <br />.49 <br />.58 <br />.67 <br />.75 .83 <br />.90 .99 1.06 1.14 <br />:. E=.009 .018 <br />.027 <br />..036 .046 <br />.056 <br />.065 <br />..074 <br />.083 .093 <br />.106 -.120 .127 .135 <br />$0° T=10 .19.29 <br />.39 .49 <br />.59 <br />.69 <br />.79 <br />.89 .99 <br />1.09 1.20 1.29 1.39 <br />E=.013 .025 <br />.038 <br />.051 .065 <br />.078 <br />.090 <br />.103 <br />.116 .129 <br />.149 .170 .170 .188 <br />35° T=.11 22 <br />.34 <br />.47 .58 <br />.69 <br />.80 <br />.93 <br />1.05 1.17 <br />1.29 1.42 1.54 1.66 <br />E=.018 .035 <br />.054 <br />.072 .086 <br />.109 <br />.131 <br />.153 <br />.175 .197 <br />.213 .230 247 264 <br />40o T=.13 .26 <br />.40 <br />.53 .67.80 <br />.93 <br />1.06 <br />1.20 1.34 <br />1.49 1.64 1.79. 1.94 <br />E=.023 .046 <br />.070 <br />.093 .117 <br />.141 <br />.172 <br />.203 <br />.234 .265 <br />277 .290 .315 .341 <br />45° T=.15 .30.44 <br />.60 .76 <br />.91 <br />1.06 <br />1.21 <br />1.37 1.52 <br />1.70 1.87 2.04 2.21 <br />E=-030 '.060 <br />.093 <br />.119 .153 <br />.184 <br />216 <br />254 <br />289 .325 <br />351 .378 .411 .445 <br />