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i 41 II TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord= 100 ft. <br />t. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Int. Angle <br />Tangent <br />External <br />1° <br />50.00 <br />22 <br />8°400.66 <br />50 <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 />40'_ <br />762.80 <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 />36.43 <br />'v :_40 <br />'488:26 <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 />, .87 <br />9 <br />450.93 <br />17.72 <br />16 <br />805.25' <br />a 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 <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 />.51 <br />40 <br />133.36 <br />1.55 <br />40_ <br />484.49 <br />..20.45 <br />w 40 <br />839.27,' <br />_•59.91 <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 />8 <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 />509.68 <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 />-66.19 <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 />', 26:50 <br />IS <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 />576.95 <br />28.9730 <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 />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 />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 />x''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 />92.92 <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 />30 <br />1087.8 <br />418.0 <br />40 <br />-383.91 <br />° -12.85 <br />40 . <br />_ 737: 37..' <br />.47.25 <br />',",,:'40 , <br />1096.4' <br />.102.35 <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. <br />Angle <br />Curve 5° <br />10° <br />15° <br />20°. <br />25° ,30° <br />35° <br />40° <br />45° <br />50° <br />55° 60° <br />65° <br />70° <br />50 <br />T=.02 <br />.03 <br />.05 <br />.06 <br />.08- ':10 <br />.:11 <br />"--.13 <br />.15 <br />.16 <br />".18 .20 <br />.21 <br />.23 <br />297.7 <br />E =.000 <br />.000 <br />.001 <br />.001 <br />.002 .002 <br />.002 <br />.003 <br />.003 <br />.004 <br />.004 .004 <br />.005 <br />.005 <br />loo <br />T =.03 <br />.06 <br />.09 <br />.13 <br />.16 .19• <br />.22 <br />-.25; <br />-28'. <br />'.31 <br />.34 .38 <br />.42 <br />.46 <br />1898.6 <br />E=.001 <br />.003 <br />.004 <br />..006 <br />.007 .008 <br />.009 <br />.011 <br />.012 <br />.014 <br />.015 ,017 <br />.018 <br />.020 <br />15o <br />T=.04 <br />.10 <br />.14 <br />.19 <br />.24 .29 ' <br />'.34 <br />.39 <br />.45 <br />.51 <br />.53 .58 <br />.63 <br />.68 <br />. 10 <br />E=.003 <br />.007 <br />.010 <br />.014 <br />.018 .023 <br />.027 <br />.029-032 <br />206.77 <br />.035 <br />.039 ,043 <br />.047 <br />.051 <br />20o <br />T=.06 <br />, ':13 <br />.19 ' <br />.26 <br />.32 .39 <br />.45 <br />.51 <br />.58 <br />".65 <br />.72 .79 <br />.84 <br />.90 <br />211.48 <br />E=006 <br />1 <br />.011 <br />'.017 <br />.022 <br />.028 .034 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 .070 <br />.076 <br />.083 <br />25o <br />T=:08 <br />.16 <br />.24 <br />.33 <br />.40 ..49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 .99 <br />1:06 <br />1.14 <br />1598.0 <br />E=.009 <br />018 <br />.027 <br />'.036 <br />.046 .056 <br />.065 <br />:074 <br />.083 <br />.093 <br />.106 .120 <br />.127 <br />_135 <br />TABLE L 7- Tangents and Externals to a-1° Curve, ' <br />Chord =100 ft. <br />Int: 'Tangent <br />Angle <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />220 <br />1113.7 <br />107.24 : <br />29° <br />1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.9 <br />10/ <br />1122.4 <br />108.90 <br />101 <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 />202.42 <br />37 <br />1917.1 <br />312:2 <br />( 10 <br />1174.4 <br />119.12 <br />1.10 ' <br />1544.2 <br />204.44 <br />. 10 <br />1926.4 <br />315.2- <br />1 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 />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 />348.6 <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 />50 <br />1314.0 <br />148.75 <br />'50 <br />1688.1 <br />243.5 <br />50 <br />2076.0 <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 />,130 <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 />275.3 <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 />1455.1 <br />.181.89 <br />1834.1 <br />286.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />1464.0 <br />,184.08 <br />.30 <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 />Angle • Curve 5° <br />.10° <br />.156 <br />.20° 25° <br />30° <br />35°' 40° <br />45° <br />1 50° <br />55° <br />60° <br />65° <br />70° <br />2p° T=.06 <br />.13.19 <br />.26 .32 <br />-.39 <br />.45 .51 <br />.58 <br />•.65 <br />.72 <br />.79 <br />.84 <br />.90 <br />E=.006 <br />.011 <br />.017 <br />.022 .028 <br />.034 <br />.038 .045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 <br />.083 <br />25° T=:08 <br />.16 <br />.24 <br />'..33 .40 <br />.49 <br />.58 .67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.06 <br />1.14 <br />E =.009 <br />.018 <br />.027 <br />.036 .046 <br />.056 <br />'.065 .074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 <br />.135 <br />309 ' T=.10' <br />.19 <br />.29 <br />.39 .49 <br />.59 <br />.69 .79.89 <br />.99 <br />1.09 <br />1.20 <br />1.29 <br />1.39 <br />E=.013 <br />.025 <br />.038 <br />.051 .065 <br />.078 <br />.090 .103 <br />.116 <br />.129 <br />.149 <br />.170 <br />.179 <br />.188 <br />35° T=.11 - <br />.22 <br />.34 <br />.47 .58 <br />.69 <br />.80 .93 <br />1.05 <br />1.17 <br />1.29 <br />1.42 <br />1.54 <br />1.66 <br />E=.018 <br />.035 <br />.054 <br />.072 .086 <br />.109 <br />.131 .153 <br />.175 <br />.197 <br />.213 <br />.230 <br />.247 <br />.264 <br />40° T=.13 <br />.26 <br />.40 <br />.67 <br />.80 <br />.93 1.06 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 <br />1.94 <br />E=.023 <br />.046 <br />.070 <br />..53 <br />.093 .117 <br />.141 <br />.172 .203 <br />.234 <br />.265 <br />.277 <br />.290 <br />.315 <br />.341 <br />450 T=.15 <br />.30 <br />.44 <br />.60 <br />.91 <br />1.06 1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 <br />2.21 <br />E =.030 <br />..060 <br />.093 <br />,.76 <br />,-.119 .153 <br />.184 <br />.216 .254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />.445 <br />