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II TABLE I. - Tangents and -Externals to a 1° Curve. <br />Chnrrl_100 ft._ <br />Int. <br />Angle <br />Tangent <br />External <br />` Int. <br />Angle <br />Tan Tangent <br />S <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />1° <br />50.00 <br />.22' <br />S. <br />400.66 <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 />10' <br />762.50 <br />50.55: <br />20 <br />66.67 <br />.39 <br />20 <br />417.41 <br />15.18 <br />20 <br />77.1:29 <br />51.63 <br />30 <br />75.01 <br />.49 <br />30 <br />'425.79 <br />15.50 <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 <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 />'.S7 <br />9 - <br />450.93 <br />17,72 <br />'10 <br />805:25 <br />7. <br />56.3Y <br />10 <br />108.35 <br />1.02.. <br />10_ <br />459:32 <br />18.38 <br />2 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 />55.70 <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 />484.49 <br />20.45 <br />40 <br />'839.27 <br />61.14' <br />50 <br />141.70: <br />1.75 <br />50 <br />r <br />492.SS <br />21.16 <br />50 <br />'847.78 <br />62.38 <br />3 <br />150.04 <br />1.90 <br />10 <br />501.28 <br />21.59 <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 />804.82 <br />64.90., <br />20 <br />166.72 <br />` ' 2:43 <br />20 <br />518.03 <br />23.38 <br />20 <br />573.35 <br />66.18 <br />30 <br />175.06 <br />2.67 <br />30 <br />526.45 <br />24.14 <br />30 <br />891.88 <br />67.47 <br />40 <br />153.40 <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 />598.95 <br />70.09 <br />4 <br />200.03 <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 />28.97 <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 />70.86 <br />•50 <br />241.81 <br />5.10 <br />50 <br />593.79 <br />30.68 <br />50 <br />950.25 <br />75.26 <br />5 <br />250.16 <br />5.46 <br />12 <br />602.21 <br />31.56 <br />19 <br />95S.S1 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10 <br />610.64 <br />32.45 <br />10 <br />9G7.38 <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 />55.43 <br />50 <br />291.92 <br />7.43 <br />50 <br />644.37 <br />36.12 <br />50 <br />1001.7 <br />36.90 <br />6 <br />300.28 <br />7.S6 <br />13 <br />652.51 <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 />89.59 <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 />675:15 <br />39.99 <br />30 <br />1036. 1' <br />92.92 <br />•40 <br />333.71 <br />0.71 <br />40 <br />G86.60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 <br />342.OS <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 />12.20 <br />30 <br />725.90 <br />46.15 <br />•30 <br />1037.8 <br />102.35 <br />40 <br />333.91 <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 />105.60 <br />Corrections to.be Added (T =Tangent. E=External.) <br />Int. Curve 5° 10° 150 200 <br />Angle <br />250 <br />300.. <br />35° <br />400 <br />450 <br />50° <br />55° <br />60° <br />65° <br />70°. <br />5. T =.02 .03 .05 .05 <br />•..08 <br />-.10 <br />'.11 <br />.13 <br />.15 <br />.16 <br />.18 <br />.20 <br />-.21 <br />.23 <br />E=.000 .000 .001 .001 <br />.002 <br />.002 <br />.002 <br />.003 <br />.003 <br />.001 <br />.004 <br />.004 <br />.005 <br />.005 <br />10° T =.03 .00 .09 .13 <br />.16 <br />.19 <br />.22 <br />.25 <br />.28 <br />"3' <br />1508.5 <br />.38 <br />.42 <br />:46 <br />E=.001 .003 .004 .000 <br />.007 <br />.008 <br />.009 <br />.011 <br />.012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />15o T=.04 .10. '.14 .19.24 <br />115.66 <br />.29 <br />.34 <br />.39 <br />.45 <br />.51 <br />.53 <br />.58 <br />.63 <br />.68 <br />E=.003 .007 .010 .014 <br />.018 <br />.023 <br />.027 <br />.029 <br />.032 <br />.035 <br />.039 <br />.G43 <br />.047 <br />.051 <br />20° T=.06 - .13 .19 <br />10 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79.84 <br />206.77 <br />.90 <br />E =.006 .011 .017 <br />318.1 <br />.D34 <br />.035 <br />.045 <br />.051 <br />.057 <br />.063 <br />:070 <br />.076 <br />.083 <br />25° T=.08 .16 .24.49 <br />+,2%,,30-;123 <br />124.41 <br />.58 <br />.67 <br />.75 <br />.83.99 <br />1954.3 <br />324.1 <br />1.00 <br />1.14 <br />E=.009 .018 .027 <br />50 <br />.050 <br />.005 <br />.074 <br />,.053 <br />.093 <br />.106 <br />.120 <br />.127 <br />.135 <br />I <br />4 <br />1 <br />I. <br />TABLE I. - Tangents and Externals to a 1` Curve. <br />Chord =100 ft. <br />Angle <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />22° <br />1113.7 <br />107.24 <br />29° <br />1481.8 <br />158.51 <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 />19.5.25 <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 />199.52 <br />50 <br />1907.9 <br />309.3 <br />23 <br />-1165.7 <br />117.33 <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 />1952.2 <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 />1201.5 <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 />2047.5 <br />354.9 <br />'30 <br />1296.5 <br />144.85 <br />30 <br />.1670.0 <br />238.4 <br />30 <br />2U57.2 <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 />2016.0 <br />364.5 <br />26 <br />1322.8 <br />150.71 <br />33 <br />1G97.2 <br />246.1 <br />40 <br />2055.4 <br />3G7.7 <br />10 <br />1.331.6 <br />152.69 <br />10 <br />1706.3 <br />248:7 <br />1 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 />135S.0 <br />158.7240 <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.G <br />259.1 <br />50 <br />2132.7 <br />384.1 <br />27 <br />1375.6 <br />162.51 <br />34 <br />1751.7 <br />261.8 <br />41 <br />2142.2 <br />387.4 <br />10 <br />1354.4 <br />164.86 <br />10 <br />1760.8 <br />2&t.5 <br />10 <br />2151.7 <br />390.7 <br />20 <br />1393.2 <br />166.95 <br />20 <br />1.770.0 <br />2G7.2 <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 />1753.2 <br />272.6 <br />40 <br />2150.3 <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 />1506.6 <br />278.1 <br />42 <br />2199.4 <br />407.6 <br />10 <br />1437.4 <br />177.55 <br />10 <br />1515.7 <br />280.8 <br />10 <br />2209.0 <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />- 20 <br />1524.9 <br />283.6 <br />20 <br />2218.6 <br />414.5 <br />30 <br />1455.1 <br />181.89' <br />30 <br />'IS34.1 <br />236.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />1464.0. <br />184.03 <br />40 <br />1843.3 <br />259.2 <br />40 <br />2237.7 <br />421.4 <br />50_ <br />1472.9 <br />136.29 <br />50 ' <br />1S52.5 <br />.292.0 <br />5Q <br />2247.3 <br />425.0 <br />Corrections to be Added (T =Tangent. F = External.) <br />Angle <br />Curve 5° <br />10° 15° <br />20° <br />25° <br />30° <br />35° <br />40° 45° 50° <br />55° <br />60° <br />65° <br />70° <br />20o <br />T=.06 <br />.13 .19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 .5S 65 <br />.72 <br />.79 <br />.84 <br />.90 <br />E=.006 <br />.011 .017 <br />.022 <br />.028 <br />.034 <br />.038 <br />.045 .051 .057 <br />.063 <br />.070 <br />.076 <br />.083 <br />"25° <br />T=.03 <br />.16 .24 <br />.33 <br />.40 <br />.49 <br />.58 <br />.67 .75 .83 <br />.90 <br />.99 <br />1.06 <br />1.14 <br />E =.009 <br />.018 .027 <br />.036 <br />.046 <br />.05G <br />.065 <br />.074 .093 .093 <br />.106 <br />.120 <br />.127 <br />.135 <br />30° t <br />'1'=.10 <br />.19 29 <br />.39 <br />.49 <br />.59 <br />.69 <br />.79 .89 .99 <br />L09 <br />1.20 <br />1.29 <br />1.39 <br />E=.013 <br />.025 .038 <br />.051 <br />.065 <br />.078 <br />.090 <br />.103 .11G .129 <br />.149 <br />.170 <br />.179 <br />.188 <br />35° <br />T=.11 <br />.22 .34 <br />.47 <br />.58 <br />.69 <br />.80 <br />.93 1.05 1.17 <br />1.29 <br />1.42 <br />1.54 <br />1.60 <br />E=.018 <br />.035 .054 <br />.072 <br />.086 <br />.109 <br />.131 <br />.153 .175 .197 <br />.213 <br />230 <br />.247 <br />.264 <br />40° <br />T=.13 <br />.26 .40 <br />.53 <br />.67 <br />.SO <br />.93 <br />1.06 1.20 1.34 <br />1.49 <br />1.64 <br />1.79 <br />1.94 <br />E =.023 <br />.046 .070 <br />.093 <br />.Ili <br />.141 <br />.172 <br />.203 .234 .265 <br />.277 <br />290 <br />.315 <br />.341 <br />45° <br />T=.15 <br />.30 .44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />1.21 1.37 1.52 <br />1-70T1-87 <br />2.04 <br />2.21 <br />E=.030 <br />.060 .093 <br />.119 <br />.153 <br />.1841-.216 <br />.254 .289 .325 <br />.351 <br />.378 <br />.411 <br />.445 <br />