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II TABLE I. - Tangents and Externals to a 1° 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 />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 />762.80 <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 />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 />.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.OG <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 />484.49 <br />20.45 <br />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 />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 />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 />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 />1270.2 <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />.39 <br />2029.0 <br />348.6 <br />4 <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 />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.G9 <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. SG <br />6.21 <br />20 <br />619.07 <br />33.35 <br />20 <br />075.96 <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 />316.90 <br />8.76 <br />20 <br />669.70 <br />39.01 <br />20 <br />1027.5 <br />01.40 <br />30. <br />325.35 <br />9.23 <br />30 <br />G78.15 <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 />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° <br />Angle <br />10° <br />15° <br />20° 25o <br />30° <br />35° 40° <br />45° <br />50° 55° <br />60° <br />65° <br />70° <br />5- T=.02 <br />.03 <br />.05 <br />.06 .08 <br />.10 <br />.11 .13.15 <br />. 294.9 <br />.16 .18 <br />.20 <br />.21 <br />.23 <br />E=.000 <br />.000 <br />.001 <br />.001 .002-002 <br />297.7 <br />.002 .003 <br />.003 <br />.004 .004 <br />.004_.005 <br />1499.6 <br />.005 <br />10 o T=.03 <br />.06 <br />.09 <br />.13 .16 <br />.19 <br />.22 .25 <br />.28 <br />.31 .34 <br />.38 <br />.42 <br />.46 <br />E=.001 <br />.003 <br />.004 <br />.006 .007 <br />.008 <br />.009 .011 <br />.012 <br />.014 .015 <br />.017 <br />.018 <br />.020 <br />15o T=.04 ' <br />.10 <br />.14 <br />'.19 .24 <br />.29 <br />.34 .39 <br />.45 <br />.51 .53 <br />.58 <br />.63 <br />.68 <br />;E =.003 <br />007 <br />.010 <br />.014 .018 <br />.023 <br />.027 .029 <br />.032 <br />.035 .039 <br />.043 <br />.047 <br />.051 <br />20o T =.06 <br />.13-' <br />.19 <br />.26 .32 <br />39 <br />.45 .51 <br />58 <br />..65 .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 .063 <br />.070 <br />.076 <br />.083 <br />25o T=.08 <br />.16 <br />.24 <br />.33 .40 <br />.49 <br />.58 .67 <br />.75 <br />.83 .90 <br />.99 <br />1.06 <br />1.14 <br />E =.009 <br />.018 <br />i .027 <br />.038 .046 <br />.058 <br />.085 .074 <br />..083 <br />.093 .106 <br />.120 <br />.127 <br />.135 <br />TABLE I. = Tangents and'Externals to a 16 Curve.' III <br />Chord =100 f t. <br />Int. <br />Angle <br />Tangent <br />External <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 />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 />101926.4 <br />1.17 1.29 <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 •:.1945.0. <br />1.34 1.49 <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 />381972.9 <br />.325 .351 <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 />36'77 <br />10 <br />1331.6 <br />152.69 <br />10 <br />170G.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 />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 />30 <br />1834.1 <br />286.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />A 464.0 <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 <br />Curve 5° <br />10° 15° <br />20° 1 25° <br />30° <br />35° 40° <br />45° <br />1 50° 55° <br />60° 65° .70' <br />20o <br />T=.06 <br />.13 ..19 <br />.26 .32 <br />.39 <br />.45 .51 <br />.58 <br />.65 .72 <br />'.79 .84 <br />E=-006 <br />.011 .017 <br />.022 .028 <br />.034 <br />.038 .045 <br />.051 <br />.057 .063 <br />,.90 <br />.070 .076 .083 <br />25o <br />T=.08 <br />.16 . .24 <br />.33 .40 <br />.49.58 <br />.67 <br />.75 <br />..83 .90 <br />.99 1.06 1.14 <br />E=.009 <br />-,i= <br />.018 .027 <br />.036 .046 <br />.056 <br />.065 .074 <br />.083 <br />.093 .106 <br />1.127 .135 <br />301 <br />10 <br />.19.29 <br />.39 .49 <br />.59 <br />.69 .79 <br />.89 <br />.99 1.09 <br />1.20 1.29 1.39 <br />E=.013 <br />.025 .038 <br />.051 .065 <br />.078 <br />.090 .103 <br />.116 <br />.129 .149 <br />..170 ..179 .188 <br />35° <br />T=.11 <br />.22 .34 <br />.47 .58 <br />.69 <br />.80 .93 <br />1.05 <br />1.17 1.29 <br />1.42 1.54 1.66 <br />E=.018 <br />.035 .054 <br />.072 .086 <br />.109 <br />.131 .153 <br />.175 <br />..197 ..213 <br />'.230 .247 .264 <br />40° <br />T=.13 <br />.26 .40 <br />.53 .67 <br />.80 <br />.93 1.06 <br />1.20 <br />1.34 1.49 <br />1.64 1.79 1.94 <br />E =.023 <br />.046 .070 <br />.093 .117 <br />.141 <br />'.172 .203 <br />.234 <br />.265 '.277 <br />.290 .315 '.341 <br />45° <br />T=.15 <br />.30 .44 <br />.60 .76 <br />.91 <br />1.06 1.21 <br />1.37 <br />1.52 1.70 <br />1'.87 2.04 2.21 <br />E =.030 <br />'.060 .093 <br />.119 ..153 <br />.184 <br />.216 .254 <br />.289 <br />.325 .351 <br />.378 .411 .445 <br />V <br />