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II TABLE I. --- Tangents and Externals to a 1° Curve: <br />Chord =100 ft. <br />Inc.•Tangent <br />Angle <br />Curve 5° <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Incl <br />Angle <br />Tangent <br />External <br />1° <br />50.00 <br />.22 <br />8° <br />400. GG <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 />"0 <br />60.67 <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 />62.82 <br />40 <br />83.34 <br />.61 <br />40 <br />434.17 <br />16.43 <br />40 <br />788.26 <br />63.97 <br />50 <br />01.68 <br />.73 <br />SO <br />442.55 <br />17.07 <br />50 <br />796.75 <br />65.13 <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 />lOS.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 />3O <br />125:02-1.36 <br />122.63 <br />30 <br />476.10 <br />19.75 <br />30 <br />'.830.76 <br />59.91 <br />40 <br />133.86 <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 />492.58 <br />21.10 <br />50 <br />847.78 <br />62.38 <br />3 <br />150.04 <br />1.96 <br />10 <br />501,28 <br />21.69 <br />17 <br />856.80 <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 />IG6.72 <br />2.43 <br />20 <br />518,08 <br />23.38 <br />20 <br />873.35 <br />66.18 <br />30 <br />175.00 <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 />651.70 <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 />668.53 <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 />75.40 <br />40 <br />233.47 <br />4.7G <br />i 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 />503,79 <br />30.68 <br />50 <br />950.25 <br />78.26 <br />20 <br />1322.8 <br />150,71 <br />33 <br />1697.2 <br />246.1 <br />40 <br />'2085.4 <br />367.7 <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 />258.61 <br />5.83 <br />10 <br />G10,64 <br />32.45 <br />10 <br />967.381 <br />81.09 <br />20 <br />266.SG <br />6.21 <br />20 <br />619.07 <br />83.35 <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 />093.12 <br />85.43 <br />50 <br />291.02 <br />7.43 <br />50 <br />644.37 <br />38,12 <br />50 <br />1001.7 <br />86.90 <br />6 <br />`30a.:�8 <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 />8.81• <br />10 <br />661.25 <br />38.03 <br />10 <br />1018.9 <br />89.89 <br />20 <br />316.09 <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 />078.15 <br />39.99 <br />30 <br />1036,1 <br />92.92 <br />40 <br />333.71 <br />9.71 <br />40 <br />086. GO <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />.50 <br />342,08 <br />10.20 <br />50 <br />695. OG <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 />338.81 <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 />1070.2 <br />100.75 <br />30 <br />375.64 <br />12.29 <br />30 <br />728.90 <br />46.15 <br />30 . <br />1487.8 <br />102.35 <br />40 <br />333.01 <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 />1 745.85 <br />48.34 <br />50 <br />1L05.1 <br />105.60 <br />Corrections to be Added (T =Tangent. E =External.) <br />int. <br />Angle <br />Curve 5° <br />10° 15° 20° 25° 30° <br />35° 40° 45° <br />5O° <br />55° 60° <br />65° 7 <br />50 <br />T=.02 <br />.03 ' .OS .00 OF .10 <br />.11 .13 .16 <br />.16 <br />.18 .20 <br />.21 <br />188:51 • <br />E =.000 <br />.000 .001 •OO1 .002 .002 <br />.002 .003 •003 <br />.22 .25 .28 <br />.004 <br />.31 <br />.004 .004 <br />.34 .38 <br />.005 <br />2 <br />100 =,03 <br />.06 .09- .13 16 .19 <br />190.74 <br />1 =.00I <br />003 .004 .008 .007 ..008 <br />.009 011 .012 <br />.014 <br />.015 .017 <br />.018 •i <br />15° <br />T=•04 <br />.10 14 .19 .24 .29 <br />.34 .39 .45 <br />.51 <br />.53 '.58 <br />.63J <br />1130.7 <br />L-.003 <br />.007 .010 .014 .018 .023 <br />.027 .029 .032 <br />.45 51 58 <br />.035 <br />.65 <br />.039 .043 <br />.72 <br />.047 <br />200 T = 06 <br />.18 :19 .26 .82 3B <br />-1148,4. <br />E =.000 <br />.011 .017 .022 A28 •034 <br />.038_ .045 .051 <br />.057 <br />.063 .070 <br />.076 <br />25 o <br />TL.08 <br />78 .24 33 40 .40 <br />.56 .67 .75 <br />.83 <br />.90 .99 <br />.1.00 1• <br />50 <br />% =.009 <br />,018 .027 .030 .048 .058 <br />.065 .074 .083 <br />.093 <br />.108 .120 <br />.127 <br />3 <br />05 <br />6 <br />20 <br />51 <br />0 <br />35 <br />TABLE I. - Tangents and Externals to a 1° Curve: IFI <br />Chord =100 f t. <br />Int. <br />Angle' <br />Tangent <br />External <br />lilt, <br />Angle <br />Tangent <br />g <br />Fxtenral <br />Int. <br />Angle <br />Tangent <br />g <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 />10� <br />11_2.4 <br />108.90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />1870.9 <br />297.7 <br />2U <br />1131'.0 <br />-110.57_ <br />20 <br />1499.6 <br />192.99 <br />20 <br />ISSO.1 <br />300.6 <br />3U <br />1130.7 <br />112.25 <br />30 <br />1508.5 <br />195.25 <br />30 <br />1SS9.4 <br />303.5 <br />•'4U <br />-1148,4. <br />113,95 <br />40 <br />1517.4 <br />197.53 <br />40 <br />1893.6 <br />306.4 <br />SU <br />1157.0 <br />115.GG <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 />200.77, <br />20 <br />1935.7 <br />318:1 <br />30 <br />1101.8 <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 />5o, <br />1209.2 <br />120,20 <br />50 <br />1580.0 <br />213.86 <br />50 <br />1903.6 <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 />20 <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 />1024.9 <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 />$2. <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 />2060.6 <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 />20 <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 />154.09 <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 />253.0 <br />30 <br />2113.8 <br />377.5 <br />40 <br />1358.0 <br />158.72 <br />40 <br />1733.5 <br />250.5 <br />40 <br />2123.3 <br />380.8 <br />50 <br />136G.8 <br />160,70 <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 />r <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 />177.65 <br />10 <br />1815.7 <br />280.8 <br />10 <br />2200.0 <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 />280.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />1464.0 <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 .e <br />Angie <br />Curves° 110° <br />15° <br />20° 1 <br />25° 30° <br />35° <br />400 <br />45° <br />50° <br />55a 60° 65" <br />701 <br />zoo <br />T=.06 .13 <br />.19 <br />.26 <br />.32 .39 <br />.45 <br />I .51 <br />.58 <br />.65 <br />.72 .79 .84 <br />.90 <br />E =.006 ' .011 <br />.017 <br />.022 <br />.028 .039 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 .0"e0 .076 <br />.083 <br />25° <br />T=.08 .16 <br />.24 <br />.33 <br />.40 .49.58 <br />.67 <br />.75 <br />.83 <br />.90 .99 1.06 <br />1.14 <br />E.--009 .018 <br />.027 <br />.036 <br />.045 .058 <br />.065 <br />.074 <br />.083 <br />.093 <br />.106 .120 :127 <br />.135 <br />300 <br />T=.10 .19 <br />.29 <br />.39 <br />.49 .59 <br />.60.79 <br />.89 <br />.99 <br />1.09 1.20 1.29 <br />1.39 <br />E=.013 .025 <br />.038 <br />.051 <br />.055 .078 <br />.090 <br />.103 <br />.116 <br />.129 <br />.149 .I70 .179 <br />.188 <br />3a° <br />F=.11 .22. <br />.58 .69 <br />.80 <br />. 93 <br />1.05 <br />1.17 <br />1.29 1 1.54 <br />.42 <br />1.60 <br />E=.019 .035 <br />.054 <br />.0734 <br />2 <br />.086 .109 <br />.131 <br />.153 <br />-.175 <br />.197 <br />.213 .230 •247 <br />.264 <br />40o <br />T=.13 26 <br />.40 <br />.53 <br />.67 .80 <br />.93 <br />1.06 <br />1.20 <br />1.34 <br />1.49 1.64 1.79 <br />1.94 <br />.016 <br />.070 <br />.093 <br />.117 .141 <br />.172 <br />.203 <br />.234 <br />265 <br />.277 .290 .315 <br />.341 <br />--E=.023 <br />450 <br />T =.15 .30 <br />A4 <br />.60 <br />.76 .91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 1.87 2.04 <br />2.21 <br />E-.030 .000 <br />.093 <br />.119 <br />.153 .1 S4 <br />.216 <br />.2541 <br />.289 <br />.325 <br />.351 .3;8 .411 <br />.445 <br />