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TABLE I.-- Tangents and Externals to a 1° Curve. <br />Chord=100•ft. <br />i <br />i f�ii, • <br />I{ j �• l <br />r' <br />Angle <br />Tangent <br />7-, <br />External <br />•Angle <br />Tangent <br />External <br />Int. e. <br />Tangent <br />Extemat <br />. <br />1° <br />50.00 <br />;22- <br />8°. <br />.400.66 <br />13.99 <br />15° ' . <br />754.32 <br />49,44 <br />10P <br />5S-34 <br />' " ,30- <br />-10' <br />409.03 <br />14.58 <br />lo" <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 SO <br />30 <br />% 77077_ <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 />9111.68 <br />73 <br />50 <br />,442.55 <br />17.07 <br />50- <br />796.75 <br />55.13 <br />2 <br />%100O1 <br />'87.9 <br />T=.U4 <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 />S13:75 <br />67.50 <br />20 <br />116:68 <br />1:1920.. <br />.027 <br />"467.71. <br />19.06 <br />20 <br />822.25- <br />58.70 <br />30 <br />,125.02 <br />; ' 1:36; <br />_r 30 <br />.26 <br />19.75 <br />30,• <br />• 830.76 <br />59.91 <br />40 ' <br />`133236:' <br />• • "1`.55 <br />40• <br />'476.10 <br />434.49 <br />20,45 <br />40' <br />839.27 <br />6 1. 14 <br />50 <br />141170. <br />.1.75 <br />- '.50 <br />5492.88 <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 />1158.35 <br />2:19• <br />10:!209.68 <br />1598.0 <br />22.62 <br />_ 10'. <br />. 864.82 <br />61.90 <br />20 <br />166:72 <br />2.43" <br />20. <br />a18.08 <br />23.38. <br />20- <br />873.35 <br />66.13 <br />30 <br />175.06 <br />2.67 <br />30 <br />526.48 <br />24:14 <br />'30 <br />SSI.SS <br />67.47 <br />40 <br />183.40 <br />2.93. <br />40' <br />:534.89 <br />-24.91 <br />40 <br />590.41 <br />68.77 <br />50 <br />191.74 <br />3.21 <br />50 <br />543.29 <br />25.70 <br />50 <br />893.95 <br />70.09 <br />4-_200..OS <br />1279.0 <br />3.49 <br />-11 <br />551.70 <br />26.50: <br />1$ . <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 />0.16.03 <br />72.76 <br />20 <br />216.77 <br />4.10 <br />20 <br />508.53 <br />23.14 <br />20 <br />'924.58 <br />74.12 <br />30 <br />225.12 <br />4,42 <br />.30 <br />576:95 <br />-25.97 <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 />76.86 <br />50 <br />241.51 <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 />3 1: 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 />967.35 <br />81.09 <br />20 <br />'266.86 <br />6.21 <br />20. <br />619.07 <br />33.35 <br />20_ <br />97.5.96 <br />52.53 <br />30 <br />275.21 <br />1 6:61 <br />30 <br />627.50 <br />34.26 <br />30... <br />934.53 <br />53.97 <br />40 <br />283.57 <br />= 7.01 <br />40 <br />635.93 <br />35.18 <br />40 <br />993.12 <br />S5.43 <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'.80" <br />13 ' <br />652.81 <br />37.07 <br />" 20 <br />1010.3- <br />88.39 <br />10 <br />308164 <br />! 8.31 <br />10 <br />66 1.25 <br />38.03 <br />10.. <br />1015.9: <br />59.89 <br />20-.316.99 <br />, <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 />678f75 <br />39.99 <br />30 <br />1036.1 <br />92.92 <br />40 - <br />333:73 <br />9.71 <br />40 <br />656.60• <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 <br />3.12.08 <br />.r 10.20 <br />50 <br />"605:06 <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 />108.9 <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 />7'28.90. <br />46.13 <br />30 <br />-lOS7.S <br />102.35 <br />40 <br />383.91'' <br />12.85' <br />40 ' <br />737.37 <br />47.25 <br />40 <br />10961.4 <br />103.97 <br />50 <br />392.23 <br />13.41 <br />50 <br />.745.85 <br />48.34- <br />50 <br />1105.1 <br />105. GO <br />Corrections to be Added (T=Tangent. - E=External.). <br />Int <br />AngieI. <br />I Cun a S. <br />10° IS° <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />5° <br />T=.02 <br />.03 .05 <br />1 .06 <br />.08 <br />-.10.11 <br />112:4 <br />.13 <br />.15 <br />.16 <br />.18 <br />.20 <br />.21 ' <br />297.7 <br />E=.000 <br />.000 .001 <br />.001 <br />.002 <br />.002 <br />.002 <br />:003 <br />.0031 <br />.004 <br />.004 <br />.004 <br />•005 <br />10° <br />T=.03 <br />.06 .09 <br />,13 <br />.16- <br />.19 <br />22 <br />.25 <br />.23 <br />.31 <br />.34 <br />.38 <br />.42 <br />1898.6 <br />E-.001 <br />.003 .OU4 <br />.006 <br />.007 <br />.008 <br />.009 <br />.011 <br />.012 <br />.014 <br />..015 <br />.017 <br />.018 <br />15° <br />T=.U4 <br />.10 .14 <br />.l9 <br />.24 <br />.20 <br />:34 <br />.39 <br />.45 <br />.5l <br />53 <br />.58 <br />.G3 <br />10 <br />E =.003 <br />.007 .010 <br />.014 <br />.018 <br />.023 <br />.027 <br />.029 <br />.032 <br />.035 <br />.039 <br />.043 <br />.047 <br />20° <br />T =.OG - <br />.13.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />S4 <br />211.48 <br />E =.006 <br />.011 .017 <br />.022 <br />.028 <br />-.034 <br />.038 <br />.015 <br />.051 <br />.057 <br />.063.070 <br />1963.6 <br />.076 <br />25o <br />T=.03 <br />.16 .24 <br />.33 <br />.40 <br />.49 <br />.53 <br />.67 <br />.75 <br />.83 <br />.90 <br />go <br />1.06 I <br />1598.0 <br />E=.009 <br />.018 .027 <br />.036 <br />.046 <br />.0.56 <br />.055 <br />.0741 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 <br />70° <br />23 <br />.005 <br />.46 <br />.024 <br />.68 <br />.051 <br />.90 <br />.083 <br />.135 <br />Te�1i% L'= Tangents and Eih'ernals.to.w1o.-Curve. <br />Chord=100 ft. <br />Int. <br />-Angle <br />Tangent..External <br />Int.. <br />' Mgle <br />Taiisent <br />Ft, <br />Int. <br />.Angle <br />Tangent <br />E _ <br />° <br />-1113.7 <br />107:24 <br />29' <br />1481.8 <br />ISS:51 <br />36°'- <br />1861.7, <br />294.9 <br />W <br />112:4 <br />108.90 <br />10' <br />1.190.7 <br />190.74 <br />:101 <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 />11508.5 <br />105.25 <br />•'30 <br />1S89.4' <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 />5U <br />'1907.9• <br />'309.3 <br />Z3 <br />11E5.7 <br />117.38• <br />30 <br />71005.3 <br />202.12 <br />37 • <br />1917.1 <br />312.2 <br />10 <br />1174,4 <br />119.12 <br />`-'10 <br />1044.2 <br />.204.44 <br />10 <br />1026.4 <br />315.2 <br />20 <br />1183.1 <br />120. S7' <br />L. 20 <br />1553.1 <br />206.77 <br />20' <br />1935.7; <br />318.1 <br />30 <br />1191.8*•122.63 <br />R-.013 <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 />1054.3; <br />324.1 <br />50 <br />1309.2 <br />120.20 <br />•'50 <br />`1580.0 <br />213.56 <br />: 50 <br />1963.6 <br />327.1 <br />24 <br />1217.9 <br />125.60 <br />31 <br />1559.0 <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 />2010.2 <br />339.3 <br />342.4 <br />40 <br />50 - <br />1252.3 <br />1261:5 <br />135.35 <br />137.23 <br />40 <br />x••50 <br />1624.9 <br />,1633.9 <br />226.0' <br />225.4 <br />r40 <br />- 50, <br />2019.6,345.5' <br />.76 <br />25 <br />1270.2 <br />139.11 <br />'52 <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 />4287.7 <br />112.93 <br />'20 <br />X1661.0 <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 />145,75 <br />` ' 50' <br />1GSS.1 <br />243.5 <br />•=50 <br />2076:0 <br />304.5 <br />26 <br />1322.8 <br />150.71 <br />33 "' <br />'1(,97.2 <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 />209 4. 9 <br />371.0 <br />'20 <br />13.10.4 <br />154.69 <br />.120 <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 />1306.8 <br />160.76 <br />•50 <br />!1742.6 <br />; 259.1 <br />50 <br />'2132.7 <br />84:1 <br />334:1- <br />27 <br />27 <br />1375:0 <br />162.81 <br />'34 <br />11761.7 <br />261:8- <br />41 <br />2142.2 <br />387.4 <br />10 <br />.1334:4 <br />104.86 <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 />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 />1785.2 <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 />23 <br />1425.6 <br />175.41- <br />35 <br />1806.6 <br />278.1 <br />' 42 <br />2199.4 <br />4076 <br />10 <br />1437.4 <br />177.55 <br />10• <br />'1815.7 <br />2SO.8 <br />10 <br />'2209.0 <br />411.1 <br />20 <br />1446.-3 <br />179.72 <br />20 <br />1824.9 <br />253.6 <br />'20 <br />2218.6 <br />414.5 <br />30 <br />1455.1 <br />181.89 <br />30 <br />1534.1 <br />256.4 <br />-30 <br />2223:1' <br />418.0 <br />40 <br />1464.0 <br />1S4.03 <br />40 <br />1343.3 <br />2S9.2 <br />40 <br />2237.7 <br />421.4 <br />50 <br />1472.9•'156.29 <br />50 <br />1852.. <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 />100, <br />I5° <br />20° <br />25° <br />30° 35P, <br />4D°' <br />`45° <br />501 <br />55° <br />-60° <br />65° 70° <br />20° <br />'1'=.06 <br />.13 <br />.19 <br />.26 <br />.32• <br />.39 .45 <br />,S1 <br />'.58 <br />.65 <br />.72 <br />.79 <br />.84. .90 <br />E =.006 <br />011 <br />.017 <br />.022 <br />:028 <br />.034 .038 <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 .083 <br />25° <br />T=.n3 <br />.18 <br />24. <br />.33 <br />.40 <br />.40 .58 <br />.G7 <br />.75 <br />•83 <br />.90 <br />.99 <br />1.06 1.14 <br />E =.009 <br />.018 <br />.027 <br />.036 <br />.046 <br />.056 .065 <br />.074 <br />.083 <br />.093 <br />.JOG <br />.120 <br />.127 .135 <br />30° <br />T=.10 <br />.19 <br />.39 <br />.49 <br />.50 .69 <br />.'9 <br />.89 <br />.99 <br />1.09 <br />1.20 <br />1.29 1.39 <br />_� <br />R-.013 <br />..025 <br />.29 <br />.038 <br />.051 <br />.065 <br />.073 .000 <br />.103 <br />.116 <br />.120 <br />.149 <br />.170 <br />.179 .188 <br />35° <br />T=.11 <br />.23 <br />34 <br />.47 <br />.58 <br />.69 .80 <br />.03 <br />1.05 <br />1.42 <br />1.54 1.66 <br />E =.018 <br />.035 <br />, <br />.054 <br />.072 <br />.086 <br />.109 .131 <br />.153 <br />.175 <br />.230 <br />.247 .284 <br />40° <br />T=,13' <br />6 <br />AO <br />'.53 <br />G7 <br />.80 .93 <br />1.06 <br />120 <br />1.64 <br />1.79 1.94 <br />023 <br />.030 <br />.070 <br />.D93 <br />.117.141 <br />.172 <br />.203 <br />.231 <br />jt�.341.49 <br />_90 <br />.315 .341 <br />45° <br />T=15 <br />30 <br />.44 <br />.60 <br />.76 <br />191 1.06 <br />1.21 <br />1.37 <br />1.87 <br />2.04 2.21E <br />=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 216 <br />.254 <br />.2°"9 <br />.373 <br />.411 .445 <br />