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TAsl.r 1. - Tangents and Externals to a 1° Curve. <br />Chord71004 L <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 />19 <br />50.00 <br />.22 <br />8° <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 />"0 <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.S2 <br />40 <br />83.34 <br />.G1 <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 />.97 <br />9 - <br />450.03 <br />17.72 <br />10. <br />905.25 <br />56.31 <br />10 <br />108.35 <br />1.02 <br />101 <br />459.32' <br />18.38 <br />10• <br />813.75 <br />57.50 <br />20 <br />116.68 <br />1 19 <br />2W <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 />59.91 <br />40 <br />133.3G <br />1.55 <br />46• <br />484.49 <br />20.45 <br />4U <br />839.27- <br />61.14 <br />50 <br />14 L. 70 <br />1.75 <br />50 <br />-992;88 <br />21.16 <br />50 <br />847.78: <br />62.38 <br />3 <br />150:04 <br />1:96 <br />10 t <br />501.26 <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 />160.72 <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 />>59. <br />543.29 <br />25.70 <br />50 <br />898.95 <br />70.09 <br />4 <br />200.OS''`. <br />3:49 <br />11t '! <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 />218:77 <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 />( <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. EG <br />6.21 <br />s • 20 <br />819.07 <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 />83.11 <br />40 <br />233.57, <br />7.01 <br />40' <br />-,63.5.93 <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 />fi <br />30q.2B: <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 />'•601.25 <br />38.03 <br />10 <br />1018.9 <br />89.89 <br />20, <br />;' MAD' <br />8.76 <br />20 <br />GG9.70 <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 />92.02 <br />`.:40'- <br />.333'-71 <br />•9.71 <br />40 <br />056. 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 />356.44 <br />10.71 <br />14. <br />703.51 <br />43.03 <br />21 <br />1061.9 <br />97.57 <br />•10 <br />3.;8.B1 <br />11.22 : <br />10 <br />711.07 <br />44.07 <br />10 <br />1070.6.- <br />99.16 <br />-20-.367.17 <br />I446.3 <br />11.75 <br />•120. <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 />33301 <br />12.85 <br />40 <br />'737.37 <br />47.25 <br />40 <br />1096:4 <br />103.97 <br />50392'.28 <br />'1472.9 <br />13.41 <br />56 <br />245.85 <br />48.34 <br />50' <br />1105:1 <br />.105.60 <br />Corrections to be Added (T Tangent. •E=External.)" <br />Angle <br />Curve 5° <br />10° <br />15' 20° 25° <br />30° <br />'35' <br />49° <br />45° <br />50° <br />55' 60° <br />'65° <br />70° <br />5° <br />T=.02 <br />.03 <br />..05 .06 .08 <br />.10 <br />.I1 <br />.13 <br />.15 <br />.16 <br />`.18 .20.21 <br />1490.7 <br />-.23 <br />10' <br />E -.000 <br />.000 <br />MI. .001 .002 <br />.002 <br />.002 <br />..003 <br />.003 <br />'.004 <br />.004 .004 <br />:005 <br />.005 <br />]0° <br />T =.03 <br />.06: <br />".09 .13 .16 <br />.19 <br />.22 <br />-.25 <br />.28 <br />.31 <br />.34 138 <br />':42 <br />J45- <br />40' <br />E=.001-- <br />..003 <br />'.'A04 .006 .007',".008 <br />1398.6' <br />.009 <br />.011 <br />.012 <br />.014 <br />T=.04 <br />.015 .017 <br />.018 <br />.020 <br />150 <br />' <br />':10' <br />.14 .19 -`4 <br />x.'.29 <br />.34 <br />'.3945 <br />1535:3.1 <br />.51 <br />.53 :58 <br />.:63 <br />.68 <br />10 <br />E=.003 <br />-.OD7 <br />.010 .014 _018 <br />':023 <br />.027 <br />.029 <br />.032 <br />.036 <br />.039 .043 <br />.047 <br />.051 <br />20'' <br />T' -.OG <br />.18 <br />.90 <br />AD .26 .32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 .79.84 <br />209.12 <br />30 <br />E=.000, <br />.011 <br />.017 •.022 .028 <br />..034 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 '.070 <br />.076 <br />-0183 <br />25° <br />T e.08 t, <br />.16 <br />24 .33 .40 <br />L.O6 <br />1.14 <br />.49 <br />58 <br />.67 <br />.75 <br />.83 <br />.90 .99 <br />31 <br />.E_ .00B <br />.018 <br />,:027 .036 .040 <br />.056 <br />.095 <br />".074 <br />.083 <br />: A93 <br />.1.06 .120 <br />.127 <br />.135 <br />TAnrm I. =-'Tangen6.,and External s,to a •1° Curve. III <br />Chord =100 ft. <br />Int. <br />Angle' <br />Tangtnt <br />ICatenlal <br />Int.. ' <br />Angle '- <br />Tanment <br />Fxtcnal <br />Int.. <br />Angle <br />Tange.aLl <br />External <br />22*k-*' <br />111'-3;Z <br />107.24 <br />294 <br />1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.9 <br />-- 101. <br />1'122-4' <br />108.UU <br />.10' <br />1490.7 <br />190.74 <br />10' <br />:1870.9 <br />297.7 <br />`20 <br />Id:31 0 <br />110.57 <br />20.• <br />1499:4 <br />192.99 <br />20 <br />' 183611 <br />300.6 <br />25° <br />T =.08 I6 <br />112.2) <br />'30 `• <br />loU5.o <br />195,25 <br />30 <br />'1839.1 <br />303.5 <br />_1139;'1 <br />140 <br />.99 1.06 <br />113:05 <br />40' <br />1517:4' <br />197.53 <br />40 <br />1398.6' <br />306.4 <br />50 <br />,113.8"4- <br />1157'0 <br />115.66 ' <br />'50 <br />1520.3 <br />199.82 <br />50 <br />1907.9 <br />309.3 <br />23 <br />11G5.7' <br />117.33 <br />30 <br />1535:3.1 <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 />.170 .179 <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 />120.20 <br />50 <br />1580.0- <br />21.3.86 <br />50 <br />1963.G <br />327.1 <br />24 <br />-1217:0 <br />128.00 <br />31 <br />1589.01: <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 />1901.5 <br />336.3 <br />30 <br />1244.0 <br />133.50 <br />30- <br />1615.9 <br />221.5 <br />30 <br />2000.0 <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 />30 <br />1261.5 <br />137.23 <br />56 <br />1633.9 <br />228.4 <br />50 <br />2010.6 <br />345.5 <br />251270.'2 <br />139.11 <br />32 <br />1043.0 <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 />2038A <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 />1070.0 <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 />SU <br />1314.0 <br />148.75 <br />'gi50, <br />1688.1 <br />243.5 <br />50 <br />2076,0 <br />364.5 <br />'26 <br />1822.$ <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 />152.09 <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 />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 />16 <br />1384.4 <br />1G4.86 <br />10 <br />1760.8 <br />264.5 <br />10 <br />2151'._4: <br />390.7 <br />20 <br />1393.2 <br />166.05 <br />20 <br />1770.0 <br />267.2 <br />20 <br />•2161:2. <br />r 394.1 <br />30 <br />1402.0 <br />169.04 <br />30 <br />1779.1 <br />269.9 <br />302170.8 <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 />I446.3 <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 />.1464.0 <br />184.03 <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 />I Curve 5° 1D° <br />15° <br />20° <br />25° <br />-30° <br />35° <br />40° <br />45° <br />50° 55° <br />60° 65° <br />70° <br />20°� <br />'T =.08 .13 <br />.19 <br />.26 <br />.32 <br />'.39 <br />.•.45 <br />.51 <br />.58 <br />.65 .72 <br />.79. ,.84 <br />.90 <br />E =.006 .011 <br />.017 <br />.022 <br />.028 <br />.034 <br />.038 <br />.015 <br />.OSI <br />.057 .063 <br />.070 •476- <br />.083 <br />25° <br />T =.08 I6 <br />.24 <br />.33 <br />40 <br />.49 <br />-.53 <br />.67 <br />.75 <br />.83 .90 <br />.99 1.06 <br />1.14 <br />E =:009 .018 <br />.027 <br />.036 <br />.046 <br />.055 <br />'AG5 <br />.074 <br />.033 <br />•093 .106 <br />.120 ..127 <br />.135 <br />3D° <br />T=.10 .12 <br />.29 <br />.39 <br />a9 <br />.59 <br />•:69 <br />.79 <br />.89 <br />;D911.09 <br />1.20 1:29 <br />1.39 , <br />E =.013 -025 <br />.036 <br />..051 <br />.055 <br />.078 <br />.070 <br />,103 <br />.116 <br />:129 ;.149 <br />.170 .179 <br />.188 <br />35° <br />T=•ll 22 <br />-.34 <br />.47 <br />.58 <br />.69 <br />.80 <br />.03 <br />1.05 <br />1.17 1.29 <br />1.42 1.54 <br />1.66 <br />E =:018 .035 <br />.054 <br />.072 <br />.086 <br />.109 <br />.131 <br />.153 <br />.175 <br />.197 .213 <br />.230 :.247 <br />264 <br />-40' <br />T=.13 .^6 <br />.40 <br />.53 <br />.67.80 <br />:93 <br />1.06 <br />1.20 <br />1.34 1A9 <br />1.64 1.79' <br />1.94 <br />E=-023 .016 <br />T=:15 :30 <br />.070 <br />.093_ <br />.00.76 <br />.117 <br />.141 <br />,.172 <br />.203 <br />234 <br />.265 .27? <br />290 ,.315 <br />-.341 <br />45° <br />.44 <br />01 <br />1.05 <br />1.21 <br />1.37 <br />1.52 1.70 <br />1.87 2,04 <br />2621 <br />E=:030- .060 <br />:093 <br />, .119 <br />.153 <br />.184 <br />:216 <br />'.254 <br />`..289 <br />':.325 .351 <br />'.378 All <br />.445 <br />