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II TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord =100 It. <br />Angle <br />Tangent <br />External <br />"lnt. <br />Angle <br />Tangent <br />External <br />Int. <br />Angie <br />Tangent <br />�� n <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 />l0' <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 />437.71 <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 />133.36 <br />1.55 <br />40 <br />484.49 <br />20.45 <br />40 <br />839.27 <br />61.1'4 <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 />804.82' <br />64.90 <br />20 <br />166.72 <br />2.43 <br />20 <br />518.08, <br />23.38 <br />L20 <br />873.35. <br />66.18 <br />30 <br />175.06 <br />2.67 <br />30 _ <br />526.4S <br />24.14 <br />30 <br />881.88 <br />67.47 <br />40 <br />183.40 <br />2.03 <br />40 <br />534.89 <br />24.91 <br />40 <br />890.41. <br />08.77 <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 />200.68 <br />3.49 <br />1.1 <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 />72.70 <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 />76.86 <br />50 <br />241.81 <br />5.10' <br />' 50 <br />593.79 <br />30.68 <br />50 <br />950.25 <br />78.20 <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 />258.51 <br />5.83 <br />16 <br />610.64 <br />32.45 <br />.10 <br />967.38 <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 />_ <br />34.26 <br />30.1 <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 />316.99 <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 />678.15 <br />30.99 <br />30 <br />1036:1 <br />92.92. <br />40 <br />333.71 <br />9.7.1 <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 '1070.6 <br />2209:0 <br />99.16 <br />20 <br />367.17 <br />1L.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 />46.13 <br />30" <br />1087.8 <br />102.35 <br />40 <br />383.91 <br />12.85 <br />4U <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 />60 <br />1105.1 <br />165.60 <br />Corrections to be Added (T =Tangent. E=External.) - <br />Int. <br />Anglo Gi�rve 5 <br />10° <br />15° <br />20° 25° <br />30° <br />35°" <br />40° 1 45° <br />50° 550 <br />601 65° <br />70° <br />6° T=A2 <br />.03 <br />.05 <br />.00 '' 03 <br />le.11 <br />36° <br />.13 .15 <br />.16 .18 <br />.20 .21 <br />.23 <br />E =.000 <br />.000 <br />.001 <br />_001 .002 <br />_.002 <br />.002 <br />.003 .003 <br />.004 .004 <br />.004 .005 <br />.005 <br />10° T-103 <br />.06 <br />.09 <br />.13 .16 <br />.19 <br />.22 <br />.25 AS <br />.31 .34 <br />.38 1 .42.46 <br />30 <br />r=,001 <br />.003 <br />.004 <br />X06 .007 <br />.008 <br />.009 <br />.011 .012 <br />.014 .015 <br />.017 .018 <br />.020 <br />150 T =.04 <br />.10 <br />.14 <br />.19 .24 <br />.29 <br />.34 <br />.39 .45 <br />.51 .53 <br />.58.63' <br />.68 <br />E =.003- <br />:007 <br />.010 <br />.014 .018 <br />.023 <br />.027 <br />.029 .032 <br />1 03 .039 <br />.043 .047 <br />.051 <br />20° T=•06- <br />.13 <br />'.10 <br />.26 .32 <br />.39 <br />.45 <br />.51 .58 <br />.65.72 <br />':79 .84 <br />.90 <br />E =.006 <br />.011 <br />.017 <br />_022 .028 <br />.034 <br />.038 <br />X45 .051 <br />.057 .063 <br />.070 .076 <br />.083 <br />25° T=.08 . <br />.16 <br />.24 <br />, .33 .40 <br />.40 <br />.58 <br />_67 .75.83 <br />.90 <br />.99 1.00 <br />1.14 . <br />E=.009 <br />.013 <br />.027 <br />.030 .046 <br />.056 <br />.065 <br />.074 .033 <br />.093 .106 <br />.120 .127 <br />.129 <br />..TABLE I. - Tangents and Externals to a 1° Curve, III <br />Chord =100 ft: <br />Angle ..Tangent External <br />Corrections to be Added (T -Tangent. E=External:) <br />lilt <br />Tangent <br />External <br />Int <br />Angle <br />Tangent <br />External <br />2g°' <br />1113.7 <br />107.24 ! <br />`29° <br />14S1.8� <br />188.51 <br />36° <br />18r,1.7 <br />294.9 <br />10' <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 />300,4 <br />50_, <br />1157.0 <br />115.66 <br />50 <br />1525.3 <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 />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 />60 <br />1963.6 <br />327.1 <br />24 <br />1217.0 <br />'128.00 <br />31-' <br />1589.0' <br />216.3 <br />36 <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.() <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 />1033.9 <br />228.4 <br />50 <br />2019.6 <br />345.5 <br />25 <br />1270.2 <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 />2038.4 <br />351.8 <br />20 <br />1287.7 <br />142.93 <br />20 <br />1601.0 <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 />26 - <br />1322.8 <br />150.71 <br />33' <br />'1697.2 <br />246.1 <br />40. <br />20$5.4 <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 />154.69 <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 />136G.8 <br />160.76 <br />50 <br />1742.6 <br />250:1 <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 />-so <br />1402.0 <br />169.04 <br />30 <br />1779.1 <br />269.9 <br />30 <br />12170.8, <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 />7.8 <br />1428.6 <br />175.41 <br />35 - <br />1806.6 <br />'278:1• <br />422199.4„ <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 />2218.0 <br />414.5 <br />30 <br />1450.1 <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 />184.08 <br />40 <br />1843.3 <br />289.2 <br />40 <br />2237.7 <br />.421.4 <br />50- <br />1472.9 <br />180.29 <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 />Angle Carve S° <br />10°. <br />15° <br />20° 25°• 30° <br />35° <br />40° 45° <br />50°. 55° 600 65° '700 <br />20° , T=.06 <br />.13. <br />.19 <br />,26 .3239 <br />.45 <br />.5l ' 58 <br />.85 .72' .79 .84 .90 <br />E=.006 <br />.011 <br />.017 <br />.022 .028 :034 <br />.038 <br />.045 .051 <br />.057 .063 .070 .076 .083 <br />25°• T=:08 <br />.16 <br />.24 <br />.33 .40 .40 <br />.58 <br />:67 .75 <br />.83 .90 .99 1.06 1.14 <br />E=.000' <br />.018 <br />.027 <br />.036 .046 .056 <br />.065 <br />.074 .083 <br />.003 A06' .120 .127 .135 <br />30° T=.10 <br />'E <br />.10 <br />.29 <br />.29 .49 .59 <br />.69 <br />.79` .89 <br />.99' 1.09 1.20 1.29 1.39 <br />-.013 <br />.025 <br />.038 <br />.051 .065 .078 <br />.090 <br />.103 .11fi <br />.129 .149 .170 .179 .188 <br />35-.. .T=.11 <br />.22 <br />.34 <br />.47 .58 .69 <br />.80 <br />.93 1.05 <br />17 1. 1.42 1.54 1.66 <br />1:'197,':213 <br />E=.018. <br />.035 <br />.054 <br />:072 .086 ,.109 <br />.131 <br />:153 .175 <br />:197 ,213 .230 .247 .204 <br />40° T-,13 _ <br />' <br />2G <br />.40 <br />.53 .67 .80 <br />A3. <br />1.06 1.20 <br />1.34 1.49 1.64 1.79 1.94 <br />_ : E=:023 <br />-7- <br />.040 <br />.070 <br />".093 .117 :141 <br />:172 <br />,208 .234 <br />.265 .277 .290 .315 .341 <br />qg° . 1-5 <br />E <br />.30 <br />.44' <br />.60 .76 .91' <br />1.06 <br />1.21 1.37. <br />1.52e 1.70 1.87. 2.04 2.21 <br />x,030 <br />OGO <br />•093 <br />.119 .153 .184 <br />.216 <br />.264 .289 <br />.325 .351, .378 .411 •.445 <br />