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II . TABLE I. - Tangents and Externals to a 1° Curve. - <br />Choi'd =100 ft. <br />Int.ant. <br />Angle <br />Tangent <br />Externa! <br />1 . <br />Angle,.- <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />_ <br />External <br />1° <br />50.00 <br />:228°' <br />20° <br />400.66 <br />.13.99 <br />15° <br />754.32 <br />49.44 <br />'10' <br />58:'34' <br />.30' <br />40'' <br />"409.03 <br />14.58 <br />10'. <br />762.80. <br />. 50.55 <br />20 <br />06:67' <br />,.39 <br />20 <br />417.41 <br />15.18 <br />..'20°. <br />i771t29' <br />51.68 <br />30 <br />75.0 1 <br />.49 <br />30 <br />425.79 <br />15.50 <br />-30 <br />779:77" <br />52.82 <br />40 <br />83:34.61' <br />-.19 <br />40 <br />434.17 <br />16.43 <br />40' <br />788.26' <br />53.97 <br />50 <br />91.68 <br />.73 <br />Y <br />50 <br />442.55 <br />17.07 <br />50 <br />79G.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 />5750 <br />20 <br />116.68 <br />1:19 <br />20 <br />467.71 <br />19.06 <br />20 <br />522.25 <br />58..70 <br />30 <br />425.02 <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 />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 />547.78. <br />62.33, <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 />564.82 <br />G4.90 <br />"20 <br />166.72' <br />" 2.43 <br />20 <br />518.08 <br />23.38 <br />20 <br />573:35, <br />G6.IS <br />30 <br />175.06 <br />2:67 <br />30 <br />526.48 <br />24.14 <br />30 <br />581.88" <br />67.47 <br />40 <br />183.40 <br />2.93 <br />40 . <br />534.59 <br />24.91 <br />40 <br />890.41 <br />GS. 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 <br />200.08 <br />3.49 <br />11 <br />551.70 <br />26.50, <br />13 <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 />US. 53 <br />25.14 <br />20" <br />924.53 <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 />76.56 <br />50 <br />241.81 <br />,. 5.10 <br />50 <br />-593.79 <br />30.68 <br />. 50 <br />950.25 <br />73.26 <br />5 <br />250.16 <br />5.46 <br />12, <br />602.21 <br />31.56 <br />19, - <br />95S.31 <br />79.67. <br />10 <br />255.51 <br />5.S3 <br />10 <br />610.64 <br />32.45 <br />10 <br />967.38 <br />81.09". <br />20 <br />266.56 <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 />G27.50 <br />34.26 <br />30 <br />984.53 <br />83.97 <br />40- <br />233.57 <br />7.01 <br />.._ 40- <br />-.G35.G3 <br />35.18 <br />40 <br />993.12 <br />85.43 <br />50. <br />291:92 <br />7.43 <br />50' <br />G44.37_ <br />36.,12" <br />50 <br />1001.7 <br />86.90 <br />6 <br />300.28 <br />7.55 <br />13- <br />652.51 <br />37.07 <br />20 <br />1010.3 <br />58.39 <br />10 <br />305.64' <br />8.31 <br />10 <br />661.25 <br />3S.03 <br />10 <br />1018.9 <br />S9.S9 <br />+20. <br />3 10. 99' <br />8.76 <br />20' <br />669.70 <br />39.01 <br />20 <br />1027.5 <br />, <br />91.40 <br />30 <br />325.35 <br />9.23 <br />30. <br />.675.15 <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 />2170.8 <br />94.46 <br />50 <br />3412..0& <br />10.20 <br />50 <br />695:065. <br />42.00 <br />.1044.7 <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 />3S3-91 <br />12.85 <br />40 <br />737.37 <br />47.25 <br />40 <br />109 G.4 <br />`103.97 <br />50 <br />392.25 <br />13,.41 1 <br />50 <br />745.85 <br />43.34' <br />5U <br />1195.1 <br />105.60 <br />Corrections•to be Added (T=Tangent. E=External.) <br />Int. <br />TangentI <br />External <br />Int. <br />•Angle <br />Tangent <br />External <br />Int. <br />Angle _ <br />Tangent <br />External <br />22? ' <br />1113:7 <br />Curve 5° 10 1° <br />Angle ° 15 <br />20° <br />25° <br />' 30 ° <br />35° 40° <br />45° <br />50° <br />55° <br />60° <br />65° <br />70° <br />5o T=.02 03 .05 <br />"06 <br />..as ' <br />.10 <br />.11 .13 <br />.15 <br />.16 <br />.18 <br />.20 <br />.21 <br />.23 <br />E =.000 .000 .001 <br />.001 <br />.002 <br />.002 <br />.002 .003 <br />.003 <br />.004 <br />.004 <br />.004 <br />,005 <br />•005 <br />10° T =.03 O6 .09 <br />.13 <br />-.16 <br />-.19 <br />22 '.25 <br />.28 <br />-"3 -1 <br />.34 <br />.38 <br />.42 <br />.46 <br />E =.001 .003 .004 <br />.006 <br />.007 <br />.008 <br />.009 .011 <br />.012 <br />:.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />35° T =.04 .10 .14 <br />.19 <br />.24 <br />29 <br />.34 .39 <br />.45 <br />.51• <br />.53 <br />.58 <br />G3 <br />.68 <br />E=-003 _.007 "010 <br />.014' <br />.018 <br />.023 <br />.027 .029 <br />"032 <br />.035 <br />"039 <br />.013 <br />.047 <br />.051 <br />20° T=.06 13 .19 <br />.26 <br />.32 <br />.39 <br />.45 .51 <br />.58 <br />.65 <br />.72' <br />.70 <br />.84 <br />321.1 <br />E =.006 .011 .017 <br />.022 <br />.028 <br />..034 <br />.038 .015 <br />.051 <br />"0.17 <br />"m3 <br />.070 <br />.076 <br />.90 <br />.083 <br />T=.08 .16 .24 <br />.33 <br />.40 <br />'.49.58 <br />.67 <br />.75 <br />.83 <br />.00 <br />'.99 <br />1.06 <br />1.14 <br />E =.009 .018 .027 <br />.036 <br />.046 <br />.056 <br />.065 .074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 <br />.135 <br />TABLE L - Tangent's and Extern'a'ls to a 1° Curve. <br />Chord =100 f t. <br />�nt' ' <br />Angle <br />TangentI <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 />1451.8 <br />188.51 <br />36° <br />18G1.7 <br />294.9 <br />1(K <br />.1122.4.- <br />?108:90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />1570.9 <br />'..'97.7 <br />_;•20 <br />1131:0; <br />" <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 />411: <br />i1148.4, <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 />1520.3 <br />199.82 <br />50 <br />1907.9 <br />309.3 <br />23. - <br />1105.7. <br />117.38 <br />30 <br />1535.3 <br />202.12 <br />37 <br />1917.1 <br />t 312.2 <br />=-10- <br />1174:4. <br />.119.12 <br />10 <br />1544.2 <br />-204.44 <br />10 <br />19261.4 <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 />1562.4 <br />209.12 <br />30 <br />1945.0 <br />321.1 <br />40: <br />1200.5' <br />124.41 <br />40 <br />15571'.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 />19G3.6 <br />327.1 <br />.24 <br />3217.9_ <br />128.00 <br />31 <br />1589.0 <br />216.3 <br />38 <br />1972.9 <br />330.2 <br />:10 <br />1220.0 <br />129.52 <br />10 <br />1598.0 <br />218.7 <br />10 <br />1952.2 <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 />.093 <br />X19 <br />.153 <br />,,.184 <br />:21G <br />.254 <br />.289 <br />.325 <br />.351 <br />25 <br />1270.2 <br />139.11 <br />32." <br />1G43.0 <br />230.9. <br />39 • <br />2029"0 <br />343 <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 />2042.8- <br />354.9 <br />30 <br />1296.5 <br />144.85 <br />30 <br />1670.0• <br />238.4 <br />30, <br />'2657.2' <br />358.1 <br />40 <br />1305.3 <br />140.79 <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 />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 />13-58.0 <br />158.72 <br />40 <br />1733.5 <br />256.5 <br />40 <br />21.23.3 <br />380.8 <br />50 <br />13GG.S <br />160.76 <br />50 <br />1742.6 <br />259.1 <br />50 <br />2132.7 <br />354.1 <br />27 . <br />1375.6 <br />162.81 <br />34 <br />1751.7 <br />261.8 <br />41• <br />2142.2 <br />337.4 <br />- 10 <br />1384.4 <br />164.86 <br />10 <br />1760.8 <br />261.5 <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 />2150.3 <br />400.3 <br />_"50 <br />1419.7 <br />173'.27.' <br />ti .50 <br />1797.4 <br />275.3 <br />50 <br />2159.9 <br />404.2 <br />28-': <br />1428.G <br />175.41 <br />.35 <br />1806.6 <br />275.1 <br />42 <br />2199.4 <br />407.6 <br />10 <br />1437.4 <br />177.55 <br />10 <br />1S15.7 <br />280.8 <br />'10 <br />2209.Oa <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />20 <br />1324.9 <br />283.6 <br />20 <br />2218.6 <br />.414.5 <br />'30 <br />1455.1 <br />181.59 ' <br />30. <br />1834.1 <br />280.4 <br />30 <br />2228.1 <br />418.0 <br />f0 <br />7464.0 <br />134.03 <br />40 <br />1843.3 <br />289.2 <br />40 <br />2237.7 <br />421.4 <br />50 <br />1472.9 <br />156.29 <br />50 <br />1552.:1 <br />- 292.0 <br />50 <br />2247.3 <br />425.0 <br />Corrections to be Added (T =Tangent. E = External.) <br />Int.Curtie <br />Angle <br />_ 5° <br />10° <br />15° <br />2U° <br />25° <br />30°, <br />35° <br />40° <br />M1S° <br />50° <br />55° <br />60° <br />65° 70 ° <br />20° ` <br />T=.06 <br />.13 <br />.19 <br />.20 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84 .90 <br />E=.006 <br />.011 <br />.017 <br />."022 <br />.028 <br />.034 <br />"038 <br />"045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 .083 <br />25°' <br />T= .08 <br />16 <br />.24 <br />33 <br />.40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.06 1.14 <br />E ="009 <br />.O1S <br />.027 <br />!036 <br />.046 <br />.056 <br />.065 <br />.074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 .135 <br />30° <br />T=.10 <br />.19 <br />.29 <br />.39 <br />:19 <br />.59 <br />.69 <br />.79 <br />.89 <br />.99 <br />1.09 <br />1.20 <br />.1 29 1.39 <br />E =.013 <br />.025 <br />.038 <br />.051 <br />.065 <br />.078 <br />.090 <br />.103 <br />.116 <br />.129 <br />.149 <br />.170 <br />.179 .188 <br />35° <br />-T <br />.22 <br />-.34 <br />:.47 <br />.58 <br />.69 <br />.80 <br />.93 <br />1.05 <br />1.17 <br />'.197 <br />1.29 <br />1.42 <br />1.54 1.66 <br />E=.01S <br />.035 <br />'.054 <br />.072 <br />.086 <br />.109 <br />.131. <br />.153 <br />.175 <br />.213 <br />.230 <br />.247 .264 <br />400. <br />T=.13 <br />.2G <br />M1O <br />.53 <br />G7 <br />.80 <br />.93 <br />1.06 <br />120 <br />1.34 <br />1"49 <br />1"64 <br />1.79 1.94 <br />E=.623 <br />.040 <br />.070 <br />.093 <br />.117 <br />.141..172 <br />.203 <br />234 <br />.2651 <br />.277 <br />.290 <br />.315 .341 <br />45° .- <br />T=.15 <br />..30 <br />.44 <br />.00 <br />.70 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.53 <br />1.70 <br />1.87- <br />2.04 2.21 <br />E=.030 <br />.060 <br />.093 <br />X19 <br />.153 <br />,,.184 <br />:21G <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 -,.445, <br />