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II TABLE I. - Tangents and Externals to a V Curve. <br />Chord= 100 ft.- <br />Int. <br />t: <br />Int. <br />Angle <br />Tangent <br />External <br />Int. - <br />Angle <br />•Tangent <br />` ' <br />External <br />- Int. <br />Angle <br />Tangent <br />External <br />to <br />50:00 <br />22 ; <br />'S' - - <br />" 400:66 <br />. -13:99 <br />lb' ' <br />:754.32 <br />49.44. <br />101 <br />58.34 <br />.30 <br />10' <br />409.03 <br />14.58 <br />10' <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 />61.68 <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 />b0 <br />,: 91.68 <br />.73 <br />'50 . <br />4.42.55, <br />...17.07, <br />,. 50 ...796.7, <br />.84 <br />55.13 <br />2 -.,; <br />100.01 <br />:87-' <br />.. 0.' <br />450.93 <br />.:.:17:72 <br />10 . <br />805.25'. <br />56.31. . <br />30' <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 />:467.71'` <br />'19:06 <br />: 20 <br />822.25 <br />-.58.70 <br />30 <br />•125.02 <br />1.36 <br />, 30,1 <br />1562.1 <br />19: 75 - <br />-30 <br />• 830 <br />59..91 <br />"40_- <br />133.36 <br />." 1.55. <br />1- 40"'.484.49' <br />.476.10. <br />;•20.45 <br />•: .40 .'.839*.27 <br />,76 . <br />61.14 <br />56 <br />141.70 <br />1.25. <br />'50 <br />492.88 <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 />158.38. <br />2.19. <br />.10 <br />509.68. <br />22.62 <br />.- 10 <br />864:82. <br />'64.90 <br />20 <br />166.72 <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 />1615.9 <br />- 24.14 <br />30 <br />881.88 <br />67.47 <br />40 <br />183.40 <br />2.93 <br />40, <br />,526.48 <br />'534.89.._24.91 <br />226.0 . <br />40 <br />890.41 <br />68.77 <br />50 <br />191.74 <br />3.21 <br />50- <br />643.29 <br />25.70 <br />50 <br />898.95 <br />70.09 <br />a <br />'200.08 <br />3.49 <br />11 <br />,551.70 <br />..26.50` <br />18 -" <br />" 907149'' <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 />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.,.28.97. <br />238.4 <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 />78.26 <br />b <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 />266.86 <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 />,-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 />993.12 <br />85,43 <br />50 <br />291.92 <br />.7.43 <br />.60 <br />644.37 <br />.•36.12 <br />50.. <br />1001.7 <br />86:90 <br />6 <br />300..28 <br />7.86 <br />"1337.07 <br />1751.7 <br />261.8 <br />20* <br />1010.3 . <br />88.39 <br />10 <br />308.64 <br />8.31 <br />10 . <br />_ 661'. 25652.81, <br />38.03 <br />'. -16'' <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 />39.99 <br />30 <br />1036.1 <br />92.92 <br />40 <br />.'333.7r <br />:'_- 9.71 <br />40, <br />686.60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 <br />342.08..'10.20 <br />173.27 <br />.". 50:_. <br />695.06 <br />42.00 <br />50 <br />1053.3 -. <br />96.01 <br />7 <br />_.35Q.44,-_10.71 <br />175.41 <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 />2218.6 <br />100.75 <br />30 <br />375!54 <br />181.89 <br />. 30 <br />728.90 <br />46.18. <br />30:: <br />1087.8., <br />'102.35 <br />40 <br />383.91 <br />-,12.29' <br />12.85 <br />40' <br />-737.37 <br />­ 47.25 <br />40 <br />11079,2 <br />1096.4 <br />103.97 <br />50 <br />392:28 <br />13.41 <br />50_ <br />745.85 <br />1 '48.34 <br />50 <br />1105.1 <br />105'•60 <br />Corrections to be Added (T =Tangent. E=External.) <br />Int. <br />Angle <br />Carve 5° <br />10° 15° 20°' 1 25° 300- 35° 40° 1 45' <br />SO- <br />550 <br />60° <br />65° <br />-70° <br />bo <br />T=.02.03 <br />.05 .06 :08 .10 -.11 .13 .15 <br />.16 <br />.18 <br />.20 <br />.21 <br />.23 <br />1861.7 <br />E =.000 <br />.000 .001 .001 x.002 .007, ..002 .003 <br />.004 <br />.004 <br />.004 <br />.005 <br />.005 <br />loo <br />T =.03 <br />.06 .09 :13, -.16 .19 .22 .25 "-.28. <br />'.31 <br />.34 <br />.38 <br />.42 <br />.46 <br />192.99 <br />E =.001 <br />.003 .004 ':006 .007 .008 .009 .011 _012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />15° <br />T=.04 <br />.10 .14 .19 .24 '.29 .34 .39 .45 <br />.51 <br />.53 <br />.58 <br />.83 <br />.88 <br />40 <br />E =.003 <br />.007 .010 .014 .018 .023 .027 .029 .032 <br />.035 <br />.039 <br />.043 <br />.047 <br />.051 <br />20° <br />T=.06 -.13 .19 .26 .32 .39 .45 .51 .58 <br />.65 <br />.72 <br />.79 <br />.84 <br />.90 <br />2g <br />E=.006 <br />.011 .017 .022 .028 .034 .038 .045 .051 <br />.057 <br />.063 <br />1 .070 <br />..076 <br />.083 <br />250 <br />T=.08 <br />.16 .24 .33 .40 .49 .58 .67 .75 <br />.83 <br />.90 <br />.99 <br />1.06 <br />4.14 <br />1926.4 <br />E =.009 <br />.018 .027 .036 .046 .056 .065 .074 .083 <br />.093 <br />.106 <br />.120 <br />.127 <br />.135 <br />i TABLm L --Tangents and Externals to a 1° Curve. <br />j Chord =100 ft. - <br />Int. <br />Angle <br />10° <br />External <br />Int. <br />Int. <br />Angle <br />Tangent <br />External <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 />!0F <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 />:306.4 <br />50 <br />1157.0 <br />115.66 <br />50 <br />1526.3 <br />199.82 <br />50 +, <br />1907.9. <br />309.3 <br />2g <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 />50 <br />1963.6 <br />327.1 <br />24 <br />1217.9 <br />128.00 <br />31 <br />1589.0 <br />216.3 <br />38 <br />1672.9 <br />330.2 <br />10 <br />1226.6 <br />129.82 <br />10 <br />1598.0 <br />2L8.7 <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 />1624.9. <br />226.0 . <br />.40 <br />-2010.2 <br />7342.4 <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 />32 <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 ..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 />2066.6 <br />361.3 <br />50 <br />13140 <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 />_ <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 />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 />140 <br />1788.2 <br />272.6 <br />40 .'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 />3b <br />1806.6.278.1 <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 />'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 />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 f <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 />Intle : G�rve 50 <br />Angl <br />10° <br />15° <br />20° <br />250 <br />30° <br />35° <br />40° <br />1 45° <br />• 50° <br />55° <br />. 600 <br />1 650 7'00 <br />20o.T=.08 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39.45 <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° T=.08 <br />.I6 <br />.24. <br />.33 <br />:40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.08 1.14 <br />E=_009" <br />-.018. <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° T=.10 <br />.19 <br />.29 <br />.39 <br />'.49 <br />.59_ <br />.69.79 <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° T=.11 <br />.22 <br />.34 <br />.47 <br />.58 <br />.69 <br />.80 <br />.93 <br />1.05 <br />1.17 <br />1.29 <br />1.42 <br />1.54 1.86 <br />E =.018 <br />.035 <br />-.054 <br />.072 <br />.086 <br />.109 <br />.131 <br />.153 <br />.175 <br />.197 <br />:213 <br />.230 <br />.247 .264 <br />400. T=.13 <br />.26 <br />.40 <br />.53 <br />.67 <br />.80 <br />.03 <br />1.08 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 1.94 <br />E=.023 <br />..046 <br />.070 <br />:093 <br />.117 <br />.141 <br />.172.203 <br />.234 <br />.265 <br />.277 <br />.290 <br />.315 .341 <br />45° T=•15 <br />.30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06, <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 2.21 = <br />E=-030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 .445 <br />