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TABLE I. - Tangents and Externals to a V Curve: <br />Chord= 100 ft. <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 />1° <br />50:00 <br />- '.22. <br />-�8' <br />400:66 <br />' 13.99 <br />-15" ' <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 />417:41x;.:15.18. <br />.34 <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 />E =.003 :007 <br />91.68 <br />1.73-•:' <br />50,. <br />442:55 <br />17.07 <br />50 <br />798.75 <br />55.13 <br />4•a•• <br />.100:01, <br />87 <br />9 <br />450.93 <br />17:72 <br />•18 <br />805.25 <br />56.31 <br />10'. <br />=108.35";;--'1:02 <br />.038 <br />10, <br />459.32 <br />`18:38 <br />10 <br />813.75 <br />57.50 <br />0-20 <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'- <br />.476:.10- <br />C 19.75 <br />'30 <br />830.76 <br />59.91 <br />•1,---••40, <br />133-.36,' <br />'-1:55 <br />-40, <br />'484.49--• <br />20.45 <br />40 <br />839.27 <br />61.14 <br />50,,-^141.70 <br />4209.2 <br />"1.75, <br />50.. <br />492.85 <br />, 21.16 <br />50.. <br />8417.78 <br />62.38 <br />" <br />'150:04. <br />1.96 <br />10- ':, <br />'501:28 <br />21.-S9 <br />17 ' -. <br />856.30 <br />63.63 <br />•8". <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 />- 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....24.91 <br />226.0 <br />40 <br />890.41 <br />68.77 <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 />25„ <br />,+200.08 <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />39 <br />2029.0 <br />348.6 <br />4 <br />1279.0 <br />- ' 3'49 ` <br />' :u: <br />551.70 <br />''26.50 <br />19•-- - <br />907.49 <br />71.42 <br />10 <br />208.43 <br />3.7.9 <br />10 <br />560.11 <br />27.31 <br />10 .'•916.03 <br />2047.8 <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 <br />t 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 />78.26 <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 />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 />266.56. <br />=. 6.21:. <br />%' , <br />.619.07 <br />-: 33.35' <br />. ;.::20- <br />975.96 <br />82.53 <br />30 <br />275.21 <br />6.61, <br />.20 <br />', 30 <br />627.50. <br />•:34.26 <br />" '- 30 <br />084.53 <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 />8 <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 ,•669.70 <br />1788.2 <br />39.01 <br />20 <br />1027.5 <br />91.40 <br />30 <br />1419.7 <br />9.23 <br />30' <br />678.15 <br />39.99 <br />30 <br />1036.1 <br />92.92 <br />40 <br />.325.35 <br />333.71• <br />- 9.71 <br />40 <br />686.60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 ''342.08' <br />1437.4 <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 />-358.81-22 <br />181.89 <br />.: --• 10 " <br />711.97 <br />44.07 <br />10 <br />1070.6 <br />99.16 <br />20 <br />367.17 <br />11.11.75, <br />207 <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 />383.91 <br />12.85 <br />40. <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 />50 <br />1105.1 <br />_ <br />105.60 <br />Corrections to be Added (T =Tangent. E=External.) <br />let25° <br />Angle Curve 5° 10° <br />15° 20° y30° <br />,35� <br />40° <br />45° 50° <br />550 <br />60° <br />65° <br />70° <br />50 T=.02 .03 <br />.05 .O6 .., :08- .10 <br />- .11 <br />.13_15 <br />.16 <br />.18 <br />.20 <br />.21 <br />•23 <br />E=.000 .000 <br />.001 .001 .002 ...002 <br />.002 <br />.003 <br />.003 •.004 <br />.004 <br />.004 <br />.005 <br />.00 <br />loo T =.03 O6 <br />.09,-:13' .16 .19 <br />.22 <br />.25 <br />`.28` .31 <br />.34 <br />.38 <br />.42 <br />•41 <br />E=.001 .003 <br />.004 .006 .007 -..008 <br />..009 <br />.011 <br />.012 .014 <br />.015 <br />.017 <br />.0180- <br />303.5 <br />150 T=.04 .10-; <br />�.14 .19 .24 .29 <br />.34- <br />.39 <br />.45 .51 <br />".53 <br />.58 <br />.63 <br />.6E <br />E =.003 :007 <br />.010 .014 .018 .023 <br />.027 <br />.029 <br />.032 .035 <br />.039 <br />.043 <br />.047 <br />•OE <br />20° T=.0V .13 <br />'.19, .26 .32 .39 <br />.45 <br />.51 <br />.58 .65` <br />.72 <br />.79 <br />.84 <br />•91 <br />E =.006 .011 <br />.017 .022 .028 .034 <br />.038 <br />.045 <br />.051 :057 <br />.063 <br />.070 <br />.076 <br />.Ot <br />25 o JT=.08 .16 <br />.24 `.33 .40 .49 <br />.58 <br />.67 <br />.75 .83 <br />'.093 <br />.90 <br />.99 <br />1.06 <br />�•19 <br />'.1 <br />;E =.009 .018 <br />.027 .030 .616 .056 <br />.065 <br />.074 <br />.083 <br />.106 <br />.120 <br />.127 <br />-321.1 <br />,TABLE L =- Tangents and Externals to a 1' Curve. <br />Chord =100 f t. <br />fit•Tangent <br />"'Angle <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />-Int. <br />Angle <br />Tangent <br />External <br />1113.7 <br />107.24 <br />29° <br />1481.8 <br />188.51 <br />36° <br />1861.7 <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 />306.4 <br />i '50 ! <br />1157.0 <br />115.66 <br />50 <br />1526.3 <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 />4209.2 <br />126.20 <br />50 <br />1580.0 <br />213.86 <br />50 <br />19636 <br />-327.1 <br />'24 <br />1217.9 <br />128.00 <br />31 <br />1589.0 <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 />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 />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 <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 />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 />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 />1374.2 <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 />164186 <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 />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 />I <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 <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 />Curve 5* <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />550 <br />60° <br />650 70° <br />200:, <br />T=.06 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84 .90 <br />E=.000 <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 />25o <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 />:018 <br />.027 <br />.036 <br />.046 <br />.055 <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 />.49 <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=11 <br />.22 <br />.34 <br />.47 <br />.58 <br />1 .69 <br />.80 <br />.93 <br />1.05 <br />1.17 <br />1.29 <br />1.42 <br />1.54 1.66 <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 />40° <br />T=.13 <br />.20 <br />.40 <br />.53 <br />.67 <br />.80 <br />.93 <br />1.06 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 1.94 <br />E=.023 <br />.040 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 <br />.277 <br />.290 <br />.315 .341 <br />45° <br />T=15 <br />.30 <br />.44 <br />.60.76 <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 />