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II TABLE I. - Tangents and Externa18 to a 1' Curve. <br />Chard � 100' ft. <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle• <br />Tangent <br />g <br />Fzternal <br />Ink <br />.Angle <br />Tan ent <br />,g <br />External <br />1' <br />50.00 <br />_ .22-_:, <br />8:. <br />400. GG'. <br />13.99 <br />15° <br />754.32�J <br />49.44 <br />10' <br />58.34 <br />.30 <br />10' <br />409:03 <br />14.53 <br />" 10' <br />'762.80 <br />_ 50.55 <br />�0 <br />60.67 <br />.39. <br />'` 20 <br />417.41 <br />15.18 <br />20 <br />771.29 <br />51.68 <br />30 <br />75.01 <br />.40 <br />30 <br />425.79 <br />15.80X30 <br />151 <br />779.77 <br />52.62 <br />40 <br />83.34 <br />,G1 <br />40 <br />434.17 <br />16.43 <br />40 <br />788.26 <br />53.97 <br />60 <br />. 91.G8 <br />.73 <br />50 <br />442.55 <br />17.07 <br />: 50 <br />796.75 <br />_'55.13 <br />2 <br />100.01 <br />S7 <br />0.. <br />450.93 <br />17.72 <br />is <br />805.25 <br />5G.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 />407.71 <br />.19.06 <br />20 <br />822.25 <br />58.70 <br />"0 <br />1255.02 <br />.1.36 <br />30 <br />476.10 <br />19.75 <br />".30 <br />830:7G. <br />59.91 <br />40 <br />-.133.36 <br />1.55 <br />40 <br />484.49 <br />20.45 <br />-40 <br />839127, <br />-61.14 <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 />.16 <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 />1GG..72 <br />2.43 <br />20 <br />518'.08 <br />23.38 <br />20 " <br />'873.35 <br />66.18 <br />30 <br />175.OG <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 />50" <br />543:29 <br />25.70 <br />50 <br />898.95 <br />70.09 <br />4 <br />200,08 <br />3.49 <br />11 <br />551.70 <br />26.50 <br />18 <br />007..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 />508.53 <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 />75.40 <br />40' <br />233.47 <br />4.70-. <br />"•' 10- <br />585.36 <br />29.82 <br />- -40 <br />941.69 <br />76. RG <br />50 <br />241.81 <br />-5,10 <br />'f 50 <br />593:79 <br />30.68 <br />50 <br />9:10.25. <br />78.26 <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 />5 1250.16 <br />1331.6 <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 />'G27.50 <br />34.,26 <br />30_ <br />`984.53 <br />83.97 <br />40 <br />233:57 <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 />3001.7 . <br />86.90 <br />6 <br />300.`98 <br />7 -SG <br />13 <br />652.81 <br />37.07 <br />20, <br />1010.3 <br />88.39 <br />10 <br />308:648.31 <br />166.95 <br />10 ' <br />661.25 <br />38:03 <br />10- <br />1018.9 <br />89.89 <br />20 <br />31$: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 />' 333.71 <br />9.71 <br />'40 <br />686.60 <br />40.99 <br />40 <br />1044:7 <br />94.46 <br />50 <br />342.OS <br />10.20 <br />50 <br />695,06 <br />42.00 <br />50 <br />10533 <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 />338:81 <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 />-875:54 <br />12.29 <br />30: <br />728.90 <br />' 46.18. <br />30 <br />1987.8 <br />102.35 <br />40 <br />333:91 <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 />45.34 <br />50 <br />1105.1 <br />'105.60 <br />Corrections to be Added (T =Tangent. E = External.) <br />I°4 <br />••Angle <br />-Curve 5° <br />10', <br />15° 20° <br />25° <br />30° <br />35° `40° <br />45° <br />50° 55° '600, 65° <br />70° <br />50: <br />T=-02 <br />.03 <br />05 .06 <br />.08 <br />.10 <br />.11 .13 <br />.15- <br />.16 .18 .20 .21 <br />.23 <br />103.90 <br />-E=.000 :'.000 <br />1490.7 <br />.001 .001 <br />.002 <br />.16 <br />.002 <br />- .19 <br />.002 .003 <br />.22 .25 <br />.003 <br />:28 <br />.004 .004 .004 .005 <br />31 .34. .36 . 2 <br />;:005 <br />.40 <br />T=-.03 . .06' <br />30" <br />.09. :13 <br />_ <br />E=.001 <br />.003 <br />.004 .006 <br />.007 <br />.008 <br />.009 .011 <br />.012 <br />.014 .015 .017 .018 <br />.020 <br />151 <br />T=.04 <br />.10 <br />14 .18 <br />24. <br />.29 <br />'.34 .39 <br />.45 <br />51 53 -.58 1 .63- <br />AS <br />1898.6 <br />Em.003 <br />.007 <br />'.010 .014 <br />.018 <br />.023 <br />.027 .029' <br />.032 <br />.035 :039 .043 .047 <br />';051 <br />20° <br />T=,.06 . <br />.13 <br />19 28 <br />.32 <br />.39 <br />.45 .51 <br />.58 <br />.05 ..72-..79 .84 <br />.90 <br />10 ; <br />E=.006' <br />.011 <br />017 .022 <br />.028 <br />.034 <br />.038 .04 <br />1926.4 <br />315.2 <br />20 <br />25° <br />T=.08 <br />.16 <br />.24 .99 <br />.40 <br />.49 <br />.58 .67 <br />318.1 <br />-.30 <br />1191:8 <br />122.63 <br />30 <br />.Ot8 <br />.027 .036 <br />.040 <br />.050 <br />.085 .07 <br />40 <br />1200.5 <br />124.41 <br />5 .051 .057 .003 .070 .078 '..083 <br />.75 .83 .90 .99 1.08 1.14 <br />4 .083 .093 .108 ..120 .127 ..135 <br />i <br />Thiii:e' I: = 'PE'Lilgen6 an&Externals to a V Curve. III <br />Chord =100 ft. <br />' fit' <br />AnBIe <br />Tan et t <br />g <br />Ex <br />Int. <br />Angle <br />Tangent <br />l xtcrual <br />lot. <br />Angle _• <br />Tangent <br />External <br />22°. ' <br />:711.3.7 <br />.107.24 <br />29° - <br />'1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.9 <br />'101- <br />"1123.4 <br />103.90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />1870.9 <br />297.7 <br />2u ' <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 />1`139.7 <br />112:25 <br />30 <br />1508:5 <br />195.25 <br />30 <br />1889.4 <br />303:5 <br />40 <br />7'148.4 <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 />23 <br />1165:7 <br />117.33 <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.t <br />209.121 <br />80 <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 />5o <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 />1922,9 <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 />11991.5 <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 />26 <br />:1270.2. <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />39 <br />2029.0 <br />348.6 <br />40 <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 />146.7940 <br />167M: <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 />1358:0 <br />158.72 <br />40 <br />' <br />258.5. <br />40 <br />"2123.3 <br />' 380.8 <br />50 <br />1366.8. <br />160.76- <br />50 <br />_1733.5 <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 />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 />175.41v <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 />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 />18L.69 <br />30 <br />1834.1 <br />286.4 <br />30 <br />2228:1 <br />418.0 <br />40• <br />1 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 />1652.5 <br />292.0 <br />50 <br />2247.3 <br />425.0 <br />Corrections to be Added- (T=Tangent. E=External.) <br />lat <br />Angle Curve 5° <br />'10° <br />15° <br />209 <br />25° 30° <br />35° 40° <br />45° 50° 55° 6& 60• 70° <br />2qo ' •T =.08 '.,'.13 <br />.19 <br />.26 <br />.32 .39 <br />.45 .51 <br />.58 .65 .72 .79.84 .90 <br />E =.006 <br />.011 <br />•.017 <br />.9122 <br />.028 .034 <br />:038 .0-45 <br />.051 ,.057 ..063 .070 -.076 .083 <br />'25° T=.08 <br />_16 <br />.24 <br />.33 <br />.40 .49 <br />.58• .67 <br />.75 .83 .90 ..99 1.08 11.14 <br />B=.009'. <br />.018 <br />.027 <br />.036 <br />.046 .056 <br />.065 .074 <br />.083 .093 ..105 .120 .127 .135 <br />30° T=.10 <br />Ali <br />.29 <br />.39 <br />.49 .59 <br />.59 .79 <br />.89.07 .90 1.09 1.20' 1.29 1.39 <br />E=.013 <br />.025 <br />.038 <br />.051 <br />.065 8 <br />A90 .103 <br />.116 .129 .149 _170 .179 .188 <br />5- -, . T=.11 : <br />.22 <br />•.34 <br />47 <br />1012 <br />SB .69 <br />.80 .03. <br />1.05 I.17 1.29 1.42 4.54 1.66 <br />E =,018" <br />•035 <br />.054 <br />.072 <br />.086 .109 <br />.131 .153 <br />.175 .197 .213 .230 .247 .204 <br />�qo T=.13 <br />:26 <br />•.40 <br />.53 <br />.67 .80 <br />.93 L.00 <br />1.20 1.34 1.49 1.64 1.79 1.94 <br />E =.023 <br />.046 <br />.070 <br />.093 <br />.117 .141 <br />.1,72 -.203 <br />.234 .265 .277 .290 .315 341 <br />.30 <br />.60r <br />.44 <br />.76 .9I <br />1 1.06 1.21 <br />1.37 1.52 1.70 1.87 2.04 2.21 <br />_ & =•030 <br />.060 <br />.D93...119 <br />.153 ,.184 <br />.216 .254 <br />.289 .325 .351 .378 .411 .445 <br />