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TABLE I. - Tangents and Ei-ternals to a V Curve. <br />Chord =100 f t. <br />Int.:Int.. <br />Angle <br />%10 <br />Tangent <br />Exte nal <br />Angler <br />Tangent <br />External <br />Int. <br />.Angle... <br />Tangent <br />External <br />5o T=.02 <br />.03 .05 .O6.08 <br />10 <br />-8°' <br />.13 .15 .16 <br />.13 <br />20 <br />.21 <br />.23 <br />E=.000 <br />50.00 <br />.22 <br />.002 <br />"4607W <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 />10' <br />762.80 <br />50.55 <br />20 <br />66.67- <br />_ ,.39 <br />20 <br />17,.41 <br />15.15 <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 .,108.35 <br />I6 .24 .33 .40 <br />1.02 <br />10 <br />459.32 <br />18.3S <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 <br />476.10 <br />19.75 <br />30 <br />S30.76 <br />59.91 <br />40 <br />.133.36 <br />1.55 <br />40 <br />484.49 <br />20,45 <br />40 <br />539.27 <br />..61.14 <br />50 <br />141.70 <br />1.75- <br />50 <br />492.S8 <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 />21.59 <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 />175.00 <br />2.67 <br />30 <br />626.48 <br />24.14 <br />30 <br />881.58' <br />67.47 <br />40 <br />153.40 <br />2.03 <br />40 <br />534.89 <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 />598.95 <br />70.09- <br />4 <br />200.08 <br />3.49 <br />11 <br />551.70 <br />26.50 <br />18 <br />907.40 <br />71.42 <br />10 <br />208.43 <br />3.79 <br />30 <br />560.11 <br />27:31 <br />10 <br />016.03 <br />72.76 <br />20 <br />216.77 <br />4.10 <br />20 <br />568.53 <br />25.14 <br />20 <br />024.58 <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 />555.36 <br />29.82 <br />40 <br />'041.60 <br />7G. SG <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 />5 <br />250.16 <br />5.46 <br />12 <br />602,21 <br />31.56 <br />19 <br />958.51 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10' <br />G10.64 <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 />627.50 <br />34.26 <br />30 <br />954.53. <br />53.97 <br />40 <br />253.57 <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 />G44.37 <br />36.12 <br />50 <br />1001.7_ <br />86.90 <br />6 <br />300:28 <br />7. SO <br />13 <br />652.S1 <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 />35.03 <br />10 <br />1018:9 <br />89.59 <br />20 <br />-316.00 <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 />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 />1044.7 <br />9.1 .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 <br />1070.6 <br />09.16 <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 />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 />. 4S.34 1 <br />50 <br />1105.1 <br />105.60 <br />Corrections to be Added (T =Tangent. E=External.) - <br />Int. Curve 5° <br />Angle <br />10° 15° 20° 25° <br />30° <br />35° <br />40° 45° 50° <br />55° <br />60° <br />65° <br />70° <br />5o T=.02 <br />.03 .05 .O6.08 <br />10 <br />.11 <br />.13 .15 .16 <br />.13 <br />20 <br />.21 <br />.23 <br />E=.000 <br />.000 .001 .001 .002 <br />.002 <br />.002 <br />.003 .003 .004 <br />.004 <br />.004 <br />.005 <br />.005 <br />10° T=.03 <br />.06 .09 .13 .16 <br />.19 <br />.22 <br />.25 .28 .31 <br />.34 <br />.38 <br />.42 <br />.46 <br />E=.001 <br />.003 .004 .006 .007 <br />.008 <br />.009 <br />.011 .012 .014 <br />.015 <br />.017 <br />.018 <br />.020 <br />15. T=.04 <br />.10. .14 .10 .24 <br />.29 <br />.34 <br />.39 .45 .51 <br />..53 <br />.58 <br />.63 <br />.68 <br />E =.003 <br />.007 .010 .014 .018 <br />.023 <br />.027 <br />.029 .032 .035 <br />.039 <br />.013 <br />.017 <br />.051 <br />20' T =,06 <br />.13 .19 .26 .32 <br />.39 <br />.45 <br />.51 .58 G5 <br />.72 <br />.79 <br />.84 <br />.90 <br />E=.006 <br />.011 .017 .022 .028 <br />.034 <br />-.038 <br />.01:; .Q51 ,057 <br />.OG3 <br />.070 <br />.076 <br />.083 <br />25° T=.08 <br />I6 .24 .33 .40 <br />.49 <br />.58 <br />.67 .75 .S3 <br />.90 <br />.99 <br />1.06 <br />1.14 <br />E =.000 <br />.018 .027 .036 .046 <br />.056 <br />.065 <br />.074 .083 .093 <br />.106 <br />.120 <br />.127, <br />.135 <br />TABLE L - Tangents and Externals to a 1° Curve. III <br />Chord =100 ft. <br />Int. <br />Angle <br />Tan <br />1113 .T <br />4 <br />29777'1481.5 <br />25° <br />_ <br />Int. <br />Angle <br />Tangent <br />External <br />22°' <br />158.51 <br />36° <br />1861.7 <br />294.9 <br />10' <br />10' <br />1490.7 <br />190.74 <br />10' <br />.1870.9 <br />297.7 <br />20" <br />.1122.41.`108.90 <br />1131.0 <br />110.57 <br />20 .1499.6 <br />.13 <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 />.017 <br />1148.4 <br />113.95 <br />40 <br />1517.4 <br />197.53 <br />40 <br />1898.6 <br />306.4 <br />.40 <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 />11G5.7 <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 />123.00 <br />•31 <br />1559.0 <br />21G.3 <br />38 <br />1972.9 <br />330.2 <br />10 <br />.131 <br />129.82 <br />10 <br />.1598:'0 <br />218.7 <br />10 <br />1952.2, <br />333.2 <br />20 <br />.1226.6 <br />•1235.3 <br />65 <br />20 <br />1606.9 <br />221.1 <br />20 <br />1991.5 <br />336.3 <br />30 <br />1244.0 <br />.131 <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 />22G.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 />2.04 2.21 <br />139.11 <br />32 <br />1643.0 <br />230.9 <br />39 <br />2029.0 <br />348.6 <br />10 <br />.1270.2 <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 />1658.1• <br />243.5 <br />50 <br />2076.0 <br />364.5 <br />26 <br />1322.8 <br />150.71 <br />33 <br />1G97.2 <br />246:1 <br />40 <br />2085.4 <br />367.7 <br />10 <br />1331.6 <br />152.69 <br />10 <br />3,706.3 <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 />1.56.70 <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 />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 />2199.4 <br />407.6 <br />10 <br />1437.4 <br />177.55 <br />10 <br />1515.7 <br />280.S <br />10 <br />2209.0 <br />411.1 <br />20 <br />1446.3 <br />179.72 <br />20 <br />1824.9 <br />283.G <br />20 <br />2218.6 <br />414.5 <br />30 <br />14555.1' <br />181.59 <br />30 <br />1834.1' <br />286.4 <br />30 <br />2228.1 <br />418.0 <br />4U <br />1464.0 <br />154.08 <br />40 <br />'1843.3 <br />289.2 <br />40 <br />2237.7 <br />421.4 <br />50 <br />1472.9 <br />1 1SG.29 <br />50 <br />1S52.5 <br />292.0 <br />50 <br />2247.3 <br />425.0 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int.CurvcS° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />SD' <br />55° <br />60° <br />65° 70° <br />Angle: <br />20o T=.06 <br />.13 <br />.19 <br />.20 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84 .90 <br />E=.00G <br />.011 <br />.017 <br />.022 <br />.03S <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 .083 <br />T=.08 <br />.16 <br />24 <br />.33 <br />*.4.49 <br />.58 <br />.G7 <br />.75' <br />.S3 <br />.90 <br />.00 <br />1.06. 1.14 <br />25' <br />E =.009 <br />.018 <br />.027 <br />.030 <br />.065 <br />.074 <br />.083 <br />.093 <br />.106 <br />.120 <br />.127 .135 <br />30o T=.10 <br />.19 <br />29 <br />.39 <br />.69 <br />.79 <br />.89 <br />.99 <br />1.00 <br />1.20 <br />1.29 1.39 <br />E=.013 <br />.025 <br />.038 <br />.051 <br />.055 <br />.78 <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 />.G9 <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 />40o T=.13 <br />.26 <br />.40 <br />.53 <br />.67 <br />.30 <br />.fl3 <br />1.06 <br />13.0.1.34 <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 <br />.2803 <br />.234 <br />.265 <br />.277 <br />.200 <br />..315 .341 <br />450 T=.15 <br />30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />131 <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 />311 <br />354 <br />.289 <br />.325 <br />351 <br />.378 <br />.411 .445 <br />