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II TALE I. - Tangents and Externals to a 1° 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. <br />13,90, <br />15° ` <br />754.32 <br />49.44 <br />10' <br />58.34 <br />.20 <br />I0' <br />-GG <br />409.03 <br />14.58 <br />1lY <br />762.80 <br />50,55 <br />20. <br />66.67 <br />.89 <br />20 <br />417.41 <br />15.18 <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 />706.76 <br />55.13 <br />2 <br />100.01 <br />.67 <br />9 <br />450193 <br />17.72 <br />16 <br />805.25 <br />56.31 <br />10 <br />108.85 <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 />LID, <br />20 <br />467171 <br />19.00 <br />20 <br />822.25 <br />58.70 <br />00 <br />125:02 <br />1.36 <br />.30 <br />476'.10 <br />19:75 <br />30 <br />830.76 <br />59.91 <br />40- <br />133.30 <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 />847.78 <br />62.38 <br />3 <br />150.04' <br />1.96 <br />10 <br />501.28 <br />21.89 <br />17 <br />556.30 <br />63.63 <br />10 <br />158.39 <br />2.19 <br />10 <br />'509.68, <br />22.62,. <br />10 <br />864.82 <br />- 64.90 <br />,20 <br />106.72 <br />'2.43 <br />I 20 <br />518.08 <br />23.38 <br />20' <br />873.35 <br />66.19 <br />30 <br />175.OG <br />2.67 <br />I 30 <br />526.48 <br />24.14 <br />30 <br />8S1.88 <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 />65.77 <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 />16; <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 />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 />28.97 <br />30 <br />033.13 <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 />76.80 <br />50 <br />241.81 <br />5.10 <br />50 <br />593.79 <br />30.68 <br />50 <br />950.25 <br />78.20 <br />6 <br />250.16 <br />6.46 <br />12 <br />602.21 <br />31.66 <br />10 <br />958.81 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />10 <br />G1O.64 <br />32.45 <br />10 <br />967.38 <br />81.09 <br />20 <br />266.80 <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 />964.53 <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 />291.02 <br />7,43 <br />50 <br />644.87 <br />36.12 <br />50 <br />1001.7 <br />86.90 <br />0 <br />.300.23 <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 />G61.25 <br />38.03 <br />10 <br />1018.9 <br />89.89 <br />20 <br />316.90 <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 />078.15 <br />39.99 <br />30 <br />1036.1 <br />92.92 <br />40 <br />x33.71 <br />9.71 <br />40 <br />680.60 <br />40.99. <br />40 <br />1044.7 <br />94.46 <br />50 <br />3421,08 <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 />338.81 <br />-11.22 <br />10 <br />711.97 <br />44.07 <br />• .- 10 <br />, <br />1070,0" <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 />375.64. <br />12.20 <br />.30 <br />728.90. <br />46.18 <br />30 <br />1087.8 <br />.102.35 <br />40 <br />333.01 <br />12.85 <br />40 <br />737.:37 <br />47.25 <br />40 <br />1096.4 <br />103.97 <br />LO <br />392.28 <br />13.41 <br />50 <br />745.85 <br />48.34 <br />50 <br />.1105.1 <br />105.60 <br />Corrections to be Added (T = Tangent. .E = External.) - <br />P°4r Curs° 5° <br />Angle <br />10° I5° 20° 25° 30° <br />1 35° 1 49° 1 45° 50° 55° 60° <br />65° <br />70° <br />So ' .T=.02 <br />.03 _05 .00 .08 '.10.11 <br />.13 .15 ,16 .18 .20 <br />.21 <br />.23 <br />E=.000 <br />.000 .001 .001 :.OU .002 <br />(Ri .09 .13 16 .19 <br />.002 .003 .003 .,004 .004 ..004 <br />.22 .25 M .31 .84 .38 <br />.005 <br />.. 2 <br />.005 <br />.46 <br />10° T=.03 <br />E =AOI <br />.003 .004 .006 .007 .008 <br />.009 .011 .012 .014 .015 .017 <br />.018 <br />.020 <br />10' <br />10 .14 .19 .24 .29 <br />.34 . .39 .45 .51 .53 .58 <br />--.63 • <br />.68 <br />E=.003 <br />.007 .010 .014 .018 .023 <br />.027 .029 •.032 035 .039 .043 <br />•.047 <br />.051_ <br />20° T- 06 <br />13 .19 1 .26 .32 .39 <br />.46 .51 .58 .65 .72 .79 <br />.84 <br />.90 <br />E =,006 <br />All .017 .022 .028 .034 <br />.038 .045 .051 .057 .063 .070 <br />.076 <br />.083 <br />25' T=.08 <br />16 .24 ,33 .40 49 <br />.58 .67 .75 .83 .90 .99 <br />1.06 <br />1.14 <br />E=,008 <br />018 .027 .036 .048 056 <br />.065 .074 .083 .093 .106 :120 <br />.127 <br />.135 <br />TABLE I. - Tangents and Externals to a 1° Curve.' III <br />- C hord'-100 ft. <br />Int' <br />Angle <br />Tangent <br />lIxternal <br />Int <br />Angle <br />Tangent <br />ExtUllal <br />Int. <br />Angle . <br />Tangent <br />External <br />221- <br />1113.7 <br />107.24 <br />29°' <br />1481.8 <br />188.51 <br />36° <br />1861.7 <br />294.9 <br />10P <br />11'22.4 <br />108.90 <br />10' <br />1490.7 <br />190.74 <br />-• 30' <br />1870'.9 <br />297:7 <br />2U <br />1131:0 <br />.110.57 <br />-120 <br />1499.6 <br />192,99 <br />20 <br />1880.1 <br />300.6 <br />3U ' <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 />LU <br />1157.0 <br />115.60 <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.I <br />312.2 <br />10 <br />1174.4 <br />119.12 <br />-.10 <br />1544.2 <br />204.44 <br />- 10 <br />1020:4 <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 />1972.9. <br />330.2 <br />-ID <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 />1G24.9 <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 />2019:0. <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 />1097.2 <br />246.1 <br />40 <br />20S5,4 <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 />171513 <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 />4D <br />3733.5 <br />256.5 <br />40 <br />2123.3 <br />380.8 <br />50 <br />1366.8 <br />160.76 <br />5D <br />1742.0 <br />259.1 <br />50 <br />2132.7 <br />384.1 <br />27 ." <br />1375.6 <br />162,'81 <br />34' <br />1751.4 <br />261.8 <br />41 <br />2142:2 <br />389.4 <br />10 <br />1384.4 <br />164,66 <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 />2402.0 <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 />60 <br />2189 9 <br />'404.2 <br />28-- <br />1428.6 <br />175.41 <br />35 <br />18066.6 <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 />2218:0 <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 />224T.3 <br />425.0 <br />Corrections to be Added (T -Tangent. E External.) <br />Int. <br />Angle <br />,. Curve 5° 10°. <br />15° <br />20° <br />25° 30° 1 <br />35° 140° <br />45° 1 50° 55! <br />60°- 65° 70° <br />200T <br />-.013.I3 <br />.19 <br />.26 <br />.32 .39 <br />.45 .51 <br />.58 .65 72 <br />.79 .84 :90 <br />, E =.000 .011 <br />.017' <br />.022 <br />.028 .034 <br />.0381.045 <br />.051 .057 .063 <br />.070 .076 .083 <br />25° <br />T =.08 .16 <br />.24 <br />.33 <br />.40 ..49 <br />•.58 .67 <br />.75 .83 <br />1.06 1.14 <br />E =.009 .018 <br />.027 <br />.030 <br />'.046 .056 <br />.005 .074 <br />.033 .093 <br />+?(0'6..127 .135 <br />300 <br />T=,10 .19 <br />.29 <br />AD <br />.49 .59 <br />.69 .79 <br />.80 .99 <br />1.29 1.39 <br />E =.013 ..025 <br />.038 <br />.051 <br />AG5 .078 <br />.030 .103 <br />.116 .129 <br />.179 .188 <br />35° <br />T=.11 .22 <br />.34 <br />.47- <br />'.58 .60 <br />80 .93 <br />1.05 1.17 1.20 <br />1.42 1.54 1.66 <br />E=.018 ..035 <br />.054 <br />.072 <br />.086 .109 <br />.131 .153 <br />.175 .197 .213 <br />.230 .247 .264 <br />.26 <br />,4p <br />.53 <br />.87 .80 <br />.93 1.06 <br />1.20 1.34 kA9 <br />1:04 1.79 1.94 <br />E =.023 .046 <br />T=.15 .30 <br />:070 <br />.44 <br />.093 <br />.69 <br />.117 .141 <br />.76 .91 <br />..172 .203 <br />LOB 1.21 <br />.234 .205 .277 <br />1.37 1.52 1.60 <br />.290 .315 341 <br />1.87 2.04 2,2h <br />450 <br />E=.030 .00 <br />.093 <br />.119 <br />.153 .184 <br />.210 .254 <br />.289 .325 351 <br />.378 .416 .445 <br />Mine <br />