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a II <br />TABLE I. - Tangents and Externals to a 1° Curve. <br />Chord =100 ft. <br />Int. <br />Angle <br />Tangegt <br />Exter al <br />'Int. ' <br />' 'Angle4 <br />'Tangent <br />-Angle <br />External <br />Int' <br />Tangent <br />External <br />1° <br />50:66-' <br />.:22. <br />8° <br />400.GG <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 />417:41 <br />15.18 <br />.20 <br />771.29 <br />51.68 <br />30 <br />'75.01':Q <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 />442.55• <br />17.07 <br />50' <br />7961 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:. <br />•108.35- <br />".Y-1.02 <br />" 10 <br />459.32 <br />18:38 <br />10 , <br />813:75 <br />5750 <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.Z <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 />7133.36 <br />1:55 <br />40. <br />484.49. <br />20.45 <br />40 <br />839.27 <br />61:14 <br />750 <br />;141':70. <br />1.75' <br />-50 <br />492.83 <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 />.1.7 <br />'856.30 <br />-.63:63 <br />=•^ 10 • <br />7-158,38 <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 />518.03; <br />^-23.38. <br />_ 20 .-873.35 <br />1991.5 <br />1:66:18 <br />30 <br />175.06 <br />2.67 <br />30'526.48, <br />1615.9 <br />.•24.14 <br />30 <br />881.88 <br />67.47 <br />40 <br />183.40 <br />2.93 <br />40..>534.89.' <br />1624.9 <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 />L <br />'200:08 <br />3:49 = <br />11P <br />-551.70' <br />-26.5 <br />38 = <br />907-:.49:: <br />71.42 <br />10 <br />208.43 <br />3.79 <br />10 <br />560.11 <br />27.31 <br />10 ..916.03-. <br />2029.01 <br />72.76 <br />20 <br />216.77 <br />4.10 <br />20, <br />1568.53 <br />28.14 <br />20, <br />924.58 <br />74.12 <br />30 <br />225.12 <br />-11.42 <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 />'585.36 <br />29.8240 <br />30 <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 />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 />266.86, <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 />50 <br />644.37 <br />'36.12 <br />50 . <br />1001.7 <br />86.90 <br />6 <br />300.28 <br />., 7.86 <br />13 <br />652.51 <br />Y37.07 <br />20 - <br />1010.3 a. <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 <br />669.70 <br />..39.01 <br />20 <br />.1027.5 <br />91.40 <br />30 <br />1393.2 <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 />_ <br />9.71 <br />40 <br />686.60 <br />'• 40.99 <br />40. <br />1044.7 <br />94.46 <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 />7.11'.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 />-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 />105.60 <br />_.,., <br />Corrections to be Added (T =Tangent. E =External.) <br />Angle <br />Curve 5° <br />10° 15° 20° <br />25° <br />30°' 35°--, <br />40° 45° <br />x.13 <br />'50° <br />55° <br />60° 65° <br />70° <br />5° <br />T=.02 <br />.03 .05 .O6 <br />,; O8 <br />.10 .11 <br />.15 <br />.16 <br />.18 <br />.20 .21 <br />.23 <br />108.90 <br />E=.000 <br />.000 .001 .001 <br />.002 <br />..002 •.002 <br />_.003 .003 <br />; .004 <br />.004 <br />.004 .005 <br />.005 <br />10° <br />T =.03 <br />.06 .09 -'.13 <br />.16 <br />.19 .22 <br />.25 .28. <br />.31 <br />.34 <br />.38 .42 <br />.46 <br />1508.5. <br />E=.001 <br />.003 .004 .006 <br />.007 <br />..008 ,.009 <br />.011 .012 <br />.014 <br />.015 <br />.017 .018 <br />.020 <br />15° <br />T =.04 <br />.10- .14 .19 <br />.24 <br />.29 .34 <br />.39 .45 <br />al <br />:53 <br />.58 .63 <br />.68 <br />" '50- ! <br />E=.003 <br />::007 '.010 .014 <br />.018 <br />.023 .027 <br />.029 .032 <br />.035 <br />'.039 <br />.043 .047 <br />.051 <br />20° <br />T=.OG'.13 <br />'.19 .26 <br />.32 <br />.39 .45 <br />.51 .58 <br />.65 <br />.72 <br />.79 .84 <br />.90 <br />'315.2 <br />E =:006 <br />.011 :017 .022 <br />.028 <br />.034 .038 <br />.045 .051 <br />.057 <br />.063 <br />.070-.076 <br />.083 <br />25° <br />T=.08 <br />.16 .33 <br />.40 <br />.49 .58 <br />.67 .75 <br />.83 <br />.90 <br />.99 1.06 <br />4.14 <br />x-135 <br />1200.5 <br />E =.009 <br />.018 :027 .036 <br />.048 <br />.056 .065 <br />,074 .083 <br />.093 <br />.106 <br />.120 .127 <br />1209.2 <br />,T"BL"B L = Tanteiits and-Ext6m s to a 1° Curve ' <br />Chord=100 ft. <br />" Int''.•' <br />Aagle <br />�Taiigent <br />External <br />Int• <br />Angle <br />Tangent <br />External <br />Int. <br />Angle . <br />Tangent <br />External <br />45° <br />1113.7, <br />107.24 <br />:29°,-' <br />1481.8 <br />188.51 <br />36° <br />1861.7:' <br />•. 294:'9 <br />1W <br />1122.4 <br />108.90 <br />10' <br />1490.7 <br />190.74 <br />10' <br />'1870.9 <br />•.297.7 <br />.84 .90 <br />1131.0, <br />110.57 <br />20 <br />1499.6 <br />192.99 <br />'20 <br />1880.1, <br />300.6 <br />--20 <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 />•` <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 />1 •' 50 <br />-1157.0 <br />115.66 <br />50 <br />1526.3 <br />199.82 <br />" '50- ! <br />1907.9 <br />309.3 <br />28 <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 />119.1210 <br />.49 <br />1544.2, <br />204.44 <br />10 <br />1926.4• <br />'315.2 <br />BO <br />1183.1- <br />120.87 <br />s .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 />• ,: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 />.093 <br />'.119 <br />.153 <br />.184 <br />.216 <br />254 <br />i <br />t <br />.351 <br />s28 <br />1270.2 <br />139.11 <br />32-' <br />1643.0 <br />230:9 <br />39 - <br />2029.01 <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 />'201287.7 <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 />' <br />1314.0 <br />I <br />148.75 <br />'50 <br />1688.1 <br />243.5 <br />50 <br />2076.0; <br />364.5 <br />28 - <br />1322.8 ,-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 />172.1.4 <br />253.9 <br />30 <br />2113.8- <br />377.5 <br />40 <br />1358.0 <br />153.72 <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 />t27 ' <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 />1400.8 <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 />-40 <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 />o 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 />j421.4 <br />'50 <br />1472.9 <br />186.29 <br />50 <br />1852.5 <br />292.0 <br />50 <br />2247.31 <br />425.0 <br />Coirectio is to be Added'(T=Tarige-iit. E=External:) <br />Int <br />Anglo <br />CuitieS°' <br />10° <br />15°. <br />20° <br />25° <br />30° <br />35° <br />40° <br />45° <br />50° <br />55° <br />60°"65* <br />`70' <br />ZOo.: <br />T=.06'. <br />•.13 <br />'.19 <br />.26 <br />..32 <br />.39 <br />':034 <br />-.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 />,.038 <br />'.:045 <br />.051 <br />.057 <br />-.063 <br />...070 <br />-.076 -.083. <br />25° <br />„ 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 />1.06 1.14 <br />E =:009 <br />O1S <br />:027 <br />:036 <br />'.046 <br />.056 <br />.065 <br />.074 <br />.083 <br />.093 <br />:106 <br />-.120 <br />-.12Z .135 <br />30°: <br />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° <br />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 1.66 <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 />400 <br />T=:13 <br />.26 <br />.40' <br />.53 <br />.67 <br />.80 <br />.03' <br />1.06 <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 <br />.203 <br />.234 <br />.265 <br />.277 <br />.290 <br />.315 .341 <br />45° <br />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 />.239 <br />325 <br />.351 <br />378 <br />.411 .445 <br />