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I k I- <br />TABLE I. - Tangents and Externals to'A 1° Curve. <br />M nrrl =100 ft. <br />Angle <br />Tangent <br />External <br />'Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />43° <br />22-57.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />3110.9 <br />790.1 <br />10' <br />.315 <br />432.0 <br />I(Y <br />2681.9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />_2260.6 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.G <br />800.'4 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />'605.3 <br />30 <br />3143.4 <br />805.6 <br />40 <br />2295.6 <br />442.8 <br />4D <br />2712.5 <br />609.6 <br />40 ' <br />3154.2 <br />810.9 <br />50 <br />2365:2 <br />446.4' <br />50 <br />2722.7, <br />614.0 <br />50 <br />3165.1 <br />'816.1 <br />�¢ <br />2314.9 <br />450.0 <br />512732.9 <br />2.57 .60 <br />613.4 <br />,58 <br />3176.0 <br />3186.% <br />821.4 <br />826.7 <br />10 <br />20 <br />.2324.6• <br />2334:3 <br />453.6 <br />457.3 <br />10 . <br />20 <br />2743:1 <br />2753.4 <br />622.8 <br />'627.2 <br />.10 <br />20 <br />3197.8 <br />832.0 <br />30 <br />234:4. 1. <br />461.0' <br />' 30 <br />2763.7 <br />631.7 <br />30 <br />40 <br />3208.8 <br />3219.7 <br />837.3 <br />40 <br />50 <br />2353.8 <br />2363.5 <br />464.0 <br />468.4 <br />40 <br />50 <br />2773.9 <br />2784.2 <br />636.2- <br />-640.7 <br />50 . <br />3230.7 <br />.842.7 <br />848.1 <br />45'. <br />2373.3 <br />472.1 <br />52 <br />2794.5 <br />645.2 <br />'649.7 <br />59 <br />10 <br />3241.7 <br />3252.7 <br />853.5 <br />858.9 <br />10 <br />2393.1 <br />2392.8 <br />475.8 <br />`_479.0 <br />10 <br />20 <br />2SO4.9 <br />2815.2 <br />654.3 <br />20 <br />,3263.7 <br />864.3 <br />20 <br />30 <br />2402.6 <br />483.4 <br />30 <br />2S25.6 <br />658.8- <br />30 <br />3274:8 <br />869.8 <br />40 <br />2412.4 <br />487.2 <br />40 <br />2835.9 <br />603.4 <br />40 <br />.3285.8.875.3 <br />-880.8 <br />50 <br />2422.3 <br />491.0' <br />50 <br />2846.3. <br />668.0. <br />a <br />50 <br />3296:0 <br />1768.2 <br />46 <br />2432:1 <br />494.S <br />'53. <br />2856.7' <br />672.7 <br />60 <br />10 <br />3308.0 <br />3319.1 <br />SSG. 4 <br />892.0 <br />10 <br />2441.9 <br />498.7 <br />502.5_ <br />10 <br />20 <br />2867.1 <br />2577.5 <br />677.3. <br />682.0 <br />20 <br />3330.3 <br />597.5 <br />20 <br />30 <br />2451.8, <br />2461:7 <br />506.4. <br />30 <br />2SS8.0 <br />656.7 <br />30 <br />3341.4- <br />903.2 <br />-=40 <br />2471.5 <br />510.3' <br />40 <br />2898.4 <br />•691.4 <br />40 <br />50 <br />3352.6 <br />3363.8 <br />90S.8 <br />'914.5 <br />50.'2481.4 <br />3801.4 <br />514.3, <br />50 <br />2908.9 <br />696.1 <br />10 <br />4908.0 <br />IS14.7 <br />472491.3 <br />3816.4 <br />518.2 <br />54' <br />2919.4 <br />700.9 <br />705.7 <br />61 <br />10 <br />3375.0 <br />920.2 <br />925.9 <br />10 <br />2501.2, <br />522.2 <br />10 <br />20 <br />2929.9 <br />2940.4 <br />710.5 <br />20 <br />.3386.3 <br />3397.5 <br />'931.6 <br />20 <br />30 <br />2511.2 <br />2521.1 <br />526.1 <br />530.1 <br />30 <br />2951.0 <br />715.3 <br />30 <br />3408.8 <br />-937.3 <br />40 <br />2531.,1 <br />534.2 <br />40 <br />2951.5 <br />720.1 <br />725.0 <br />40 <br />50 <br />.3420..1 <br />3431.4 <br />. 943.1 <br />948.9 <br />50 • <br />'2541.0 <br />538.2 <br />50 <br />2972.1 <br />1492.4 <br />8.2 <br />4990.7 <br />.ISG2.2 <br />48 <br />2551.0 <br />542.2' <br />55 - <br />2952.7 <br />729.9 <br />02 <br />3442.7 <br />954:8 <br />960.6 <br />10 <br />2561.0 <br />546.3 <br />10. <br />20 <br />2993.3 <br />3003.9 <br />734.8 <br />739.7 <br />10 <br />20 <br />3454.1 <br />3465.4 <br />966.5 <br />20 <br />30 <br />257 1. 0 <br />2581.0 <br />550.4 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />-30 <br />3476.8- <br />`3488.3 <br />972.4 <br />40 <br />2591.0 <br />558.6 <br />40 <br />3025.2 <br />749.6 <br />40 <br />50 <br />3499.7 <br />978.3 <br />984.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3035.8 <br />754.6 <br />50 <br />;5054.3 <br />1910.7 <br />49 <br />1 2611.2 <br />566.0 <br />56 <br />3046.5 <br />759.6 <br />63 <br />10 <br />3511.1 <br />3522.6 <br />990.2 <br />996.2 <br />10 <br />2621.3 <br />571.1 <br />10 <br />20 <br />3057.2 <br />3067.9 <br />764.6 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />20 <br />30 <br />2031:3 <br />2641.4 <br />575.3 <br />579.5 <br />30 <br />3078.7 <br />774.7 <br />30 <br />40 <br />35.15.6 <br />3557.2 <br />100S.3 <br />1014.4 <br />4.0 <br />'2651.5 <br />583.8 <br />40 <br />50 <br />3089.4 <br />3100.2 <br />779.8 <br />784.9 <br />50 <br />3568.7 <br />1420.5 <br />50 <br />2661.6 <br />588.0 <br />• 40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />Corrections to be Added (T =Tangent. E =External,) <br />Angle <br />Curve 5° 10° <br />15° ZO° 2� 30° a5° 4a° 45° <br />501 55° <br />60° <br />65° <br />70° <br />Tangent <br />T=.£3 .26 <br />.40 .53 .67 :80 °3 .1051.20 <br />1.34 1,49 <br />277 <br />1.64 <br />: 90 <br />1.79 <br />1:94 <br />40° <br />E =.0_3 .046 <br />.070 .G93 .117 .14( .172 .203 .234 <br />.2G5 <br />10' <br />.315 <br />.341 <br />10' <br />T=.15 , .30 <br />.44 CO..'r6 :91 1.06 1.21 1.37 <br />1.52 1.70 <br />1.87 <br />2.04' <br />2 ?1 <br />.445 <br />45° <br />=.030 OGO <br />.093 .119 ..153 .184 .210 .254 .239 <br />.325 .351 <br />.379 <br />.411 <br />4667.4 <br />1660.5 <br />1-.17 84. <br />.5l' .68 .85 1.02 1.19 1.3G 1..54 <br />305 <br />1.72 1.91 <br />.425 <br />2.10 <br />.457 <br />2.29 <br />•.50$ <br />2.48 <br />50° <br />E =.037 .075 <br />.116 .151 .189 .227 266 .345 <br />.354 <br />3626.8 <br />1051.4 <br />X550 <br />4137.4 <br />T =.19 ?8 <br />.57 : 6 .95 1.14 1:33 1.52 1.72 <br />1-92 2.14 <br />2.35 <br />2.56 <br />2.77 <br />Sa° <br />E=.046 A93 <br />.142' .188 -239 233 .332 3-81 .420 <br />.479 .530 <br />.532 <br />641 <br />.07 <br />60° <br />3650.2 <br />1 0, 1.340 1 368 1. 91 <br />1.516 <br />2.17 675 2 G36 <br />2.57 .60 <br />2.93 774,, <br />651 <br />4723.2 <br />E =.050 .122 <br />.168 .25 <br />2.38 2.G3 <br />2.88 <br />3.3.13 <br />3.39 <br />1360.1 <br />T=W3 .46 <br />1.64 <br />69 .93 11.16 1.40 1.64 1.88 2.13 <br />65° <br />- g =.067 .135 <br />204 .273" .3,! .483 .554 .625 <br />.697 .711 <br />.R4.51.922,1.01 <br />4183:5 <br />1367.6 <br />mA>37,E 1. -. Tangents and Externals to.a,1° Curd(;' V <br />Chord =100 €t. <br />Ine <br />Angle ..__ <br />Tangent <br />External <br />Int' <br />Angle <br />Tangent <br />g <br />External. <br />Int' <br />-' Angle. <br />Tangent <br />External <br />64° <br />3580.3 <br />.. .. <br />1026:6. <br />71' <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4653.0 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.5 <br />30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1669.2 ' <br />.40 <br />3626.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4 095. 2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />.1345.1 <br />.50- <br />4709.2 <br />1086.9 <br />65 <br />3650.2 <br />1063.9 <br />22 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />10 <br />3661.9 <br />1070.2 <br />10 <br />4175.6 <br />1360.1 <br />.10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4183:5 <br />1367.6 <br />20: <br />4751,2 <br />1713.7 <br />80 <br />3685.4 <br />1082.9 <br />30 <br />4201.2 <br />1375.2 <br />30 <br />4765.3 <br />1722.7 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4214.0 <br />1382.8 <br />40 <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390.4 <br />50,' <br />4793,6 <br />1740.8 <br />66• <br />3720.9 <br />1102.2 <br />73 <br />4239.7 <br />1398.0 <br />80 .e <br />4807.7 <br />1749.9 <br />10 <br />3732.7. <br />1108.6 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />4822.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4265.6 <br />1413.5 <br />20 <br />4836.2 <br />1768.2 <br />30 <br />3756.5 <br />1121.7 <br />30 <br />4278.5 <br />1421.2 <br />20 <br />4850.5 <br />1777.4 <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40- <br />4864.8 <br />1786.7 <br />50 <br />3780.4 <br />1134.8 <br />50 <br />4304.6 <br />1436.8 <br />50 <br />4879.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />. 74 <br />4317.6 <br />14446 <br />81 <br />4893.6 <br />1S05.3 <br />10 <br />3801.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />IS14.7 <br />20 <br />3816.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4' <br />20 <br />4922.5 <br />1824.1 <br />30. <br />3828.4 <br />1161.3 <br />30 <br />4356.9 <br />1468.4 <br />_30 <br />4937.0 <br />1533.8 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />�10 <br />4951.5 <br />.1S43.1 <br />50. <br />3352.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4956.1 <br />1852.6 <br />63 <br />38G4.7 <br />1181.6 <br />75 <br />4396.5 <br />1492.4 <br />8.2 <br />4990.7 <br />.ISG2.2 <br />10 <br />3876.3 <br />1188.4 <br />10 <br />'4409.8 <br />1500.5 <br />10 <br />4995.4 <br />20 <br />38S9.0 <br />1195.2 <br />•20 <br />'4423.1, <br />1508.6 <br />20 <br />5010.0 <br />,1871.8 <br />;1881.5 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />4436.4 <br />1516.7 <br />30. <br />,5024.8 <br />189L.2 <br />40 <br />3913.4 <br />1208.9 <br />A0 <br />.4449.7 <br />1524.9 <br />40 <br />5039.5 <br />,1900.9 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />;5054.3 <br />1910.7 <br />69 <br />3937.9 <br />1222.7 <br />76 <br />447G.5 <br />1541.4,: <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3950.2' <br />1229.7 <br />I0 <br />',44S9.9 <br />1549.7 <br />10 <br />'5084.0 <br />1930.4 <br />.20 <br />3962.`5 <br />1235.7 <br />'•20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />.1940.3 <br />30 <br />3974:8 '.1243.7 <br />80 <br />:4510.9 <br />1566.3. <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3987_2 <br />1250.3 <br />• 40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />8999.5 <br />1257.9 <br />50 <br />4544.0, <br />1583.1 <br />50- <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1205.0 <br />77 <br />4557.0 <br />.1591.6 <br />84 <br />5159.0 <br />'1980.4 <br />10 <br />404.4 <br />1272.1 ' <br />10 <br />.4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />"720 <br />4036.8 <br />.1279.3 <br />20 <br />4584:8 <br />1608.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4049.3 <br />1286.5 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5204.4 <br />-2010.8 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4612,2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />.4074.4 <br />1300.9 <br />50 <br />4626.0 <br />1634,4 <br />50 <br />5234.9 <br />-2031.4 <br />Corrections to be Added (T =Tangent.. E=External.) <br />t. curve 5° 10° <br />15° <br />20° <br />1 25° <br />30° <br />3a° <br />40° 1 <br />45° <br />50° <br />55° 60° <br />65' <br />70' <br />1 <br />00° T=.21 .42 <br />.G3.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 2.60 <br />2.83 <br />3.07 <br />E=.056 .112 <br />.168 <br />.225 <br />.283 <br />.310 <br />.398 <br />.457 <br />.616 <br />,575 <br />.636 .697 <br />.774 <br />'.851 <br />e5° T=.23 .46 <br />69 <br />93 '1.16 <br />1.40 <br />1.64 <br />1.83 <br />2-13 <br />2.38 <br />2.63 2.88 <br />3.13 <br />3.39 <br />E=.087 .135 <br />.204 <br />.273 <br />'.343 <br />.412 <br />.483 <br />.554 <br />.625 <br />..597 <br />.711 .845 <br />.922 <br />1.01 <br />T=•25 - . .51 <br />.70 <br />I.02 ,1.28 <br />1.54 <br />1.80 <br />2.06. <br />2.33 <br />2.60 <br />2.88 3.16 <br />3.44, <br />-172 <br />P=.080 .159 <br />.240 <br />.321 <br />.403 <br />.485 <br />.563..552 <br />.735 <br />.819 <br />.90E .994 <br />1.03. <br />1.17 <br />75° T=.27 .56 <br />.$3 <br />1.12 <br />1.40 <br />1.U9 <br />1.98 <br />2.27 <br />2-57 <br />2.87 <br />3.16 3.47 <br />3.7B <br />4.09 <br />^ E=.095 .182 <br />-286 <br />383 <br />.450 <br />.578 <br />.678 <br />.777 <br />.577 <br />.977 <br />1.07 1.18 <br />1.29 <br />1 39 <br />SO° T=.30 .61 <br />.91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2,40 <br />2.78 <br />3.10 <br />3.44 3.78 <br />4.12 <br />4.46 <br />E =,1I0 X20 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1-02 <br />1.13 <br />1.25 1.38 <br />1.50 <br />1.62 <br />$an - 9'=.33 G6 <br />1.00 <br />1.33 <br />l.G$ <br />2.02 <br />3.35 <br />3.70 <br />3.05 <br />3.40 <br />3.77 4.I4 <br />4.55 <br />4.89 <br />E-.128 .259 <br />` <br />.391 <br />.524 <br />.657 <br />.790 <br />.926 <br />1.p6 <br />1-20 <br />1.34 <br />1.47 1.62 <br />1.76 <br />1.91 <br />1 <br />