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IV` <br />TABLE I.Tangents- and Externals to a 1' Curve. <br />Chord =100 "ft. <br />Int. <br />'-'Angle <br />Tangent <br />External <br />Inc. <br />.Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />43° <br />2257.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />3110.0 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />2681.9 <br />'596.6 <br />10' <br />3121.7 <br />-795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.6 <br />800.4 <br />'30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />605.3 <br />30 <br />31.13.4 <br />805.6 <br />.40 <br />2295:6 <br />442.8 <br />40 <br />2712:5 <br />609.6 <br />.40 <br />3154.2 <br />•810.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614.0 <br />50. <br />3I65.1 <br />516.1 <br />44 <br />2314.9 <br />450.0 <br />61 <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />821.4 <br />10 <br />2324.6 <br />453.6 <br />.10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />826.7 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />627.2 <br />20 <br />3197.8 <br />832.0 <br />.30 <br />2344.1 <br />461.0 <br />30 <br />2763.7 <br />631.7 <br />30 <br />3208.8 <br />837.3 <br />40 <br />2353.8 <br />46.1.6 <br />40 <br />2773.9 <br />636.2 <br />40 <br />3219.7 <br />842.7 <br />50 <br />2363.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />.45 <br />2373.3 <br />472.1 <br />52 <br />.2794.5 <br />645.2. <br />59 <br />3241.7 <br />853.5 <br />10 <br />2383.1 <br />475.8 <br />10 <br />2804.9 <br />649.7 <br />10' <br />3252:7 <br />858.0 <br />20 <br />2392.8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />864.3 <br />30 <br />2402.6. <br />483.4 <br />30 <br />2825.6- <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 />663.4 <br />40- <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />665.0 <br />50 <br />3296.9 <br />SS0.8 <br />46- <br />2432.1 <br />494.5 <br />53 <br />2856.7 <br />672.7 <br />00 <br />3308.0 <br />886.4 <br />10 <br />2441.9 <br />498.7 <br />10 <br />2567.1 <br />677.3 <br />_ <br />10 <br />3319:1 <br />592.0 <br />20 <br />2451.S <br />502.5 <br />20. <br />2877.5 <br />682.0 <br />20 <br />33361.3 <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2388.0 <br />6S6.7 <br />30 <br />3341,.4 <br />003.2 <br />40 <br />2471.5 <br />510.3 <br />.40 <br />2S98.4 <br />691.4 <br />40 <br />3352.G <br />90S.S <br />50 <br />24S1.4 <br />514.3 <br />50, <br />2905.9 <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />47 <br />2491.3 <br />518.2 <br />54 <br />2019.4 <br />-700.9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />2929.9 <br />705.7 <br />10 <br />3356.3 <br />025.9 <br />.20 <br />2511.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />9:11.6 <br />30 <br />2521'.1 <br />.530.1 <br />30. <br />2951.0 <br />715.3 <br />30 <br />3.105.8 <br />037.3 <br />40 <br />2531.1 <br />534.2 <br />40 <br />29611.5 <br />720.1 <br />40 <br />3420.1 <br />943.1 <br />50 <br />2541.0 <br />533.2 <br />50 <br />2972.1 <br />725.0 <br />50 <br />3431.4 <br />945.9 <br />48 <br />2551.0 <br />542.2 <br />55 <br />2982'.7. <br />729.9 <br />62 <br />3442.7 <br />954.5 <br />10 <br />2561.0 <br />546.3 <br />10 <br />•2993.3 <br />734.8 <br />10 <br />3454.1 <br />960.6 <br />20 <br />2571.0 <br />550.4 <br />20 <br />3003.9 <br />739:7 <br />20 <br />3465.4 <br />966.5 <br />.20 <br />30 <br />2581.0 <br />554.5 <br />30, <br />3014.5 <br />744.6 <br />30 <br />.5113.9 <br />972.4 <br />.40 <br />2591.0. <br />558.6 <br />40 <br />'3025.2 <br />749.6 <br />40 <br />,3476.8 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />-3035.8 <br />754.6 <br />50 <br />3499.7 <br />984.3 <br />49 <br />2611.2 <br />566.9 <br />56 <br />. 304 6.5 <br />75 <br />750.6 <br />63 <br />351.1".1. <br />990. 20 <br />10 <br />2621.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />10 <br />3522.G <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3067.0 <br />769.7 <br />20 <br />3534.1 <br />1002.3 <br />30 <br />2641.4 <br />579.5 <br />30 <br />3078.7 <br />774.7 <br />30 <br />3545.6 <br />1005.3 <br />40 <br />2651.5 <br />583.8 <br />- 40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />60 <br />2661.6 <br />588.0 <br />50 <br />3100.2 <br />781. 9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added (T=Tangent. E=External.) <br />Angle <br />C+uva 5° 10° 151 20° 25° <br />30° 35° 1 40° 45° 50° <br />1 55° <br />1 60° 1 65° <br />70° <br />fit' <br />Angle <br />Tangent <br />g <br />1 1 <br />1 <br />G4° <br />11.641 <br />1026.6 <br />•40° <br />E=.023 .046 070 093 117 <br />.141 .172.20 2.34 6.5 <br />.203 234 <br />277.49 <br />2901.79 .3151.94 <br />.34 <br />45 ° <br />-3591.9 <br />06 <br />1.216 1.254 1.259 1.325 <br />1.351 <br />1.378 2.411 <br />2 2 <br />10' <br />E =.030 060 .093 .119 .153 <br />.184 <br />20 <br />:3603.5 <br />1 <br />44 <br />5� o <br />T=.17 .34 .51 .68 .85' <br />1.02 1.19 1.36 1.54 1.72 <br />1,91 <br />2.10 2.29 <br />2.45 <br />30 <br />E=.037 -.075 .116 .151 .189 <br />.227 .266 .305 .345 -.334 <br />.4 5 <br />.467 :508 <br />.551 <br />30 <br />T=.19 .38 .57. .76 .05 <br />1.14 1.32 1.52 1.72 1.92 <br />2.14 <br />2.35 2.561 <br />2.77 <br />55° <br />E=.046 1 .093 :142 .188 .236 <br />.283 .332 3.81 .420 .479 <br />,510 <br />.552 .641 <br />.7 <br />50 <br />T=.21 .42 .63 84 1.05 <br />1.27 1.49 1.71 1.94 2.17 <br />2.38 <br />2.60 2.83 <br />3.07 <br />600 <br />E=.056 .112 .168 225 .283 <br />.340 .398 .457 .516 .575 <br />.636 <br />.697 .774 <br />.85 <br />650. <br />T=23 .46 69 93 1.16 <br />1.40 1.64 1.88 2.13 2.38 <br />2.63 <br />2.89 3.13 <br />3.39 <br />10 <br />E=.067 .135 .204 273 .343 <br />Al2 .483 .554 .625 .697 <br />.711 <br />.845 .922 <br />1.01 <br />TABLE I. - Tangents and Externals to a 1° Curve, j1 <br />- Chord =100 it. <br />Int. <br />Angle <br />Tangent <br />External <br />.. <br />Int' <br />Angle <br />Tangent <br />g <br />External <br />fit' <br />Angle <br />Tangent <br />g <br />External <br />G4° <br />3580.3 <br />1026.6 <br />711 <br />40SGA <br />1308.2. <br />7S° <br />4639.8' <br />1G43.0 <br />10' <br />-3591.9 <br />1032.8 <br />10' <br />4099.5 <br />-1315.6: <br />10' <br />:4653.6 <br />1651.7 <br />20 <br />:3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />.1667.4 <br />1660.5 <br />30 <br />3615'.1 <br />1045.2 <br />30 <br />412.1.S <br />1330.3, <br />30 <br />4681.3 <br />1669.2 <br />40 <br />362(1.8 <br />1051.4 <br />40 <br />4137.4 <br />1337.7. <br />40 <br />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />.50 <br />4150.1 <br />1315.1 <br />50 <br />.4709.2 <br />1656.9 <br />G5 <br />3650.2 <br />1063.9 <br />72, <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 />4158.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />36fi5.4 <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 />1059.3 <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 />1395.0 <br />80 <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.G <br />1115.1 <br />20 <br />4265.0 <br />1413.5 <br />20 <br />4 836. 2 <br />1768.2 <br />30 <br />3756.5 <br />1121.7 . <br />30 <br />4278.5 <br />142t.2 - <br />30 <br />4550.5 <br />1777.4 <br />40 <br />3765.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />4364.5 <br />1786.7 <br />50 <br />3750.4 <br />1131.8 <br />50 <br />4304.6 <br />14361.8 <br />50 <br />.1879,2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 <br />4317.G <br />1444.6 <br />SI <br />4S93.6 <br />1805.3 <br />10 <br />3804.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />'0 <br />4005.0 <br />1814.7 <br />20 <br />3816.4 <br />1154.7 <br />20 <br />4343.5 <br />1.460.4 <br />20 <br />4922.5 <br />1824.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4356.9 <br />146S.4 <br />30 <br />4937.0 <br />1333.6 <br />40 <br />3840.5 <br />1168:1 <br />40 <br />4370.1 <br />1476.4 <br />10 <br />4951.5 <br />184.4.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4906.1 <br />1852.6 <br />63 <br />3804.7 <br />1181.6 <br />75 <br />4396.5 <br />1192.4 <br />82 <br />49S0.7 <br />1562.2 <br />10 <br />3876.5 <br />1158.4 <br />10 <br />4109.8 <br />1500.5 <br />10 <br />4995.4 <br />1S71.8 <br />20 <br />3859.0 <br />1195.2 <br />20 <br />4423.1 <br />1505.6 <br />20 <br />5010.0 <br />1SS1.5 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />-4:361.4 <br />1516.7 <br />30 <br />5024.8 <br />1591.2 <br />40 <br />3913.4 <br />1208.9 <br />4449.7 <br />1524.9 <br />40 <br />5039.5 <br />1900.9 <br />50 <br />3925.6 <br />1215.5 <br />,40 <br />50 <br />4463:1 <br />1533.1 <br />50 <br />5054.3 <br />1010.7 <br />G9 <br />3937:9 <br />1222.7 <br />7G <br />4476.5 <br />15411.4 <br />53 <br />5069.2 <br />1940.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />44889.9 <br />154.9.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />3962.5 <br />1230.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1910.3 <br />30 <br />3974:5 <br />1243.7 <br />30 <br />4516.9 <br />156 G.3 <br />30 <br />.5113.9 <br />1950.3 <br />40 <br />3987:2 <br />1250.8 <br />40 <br />4530.4 <br />1:574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />3999.5 <br />1257.9 <br />50 <br />4514.0 <br />1553.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1265.0 <br />77 <br />4557.6 <br />1591.6 <br />84 <br />5159.0 <br />1980:4 <br />10 <br />0 <br />40..4.4 <br />i.,.l <br />1_272 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <br />4030.8 <br />1279.3 <br />20 <br />458-I.S <br />1605.6 <br />20 <br />5159.3 <br />2000.6 <br />30 <br />4049.3 <br />12SG.5 <br />30 <br />4595.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.5 <br />1293.6 <br />.40 <br />46,12.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1. <br />50 <br />4074.4, <br />1300.9 <br />50 <br />402G.0 <br />1634.4 <br />50 <br />5234.9 <br />2031.4 <br />Corrections to be Added (T =Tangent. E =External.) <br />t 0 <br />Cure 5° <br />10' <br />15° <br />20° <br />25° <br />1 30° <br />1 35° <br />1 40° <br />45° 1 <br />50° <br />55° <br />60° <br />65° <br />1 70° <br />i0o <br />T=.21 <br />.42 <br />.63 <br />.E4 <br />1.05 <br />1.27 <br />11.49 <br />11.71 <br />1.34 <br />2,17 <br />2.38 <br />2.83 <br />3.07 <br />E =.056 <br />.112 <br />.163 <br />.225 <br />.283 <br />.340 <br />.395 <br />.457 <br />.516 <br />.575 <br />.636 <br />.774 <br />.851 <br />i5° <br />T=.23 <br />.46 <br />.G9 <br />.93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.63 <br />3.13 <br />3.30 <br />E =.067 <br />.135 <br />.204 <br />.273 <br />.343 <br />.412 <br />.433 <br />.554 <br />.625 <br />.697 <br />.711. <br />.922 <br />1.01 <br />,0° <br />T=.25 <br />.51 <br />.76 <br />1.02 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />F,2.8 <br />3.44 <br />3.72 <br />E =.080 <br />.159 <br />.240 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />1.08 <br />1.17 <br />i5° <br />T=•27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2.97 <br />3.16 <br />3.78 <br />4.09 <br />E=.095 <br />.182 <br />.286 <br />.383 <br />.480 <br />.578 <br />.678 <br />.771 <br />.677 <br />.477 <br />1.07 <br />1.29 <br />1.39 <br />i0° <br />T=.30 <br />.61 <br />.91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />E =.110 <br />220 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.9G3 <br />1.02 <br />1.13 <br />1.25 <br />1.38 <br />1.50 <br />11.62 <br />l5° <br />T=•33 <br />65 <br />LOU, <br />1.33 <br />LG8 <br />2.02 <br />2.3G <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />14.89 <br />E=.128 <br />259 <br />.391 <br />.524 <br />.657 <br />.790 <br />226 <br />1.06 <br />1.20 <br />11.34 <br />1.47 <br />1.62 <br />1.76 <br />11.91 <br />