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f` <br />IV TABLE I. - Tangents and Externals to a 1° Curve. <br />I <br />Chord= 100 ft. <br />Angle <br />Tangent <br />External <br />AIng`le <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />43° <br />2257.0 <br />428.5 <br />50° • <br />2671.8 <br />592.3 <br />57°, <br />3110.9 <br />790.1 <br />10' <br />2266.6 <br />432.0 <br />101 <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 />3143.4 <br />:SU5.6 <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 />3165.1 <br />810.1 <br />44 <br />2314.0 <br />450.0 <br />51 <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 />82G.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 />4G4.6 <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 />858.9 <br />20 <br />2392.8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />564.3 <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 />668.0 <br />.50 <br />3296.9 <br />SS0.8 <br />46 <br />2432.1 <br />494:8 <br />53 - <br />2856.7 <br />672.7 <br />60. <br />3305:0 <br />886.4 <br />10 <br />2441.9 <br />498.7 <br />10 <br />2867.1, <br />677.3 <br />10' <br />3319.1 <br />892.0 <br />20 <br />2451.8 <br />5025 <br />20 <br />2577.5 <br />682.0 <br />20 <br />3330.3 <br />897.5 <br />30 <br />2461.7 <br />506.4 <br />30 <br />2888.0 <br />686.7 <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 />3352.6 <br />908.8 <br />50 <br />2481.4 <br />514.3 <br />.50 <br />2908.9' <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />47 - <br />2401.3 <br />518.2 <br />54 <br />2919.4' <br />700.0 <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 />3386.3 <br />925.9 <br />20 <br />2511.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />931.6 <br />30 <br />2521.1 <br />530.1,30_ <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 />2961.5 <br />720.1 <br />40 <br />3420.,1 <br />943.1 <br />50 <br />2541.0 <br />538.2 <br />50 <br />•2972.1 <br />725.0 <br />50 <br />3431.4 <br />. 948.9 <br />48 <br />2551.0 <br />542:2 <br />55 . <br />2982.7 <br />729.9. <br />62 <br />3442.7 <br />954.8 <br />10 <br />2561.0 <br />540.3 <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 />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />30 <br />3.176.8 <br />972.4 <br />40 <br />2591.0 <br />558.6 <br />40 <br />3025.2 <br />- 749.6 <br />40 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />1. 50 <br />3035.8 <br />754.6 <br />50 <br />3.199.7 <br />084.3 <br />49 <br />2611.2 <br />566.9 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />090.2 <br />10 <br />2621.2 <br />571.1 <br />10 <br />3057.2 <br />764.6 <br />10. <br />3522.6 <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3067.9 <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 />1008.3 <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 />.50 <br />2661.6 <br />588.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added .(T = Tangent. E=External.)- <br />Angle <br />(rove 5°' <br />10° 15° 20° <br />25° 1 30° 35° <br />40° 45° <br />500 556 <br />60° '650 700 <br />40° <br />T=.13" <br />..26 .40 ,.53 <br />.67 .80 .93 <br />.106 1.20 <br />1.34 1.49 <br />1.64" 1.79 1.94 <br />1308.2 <br />E=.023 <br />.046 .070 .093 <br />.117 .141 .172 <br />.203 .234 <br />.285 .277 <br />290 .315 .341 <br />45° <br />T=.15 <br />.30 .44' .60 <br />.76' .91 1.06 <br />1.21 1.37 <br />1.52 1.70 <br />1.87 2.04 2.21 <br />3603.5 <br />E=.030 <br />.060 .093 .110 <br />.153 .184 ..216 <br />.254 .289 <br />.325 .351 <br />_.378 .411 .445 <br />50°T=.17 <br />30 <br />.84 .51 .68 <br />.85 1.02 1.19 <br />1.36 1:54 <br />1.72 1.91 <br />2.10 2.29 2.48 <br />30 <br />E=.037 <br />.075 .116 .151 <br />.189 .227 .266 <br />.305 345 <br />.384 .425 <br />.467 .508 .550 <br />550 <br />T=.19 ' <br />.38 .57 .76 <br />.95 1.14 1.32 <br />1.52 1.72 <br />1.92 2.14 �- <br />2.35 2.56 2.77 <br />1057.7 " <br />E=.046 <br />.093 .142 .188 <br />.236 .283 .332 <br />3.81 .420 <br />.479 .530 <br />.582 .641 .700 <br />60° <br />T=.21 <br />.42 '.63 .84 <br />1.05 127' 1.49 <br />1.71 1.94 <br />2.17 2.38 <br />2.60 2.R3 3.07 <br />4723.2 <br />E=.056 <br />.112 .168 .225 <br />.283 .340 398 <br />.457 .516 <br />.575 .636 <br />.697 .774 .851 <br />65° <br />T=.23 <br />.46 69 93 <br />1.16 1.40 1.64 <br />1.88 2.13 <br />2.38 2.63 <br />2.88 3.13. 3.39 ' <br />20 <br />E=.067 <br />.135 .204 273 <br />.343 .412 .483 <br />.554 .625 <br />.697 .711 <br />.845 .922 1.01 <br />TABLE I. - Tangents and Externals to a P Curve, 4 <br />Chord= 100 ft. <br />Int. <br />' Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tangent <br />External' <br />Int. <br />Angle <br />Tang <br />Tan ent <br />mal <br />External <br />60° 65° <br />3580.3 <br />1026.6 <br />71° <br />4056.9 <br />1308.2 <br />781 <br />.4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />1e' <br />4099.5 <br />1315.6 <br />10' <br />4653.6 <br />1551.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 . <br />4057.4 <br />1850.5 <br />30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1639.2 <br />40 <br />3626.8 <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 />1345.1 <br />50 <br />4709.2 <br />1656.9 <br />65 <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 />.1701.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4188.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <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 />.173 L.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 "' <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 />4265.0 <br />1413.5 <br />• 20 <br />4836.2 <br />1785.2 <br />30 <br />"3756.5 <br />1121.7 <br />30 <br />4278.'5 <br />1421.2 <br />30 <br />4850.5 <br />1777.4 <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4291.5 <br />1129.0 <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 />4&79.2 <br />1796.0 <br />67 <br />3792:4 <br />1141.4 <br />74 <br />4317.6 <br />1444.6 <br />81"- <br />4893.6 <br />1805.3 <br />10 <br />3804.4 <br />1148.0 <br />10 <br />4330.7 <br />1452.5 <br />10; <br />4908.0 <br />1814.7 <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 />146S.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />.40 <br />4951.5 <br />1843.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4960.1 <br />185.6 <br />68 <br />3864.7 <br />1181.6 <br />75 <br />"4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10- <br />4995.4 <br />1871.8 <br />20 <br />3889.0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />188L.5 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />4436.4 <br />1516.7 <br />30- <br />5024.8 <br />189 L. 2 <br />40 " <br />.3913.4 <br />1208.9 <br />.40 <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 />4476.5 <br />1541.4 <br />83 <br />5009.2 <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4459.9 <br />1549.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />3999.5 <br />1257.0 <br />50 <br />4544.0 <br />.1583.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.0 <br />1265.0 <br />77 <br />4557.6 <br />1501.6 <br />84 <br />5159.0 <br />1980.4 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <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 />52U4.4 <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 />462610 <br />1634.4 <br />.50 <br />5234.9 <br />2031.4 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int. <br />C rve 5° <br />10° <br />15° 1 <br />20° 1 25° <br />30° <br />35° 1 <br />40° 45° 50° <br />55° <br />60° 65° <br />70° <br />e <br />- <br />- <br />.Angl27 <br />000 <br />112 <br />.05 <br />1. <br />1.340 <br />1.398 .49 <br />17 <br />1.457 .71 1.516 ? <br />2 <br />2.774 .83 <br />3.07 <br />E= O% <br />..21 <br />.225 <br />168 <br />S3 <br />575 <br />830 <br />697 <br />S51 <br />T=.23 <br />1.15 <br />1.40 <br />1.64 <br />1.88 2.13 2.38 <br />2.711 <br />2.883.13 <br />650 <br />- 007 <br />.135 <br />.204 <br />.273 .343 <br />412 <br />.483 <br />554 .625 .697 <br />845 .922 <br />1.31 <br />70° <br />.02 1 <br />1.23 <br />.54 <br />1.80 <br />1 <br />2.652 .06 2.735 2.81.88 <br />2 <br />3.994 <br />E=,080 <br />.159 <br />.240 <br />.321 403 <br />.485 <br />868 <br />9 <br />906 <br />1.08 <br />1.17 <br />75° <br />1.121 <br />1.69 <br />1 <br />.57 ? <br />2.77 2 <br />E=.095 <br />152 <br />.280 <br />.383 480 <br />.578 <br />.6778 <br />7 .877 977 <br />1.07 <br />1.18 1.29 <br />1.39 <br />1.44:225 1.553 <br />1.671 <br />2.787 .15 <br />80°=.110 <br />.220 <br />.332 <br />?903 1.02 1.13 <br />1.2 <br />1.38 1 50 <br />1.62 <br />85° <br />^1 = 33 <br />68 <br />1.00 <br />1.33 1.68 <br />2.02 <br />2.38 <br />2.70 3.05 3.40 <br />3.77 <br />4.14 4.55 <br />4.89 <br />E=,128 <br />259 <br />.391 <br />.524 ..657 <br />.790 <br />.928 <br />1.08 1.20 1.34 <br />247 <br />1.62 276 <br />1.91 <br />