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Iv TABLE I. Tangents, and Externals to a 1° Curve. <br />Chord= 100 ft. <br />Int. <br />Angle <br />' <br />Tangent <br />External <br />Int. <br />Angie <br />Tangent <br />External <br />Iat. <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 />3110.9 <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 />3143.4 <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 />3165.1 <br />816.1 <br />44 <br />2314.9 <br />450.0 <br />51 <br />2732.9. <br />618.4 <br />58 <br />3176.0 <br />821A <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 />882.0 <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 />464.6 <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 />` G45:2 <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 />864.3 <br />30 <br />2402,6 <br />483.4 <br />30 <br />2825.5 <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 />880.8 <br />AG <br />2432.1 <br />404 8 <br />63 <br />2856.7 <br />672.7 <br />60 <br />3308.0 <br />886.4 <br />10 <br />2441.9 <br />498.7 <br />. 10_ <br />2867.1 <br />677.3 <br />1110 <br />3313.1 <br />892:0 <br />20 <br />2451.8 <br />502.5 <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330.3 <br />897.5 <br />30 ,.2461.7 <br />3828.4 <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 />60. <br />3363.8 <br />914.5 <br />47 , <br />2491.3 <br />'- 518.2 <br />54 . <br />2919.4 <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 />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 <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 />054.8 <br />10 <br />2501.0 <br />546.3 <br />10 <br />2993.3 <br />734.8 <br />10 <br />3454.1 <br />960.0 <br />20 <br />" <br />2571.0 <br />550.4 <br />20 <br />3003.9 <br />739.7 <br />20 <br />3465.4 <br />906.5 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014.5 <br />744.6 <br />•30- <br />3476.8 <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 />50 <br />'3035.8 <br />754.6 <br />50 <br />3499.7 <br />984.3 <br />49 <br />2611.2 <br />5G6,9 <br />- 56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <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 />3545.0 <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 />C 5°• <br />10° IS- 202 <br />� <br />25° 30° <br />35° 40° 45° <br />50° <br />55° <br />40°• 65° 70° <br />40° <br />T=.13 <br />.26 40 .53 <br />.67.BO <br />.93 .106 1.20 <br />1.34 <br />1.49 <br />1.64 1.70: 1.94 <br />4639.8 <br />E=.023 <br />.046 '.070 .093 <br />.117 .141 <br />.172 .203 .234 <br />.265 <br />'.277 <br />390 .315 ..341 <br />•45° <br />'r=.15 <br />.30 ,44 .60 <br />.76 .91 <br />1.06 1.21 1.37 <br />1.52 <br />1.70 <br />1.87 2.04 2.21 <br />1322.9 <br />E =.020 <br />MG .093 .119 <br />_.153 .164 <br />216 .254 .289 <br />.325 <br />.351 <br />.378 All .445 <br />50° <br />T=.17 <br />.34 .61 .68 <br />.85 1.02 <br />1.19 1.36 1.54 <br />1.72 <br />1.91 <br />2.10 2.29 2.48 <br />40 <br />E .037 <br />.075 .116 .151 <br />.189 .227 <br />.266 .305 .345 <br />.384 <br />.425 <br />.467 .508 '.550 <br />1057.7 <br />T=.19 <br />.38 .57 .76 <br />.05 1.14. <br />1.32 1.52 1.72 <br />1.92 <br />2.14 <br />2.35 2.56 2.77 <br />3B50.2 <br />E =.046 <br />.093 .142 .188 <br />.236 .283 <br />..332 3.81 .420 <br />.479 <br />.530 <br />,582 .691 .Z00 <br />60° <br />T=.21 <br />.42 -.63 84 <br />1.05 1.27' <br />1.49 1.71 1.94 <br />2.17 <br />2.38 . <br />2.60 2.83 3.07 <br />1704.7 <br />E=.056 <br />.112 ..168 .225 <br />.283 .340 <br />.398 .457 .516 <br />.575 <br />.636 <br />.697 .774 ..851 <br />65° <br />T=.23 <br />.46 ' 69 93 <br />1.16 1.40 <br />1.64 1.88 2.13 <br />2.38 <br />2.63 <br />2.88 3.13 3.39 ' <br />30 <br />E=.067 <br />.135 .204 273 <br />343 .412 <br />'.483 .554 .625 <br />.697 <br />.711 <br />.845 :922 L01 <br />TABLE I. -- Tangents and Externals to a 10 Curve. V <br />Chord =100 ft. <br />Int. <br />An <br />Tangent <br />External <br />Tnt. <br />Angie <br />Tangent <br />External <br />Int. <br />Tangent <br />External <br />64° <br />3580.3 <br />1026.6 <br />71° <br />4086.9 <br />1308.2 <br />781 <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 />4653.6 <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 />4695.2 <br />1678.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4150.1 <br />]345.1 <br />50 <br />4709.2 <br />1686.9 <br />65 - <br />3B50.2 <br />1063.9 <br />72 <br />4162.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />10 <br />3G61.9 <br />1070.2 <br />1,0 <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 />4188.5. <br />1307.6 <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 />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390,4 <br />50 <br />4703.0 <br />1740.8 <br />60 <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 />4265,6 <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 />30 <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 />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 />3810.4 <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 />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />495t.5 <br />1843.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />.40 <br />50 <br />4966.1 <br />1852.6 <br />68 <br />3864.7 <br />1181.6 <br />75 <br />439G.5 <br />14.92.4 <br />82 <br />+1980.7 <br />18622 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4998,4 <br />1871..8 <br />20 <br />3889.0 <br />1.195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010,0 <br />1881.5 <br />30 <br />3901.2 <br />1.202.0 <br />30 <br />443G.4 <br />1516;7 <br />30 <br />5024.8 <br />1897,.2 <br />40 <br />3913.4 <br />1208.9 <br />40 <br />4449.7 <br />1524.0 <br />40 <br />559.5 <br />1900.9 <br />50 <br />3925.6 <br />'1215.8 <br />60 <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />L9i0.7 <br />60 <br />3937.9 <br />1222.7 <br />76 <br />4476.5 <br />1541.4 <br />83 <br />5069, a, <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4489.9 <br />1549.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />39G2.5 <br />123G.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3974.9 <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 />3499.5 <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 />.1265.0 <br />77 <br />4557.6 <br />1591.E <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 />5204.4 <br />2010.8 ' <br />40 <br />4061.8' <br />1293.0 <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 />�'re 5° <br />100 19 <br />20° <br />25° <br />30° <br />35° <br />40° <br />45` 50° 55° <br />60° <br />65° <br />70° <br />Angle. <br />T=.21 <br />.42 .03 <br />.84 <br />1.05 <br />1.227 <br />1.49 <br />1.71 <br />1.94 2.17 2.38 <br />2.60 <br />2.33 <br />07 <br />E=.056 <br />.112 .168 <br />.225 <br />.283 <br />.840 <br />.398 <br />.457 <br />.516 .575 .630 <br />.697 <br />.774 <br />.851 <br />T=.23 <br />.46 .69 <br />.93 <br />1.10 <br />1.40 <br />1.64 <br />1.88 <br />2.13 2.33 2.63 <br />2.88 <br />3.13 <br />3.39 <br />b5° E=.057 <br />-.135, .204 <br />.273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 .697 .711 <br />.845 <br />.922 <br />1,01 <br />,T-.25 <br />.51 .76 <br />1.02 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.60 2.88 <br />3.16 <br />3.44 <br />3.72 <br />E=.080 <br />.159 240 <br />.321 <br />.403 <br />.485 <br />,558 <br />.2.33 <br />.652 <br />.735 .619 .906 <br />.994 <br />1.08 <br />4.17 <br />75 T=.27 <br />.56 .83 <br />1,12 <br />1.40 <br />1.69 <br />1.18 <br />2.27 <br />2157 2.87 3.16 <br />3.47 <br />3.78. <br />4.09 <br />E=.095 <br />.182 .286 <br />.383 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 .977 1.0T <br />1.18 <br />1.29 <br />1.39 <br />80. T=.30 <br />.61 .91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 3.10 3.44 <br />3,78 <br />4.12 <br />4.46 <br />E=.110 . <br />.220 .332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1-02 1.13 1.25 <br />1.38 <br />1.50 <br />1.62 <br />T=.33 <br />.66 1.00L33 <br />1.68 <br />2.02 <br />2.35 <br />2,70 <br />3.05 3.40 3.77 <br />4.14 <br />4.55 <br />4.89 <br />E=.128 <br />.259 391 <br />.524 <br />.0571 <br />790 <br />.926 <br />1.00 <br />1.20 1.34 1.47 <br />1.62 <br />1.76 <br />1.91 <br />