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IV <br />.TABLE IV. -TANGENTS AND EXTERNALS TO A I° CURVE. <br />Central <br />Angle <br />Tangent <br />Extern.11.Angle <br />Central <br />Tangent <br />External <br />Central <br />Aagle <br />Tangent <br />External <br />1.31-' <br />1589.0 <br />216.3 <br />410 <br />2142.2 <br />387.4 <br />51° <br />2732.9 <br />618.4 <br />101 <br />1598.0 <br />218.7 <br />10' <br />2151.7 <br />390.7 <br />I0 <br />2743,1 <br />622.8 <br />20 <br />1606.9 <br />221.1 <br />20 <br />2161.2 <br />394.1 <br />20 <br />2753.4 <br />627.2 <br />30 <br />1615.9 <br />223.5 <br />30 <br />2170.8 <br />397.4 <br />30 <br />2763.7 <br />631.7 <br />40 <br />1624.9 <br />226.0 <br />40 <br />2180.3 <br />400.8 <br />40 <br />2773,9 <br />636.2 <br />50 <br />1633.9 <br />228.4 <br />50 <br />2169.9 <br />404.2 <br />50 <br />2784,2 <br />640.7 <br />32 <br />1643.0 <br />230.9 <br />42 <br />2199.4 <br />407.6 <br />62 <br />2794.5 <br />645,2 <br />10 <br />1652.0 <br />233.4 <br />10 <br />2209.0 <br />411,1 <br />10 <br />2804.9 <br />649,7 <br />20 ' <br />1661.0 <br />235.9 <br />20 <br />2218.6 <br />414.5 <br />20 <br />2815.2 <br />654.3 <br />30 <br />1670.0 <br />238.4 <br />30 <br />2228:1 <br />418.0 <br />30 <br />2825.6 <br />658.8 <br />40 <br />1679.1 <br />241.0 <br />40 <br />2237.7 <br />421.4 <br />40 <br />2835.9 <br />40 . <br />50 <br />-1688.1 <br />243.5 <br />50 <br />2247.3 <br />425.0 <br />50 <br />2846.3 <br />.663.4 <br />668.0 <br />33 <br />1697.2„ <br />246.1 <br />43 <br />2257.0 <br />428.5 <br />53 <br />2856.7 <br />672.7 <br />10 <br />1706.3_ <br />248.7 <br />10 <br />2266.6 <br />-432.0 <br />10 <br />2867.1 <br />677.3. <br />20 <br />1715.3 <br />251.3 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2877.5 <br />682.0 <br />30 <br />1724.4 <br />253.9 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2888.0 <br />686.7 <br />40 <br />1733.5 <br />256.5 <br />40 <br />2295.6 <br />442.8' <br />40 <br />2898.4 <br />691.4 <br />50 <br />1742.6 <br />259.1- <br />50 <br />2305.2 <br />446.4 <br />50 <br />2908,9 <br />696.1 <br />34' <br />1751.7 <br />261.8 <br />44 <br />2314:9 <br />450.0 <br />54 <br />2919.4 <br />700.9 <br />10 <br />1760.8 <br />264.5 <br />10 <br />2324.6 <br />453.6 <br />10 <br />2929.9 <br />705.7 <br />20 <br />1770.0 <br />267.2 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2940.4 <br />710.5 <br />30 <br />1779.1 <br />269.9 <br />30 <br />2344.1 . <br />461.0 <br />30 <br />2951.0 <br />715.3 <br />40 <br />1788.2 <br />272.6 <br />40 <br />2353.8 <br />464.6 <br />40 <br />2%1.5 <br />720.1 <br />50 <br />1797.4! <br />275.3 <br />50 <br />2363.5 <br />468.4 <br />50 <br />2972,1 <br />- 725.0 <br />35 <br />IBM. 6 <br />278.1 <br />45 <br />2373,3, <br />472.1 <br />55 <br />2982,7 <br />729.9 <br />-10 <br />1815.7 <br />280,8 <br />10 <br />2383:1 <br />475.8 <br />10 <br />2993.3 <br />734.8 <br />20 <br />1824.9 <br />283,6 <br />20 `' <br />2392.8 <br />479.6 <br />20 <br />30013,9 <br />739.7 <br />30 <br />1834.1 <br />286.4 <br />30 <br />2402.6 <br />483.8 <br />30 <br />3014.5 <br />744.6 <br />40 <br />I843.3 <br />289;2 <br />40 <br />2412.4 <br />487.2 <br />40 <br />3025.2 <br />749.6 <br />50 <br />1852.5 <br />292,0 <br />50 . <br />2422.3 <br />491.0 <br />50 <br />3035.8 <br />754.6 <br />38 <br />186I.7 <br />294.9 <br />46 <br />2432.1 - <br />494.8 <br />56 <br />3046.5. <br />759,6 <br />10 <br />1870.9 <br />297.7 <br />10 <br />2441.9 <br />498.7 <br />10 <br />3057.2 <br />764.6 <br />20 <br />1880.1 <br />300.6 <br />20 <br />2451.8 <br />502.5 <br />20 <br />3067.9 <br />769,7 <br />30 <br />18893 <br />303.530 <br />5374.2 ' <br />2461.7 <br />506.4 <br />30 <br />3078.7 <br />774,7 <br />40 <br />1898,6 <br />306.4 <br />40 <br />2471,5 <br />510.3 <br />40 <br />3089,4 <br />779,8 <br />50 <br />1907.9 <br />309.3 <br />50- <br />2481,4 <br />514.3 <br />50 <br />3100.2 <br />784.9 <br />37 <br />1917,1 <br />312.2 <br />47 <br />2491.3 <br />518.2 <br />51 <br />3110.9 <br />790.1 <br />10 <br />1926,4 ' <br />315.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />3121.7 <br />795.2 <br />20 <br />1935.7 <br />318.1 <br />20 <br />2511.2 <br />526.1 <br />20 <br />3132.6 <br />800.4 <br />30 <br />1945.0 <br />321.1 <br />30 <br />2521.1 <br />530.1 <br />30 <br />3143.4 <br />805.6 <br />40 <br />1954.3 <br />324.1 <br />40 <br />2531.1 <br />534.2 <br />40 <br />3154.2 <br />810.9 <br />50 <br />1963.6 <br />327.1 <br />50 <br />2541.0 <br />538,2 <br />50 <br />3165.1 <br />816.1 <br />38 <br />1972.9 <br />330'.2 <br />48 <br />2551.0 <br />542.2 <br />68 <br />3176.0 <br />821.4 <br />10 <br />1982.2 <br />333.2 <br />10 <br />2561.0 <br />546.3 <br />10 <br />3186.9 <br />826.7 <br />20 <br />1991.5 <br />336.3 <br />20 <br />2571.0 <br />550.4 <br />20 <br />3197.8 <br />832.0 <br />30 <br />2000,9 <br />339.3 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3208.8 <br />637.3 <br />40 <br />2010:2 <br />342.4 <br />40 <br />2591.0 <br />558.6 <br />40 <br />3219.7 <br />842.7 <br />50 <br />2019:6' <br />345.5 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3230.7 <br />848.1 <br />38 <br />2029,0 <br />348.6 <br />49 <br />2611.2 <br />566.9 <br />59 <br />3241.7 <br />853.5 <br />10 <br />2038.4 <br />351.8 <br />10 <br />2621.2 <br />571.1 <br />10 <br />3252.7- <br />$58.9 <br />20 <br />2047.8 <br />354.9 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3263.7' <br />864.3 <br />30 <br />2057.2 <br />358.1 <br />30 <br />2641.4 <br />579.5 <br />30 <br />3274.8 <br />869.8 <br />40 <br />2066-6 <br />361.3 <br />40 <br />2651.5 <br />583.8 <br />40 <br />3285.8 <br />875.3 <br />50 <br />2076.0 <br />364.5 <br />50 <br />2661.6 <br />588.0 <br />50 <br />3296.9 <br />880.8 <br />40 <br />2085.4 <br />367.7 <br />50 <br />2671.8 <br />592.3 <br />80 ` <br />3308.0 <br />886.4 <br />10 <br />2094.9 <br />371.0 <br />10 <br />2681.9 <br />596.6 <br />10 <br />3319.1 <br />892:0 <br />20 <br />2104:3 <br />374.2 <br />ZO <br />2692:1 <br />600.9 <br />20 <br />3330.3- <br />897.5 <br />30 <br />2113,8 <br />377.5 <br />30 <br />2702.3 <br />605.3 <br />30 <br />3341.4 <br />903.2 <br />40 <br />2123,3 <br />380.8 <br />40 <br />2712.5 <br />609.6 <br />40 <br />3352.6 <br />908.8 <br />50 <br />2132,7 <br />384.1 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3363.8 <br />914.5 <br />4879.2 <br />TABLE IV. -TANGENTS AND EXTERNALS TO A 10 CURVE. <br />Central <br />Tangent <br />External <br />Central <br />Tangent <br />F.xtemnl <br />Central Tangent External <br />Angie <br />Angle <br />Angle <br />61° <br />3375,0 <br />920.2 <br />71° <br />4086.9 <br />1308.2 <br />81' <br />4893.6 <br />1805.3 <br />101 <br />3386,3 <br />MA <br />10, <br />4099.5 <br />1315.6 <br />101 <br />4908.0 <br />1814.7 <br />20 <br />3397,5' <br />931.6 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4922.5 <br />1824.1 <br />30 <br />3408.8 <br />937.3 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3420.1 <br />943.1 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4951.5 <br />1843.1 <br />50 <br />3431.4 <br />948.9 <br />50 <br />4150.1 <br />1345.1 <br />50 <br />4966.1 <br />1952.6 <br />62 <br />3442,7 <br />954.8 <br />72 <br />4162.8 <br />1352.6 <br />88 <br />4980.7 <br />1862.2 <br />10 <br />3454.1 <br />960.6 <br />10 <br />4175.6 <br />1360.1 <br />10 <br />4995.4 <br />1871.8 <br />20. <br />3465.4 <br />966.5 <br />20 <br />4188.5 <br />1367.620 <br />5010.0 <br />1881.5 <br />30 <br />3476.8 <br />972.4 <br />30 <br />4201.2 <br />1375.2 <br />30 <br />5024.8 <br />1891.2 <br />40 <br />3488.3 <br />978.3 <br />40 . <br />4214.0 <br />1382.8 <br />40 <br />5039.5 <br />1900.9 <br />50 <br />3499.7 <br />984.3 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />5054.3 <br />1910.7 <br />63 <br />3511.1 <br />990.2 <br />73 <br />4239.7 <br />-1398.0 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3522.6 <br />996.2 <br />10 <br />.' <br />4252.6 <br />1405.7 <br />10 <br />5084.0 <br />1930.4 <br />20 <br />3534.1 <br />1002.3 <br />20 <br />4265 6 <br />1413.5 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3545.6 <br />1008.3 <br />30. <br />4278.5 <br />1421.2 <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3557.2 <br />1014.4 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />5128.9 <br />1960.2 <br />50. <br />3568.7 <br />1020.5 <br />.50 <br />4304.6 <br />1436.8 <br />50 <br />5143.9 <br />1970.3 <br />64 <br />3580.3 <br />1026.6 <br />74 <br />4317.6 <br />1444.6 <br />84 <br />5159.0 <br />1980.4 <br />10 <br />3591.9 <br />1032.8 <br />10 <br />4330.7 <br />1452._5 <br />10 <br />5174.1 <br />1990,5 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />5189.3 <br />2000,6 <br />30 <br />3615.1 <br />1045. 2, <br />30 <br />4356.9 <br />1468.4 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4370.1 <br />1476.4 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />3638.5 <br />1057.7 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />5234.9 <br />2031,4 <br />65 <br />3650.2 <br />1063.9. <br />76' <br />4396.5 <br />1492.4 <br />85 <br />5250.3 <br />2041.7 <br />10 <br />3661.9 <br />1070.2 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />5265_6 <br />2052.1 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4423.1 . <br />1508.6 <br />20 <br />5281.0 <br />2062.5 <br />30 <br />3685.4 <br />.1082.9 <br />30 <br />4436.4 <br />1516.7 <br />30 <br />5296.4 <br />2073.0 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4449.7 <br />1524.9 <br />40 <br />5311.9 <br />2083.5 <br />50 <br />3709.0. <br />„ 1095.7 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />5327.4 <br />2094.1 <br />66 <br />3720.9 ' <br />I102.2 <br />76 <br />4476.5 <br />1541.4 <br />86 <br />5343.0 <br />2I04.7 <br />'10 <br />3732.7 <br />1108.6 <br />10 <br />4489.9 <br />1549.7 <br />10 <br />5358.6 <br />2115.3 <br />3744.6 <br />1115.1 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5374.2 ' <br />2126.0' <br />.20 <br />30 <br />3756.5 <br />1121.7 <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5389.9 <br />' 2136.7 <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5405.6 <br />2147.5 <br />50 <br />3780.4 <br />1134.8 <br />.50 <br />4544.0 <br />1583.1 <br />50 <br />5421.4 <br />2158.4 <br />67 1 <br />3792.4 <br />1141.4 <br />77 <br />455746 <br />1591.6 <br />87 <br />5437.2 <br />2169.2 <br />10 <br />3804.4 <br />1148.0 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5453.1 <br />2180.2 <br />20 <br />'3316.4 <br />1154.7 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5469.0 <br />2T91.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5484.9 <br />2202.2 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5500.9 <br />2213.2 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5517.0 <br />2224.3 <br />66 <br />3864.7 <br />1181.6 <br />78 <br />4639.8 <br />1643.0 <br />88 <br />5533.1 <br />2235.5 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4653.6 <br />165L 7 <br />10 <br />5549.2 <br />2246.7 <br />20 <br />3889.0 <br />1195.2 <br />20 <br />4667.4 <br />1660.5 <br />20 <br />5565.4 <br />2258.0 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />4681.3 <br />1669.2 <br />30 <br />5581.6 <br />2269.3 <br />40 <br />3913.4 <br />1208.9 <br />40 <br />4695.2 <br />1678.1 <br />40 <br />5597.8 <br />2280.6 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4709.2 <br />1686.9 <br />50 <br />5614.2 <br />2292.0 <br />69 <br />3937.9 <br />1222.7 <br />79 <br />4723.2 <br />1695.8 <br />89 <br />5630.5 <br />2303.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4737.2 <br />1704.7 <br />10 <br />5646.9 <br />2315.0 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4751.2 <br />1713.7 <br />20 <br />5663.4 <br />2326.6 <br />30 <br />- 3974.8 <br />1243.7 <br />30 <br />4765.3 <br />1722.7 <br />30 <br />5679.9 <br />2338.2 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4779.4 , <br />1731.7 <br />40 <br />5696.4 <br />2349.8 <br />50 <br />. 3999.5 <br />1257.9 <br />50 <br />4793.6 <br />1740.8 <br />50 <br />5713.0 <br />2361.5 <br />70 <br />4011.9 <br />1265.0 <br />80 <br />4807.7 <br />1749.9 <br />90 <br />5729.7 <br />2373.3 <br />10 <br />4024.4 <br />1272.1 <br />10 <br />4822.0 <br />1759.0 <br />10 <br />5746. <br />2385.1 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4836.2 <br />1768.2 <br />20 <br />5763.1 <br />2397.0 <br />30 <br />4049.3 <br />1286.5 <br />30 <br />4850.5 <br />1777.4 <br />30 <br />5779.9 <br />2408.9 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4864.8 <br />1786.7 <br />40 <br />57%.7 <br />2420,9 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />4879.2 <br />1796.0 <br />50 <br />5813.6 <br />2432.9 <br />