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VI' <br />TABLE IV. -TANGENTS AND EXTIE NALS TO A 1°. CURVE. <br />Central <br />Angle <br />Tangent <br />External <br />Centra] <br />Angles <br />Tangent External <br />Ce n trnl <br />Angle <br />Tangent <br />External <br />910 • <br />5830.5 <br />2444.9 <br />1010 <br />j 6950.6 3278.1 <br />1110 <br />8336.7 <br />4386.1 <br />10' <br />5847.5 <br />2457.1 <br />•10' <br />6971.3 3294:1 <br />10' <br />8362.7 <br />4407.6 <br />20 <br />5864.6 <br />2469.3 <br />20 <br />6992.0 3310.1 <br />20 <br />8388:9 <br />4429.2 <br />30 <br />5881.7 <br />2481.5 <br />30 <br />7012.7. 3326.1 <br />30 <br />8415.1 <br />4450.9 <br />40 <br />5898.8 <br />2493.8 <br />`40 <br />7033.6 3342.3 <br />40 <br />8441:5 <br />4472.7 <br />50 <br />5916.0 <br />2506.1 <br />50 <br />7054.5 3358.5 <br />50 <br />8468.0 <br />4494.6 <br />92 <br />5933:2 <br />2518.5 <br />102 <br />7075.5 3374.9 <br />112 <br />8494.6 <br />4516.6 <br />10 <br />5950.5 <br />2531:0 <br />10 <br />7096.6 3391.2 <br />10 <br />R521.3 <br />4538.8 <br />20 <br />5967.9 <br />2543.5 <br />20: <br />7117.8 3407.7 <br />20 <br />8548.1 <br />4561.1 <br />30 <br />5985.3 <br />2556.0 <br />30 <br />7139.0 3424.3 <br />30 <br />8575.0 <br />4583.4 <br />'40 <br />6002.7 <br />2568.6 <br />40 <br />7160,3 3440.9 <br />40 <br />8602.1 <br />4606.0 <br />50 <br />6020,2 <br />2581.3 <br />50- <br />7181:7 3457.6 <br />50 <br />8629.3 <br />4628.6 <br />93 <br />6037.8 <br />2594.0 <br />103 <br />7263.2 3474.4 <br />•113 <br />8656:6 <br />4551.3 <br />10• <br />6055 4 <br />2606.8 <br />10 <br />7224.7 3491.3 <br />1 10 <br />8684.0 <br />'4674.2 <br />20 <br />6073:1 <br />2619.7, <br />20 <br />7246.3 3508.2 <br />20 <br />8711.5 <br />4697.2 <br />30 <br />6090.8 <br />2637.6 <br />30. <br />7268.0 3525.2 <br />30 ' <br />8739.2 <br />4720.3 <br />40 <br />6108.6 <br />2645.5 <br />40 <br />7289,8 . 3542.4 <br />40 <br />8767.0 <br />4743.6 <br />50 <br />6126.4 <br />2658.5 <br />50 <br />7311,7 3559-6 <br />50 <br />•8794.9 <br />4766.9 <br />94 ' <br />6144,3 <br />2671.6 <br />104 <br />7333.6 3576.8 <br />1.14 <br />8822.9 <br />4790.4 <br />10' <br />' 6162.6 <br />2684.7 <br />I0 <br />7355.6 3594.2 <br />10 <br />8851.0 <br />4814.1 <br />20 <br />6180.2 <br />2697.9 <br />20 <br />7377.8 3611.7 <br />20 <br />8879.3 <br />4837.8 <br />30 <br />6198.3 <br />2711.2 <br />30 <br />7399.9 3629.2 <br />30 <br />8907.7 <br />4861.7 <br />40 <br />6216.4 <br />2724.5 <br />40 <br />7422.2 3646.8 <br />40 <br />8936.3 <br />4885.7 <br />50 <br />6234.6 <br />2737.9 <br />50 <br />7444.6. 3664.5 <br />50 <br />8965.0 <br />4909.9 <br />.95' <br />6252.8 <br />2751.3, <br />105. <br />7457.0 3682.3• <br />llb <br />8993.8 <br />4934.1 <br />•10 <br />6271.1 <br />2764.8 <br />10 <br />7489.6 3700.2 <br />10 <br />'9022.7 <br />4958.6 <br />20 <br />6289.4 <br />2778.3 <br />20 <br />7512.2 3718.2 <br />20 <br />9051,7 <br />4983.1 <br />30 <br />6307.9 <br />2792-0 <br />30 <br />7534:9 3736.2 <br />30 <br />91180,9 <br />5007.8 <br />40_ <br />6326.3 <br />2805.6 <br />40 <br />7557:7 • 3754.4 <br />40 <br />9110.3 <br />5032.6 <br />50 <br />6344.8 <br />2819.4 <br />50 <br />7580.5 3772.6 <br />50 <br />9139.8 <br />5057.6 <br />96 <br />636314 <br />2933.2 <br />106 <br />7603'.5 3791.0 <br />116 <br />9169.4 <br />5082.7 <br />10 <br />6382.1 <br />2847.0 <br />10 ' <br />7526.6 3809.4 <br />10 <br />9199.1 <br />5107.9 <br />20 <br />' 6400:8 <br />2861.0 <br />20 <br />7649.7 3827.9 <br />20. <br />9229.0 <br />5133.3 <br />30 <br />6419.5 <br />2875.0 <br />30 <br />7572.9 3846.5 <br />30 <br />9259.0 <br />5158.8 <br />40 <br />6438.4- <br />2889.0 <br />40 <br />7695.3 3865.2 <br />40 <br />9289.2 <br />5184.5 <br />50 <br />6457.3 <br />2903.1 <br />50 <br />7719.7 3684.0 <br />50 <br />9319.5 . <br />5210.3 <br />97 <br />6476.2 <br />2917.3 <br />107 <br />7743.2 3902.9' <br />117 <br />9349.9 <br />5236.2 <br />10 <br />6495.2 <br />2931.6 <br />10 <br />7766.8 3921.9 <br />10 <br />9380.5 <br />5262.3 <br />20 <br />5514.3 <br />2945.9 <br />20 <br />7790.5 3940.9 <br />20 <br />9411.3 <br />5288.6 <br />30 <br />6533.4 <br />2960.3 <br />30 <br />'7814.3 3960.1 <br />30 <br />9442.2 <br />5315:0 <br />40 <br />6552.6 <br />2974.7 <br />40 <br />7838,1 3979.4 <br />40 <br />9473.2 <br />5341.5 <br />50 <br />6571.9 <br />2989.2 <br />50 <br />7862.1 3998.7 <br />50 <br />9504.4 <br />5368.2 <br />986591.2 <br />3.81 <br />3003.8 <br />108 <br />7886.2 4018.2 <br />118 <br />9535.7 <br />5395.1, <br />10 <br />6610.6 <br />3018.4 <br />10 <br />7910.4 4037.8 <br />10 <br />9567.2 <br />5422.1 <br />20 <br />6630..1 <br />3033.1 <br />20 <br />7934,6 4057.4 <br />20 <br />9598.9 <br />5449.2 <br />30 <br />6649.6 <br />3047.9 <br />30' <br />7959.0 4077.2 <br />30 <br />9630.7 <br />5476.5 <br />40 <br />6669.2 <br />3062.8 <br />40 <br />7983.5 4097.1 <br />40 <br />9662.6 <br />5504.0 <br />50 <br />6688.8 <br />'3077.7 <br />50 <br />6008-0 4117.0 <br />50 <br />9694.7 <br />5531.7 <br />99 <br />6708.6 <br />3092.7 <br />109 <br />8032.7 4137.1 <br />119 <br />9727.0 <br />5559.4 <br />10 <br />6728.4 <br />3107.7 <br />10 <br />8057-4 4157.3 <br />10 <br />9759.4 <br />-5587.4 <br />20 <br />6748.2 <br />3122.9 <br />20 ' <br />8082.3' 4177.5 <br />20 <br />9792.0 <br />5615.5 <br />30 <br />6768.1 <br />3138.1 <br />30 <br />8107.3 4197.9 <br />30 <br />9824.8 <br />5643.8 <br />40 <br />6788.1 <br />3153.3 <br />40 <br />8132,3 4218.4 <br />40 <br />9857.7 <br />. 5672.3 <br />50' <br />6808.2 <br />3168.7 <br />50 <br />8157.5 4239.0 <br />50 <br />9890.8 <br />5700.9 <br />100 <br />6828.3 <br />3184.1 <br />110 <br />8192,8 4259.7 <br />120 <br />9924.0 <br />5729.7 <br />10 <br />6848.5 <br />3199.6 <br />10 <br />8208.2 4280.5 <br />10 <br />9957.5 <br />5758.6 <br />20 <br />.6868.6 <br />3215.1 <br />20 <br />8233.7 4301.4 <br />20 <br />9991.0 <br />5787.7 <br />30 <br />6889.2 <br />3230.8 <br />30 <br />8259-3 4322.4 <br />30 <br />10025.0 <br />5817.0 <br />40 <br />6909.6 <br />3246.5 <br />40 <br />8285.0 4343.6 <br />40 <br />10059.0 <br />5846.5 <br />50 <br />6930.1 <br />3262.3 <br />50 <br />8310.8 4364.8 <br />.50 <br />10093.0 <br />5876.1 <br />.289 <br />VII <br />TABLE V. -CORRECTIONS FOR TANGENTS AND EXTERNALS. <br />'these corrections are to be added to the approxi[nate values, Found by dividing <br />the tangent, or external, for a 10 curve (Table IV) by the degree of curve, in order <br />to obtain the true tangents, or externals. Intermediate values may be obtained by <br />interpolation, <br />FOR TANGENTs ADD - <br />ocn..xeL of CURVE <br />Central <br />Angle <br />5° <br />10° <br />15° <br />20° <br />25° <br />30°[35° <br />40° <br />45° <br />50° <br />55° <br />60° <br />65° 1 <br />70- <br />100 <br />,03 <br />.06 <br />.09 <br />.13 <br />.16 <br />.19 <br />.22 <br />.25 <br />.28 <br />.31 <br />.34 <br />.38 <br />'.42 <br />.46 <br />150 <br />.04 ..10 <br />.14 <br />.19 <br />.24 <br />.29 <br />.34 <br />.39 <br />.45 <br />.51 <br />.53 <br />.58 <br />'63 <br />.68 <br />20° <br />.06 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />.65 <br />.72 <br />.79 <br />.84 <br />.90 <br />250 <br />.08 <br />.16 <br />.24 <br />.33 <br />..40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.06 <br />1.14 <br />$0° <br />.10 <br />.19 <br />.29 <br />.39 <br />.49 <br />.59 <br />.69 <br />.79 <br />.89 <br />.99 <br />1.09 <br />1.20 <br />1.29 <br />1.39 <br />350 <br />,11 <br />22 <br />..34 <br />.47 <br />.58 <br />.69 <br />.70 <br />.81 <br />.92 <br />1.04 <br />1.29 <br />1.42 <br />1.54 <br />1.66 <br />400- <br />13 <br />.26 <br />.40 <br />.53 <br />.67 <br />.80 <br />.93 <br />1.06 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 <br />1.94 <br />450 <br />.15 <br />.30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 <br />2.21 <br />500' <br />17. <br />.34 <br />.51 <br />'.68 <br />.85 <br />1,02 <br />1.19 <br />1.36 <br />1.54.1.72 <br />1.91 <br />2.10 <br />2,29 <br />2.48 <br />55° <br />.19 <br />.38 <br />.57 <br />.76 <br />.95 <br />1,14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 <br />2.56 <br />2.77 <br />60° <br />.21 <br />A2 <br />.63 <br />.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 <br />2.60 <br />2.83 <br />3.07 <br />65° <br />.23 <br />.46 <br />.69 <br />_93 <br />1.16 <br />1,40 <br />1.64 <br />'1.88 <br />2.13 <br />2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 <br />70° <br />,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 />3.16 <br />3.44 <br />3.72 <br />75°: <br />27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />80° <br />,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 />851 <br />.33 <br />.66 <br />1. DO <br />1.93 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />90° <br />.36- <br />'.72 <br />1,09 <br />1.45 <br />1.93 <br />2,20 <br />2,57 <br />2,94 <br />3.32 <br />3.70 <br />4.10 <br />4.50 <br />4.91 <br />5.32 <br />95° <br />39 <br />79 <br />1.19 <br />1.55 <br />2.00 <br />2.40 <br />2.80 <br />3.20 <br />3.61 <br />4.02 <br />4.40 <br />4.98 <br />5.38 <br />5.83 <br />1001• 1.43 <br />.86 <br />1.30 <br />1.74 <br />2:18 <br />2,62 <br />3.06 <br />3.50 <br />3.95 <br />4.40 <br />4.88 <br />5.37 <br />5.85 <br />6.34 <br />110° <br />.51 <br />1.03 <br />1:56 <br />2.08 <br />2.61 <br />3.14 <br />3.67 <br />4.21 <br />4.76 <br />5.31 <br />5.86 <br />6.43 <br />7.01 <br />7.60 <br />120° <br />62 <br />1.25 <br />1.93 <br />2.52 <br />3.16 <br />3.81 <br />4,45 <br />5.11 <br />5.77 <br />6.44 <br />7.12 <br />7.80 <br />8.50 <br />9.22 <br />FOR EXTERNALS ADD <br />DEGREE OF CUEVE <br />Central. <br />Angle <br />5° <br />10-6 <br />is <br />20° <br />25° <br />30° 135° <br />40° <br />45° <br />50° <br />55° <br />60-f65- <br />1 70- <br />100 <br />.001 <br />.003 <br />.004 <br />.006 <br />.D07 <br />.008 <br />.009 <br />.011 <br />.012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />160 <br />.003 <br />.007 <br />.010 <br />.014 <br />.018 <br />.023 <br />.027 <br />.029 <br />_032 <br />-035 <br />.039 <br />.043 <br />.047 <br />.051 <br />200 <br />.006 <br />.011 <br />.017 <br />.022 <br />.028 <br />.034 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 <br />.083 <br />250 <br />009 <br />.018 <br />.027 <br />.036 <br />.D46 <br />.056 <br />.065,.074 <br />.063 <br />.D93 <br />.106 <br />.120 <br />.127 <br />.135 <br />300 <br />.013.025 <br />.038 <br />.051 <br />.065 <br />.078 <br />:090 <br />.103 <br />.116 <br />.129 <br />.149 <br />.170 <br />.179 <br />.188 <br />350 <br />.018 <br />.035 <br />.054 <br />.072 <br />.086 <br />.109 <br />.131 <br />.153 <br />.175 <br />.197 <br />.213 <br />.230 <br />.247 <br />.264 <br />400 <br />.023 <br />.046 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />,234 <br />.265 <br />.277 <br />x.290 <br />.315. <br />341 <br />450 <br />.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />'.445 <br />NO <br />.037 <br />.075 <br />.116 <br />.151 <br />.189 <br />.227 <br />.266 <br />.305 <br />.345 <br />.384 <br />.425 <br />.467 <br />.508 <br />.550 <br />55° <br />.046 <br />.493 <br />.142 <br />.188 <br />.236 <br />.283".332 <br />.381 <br />.420 <br />.479 <br />'530 <br />.582 <br />.641 <br />.700 <br />600 <br />.056 <br />.112 <br />.168 <br />.225 <br />.283 <br />.340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 <br />.851 <br />650 <br />.067 <br />.135 <br />.204 <br />.273 <br />.343 <br />.412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />700 <br />.080 <br />.159 <br />.240 <br />.321 <br />.403 <br />.485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.994 <br />1.08 <br />1.17 <br />750 <br />.095 <br />.182 <br />.286 <br />.383 <br />.480 <br />.578 <br />.678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />800 <br />.110 <br />.220 <br />.332 <br />.445 <br />.558 <br />.671 <br />.787 <br />.903 <br />1.02 <br />1.13 <br />1.25 <br />1.38 <br />1.50 <br />1.62 <br />850 <br />.128 <br />.259 <br />.391 <br />.524 <br />.657 <br />.790 <br />.926 <br />1.06 <br />1.20 <br />1.34 <br />1.47 <br />1.62 <br />1.76, <br />1.91 <br />900 <br />.149 <br />.299 <br />.450 <br />.603 <br />.756 <br />.910 <br />1.07 <br />1.22 '1.38 <br />1.54 <br />1.70 <br />1.87 <br />2.03 <br />2.20 <br />950 <br />.174 <br />.350 <br />.522 <br />.706 <br />.985 <br />1.06 <br />1.25 <br />1.43 <br />1.62 <br />1.80 <br />1.99 <br />2.18 <br />2.38 <br />2.53 <br />1000 <br />.200 <br />.401 <br />.604 <br />.800 <br />1.01 <br />1.22 <br />1.43 <br />1.64 <br />1.65 <br />2.06 <br />2.28 <br />2.50 <br />2.73 <br />2.96 <br />1100 <br />.268 <br />.536 <br />.806 <br />1.08 <br />1.35 <br />1.63 <br />1.91 <br />2.20 <br />2.48 <br />2.76 <br />3.05 <br />3.35 <br />3,66 <br />3.96 <br />1201 <br />:360 <br />.721 <br />1.08 <br />1.45 <br />1.82 2.19 <br />2.57 <br />2.95 <br />3.33 <br />3.72 <br />4,11 <br />4.50 <br />4.91 <br />5.32 <br />