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VI TABrA-,L _ Tangents and'Externals to a 1'Curve. <br />Cb ord =100 ft. <br />Angle' <br />Tangent <br />External <br />.. Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />B5'• '' <br />15250.3 <br />2041.7 <br />92°.- 1 <br />5933.2 <br />2518':'5 <br />99° <br />6708.6 <br />3092.7 <br />' -'-10' <br />5265.6 <br />> 2052.1 <br />10' <br />.5950:'5 <br />.2531.0 <br />'101. <br />• 6728.4 <br />3107.7 <br />:20 <br />5281:0 <br />•2062.5 <br />( 20 ' <br />'5967.9 <br />2543.5 <br />20' <br />,6748.2 <br />3122.9 <br />30 <br />:5296.4 <br />2073.0 <br />30 <br />'5985.3 <br />2556.0 <br />30 <br />'6768.1 <br />3138.1 <br />'40; <br />.5311.9 <br />.2083.5 <br />- •40 <br />6002.7 <br />2568.6 <br />40 <br />:6788.1 <br />'3153.3 <br />50 <br />+5327:4 <br />2094.1 <br />50 <br />6020.2 <br />'.2581.3 <br />'50 <br />•6808.2 <br />3168.7 <br />86 -" <br />.5343.0 <br />2104:7 <br />93 <br />6037.8 <br />2594.0 <br />100 <br />6828.3 <br />3184.1 <br />10' <br />:5358.6 <br />:2115.3 <br />10 <br />6055.4, <br />'.2606.8 <br />•16 <br />'6848.5 <br />• 3199.6 <br />20 <br />'5374.2 <br />2126.0 <br />20 <br />6073.1 <br />12619.7 <br />20 <br />6868.8 <br />3215.1 <br />30- <br />'5389.9 <br />2136.7 <br />30 <br />6090.8 <br />2632.6 <br />130 <br />-6889.2 <br />3230.8 <br />•40 <br />15405.6 <br />2147.5 <br />40 <br />.6108.6 <br />2645.5 <br />40 <br />6909.6 <br />'3246.5 <br />.50 <br />:5421.4. <br />12158.4 <br />50 • <br />6126.4 <br />.2658.5 <br />50'.. <br />6930.1 <br />3262.3 <br />871. <br />'5437:2 <br />;2169.2 <br />94 . <br />6144.3 <br />2671.6' <br />101.- <br />16950.6 <br />3278.1 <br />-• 10 <br />•5453.1 <br />'2180.2 <br />10 '• <br />6162.6 <br />2684.7 <br />-•10 • <br />.6971.3 <br />3294.1 <br />20 <br />_7934.6 <br />4057.4 <br />••20 <br />6180.2 <br />2697.9 <br />-20 <br />6992.0 <br />3310.1 <br />30 <br />,5469.0 <br />5484.9 <br />•2191.1 <br />2202.2 <br />30 <br />6198:3 <br />'2711.2 <br />30 <br />-7012.7 <br />3326.1 <br />-40. <br />'5500.9 <br />,2213.2 <br />.: •40 <br />6216.4 <br />-2724.5 <br />`• 40 <br />7033.6 <br />3342.3 <br />�50 <br />;5517.0 <br />3 <br />:2224.3 <br />-50 <br />:6234.6 <br />2737.9 <br />50 <br />7054.5 <br />3358.5 <br />109 <br />5533.1 <br />2235.5 <br />:95• <br />6252.8 <br />-2751.3 <br />102'- -, <br />7075.5 <br />3374.9 <br />'3391:2 <br />30 <br />5549.2 <br />2246.7 <br />10 <br />•6271.1 <br />'2764.8 <br />10- <br />'7096.6 <br />5587.4 <br />205565.4 <br />8082:3 <br />2258.0 <br />20:' <br />8879.3' <br />2778:3 <br />20 <br />7117.8 <br />3407.7 <br />0 <br />30: <br />•5581_.6' <br />`2269.3 <br />.6289.4 <br />30 <br />6307.9 <br />.2792.0 <br />30 <br />7139.0 <br />3424.3 <br />-`40 <br />:8132:3 <br />2280.6 <br />-40 <br />6326.3- <br />-2805.6 <br />40. <br />7160.3 <br />3449.9 <br />-50. <br />.5597.8 <br />•5614:2 <br />:2292.0 <br />50 - <br />;6344.8 <br />;2819.4 <br />b0" <br />i <br />7181.7 <br />3457.6 <br />89 ! <br />5630.5 <br />'2303:5 <br />96 <br />'6363.4 <br />'2833.2 <br />103 <br />7203:2 <br />' 3474.4 <br />10' <br />5646.9 <br />2315.3 <br />10 <br />•6382.1, <br />2847.0 <br />10 <br />7224.7 <br />3491.3 <br />20- <br />5663.4 <br />2326.6 <br />20 <br />6400;8` <br />:2861.0 <br />_ 20, <br />7246.3 <br />3508.2 <br />30 <br />,5679.9 <br />;2338.2 <br />30 <br />6419.5 <br />'2875.0 <br />30 <br />.7268.0 <br />3525.2 <br />=•'40- <br />5696.4 <br />2349.8 <br />40 <br />6438.4 <br />2889.0 <br />40 <br />7289.8 <br />3542.4 <br />-'50 <br />.5713.0 <br />2361.5 <br />50 - <br />•6457.3 <br />-2903.1 <br />50 <br />7311.1 <br />3559.6 <br />90'- <br />*5729.7• <br />2373.3 <br />f97• �' <br />6476.2 <br />.2917.3 <br />104 <br />7333:6- <br />3576.8 <br />10 <br />`5746.3 <br />2385.1- <br />•10 ' <br />6495.2 <br />2931.6 <br />10 <br />7355.6 <br />3594.2 <br />.20 <br />5763.1 <br />2397.0 <br />20 <br />6514.3' <br />2945.9 <br />20 <br />7377.8 <br />3611.7 <br />30 <br />'5779.9 <br />2408.9 <br />30 <br />'6533.4 <br />`2960.3 <br />30 <br />7399.9 <br />3629.2 <br />'40 <br />.5796.7 <br />2420.9 <br />•40 <br />6552.6 <br />2974.7 <br />40 ' <br />,7422.2 <br />3646.8 <br />50• <br />'5813.6 <br />2432.9 <br />50 <br />6571.9 <br />2989.2 <br />50- <br />7444.6 <br />3664.5 <br />i <br />r <br />'5830.5 <br />2444.9 <br />98 <br />6591.2 <br />3003.8 <br />105. <br />7467.0 <br />3682.3 <br />- <br />-10, <br />5847.5 <br />2457.1 <br />10 <br />6610.6 <br />3018.4 <br />10 <br />7489.6 <br />3700.2 <br />20- <br />-5864.6 <br />2469.3 <br />• 20 <br />6630.1 <br />3033.1 <br />20 <br />7512.2. <br />3718.2 <br />30 <br />.5881.7 <br />2481.5 <br />80 '- <br />6649.6 <br />.3047.9 <br />30 <br />7534.9- <br />3736.2 <br />40• <br />'.5898.8 <br />2493.8 <br />40 : <br />6669:2 <br />3062.8 <br />40,- <br />7557.7' <br />3754.4 <br />50 <br />5916.0 <br />2506.1 <br />50 <br />6688.8 <br />3077.7 <br />50 <br />7580.5 <br />3772.6 <br />'_ 'Coiiectiolis:tobe.Added'.(T=Tangent: E.=External.): <br />Ang[e <br />Carve 5° <br />10° :15° 206 25° 30° 350 40° 45° 50° <br />55° 60° 650 70° <br />85' <br />T=.33 " <br />.66 1.00 1.33 11.68 2.02- 2.36' 2.70 3.05 3.40 <br />3.77 4.14 4.55 4.89 <br />External <br />E='.128 ' <br />..259 -1391 :524 -657 .790 .926 1.06 1.20 1.34 <br />1.47 1.62 1.76 1.91 <br />! T=.36 <br />..72 1.09' 1.45,' 1.83 2.20 2.57 2.94 3.32 3.70 <br />4.10 4.50 .4.91 5:32 <br />90° <br />: <br />D=.149 <br />299 .450 :603 .758 .910 1.07 1.22 1.38 1.54 <br />1.70 1.87 2.03 2.20 <br />': T=.39 <br />.79 1.19 1.55. 2.00 2.40 2.80 3.20 3.61 4.02 <br />4.49 4.98 5.38 5.83 <br />8362.7. <br />E =.174 <br />,.350 .522 .706 .98511.06' 1.25 1.43 1.62 1.80 <br />1.99 2.18 2.38 2.58 <br />".T_=.43-- <br />86 1.30 1.74 2.18 2.62 3.06 3.50 3.95 4.40 <br />4.88 5.37 5.85 6.84 <br />100°.'i <br />E=.200. <br />.401 .604 .809 1.01 .1.22 1.43 1.64 1.85 2.08 <br />2.28 2.50 2.73 298 <br />.. 20 <br />T=.46 ' <br />:.94' 1.42: 1.90 2.38 2.87 3.34 3.84 4.35 4.84 <br />5.35 5.87, 8.40 683 <br />7672.9 <br />E=.230 <br />.470 .700 .938 1.17 1.42 1.65 1.90 2.14 2.39 <br />2.84 2.90 3.16 3.4� <br />ri <br />TABLE I. - Tangents and Externals to a P Curve. '� <br />' - . - Choid=100 ft. - -_ .. <br />e <br />Tangent <br />External <br />Angie <br />Tangent <br />External <br />Angle' <br />Tangent <br />External <br />106°.•., <br />7603:5 <br />.3701.0 <br />'111'. <br />8336:7 <br />4386.1, <br />11601 <br />9160.4 <br />6082.7 <br />10' <br />7626.6 <br />8809.4 <br />10' <br />8362.7. <br />'4407.6 <br />10' <br />9199.1 <br />5107.9 <br />:20' <br />7649.7 <br />3827.9 <br />20 <br />. <br />8388.0 <br />-4429.2, <br />.. 20 <br />9229.0 <br />5133.3 <br />.30 <br />7672.9 <br />3846.5. <br />30 • <br />8415.1 <br />4450.9 <br />! 30 <br />9259.0 <br />6158.8 <br />40. <br />7696.3 <br />3865.2 <br />40 <br />8441.5` <br />'4472.7 <br />40' <br />9289.2 <br />6185,5 <br />50- <br />7719:7 <br />3884.0 <br />50 <br />8468.0 <br />4494.6 <br />50 <br />, <br />9319.5 <br />5210.3 <br />107 '-7743:2 <br />1.90 <br />8902.9 <br />112." <br />8494.6 <br />4516.6 <br />117 - <br />9349.9 <br />5236,2 <br />.10 <br />7766.8 <br />3921.9 <br />10 <br />-8521.3 <br />4538.8 <br />10 <br />9380.5 <br />5262.3 <br />20 <br />7790.5' <br />3940.9 <br />20' <br />8548.1 <br />4561.1 <br />:' 20 <br />9411:3' <br />5288.6 <br />30' <br />7814.3- <br />3960.1• <br />30, <br />8575.0. <br />4583.4 <br />30 <br />9442:2.' <br />5315:0 <br />T40 <br />:7838.1 <br />3979.4 <br />40`, <br />.8602.1 <br />4606.0 <br />40 <br />9473.2 <br />6341.5 <br />.50 <br />7862.1 <br />3998.7 <br />50' <br />8629.3 <br />4628.6 <br />50 <br />9504.4 <br />5368.2 <br />108,''. <br />7886.2 <br />4018.2 <br />113 ' <br />8656:6 <br />4651.3 <br />118 <br />9535.7 <br />5395.1 <br />10. <br />7910.4 <br />4037.8 <br />10 <br />8684.0 <br />4674.2 <br />10 <br />9567.2 <br />5422.1 <br />20 <br />_7934.6 <br />4057.4 <br />20 <br />8711.5. <br />4697.2 <br />20 ' <br />9598.9 <br />5449.2' <br />30; <br />7959.0 <br />4077.2 <br />30 <br />`8739.2• <br />4720.3 <br />'30 <br />9630..7 <br />5476.8 <br />.40.. <br />7983.5. <br />4097.1 <br />40 <br />8767.0.:4743.6 <br />6.44 <br />- 40 . <br />9662:6 <br />5504.0 <br />50'1 <br />:8008.0:.4117.0 <br />E=.339 <br />-50 <br />:8794:9..4766.9 <br />1:45 <br />50 <br />9694.7 <br />5531,7 <br />109 <br />" 8032.7. <br />`4137.-1 <br />114 <br />8822.9 <br />4790.4 <br />119 <br />97VA <br />5559.4; <br />10 <br />80574- <br />4157.3 <br />10 ' <br />8851.0' <br />4814.3 <br />10 <br />9759.4 <br />5587.4 <br />:20.•' <br />8082:3 <br />4177:5' <br />: 20• <br />8879.3' <br />4837:8 <br />.20 <br />9792:0 <br />5615.5 <br />30 <br />8107:3 <br />4197:9. <br />.'30 <br />8907.7 <br />4861:7 <br />30 <br />9824:8` <br />5643.8 <br />40 <br />:8132:3 <br />4218.4' <br />408936.3 <br />4885.7 <br />40, <br />9857.7 <br />5672.3 <br />-50. <br />;8157.5 <br />4239.0: <br />'•, '50 <br />8965.0 <br />4909.9 <br />50 . <br />'9890.8. <br />b?d0.9 <br />110•. '' <br />8182.8' <br />4259.7. <br />115 <br />8093.8. <br />4934.1 <br />120 <br />9924.0 <br />5729.7 <br />10 <br />8208.2 <br />4280.5: <br />- 10 <br />9022.7 <br />-10 <br />9957.5` <br />5758.6 <br />^20.• <br />,8233.7 <br />4301.4 <br />20 <br />9051:7 <br />,4958.6. <br />4983.1 <br />'20 <br />9991.0 <br />5787.7 <br />"••30.' <br />-8259.3 <br />4322.4: <br />30 <br />9080:9 <br />5007.8. <br />30 <br />10025.0 <br />5817.0 <br />-40 <br />8285.0 <br />4343.6 <br />40 <br />9110:3 <br />5032.6 <br />40. <br />10059.0' <br />5846.5 <br />50 - <br />8310.8 <br />4364.8. <br />50 <br />9139.8 <br />5057.6 <br />50- <br />10093.0 <br />5876:1, <br />_Corrections to be Added (T=Tangent. E=External.) <br />Int <br />'Curve <br />, <br />Angle <br />5° <br />- <br />10° <br />15° <br />20° <br />25° <br />30° <br />35' <br />40° <br />45° <br />'SO° <br />55° <br />60° <br />65° <br />70° <br />1006 - <br />T=.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 />E=.200 <br />,.401 <br />.604 <br />.809 <br />1.01 <br />1.22 <br />1.43 <br />1.64 <br />1.85 <br />2.06 <br />2.28 <br />2.50 <br />2.73 <br />2.96 <br />105° <br />T=.46 <br />.94. <br />1.42 <br />1.90 <br />2.38 <br />2.87 <br />3.34 <br />3.84 <br />4.35 <br />4.84 <br />5.35 <br />5.87 <br />6.40 <br />6.93 <br />E =.230 <br />.470 <br />•.700 .938 <br />1.17 <br />1.42 <br />1.65 <br />1.90 <br />2.14 <br />2.39 <br />2.64 <br />2.90 <br />3.16 <br />3.41 <br />110° - <br />.T=.50 <br />1.03 <br />1.55 <br />2.08 <br />2.60 <br />3.14 <br />3.66 <br />4.21 <br />4.76 <br />5.31 <br />5.86 <br />6.43' <br />7.01 <br />.7.59 <br />E=.260 <br />.535 ..808 <br />1.08 <br />1.36 <br />1.63 <br />1.91 <br />2.19 <br />2.49 <br />2.61 <br />3.05' <br />3.35 <br />3.65 <br />3.95 <br />115° <br />T=-54 <br />1.13 <br />1.70 <br />2.29' <br />2.86 <br />3.45 <br />4.03 <br />4.63 <br />5.23 <br />5.83 <br />6.44 <br />-7.07 <br />7.70 <br />8.35 <br />.E=.307 <br />..624 <br />.9391.26 <br />1.57 <br />1.89 <br />2.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 <br />3.88 <br />4.23 <br />4:58 <br />120°;• <br />.T=.61 <br />11.25 11.89 <br />12.52 <br />3.16 <br />3.81 <br />4.44• <br />5.11 <br />5.78 <br />6.44 <br />7.11' <br />7.80 <br />8.51 <br />9:21 <br />E=.339 <br />.720 <br />1.08 <br />1:45 <br />1.82 <br />2.20 <br />2.56 <br />2.95 <br />3.33 <br />3.72 <br />-4.101 <br />4.501-4.91 <br />5.32 <br />A <br />