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TABLE I. - Tangents and Externals to a V. Curve.- <br />��� Chord =100 A. <br />i <br />Ifs <br />(i <br />i <br />I' <br />Int. <br />Tangent <br />External <br />. Int. Tangent <br />Tan gent <br />g <br />External <br />'Angle <br />Tangent <br />External <br />85° . <br />5250.3 <br />2041.7 <br />92° ' <br />6933.2 <br />2518.5 <br />99.0'6708.6 <br />9169.4-'-SD82.7 <br />3092.7 <br />10' <br />5265.6 <br />2052.1 <br />10' <br />5950:5 <br />2531.0 <br />10' <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 />•-10 <br />6848.5 <br />3199.6 <br />20 <br />5374.2 <br />2126.0 <br />- 20 <br />6073.1 <br />2619.7 <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 />30 <br />6889.2 <br />3230.8 <br />40' <br />•5405.6 <br />2147.5 <br />'40 <br />6108.6 <br />2645.5 <br />40 <br />6909.6 <br />3246.5 <br />'-50 <br />15421.4 <br />•2158.4 <br />50' <br />6126.4 <br />2658.5 <br />50 <br />6930.1, <br />3262.3 <br />87'' - <br />5437.2 <br />2169.2' <br />94 <br />6144.3 <br />2671.6 <br />101 <br />6950.6 <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 />- 201 <br />'5469.0 <br />2191.1 <br />• 20 <br />6180.2 <br />•2697.9 <br />20 <br />6992.0 <br />3310.1 <br />30 <br />'5484.9 <br />2202.2 <br />30 <br />6198.3 <br />2711.2 <br />30' <br />.7012.7 <br />3326.1 <br />740 <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 />2224.3 <br />50 ' <br />6234.6 <br />2737.9 <br />50 • <br />7054.5 <br />.3358.5 <br />68 ' <br />5533.1 <br />2235.5 <br />95 <br />6252:8' <br />2751.3 <br />'102' <br />7075.5 <br />3374'9 <br />101 <br />•5549.2 <br />2246.7 <br />10 <br />627H <br />2764.8 <br />'10' <br />7096.6 <br />:3391.2 <br />20 <br />55,35.4 <br />2258.0 <br />20 <br />6289.4 <br />2778.3 <br />20 <br />7117.8 <br />3407.7 <br />30 <br />:5581.6 <br />2269.3 <br />30 <br />6307.9' <br />2792.0 <br />30' <br />7139.0 <br />3424.3 <br />40 <br />;5597.8 <br />2280.6 <br />40 <br />•6323.3 <br />2805.6 <br />.• •- 40 <br />7160.3 <br />344.0.9 <br />-50 <br />5614c2 <br />2292.0 <br />50 ' <br />•6344.8' <br />'2819.4 <br />50• <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 />80 <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 />7311.7 <br />3559.6 <br />90 <br />:5729.7 <br />2373:3 <br />97 <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 />91''• <br />'5830.5 <br />2444:9' <br />98 <br />6591.2 <br />3003.8 <br />105 <br />7467.0' <br />3682.3 <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 />36' <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 />1 2506.1 <br />50 <br />6688.8 <br />1 3077.7 <br />1 50. <br />7580.5 <br />3772.6 <br />i <br />I . <br />II <br />`Corrections to be'Added-(T=Tangent., E. External.) <br />Int. <br />Angle <br />Tan gent <br />g <br />Angle 'Curve 5° 10° 15' 20° 25° ,30° 350 '40° 45° 50° 55° 60° 65° 70' <br />Int. <br />Angle <br />Tangent <br />g <br />85o •- T=.33 .68 1.00 1.33 1.68 2.02 2.36 2.76 ,3.05 3.40 3.77 4.14 4.55 4:89 <br />I'• <br />�� <br />\ E=.125 .259 .391 .524 .657 .790 .926 1.06 1"20 1.34 1.47 1.62 A.1.91 <br />111°• <br />8336.7 <br />90° T=.36 .72 1.09 1.45 1.83 2.20 2.57. 2.94 3.32 3.70 4.10 4.50. 4.91 5.32 <br />'I <br />9169.4-'-SD82.7 <br />E=.149 .299 '.450 ' .603 .756 .910 11.07 1.22 1.38 1.54 1.70 1.87 2.03 2.20 <br />U;•., 10'' <br />7626:6., <br />950 T=.39 .79 1.19 1.65 2.00. 2:40 2.80 3.20 3.61 4.02 4.49 4.98 5.38 6.83 <br />10'- <br />8362.7, <br />E=.174 ..350 .522 .706 .'.985 1.06 1.25 1.43 1.62 1-.80 .1.99 2.18 2.38 2.58 <br />10' <br />9199.1; <br />1000 T=.43 • ; -.86 1.30 1.74 2.18 12.62 3.06 3.50 3.95 4.40 14.88 5.37 5.85 6.34 <br />20• <br />7649.7 <br />E=.200 '.401 .601 .809 1.01 1.22 1.43 1.64 1.85 2.06 2.28 2.50 2.73 2.96 <br />20; <br />4 105° T=.46 .94 1.42 1.90 2.38 2.87 3.34 3.84 4.35 .4.54 5.35 5.87 8.40 8.93. <br />! <br />l: E= 230 ..470 .700 :93811.17 1.42 1.65 1.90 2.14 •2.39 2.04 2.90. 3.16 3.41' <br />e <br />TABLET. - Tangents and Externals to a 1° Curve. NIT <br />. ' . :Chord•'=100 ft: - • . <br />Int. <br />Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tan gent <br />g <br />External <br />_ <br />Int. <br />Angle <br />Tangent <br />g <br />Satrnal <br />106°7603.5. <br />'3791.0 <br />111°• <br />8336.7 <br />4386.1 <br />116° <br />9169.4-'-SD82.7 <br />30 <br />U;•., 10'' <br />7626:6., <br />3809.4 <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 />8388.9 <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 />5158.8 <br />`40 <br />'7696.3 <br />3865.2 <br />'40 <br />8441.5 <br />4472._7 <br />- 40 <br />9289.2 <br />5184.5 <br />50• <br />7719.7 <br />3884.0 <br />50 <br />8468.0 <br />4494.6 <br />_ <br />50 <br />•9319:5: <br />5210.3 <br />107 <br />7743.2 <br />3902.9 <br />.112 <br />8494.6 <br />4516.6 <br />117 <br />9349.9 <br />'5236.2 <br />-10 <br />7766:9. <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 />688.6 <br />30, <br />7814.3' <br />:3960.-1 <br />-30; <br />8575.0 <br />4583.4 <br />.30. <br />9442.2.-:5315.0. <br />2.49 <br />40 <br />7838.1 <br />3979.4 <br />40- <br />8602.1' <br />-4606.0 <br />40` <br />9473.2 <br />5341.5 <br />50- <br />7862.1 <br />3998.7 <br />50•, <br />'8629.3 <br />4628.6 <br />50 <br />9504.4 <br />.6368.2 <br />108' <br />7886.2 <br />4018.2 <br />113 <br />8656:6 <br />4651.3 <br />118 <br />9535.7 <br />15395.1 <br />10 <br />7910.4 <br />4037.8 <br />•.10 <br />.8684.0 <br />•4674.2 <br />.10 <br />9567.2. <br />5:122.1 <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::4097.1 <br />1 5.32 <br />40 - <br />8767.0 <br />4743.6 <br />40 '.9662.6 <br />5504.0 <br />50 <br />8008.0 <br />'4117.0 <br />•50 <br />'8794.9 <br />4766.9 <br />50 <br />.9604.7 <br />'5531.7 <br />109 <br />8032.7, <br />4137:1 <br />114 ' <br />8822:9' <br />4790.4 <br />119 <br />'.9727:0 <br />15559.4 <br />" 10 ' <br />.8057A <br />'4157.3 <br />10 <br />8851.0 <br />4814' 1 <br />10 <br />9759.4 <br />5.587.4 <br />20 " <br />8082.3 <br />4177:5 <br />'- 20 - <br />8879.3 <br />4837.8 <br />20 <br />9792.0 <br />5315.5 <br />30 <br />:8107.3. <br />4197:9 <br />30 <br />8907.7 <br />4861.7 <br />X30 :'9824.8-'5643.8 <br />-40 <br />8132.3 <br />4218:4 <br />40 <br />'8936.3 <br />4885.7 <br />40 <br />9857.7,,5372.8 <br />50,. <br />8157.5' <br />4239.0 <br />'50 <br />8965.0'.4909.9 <br />50 <br />9390.8 <br />'5:700.9 <br />110 <br />8182.8 <br />4259.7, <br />115 <br />:8993.8. <br />4934.1 <br />120 <br />9924.0 <br />5:729.7 <br />10 <br />8208.2' <br />4280.5 <br />'10 <br />9022.7 <br />4958.6 <br />10, <br />9957.5 <br />5758.6 <br />20' <br />8233.7 <br />4301.4' <br />•20 <br />-9051.7 <br />4983.1 <br />20 <br />'9991c0,,5787.7 <br />30 <br />8259:3 <br />-4322.4 <br />30 <br />_9080.9 <br />5007.8 <br />Y30 <br />10025.0 <br />5517.0 <br />- 40'` <br />8285:0-- <br />4343.6. <br />40 <br />9110.3 <br />5032.6, <br />40 <br />10059.0 <br />5346.5 <br />50 <br />8310.8„ <br />4364.8 <br />50 <br />9139.8 <br />5057.'6 <br />.50 ' <br />10093:0 <br />5378.1'. <br />Corrections to be Added (T=.Tangent. E.= External.) <br />Int. <br />0 <br />Angle -Curve 5° <br />o• <br />10 15° <br />20 0 <br />25° <br />30 <br />35 0 <br />40 0 <br />45 o <br />50 o <br />55 c <br />60 o <br />6S ❑ <br />.70 o <br />1000, T=.43 <br />.86- 1.30 <br />1.74 <br />2.18 <br />2.62 <br />3.06'3.50 <br />3.95 <br />4.40 <br />4.88 <br />5.37: <br />5.83 <br />6.34 <br />E =.200 <br />.401 .604 <br />.809 <br />1.61 <br />1.22 <br />1.43 <br />1.64 <br />1.85 <br />2.06 <br />2.28 <br />2.50 <br />2.79 <br />2.96 <br />105° -T=.46 <br />.94 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 .700 <br />.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 />3.36 <br />3.41 <br />1100 T=.50 <br />1.03 1.55 <br />2.08' <br />2.60 <br />3.14 <br />3.66 <br />4.21 <br />.4.76 <br />5.311 <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.' T=.54 <br />1.13 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 .9391.26 <br />1.57 <br />1.89 <br />2.21 <br />2.54 <br />2.87 <br />1 3.20 <br />3.53 <br />3:88 <br />4.23 <br />4.58 <br />i2Oo T=.61 <br />1.25 1.89 <br />2.52 <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 />.72011.08 <br />1.45. <br />1.82 <br />2.20 <br />.2.56 <br />2.95 <br />3.33 <br />3.72 <br />4.10 <br />4.50 <br />4.91 <br />1 5.32 <br />