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VI TAn1.E I. - Tangents and Externals to a 1° Curve. <br />('117 nrrl _ 1 nn ft - <br />Angle <br />'Tangent <br />External <br />•Angle <br />Tangent <br />External <br />Angle' <br />Tangent <br />External <br />85° <br />5250:3 <br />2041.7 <br />92° <br />5933.2 <br />2518.5 <br />99° <br />6708.6 <br />3092.7 <br />10' <br />5265.6 <br />'5251.0 <br />2052.1 <br />10'• <br />5950.5 <br />2531.0 <br />10' <br />6728.4 <br />3107.7 <br />20 <br />2.94 3.32 3.70 4.10 <br />2062.5 <br />20 <br />59G7.0 <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 />31;3.3 <br />50 <br />5327.4 <br />2094.1 <br />50 <br />6020.2 <br />2531:3 <br />50 <br />6808.2 <br />3165.7 <br />80 <br />'5343.0 <br />2104.7 <br />93 <br />G037.8 <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 />G073.1 <br />2619.7 <br />20 <br />GM.8 <br />3215.1 <br />30 <br />5380.9 <br />2136.7 <br />30 <br />G090.8 <br />2632.6 <br />30 <br />6389.2 <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 />5421.4 <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.G <br />101 <br />6950.6 <br />3278.1 <br />.10 <br />5453.1 <br />2150.2 <br />10 <br />6162.G <br />.2684.7 <br />10 <br />6971_3 <br />3294.1 <br />20 <br />5469.0 <br />2191.1 <br />20 <br />0180.2 <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 />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 />222.4.3 <br />50 <br />6234.G <br />2737.9 <br />50 <br />7054.5 <br />3358.5 <br />88 <br />5533.1 <br />2235.3 <br />95 <br />6252.8 <br />2751.3 <br />102 <br />7075.5 <br />3374.9 <br />10 <br />5549.2 <br />2246.7 <br />10 <br />6271.1 <br />2764.8 <br />10 <br />7096.6 <br />3391.2 <br />20 <br />5565.4 <br />2258.020 <br />20 <br />6280.4 <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 />3124.3 <br />40 <br />5597.8 <br />2280.6 <br />40 <br />6326.3 <br />2505.6 <br />40 <br />71GO. 3 <br />344 0. 9 <br />50 <br />5614.2 <br />2292.0 <br />50 <br />6344.8 <br />2319.4 <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 />2315.0 <br />10 <br />6382.1 <br />2847.0 <br />10 <br />7224.7 <br />3101.3 <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 />405696.4 <br />8235.0 <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 />0470.2 <br />2917.3 <br />104 <br />7333.6 <br />3576.8 <br />10 <br />5746.3 <br />2355.1 <br />10 <br />G495.2 <br />2031.6 <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 />2405.9 <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 />6552.0 <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 />G630.1 <br />3033.1 <br />20 <br />7519.2 <br />3718.2 <br />30 <br />5881.7 <br />2481.5 <br />30- <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 1 <br />3772.6 <br />Corrections to be Added (T = Tangent. E. =External.) <br />Int. <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />g <br />External <br />Angle <br />Curve 5° <br />10° 15° 20° 25° 30° <br />35° <br />1 40° 45° 50° 55° 1 <br />60° 65° 70° <br />85° <br />T =.33 <br />.08 1.00 1.33 1.68 2.02 <br />2.36 <br />2.70 3.05 3.40 3.77 <br />4.14 4.55 4.89 <br />10' <br />E =.128 <br />.259 .391 .524 .657 .790 <br />.926 <br />1.06 1.20 1.34 1.47 1 <br />1.62 1.76 1.91 <br />90° <br />T=.30 <br />.72 1.09 1.45 1.83 2.20 . <br />2.57 <br />2.94 3.32 3.70 4.10 <br />4.50 4.91 5.82 <br />20 <br />E-140 <br />.290 .450 .603 .7561.910 <br />1.07 <br />1.22 1.38 1.54 1.70 <br />1.87 2.03 2.20 <br />95° <br />T=.39 <br />.79 1.19 1.55 12.00 12.40 <br />2.80 3.20 3.01 4.02 4.49 <br />4.98 5.83 <br />44.50.9 <br />li =.174 <br />.350 822 .706 .935 LO6 <br />1.25 <br />1.43 1.6`2 1.80 1.99 <br />15.38 <br />2.182.38 2.58 <br />100° <br />T=.43 <br />.88 1.30 1.74 12.13 12.02 <br />3.06 <br />3.50 3.95 4.40 4.88 <br />5.37 5.85 6.34 <br />5184.5. <br />E=.200 <br />.401 .605 .809 1.01 1.22 <br />1.43 <br />1.64 1.85 2.00 2 -8 1 <br />2.50 2.73 2.96 <br />105° <br />T=.46 <br />E=.230 <br />.94 1.42 11.00 12.382.87 <br />11.42 <br />1.90 <br />3.34 <br />3.81 4.35 4.84 5.35 <br />5.87 6.40 0.93 <br />3902.9 <br />112 <br />.470 .100 .033 1.17 <br />1.65 <br />2.1412.39 2.6412.9013.10 <br />3.41 <br />TABLE I: - Tangents and Externals to a 1° Curve. VII <br />'Chord=100 ft. occ <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />g <br />External <br />Int. <br />Angle <br />Tangent <br />g <br />Fxtesnal <br />c 7J D <br />106° <br />7603.5 <br />. 3791.0 <br />111° <br />8336.7 <br />4386.1 <br />116° <br />9169.4 <br />5082.7, <br />10' <br />7626,0 <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 />44.50.9 <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 />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 />7766.5 <br />3921.9 <br />10. <br />8521.3 <br />4535.8 <br />10 <br />9380.5 <br />5262.3 <br />20 <br />7790.5 <br />3940.9 <br />20 <br />5548.1 <br />4561.1 <br />20 <br />9411.3 <br />5288.6' <br />30 <br />7814.3 <br />3960.1 <br />30 <br />5575.0 <br />4583:4 <br />30 <br />9442:2 <br />5315!0 <br />40 <br />7838.1 <br />3979.4 <br />40 <br />S602.1 <br />4606.0 <br />40 <br />9473.2 <br />534'1.5 <br />50 <br />7562.1 <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 />5656.6 <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 />5476.5 . <br />40 <br />798.3.5 <br />4097.1 <br />40 <br />8767.0 <br />4743'.6 <br />40 <br />9662.6 <br />5504.0 <br />50 <br />8008.0 <br />4117.0 <br />50 <br />8794.9 <br />4766.9 <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 />9727.0 <br />5559.4- <br />10 <br />8057.4 <br />41.57.3 <br />10 <br />8851.0 <br />4814.1 <br />10 <br />9759.4 <br />5587.4 <br />20 <br />8083.3 <br />4177.5 <br />20 <br />8879.3 <br />4837.8 <br />20 <br />0792.0 <br />5615.5 <br />30 <br />8107.3 <br />4197.9' <br />30 <br />5907.7 <br />4561.7 <br />30 <br />0824.8 <br />. <br />'5643.8 <br />40 <br />8132.3 <br />4218.4 <br />40 <br />8936.3 <br />4585.7 <br />40 <br />0857.7 <br />5672.3. <br />50 <br />8157.5 <br />4239.0 <br />50 <br />8965.0 <br />4909.9 <br />50 <br />9S90.8 <br />5700.9 <br />110 <br />8182.8 <br />4259.7 <br />115 <br />8993.8 <br />4034.1 <br />120 <br />9924.0 <br />5729.7 <br />10 <br />8208.2 <br />4280.5 <br />10 <br />9022.7 <br />4958.6 <br />10 <br />9957.5 <br />5755.6 <br />20 <br />S233.7 <br />4301.4 <br />20 <br />9051.7 <br />4983.1 <br />20 <br />0991.0 <br />5787.7 <br />30 <br />3259.3 <br />4322.4 <br />30 <br />9050.9 <br />5007.8 <br />30 <br />10025.0 <br />5817.0 <br />40 • <br />8235.0 <br />4343.6 <br />40 <br />9110.3 <br />5032.6 <br />40 <br />10059.0 <br />5S,lG:5 <br />50 <br />8310. S: <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 />Ant. OW -M 5° 10° <br />Angle <br />IS- <br />20° <br />25°k-2.6 <br />35° 40° 45° <br />50° <br />55° <br />60° 65° <br />70° <br />100° T=•'3 .86 <br />1.30 <br />1.74 <br />2.18 <br />3.06 3.50 3.U5 <br />4.40 <br />4.83 <br />5.37 5.85 <br />6.34 <br />E=.200 .401 <br />.605 <br />.800 <br />1.01 <br />1.43 1.64 1.85 <br />2.00 <br />2.28 <br />2.50 `2.73 <br />2.96 <br />105° T=.48 .94 <br />1.42 <br />1.90 <br />2.33 <br />3.34 3.84 4.35 <br />4.34 <br />5.35 <br />5.87 6.40 <br />6.93 <br />E.470 <br />.700 <br />.93 <br />1.17 <br />1.65 1.00 2.14 <br />2.39 <br />MA <br />2.90 3.16 <br />3.41 <br />T=.50 1.03 <br />1.55 <br />2.08 <br />2.60 <br />MG 4 21 4.75 <br />5.31 <br />5.86 <br />61.43 7.01 <br />7.59 <br />E=200 .535 <br />.808 <br />1.08 <br />1.36 <br />1.91 2.19 2.49 <br />2.61 <br />3.05 <br />3.35 3.65 <br />3.95 <br />115• T=.54 1.13 <br />11.70 <br />2.29 <br />MG <br />3.45 <br />4.03 4.63 5.23 <br />6.83 <br />6.44 <br />7.07 7.70 <br />8.35 <br />1 =.307 .621 <br />.939 <br />1.26 <br />1..57 <br />1.89 <br />221 2.54 2.37 <br />3.20 <br />3.5,1 <br />3:88 4.'23 <br />4.58 <br />120' T=.61 1.25 <br />1.89 <br />'2..52 <br />3.16 <br />13.51 <br />4.44 5.11 5.78 <br />6.44 <br />7.11 <br />7.80 8.51 <br />9.21 <br />r =.339 .72011.08 <br />11.45 <br />1.821 <br />2.20 <br />2.56 2.95 3.33 <br />3.72 <br />4.101 <br />4.50 4.91 <br />5.32 <br />C <br />