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6 <br />VI TABLE I. _ Tangents and Externals to a V Curve. <br />Chord =100 ft_ <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle - <br />Tangent <br />I <br />External <br />I <br />Int. <br />Angle <br />Tangent <br />External <br />86-° <br />52:,0.3 <br />2041.7 <br />921 <br />5933.2 <br />2515.5 <br />99° <br />6708.6 <br />.450 .603 .756 .910 11,07 <br />10' <br />5265.6 <br />2052.1 <br />10' <br />5950.5 <br />2.531.0 <br />10' <br />G728.4 <br />,3092.7 <br />31.07.7 <br />20 <br />5281.0 <br />2062.5 <br />20 <br />5967.9 <br />2543.5 <br />20 <br />G748.2 <br />3122.9- <br />30 <br />5296.4 <br />2073.0 <br />30 <br />5985.3 <br />2556.0 <br />30 <br />6763.1 <br />3133.1 <br />40 <br />531 IA <br />2053.5 <br />40 - <br />6002.7 <br />2568.6 <br />40 <br />G78S.I- <br />3153.3 <br />50 <br />5327.4 <br />2094.1 <br />50 <br />6020.2 <br />2581.3 <br />50 <br />GSOS.2 <br />31G3.7 <br />86 <br />5343.0 <br />2101.7 <br />93 <br />6037.8 <br />2594.0 <br />1.00 <br />6828.3 <br />3184.1 <br />10 <br />5358.6 <br />211.5.3 <br />10 <br />6055.4 <br />2606.8 <br />10 <br />6548.5 <br />3109.6 <br />20 <br />.5374:2 <br />2126.0 <br />20 <br />6073.1 <br />2619.7 <br />20 <br />6568.8 <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 />6105.6 <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 />2058.5 <br />50 <br />G930.1 <br />3262,3 <br />187 <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 />65971.3 <br />3294.1 <br />20 <br />5469.0 <br />2191.1 <br />20 <br />6180.2 <br />2697.9 <br />20 <br />6,992. 0, <br />3310.1 <br />'30 <br />5484.0 <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 />621 G.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 />88 <br />5533.1 <br />2235.5 <br />95 <br />6252.8 <br />2751.3 <br />102 <br />7075.5 <br />3374.9 <br />10' <br />.5,49.2 <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 />2255.0 <br />20 <br />6289.4 <br />2779.3 <br />20 <br />7117.5 <br />3407:7 <br />30 <br />5581.0 <br />2269.3 <br />30 <br />0307.0 <br />2792.0 <br />30 <br />7139.0 <br />3424.3 <br />40 <br />5597.5 <br />2280.6 <br />40 <br />6326.3 <br />2805.6; <br />40 <br />7160.3 <br />3440.9 <br />50 <br />5614.2 <br />2292.0 <br />50 <br />(3344.8 <br />2819.4 <br />50 <br />7151.7 <br />3457.6 <br />89 <br />5630.5 <br />2303.5 <br />OG <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 />2347.0 <br />10 <br />7224.7 <br />3401.3 <br />20 <br />5663.4 <br />,2326.6 <br />20 <br />6400.8 <br />2861.0 <br />20 <br />7246.3 <br />3505.2 <br />30 <br />6679.9 <br />2338.2 <br />30 <br />6419.5 <br />2875.0 <br />30 <br />7268.0 <br />35'15.2 <br />40 <br />5696.4 <br />2349.8 <br />40 <br />G438.4 <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 />2003.1 <br />50 <br />7311.7 <br />3559.6 <br />Be <br />5729.7 <br />2373.3 <br />97 <br />647G.2 <br />2917.3 <br />104 <br />7333.6 <br />3576.8 <br />10 <br />5746.3 <br />2355.1 <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 />2405.0 <br />30 <br />6533.4 <br />2960A <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 />5513.6 <br />2432.9 <br />50 <br />6571.0 <br />2959.2 <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 />3GS2.3 <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 />5581.7 <br />2481.5 <br />30 <br />6649.6 <br />3047.0 <br />30 <br />7534.9 <br />373G.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 />'Corrections to be Added (T =Tangent. E. =External:) - <br />Angle Curve 5° 10° <br />15° 20° 25° 30° 35° <br />40° 45° 50° 55- 60° 65° <br />70° <br />85° T=.33 .06 <br />1.00 11.33 US 2.02 2.36 <br />2.7.0 3.05 3.40 3.77 4.1 4.55 <br />4.89 <br />E=.128 .259 <br />.391 .524 .657 .790 .926 <br />1.06 1.20 1.34 1.47 1.62 1.70 <br />1.91 <br />90° T=.36 .72 <br />1.09 1.45 1.33 2.20 2.57 <br />2.94 3.32 3.70 4.10 4.50 .4.91 <br />5.32 <br />E=.149 .299 <br />.450 .603 .756 .910 11,07 <br />1.22 1.38 1.54 1.70 1.87 2.03 <br />2.20 <br />9J°=.30 .79 <br />E=.174 <br />1.19 1.55- 2.00 2.40 2.80 <br />3.20 3.61 4.02 4.49 4.93 5.38 <br />5.83 <br />.350 <br />.522 .700 .985 1.06 1.25 <br />1.43 1.62 1.80 1.09 2.18 2.38 <br />2.58 <br />100° T=.43 .86 <br />1.30 1.74 12.19 2'.62 3.05 <br />3.50 3.95 4.40 4.68 5.37 15.951 <br />0.34 <br />E=200 .401 <br />AM .80911.01-11.22 1.43 <br />1.64 1:85 2.06 2.23 2.50 12.73 <br />12.06 <br />105° <br />1`1 2.33 <br />IS46.5 <br />.30 <br />1 =.230 .470, <br />. 00 93SI1.17 `1.42 1.65 <br />1.90 `2.14 2.39 2:64 2.90, 13.16 <br />13.11 <br />TABLE I. - Tangents and Externals to a 1° Curve. Vii - <br />` <br />Chord =-100 ft. <br />Int. - <br />Angle <br />Tangent1 <br />II <br />External <br />Int. <br />Angle <br />Tangent <br />I External <br />Int. <br />Angle <br />Tangent <br />External <br />106° <br />7603.5 <br />3791.0 <br />111° ' <br />_8336.7 <br />438G.1 <br />116° <br />9169.4 <br />50S2.7 <br />10' <br />7626.6 <br />3809.4 <br />10' <br />8362.7 <br />4407.6 <br />10' <br />9199.1 <br />5107.13 <br />20 <br />7&49.7 <br />3S27.9 <br />20 <br />8358.9 <br />4429.2 <br />20 <br />9229.0 <br />5113,3 <br />30, <br />7672.9 <br />IS46.5 <br />.30 <br />8415.1 <br />4450.9 <br />30 <br />9259.0 <br />5155.8 <br />..40 <br />76965.3 <br />3S65.2 <br />40 <br />8441:5 <br />4472.7 <br />40 <br />9289.2 <br />5184.5 <br />50' <br />7719.7 <br />3384.0 <br />50 <br />8468.0 <br />.449-1.G <br />50 <br />9319.5 <br />5210.X <br />107 <br />7743.2 <br />3902.9 <br />112 <br />8494.6 <br />45 16. 6 <br />117 <br />9349.9 <br />52.36.2 <br />10 <br />7766.5 <br />3921.0 <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 />8548.1 <br />4.7,61.1 <br />20 <br />941 L.3 <br />5258.6 <br />30 <br />7514.3 <br />3960.1 <br />30 <br />5575.0 <br />4583.4 <br />30 <br />9142.2 <br />5315.0 <br />40 <br />7833.1. <br />3979.4 <br />40 <br />8602.1 <br />4606.0 <br />40 <br />9473.2 <br />5341.5 <br />50 <br />'7802.1 <br />3998.7 <br />50 <br />8629.3 <br />4628.6 <br />50 <br />9503.4 <br />5368.2 <br />lag <br />7886.2 <br />401S.2 <br />113 <br />6656.6 <br />4G51.3 <br />118 <br />9535.7 <br />5395.1 <br />10 <br />7910.4 <br />4037.8 <br />10 <br />SGS4.0 <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 />5739.2 <br />4720.3 <br />30 <br />9630.7 <br />5476.5 <br />40 <br />7983.5 <br />4097.1 <br />40 <br />8767.0 <br />4743.0 <br />40 <br />9G62.G <br />5504.0 <br />50 <br />8008.0 <br />4117.0 <br />50 <br />5794.9 <br />4766.9 <br />50 <br />0694.7 <br />.5531.7 <br />109 <br />8032.7 <br />4137.1 <br />114 <br />8522.9 <br />4790.4 <br />119 <br />9727.0 <br />5559.4 <br />10 <br />8057.4 <br />4157.3 <br />10 <br />8551.0 <br />4814.1 <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 />40 <br />8936.3 <br />4885.7 <br />40 <br />98:57.7 <br />5672.3 <br />50 <br />8157.5 <br />4239.0 <br />50 <br />8065.0 <br />4909.9 <br />50 <br />9890.8 <br />5700.9 <br />110 <br />8182.S <br />4259.7 <br />115 <br />8993.9 <br />4934.1 <br />120 <br />092-1.0 <br />5729.7 <br />10 <br />8208.2 <br />4230.5 <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 />0051.7 <br />4983.1 <br />20 <br />9991.0 <br />5757:7 <br />30 <br />8259.3 <br />4322.4 <br />30 <br />0080.9 <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 />5540.5 <br />50 <br />•y <br />8310.8 <br />4364.8 <br />50 <br />0139.8 <br />5057.6 <br />50 <br />10093.0 <br />5S70.1 <br />Corrections to be Added (T = Tangent. E =External.) <br />Int. <br />Curse 5° <br />lU° 15° <br />20° <br />25° <br />30° <br />3a <br />40° <br />45° <br />50° <br />55° <br />60° <br />65'I 701 <br />e <br />Angl. <br />T=•43 <br />SG 1.30 <br />1.74 <br />2.18 <br />2.63 <br />3.06 <br />3.50 <br />3.95 <br />4.40 <br />4.98 <br />5.37 <br />5 <br />IOG° E=.200 <br />.401 .604 <br />.809 <br />1.01 <br />1.2'2 <br />` 1.43 <br />1.64 <br />1.35 <br />2.06 <br />2.23 <br />2.50 <br />2.,3 2.116) <br />].100 <br />1.9308 <br />105° E=230 <br />.470 <br />1.17 <br />1.42 <br />1.65 <br />1.90 <br />2.11 <br />2.39 <br />2_.6-1 <br />2.00 <br />3.16 3A1 <br />110° T=.50 <br />1.03 1.55 <br />'2.08 <br />'1 <br />2.60 <br />3.14 <br />"3.60 <br />4.21 <br />4.76 <br />.5.31 <br />5.50 <br />GA3 <br />7.01 7.5'3 <br />E=.260 <br />.535 .808 <br />3 <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 />3.63 3.45 <br />115, T=.54 <br />I 1.70 <br />2.2912.&6 <br />3.45 <br />4.1 <br />4.63 <br />5.^_3 <br />5.S3 <br />6.44 <br />7.07 <br />7. 0 8.35 <br />E=.307 <br />621 .939 <br />1.26 <br />1.57. <br />LEO <br />2.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 <br />3.58 <br />4.'13 4.53 <br />T=.61 <br />125 1.°"9 <br />2.521'.16 <br />3.81 <br />4A4 <br />5.11 <br />5.73 <br />0-44 <br />7.11 <br />7.80 <br />8.51 9.21 <br />120° E=.330 <br />I .720 1.03 <br />2.'LU <br />2.56 <br />2.95 <br />3.'03 <br />3.72 <br />4.[0 <br />4.50 <br />4.9115.32 <br />a <br />