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VI TABLE I: -'Tangents and Externals to a 1° Carve. <br />Chord =100 ft- <br />p <br />Int. <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />` <br />m i <br />Angle <br />Ta <br />I regent <br />External <br />85°' <br />5250.3 <br />2041.7 <br />92°'5933.2 <br />60'. 65° 70° <br />2:118.5 <br />99° <br />6708:6 <br />2.36 2.70 3.05 <br />10' <br />52G5.6 <br />`2052.1 <br />10' <br />5950.5 <br />2531.0 <br />10' <br />6728.4 <br />.3092.7 <br />3107.7 <br />20 <br />5281.0 <br />2062.5 <br />20 <br />5967.9 <br />2543.5 <br />20 <br />6743.2 <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 />G002.7 <br />2568.6 <br />40 <br />6753.1 <br />3153.3 <br />50 <br />5327.4 <br />2094.1 <br />50 <br />6020.2 <br />2581.3 <br />" 50 <br />6508.2 <br />3168.7 <br />86,`" <br />53.13.0 <br />2104.7 <br />93 <br />G637.8 <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 />2600.5 <br />10 <br />G348.5 <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 />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 />mn.2 <br />2169.2 <br />'94 <br />6144.3 <br />2671.6 <br />101' <br />6950.G <br />3278.1 <br />10 <br />5453.1 <br />21S0.2 <br />10 <br />6152.6 <br />2684.7 <br />10 <br />6971.3 <br />3204.1 <br />.20 <br />5469.0 <br />2191.1 <br />20 <br />6180.2 <br />2697.9 <br />2U <br />6992.0 <br />3310.1 <br />30 <br />5434.0 <br />2202.2 <br />30 <br />6198.3 <br />2711.2 <br />.20 <br />30 <br />7012.7 <br />3326.1 <br />40 <br />5500.0 <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 />.88 <br />.1 5533 <br />2235:0 <br />95 <br />6252.8 <br />2751.3 <br />102 <br />7075.5 <br />3374.9 <br />-10 <br />..5549.2 <br />'5565.4 <br />2246.7 <br />10 <br />6271.1 <br />2764.8 <br />10 <br />7096.6 <br />3391.2 <br />20 <br />8082.3 <br />2258.0 <br />20 <br />6289.4 <br />2778.3 <br />20 <br />7117.8 <br />3407.7 <br />30 <br />5581.0 <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 />6326.3 <br />2505.6 <br />40 <br />7160.3 <br />3440.9 <br />50 <br />5614.2 <br />2292.0 <br />50' <br />6344.8 <br />2S19.4 <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 />6352.1 <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 />2361.0 <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 />349.8 <br />40 <br />6438.4 <br />2839.0 <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 />'5763.1 <br />2385.1 <br />10 <br />6495.2 <br />2931.6 <br />'10 <br />.7355.0 <br />3594.2 <br />20 <br />2397.0 <br />20 <br />6514.3 <br />2945.9 <br />20 <br />7377.8' <br />3611.7 <br />30 <br />5779.0 <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 />5513.6, <br />2432.9 <br />50 <br />6571.9 <br />29S9.2 <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 />6610.0 <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 />'30; <br />6649.6 <br />3017.9 <br />30 <br />7534.9 <br />3730.2 <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 1 <br />2506.1 <br />50 <br />6685.3 <br />3077.7 <br />50 <br />7550.5 <br />3772.6 <br />Corrections to be' Added (T --Tangent. E. = External.) <br />Ant' <br />Tangent <br />External <br />Int. <br />Angle I <br />Tangent <br />Externa] <br />Int. <br />Angle <br />Angle Curve 5° 10° <br />15° 20° 25° <br />30° <br />35° 40° 45° <br />50° <br />55° <br />60'. 65° 70° <br />B5° T=.33 .66 <br />1.t0 1.33 1.68-12.02 <br />9169.4 <br />2.36 2.70 3.05 <br />3.40 <br />3.77 <br />4.14 4.55 4.89 <br />E-.128 .259 <br />.391 .524 .651 <br />.790 <br />.926 h.06 1.20 <br />1.34 <br />1.47 <br />1.62 1.76 1.91 <br />90° T=.36 .72 <br />1.09 1.45 1.83 <br />12.20 <br />12.57 2.94 3.32 <br />3.70 <br />4.10 <br />4.50 4.91 5.32 <br />E=.149 .299 <br />.4501 .603 .756 <br />.910 <br />1.07 1.22 1.38 <br />1.54 <br />1.70 <br />1.87 12.03 2,20 <br />95° T=.39 .79 <br />1.19 1.55 2.00 <br />2.40 <br />2.80 3. 0 3.61 <br />4.02 <br />4.49 <br />4.08 5.38 5.83 <br />E=.174 .350 <br />.522 .706 .935 <br />1.06 <br />1.2.5 1.43 1.62 <br />1.80 <br />1.99 <br />2.18 12.38 2.58 <br />100° T=.43 .86 <br />1.30 1.74 `1.13 <br />2.63 <br />3.06 3.50 3.95 <br />4.40 <br />4.88 <br />5.37, 5.S5 6.34 <br />E =.200 .401 <br />.604 .809 1.01 <br />1.22 <br />11.43 1.64 1.85 <br />2.06 <br />2.28 <br />2.50 2.73 2.96 <br />105° T=.46 .94 <br />112 1.90 2.38 <br />2.87' <br />3.34 3.34 4.35 <br />4.84 <br />5.35 <br />5.87 6.40 6.93 <br />E =.230 .4i0 <br />.700 .93311.17 <br />1.42 11.65 <br />11.00 2.14 <br />i 2.39 <br />2.64 <br />2.90 3.16 1 3.41 <br />TABLE I. - Tangents and Externals to a 1° Curve. VII <br />Chord =100 It. . <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle I <br />Tangent <br />Externa] <br />Int. <br />Angle <br />Tangent <br />External <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 />7626.6 <br />3809.4 <br />40' <br />8362.7 1 <br />41U7:6 <br />l0' <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 />3805.2 <br />40 <br />8441.5 <br />4472.7 <br />40 <br />9289.2 <br />5184.5 <br />50' <br />7719.7 <br />3SS4.0 <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 />5230.2 <br />10 <br />7766.8 <br />3921.9 <br />10 <br />8521.3 <br />4538.S <br />10 <br />9350.5 <br />5262.3 <br />1 3.45 <br />7790.5 <br />3940.9 <br />. 20 <br />8548.1 <br />4561.1 <br />20 <br />9411.3 <br />5288.6 <br />-20 <br />30 <br />7814.3 <br />3960.1 <br />30 <br />5575.0 <br />4533.4 <br />30 <br />9442.2 <br />5315.0 <br />:40 <br />7335.1 <br />3979.4 <br />40 <br />8602.1 <br />4606.0 <br />40 <br />9.173.2 <br />5341.5 <br />50 <br />7862.1 <br />3998.7 <br />50 <br />5629.3 <br />4628.6 <br />50 <br />9504:4 <br />5308.2 <br />108. <br />7836.2 <br />4018.2 <br />113 <br />S656.6 <br />4651.3 <br />118 - <br />9535.7 <br />5395.1 <br />10 <br />7910.4 <br />4037:8 <br />10 <br />5684:0 <br />4674.2 <br />10 <br />9567.2 <br />5422.1 <br />20 <br />7934.6 <br />4057.4 <br />.20 <br />8711.8 <br />4697.2 <br />2U <br />9595.9 <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 />7983.5 <br />4097.1 <br />40 <br />8767.0 <br />4743..0 <br />40 <br />9662.6 <br />5504:0 <br />50 <br />5008.0 <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 />4.137.1 <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 />5851.0 <br />4814.1 <br />10 <br />9759.4 <br />5587.4 <br />20 <br />8082.3 <br />4177.5 <br />20 <br />5879.3 <br />4837.5 <br />20 <br />9792.0 <br />5615.5 <br />, <br />30 <br />8107.3 <br />30 <br />5907.7 <br />4861.7 <br />30 <br />9324.8 <br />5643.8 <br />-40 <br />8132.3 <br />_4197.9 <br />4218.4 <br />40 <br />8936.3 <br />4SS5.7 <br />40 <br />0857.7 <br />.5G72.3 <br />50 <br />8157.5 <br />-4239.0 <br />50 <br />5965.0 <br />4900.9 <br />50 <br />9890.5 <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 />5208.2 <br />4230.5 <br />10 <br />9022.7 <br />4053.6 <br />10 <br />9957.5 <br />575S.G <br />20'. <br />5233.7 <br />4301.4 <br />20 <br />0051.7 <br />4983.1 <br />20 <br />9991.0 <br />5757.7 <br />30 <br />5250.3 <br />4322.4 <br />30 <br />90S0.9 <br />5007.8 <br />30 <br />10025.0 <br />5817.0 <br />'40 <br />8255.0 <br />4343.6 <br />40 <br />9110.3 <br />5032.G <br />40 <br />10059.0 <br />5346.5 <br />50 <br />8310.8 <br />43G4.8 <br />50 <br />9 139. 8 <br />r5057.G <br />50 <br />10093.0 <br />5876.1' <br />Corrections to be Added (T =Tangent. E =External.) <br />Int <br />Curve 5° 10° 1 15° 1 20° 25° <br />30° <br />35° <br />40' <br />45° <br />50° <br />55° <br />60° <br />('S <br />Angle <br />T-.43 1.74 2.18 <br />2.G2 <br />3.06 <br />3.50 <br />3.05 <br />4.40 <br />4.58 <br />5.37 <br />5.3,1 <br />634 <br />.3G1.30 <br />100° E=.200 .401 .664 x0 1.01 <br />1. 2 <br />1.43 <br />1_61 <br />1.35 <br />2.06 <br />2.28 <br />2.50 <br />2.73 <br />`70° <br />96 <br />T=.40 1.42 1'.00 2.33 <br />2.57 <br />3.34 <br />3.84 <br />415 <br />4.84 <br />5.35 <br />5.87 <br />6.40 <br />0.93 <br />.04 <br />10� E =.230 .4701 .700 .033 1.171 <br />1.42 <br />1.65 <br />1.90 <br />2.14 <br />2.30 <br />2.64 <br />2.90 <br />3.16 <br />3.41 <br />T=.50 1.03 2.03 2.60 <br />3.14 <br />3.G6 <br />4.^1 <br />'.76 <br />5.31 <br />5.86 <br />6.43 <br />7.U1 <br />7.59 <br />11.55 <br />110° E =.260 .535 .809 1.06 1.36 <br />1.G3 <br />1.91 <br />2.191 <br />2.49 <br />7..61 <br />3.05 <br />3.35 <br />3.651 <br />3.95 <br />T=.54 1.13 11.70 12.29 2.66 <br />1 3.45 <br />4.03 <br />3.63 <br />5.23 <br />5.33 <br />6.44 <br />7.01 <br />7.70' <br />3.35 <br />115° $=.307 .624 .939 1.26 1.57 <br />1.80 <br />2.21 <br />2.5] <br />2.67 <br />3.26 <br />3.5;1 <br />3.33 <br />•1.2314.58 <br />- T=.61 1.25 1.60 2.52 3.10 <br />1201. <br />3.51 <br />4.44 <br />I1 <br />5.78 <br />G.41 <br />7.11 <br />7.80 <br />4.50 <br />8.51 <br />4.91 <br />0.21 <br />5.22 <br />E=.339 .726 1.03' 1.45 1.82 <br />2.20 <br />12.56 <br />2. 5 <br />3.33 <br />3.721 <br />4.101 <br />iX <br />