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VI TA13LE 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 />B <br />External <br />Int' <br />Angle <br />Tangent <br />External <br />`$51 <br />5250.3. <br />2041.7 <br />92o <br />5933.2 <br />2518.5 <br />990 -' <br />6708.6 <br />3092.7 <br />'10' <br />5265.G <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 />.529G.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 />3--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 />G055.4 <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 />:5421.4; <br />2158.4 <br />50 <br />G126.4 <br />2658.5 <br />50 <br />6930.1 <br />3262.3 <br />�S ' <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 />20 <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 />5454.9 <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 />616.4 <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 />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 />2258.0 <br />20 <br />6289.4 <br />2778.3 <br />20 <br />7117.8 <br />3407.7 <br />730 <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 />2805.6 <br />40 <br />7160.3_ <br />3440.9 <br />-'50 <br />5614.2 <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 />2315.0 <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 />6100.8 <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 />:150 <br />5713.0 <br />2361.5 <br />50 <br />6457.3 <br />2903.1 <br />50 <br />7311.7 <br />3559.6 <br />-5729.7 <br />2373.3 <br />97 <br />6476.2 <br />2917.3 <br />104 <br />7333.6 <br />3576.8 <br />10.: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 />369.2 <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 />'W ': <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 />5381';7' <br />2481.5 <br />30 <br />6649.6 <br />3047.0 <br />30 <br />7534.9 <br />3736.2 <br />40 <br />5893;8 <br />2493.8' <br />40 <br />6669.2 <br />3062.8 <br />40 <br />_ <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 />Iat• <br />Angle , <br />:.Curve"50 • <br />10° <br />15° <br />20 ° <br />25° <br />30° <br />35°' <br />40° <br />45° <br />506 <br />55° <br />60° <br />65° <br />70° <br />1160 <br />. T=.33 <br />66 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <br />3.05 <br />3.40' <br />3.77 <br />4:14 <br />4.55 <br />4.89 <br />` <br />E--.128.11:256 <br />4429.2 <br />.391 <br />'.524 <br />.657 <br />'.790 <br />.92611.OG <br />3846.5 <br />1.20 <br />1.34 <br />1.47 <br />1.62 <br />1.76 <br />1.91 <br />90° <br />'T'' 36 � <br />72 <br />1;09 <br />1.45 <br />1.83 <br />2.20 <br />2.57 <br />2.94 <br />3.32 <br />3.70 <br />4:10 <br />4.50 <br />4.91 <br />5.32 <br />50 <br />E = 149 <br />..299 <br />.450 <br />.603 <br />.756 <br />.910 <br />1.07 <br />1.22 <br />1.38 <br />1.54 <br />1.70 <br />1.87 <br />2.03 <br />2.20 <br />c 950 , <br />.,T=.30. <br />..79� <br />1.19:11.55 <br />9380.5 <br />2.00 <br />2.40 <br />2.80 <br />13.20 <br />3.61 <br />4.02 <br />4.49- <br />4.98 <br />5.38 <br />5.83 <br />I <br />E=.174 <br />.350 <br />.522 <br />,.706 <br />.985 <br />1.06 <br />1.25 <br />1:43 <br />1.62 <br />1.80 <br />1.99 <br />2.18 <br />2.38 <br />2.58 <br />100°J <br />-T=.43, <br />M <br />1.30 <br />1.74 <br />2.18 <br />2.62 <br />3.00-13.50 <br />4628.6 <br />3.05 <br />4.40 <br />4.88 <br />5.37 <br />5.85 <br />6.34 <br />113 <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 />13.84 <br />4.35 14.84 <br />7959.0 <br />5.35 <br />15.87 <br />6.40 <br />6.93 <br />30 <br />E =.230 <br />.470 <br />.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 />2.00 <br />3.16 <br />3.41 <br />TABLE I. - Tangents and Externals to a 1' .Curve. VII <br />Chord= 100 ft. <br />Int: <br />Angle <br />. Tan ent <br />g <br />External <br />Int' <br />Angle <br />Tangent <br />External <br />Int <br />Angll e <br />Tangent <br />External <br />106° ' <br />7603.5 <br />3791.0 <br />111° <br />8336.7 <br />4386.1 <br />1160 <br />9169.4 <br />.5082.7• <br />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 />50 <br />9319.5-'5210.3 <br />5.31' <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 />7766.8 <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 />40 <br />7838.1 <br />3970.4 <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 />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 />5476.5 <br />40 <br />7983.5 <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 />4157.3 <br />10 <br />8851.0 <br />4814.1 <br />10 <br />9759.4".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 />9857.7 <br />5672, <br />50 <br />8157.5 <br />4239.0 <br />50 <br />8965.0 <br />4909.9 <br />50 <br />9890.8 <br />5700.9 <br />110 <br />8182.8 <br />4259.7 <br />115 <br />8993.8 <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 />'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 />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 />43G4.8 <br />50 <br />9139.8 <br />5057.6 <br />50 <br />10093.0, <br />587G.1 <br />Corrections to be Added (T =Tangent'., E =External.) <br />Int. <br />Angle <br />Curve 5° <br />10°:.15°. <br />20° <br />25° .30° .35° <br />40° <br />45° <br />SO- <br />55° <br />''60° <br />65° -70° <br />100° <br />T=.43 <br />.66 1.30 <br />1.74 <br />2.18 2.62 3.06 <br />3.50 <br />3.95 <br />4.40 <br />4.88. <br />5.37, <br />5.85 6.34 <br />E=.200 <br />.401 .604 <br />.809 <br />1.01 1.22 1.43. <br />1.64 <br />1.85 <br />2.06 <br />2.28 <br />2.50 <br />2.73 2.96 <br />1056 <br />T=.46 <br />.94 1.42 <br />1.90 <br />2.38 2.87 3.34 <br />3.84 <br />"4.35' <br />4.84 <br />5.35 <br />5.87 <br />6.40 6.93 <br />E=.230 <br />.470 .700 <br />.938 <br />1.17 1.42 1.65' <br />1.90 <br />2.14. <br />2.39 <br />2.64 <br />2.90 <br />3.16 3.41 <br />1100 <br />T=.50 <br />1.03 1.55 <br />2.08 <br />2.60 3.14 3.66' <br />4.21 <br />4.76 <br />5.31' <br />5.86. <br />6.43 <br />7.01 .:7.59 <br />E=.260 <br />.535..808 <br />1.08 <br />1.36 1.63 1.91 <br />2.19 <br />2.49. <br />2.61 <br />3.05 <br />3.35 <br />3.65 3.95 <br />115 o <br />T=.54 <br />1.13 1.70 <br />2.29 <br />2.86 3.45 4.03 <br />4.63 <br />5.23 <br />5.83 <br />6.44 <br />7.07 <br />7.70 8.35 <br />E =,307 <br />.624 .939 <br />1.26 <br />1.57 1.89 2.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 <br />3.88 <br />4.23 4.58 <br />120° <br />T=.61 <br />1 <br />1.25 1.89 <br />2.52 <br />3.16 3.81 4.44 <br />5.11 <br />5.78 <br />6.44 <br />7.11 <br />7.80" <br />8.51 9.21 <br />"5.32 <br />E =.339 <br />.720 1.08 <br />1.45 <br />1.82 2.20 2.56 <br />2.95 <br />3.33 <br />3.72 <br />4.10 <br />4.50 <br />4.91 <br />