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VI TABLE I. - Tangents and Externals to a V Curve. <br />('.h nrd = 11H1 it <br />Int. <br />Angle <br />Tangent <br />External <br />Int.I <br />Angle <br />Tangent <br />Extcmal <br />I <br />Int. <br />Angle <br />Tangent <br />External <br />85° <br />5250.3 <br />2041.7 <br />021 <br />5933.2 <br />2518.5 <br />99° <br />6703.6 <br />3092.7 <br />10' <br />5265.6 <br />2052.1 <br />10' <br />5950.5 <br />2531.0 <br />10' <br />G728.4 <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 />G768.1 <br />3138.1 <br />40 <br />5311.9 <br />2053.5 <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 />2531.3 <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 />GS28.3 <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 />,5359.9 <br />2136.7 <br />30 <br />6090.8 <br />2632.6 <br />30 <br />GS89.2 <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 />215S.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 />6050.63 <br />327S.1 <br />10 <br />5453.1 <br />2130.2 <br />.10 <br />6162.6 <br />26S4.7 <br />10 <br />6971.3 <br />3294.1 <br />20 <br />5469.0 <br />2191.1 <br />20 <br />6150.2 <br />2697.9 <br />20 <br />6992.0 <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 />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 />3353.5 <br />88 <br />5533.1 <br />2235.5 <br />95 <br />6252.5 <br />2751.3 <br />102 <br />7075.5 <br />3374.0 <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 />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 />20 <br />7139.0 <br />3424.3 <br />40 <br />5597.8 <br />2280.6 <br />40 <br />6326.3 <br />2805.6 <br />40' <br />7160.3 <br />3490-9 <br />505614.2 <br />8157.5 <br />2292.0 <br />50 <br />6344.8 <br />2319.4 <br />50 <br />7151.7 <br />3457.6 <br />89 <br />.5630.5 <br />2303.5 <br />96 <br />6363.4 <br />2533.2 <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 />6400.8 <br />2861.0 <br />20 <br />724G.3 <br />3505.2 <br />30 <br />5679.9 <br />2338.2 <br />30 <br />6419.5 <br />2575.0 <br />30 <br />7268.0 <br />3525.2 <br />40 <br />5696.4 <br />2349.3 <br />40 <br />6438.4 <br />2859.0 <br />40 <br />7289.5 <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 />07 <br />6476.2 <br />2917.3, <br />101 <br />7333.6 <br />3576.S <br />10 <br />5746.3 <br />2355.1 <br />10 <br />6495.2 <br />2931.6 <br />10 <br />7355.E <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 />36.16.9 <br />50 <br />5813.6 <br />2432.9 <br />50 <br />6571.9 <br />2989.2 <br />50 <br />7444. C, <br />3664.5 <br />01 - <br />5830.5 <br />2444.9 <br />98 <br />6591.2 <br />3003.8 <br />105 <br />7467.0 <br />3652.3 <br />10 <br />5847.5 <br />2457.1 <br />10 <br />6610.6 <br />3018.4 <br />10 <br />7459.6 <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 />3047.9 <br />30 <br />7534.0 <br />3736.2 <br />40 <br />5898.8 <br />2493.8 <br />40 <br />6669.2 <br />3062.5 <br />40 <br />7557.7 <br />3754.4 <br />50 <br />5916.0 <br />2506.1 <br />50 <br />6685.8 <br />3077.7 <br />50 <br />7550.5 <br />3772.6 <br />Corrections to he Added (T =Tangent. E. =External.) <br />Eat. <br />Angle <br />Curve 5° <br />10° 15° 20' 25° 30° 35° 40°1 45° <br />50° <br />55° <br />60° 65° 7 <br />85° <br />T=.33 <br />.66 1.00 1.33 1.68 2.02 2.36 2.70 3.05 <br />3.40 <br />3.77 <br />4.14 485 4• <br />111° <br />E =.128 <br />.250 .391 .521 ..657 .790 .926 1.06 1.20 <br />1.34 <br />1.47 <br />1.62 1.76 Ir <br />90° <br />T =.36 <br />.72 1.09 1.45 1.83 2.20 2.57 2.94 3.32 <br />3.70 <br />4.10 4.50 4.91 5. <br />4407.0 <br />E-.149 <br />.299 .4540 .603 .756 .910 1.07 1.22 1.38 <br />1.54 <br />1.70 <br />1.87 2.03 2• <br />95° <br />1 <br />T-39 <br />79 1.19 1.55 2.00 2.40 2.80 3.20 3.61 <br />4.02 <br />4.49 4.98 5.38 5. <br />1 <br />9229.0 <br />R =.174 <br />.3.50 .522 .706 .98511.00 1.25 1.43 1.62 <br />1.80 <br />1.99 <br />2.18 2.38 2, <br />100° <br />T=.43 <br />.86 1.30 1.44 2.18 12.02 3.06 3.50 3.95 <br />4.40 <br />4.88 <br />5.37 5.85 �,' <br />7696.3 <br />E= .200 <br />.401 .001 .800 LOl 1.22 1.43 1.64 1.85 <br />2.00 <br />2.28 <br />2.50 2.73 <br />105° <br />T =.46 <br />.94 1.42 1.90. 2.39 2.87 3.34 3.84 4.35 <br />4.84 <br />5.35 <br />5.67 6.40 6• <br />5468.0 <br />E =.230 <br />.4701 .700 .938 1.17 11.42 1.65 1.90 2.14 <br />2.39 <br />2.G4 <br />2.90 3.16 3. <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 />Ta ent <br />°g <br />External <br />Int. <br />Angle <br />Tan ent <br />B <br />External <br />106° <br />7603.5 <br />3791.0 <br />111° <br />8336.7 <br />438G.1 <br />118° <br />9169.4 <br />5052.7 <br />10' <br />7626.6 <br />3809.4 <br />10' <br />S362.7 <br />4407.0 <br />10' <br />9199.1 <br />5107.9 <br />20 <br />7649.7 <br />3327.0 <br />20 <br />5338.9 <br />4429.2 <br />20 <br />9229.0 <br />5133.3 <br />30 <br />7672.9 <br />3346.5 <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 />S441.5 <br />4472.7 <br />40 <br />9289.2 <br />5184.5 <br />50 <br />7719.7 <br />3884.0 <br />50 <br />5468.0 <br />4494.6 <br />50 <br />9319.5 <br />5210.3 <br />107 <br />7743.2 <br />3902.9 <br />112 <br />5494.6 <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 />9350.5 <br />5262.3 <br />20 <br />7790.5 <br />3940.9 <br />20 <br />8543.1 <br />456 1. 1 <br />20 <br />9411.3 <br />528.8.6 <br />30 <br />7814.3 <br />3960.1 <br />30 <br />8.575.0 <br />4533.4 <br />30 <br />9442.2 <br />5315.0 <br />40 <br />7838.1 <br />3979.4 <br />40 <br />5602.1 <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 />462S.6 <br />50 <br />9504.4 <br />5368.2 <br />108 <br />7856.2 <br />4015.2 <br />113 <br />8656.6 <br />465t.3 <br />118 " <br />9535.7 <br />5395.1 <br />10 <br />7910.4 <br />4037.5 <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 />9593.0 <br />5449.2 <br />30 <br />7959.0 <br />4077.2 <br />30 <br />5739:2 <br />4720.3 <br />30 <br />9030.7 <br />5476.5 <br />40 <br />7983.5 <br />4097.1 <br />40 <br />8767.0 <br />4743.6 <br />40 <br />9062.6 <br />5504.0 <br />50 <br />8008.0 <br />4117.0 <br />50 <br />S794.9 <br />4766.9 <br />50 <br />0694.7 <br />5531.7 <br />109 <br />5032.7 <br />4137.1 <br />114 <br />8822.9 <br />4700.4 <br />119 <br />9727.0 <br />5559.4 <br />10 <br />8057.4 <br />4157.3 <br />10 <br />8851.0 <br />4813.1' <br />10 <br />9759.4 <br />5587.4 <br />20 <br />8082.3 <br />4177.5 <br />20 <br />8879.3 <br />4837.S <br />20 <br />9792.0 <br />5015.5 <br />30 <br />8107.3 <br />4197.9 <br />30 <br />5907.7 <br />4861.7 <br />30 <br />9S24.S <br />5613.8 <br />40 <br />8132.3 <br />4218.4 <br />40 <br />5936.3 <br />4SS5.7 <br />40 <br />9557.7 <br />5672.3 <br />50 <br />8157.5 <br />4239.0 <br />50 <br />S965.0 <br />4900.9 <br />50 <br />9590.8 <br />5700.9 <br />110 <br />S182.S <br />4259.7 <br />115 <br />8993.6 <br />4934.1 <br />120 <br />9924.0 <br />5729.7 <br />10 <br />820S.2 <br />4250.5 <br />10 <br />9022.7 <br />4958.6 <br />10 <br />99,5 .5 <br />5758.6 <br />20 <br />S233.7 <br />4301.4. <br />20 <br />9051.7 <br />4953.1 <br />20 <br />9991.0 <br />5757.7 <br />30 <br />S259.3 <br />4322.4 <br />30 <br />9030.9 <br />5007.8 <br />30 <br />10025.0 <br />5317.0 <br />40 <br />5235.0 <br />4343.6 <br />40 <br />0110.3 <br />5032.6 <br />40 <br />ID059.0 <br />5546.5 <br />50 <br />8310.8 <br />4364.5 <br />50 <br />9139.8 <br />5057.6 <br />50. <br />10093.0 <br />5576.1 <br />Corrections to be Added (T = Tangbnt. E = External.) <br />An; le <br />Curve 5' 10° 15° 20° <br />1 25° <br />30' <br />35° <br />40° <br />45° <br />50` 55° <br />60°1 65° 70° <br />100° <br />T=.43 1 .86 1.30 1.74 <br />2.I8 <br />2.0 <br />3.06 <br />3.50 <br />3.05 <br />4.40 4.S3 <br />1 5.37 5.85 6.34 <br />E=.200 .401 .GN .809 <br />1-61 <br />1.22 <br />IA31 <br />1.64 <br />1.85 <br />2. CC 2.231 <br />2.50 2.73 2.96 <br />105° <br />T=.46 1 94 11.42 11.00 <br />2.33 <br />2.87 <br />3.34 <br />3.54 <br />4.35 <br />4.S4 5.35 <br />5.87 6.40 64.93 <br />E=.230 .470 .700 .938 <br />1.17 <br />1.42 <br />1.65 <br />1.00 <br />2.14 <br />2.39 , 2.61 <br />2.9013.161 3.41 <br />110' <br />1.03 1.55 2.05 <br />2.60 <br />3.14 <br />3.66 <br />4.21 <br />4.70 <br />5.31 5.56 <br />6 43 7.01 7.50 <br />E =.260 .5351 .SOS 1.03 <br />1.36 <br />1.633 <br />L91 <br />2.19 <br />2.40 <br />2.61 3.05 <br />3.35 3.65 3.95 <br />115' <br />1 T=.54 1.131.70 2.29 <br />2.56 <br />3.45 <br />4.03 <br />4.63 <br />5.23 <br />5.89 6.44 <br />7.07 7.;0 3.35 <br />E=.307 .6241 M9 136 <br />1.57 <br />1.89 <br />231 <br />2.53 <br />2.37 <br />3.20 , 3.53 <br />3.58 4.23 4.53 <br />1P9, <br />T=.61 1.25 1.89 2.52 <br />3.16 <br />1.81 <br />4.411 <br />5.11 <br />5.73 <br />6.44 7.11 <br />7.80 8.51 9 21 <br />I <br />E=.339 .720 1.08 1.45 <br />1 <br />1.82 <br />3.20 <br />3.5631 <br />2.051 <br />3.3313.7-2 <br />4.10 <br />i <br />4.50 ,1.011 5.32 <br />