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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 />External <br />Int. <br />Angle <br />Tangent <br />External <br />85'• <br />5250.3 <br />2041.7 <br />92' <br />5933.2 <br />2518.5 <br />09° <br />6708.6 <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 />G748.2 <br />3122.9 <br />30 <br />529 G.4 <br />2073.0 <br />30 <br />5985.3 <br />2556.0 <br />30 <br />6768.L <br />3138.1 <br />40 <br />5311.9 <br />2083.5 <br />40 <br />6002.7 <br />2568.6 <br />40 <br />MS.L <br />3153.3 <br />50 <br />5327.4 <br />2094..1 <br />50 <br />6020.2 <br />253 L 3 <br />50 <br />GSOS.2 <br />3168.7 <br />SO <br />5343.0 <br />2104.7 <br />93 <br />6037.8 <br />2594.0 <br />.100 <br />6828.3 <br />31&/.1 <br />10 <br />5358.6 <br />2115.3 ' <br />10 <br />6055.4 <br />2606.8 <br />.10 <br />6843.5: <br />3199.6 <br />20 <br />5374.21 <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 />324 G.5 <br />50 <br />5421.4 <br />2158.4 <br />50 <br />6126.4 <br />2655.5 <br />50 <br />6930.1 <br />3262.3 <br />'87 - <br />5437.2 <br />2169.2 <br />91 <br />6144.3 <br />2671.6 <br />101 <br />6950.6 <br />3275.1 <br />10 <br />5453.1 <br />2180.2 <br />10 <br />0162.6 <br />2Ga'4.7 <br />10 <br />6971.3 <br />329.1.1 <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 />220'2.2 <br />30 <br />0198.3 <br />271,1.2 <br />30 <br />7012.7 <br />'33213.1 <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 />G234.6 <br />2737.9 <br />50 <br />7054.5 <br />3353.5 <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 />1.0 <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 />30 <br />5581.6 <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 />2805.6 <br />40 <br />7160.3 <br />3440.9 <br />50 <br />5614.2 <br />2292.0 <br />50. <br />6344.3 <br />2810.4 <br />50 <br />7181.7 <br />3457.6 <br />.S9 <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.G ' <br />20 <br />6400.8 <br />2861,0' <br />20 <br />724 6. 3 <br />3508.2 <br />30 <br />5679.0 <br />2338.2 <br />30 <br />CA19.5' <br />2575.0 <br />- 30 <br />7268.0 <br />2525.2 <br />40 <br />5696.4 <br />2319.8 <br />40: <br />G438.4' <br />2889.0 <br />40 <br />7289:S <br />3542.4 <br />50 <br />5713.0 <br />236 L.5 <br />50 <br />6457.3 <br />2903.1 <br />50 <br />7311.7 <br />3559.6 <br />w <br />•00 <br />5729.7 <br />2373.3 <br />97 <br />6476.2 <br />2917.3 <br />101 <br />7333.6, <br />3576.8 <br />10 <br />.5746.3 <br />2385.1 <br />10 <br />6495.2 <br />2931.6 <br />10 <br />7355.6 <br />3594.2 <br />20 <br />57613.1 <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 />(35334 <br />2960.3 <br />30 <br />7399.9 <br />3G29.2 <br />40 <br />5796.7 <br />2420.9 <br />140 <br />65.52.6 <br />2974.7 <br />40 <br />-7422.2 <br />3G46.S <br />50 <br />5813.6 <br />2432.9 <br />50 <br />6571.9 <br />2939.2 <br />50 <br />7444.6 <br />3664.5 <br />81 - <br />5830.5 <br />2444.9 <br />0S <br />6591.2 <br />3003.3 <br />105 <br />7467.0 <br />3682.3 <br />10• <br />5847.5 <br />2457.1 <br />10 <br />6610.6 <br />3013.4 <br />10 <br />7489'.6 <br />3700.2 <br />20 <br />5864.6 <br />2469.3 <br />a 20 <br />6630.1 <br />3033.1 <br />20 <br />7512.2 <br />3718.2 <br />30 <br />5831.7 <br />2451.5 <br />30 <br />G649.G <br />3047.9 <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 />7557.7 <br />3754.4 <br />50 <br />5916.0 <br />2506.1 <br />50 <br />66S3.S <br />3077.7 <br />50 <br />7580.5 <br />3772.0 <br />Corrections" to. be -Added `(T=Tangent. 'E. -=External:) <br />Int. P- �° <br />10' 115' ' 20' 125° <br />30' 35' 40' <br />45' S0° 55; 60' <br />65' <br />70' <br />Angle <br />Tangent <br />External <br />10G° <br />7603.5 <br />3791.0 <br />8- T=.33 <br />Gfi 11.00 1.33 1.66 <br />2.02 2.36 2.70 <br />3.05 3.40 1 3.77 4.14 <br />4.55 <br />4.8D <br />E=.128 <br />.259 1.391 .524 .G57 <br />.790 .9213 1.05 <br />1.20 1.34 1.47 1.62 <br />1.76 <br />1.91 <br />90° T=-313 <br />72 1.091.45 1.83 <br />2.20 12.57 2.94 <br />11.07 <br />3.32 3.70 4.10 4.59 <br />4.91 <br />5.3'7. <br />E =.149 <br />.299 .459 .503 .755 <br />.910 JIM <br />01.38 1.54 1.70 1.87 <br />.2.03 <br />2.20 <br />95' T=.30 <br />.79 1.19 1.55 2.00 <br />2.40 2.80 3.20 <br />3.61 4.02 4:49 4.98'1_5.38 <br />8415.1 <br />5.83 <br />E=.174- <br />.350 .522 .706 .985 <br />1.06 125 1.43 <br />1.62 1.80 1.99 2.18 <br />.2.38 <br />2.58 <br />100' T=.43 <br />.86 1.30 274 2.18 <br />2.62 3.06 3.30 <br />3.95 4.40 4.83 ,5.37 <br />5.85 <br />G.,1 <br />- E =.200 <br />.401 .644 .690 1.01 <br />1.26 1.43. t.64 <br />1.85 2.06 2.28 '1.50 <br />2.73 <br />2.96 <br />105° T=.46 <br />.94 1.4.3 1.90 2.33 <br />1.- <br />2.87 3:34 3.84 <br />4.35 4.84 5.35 5.87 <br />6.44 <br />G. <br />E=.230 <br />.470 .9381.17 <br />1.42 (1.65 1:90 <br />2.14 2.39 2.64 2.90 <br />3.16 <br />3.41 <br />i <br />TABLE I. Tangents and Externals to a 1° Curve. VII <br />- <br />Chord= 100 ft. <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Int. <br />Tangent <br />External <br />10G° <br />7603.5 <br />3791.0 <br />111° <br />8336.7 <br />4386.1 <br />116' <br />91G9.4 <br />5082.7 <br />10' <br />7626.6 <br />3SO9.4 <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 />83S3.9 <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 />3305.2 <br />40 <br />8441.5 <br />4472.7 <br />40 <br />9289.2 <br />5154.5 <br />50 <br />7719.7 <br />-3384.0 <br />50 <br />8465.0 <br />4494.6 <br />50 <br />9319.5 <br />5210.3 <br />107 <br />7743.2 <br />3902.9 <br />112 - <br />8404.6 <br />4516.6 <br />117 <br />9349.9 <br />5236.2 <br />10 <br />7766.8 <br />3021.9 <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 />'5283.6 <br />3D <br />7814.3 <br />5060.1 <br />30 <br />8575.0 <br />4583.4 <br />30 <br />9442.2 <br />5315.0. <br />40 <br />7835.1 <br />3979.4 <br />40 <br />8602.1' <br />4606.0 <br />40 <br />9473.2 <br />5341.5 <br />50 <br />7862.1 <br />3095.7 <br />50 <br />8620.3 <br />4,623.6 <br />50 <br />9504.4 <br />5368.2 <br />108 <br />7386.2 <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 />4597.2 <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 />9030.7 <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 />4766.0 <br />50 <br />9094.7 <br />.5531.7 <br />l09 <br />8032.7- <br />4137.1 <br />114 <br />8522.9 <br />4790.4 <br />119 <br />9727:0 <br />5550.4 <br />10 <br />8057.4 <br />4157.3 <br />10 <br />SS51.0 <br />4814.1 <br />10 . <br />9759.4 <br />5587.4 <br />20 <br />-8082.3 <br />.4177.5 <br />20 <br />•SS79.3. <br />4837.8 <br />-20 <br />9792,0 <br />5615.5 <br />30 <br />8".07.3 <br />4197.9 <br />30 <br />5907.7 <br />4861.7 <br />33 <br />9824.8 <br />5643.8 <br />40 <br />5132.3 <br />4218.4 <br />40 <br />8936.3 <br />4RS5.7 <br />4D <br />9857.7• <br />5672.3 <br />50 <br />5157.5 <br />4239.0 <br />- 50 <br />5965.0 <br />4909.9 <br />5D <br />9890.8 <br />5700.9 <br />110 <br />8182.5 <br />4259.7 <br />115 <br />8903.S <br />4934.1 <br />120 <br />9924.0 • <br />5729.7 <br />10 <br />8208.2 <br />4280.5 <br />10 <br />90'22.7 <br />4958.E <br />10 <br />9957.5 <br />5758.6 <br />20' <br />8233.7 <br />4301.4 <br />20 <br />90:31.7 <br />49S3.1 <br />20 <br />9991.0 <br />5787.7 <br />30 - <br />8259.3 <br />4322.4 <br />30 <br />9030.9 <br />.5007.8 <br />- 30 <br />10025.0 <br />5817.0 <br />40 <br />8285.0 <br />4343.6 <br />40 <br />.0110.3 <br />5032:6 <br />40 <br />10059.0 <br />5346.5 <br />50 <br />8310.8 <br />43&1.6 <br />50 <br />0139.8 <br />5057:6 <br />r 50 <br />10093;0 <br />5376.1 <br />Corrections to be Added (T =:tangent. E = External.) <br />Int. <br />AngEe <br />C¢rre 5' <br />101 <br />IS° 20' <br />, 26°) <br />30' <br />35° <br />1 40' <br />45' <br />S0' <br />I !!° <br />60° <br />65'1 <br />70' <br />100' <br />T = <br />86 11.30 <br />11.74 <br />2.14 <br />262 <br />3.06 <br />3.50 <br />3.95 <br />#.4D <br />4.88 <br />5.37 <br />5.85 <br />6.34 <br />E =.200 <br />,401 <br />.601 M. <br />1.01 <br />1.221 <br />1.41 <br />LG4 <br />1.85 <br />2.06 <br />2.28 <br />2.50 <br />2.73 1 <br />2.96 <br />T=.46 <br />01 <br />1.42 1.90 <br />2.38 <br />".37 <br />13.34 <br />3.64 <br />4.35 <br />4.84 <br />5.315 <br />5.67 <br />1.40 <br />6.03 <br />105° <br />E=.230 <br />_ .470 <br />.700 .93 <br />1.17 <br />1.4211.6.511.9912-14 <br />2.39 <br />2.6! <br />2.90 <br />3.16 <br />3.41 <br />T=.50. <br />1.03 11.55' <br />2.04 <br />2.G0 <br />3.1.11 <br />3.66 <br />4.21 <br />4.76 <br />5.31 <br />5.86 <br />6.43 <br />7.01 <br />7.59 <br />E-260 <br />.535 <br />.808 1.08 <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 />3.65 <br />3.05 <br />115° <br />T=.54 <br />L13 <br />1.70 1 <br />1 2.86 1 <br />3.45 <br />4.03 <br />1 4.63 <br />5.23 <br />rs.S31 <br />6.441 <br />7.07 <br />7.70 <br />8.35 <br />E =.307 <br />.6241 <br />.9391 1.26 <br />1.57 <br />1.89 <br />2 21 <br />'2.54 <br />2.37 <br />3.20 <br />3.53 <br />3.88 <br />4.23 <br />4.58 <br />120' <br />^.'=-61 <br />1.25 <br />1.89 2,52 <br />3.10 <br />3.51 <br />4.44 <br />5.11 <br />5.73 <br />6.341 <br />.7-111 <br />7.80 <br />8.511 <br />0.2L <br />E=.330 <br />.720 1.08 1.45 <br />1 1.82 2.20 <br />2.56 <br />2.C,5 <br />3.33 <br />3.73 <br />4,10 <br />, 4.30 <br />4.01 <br />5.32 <br />