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T"L'E I. - Tangents and Externals to u 1° Curve. <br />Chord=1nn ft <br />Int. <br />Angle <br />Tangent <br />External. <br />Int.Int. <br />Angle ' <br />I Tangent <br />External <br />Angle <br />I Tangent <br />External <br />86°' <br />"5250.3. <br />2041.7 <br />92° `" <br />5933.2 <br />2518.5 <br />9' <br />6708.617 <br />.259 .391 <br />-`1(' <br />,5205.6 <br />2052.1 <br />10' <br />5950.5 <br />2531.0 <br />10' <br />6728.4; <br />3107..3002.7 <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 />6768.1; <br />3138.1 <br />'40 <br />5311.9 <br />2053.5 <br />40 <br />6002.7 <br />2568.6 <br />40 <br />6788.11 <br />3153.3 <br />50 <br />5327.4 <br />2094.1 <br />50- <br />6020.2 <br />2581.3 <br />50 <br />6808.21 <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 />5355.6. <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 ':6889.2; <br />0442.2 <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 />2658.5 <br />50 ! <br />'6930.1, <br />3262.3 <br />67 1 <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 />p 10 <br />'6971.31 <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 />.5484.9 <br />'5500.9 <br />2202.2 <br />30. <br />6198.3 <br />2711.2 <br />30 <br />7012.7, <br />3326.1 <br />40 <br />7953:54097.1 <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 />i <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 />2255.0 <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 />2505.6 <br />" . 40 <br />7160.3 <br />3440.9 <br />50 <br />5614.2 <br />2292.0 <br />50- <br />6344.8 <br />2519.4 <br />50 <br />7151.7 <br />3457.6 <br />.89' ' <br />5630:'5, <br />2303.5 <br />96 <br />6363.4 <br />28332 <br />103 <br />72M.2;'3474.4 <br />'5729.7 <br />10 <br />5W.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 />'7246.3; <br />3508.2 <br />-30 <br />`5679.9 <br />2333.2 <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 />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 />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 />29.15.9 <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 />7399:0 <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 />'5813.6 <br />2432.9 <br />50' <br />6571.9 <br />2989.2 <br />50 <br />7444.6 <br />3664.5 <br />91' ' <br />'5930.5. <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 />7489.6. <br />3700.2 <br />20 <br />5364.0 <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 />7534.9 <br />3736.2 <br />40 <br />.5598.8 <br />2403.8 <br />40, <br />6669.2 <br />3052.8 <br />40 <br />7557.7 <br />3754.4 <br />50 <br />5916.0,1 <br />2506.1. <br />50 <br />6688.8 <br />3077.7 <br />50 <br />Z589.5;1 <br />3772.6 <br />Corrections to be Added (T=Tangent. E.=External.) <br />Int. <br />,Augle <br />Curve 5° <br />10° 15° <br />20° 25° .30° "35° <br />40° 45° <br />50° <br />55° ,60° 65° <br />70° <br />85° <br />T=.33 <br />.66 1.00 <br />1.33 1.68 2.02 2.30 <br />12.70 3.05 <br />3.40 <br />3.17 4.14 4.55 4.89 <br />116° <br />E =.128 <br />.259 .391 <br />.524 .657 .790 .926 <br />1.06 1.20 <br />1.34 <br />1.47 1.62 -1.76 <br />1.91 <br />90° <br />T=.36 <br />.72 1.09 11.45 <br />11.83 2.20 2.57, <br />2.94 3.33 <br />3.70 <br />4.10 4.50 4.91 <br />5.32 <br />8358:9 <br />E=.149 <br />.299 .450 <br />.603 .750 .010 1.07 <br />1.22 1.38 <br />1.54 <br />1.70 1.87 2.03 <br />2.20 <br />95° <br />T=.39 <br />79 1.10 <br />1.55 2.00 12.40 2.50 3.20 3.61 <br />4.02 <br />4.49 4.9815.3815.&3 <br />40 <br />7696.3 <br />'E =.174 <br />.350 .522 <br />.706 .985 1.06 1.25 <br />1.43 1.62 <br />1.50 <br />1.99 2.18 2.35 <br />2.55 <br />100° <br />T=.43 <br />.86 1.30 <br />1.74 2.18 2.62 3.06 <br />3.50 3.95 <br />4.40 <br />4.58 5.37 1 5.55 <br />6.34 <br />5210.31, <br />E =.200 <br />.401 .601 <br />.509 1.01 1.22 1.43 <br />1.61 1.85 <br />2.05 <br />2.28 2.50 2.73 <br />MG <br />105° <br />T=.46 <br />94 1.42 <br />1.90 2.38 2.57 3.34 <br />3.84 4.35 <br />4.84 <br />5.35 5.87 6.40 <br />6.93 <br />10 <br />E =.230 <br />.470 .700 .03811.17 1.42 1.65 <br />1.90 2.14 <br />2.39 <br />2.84 2.00 3.10 13.41 <br />e <br />TABLE I. - Tangents and Externals to a V Curve. VII` <br />_• "'Chord=100 ft.. " <br />-Int. <br />Angle . <br />-' <br />Tangent <br />- ' <br />External <br />' Int. <br />Angle <br />Tangent <br />- <br />External <br />" Int. ' <br />.Angle <br />Tangent <br />External <br />106° <br />7603.5' <br />3791'.0 <br />1111 <br />`5336.7 <br />4386.1 <br />116° <br />9169.4 <br />5082.7 <br />10' <br />'7620:6 <br />3809.4 <br />10 <br />8362.7 <br />4107.6 <br />10' <br />9199.1 <br />5107.9 <br />20 <br />7649.7 <br />3327.9 <br />20 <br />8358:9 <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 />0259:0 <br />5158.8 <br />40 <br />7696.3 <br />3865.2 <br />-40 <br />8441.5 <br />4472.7 <br />40 <br />0280.2 <br />5184.5 <br />50 <br />'7719.7' <br />3884.0 <br />50 <br />5463.0 <br />4494.6 <br />50 <br />9319.5 <br />5210.31, <br />107 <br />7743:2' <br />3902.9 <br />112 <br />8494.6 <br />4516.6 <br />117 <br />0349.9 <br />5236.2 <br />10 <br />77G6.8 <br />3921.9 <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 />4561.1 <br />20' <br />9411.3. <br />5258.6 <br />30 <br />7814.3 <br />3900.1 <br />30' <br />8575.0 <br />4553.4 <br />30 <br />0442.2 <br />5315.0 <br />40 <br />.7838.1, <br />3979.4 <br />. 40 <br />5602.1 <br />4606.0 <br />40 <br />9173.2 <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 />7856.2 <br />4018.2 <br />11.3 <br />8656.0 <br />4651.3 <br />118 <br />9535.7 <br />:1305.1 <br />10 <br />7910.4 <br />4037.8 <br />10 <br />8654:0 <br />4674.2 <br />10 <br />0567.2 <br />5422.1 <br />20 <br />7934.6 <br />4057.4 <br />20 <br />5711.5 <br />.4697:2` <br />20 <br />95J8.9 <br />5440.2' <br />30 <br />'7959.0 <br />4077.2 <br />30 ' <br />8739.2 <br />4720.3 <br />30 • <br />9630.7 <br />547G.5 <br />40 <br />7953:54097.1 <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 />" <br />10 <br />5057.4 <br />4157.3 <br />10 <br />8851.0 <br />4814.1 <br />10 <br />9759.4 <br />5587.4 <br />20 <br />5082.3 <br />4177.5 <br />20 <br />8879.3 <br />4837.8 <br />20 <br />9792.0 <br />5615.5 <br />30 <br />5107.3 <br />4197.9 <br />30 <br />5907.7 <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 />5672.3 <br />50 <br />8157.5 <br />4239.0 <br />50 <br />5965.0 <br />4909.9 <br />50 <br />9890.3 <br />5700.9 <br />110 <br />8182.8 <br />4259.7 <br />115 <br />5903.5 <br />4934.1 <br />120 <br />9924.0 <br />'5729.7 <br />10 <br />8208.2 <br />4250.5 <br />10 <br />9022.7 <br />4958.6 <br />l0 <br />9957.5 <br />5758.6 <br />20' <br />8233.7 <br />4301.4 <br />20 <br />9051.7 <br />4953.1 <br />20 <br />9991.0 <br />5787.7 <br />30 <br />8259.3 <br />4322.4 <br />30 <br />9050.9 . <br />5007.5 <br />30 ;10025.0 <br />5817.0 <br />40 <br />8285.0 <br />4343.6 <br />40 <br />9110.3 <br />5032.6 <br />40 .10059.0 <br />5846.5 <br />50 <br />8310.8 <br />4364.8 <br />50' <br />9139.8 <br />5057.6' <br />50 <br />10093.0 <br />5870.1 <br />Corrections to be Added (T =Tangent. E =External.) <br />Int. <br />Curve 5° 10° 15° <br />20° <br />25° 30° 35° 40°I 45° <br />SO° <br />55° <br />60° <br />65° <br />70° <br />Angie <br />43 <br />1.601 <br />1.5091 <br />12.62 <br />69 <br />5.7 <br />G.31 <br />100° <br />.600 .401 <br />r= <br />1.0.74 1 1.22 1. 43 1.60 1.5 <br />2.06 <br />2.28 <br />2.301 <br />2.751 <br />3 <br />2.96 <br />T=.40 1.42 <br />1.90 <br />2.33 2.57 3.34 3.54 4.35 <br />4.81 <br />5.35 <br />5.87 <br />6.40 <br />6.93 <br />105° <br />.94 <br />E =.230 .4701 .700 <br />.935 <br />1.17 1.42 1.65 1 �0 2.14 <br />2.39 <br />2-61 <br />2.90 <br />3.13 <br />3.41 <br />T=.50 1.03 1.55 <br />'2.08 <br />2.50 3.14 3.GG' 4. 21 4.76 <br />5.31 <br />..5 .96 <br />G.43 <br />7.01 <br />7.,39 <br />110° <br />E=.260 .5351 .SOS <br />1.08 <br />1.36 1.631'1.91 2.19 2.49 <br />2.61 <br />3.05 <br />3.35 <br />3.65 <br />3.05 <br />1.62411.939 <br />3.45 <br />115° <br />E =,307 <br />1.20 <br />1.57 1.E9 2. C1 ?.64 2.57 <br />3.20 <br />'.531 <br />3.88 <br />4.23 <br />4.58 <br />'1'=.61 1.25 1.89 <br />2.52 <br />3.10 3.81 4.4-11 5.1 L 5.786.44 <br />7.11 <br />":80 <br />9.51 <br />9.21 <br />190° <br />E=.339 .720 1.08 <br />1.45 <br />1.821 2.20 2.50 2.95 3.33 <br />3.72 <br />4.10 <br />4.50 <br />4.011 <br />5.32 <br />