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TABLE I.' -,Tangents and Externals to,a 1° Curves <br />PlInrrl =Ann fl <br />­ <br />Int.. <br />Angle . <br />Tangent <br />External <br />Angle' <br />Tangent <br />Extemal <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 />.99° <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 />6728.4 <br />3107.7 <br />20 <br />5281.0 <br />2062.5 <br />20 <br />6967.9 <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 />2083.5 <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 />2581.3 <br />50 <br />6808.2 <br />3168.7 <br />80 ' <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 />6055.4 <br />2600.8 <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 />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 />;6950.6 <br />3278.1 <br />'10 <br />5453.1 <br />2180.2 <br />10 <br />6162.6 <br />2684.7 <br />10 <br />6971:31 <br />3294.1 <br />20 <br />5469.0 <br />2191.1 <br />20 <br />6180.2 <br />2697.9 <br />20, <br />6902.0' <br />3310.1 <br />;30 <br />5484.9 <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 />140 <br />6216.4 <br />2724.5 <br />40 <br />7033.6 <br />3342.3 <br />5,0 <br />5517.0 <br />2224.3 <br />.,50' <br />6234.6 <br />2737.9 <br />50 <br />7054.5 <br />3358.5 <br />B8. <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 />2778.320 <br />20 - <br />7117.8 <br />3407.7 <br />30 <br />`40 <br />5581.6 <br />2269.3 <br />30 <br />6307.9 <br />.2792.0 <br />1 <br />7139.0 <br />3424.3 <br />40 <br />5597.8 <br />2280.6 <br />.40. <br />6324.3 <br />2805.6 <br />-30� <br />40 <br />.7160.3 <br />3440.9 <br />PD. <br />5614.2 <br />2292.0 <br />50 <br />6344.8 <br />2819.4 <br />.50 <br />7181.7 <br />3457.6 <br />69- <br />5630.5 <br />2303.5 <br />90 <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 />6400.8 <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 />60 <br />5713.0 <br />2361.5 <br />b0 <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 />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 />_ <br />40 <br />5796.7 <br />2420.9 <br />40 <br />6552.6 <br />2974.7 <br />407 <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 />5830.5 <br />2444:9 <br />98 <br />6591:2 <br />3003.8 <br />1057467.0 <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 />7512.21 <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 />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 <br />2506.1 <br />50, <br />6688.8 <br />3077.7 <br />50' <br />7580.511 ' <br />3772.6 <br />Corrections to be Added (T = Tangent. E. = External.) <br />-Int.,Curve <br />Angle <br />5° <br />. <br />10° 15° 20° 25° 30° 35° <br />40° <br />45° <br />50° <br />55° I 606 65° 70° <br />15° <br />T=.33 <br />.66 1.00 1.33 1.68 2.02 2.36 <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />414 4.55 4.89 <br />116° <br />E=.128 <br />,259 .391 .524 .657 .790 .926 <br />1.06 <br />1.20 <br />1.34 <br />1.47 <br />1.62 1.76 1.91 <br />.90° <br />T=.36 <br />.72 1.09 1.45 1.83 2.20 2.57 <br />2.94 <br />3.33 <br />3.70 <br />4.10 <br />1 4.50 4.91 5.32 <br />8388.9 <br />E=.149 <br />.299 .450 .603 .756 .910 1.07 <br />1:22 <br />1.35 <br />1.54 <br />1.70 <br />1 1.87 1 2.03 2.20 <br />95° <br />T=.39 <br />.79 1.19 1.55 2.00 2.40 2.80 <br />3.20 <br />3.61 <br />4.02 <br />4.49 <br />4.98 5.38 5.83 <br />3865.2 <br />E=.174 <br />.350 .522 .706 -.985 1.06 1.25 <br />1.43 <br />1.62 <br />1.80 <br />1.99 <br />2.18 2.38 2.58 <br />100° <br />T=.43 <br />.86 1.30 1.74 2:18 2.62 3.06 <br />3.50 <br />3.95 4.40 <br />4.88 <br />5.37 5.85 6.34 <br />5210.3 <br />E=.200 <br />.401 .604 .809 1".O1 1.22 1.43 <br />1.64 <br />1.85 <br />2.06 <br />'2.28 <br />2.50 2.73 2.96 <br />105°; <br />' T=.46., <br />.94 1.42' 1.90 2.38 2.87 3.34 <br />3.84 <br />4.35 <br />4.84 <br />5.35 <br />5.87 6.40 6.93 <br />10- <br />E=.230 <br />.470 .700 .938 1.17 1.42 1.65 <br />1.90 <br />2.14' 2.39 <br />2.64 2.90 3.16 3.41 <br />TABLE I. - Tangents and Externals to a_1° Curve. VII <br />Chord =100 ft. <br />Int. <br />Angle"- <br />Tangent <br />- <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />i <br />106° <br />7603:5 <br />$791.0 <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 />10' <br />8362.7 <br />4407.6' <br />10' <br />9199.1 <br />5107.9 <br />720 <br />7649:7; <br />3827.9 <br />20 <br />8388.9 <br />4420.2 <br />20 <br />9229.0 <br />5133.3 <br />=_;W <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 <br />5210.3 <br />107 t <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 .'5288.6 <br />3.41 <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 />5.31 <br />3979.4 <br />"• 40 <br />8602:1 <br />4606.0 <br />40 <br />9473.2 <br />5341.5 <br />'50 <br />_7838.1 <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 />4.63 <br />'. 10 <br />;8684.0 <br />4674.2 <br />10 <br />9567.2 <br />.5422.1 <br />20 <br />11=.307 <br />.4037.8 <br />4057 .4, <br />20'., <br />8711:5 <br />4697.2 <br />-20 <br />9598.9-: <br />5449.23 <br />130 <br />-7934.6 <br />7959.0. <br />4077.2' <br />." 30 <br />`8739.2 <br />4720.3 <br />30 <br />-9630.7 <br />.5476.5 <br />-1.89 <br />7983:5' <br />4097.1, <br />- 40 <br />8767:0 <br />4743.6 <br />409662.6''5504.0 <br />6.44 <br />7.11 <br />.740 <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•-5559.4` <br />5.32 <br />.10' <br />8057.4 <br />4157.3 <br />,' 10 <br />8851.0' <br />4814.3 <br />•10 <br />9759.4 <br />5587:4 <br />20 <br />8082.3" <br />4177:5, <br />20 <br />8879.3 <br />4837.8 <br />20 - <br />9792.0 <br />'982418 <br />5615.5 <br />30 <br />8107.3 <br />4197.9' <br />30 <br />8907.7 <br />4861.7 <br />30 <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 />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 />4301.4 <br />20 <br />9051.7 <br />4983.1 <br />20 <br />9991.0 <br />.5787.7 <br />30 <br />,8233.7 <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 />_. <br />8310.8 <br />4364.8 <br />50 <br />9139.8 <br />.5057.6 <br />60 .10093.0 <br />5876.1- <br />L Corrections to be Added (T = Tangent. E = External.) <br />Int.Curve <br />5° <br />10° <br />15° <br />20° <br />25° <br />30° <br />35° <br />40-1,45-1 <br />50° <br />55° <br />60° <br />65° <br />70° <br />Angle. <br />T=.43 <br />.86 <br />1.30 <br />1.74 <br />2.18 <br />2.62 <br />3.06 <br />3.50 <br />3.95 <br />4.40 <br />4.38 <br />5.37 <br />5.85 <br />6.34 <br />100°,' <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 />T=.46 <br />.94 <br />1.42 <br />1.90 <br />2.38 <br />2.87 <br />3.34 <br />3.84 <br />4.35 <br />4.84 <br />5.35 <br />5.87 <br />6.40 <br />6.93 <br />105° <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 />2.90 <br />3.16 <br />3.41 <br />110°.; <br />T=.50 <br />1.03 <br />1.55 <br />2.08 <br />2.60 <br />3.14 <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 />i. "E =.260 <br />.535 <br />.808 <br />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 />3.95 <br />115° <br />' .,T=.54 <br />1.13 <br />1.70' <br />2.29 <br />2.86 <br />3.45 <br />14.03 <br />4.63 <br />5.23 <br />5.83 <br />6.44 <br />7.07 <br />7.70 <br />8.35 <br />11=.307 <br />.624 <br />.939 <br />1.26 <br />1.57 <br />1.89 <br />2.21 <br />2.54 <br />2.87 <br />3.20 <br />3.53 <br />3.88' <br />4.23 <br />4.58 <br />T=.61 <br />1.25 <br />-1.89 <br />2.52 <br />3.16 <br />3.81 <br />4.44 <br />5.11 <br />5.78 <br />6.44 <br />7.11 <br />7.80 <br />8.51 <br />9.21 <br />120° <br />. E=.339 <br />.720 <br />1.08 <br />1.45 <br />1.82 <br />2.20 <br />2.56 <br />2.95 <br />3.33 <br />3.72 <br />4.10 <br />4.50 <br />4.91 <br />5.32 <br />