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VI TAslm L.- Tangents -and Externals to a 1° Curve.' <br />Chord= 100 ft. <br />Int. <br />Angle <br />T ent <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 />.7 <br />92°• • <br />5933.2 <br />,2518.5 <br />99° <br />6708.6 <br />3092.7 <br />10' <br />5265.6 <br />,2041 <br />2052.1 <br />10' <br />'5950:5 <br />2531.0 <br />10' <br />6728.4•3107.7 <br />.350 .522 .706 .985 1.08 1.25 1.43 1.62 1.80 <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 />7696:3 <br />'2083.5 <br />40 <br />6002.7 <br />'2568.6 <br />40 <br />6788.1 <br />3153.3 <br />50 <br />,5311.9 <br />5327.4 <br />'2094.1 <br />50 - <br />6020.2' <br />2581.3 <br />50 <br />'6808.2 <br />3168.7 <br />66=- <br />-5343.0 <br />2104:7 <br />93 ' <br />6037.8 <br />2594.6 <br />,100 -' <br />6828.3 <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 />:5374.22126.0 <br />3940:9 <br />20 <br />6073.1 <br />'2619.7 <br />-20 <br />6868.8 <br />3215.1 <br />-80 <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 />3979.4 <br />••40 <br />6108.6 <br />.2645.5 <br />40 <br />6909.6 <br />3246.5 <br />b0 <br />5421.4 <br />,2147.5 <br />.2158.4 <br />r <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 />.7910.4 <br />2180.2 <br />10 <br />6162.6 <br />2684.7 <br />10- <br />6971:3 <br />3294.1 <br />''-20 <br />.5453.1 <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 />'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 />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 />-80 <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 />.6323.3 <br />2805.6 <br />40 <br />'7160.3 <br />3440.9 <br />50 <br />:5614.2 <br />12292.0 <br />50- <br />•6344.8= <br />2819.4 <br />- :50 <br />:7181.7 <br />3457.6 <br />110 <br />8182.8 <br />4259.7 <br />115 <br />8993.8 <br />4934.1 <br />120 - <br />{ <br />5729.7 <br />69 <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 />2315.3 <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 />80 <br />7268.0 <br />3525.2 <br />40 <br />5696.4 <br />4364.8 <br />40-. <br />6438.4 <br />2889.0 <br />40 <br />'7289.8 <br />3542.4 <br />. <br />50 <br />,5713.0 <br />.2349.8 <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 />2945.9 <br />20- <br />7377.8 <br />3611.7 <br />30 <br />5779.9 <br />2408.9 <br />- 30 <br />653314 <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 />;3646.8 <br />b0 <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 />105 <br />7467.0 <br />'3682.3 <br />10 <br />•2457.1 <br />10• <br />6616.6 <br />3018.4 <br />10 <br />:7489.6 <br />3700.2 <br />20 <br />.5847.5 <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 />7534.9 <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 />. <br />50 <br />6688.8 <br />.3077.7 <br />50 <br />7580.5 <br />3772.6 <br />;-'Cor"rection to be Added"(T =Tangent.. 'E. =External.) <br />Angle <br />`Curve 5° <br />10°' 15°. 20° 1 25° 30° 35° 40° 45° 50° <br />55° 60° 65° 70- <br />S. <br />T=.33 ' <br />66. 1.00 1.33 1.65 2.02 2.36. 2.70 3.05 3.40 <br />3.77 4:14 4.55'' 4.89 <br />External <br />E=.128 <br />.259 .391 .524 -:657 .790 .926 1.08 1.20 1.34 <br />1.47 1.62 1.76 1:91 <br />111° <br />T=.36' <br />1.09 1.45 1.83 2.20 12.57 2.94 3.32 3.70 <br />4.10 4.50 4.91; 5.32' <br />90° <br />E =.149 <br />.72 <br />.299 .450 .603 •.756 .910 1.07 1.22 1.38 1.54' <br />1.70 1.87 2.03 2.20 <br />3809.4 <br />T=.39 <br />.79 1.19 1.55' 2.00, 2.40 2.80 3.20 3.61 4.02 <br />4.49 4.98 .5.38 5.83 <br />950.: <br />E=.174 <br />.350 .522 .706 .985 1.08 1.25 1.43 1.62 1.80 <br />1.99 2.18 2.38 2.58 <br />; <br />T=.43. <br />1.30 1.74 2.18 2.62 3.06 3.50 3.95 4.40 <br />4.88 '5.37 -b.8b 6.34 <br />100o <br />E=-200 <br />.86 <br />401 .604 .809 1.01 1.22 1.43 1.84 1.85 2.06 <br />2.28 2.50. 2.73' 2.96 <br />leo <br />:T=.48 <br />.94 1.42 1.90 2.38 2.87 3.34 3.84 4.35 4.84 <br />5.35 5.87 6.40, 6.93 <br />8415.1 <br />E =.230 <br />.470 .700 .938 1.17 1.42 1.65 1.90 2.14 2.39 <br />2.64 2.90 3.18 MI <br />0 <br />f' <br />TABLE I. - Tangents and Externals to a P Curve. <br />Chord=100 ft. <br />'. <br />Tangent <br />External <br />IIIc' <br />Angle" <br />Tan Tangent <br />External <br />Int. <br />Angle <br />TangentAngle <br />External <br />106°i <br />7603.5 <br />3791_.0 <br />111° <br />8386.7 <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 />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 />b0 <br />7719.7 <br />3884.0 <br />50 <br />8468.0 <br />4494.6 <br />50 <br />9319.5- <br />5210.3 <br />107 <br />7743.2 <br />-3902.9 <br />H2-: <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 />3979.4 <br />40 <br />8602:1 <br />'4606.0 <br />40 <br />9473.2 <br />5341.5 <br />SO.,- <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 .'7934.6 <br />T=•61 <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 />30.9630.7 <br />E =.339 <br />5476.8 <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 />.8008.0 <br />4117.0 <br />50 <br />.8794.9. <br />4766.9 <br />50. <br />9604.7 <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 <br />5587.4 <br />':20 <br />8082.3''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 />5672.3 <br />50 <br />8157.5 <br />4239.0 <br />-'.60 <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 />56 <br />'8310.8 <br />4364.8 <br />50 <br />9139.8 <br />5057.6 <br />50. <br />10093.0 <br />5876.1 <br />Corrections to be 'Added, (T=Tangent. E=External.) ' <br />Angle <br />;Curve 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 />650 <br />700 <br />1001 <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 />4.88 <br />5.37 <br />5.85 <br />6.34 <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 />3.84 <br />4.35 <br />4.84 <br />5.35 <br />0 <br />6.93 <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 />16 <br />3.41 <br />110' <br />- T=.50 <br />1.03 <br />-..535 <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 />1 <br />7.59 <br />E=.200 <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 />5 <br />3.95 <br />1150• <br />. T=.54 <br />1.13 <br />1.70 <br />2.29 <br />2.86 <br />3.45 <br />4.03 <br />4.63 <br />5.23. <br />5.83, <br />6.44 <br />0 <br />T4*5O4:91 <br />8.35 <br />E=.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 <br />4.58 <br />1201 <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 />0.44 <br />7.11.1 <br />9.21 <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 />1 <br />5.32 <br />