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VI TABLE I. - Tangents and Externals to a.l° Curve. <br />Cliord=100 ft. <br />Int. <br />1 Angle ' <br />Tangent,) <br />xtenial <br />Int. <br />.Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />'- <br />+5250.'3. <br />2041.7 <br />92° . <br />3933.2 <br />2518.5 <br />99° <br />'6708.6' <br />3092:.7 <br />,85P <br />10' <br />5265:G <br />2052.1 <br />10' <br />:;950.5 <br />2531.0 <br />10' <br />6728.4 <br />3107.7 <br />20 <br />5251:0 <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 />159S5.3 <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 />S 40 <br />'6788.1. <br />3153.3 <br />'-50 <br />5327.4 <br />2094.1 <br />..••50. <br />6020.2 <br />25S1.3 <br />50 <br />6803:2 <br />3163.7 <br />X86 ; <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 />S .10 <br />6055.4 <br />2606.8 <br />10 <br />!6848.5 <br />3199.6 <br />'720 <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.G <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 />16909.6 <br />3246.5 <br />50 <br />5421.4 <br />2158.4 ' <br />-.. 50` <br />6126.4 <br />2658.5 <br />150 <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 />{G950.6 <br />3278:1 <br />10 <br />•5453'-.1 <br />2180.2 <br />;..10� <br />6162.6 <br />2684.7 <br />10 <br />.6971.3 <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 />2202.2 <br />30' <br />6198.3 <br />2711.2 <br />'.,t30 <br />7012.7 <br />3326.1 <br />•`.40 <br />5500.9 <br />2213.2 <br />t' 40' <br />6210.4 <br />2724.5 <br />'40 <br />7033.6 <br />3342.3 <br />50 <br />'5517.0 <br />2224.3 <br />40 <br />6234.6 <br />2737.9 <br />50 <br />47054.5' <br />3358.5 <br />,88 '. <br />5533.1 <br />2235':5 <br />"95"'1 <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 />i 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 />5597.5 <br />2280.6 <br />40. <br />6326.3 <br />2805.6 <br />'40 <br />7160;:3 <br />3440.9 <br />505614.2 <br />!8132:3 <br />2292.0 <br />50 <br />6314.8 <br />2319.4 <br />50 <br />.7151:7 <br />3457.6 <br />i.89.'5630:5 <br />.8157:5 <br />2303.5 <br />96 <br />6363.4 <br />2833.2 <br />103 <br />7203:2 <br />3474'.•1 <br />.10 <br />5646.9 <br />2315.0 <br />10' <br />:6332.1 <br />2847.0 <br />10 <br />7224:7 <br />3491.3 <br />' 20 <br />5663.4' <br />2326.6_� <br />20 <br />.-6100.8 <br />2861.0 <br />',20 <br />.7'246.3 <br />3508.2 <br />30 <br />5679.9 <br />2338.2 <br />30 <br />G119,5 <br />2875.0 <br />30 <br />7268.0 <br />3525.2 <br />i't 40 - <br />5696.4 <br />2349.5 <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 />U10 <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 />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 />i . 50 <br />7444.6 <br />3664.5 <br />91 '- <br />5830.5' <br />2444.9 <br />98'' <br />:G591.2 <br />3003.8 <br />105 _. <br />'7-167.0 <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 />•6630A <br />3033.1 <br />�.'20 <br />.7312.2 <br />3718.2 <br />30 <br />5381.7 <br />2481.5 <br />'30 <br />'6649.6 <br />3047.9 <br />30 <br />7534.9 <br />3736.2 <br />40 <br />15M.8 <br />2493.8 <br />40 <br />'6609.2 <br />3062.8 <br />1 40 <br />7557.7 <br />3754.4 <br />50 <br />5916.0 <br />2506.1• <br />50 <br />.•6688.8 <br />3077.7 <br />4. 50 <br />7580.5 <br />3772.6 <br />Corrections- tobetAdded (T= Tangent. '-E External.) <br />Ict. ' <br />Curve 5° ' <br />' 10° ' 15° :.20° - '25° ' 30° ' 35° . '40° '45° `50" . 55 <br />60° 65° 70° <br />Angle <br />.. <br />- - <br />. <br />External <br />.T=:33 ' <br />.68. 1.00. 1.33. 1.68 2.02 2.36 2.70 3.05 3.40 3.77 <br />2.06 <br />4.14 4.55 14.19 <br />111° <br />E=.128•• <br />.259 .391 .524 .657 .790 .926 1'.20 i.34 1.47 <br />1.62 1.76 1.91 <br />9169.4_ <br />T=AG. <br />':72 - 1.09. 1.45. 1.83 12.20 2.57.12.94 3:32 .3.70 4.10 <br />4.50 4.91 5.32 <br />90° <br />13=119 <br />.299 .450 '.603 .7561;910 1.07:11.22 .1.38 1.54 1.70 <br />1.87 .2.03 2.20 <br />10'. <br />T=.39' : <br />.79 1_.19 1.55 2.00> 2.40 2.80 3.20 3.61 4.02 4.49 <br />4.98 5.38 5.83 <br />9 <br />E =:174. <br />.350' .522 .706 .98511 1.25 1.43 1:62 1.80 1.99 <br />2.18 2.38 2.58 <br />1.74- <br />T=33. <br />.86.11.30-11.74 2:18.2.62 3.06 3.50 3.9a 4:40 4.88 <br />5.37 5.8518.34 <br />100° <br />E =:200 <br />.401 .604 .809 1.01 1.22= 1.43` 1:64 7.85 2.06 2.28 <br />2:50 j 2.73 2.96 <br />105° <br />T=AG <br />.94 11.42 1.90 • 2.38 2:87 3.34 4.84. 5.35 <br />5.87 0.40 6.93 <br />-5158.8 <br />E=,230 <br />13.84-,4.35 <br />.470 .700+ .938 1.17 1.42 1.65, 1.00 2.14 229 2.64 <br />2.90 3.16 3.41 <br />TABLE I. - Tangents and Externals to a 1° Curve. VII <br />_ <br />Chord 100 ft.. <br />Int. ,y <br />Angle - <br />" Tangent <br />r-_ ' <br />External <br />'I'.it. <br />':.Angle <br />Tangent <br />External <br />Int. <br />Angle, <br />Tangei,t <br />External <br />106° . <br />;7603:5. <br />3791:0; <br />111° <br />;8336.7 <br />4386.1 <br />116° <br />9169.4_ <br />5082:7• <br />L 10, <br />7626.6' <br />3809:4: <br />:r .10' <br />• <br />8362.7,;4407.6 <br />•50° <br />10'. <br />9199:1 <br />5107.9 <br />-;20' <br />7649.7 <br />3827.9 <br />20 <br />8388.9.;:4429..2 <br />1.74- <br />20, <br />9229.0 <br />.5133.3 <br />30'.;'7672.9. <br />4.40 <br />3546.5 <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 />77.19.7 <br />3884.0 ; <br />_' <br />50 <br />8468.0 ; <br />: 44'94._6 <br />50 <br />. 9319.5 <br />5210.3 <br />'107 <br />. 7743.2 <br />3902.;9 <br />112 <br />8494.6'4'516.6 <br />8.40 <br />117• <br />9349':9. <br />5236.2 <br />.10' <br />7760.8' <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 />" 50 <br />7862:1 <br />3995.7 <br />50 <br />8629:3 <br />4628.6 <br />:50 <br />"9504.4 <br />5368.2 <br />2.86 3.45 <br />.4 U3 <br />4.63 <br />b.23, <br />b.83 <br />6.44 <br />7.07 <br />7.70 <br />8.35 <br />108.1 <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' <br />7934.6 <br />:4057.4 <br />` 20 ' <br />8711.5..4697.2 <br />6.44 <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 />.0630.7 <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 />.S008:0 <br />4117.0 <br />=:50 <br />'5794.9 <br />4766:0 <br />50` <br />9694.7 <br />5531.7. <br />109 ;•} <br />8032,T <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 <br />.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 />•.t 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 />;j50 <br />.8157:5 <br />4230.4 <br />50 <br />8965.0• <br />4909,.9 <br />50 . <br />9890.8 <br />5700.9 <br />110;. "`''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`.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'.10025.0 <br />5817.0 <br />40 : <br />-8285.0` <br />4343.6 <br />-'40 <br />9110:3'.5032'.:6' <br />40',' <br />10059,0 <br />5846.5, <br />j '50 <br />5310:5 <br />4364.8 <br />50 <br />9139.8 <br />5057.6 <br />50:..10093.0 <br />5876.1• <br />yd <br />7.44 <br />Corrections to be Added (T =Tangent. E = External.) <br />Int:'- <br />Angle <br />Curve 5° <br />.10° <br />15° <br />20° 11 <br />25° 30° <br />35° <br />40° <br />:45° <br />•50° <br />55° <br />60° <br />65° <br />70° <br />T=.43 <br />.86 <br />1.30 <br />1.74- <br />2.18 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 =.2G0 <br />.401 <br />.604 <br />:809 <br />1.01 1.22 <br />1.43 <br />1.64 <br />1.85' <br />2.06 <br />2.28 <br />2.50 <br />2.73 <br />2AG <br />105° <br />T=.46 <br />.94 <br />1.42 <br />1.90 <br />2.38 2.87 <br />3.34 <br />3.84 <br />`4.35 <br />4.84 <br />5.35 <br />5.87 <br />8.40 <br />8:93 <br />- E =.230 <br />.470 <br />.700 <br />:938 <br />1.17 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=.60 <br />1.03 <br />1.55 <br />2.08 <br />2.60 3.14 <br />3.66 <br />4.21 <br />4:76 <br />5.31 <br />5.86 <br />6.43 <br />7.01 <br />x7.69 <br />E =.260 <br />'.535 <br />.808 <br />1.08 <br />1.36 1.63 <br />1.91 <br />2.19 <br />2.49 <br />8.61 <br />3.05 <br />'3.35 <br />3.65 <br />3:95 <br />1150 <br />T=.54 <br />1.13 <br />1.70 <br />2.29 <br />2.86 3.45 <br />.4 U3 <br />4.63 <br />b.23, <br />b.83 <br />6.44 <br />7.07 <br />7.70 <br />8.35 <br />E =.307 <br />.624 <br />.939 <br />1.26 <br />1.57 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 />120°.; <br />T=.61 <br />1.25 <br />1.89 <br />2.52 <br />3:16 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 />E =.339 <br />,.720 <br />1.08 <br />1.45 <br />1.82 2.20 <br />2.-'5 <br />2.95 <br />3.33 <br />3.72. <br />4.10 <br />1 4:50 <br />4.91 <br />'5.32 <br />Z/ <br />