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TABrm L _ Tangents and Externals.to a 1'.Curve. <br />(';hntd=100 ft: <br />Int. _ . <br />:Engle'' <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 />99° <br />6708.6 <br />3092.7 <br />':•+10' <br />15265.6 <br />2052.1 <br />101: <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 />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 />'2083.5 <br />40 ; <br />6002.7 <br />2568.6 <br />40. <br />,6788.1 <br />3158.3 <br /><•'b0" <br />15327.4 <br />'2094.1 <br />.••50 <br />6020.2 <br />.2581.3 <br />50- <br />6808.2 <br />3168.7 <br />so- <br />5343.0 <br />2104.7 <br />93' <br />6037:8 <br />2594:0 <br />400 <br />6828.3 <br />31841 <br />10 <br />6358. 62115.3 <br />3921,9 <br />-.YO.•. <br />'6055.4 <br />2606.8 <br />10 <br />6848.5 <br />3199.6 <br />.2V <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 />3236.8 <br />-.40 <br />'5405:6 <br />•2147.5 <br />'40 <br />:6108.6 <br />2645.5 <br />.401 <br />6909.6 <br />3246.5 <br />'50' <br />'5421.-4 <br />2158.4 <br />50 . <br />'6126.4•'2658.5 <br />4628.6 <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 />6971.3 <br />13294.1, <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 />e5484.9 <br />12202.2 <br />r 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 />b0= <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 />. <br />6252:8 <br />2751.3 <br />102 <br />7075.5 <br />'3374.9 <br />10= <br />5549:2 <br />2246.7 <br />.95•• <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 />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 />6323.3 <br />2805.6 <br />=- 40 <br />7160:3 <br />3440.9 <br />`50• <br />'5614:2 <br />.2292.0 <br />50 <br />6344.8 <br />2819.4 <br />50 <br />7181.7 <br />3457.6 <br />89 " : <br />5630.5•.2303.5 <br />4259.7 <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 />M <br />5663:4 <br />.2326.6 <br />_ <br />20 r <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 />80 <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'.3576.8 <br />10. <br />'5746.3.;2385.1 <br />M <br />6495.2' <br />2931.6 <br />. 10 <br />7355.8 <br />3594.2 <br />20' <br />5763:1 <br />20 <br />6514.3 <br />2945.9 <br />20 <br />7377-.8 <br />3611.7 <br />30- <br />•5779.9 <br />.2397.0 <br />2408.9 <br />30.' <br />6533.4 <br />.2960.3 <br />'30.. <br />7399.9' <br />3629.2 <br />40a <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 />3664.8 <br />91- '' <br />'5930.5 <br />, 2444.9 <br />:98 <br />6591.2 <br />.3003.8• <br />105 C - <br />7467.0 <br />363 <br />82: <br />, <br />:10= <br />5847.5 <br />2457.1 <br />t 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 />7512.2 <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 />b0 <br />`5916.0 <br />2506.1 <br />50 <br />6688.8 <br />3077.7 <br />50 <br />.7580.5 <br />3772.6 <br />Corrections to be Added- (T =Tangent.- E.=External.) <br />Int' <br />Curve 5° <br />14°' 15° '20° 25° -30' 35°. 40° 45° <br />'°. 55° 60' 65° 701 <br />50 <br />Angle <br />External <br />Int. <br />',Angle . <br />Tan8'-t'Eztanal <br />10°. <br />'T=.33 <br />1.00 1.33' 1.88: 2.02 2.36 2.70 <br />3.40 3.77 4.14 4.55 4:89 <br />$5o' <br />E=.128 ' <br />.68 <br />1:11 <br />.259 .391 .524 .657 .790 .926 1.06 1.20 <br />1.34 1.47 1.62 1.76 1.91 <br />' <br />'T=.36 <br />1.09 1.45 1.83 2.20 (IN* 2.94 3.32 <br />3.70 4.10 4.50 .4.91. 5.32 ' <br />900 <br />E=.149 <br />.72 <br />.299 .450 .603 :756 .910 1.07 1.22 1.38 <br />1.54 1.70 1.87 2.03 2.20 <br />95°c. <br />T=.39 <br />.79 1.19, 1.55 2.00' 2.40 2.80 3:20 3.61 <br />4.02 4.49 4.98 5.38 5.83 <br />'7649.7_ 3827.9 <br />E=.174 <br />.350 .522 '.706 .985 1.06 1.25 1.43 1.82 <br />•1.80 1.99 2.18 .2.38 2.58 <br />4429.2 <br />T=.43 <br />.86' 1.30 1.74' 2.18 2.62 3.064 3.50 3.95 <br />4.40 4.88 5.37 5:85 6:34 <br />100' <br />:, <br />E=.200' <br />.401 .604 •.809 1.01 1.22 1.43' 1.64 1.85 <br />2.06 2.28 2.50 2.73 2.96 <br />8415.1' <br />4450.9 <br />1.42 1:90 2.38 ' 2.87 3.34, 3.84 4.35 <br />4.84 5.35 5.87 6.40 8.93 <br />5158.8 <br />.T=.46 <br />E=.230_ <br />.94 <br />470 .700 .938 1.17 1.42. 1.65 1.90 2.14 <br />2.39 2.84 2.90 3A6 341 <br />k <br />TABLE I. - Tangents and Externals to a 1° Curve., VU <br />Chord =100 ft. <br />Int• <br />An <br />Tan ent <br />g, <br />External <br />'-Int. <br />External <br />Int. <br />',Angle . <br />Tan8'-t'Eztanal <br />10°. <br />106°'• <br />.7603.5 <br />3791.0 <br />-Angle <br />111° <br />-Tangent <br />8336.7 <br />4386.1. <br />116° <br />916P.4 <br />5082.7 <br />.10" <br />7626.6 <br />3809.4 <br />10, <br />8362.7- <br />4407.6: <br />- 10'. <br />' 91964.1 - <br />105° <br />20' <br />'7649.7_ 3827.9 <br />1.42 <br />20. <br />8388.9 <br />4429.2 <br />20: <br />9229.0 <br />.'5107.9 <br />.8133.8 <br />30: <br />7672:9 <br />3846:5 <br />30' <br />8415.1' <br />4450.9 <br />30 <br />92591.0 <br />5158.8 <br />40, <br />7696:3 <br />3865:2 <br />:40 <br />8441:5 <br />4472:7 <br />40, <br />92591.2 <br />5184.8 <br />:. 50: <br />7719.7: <br />'3884.0' <br />'50 , <br />8468.0' <br />4494.6• <br />50 <br />93.19.5 <br />5210.8 <br />107 <br />7743.2- <br />3902.9 <br />112 1 <br />8494.6 <br />"4516.6 <br />117 <br />9349.9 <br />5238,2 <br />10 <br />7766'.8• <br />3921,9 <br />•r 10 <br />'8521.3 <br />4538.8 <br />10 <br />-9380.5 <br />5208.8 <br />`-20. • <br />7790:5 <br />3940:9 <br />_,20 <br />8548.1 <br />4561.1 <br />20- <br />94IT. 3 <br />528.8.6 <br />- • 30 <br />7814.3 <br />3960:1• <br />-30 <br />8575.0. <br />4583:4 <br />30 ' <br />9442x2 <br />5315.0 <br />40 <br />7838.1 <br />3979:4 <br />40' <br />8602.1. <br />4606.0 <br />40 <br />94'7$.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 />168 <br />7886:2 <br />4018.2 <br />113 <br />8656.6 <br />4651.3' <br />118 <br />95315.7 <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 />4697.2 <br />20 <br />9598:9 <br />5449.2 <br />W. <br />:7959.0; <br />`4077.2 <br />30 <br />8739.2 <br />4720.3 <br />30 <br />9631D.7' <br />5476.8 <br />44 <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 />4117.6 <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 r <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 />97592.0 <br />5615.8 <br />30'• <br />8107:3.'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 />9557.7. <br />5672.8 <br />'50j <br />8157:5` <br />4239.0 <br />.'50 <br />'8965.0•.4909.9 <br />50 <br />9890.8 <br />5700.9 <br />119 <br />8182.8' <br />4259.7 <br />115.. <br />8993:8 <br />4934.4 <br />120 <br />99.,4.0 <br />5729.7 <br />10. <br />8208.2- <br />4280.5 <br />10 <br />9022:7 <br />4958.6 <br />10 <br />99517.5 <br />'5758.6 <br />20 <br />8233.7 <br />4301.4 <br />.- _20 <br />_9051. <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 />100;69.0 <br />.5846:8 <br />.50 <br />8310.8. <br />4364.8 <br />50 <br />9139.8 <br />5057.6 <br />50 <br />101793.0' <br />5876.1 <br />Corrections to be Added: (T.= Tangent. E=Extemal,) <br />Int. . <br />•:fie 5° <br />Angle . <br />10°. <br />15° <br />20° 25° 30° 35° 40° 45° SO° <br />55°' <br />60° 65° 700 <br />100o <br />T.43 <br />.86 <br />1.30 <br />1.74 2.18 2.62 3.06 3.50 3.95 4.40 <br />4.83.1,5.37 <br />5.85 6.34 <br />E'=.200 <br />...401 .601 <br />.809 1.01 1.22 1.43 1.64 1.85 2.06 <br />2.28 <br />.2.50 2.73 2.96 <br />105° <br />T=.46 <br />.94 <br />1.42 <br />1.90 2.38 2.87 3.34 3.84 4.35 4.84 <br />5.35 <br />5.87 6.93 <br />E=.230 <br />.470 <br />.700 <br />.938 1.17 1.42 1.65 1.90 2.14 2.39 <br />2.66 <br />-6.40 <br />2.90 3.16 3.41 <br />110° ; <br />T=.50 <br />1.03 <br />1.55 <br />2.08 2.60 3.14 3.66 4.21 4.76 5.31 <br />5.86 <br />6.43 7.01 7.59 <br />E=.260 <br />•.535 <br />.808 <br />1:08 1.36 1.63 1.91 2.19 2.49 2.61 <br />3.05 <br />3.35 3.65 3.95 <br />1150: <br />T=.54 <br />1.13 <br />1.70 <br />2.29 12.86 3.45 4.03 4.63 5.23' 5.83 <br />6:41 <br />7.07 7.70 8:35 <br />E=.307 <br />.624 <br />.939 <br />1.26 1.57 1.89 2.21 2.54 2.87 3.20 <br />3.53 <br />3.88 4.23 4.58 <br />120'.. <br />T=.61 <br />1.25 <br />1.89 <br />2.52 3.16 3.81 4.44 5.11 5.78 6.44 <br />-7:111 <br />7.80 8.51 9.21 <br />- <br />E =.339 <br />-.720 1.08 <br />1.45 1.82 2.20 ,2.56 2.95 3.33 3.72 <br />4.10 <br />4.50 4.91 5.32 <br />Al <br />