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TABLE 1: - TAngents and Externals to a 1' Curve, <br />ChrirA-1M ft - <br />Int. <br />"Angle <br />Tangent <br />_ <br />rsternal <br />Int. <br />%Angle ' <br />= <br />Tangent <br />F.,xternal <br />Int. <br />Angle <br />{ <br />1 Tangent) <br />External <br />85° <br />5250.31 <br />2041:7 <br />2041':7 <br />°. <br />92°. <br />5933.25250,31 <br />5933.2 <br />2518.5', <br />9�° <br />6708.6 <br />8092.71'6708.6 8092.7 <br />10' <br />'-5265.6 <br />•2052.1 <br />LO' <br />5950.5 <br />2531.0 <br />10' <br />6723.4 <br />3107.7 <br />20 <br />5281.0 <br />2062.5 <br />20 <br />5067,9 <br />2543.5 <br />20 <br />G748:2' <br />3122.9 <br />30 <br />5296.4 <br />2073.0 <br />30 <br />598.x.3 <br />2556.0' <br />- 30 <br />674GS.1 <br />31.38.1 <br />40 <br />5311.9 <br />2083.5 <br />40. <br />6002,7 <br />25GS.6 <br />•40 _ <br />G788:1..31.53.3 <br />4.4fl 4.96 1 5.38 5.83 <br />50 <br />5327.4 <br />2094.1 <br />50 <br />6026.2 <br />258 t.3 <br />-.50 <br />" 6808:2, <br />3168.7 <br />:86 <br />5343.01 <br />2141:7 <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 />2606.5 <br />,'.10 .:6848.5 <br />185 2.06 <br />3100.6 <br />•20 <br />5374.2' <br />2126.0 <br />-,20 <br />6073.1 <br />2619.7 <br />20 i <br />6868.8 <br />3215.1 <br />30 <br />5389.9 <br />2136.7 <br />30, <br />'6090.8 <br />2632.0 <br />30 <br />'6889.2 <br />3230.8 <br />-'40 <br />54.05.6 <br />2147.5 <br />40! <br />6108.6 <br />2845.5 <br />40 <br />6909.6 <br />,3246.5 <br />50 <br />5421.4 <br />2168.4 <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 />2130.2 <br />10= <br />6162.6 <br />26S4.7 <br />- 10 <br />'097.3 <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 />'6195.3 <br />2711.2 <br />30 <br />7012.7 <br />3326.1 <br />4D <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 />335S.5 <br />88 <br />5533:'1 <br />2235x5 <br />95 <br />6252.8 <br />2751.3 <br />102 <br />70'75.5 <br />3374.9 <br />!10 <br />5549.2 <br />2246.7 <br />-• 10- <br />6279..1 <br />2764.8 <br />10 <br />7096.G <br />339 t.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 />6326.3 <br />2805.6 <br />40 <br />71.60.3 <br />3140.0 <br />50 <br />5614.2 <br />2292.0 <br />50 <br />6344.8 <br />2819.4 <br />50 <br />7151:7 <br />3457.6 <br />'89 <br />5630.5 <br />2303.5 <br />06- - <br />6363.4 <br />2833.2 <br />103• <br />7203.3 <br />3474.4 <br />- 10 <br />5646.9 <br />2315.0 <br />10 <br />6332.1 <br />2647.0 <br />•'10 <br />7224:7 <br />3401.3 <br />26 <br />5663:4 <br />2320,6 <br />-20' <br />6400.8 <br />2861.0 <br />20, <br />7246.3 <br />3503.2 <br />30 <br />5679.9 <br />2338.2 <br />30 <br />6419.5 <br />2875.0 <br />3U <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 />i 50 <br />5713:0 <br />2361.5 <br />50 <br />6457.3 <br />2903.1 <br />5U <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 />"110 <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 />120 <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 />50' <br />7444.6 <br />3664.5 <br />91 <br />5s30.5 <br />2444.9 <br />9 - <br />6591.2 <br />3003.8 <br />105 <br />7467.0 <br />3682.3 <br />10 <br />5847.5 <br />2457.1 <br />10 <br />6610.11 <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 />1 2481.5 <br />30 <br />6649.6 <br />3047.0 <br />30 <br />7534.9 <br />3736.2 <br />40 <br />5898.8 <br />2193.8 <br />40 <br />6069.2 <br />3062.8 <br />40 <br />7557.7 <br />3754.4 <br />50 <br />5916.0 <br />2.506.1 <br />50 <br />6088.8 <br />3077.7 <br />50 <br />7580.5 <br />3772.6 <br />Corrections to be Added (T7 =Tangent. E.External.) <br />Ole <br />Curve 5° <br />10° 15° 20' <br />251 <br />30° <br />351- <br />40' <br />45° 50° <br />55' 60' 65' 70- <br />- <br />T=:33 <br />.66. 1.001.33 <br />1.68 <br />2.02 <br />2.35 <br />2.70 <br />3.05 3.40' <br />3.77 4.14 4,55 4.89 <br />E=.128 <br />.259 .391 .524..657 <br />10' <br />..790 <br />.926 <br />1.06 <br />1.20 1.34 <br />1.47: 1.62 1.76 1.91 <br />901 <br />T=.36 <br />.72 1.09 .1.451.83 <br />20 <br />2.20 <br />2.57 <br />2.94 <br />3.32 j 3.70. <br />4.10 4.50. 4.91 5.32 <br />30 <br />E=149 <br />.299 .450 .603 <br />,758.910 <br />8415.1 <br />1.07 <br />1.2211.3811.54 <br />9259.0 <br />1.70 1.87 2.03 2.20 <br />95° <br />T=.39 <br />.79 1.19 1.55 <br />2.00' <br />3.40' <br />2.Sp <br />3.20 <br />1 M,714.02- <br />4.4fl 4.96 1 5.38 5.83 <br />50 <br />E =.174 <br />.350 .522 .790 <br />.985 <br />1.06 <br />1.25 <br />1.43 <br />1 1.62 1 1.80 <br />1.99 1 2.16 12.38 2.58 <br />100' <br />T=.43 <br />.86 1.30 1.74 <br />218' <br />2.fi2 <br />3.06 <br />380 <br />3.95 4.40 <br />4,88 5.37 5.85 6.34 <br />" 10 <br />E =.200 <br />.401 .664 ,800 <br />1.01 <br />1.22 <br />1.43 <br />1.64 <br />185 2.06 <br />2.28 2.50 2.73 2.06 <br />105° <br />T=.46.94 <br />1.42 1.90 <br />US <br />2.87 <br />3.34 <br />3.84 <br />4.35 4.84 <br />5.35 5.87 6.40 G.9? <br />"2 <br />30 <br />E =230 <br />.470 .7001 .93311.17.11.42 <br />30 <br />8575.0 <br />11.65 <br />MG <br />2.14 2.39 <br />2.64 JO 3.16 3.41 <br />TABLE I.Tangents and Externals Via P Curve. 'VII <br />Chord= 100 it. <br />Int. <br />iingle <br />TangentlExternal <br />10° IS' 20' 25' <br />Int. <br />Angle <br />Tangent <br />EZternal <br />Int. <br />Angle <br />Tangent <br />External <br />106° <br />7603.5 <br />3791.0 <br />111' <br />333G.7 <br />'4386.1 <br />116° <br />9169.4 <br />5082.7 <br />7626 .6, <br />3S09.4 <br />10' <br />83G2.7 <br />4407.6 <br />10' <br />9199.1 <br />5107.9 <br />.10' <br />20 <br />7649.7. <br />3S37'.9 <br />20 <br />8333.9 <br />4429.2 <br />20 <br />0229.0 <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 />844 L.5 <br />4472.7 <br />40 <br />9289.2 <br />5184.5 <br />50 <br />7719.7 <br />3S84.0, <br />50 <br />84GS.0 <br />4494.6 <br />50 <br />9319.5 <br />5210.3, <br />10:.7743.2 <br />3.16 <br />3902:0''112 <br />1 <br />8404.G <br />4.516.6 <br />117' <br />'9349.9. <br />5236.2 <br />" 10 <br />7766.8 <br />3921.9 <br />10 <br />5521.3 <br />-4538.8 <br />'10 <br />9380.5' <br />5262.3 <br />" 20- <br />7790.5 <br />3940.0 <br />20 <br />$548..1 <br />4561.1 <br />-20 <br />0411.3 <br />:5288.6 <br />30 <br />7814.3 <br />3960.t <br />30 <br />8575.0 <br />_4583.4 <br />30 <br />.9442.2 <br />5315.0 <br />-40. <br />7838.1 <br />3'370.4 <br />40 <br />.8602.1 <br />460G.0 <br />40 <br />9473.2 <br />5341.5' <br />' 50 <br />7862.1 <br />3995.7 <br />50 <br />S620.3:-4628.6 <br />50 <br />9501-.4 <br />'5368.2 <br />108 <br />7SSG.2 <br />•1018.2 <br />113 <br />8656:6 <br />4651.3. <br />118 ' <br />•9535.7 <br />`539:1.1 <br />10 <br />7910.4 <br />4037.8 <br />_10 <br />S63-1.0 <br />4674.2 <br />10 <br />9567.2 <br />5422,1 <br />20. <br />7934.6 <br />4057.4 <br />20 <br />671L5 <br />4697.2 <br />20 <br />9598.9 <br />5449-2 <br />30 <br />7959.0 <br />4077.2 <br />30 <br />5739:2 <br />4720.3 <br />30' <br />9630.7 <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 />:150.1.0 <br />50 . <br />8005.0 <br />•4117.0. <br />.50 <br />879419 <br />4766.0 <br />-50 ' <br />9694:7 <br />5531.7 <br />109 <br />8032.7 <br />4131.1 <br />114 <br />SS22.0 <br />-4790;4 <br />119 <br />9727.0, <br />5550.4 <br />10 <br />8057.4 <br />4157.3 <br />10 <br />SS51.0 <br />-4814.1 <br />10 <br />97:59.4 <br />5587.4 <br />20 <br />20 <br />8879.3. <br />4337.8 <br />.20 <br />9792.0 <br />5615.5 <br />30 <br />:8(182.3-•4177.5 <br />4197.9 <br />30 <br />5907.7 <br />1361.7 <br />30 <br />9324.3 <br />5G43.8 <br />40• <br />.8107.3 <br />8132.3 <br />4'218.4 <br />40 <br />.3936:3 <br />'4385.7. <br />10 <br />9837.7 <br />5672.3 <br />50 . <br />8157.5 <br />4239.0 <br />50 <br />:&96,5.0 <br />4909:9 <br />50 <br />9390.3 <br />5700.9 <br />119 - <br />8182.8 <br />4350.7 <br />115. <br />6J93.8•:4134.1 <br />.120 - <br />9924.,0 <br />5729.7 <br />10' <br />8208.2 <br />4280:5 <br />•`i0 <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 />IJ051:T <br />^0 <br />9991,0 <br />5797.7 <br />30 <br />5259.3 <br />4322.4 <br />30 <br />9080.9. <br />_4953.1 <br />5007.8 <br />30. <br />10025.0 <br />5817.0 <br />40 <br />8285.0 <br />4343.0 <br />40 <br />9110:3 <br />5032.6 <br />40 <br />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 />5876.1 <br />Corrections to be Added (T =Tangent. E =External.) <br />Intl <br />Carve 5' <br />10° IS' 20' 25' <br />30' <br />35' <br />40' <br />45° <br />50'( <br />55 60° <br />65° <br />701 <br />Angle <br />Y'=.4H <br />.80 '1.30 1.74 2.1S <br />2.62 <br />3.06 <br />3:50 <br />3.95 14.40 <br />4.88 5:37 <br />5.85 <br />U. <br />100,. <br />.601 .8091.01.1.22 <br />1.4311.61 <br />1.85 <br />2:06 <br />2.23 2.510 <br />2.73 <br />2.96 <br />T=.494 <br />11.42 1.90 2.35 <br />2.87 <br />3.31.1 <br />3.84 <br />4.35 <br />4.8,1 <br />6.35 5.8'7 <br />6.40 <br />693 <br />los° <br />E=.2.4701, <br />.7010 .933 117 <br />1.42 <br />1-(3.51 <br />2.39 <br />3.61 2.00 <br />3.16 <br />3.41 <br />1 <br />i=.50 <br />1.03 11.55 2.03 2.60 <br />3.14 <br />3-66 <br />4.'21 <br />4.76- <br />5.31 <br />5.86 6.43 <br />7.01 <br />7.50 <br />L1 D" <br />-.260 1 .535 .808 1:08 1.36 <br />T=.54 11.13 i 1.70 2'.25 2.86 <br />1.63.1 i <br />3.45 4.03 <br />2.19 <br />1 4.63 <br />M9 <br />5.23 <br />2-61 <br />8.63 <br />9.05 3.35 <br />5,4, 7.07 <br />3.65 <br />7.701 <br />3.9.5 <br />8.35 <br />118' <br />T =.307 <br />1 .621 .9301 1.25 1571 <br />1.89 <br />?.^-1 <br />, 2.31 <br />!.87 <br />3.20 <br />1 3.53 88 <br />4',3 <br />; -1.53 <br />_ <br />L'0-' <br />T= -U1 <br />635 �J 1.68 8.52 3.10 <br />2D11.03 1.45 1.92 <br />3.91 <br />2.20 <br />4.41 <br />:1.56 <br />e.n� <br />2.96 <br />"-73 <br />? 3.'.3 <br />6.41 <br />" 3.7 <br />7.11 7.5t� <br />4.10 4kU <br />i 5.51 <br />4911 <br />9.21 <br />5.32 <br />E�.33'J <br />ASD <br />