|
VI TABLED I. - Tangents and Externals to a 1° C url'e
<br />Int.Int.
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />I
<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 />1 10'
<br />5950.5
<br />2531.0
<br />10;
<br />0728.4
<br />3107.7
<br />20
<br />5281.0
<br />2062.5
<br />1 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 />2033.5
<br />40'
<br />6002.7
<br />2568-6
<br />40
<br />0788.1
<br />31x3.3
<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 />88
<br />5343.0
<br />2104:7
<br />93 -
<br />6037.8
<br />2594.0
<br />117
<br />6828.3
<br />3184.1
<br />10
<br />5358.6
<br />2115.3
<br />- 10
<br />6055:4
<br />2606.8
<br />,100
<br />10
<br />6848.5
<br />-3199.6
<br />20
<br />5374.2
<br />2126.0
<br />1 20'
<br />'6073.1
<br />2619.7
<br />'20
<br />6868.8
<br />3215.1
<br />30
<br />5389.9
<br />213G.7
<br />30
<br />6090.8
<br />2532.6
<br />30',
<br />6889:2
<br />3230.3
<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 />2553.5
<br />50
<br />i
<br />6930.1
<br />3262.3
<br />87
<br />6437.2
<br />2169.2
<br />94
<br />6144.3
<br />2671.6
<br />101 "-
<br />6950.6
<br />32 5.1
<br />- 10
<br />5453.1
<br />2130.2
<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 />130
<br />7012.7
<br />3326.1
<br />.40
<br />5500.9
<br />2213.2
<br />.40
<br />0216.4
<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 />68
<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 />2240,7
<br />10
<br />0271.1
<br />2764.8
<br />1 10
<br />7096.6
<br />3391.2
<br />20
<br />5565.4
<br />2258,0
<br />'20
<br />0280:4
<br />2778.3
<br />i - 20
<br />7117:8
<br />3407.7
<br />- 30
<br />55S1.6
<br />2269.3
<br />30
<br />0307.9
<br />'2792.0
<br />30
<br />7139.0
<br />3424,3
<br />40
<br />5597.8
<br />2280.6
<br />-'40
<br />0326,3
<br />2805.6
<br />40
<br />. 71G0:3
<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
<br />2303'.5
<br />96
<br />6363.4
<br />2833:2
<br />103
<br />7243.2
<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 />50
<br />5713,0
<br />2361.5
<br />50
<br />6457.3
<br />2903.1
<br />50
<br />7311.7
<br />3559,6
<br />00 -
<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 />.649.5-2
<br />2931.6
<br />10
<br />: 7355.0
<br />3594.2
<br />20
<br />5703.1
<br />2397.0
<br />20
<br />6514-3'
<br />2945.9
<br />20
<br />7377.8
<br />3011.7
<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 />6.552-6
<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 />3064.5
<br />91
<br />5830.5
<br />2444.0
<br />98'
<br />6501.2
<br />3003.8
<br />195
<br />-7467.6
<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 />7512.2
<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 />5393.8
<br />2493-8
<br />40-
<br />0669.2
<br />3062,5
<br />40
<br />7557.7
<br />3754.4
<br />50
<br />5916.0
<br />1 2500,1
<br />50
<br />1 6088.8
<br />1 3077.7
<br />50
<br />7580.5
<br />3772.6
<br />Corrections -to be Added (T --"Tangent. E. =External.)
<br />Int.
<br />Angle Cun•e 5°
<br />110°. 15° 1 20°.
<br />25° 30°
<br />35° 40° 45°
<br />50° 55° 60° 651
<br />70°
<br />85° T=.33
<br />.66 1.00 1.33
<br />LM 2.02
<br />2.36 2.70 3.05
<br />3.40 3.77 4.14 4.55
<br />4-89
<br />E=,128
<br />.259 .391 .524
<br />.657 .790
<br />.926 1, 05 1.20
<br />1.34 1.47 1.52 1.76
<br />1.91
<br />90° T=-36
<br />-.72 1.09 1.45
<br />1.83 2-20
<br />2.57 5.94 3,32
<br />3.70 4.10 4-50 4.91
<br />5.32
<br />E =.149
<br />:299 .450 .603
<br />.756 .910
<br />1.07 IM 1,33
<br />1.54 1.70 1.87 2.03
<br />5.20
<br />95° T-,39.79
<br />1.19 1:55
<br />2,00 2.40
<br />280 3.20 3.61
<br />4.02 4.49 4.98 5.33
<br />5.83
<br />_
<br />E =-174
<br />,350 .522 .706
<br />.985 1.06
<br />1.25 1.43 1.62
<br />.1.80 1.99 2.18 2.38
<br />2.53
<br />100° T=.43
<br />,86 1.30 11.74
<br />12.18 2.02
<br />3.06 3.50 3.95
<br />4.40 4.88 5:37 5.85
<br />6-34
<br />E=.260
<br />.401 .5011
<br />22
<br />1.43 1.64 1.85
<br />2:06 2-28 2,50 2.73
<br />2.96
<br />105° T=-40
<br />.04 1.42 1.90
<br />2.38 2.87
<br />3,31 3,84 4.35
<br />4.84 5 ,67 .35 5 6.40
<br />6.92
<br />E =,230
<br />.4.70 .7001 .033
<br />1.17 1-42
<br />11.65 1.90 2.14
<br />2.39 2.64 190 3.16
<br />3.41
<br />TABLE I. - Tangents and Externals to a 1' Curve. VU
<br />Chord =100 it.
<br />Int.
<br />Angle
<br />Tangent
<br />External -
<br />Int.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />g
<br />External
<br />106°
<br />7603.5
<br />3791.0
<br />111°
<br />8336.7
<br />4386-1
<br />110°
<br />9169.4
<br />5082.7
<br />10'
<br />7626.6
<br />3809.4
<br />10'
<br />5362.7 '
<br />4107-6
<br />10'
<br />9199.1
<br />5107.9
<br />.20
<br />7649.7
<br />3827,9
<br />20
<br />83S8.9
<br />4429-2
<br />20
<br />9229.0
<br />5133.3
<br />30
<br />7672.9
<br />1.90
<br />30
<br />5415.1
<br />4450-9
<br />30
<br />9259.Q
<br />5158.8
<br />40
<br />7696.3
<br />.3640.5
<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 />8463.0'
<br />4494.6
<br />60
<br />9319.,5
<br />5210.3'
<br />107
<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
<br />5288.6
<br />30
<br />7814.3
<br />3960.1
<br />30
<br />8575,0
<br />4583,4
<br />1 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 />3998.7
<br />50
<br />5629.3
<br />4628,0
<br />50
<br />9504.4
<br />5368.2
<br />108-
<br />7886.2
<br />4016.2
<br />113
<br />8656.6
<br />4(',51.3
<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 />9507.2.
<br />5422.1
<br />20
<br />7934.6
<br />4057.4
<br />20
<br />8711.5-
<br />4697.2
<br />20
<br />9598.0
<br />5449.2
<br />30
<br />7959.0
<br />4077.2'
<br />30
<br />8739-2
<br />4720.3
<br />30
<br />9030.7
<br />5476.5
<br />40
<br />7953.5
<br />4097.1-
<br />40
<br />8767-0
<br />4743.6
<br />40
<br />9602.6
<br />5504-0
<br />50
<br />8008.0
<br />4117.0
<br />50
<br />8794-9
<br />4766.9
<br />_
<br />50
<br />9694.7
<br />5531.7
<br />109'
<br />8032.7
<br />4137.1
<br />114
<br />8822.0
<br />4790'.4
<br />119
<br />9727.;0.:'5559:4
<br />10
<br />8057.4
<br />4157.3
<br />10
<br />8851.0
<br />•1874.1
<br />ID
<br />9750.4
<br />_
<br />5587.4
<br />20
<br />4177.5,
<br />20
<br />8879.3
<br />4837.8'
<br />20
<br />9792.0
<br />5615.5
<br />.•8082.3
<br />30
<br />8107.3
<br />'4197.9
<br />30
<br />8907.7'
<br />486 t. 7
<br />30'
<br />9824.8'
<br />5643,8
<br />•40.
<br />8132.3
<br />4215.4
<br />40
<br />8930.3
<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 />-1934.1
<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 />430tA
<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 />36
<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 />8310.3
<br />4364.8
<br />50
<br />9139.8
<br />.5057.6
<br />50
<br />10093.0
<br />5876.1
<br />I
<br />Corrections to be Added (T Tangent. E=External.)
<br />Int.
<br />Angle
<br />Cu"D 5' 10° 15°
<br />20°
<br />25*
<br />30°
<br />.'35*
<br />40'
<br />45°
<br />50°
<br />55° 601
<br />70°
<br />T=,43 AG 1.30
<br />1.74
<br />2,18
<br />2-62
<br />3.06
<br />3,5D
<br />3.95
<br />4.40
<br />1651
<br />4,88 5.37
<br />5.85
<br />6.34
<br />1001
<br />F=,200 A01 ,601
<br />.809
<br />1.01
<br />1-22
<br />1.43
<br />1,61
<br />1.85
<br />.2.06
<br />2-28 2,50
<br />2,73
<br />2,96
<br />T=.46 1.42
<br />1.90
<br />2.38
<br />2.87
<br />3.34
<br />18.1
<br />4.35
<br />4.34
<br />5.35 5-87
<br />UAU
<br />6.93
<br />105°
<br />_94
<br />E=.230 AM .,00
<br />.938
<br />1.17
<br />1.42
<br />1.05
<br />-1:90
<br />2.14
<br />2.39
<br />2.64 2,901
<br />3.16
<br />3.41
<br />110°
<br />T=.50 1.03 11.55
<br />2-08
<br />2.60
<br />3.14
<br />3.66
<br />4.21
<br />4.70
<br />5.31
<br />5.86 6.43
<br />7,01
<br />7.59
<br />1
<br />E=-260 .535 -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 3.35
<br />3.65
<br />3,95
<br />115°
<br />T=-54 11.13 1.70
<br />2.29
<br />2-80
<br />3.45
<br />4.03
<br />4.63
<br />593
<br />55.83
<br />6-14 7.07
<br />7.70
<br />8.35
<br />.62.1 .9391
<br />IM
<br />1.x7
<br />1.89
<br />2,21
<br />'2.54
<br />2.87
<br />3.20
<br />3-53 3.88
<br />4.23
<br />4.58
<br />_8=307
<br />120°
<br />T=-61 1.25 1.89
<br />2-52
<br />3.16
<br />3.81
<br />4-14
<br />6.11
<br />5.78
<br />G.44
<br />7.11 7,80
<br />8.51
<br />9.21
<br />E= -33J 724 1.08
<br />i.45
<br />1.82
<br />2.30,
<br />2-56
<br />2.95
<br />3.33
<br />173
<br />41D 4.50
<br />4.91
<br />5.32'
<br />
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