|
VI
<br />TABLE IV.�TANGFNTS AND EXTERNALS TO A 10 CURVE.
<br />Central,Central
<br />Tangent
<br />Externa9
<br />interpolation.
<br />Tangent
<br />External Centl:al
<br />'Tangent
<br />Extenial
<br />Angle
<br />Angle
<br />. Angle
<br />Anglo
<br />919
<br />5830.5
<br />2444.9'
<br />1010
<br />6950,6
<br />3278:1
<br />1110
<br />8336.7
<br />4386.1
<br />10'
<br />5847.5-
<br />2457.1'
<br />10�
<br />. 6971:3
<br />3294.1
<br />101
<br />8362.7
<br />4407.6
<br />20
<br />5%C6
<br />2469.3
<br />20
<br />6992:0
<br />3310.1
<br />20
<br />8388.9
<br />.4429.2
<br />30
<br />5881:7
<br />2481.5,
<br />30
<br />7012.7
<br />3326.1
<br />30
<br />8415.1
<br />•4450.9
<br />40 .
<br />5898.8
<br />2493.8
<br />40
<br />7033.6
<br />3342.3
<br />40
<br />8441.5'
<br />4472.7
<br />50
<br />5916.0
<br />2506.1
<br />50
<br />7054.5
<br />3358,5
<br />50
<br />8468.0
<br />4494.6
<br />92 -
<br />5933.2
<br />2518.5
<br />102
<br />7075.5
<br />3374.9
<br />112
<br />8494.6
<br />4516.6
<br />10
<br />5950.5
<br />2531,0
<br />10
<br />7096.6
<br />3391.2
<br />10
<br />8521.3;
<br />4538.8
<br />20
<br />5967.9
<br />2543.5
<br />20
<br />7117.8
<br />3407.7
<br />20
<br />8548.1
<br />4561.1
<br />30
<br />5985.3
<br />2556,0
<br />30
<br />•7139.0
<br />3424.3
<br />30
<br />8575.0
<br />4583.4
<br />40
<br />6002,7
<br />2568.6
<br />40
<br />7160.3
<br />3440.9
<br />40
<br />8602.1
<br />4606.0
<br />50
<br />6020.2
<br />2581.3
<br />50
<br />7181..7
<br />3457.6
<br />50
<br />8629.3
<br />4628.6
<br />93
<br />6037:8`
<br />2594.0
<br />103
<br />7203.2
<br />3474.4
<br />113
<br />8656.6
<br />4651.3
<br />10
<br />6055 4
<br />2606.8
<br />10
<br />7224.7
<br />3491.3
<br />10
<br />8684.0'
<br />4674.2
<br />20
<br />6073.1
<br />2619.7
<br />20
<br />7246:3
<br />3508.2
<br />20
<br />8711.5
<br />` 4697.2
<br />30
<br />6090.8
<br />2632.6
<br />30,
<br />7268.0
<br />3525.2
<br />30
<br />8739,2
<br />4720.3
<br />40.
<br />6108.6
<br />2645.5
<br />40
<br />7289.8.
<br />3542.4
<br />40
<br />8767.0
<br />4743.6
<br />50
<br />6126.4
<br />2658.5
<br />50
<br />7311.7
<br />3559.6
<br />50
<br />8794.9
<br />4766.9
<br />94
<br />6144.3
<br />2671.6
<br />104
<br />7333.6
<br />3576.8
<br />114 .
<br />8822.9
<br />4790.4
<br />10
<br />6162.6
<br />2684.7
<br />I0
<br />7355.6
<br />3594.2
<br />10
<br />8851.0'
<br />4814.1
<br />20
<br />6180.2
<br />2697.9
<br />20
<br />7377.8
<br />3611.7
<br />20
<br />8879.3
<br />4837.8
<br />30
<br />6198.3
<br />2711.2
<br />30
<br />7399.9'
<br />3629,2
<br />30 .
<br />8907.7
<br />4861.7
<br />40
<br />6216.4
<br />2724.5
<br />40.
<br />7422.2
<br />3646,8
<br />40
<br />8936.3
<br />4885.7
<br />50
<br />6234.6"
<br />2737.9
<br />50
<br />7444.6.
<br />3664.5
<br />50
<br />8965.0
<br />4909.9
<br />4.09
<br />80°
<br />r
<br />.61
<br />.91
<br />1.22
<br />1,53
<br />1.84
<br />2.15
<br />95
<br />6252.8
<br />2751.3
<br />105
<br />7467.0
<br />3682.3
<br />115
<br />8993.8
<br />4934.1
<br />.10
<br />6271.1
<br />2764.8
<br />10
<br />7489,6
<br />3700.2
<br />'10
<br />9022.7
<br />4958.6
<br />20
<br />6289:4
<br />2778.3
<br />.20
<br />7512.2
<br />'3718.2
<br />20
<br />90.51.7
<br />4983.1
<br />30
<br />6307.9
<br />2792.0
<br />30
<br />- 7534.9
<br />3736.2
<br />30
<br />9080.9
<br />5007.8
<br />•40-
<br />6326.3
<br />'2805.6
<br />40
<br />7557.7
<br />3754.4
<br />40
<br />9110.3
<br />5032.6
<br />50'
<br />6344.8
<br />2819.4
<br />50
<br />7580.5
<br />3772.6
<br />50
<br />9139.8
<br />5057.6
<br />96
<br />6363,4
<br />2833.2
<br />•106
<br />7603.5
<br />3791.0
<br />116
<br />9169.4
<br />5G82.7
<br />10
<br />6382.1
<br />2847.0
<br />10
<br />7626.6
<br />3809.4
<br />10
<br />9199.1
<br />5107.9
<br />20
<br />6400:8
<br />2861.0
<br />20
<br />7649.7
<br />3827.9
<br />20
<br />9229.0
<br />5133.3
<br />30
<br />6419.5
<br />2875.0
<br />30
<br />7672.9
<br />3846.5
<br />30
<br />9259.0
<br />5158.8
<br />-40
<br />6438.4
<br />2889.0
<br />40
<br />7696.3
<br />3865.2
<br />40
<br />9289.2
<br />5184.5
<br />50
<br />6457,3
<br />2903.1
<br />50
<br />7719.7
<br />3884.0
<br />50
<br />9319.5
<br />5210.3
<br />97
<br />6476.2
<br />2917.3
<br />107
<br />7743.2
<br />3902.9
<br />117
<br />9349.9
<br />5236.2
<br />10
<br />6495.2
<br />550
<br />10
<br />7766.8
<br />3921.9
<br />10
<br />. 9380.5
<br />5262.3
<br />20'
<br />6514.3
<br />_2931.6
<br />2945.9
<br />20
<br />7790.5
<br />3940.9
<br />20
<br />9411.3
<br />5288.6
<br />30
<br />6533.4
<br />2960.3
<br />30
<br />7814.3
<br />3960.1
<br />30
<br />9442.2
<br />5315,0
<br />40
<br />6552.6
<br />2974.7
<br />40
<br />7838.1
<br />3979.4
<br />40
<br />9473.2,
<br />5341.5
<br />50
<br />6571.9
<br />2989.2
<br />50
<br />7862.1
<br />3998.7
<br />50
<br />9504.4
<br />5368.2
<br />98
<br />6591.2
<br />3003.8
<br />108
<br />7886.2
<br />4018.2
<br />118
<br />9535.7
<br />5395,1
<br />10
<br />6610.6
<br />3018.4
<br />10
<br />7910.4
<br />4037.8
<br />10
<br />9567.2
<br />5422.1
<br />20
<br />6630,1
<br />3033.1
<br />20.
<br />7934.6
<br />4057.4
<br />20
<br />9598.9
<br />5449.2
<br />30
<br />6649.6
<br />3047.9
<br />-116
<br />7959.0
<br />4077.2
<br />30
<br />9630.7
<br />5476,5
<br />40
<br />6669.2
<br />3062.8
<br />.30
<br />40
<br />7983.5
<br />4097.1
<br />40
<br />9662.6
<br />5504.0
<br />50
<br />6688.8
<br />3077.7
<br />50
<br />5008.0
<br />4117.0
<br />50
<br />9694.7 '
<br />5531.7
<br />99
<br />6708.6
<br />3092.7
<br />109
<br />8032.7
<br />4137.1
<br />119
<br />9727.0
<br />5559.4
<br />10
<br />6728.4
<br />3107.7
<br />10.
<br />8057.4
<br />4157.3
<br />.10
<br />9759.4
<br />5587.4
<br />20
<br />6748.2
<br />3122.9
<br />20
<br />8082.3
<br />4177.5
<br />20
<br />9792.0
<br />5615.5
<br />30
<br />6768.1
<br />3158.1
<br />30
<br />8107.3
<br />4197.9
<br />30
<br />9824.8
<br />5643.8
<br />40
<br />6788.1
<br />3153.3
<br />40
<br />8132.3
<br />4218.4
<br />40
<br />9857.7
<br />5672.3
<br />50
<br />6808.2
<br />3168.7
<br />50
<br />8157.5
<br />4239.0
<br />50
<br />9890.8
<br />5700.9
<br />100
<br />6828,3
<br />3184.1
<br />110
<br />8182.8
<br />4259.7
<br />120
<br />9924.0
<br />5729.7
<br />10
<br />6848.5
<br />3199.6
<br />10
<br />8208.2
<br />4280.5
<br />10
<br />9957,5
<br />5758.6
<br />20
<br />6868.8
<br />3215.1
<br />20
<br />8233.7
<br />4301.4
<br />20
<br />9991.0
<br />5787.7
<br />30
<br />6689.2
<br />3230,8
<br />30
<br />8259.3
<br />4322.4
<br />30
<br />10025,0
<br />5817.0
<br />40
<br />6909.6
<br />3246.5
<br />40
<br />8285.0
<br />4343.6
<br />40
<br />I0059.0
<br />5846.5
<br />50
<br />6930.1
<br />3262.3
<br />50
<br />8310.8
<br />4364.8
<br />50
<br />10093,0
<br />5876.1
<br />.578
<br />i
<br />f
<br />VII
<br />TABLE V. -CORRECTIONS FOR TANGENTS AND EXTERNALS.
<br />These corrections are to he added to the approximate values, found by dividing
<br />the tangent, or external, for a 1 ° curve (Table IV) by the degree of carve. in order
<br />to obtain the true tangents, or externals. Intermediate values may be obtained by
<br />interpolation.
<br />- FOR TANGI:.:N'r5 ADD
<br />DEGRFE OF CURVE
<br />Central
<br />-
<br />Angle
<br />50"
<br />100
<br />150
<br />200
<br />250
<br />300
<br />35°
<br />4001459
<br />500
<br />550
<br />60° 65-170-
<br />50700100
<br />10,
<br />_03
<br />.06
<br />.09
<br />.13
<br />.16A9
<br />.22
<br />.25
<br />.28
<br />.31
<br />.34
<br />38 42
<br />.46
<br />15°
<br />04
<br />10
<br />.14
<br />.19
<br />.24
<br />.29
<br />,34
<br />.39
<br />.45
<br />.51
<br />.53
<br />.58� .63
<br />,68
<br />20°
<br />06
<br />.13
<br />.19
<br />26
<br />.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79 .84
<br />.90
<br />250
<br />08-
<br />.Ifi
<br />.24
<br />'.33
<br />.40
<br />.49
<br />.58
<br />.67
<br />.75
<br />.83
<br />.90
<br />.99 1.06
<br />1.14
<br />30°;
<br />.10
<br />.19
<br />.29,
<br />.39
<br />.49
<br />.59
<br />.69
<br />.79
<br />.B9
<br />.99
<br />1.09
<br />1.20 1.29
<br />1.39
<br />359
<br />.I1
<br />`,22
<br />,34
<br />.47
<br />.58
<br />.69
<br />'.70
<br />.81
<br />.92
<br />1.04
<br />1.29
<br />1.42 1,54
<br />1.66
<br />400 '
<br />.13
<br />.26
<br />.40
<br />.53
<br />'.67
<br />.80
<br />.93
<br />1.06
<br />1.20
<br />1.34
<br />1.49
<br />1.64 1.79
<br />1.94
<br />450
<br />.15
<br />.30
<br />.44
<br />.60
<br />.76
<br />.91
<br />1.06
<br />1.21
<br />1.37
<br />1.52
<br />L70
<br />1.87 2.04
<br />2.21
<br />50°
<br />.17
<br />.34
<br />.51
<br />.68
<br />.85
<br />1.02
<br />1.19
<br />1.36
<br />1.54
<br />1.72
<br />1.91
<br />2.10 2.29
<br />2.48
<br />55°
<br />.19
<br />.38
<br />.57
<br />.76
<br />.95
<br />1.14
<br />1.32
<br />1.52
<br />1.72
<br />1.92
<br />2.14
<br />2.35 2.56
<br />2.77.
<br />600
<br />.21-
<br />.42
<br />.63
<br />.84
<br />1.05
<br />L27
<br />1.49
<br />1.71
<br />1.94
<br />2.17
<br />2.38
<br />2.60 2:83
<br />3.07
<br />650
<br />.23
<br />.46
<br />.69
<br />.93
<br />1.16
<br />1.40
<br />1.64
<br />1.88
<br />2.13
<br />2.38
<br />2.63
<br />2.88 3.13
<br />3.39
<br />700
<br />.25
<br />-.51
<br />.76
<br />1.02
<br />1.28
<br />1.54
<br />1.80
<br />2.06
<br />2.33
<br />2.60
<br />2.68
<br />3,16 3.44
<br />3.72
<br />750
<br />.27
<br />.56
<br />.83
<br />1.12
<br />1.40
<br />1.69
<br />1.98
<br />2.27
<br />2.57
<br />2.87
<br />3.16
<br />3,47 3.78
<br />4.09
<br />80°
<br />.30
<br />.61
<br />.91
<br />1.22
<br />1,53
<br />1.84
<br />2.15
<br />2.46
<br />2.78
<br />3,10
<br />3.44
<br />3,78 4.12
<br />4.46
<br />85° .
<br />.33
<br />.66
<br />1.00
<br />1.33
<br />1,68
<br />2.02
<br />2.36
<br />2.70
<br />3.05
<br />3.40
<br />3.77
<br />4,14 4.55
<br />4.89
<br />900
<br />.36
<br />.72
<br />1.09
<br />1.45
<br />1,83
<br />2.20
<br />2.57
<br />2.94
<br />3.32
<br />3.70
<br />4.10
<br />4.50 4.91
<br />5.32
<br />950
<br />.39
<br />.79
<br />1.19
<br />1.55
<br />2.00
<br />2.40
<br />2.80
<br />3.20
<br />3.61
<br />4.02
<br />4,40
<br />4.98.5.38
<br />5:83
<br />100°
<br />.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 5.85
<br />6.34
<br />1109
<br />.51
<br />1.03.1.56
<br />2.08
<br />2.61
<br />3.14
<br />3.67
<br />4.21
<br />4.76
<br />5.31
<br />5.86
<br />6.43 7.01
<br />7.60
<br />1200
<br />62
<br />1.25
<br />1.93
<br />2.52
<br />3,16
<br />3.81
<br />4.45
<br />5.11
<br />5.77
<br />6.44
<br />7.12
<br />7.80 8.50
<br />9.22
<br />ICOR EXTERNALS ADD
<br />Central
<br />DECREE OF CURVE.
<br />.Angle'
<br />50
<br />1100
<br />150
<br />2002501
<br />300
<br />350
<br />40°
<br />45° 1
<br />600
<br />550
<br />60-
<br />65°
<br />70-
<br />10o
<br />.001
<br />.003
<br />.004
<br />.006
<br />.007 ..008
<br />.009
<br />.011
<br />.012
<br />,014
<br />-015
<br />.017
<br />.018
<br />.020
<br />150
<br />.003
<br />.007
<br />.010
<br />.014
<br />.018
<br />.023
<br />.027
<br />.029
<br />.032
<br />.035
<br />.039
<br />.043
<br />.047
<br />.051
<br />201
<br />.006
<br />.011
<br />.017
<br />,022
<br />.028
<br />,034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.063
<br />.070
<br />.076
<br />.083
<br />260
<br />.009
<br />.018
<br />.027
<br />.036
<br />.046
<br />.056
<br />.065
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />300
<br />.013
<br />.025
<br />.038
<br />.051
<br />.065
<br />.078
<br />.090
<br />.103
<br />-116
<br />.129
<br />.149
<br />.170
<br />.179
<br />.188
<br />350
<br />.018
<br />.035
<br />.054
<br />.072
<br />.086
<br />:109
<br />.131
<br />.153
<br />.175
<br />.197
<br />.213
<br />.230
<br />-247,.264
<br />401
<br />.023
<br />.046
<br />.070
<br />.093
<br />.117
<br />.141
<br />.172
<br />.203
<br />.234
<br />.265
<br />.277
<br />.290
<br />.315
<br />.341
<br />450
<br />.030
<br />.060
<br />,093
<br />,119
<br />.153
<br />.184
<br />.216
<br />.254
<br />.289
<br />.325
<br />.351
<br />.378
<br />.411
<br />.445
<br />501
<br />.037
<br />.075
<br />.116
<br />.151
<br />-189 '.227
<br />.266
<br />.305
<br />.345
<br />.384
<br />.425
<br />.467
<br />.508
<br />.550
<br />550
<br />.046
<br />.093
<br />.142
<br />.188
<br />.236
<br />.283
<br />.332
<br />.381
<br />.420
<br />.479
<br />'530
<br />.582
<br />.641
<br />.700
<br />600
<br />.056
<br />,112
<br />.168
<br />.225
<br />.283
<br />.340
<br />.398
<br />.457
<br />.516
<br />.575
<br />.636
<br />.697
<br />.774
<br />.851
<br />650
<br />.067
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />-483
<br />.554
<br />.625
<br />.697
<br />.711
<br />.945
<br />.922
<br />1.01
<br />70°
<br />.080
<br />.159
<br />.240
<br />.321
<br />.403
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.906
<br />.994
<br />1.08
<br />1.17
<br />75°
<br />.095
<br />.182
<br />.286
<br />.383
<br />.480
<br />.578
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18
<br />1.29
<br />1.39
<br />60°
<br />.110
<br />.220
<br />.332
<br />.445
<br />.558
<br />.671
<br />.787
<br />.903
<br />1.02
<br />1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.62 .
<br />850
<br />.128
<br />,259
<br />.391
<br />.524
<br />.657
<br />.790
<br />.926
<br />1.06
<br />1.20
<br />1.34
<br />1.47
<br />1.62
<br />1.76
<br />1,91
<br />900
<br />.149
<br />.299
<br />.450
<br />.603
<br />.756
<br />.910
<br />1.07
<br />1.22
<br />1.38
<br />1.54
<br />1.70
<br />1.87
<br />2.03
<br />2.20
<br />950
<br />.174
<br />.350
<br />.522
<br />.706
<br />.985
<br />1.06
<br />1.25
<br />1.43
<br />IL62
<br />1.80
<br />1.99
<br />2.18
<br />2,38
<br />2.53
<br />1000
<br />.200
<br />,401
<br />.604
<br />801.01
<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 />11011
<br />.268
<br />.536
<br />.806
<br />1,08
<br />1.35 1,63
<br />1.91
<br />2.20
<br />2.48
<br />2.76
<br />3.05
<br />3.35
<br />3.66
<br />3.96
<br />1200
<br />.360
<br />.721
<br />1,08
<br />1.45
<br />1.82 2.19
<br />2.57
<br />2,95
<br />3.33
<br />3.72
<br />4.11
<br />4.50
<br />4.9±5
<br />32
<br />
|