|
a
<br />.TABLE IV. -TANGENTS AND'EXTERNALS. TO A 19 CURVE.
<br />Central
<br />Angle
<br />1'angerd
<br />-11
<br />Bxtern¢l
<br />I Central (
<br />Angle
<br />Tangent
<br />External I Central
<br />Angle
<br />1'angcnt
<br />E7cternal
<br />914'
<br />5830.5
<br />2444.9
<br />1010
<br />6950.6
<br />3278.1
<br />1110
<br />8336.7
<br />4386.1
<br />,101
<br />5847.5
<br />'2457.1
<br />101
<br />6971.3
<br />3294.1
<br />10,
<br />8362.7
<br />4407.6
<br />20
<br />5864.6
<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 />.
<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 />93.1
<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 />e '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 />10
<br />7355.6
<br />3594.2 '
<br />•10
<br />8851.0
<br />4814.1 '
<br />20
<br />76190.2
<br />2697.9
<br />20
<br />7377.8
<br />8611.7 .
<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 />95
<br />6252.8
<br />2751.3 .
<br />105 ,
<br />7467.0
<br />3682:3
<br />115 '
<br />8993.8
<br />4934,1 '
<br />..
<br />10
<br />6271.1
<br />2764.8
<br />10
<br />7489.6 ;
<br />8700.2
<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 />9051.7
<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 />150;
<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 />5082,7 '
<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 />2961.0
<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 />931915
<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 f
<br />10
<br />6495.2
<br />'2931.6
<br />10
<br />7766.8•
<br />x3921.9
<br />10 .
<br />9380.5
<br />5262.3
<br />20,
<br />6514.3
<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 />30
<br />7959.0
<br />4077.2
<br />30
<br />9630.7
<br />5476.5
<br />40
<br />;6669:2•
<br />3062.8:
<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 />8008.0'
<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 />-9';27.0
<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 />3138.1
<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 />,
<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 />6889,2
<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 />10059.0
<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 />.321
<br />t
<br />VII
<br />• TABLE V. -CORRECTIONS FOR TANGENTS AND EXTFRNAI.S.
<br />These corrections are to be added to the approximate values, found by dividing
<br />the tangent, or external, for a 10 curve ('fable IV) by the degree of curve, in order
<br />to obtain the true tangents, or externals. intermediate values may be obtained by
<br />interpolation.
<br />FOR TANGENrs Aon
<br />DF.GREL OF CLJ R VE
<br />Central
<br />Angle
<br />S. 10° 115-120°
<br />25°
<br />130°
<br />35°
<br />1 40°,
<br />45°
<br />50-155-
<br />1 60° 65°
<br />70-
<br />10,
<br />.03 .06
<br />.09
<br />.13
<br />.16
<br />.19
<br />.22
<br />.25
<br />.28
<br />.31
<br />.34�
<br />.38I
<br />.42
<br />.46
<br />15°
<br />.04 .10
<br />.14
<br />.19
<br />.24
<br />.29
<br />.34
<br />.39
<br />.45
<br />.51
<br />.53
<br />58
<br />.63
<br />.68
<br />201
<br />.06 .13
<br />.19
<br />.26
<br />.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />.84
<br />.90
<br />250
<br />.08 .16
<br />.24
<br />.33
<br />.40
<br />.49
<br />.58
<br />.67
<br />.75
<br />.83
<br />.90
<br />.99
<br />1.06
<br />1.14
<br />300
<br />.10 .19
<br />.29
<br />.39
<br />.49
<br />.59
<br />.69
<br />.79
<br />.89
<br />.99
<br />1.09
<br />1.20
<br />1.29
<br />1.39
<br />350
<br />.11 .22
<br />.34
<br />.47
<br />.58
<br />.69
<br />'.70
<br />.81
<br />.92
<br />1.04
<br />1.29
<br />1.42
<br />1.54
<br />1.66
<br />400
<br />:13 .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
<br />1.79
<br />1.94
<br />450
<br />.15 .30
<br />.44
<br />.60
<br />.76
<br />.91
<br />1.06
<br />1.21
<br />1.37
<br />1.52
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />600
<br />11 .34 ..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
<br />2.29
<br />2.48
<br />650
<br />.19 .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
<br />'2.56
<br />2.77
<br />600
<br />.21 .42
<br />.63
<br />.84
<br />1.05
<br />1.27
<br />1.49
<br />1.71
<br />1.94
<br />2.17
<br />2,38
<br />2,60
<br />2.63
<br />3.07
<br />65°
<br />.23 .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
<br />3.13
<br />3.39
<br />700
<br />.25 .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 />2.88
<br />3.16
<br />3.44
<br />3.72
<br />750
<br />.27 .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
<br />3.78
<br />4.09
<br />800
<br />.30 .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
<br />4.12
<br />4.46
<br />850
<br />.33 .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
<br />4.55
<br />4.89
<br />900
<br />.36 .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
<br />4.91
<br />5.32
<br />950
<br />.39 .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
<br />5.38
<br />5.83
<br />1000
<br />.43 .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
<br />5.85
<br />6.34
<br />110°
<br />.51 1.03
<br />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
<br />7.01
<br />7.60
<br />1200
<br />.62 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
<br />8.50
<br />9.22'
<br />' FOR EXTERNALS ADD
<br />DEGREE OF CURVE
<br />Central
<br />Angle
<br />5o
<br />100
<br />150
<br />20°
<br />25°
<br />30° 135°
<br />40°
<br />45° 150°
<br />55°
<br />60°
<br />65°
<br />70-
<br />10'
<br />.001
<br />.003
<br />.004
<br />.006
<br />.007
<br />.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 ..034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.063
<br />.070
<br />.076
<br />.083
<br />25o_
<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 />301
<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 />351
<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
<br />.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 />50°
<br />.037
<br />..075
<br />.116
<br />.151
<br />.189
<br />.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 />659
<br />.067
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />.483
<br />.554
<br />.625
<br />.697
<br />.711
<br />.845
<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 />750
<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 />80° '
<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 />85°
<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 1.06
<br />1.25
<br />1.43
<br />1.62
<br />1.80
<br />1.99
<br />2.18
<br />2.38
<br />2.53
<br />100°
<br />.200
<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 />2.96
<br />110°
<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 />120°
<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 />4.91
<br />5.32
<br />d
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