|
TABLE VII. -CORRECTION$ FOR TANGENTS AND EXTERNALS
<br />These corrections are to be added to the approximate values, found by dividing the
<br />tangent, or external. for a I' curve (Table VI) by the degree of curve, in order to obtain
<br />the true tangents, or externals. Intermediate values may be obtained by interpolation.
<br />FOR TANGENTS ADD
<br />D 10. 20 30 40 50 60 70 80 90 100 ft, D 200 300 400 500
<br />4°
<br />6
<br />.00
<br />.00
<br />.01
<br />.01
<br />DEGREE
<br />AB
<br />Cone
<br />-01
<br />.00
<br />.02
<br />1
<br />109.99
<br />299.97
<br />Central
<br />499.85
<br />5°
<br />101
<br />15'
<br />20°
<br />250
<br />30°
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />601
<br />65'
<br />Angle
<br />70°
<br />10°
<br />f)3
<br />.06
<br />.09
<br />,13
<br />.16
<br />.19
<br />.22
<br />.26
<br />.28
<br />.31
<br />.34
<br />.38
<br />.42
<br />.40
<br />18°
<br />04
<br />.SO
<br />.14
<br />.19
<br />.24
<br />.29
<br />.34
<br />.39
<br />.45
<br />.51
<br />.53
<br />.58
<br />.83
<br />.BS
<br />30° °
<br />OB
<br />.13
<br />.19
<br />.2B
<br />.32
<br />.39
<br />.95
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />.84
<br />.90
<br />98°
<br />.08
<br />.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 />30° .a
<br />.10
<br />:19
<br />.29
<br />.39
<br />.49
<br />.59
<br />.69
<br />.79
<br />.89
<br />.991.00
<br />,20
<br />1.20
<br />1.29
<br />1.39
<br />39°
<br />9
<br />.22.34
<br />297.54
<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 />60°
<br />,11
<br />.13
<br />.26
<br />, 40
<br />.53
<br />.67
<br />.80
<br />'. 93 1,06
<br />,07
<br />1.20
<br />1.34
<br />1.49
<br />1.64
<br />1.79
<br />1.94
<br />d8'
<br />.15
<br />.30
<br />, 44
<br />.60
<br />.76
<br />.91
<br />1.06 1.21
<br />98
<br />1.37
<br />1.52
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />80'
<br />.17,
<br />.. 34
<br />.51
<br />.68
<br />.85
<br />1.02
<br />1.19 1,361-54
<br />470.65
<br />461.80
<br />30
<br />1.72
<br />1.91
<br />2.10
<br />2.29
<br />2.48
<br />88°
<br />.19
<br />.38
<br />.57
<br />.78
<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 />000
<br />.50
<br />.42
<br />.83
<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 />2.83
<br />3.07
<br />030
<br />.21
<br />.23
<br />.46
<br />, 69
<br />.93
<br />1,18
<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 />TO'
<br />.62
<br />.69
<br />.70
<br />.77
<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 />8, I6
<br />3.44
<br />3.72
<br />TV
<br />.25
<br />.27
<br />.81
<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
<br />3.78
<br />4.09
<br />30°
<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
<br />4.12
<br />4.46
<br />' 680
<br />.33
<br />',65
<br />1, 00
<br />1.33
<br />1.68
<br />2,02
<br />2.36
<br />2. T9
<br />3.05
<br />3 , 40
<br />3.77
<br />4. 14
<br />4.55
<br />4.89
<br />00'
<br />.36
<br />.72
<br />1.09
<br />1.48
<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 />4.01
<br />5.32
<br />900
<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
<br />5.38
<br />5.83
<br />1000
<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 />8.37
<br />5.85
<br />6.34
<br />110°
<br />,51
<br />1.03
<br />1, 58
<br />2.08
<br />2.013.14
<br />3.67
<br />4.21
<br />4.76
<br />5 , 31
<br />5.86
<br />8.43
<br />7.01
<br />7.60
<br />180°
<br />.6211M
<br />239 93
<br />I,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 />8,550
<br />9.22
<br />FOR EXTERNALS ADD
<br />Central
<br />DEGREE OF OVRVE
<br />Angle
<br />244.51
<br />212.92
<br />Norn.-When a chord of less than -100 ft. is used the corrections given in the above
<br />table should be added to the nominal length of chord to get the length whioh should be
<br />in 100
<br />used order that the ft. points will check with those obtained by using the standard
<br />100 ft, chord, Thus in locating a 14° curve by 25 ft, chords measure 25'.06 for each chord.
<br />Long chords are useful in passing obstacles,
<br />TABLE M -MIDDLE OKDINATES FOR BAILS IN FEET
<br />Deg.
<br />LENGTH OF RAILS
<br />Deg.
<br />LENGTH OF RAILS
<br />of
<br />of
<br />50
<br />100
<br />150
<br />20'
<br />250
<br />30°
<br />350
<br />400
<br />45°
<br />506
<br />55'
<br />60'
<br />650
<br />70°
<br />10'
<br />.001.003
<br />Curve
<br />.004
<br />.006
<br />,W7
<br />.008
<br />.009
<br />.011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />.020
<br />10°
<br />003.007
<br />22
<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 />SO°
<br />.017
<br />.022
<br />.028..034
<br />.045-08
<br />.038
<br />.045
<br />.051
<br />•.057
<br />.063
<br />.070
<br />.076
<br />.063
<br />S6'
<br />.006.011
<br />.009
<br />,018
<br />:027
<br />.OSB
<br />.046
<br />.056
<br />.065
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />80°018.025
<br />.306
<br />. 0.38
<br />.O51
<br />.065
<br />.078
<br />.090
<br />.703
<br />.118
<br />.129
<br />.149
<br />.170
<br />.179
<br />.186
<br />88°
<br />.423 .371
<br />.035
<br />.054
<br />.072
<br />.086
<br />.109
<br />.131
<br />,163
<br />.175
<br />.197
<br />.213'.230
<br />.247
<br />.264
<br />400
<br />,018
<br />023.046
<br />.445.392
<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 />480
<br />,030
<br />.W0
<br />.093
<br />.119
<br />.153
<br />.184
<br />.216
<br />.254
<br />.289
<br />,326
<br />.351
<br />.378
<br />.411
<br />.445
<br />00'
<br />.074
<br />.061
<br />.1.16
<br />.181
<br />.189
<br />.227
<br />,266
<br />.305
<br />.345
<br />.384
<br />.425
<br />.487
<br />.508
<br />.550
<br />Sd0
<br />.037.075
<br />.093
<br />.142
<br />.188
<br />.236
<br />.283
<br />.332
<br />.361
<br />.420
<br />.470
<br />.530
<br />.582
<br />.641
<br />.700
<br />00'
<br />.046
<br />056.112
<br />.112
<br />.186
<br />.225
<br />.283
<br />.340
<br />.398
<br />,457
<br />.510
<br />.576
<br />.636
<br />.697
<br />.774
<br />.851
<br />9$0
<br />.067
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />ASS
<br />.554
<br />.628
<br />.697
<br />.711
<br />.845
<br />.922
<br />L.01
<br />70'
<br />.236
<br />.206.
<br />.240
<br />.321
<br />.403
<br />.485
<br />.588
<br />.652
<br />.735
<br />.819
<br />.906
<br />.994
<br />1.08
<br />1.17
<br />700
<br />,080.159
<br />.254
<br />.286
<br />.383
<br />.480
<br />.578
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />LIS
<br />1.29
<br />1.39
<br />000
<br />,095,162
<br />.110.220
<br />_
<br />.334.29b
<br />.332
<br />.445
<br />.558
<br />,871
<br />.787
<br />.903
<br />1.02
<br />1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.62
<br />No
<br />.128.259
<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 />000
<br />.149
<br />.299
<br />.450
<br />.603
<br />.756
<br />.910
<br />L.07
<br />1.22
<br />1.38
<br />1.54
<br />1.70
<br />1,87
<br />2.03
<br />2.20
<br />00°
<br />.522
<br />.706
<br />.985
<br />1.06
<br />1.25
<br />1.43
<br />1.62
<br />1.80
<br />1.99
<br />2.18
<br />2.38
<br />2.58
<br />100°
<br />.174.350
<br />.804
<br />AN
<br />1.01
<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 />110°
<br />.200
<br />268.536
<br />,401
<br />.8(161.08
<br />1.35
<br />1,63
<br />1.91
<br />2.20
<br />2.48
<br />2.76
<br />3.05
<br />3.35
<br />3,86
<br />3.96
<br />11100
<br />.360
<br />.721
<br />1.08
<br />1.45
<br />L82
<br />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 />TABLE VIII.-CORRECPIONS FOR SUB -CHORUS AND LONG CHORDS
<br />FOR SUB -CHORDS ADD Excess LONG CHORDS
<br />of Are
<br />per i
<br />D 10. 20 30 40 50 60 70 80 90 100 ft, D 200 300 400 500
<br />4°
<br />6
<br />.00
<br />.00
<br />.01
<br />.01
<br />.01
<br />.01
<br />.01
<br />-01
<br />.00
<br />.02
<br />1
<br />109.99
<br />299.97
<br />399.92
<br />499.85
<br />0
<br />.00
<br />.01
<br />,01
<br />.02
<br />.01
<br />.02
<br />.02
<br />.03
<br />.02
<br />.03
<br />.02
<br />.03
<br />.02
<br />.03
<br />.01
<br />.02
<br />.01
<br />.01
<br />. .05
<br />.08
<br />8
<br />8
<br />199.97
<br />I99.93
<br />299,88
<br />299.73
<br />399.70
<br />399.32
<br />499.39
<br />498.63
<br />10
<br />.01
<br />.02
<br />.03
<br />.04
<br />.05
<br />.05
<br />.05
<br />.04
<br />.02
<br />.13
<br />d
<br />199.88
<br />299.51
<br />398.78
<br />497,57
<br />18
<br />14
<br />.02
<br />'.02
<br />.04
<br />.05
<br />.05
<br />.06
<br />.07
<br />.07
<br />.07
<br />.05
<br />.03
<br />.18
<br />3
<br />199.81
<br />299.24
<br />398.10
<br />496.20
<br />16
<br />.03
<br />.06
<br />.07
<br />.09
<br />.08
<br />_11
<br />.09
<br />.12
<br />.10
<br />.12
<br />.09
<br />.12
<br />.07
<br />.09
<br />.04
<br />,05
<br />.25
<br />.33
<br />6
<br />7
<br />199.73
<br />199.63
<br />298.90
<br />298, 5I
<br />397.26
<br />396.28
<br />494.53
<br />492.57
<br />16
<br />20
<br />.04
<br />.08
<br />,11
<br />.14
<br />.15
<br />.16
<br />.15
<br />,12
<br />.07
<br />41
<br />3
<br />199.51
<br />298.05
<br />395.14
<br />490.31
<br />.05
<br />-LO
<br />.14
<br />.17
<br />.19
<br />,20
<br />.18
<br />,15
<br />.09
<br />.51.
<br />9
<br />199.38
<br />297.54
<br />393.86
<br />487.75
<br />99
<br />94
<br />.00
<br />.12
<br />.17
<br />.21
<br />.23
<br />.24
<br />.22
<br />.18
<br />.10
<br />.62
<br />10
<br />199.24
<br />296.96
<br />392.42
<br />484.90
<br />26
<br />,07
<br />.14
<br />.20
<br />.25
<br />.28
<br />.28
<br />.26
<br />.21
<br />.12
<br />74
<br />18
<br />198.90
<br />295,63
<br />389.12
<br />478.34
<br />98
<br />.09
<br />AD
<br />.17
<br />.10
<br />.24
<br />,27
<br />.29
<br />.34
<br />.32
<br />.37
<br />.33
<br />.38
<br />.31
<br />.36
<br />,25
<br />,29
<br />.15
<br />.17
<br />BB
<br />1.00
<br />14
<br />16
<br />198.51
<br />198.05
<br />294.06
<br />292.25
<br />385.22
<br />380,76
<br />470.65
<br />461.80
<br />30
<br />.11
<br />.22
<br />.31
<br />.39
<br />.43
<br />,44
<br />.41
<br />.33
<br />.19
<br />1.15
<br />18
<br />197.54
<br />290.21
<br />375.74
<br />452.02
<br />32
<br />34
<br />.13
<br />.25
<br />.36
<br />.44
<br />.49
<br />.50
<br />.47
<br />..38
<br />.22
<br />1.31
<br />90
<br />196.96
<br />287.94
<br />370.17
<br />441.15
<br />36
<br />.15
<br />.17
<br />.28
<br />,82
<br />.40
<br />.45
<br />.50
<br />.56
<br />.55
<br />.62
<br />.57
<br />.04
<br />.53
<br />.59
<br />.43
<br />,48
<br />.25
<br />.28
<br />1.48
<br />1.66
<br />22
<br />24
<br />196.32
<br />195.63
<br />285.44
<br />282.71
<br />364.06
<br />357.43
<br />429.30
<br />416.53
<br />38
<br />40
<br />.18
<br />.21
<br />.36
<br />.40
<br />,51
<br />.66
<br />.62
<br />.69
<br />.70
<br />.77
<br />.71
<br />.79
<br />.60
<br />.73
<br />.53
<br />.59
<br />,31
<br />.35
<br />1.86
<br />2.06
<br />96
<br />98
<br />194.87
<br />194.06
<br />279.76
<br />276.59
<br />350.30
<br />342.69
<br />402.89
<br />388.43
<br />as
<br />d6
<br />.28
<br />.25
<br />.44
<br />.48
<br />.62
<br />.88
<br />.76
<br />.84
<br />.85
<br />.94
<br />,87
<br />.96
<br />.81
<br />.89
<br />.05
<br />.72
<br />.38
<br />.42
<br />2.28
<br />2.50
<br />30
<br />39192.25
<br />193.18
<br />273.20
<br />269.61
<br />334.81
<br />32B.OS
<br />373.20
<br />357.28
<br />d0
<br />de
<br />.27
<br />.30
<br />.52
<br />.87
<br />.75
<br />, 81
<br />.92
<br />1.00
<br />1,02
<br />1.12
<br />1.05.98
<br />1.14
<br />1.06
<br />-78
<br />.86
<br />.46
<br />.50
<br />2.74
<br />2.99
<br />34
<br />36
<br />191.26
<br />190.21
<br />265.81
<br />261.80
<br />317.12
<br />307.77
<br />340.73
<br />323.61
<br />80
<br />.32
<br />.62
<br />.89
<br />1.09
<br />1.21
<br />1.24
<br />1,15
<br />.98
<br />.55
<br />3.24
<br />38
<br />189.10
<br />257.60
<br />298.03
<br />305.99
<br />82
<br />.35
<br />.67
<br />.96
<br />1.18
<br />1.31
<br />1.35
<br />1.25
<br />1.01
<br />.59
<br />3.52
<br />40
<br />197.94
<br />253.21207.
<br />94
<br />287.94
<br />04
<br />.38
<br />.73
<br />1.04
<br />1.28
<br />1.42
<br />1.46
<br />1.35
<br />1.09
<br />.64
<br />3.80
<br />d9
<br />186.72
<br />248,63
<br />277.51
<br />269.54
<br />06
<br />.41
<br />.78
<br />1.12
<br />1.38
<br />1.53
<br />1.67
<br />1.46
<br />1.17
<br />.69
<br />4.09
<br />4d
<br />185.44
<br />243, 87
<br />266.78
<br />250.85
<br />OB
<br />.44
<br />.84
<br />1.20
<br />1.48
<br />1. 65
<br />1.69
<br />L 67
<br />1.26
<br />.74
<br />4.40
<br />46
<br />184. 10
<br />239 93
<br />255.78
<br />231.95
<br />60
<br />.47
<br />.911.20
<br />1,59
<br />1.T6
<br />1.81
<br />1.681.35
<br />,80
<br />4.72
<br />48
<br />182.71
<br />,
<br />233.83
<br />244.51
<br />212.92
<br />Norn.-When a chord of less than -100 ft. is used the corrections given in the above
<br />table should be added to the nominal length of chord to get the length whioh should be
<br />in 100
<br />used order that the ft. points will check with those obtained by using the standard
<br />100 ft, chord, Thus in locating a 14° curve by 25 ft, chords measure 25'.06 for each chord.
<br />Long chords are useful in passing obstacles,
<br />TABLE M -MIDDLE OKDINATES FOR BAILS IN FEET
<br />Deg.
<br />LENGTH OF RAILS
<br />Deg.
<br />LENGTH OF RAILS
<br />of
<br />of
<br />Curve
<br />Curve
<br />32
<br />30
<br />28
<br />26
<br />24
<br />22
<br />20
<br />32
<br />30
<br />28
<br />26
<br />24
<br />22
<br />20
<br />10
<br />.022
<br />.020
<br />.016
<br />.013
<br />.011
<br />.009
<br />.008
<br />18'
<br />.356 .813
<br />.273.236
<br />S
<br />.045-08
<br />W4
<br />.029
<br />.025
<br />.021
<br />.017
<br />17
<br />.378.333
<br />.290
<br />.200
<br />,170
<br />.139
<br />3
<br />.037
<br />.058
<br />.061
<br />.044
<br />.037
<br />.031
<br />.026
<br />18
<br />, 400 .351
<br />.306
<br />.252
<br />.265
<br />.213
<br />.180
<br />.190
<br />.148
<br />d
<br />.099
<br />.079
<br />.069-060
<br />.050
<br />.042
<br />.035
<br />10
<br />.423 .371
<br />.324
<br />.225
<br />.201
<br />.156
<br />0
<br />.112:099.086.074.063.053.044
<br />20
<br />.445.392
<br />.341
<br />.280
<br />. 296
<br />.238
<br />.212
<br />.165
<br />5
<br />.134
<br />.117
<br />.102
<br />. G&B
<br />.076
<br />.064
<br />.052
<br />21
<br />.466
<br />410
<br />357
<br />.260
<br />.222
<br />.174
<br />7
<br />.156
<br />.137
<br />.120
<br />.104
<br />.088
<br />.074
<br />.061
<br />29
<br />.487 .430
<br />.375
<br />.309
<br />.262
<br />.182
<br />0
<br />.179
<br />. 158
<br />.137
<br />.119
<br />.100
<br />.085
<br />.070
<br />99
<br />.5f19� 450
<br />.390
<br />.326
<br />.338
<br />.275
<br />.287
<br />.233.191
<br />.243
<br />, 199
<br />0
<br />.201
<br />.175
<br />.153
<br />.133
<br />.112
<br />.095
<br />.078
<br />94
<br />.'5531 469
<br />.408
<br />10
<br />11
<br />.223
<br />.245
<br />.198
<br />.216
<br />.171
<br />.188
<br />,148
<br />.163
<br />.125
<br />.139
<br />.106
<br />.117
<br />.087
<br />,096
<br />93
<br />96
<br />.552 .486
<br />.573 .506
<br />.424
<br />.441
<br />.354 .299
<br />.367 .30
<br />.253
<br />.263
<br />.208
<br />.216
<br />19
<br />.268
<br />.236
<br />.206.
<br />179
<br />-151
<br />.128
<br />.105
<br />27
<br />.594 , 524
<br />.457
<br />.382 .323
<br />.396
<br />.274
<br />.284
<br />.225
<br />18
<br />.290
<br />.254
<br />.222
<br />.192
<br />. 163
<br />.138
<br />.113
<br />98
<br />.618 .545
<br />.475
<br />.335
<br />.233
<br />11'112,
<br />10
<br />_
<br />.334.29b
<br />.276
<br />.239
<br />.257
<br />.207
<br />.223
<br />.175
<br />.188
<br />.148.122
<br />.159
<br />.131
<br />9f1
<br />S8
<br />.636 ,564
<br />.660 .583
<br />.491
<br />.508
<br />.411 .348
<br />.424 ,
<br />.438 .374
<br />361
<br />.294
<br />.303
<br />.313
<br />.242
<br />.260
<br />..259 "
<br />
|