|
TABLE V11.: --(TORR_ ECTION6 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 1° curve (Table VI) by the degree of curve in order to obtain ;
<br />the true tangents, or externals. Intermediate values may be obtained �y interpolation.
<br />FOR TANGENTS ADD
<br />Central
<br />DEGREE OF CURVE
<br />Angle
<br />50
<br />100
<br />151
<br />201
<br />25°
<br />301
<br />351
<br />401
<br />451
<br />'S0°
<br />55°
<br />600
<br />650
<br />701
<br />10°
<br />.03
<br />.06
<br />.09
<br />.13
<br />.16
<br />"19
<br />.22
<br />"25
<br />.28
<br />.al
<br />.34
<br />.38
<br />.42
<br />:46
<br />140
<br />.04
<br />.10
<br />.14
<br />.19
<br />.24
<br />'.29
<br />.34
<br />.39
<br />.45
<br />.51
<br />.53'.58
<br />.01
<br />.63
<br />..68
<br />200
<br />.06
<br />.13
<br />.19
<br />.26
<br />.32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.05
<br />.72
<br />.79
<br />.84
<br />.90
<br />260
<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 />80°
<br />10
<br />.19
<br />.29
<br />.38,.49
<br />497.57
<br />.59
<br />.69
<br />.79
<br />.89
<br />.99
<br />1.09
<br />1.20
<br />1.29
<br />1.39
<br />86'
<br />:11
<br />.22
<br />.34
<br />.47
<br />.58
<br />.89
<br />.70
<br />'81
<br />'.. B2
<br />1.04
<br />1.29
<br />1.42
<br />1:54
<br />1.66
<br />4�i0°
<br />.13
<br />.26
<br />,40
<br />.53
<br />.67
<br />.80
<br />. 93
<br />1. 013
<br />1.20
<br />1.34
<br />1.49
<br />1.64
<br />1 79
<br />1.94
<br />65°
<br />.15
<br />.30
<br />.44
<br />.60
<br />.70
<br />.91
<br />1.06
<br />t, 21
<br />1. 37
<br />1, b2
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />60°
<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 />1,212
<br />. 10
<br />2.29
<br />2.48
<br />46°
<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
<br />2.56
<br />2.77
<br />600
<br />.21
<br />'.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 />2.83
<br />3.07
<br />469
<br />.23
<br />.46
<br />.69
<br />.93
<br />1.16
<br />1.40
<br />L64
<br />1.88
<br />2.13
<br />2"38
<br />2.63
<br />2.88
<br />3.13
<br />3.39
<br />TO,
<br />.25
<br />.51
<br />,76
<br />1.02
<br />1428
<br />1.54
<br />1.80
<br />2.06
<br />2.33
<br />2-602.68
<br />294.06
<br />3. l6
<br />3.44
<br />3.72
<br />T6°.
<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
<br />3,79
<br />4.09
<br />80°
<br />.30
<br />.61
<br />:91
<br />1.22
<br />I; 43
<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 />f18°
<br />.33
<br />.66
<br />1.00
<br />1.33
<br />1.68
<br />2.02
<br />2.30
<br />2.70
<br />3.05
<br />3,40
<br />3.77
<br />4-14
<br />4.55
<br />4.89
<br />90°
<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
<br />4. b0
<br />4.9]
<br />5.32
<br />98'
<br />39
<br />.79
<br />1:19
<br />L.55
<br />2.00
<br />2.40
<br />2.80
<br />3.20
<br />3.61
<br />4:024.10
<br />.45.26
<br />0 4.98
<br />5.38
<br />5.83
<br />100°
<br />.43
<br />.861.30
<br />416.53
<br />1.74
<br />2, IS
<br />2.62
<br />3.06
<br />8.50
<br />3.05
<br />4.40
<br />4.88
<br />5.37
<br />5.85
<br />6.34
<br />110°
<br />.51
<br />1.03
<br />1.56
<br />2.08
<br />2.8 Y
<br />3.14
<br />3.67
<br />4.21
<br />4.76
<br />5.31
<br />5.88
<br />0.48
<br />7.01
<br />7.00
<br />120°
<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
<br />8.50
<br />9.22
<br />FOR ExTERNALB ADD
<br />2.28
<br />DEGREE OF CURVE
<br />Central
<br />273.20
<br />Angle
<br />373.20
<br />44
<br />.25
<br />.48
<br />.68
<br />,84
<br />.94
<br />.06
<br />.89
<br />.72'.42
<br />2,.50
<br />82
<br />192,25
<br />209,61
<br />50
<br />100
<br />18°
<br />200
<br />250
<br />300
<br />350
<br />400
<br />450
<br />50°
<br />55°
<br />600
<br />650
<br />701
<br />100
<br />.001,003
<br />317.12
<br />.004
<br />.005
<br />.007
<br />.008
<br />.009
<br />.011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />.020
<br />180
<br />.003 .007
<br />201,80
<br />.010
<br />.014
<br />.018
<br />.023
<br />.027
<br />.029
<br />.032
<br />W
<br />.039
<br />.043
<br />,047
<br />.051
<br />90°
<br />.006
<br />All
<br />.017
<br />.022
<br />.028
<br />.034
<br />.038
<br />.045
<br />.051
<br />.057
<br />.063
<br />.070
<br />.076
<br />.08$
<br />051
<br />.009.015
<br />40
<br />.027".036
<br />253.21
<br />.048
<br />.056
<br />.065
<br />.074
<br />.083
<br />.093
<br />.106
<br />.120
<br />.127
<br />.135
<br />80°
<br />.013 .025
<br />3.80
<br />.038
<br />.051
<br />.065
<br />.078
<br />.090
<br />.103
<br />.116
<br />.129
<br />,149
<br />.170
<br />.179
<br />ASS
<br />869
<br />.018.035
<br />.054
<br />.072
<br />.086
<br />.109
<br />.131
<br />.153
<br />•.IT5
<br />.LOT.213'
<br />.84
<br />.230
<br />.247
<br />.264
<br />40°
<br />.023.046
<br />I.26
<br />.070
<br />.093
<br />.117
<br />.141
<br />,172
<br />.203
<br />.234
<br />.265
<br />.277
<br />.290
<br />.315
<br />.941
<br />48°
<br />030.060
<br />1.68
<br />.093
<br />.119
<br />.163
<br />.184
<br />.216
<br />.254
<br />.289
<br />.825
<br />,.351
<br />.378
<br />.411
<br />.445
<br />80".
<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 />480
<br />046.003
<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 />601
<br />.056
<br />.112
<br />.168
<br />.225
<br />.283
<br />.340
<br />.398
<br />.457
<br />.516
<br />.575
<br />.836
<br />.597
<br />.774
<br />.861
<br />86°
<br />.067
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />AS3
<br />.554
<br />.625
<br />.697
<br />.711
<br />.845
<br />' .922
<br />1.01
<br />70°
<br />.080.159
<br />.025
<br />.240
<br />.321
<br />,403
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.906
<br />M4
<br />1.08
<br />1.17
<br />791
<br />.095
<br />,182
<br />,286
<br />.3S3
<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 />900
<br />.110.220
<br />.069
<br />.332
<br />.445
<br />,558
<br />,671
<br />.787
<br />.903
<br />1,02
<br />1.13.1.25
<br />.280
<br />1.38
<br />1.50
<br />1.62
<br />840
<br />.128.250
<br />.099
<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 />W
<br />,149.299
<br />.134.117.102.088.076,064.052
<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 />960
<br />.174.350
<br />7
<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 />.200.401
<br />.191
<br />.604
<br />WO
<br />101
<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 />.268.536
<br />.243
<br />.8061.08
<br />O
<br />1.35
<br />1,63
<br />1,91
<br />2.20
<br />2.48
<br />2.76
<br />3.05
<br />135
<br />3.66
<br />3.96
<br />1941
<br />360.7211,08
<br />.299
<br />.253
<br />1.45
<br />1.82
<br />2,19
<br />2,57
<br />2.95
<br />13.33
<br />8.72
<br />4.11
<br />4.50
<br />4,91
<br />5,32
<br />.486
<br />i
<br />TABLE VIII. --CORRECTIONS FOR SUS -CHORDS ANA LONG CRC•RDS
<br />FOR SUB -CHORDS ADD
<br />Excess
<br />TONG CHORDS
<br />of Are
<br />D
<br />10
<br />20
<br />30
<br />40
<br />50
<br />60
<br />70
<br />80
<br />90
<br />10®ft.
<br />D
<br />200
<br />300
<br />400
<br />500
<br />4'
<br />.00
<br />.00
<br />.01
<br />.01
<br />.OL
<br />,Ol
<br />,Ol
<br />.Ol
<br />.00
<br />.02
<br />1
<br />199.99 299.97
<br />399.92
<br />499.85
<br />8
<br />.00
<br />.01
<br />.01
<br />.02
<br />,02
<br />.02
<br />,02
<br />.01
<br />.01
<br />.05
<br />2
<br />199.97 299.88
<br />399.70
<br />499,39
<br />8
<br />.01
<br />.02
<br />.02
<br />.03
<br />.03
<br />.03
<br />,03
<br />.02
<br />.01
<br />.08
<br />8
<br />199.93 299.73
<br />399.32
<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 />4
<br />199.88 299.51
<br />398.78
<br />497.57
<br />18
<br />.02
<br />.04
<br />.05
<br />.06
<br />,07
<br />.07
<br />.07
<br />.05
<br />.03
<br />.18
<br />5
<br />199.81299.24
<br />398.10
<br />496.20
<br />14
<br />.02
<br />.05
<br />.07
<br />.08
<br />.09
<br />.1Q
<br />.09
<br />.07
<br />.04
<br />.25
<br />6
<br />199.73 298.90
<br />397.26
<br />494.53
<br />16
<br />.03
<br />.06
<br />,09
<br />.11
<br />.12
<br />.12
<br />.12
<br />.09
<br />,05
<br />.33
<br />7
<br />199.63 298.51
<br />396.28
<br />492.57
<br />18
<br />.04
<br />.08
<br />.11
<br />.14
<br />.15
<br />.16
<br />.15
<br />.12
<br />,07
<br />Al
<br />6
<br />199.51 298.05
<br />M. 14
<br />490.31
<br />20
<br />.05
<br />.10
<br />.14
<br />.17
<br />.19'
<br />.20
<br />.18
<br />.15
<br />.09
<br />.51
<br />9
<br />189.38
<br />297.54
<br />393.86
<br />487.75
<br />82
<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 />94
<br />.07
<br />.14
<br />.20
<br />.25
<br />.28
<br />.2S
<br />.26
<br />.21
<br />.12
<br />.74
<br />12
<br />198.90
<br />295.63
<br />389.12
<br />478.34
<br />26
<br />.09
<br />.17
<br />.24
<br />.29
<br />.32
<br />.33
<br />.31
<br />.25
<br />.15
<br />Sfi
<br />14
<br />198.51
<br />294.06
<br />385.22
<br />470.65
<br />28
<br />AD
<br />.19
<br />,27
<br />.34
<br />.37
<br />.38
<br />.36
<br />.29
<br />.17
<br />1.00
<br />16
<br />198.05
<br />292.25
<br />380.76
<br />461.86
<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 />82'
<br />.13
<br />.25
<br />.36
<br />.44
<br />.49
<br />.50
<br />'.47
<br />.38
<br />.22
<br />1.31
<br />20
<br />100.96
<br />287.94
<br />370.17
<br />441.15
<br />94
<br />.15
<br />.28
<br />.40
<br />.50
<br />.55
<br />.57
<br />.53
<br />..43
<br />.25
<br />1.48
<br />22
<br />190.32
<br />285.44
<br />364.06
<br />429.30
<br />86.17
<br />.32
<br />,45'
<br />.56
<br />.62
<br />.64
<br />'.59
<br />.45.26
<br />1.06
<br />26
<br />L9b.63
<br />282.71
<br />357.43
<br />416.53
<br />89
<br />.18
<br />.36
<br />.51
<br />.62
<br />.70
<br />.71
<br />.66
<br />.53
<br />.31
<br />1,86
<br />26
<br />104.87
<br />279.76
<br />350.30
<br />402.89
<br />40'.21
<br />.40
<br />.56
<br />.69
<br />.77
<br />.70
<br />.73
<br />,59
<br />.35
<br />2.06
<br />28
<br />104.06
<br />276.59
<br />342.60
<br />388.43
<br />48
<br />.23
<br />.44
<br />.62
<br />.76
<br />.85
<br />.87
<br />.81
<br />.65
<br />.38
<br />2.28
<br />80
<br />193.18
<br />273.20
<br />334.61
<br />373.20
<br />44
<br />.25
<br />.48
<br />.68
<br />,84
<br />.94
<br />.06
<br />.89
<br />.72'.42
<br />2,.50
<br />82
<br />192,25
<br />209,61
<br />326.08
<br />357.28
<br />46'.27
<br />.52
<br />,75
<br />.02
<br />1,02
<br />1.05
<br />.98
<br />-78'.46
<br />2.74
<br />8d
<br />191,26
<br />205.81
<br />317.12
<br />340.73
<br />02
<br />.30
<br />.57
<br />.81
<br />1.00
<br />1.12
<br />1.14
<br />1.06
<br />.86
<br />.50
<br />2,99
<br />BS
<br />100.21
<br />201,80
<br />307.77
<br />323.61
<br />00
<br />.32
<br />.62
<br />.89
<br />1.09
<br />1.21
<br />1.24
<br />1.15
<br />.93
<br />.55
<br />3.24
<br />88
<br />189.10
<br />257.80
<br />298.03
<br />305.99
<br />52
<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 />187.94
<br />253.21
<br />287.94
<br />287.94
<br />84
<br />.38
<br />.731.04
<br />1.28
<br />1.42
<br />1.46
<br />1.35
<br />1.09
<br />"84
<br />3.80
<br />42
<br />188.72
<br />248.83
<br />277.51269.
<br />54
<br />88
<br />.41'.781.121.381.631.57,1.401.17.69
<br />4.09
<br />44
<br />185 44
<br />243. K7
<br />266, 78
<br />250. 85
<br />".44
<br />.84
<br />1.20
<br />1.48
<br />1.85
<br />1.69
<br />1.57
<br />I.26
<br />.74
<br />4.40
<br />48
<br />184. 10
<br />239.93
<br />25b,78
<br />231.95
<br />40
<br />.47
<br />.91
<br />1.29
<br />1.59
<br />1.78
<br />1. S 1
<br />1.68
<br />1.35
<br />.80
<br />4.72
<br />48
<br />182.71
<br />233.83
<br />244.51
<br />212.92
<br />NorE.-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 chard to get the length which should be
<br />in that the 100 ft. check those by the
<br />used order points will with obtained using standard
<br />100 ft. chord. Thus in locating a 14° curve by 25 ft. chorda measure 25'.06 for each chord.
<br />Long chorda are useful in passing obstacles,
<br />TA13LE M -MIDDLE ORDINATES FOR RAILS IN FEET
<br />Des.
<br />LENGTH OF RAILS
<br />Deg.
<br />LENGTH OF RAILS
<br />of
<br />of
<br />- -- -
<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 />1°
<br />.022
<br />.020
<br />.016
<br />.013
<br />.011
<br />.009
<br />, 008
<br />160
<br />,356
<br />.313
<br />.273
<br />.236
<br />.200
<br />.170
<br />.139
<br />9
<br />.045
<br />.038
<br />.034
<br />.029
<br />.025
<br />.021
<br />.017
<br />17
<br />378
<br />.333
<br />.200.252
<br />.213
<br />.180
<br />.148
<br />8
<br />.037
<br />.058
<br />.051
<br />.044
<br />.037
<br />.031
<br />.026
<br />18
<br />.400
<br />.351
<br />,306
<br />.265
<br />.225.
<br />190
<br />, 156
<br />6
<br />.089
<br />.079
<br />.069
<br />.060
<br />.050
<br />.042
<br />.035
<br />19
<br />.423
<br />.371
<br />.324
<br />.280
<br />,238
<br />201.
<br />. 165
<br />6
<br />.112
<br />.099
<br />.088
<br />.074
<br />.063
<br />.053
<br />.044
<br />80
<br />.445
<br />.392
<br />.341
<br />.296
<br />, 250
<br />.212
<br />,174
<br />0
<br />.134.117.102.088.076,064.052
<br />81
<br />.466.410.357.309.202.222'.182
<br />7
<br />.158
<br />.137
<br />.120
<br />.104
<br />.088
<br />.074
<br />.061
<br />22
<br />.487
<br />430.375
<br />.325
<br />, 275
<br />.233
<br />.191
<br />9
<br />.179
<br />158
<br />-137
<br />.119
<br />A00
<br />OM
<br />.070
<br />22
<br />.509
<br />450
<br />.390
<br />.338
<br />.287
<br />.243
<br />.199
<br />O
<br />.201.175
<br />.153
<br />.133
<br />,112
<br />.095
<br />.078
<br />24
<br />.531
<br />469.408
<br />.354
<br />.299
<br />.253
<br />.208
<br />10
<br />,223
<br />.196
<br />.171
<br />.148
<br />.125.106
<br />.087
<br />28
<br />.552
<br />.486
<br />.424
<br />.367
<br />.311
<br />.263
<br />.216
<br />11
<br />.245
<br />.216
<br />.188
<br />.183
<br />.139
<br />,117
<br />.0%
<br />88
<br />.573
<br />.506
<br />.441
<br />.382
<br />.323
<br />.274.225
<br />18
<br />.208
<br />.236
<br />.200.179
<br />.151
<br />. 12$
<br />.105
<br />87
<br />.594
<br />.524
<br />.457
<br />.306
<br />.335
<br />.284
<br />.233
<br />19
<br />"290.254.222.192.163.138.113
<br />U
<br />.018.545.475.411
<br />.348
<br />.204
<br />.242
<br />,16
<br />.312
<br />275
<br />.230
<br />-207
<br />.175
<br />-148
<br />.122
<br />80
<br />838
<br />.564
<br />.491
<br />-424
<br />.361
<br />.3W
<br />250
<br />10
<br />.334
<br />.295
<br />.257
<br />.223.188
<br />.159
<br />.131
<br />SO
<br />6811
<br />.5&�
<br />.508
<br />-4381,3741-31,31.259
<br />C
<br />
|