|
TABLE VII. -CORRECTIONS FOR'.TANOENTB AND EXTERNALS
<br />These corrections 'are to be added to the i}pproxhmate values, found by dividingg the
<br />tangent, or external, ;for a,1°;curve (Table VI) 6y the degree of cue've, in order to obtain
<br />the true tangents, or externals. lateimediate values may be obtained by interpolation,
<br />,j Foi �TAN6ENT8 ADD
<br />a t
<br />Cws
<br />i tDsassE ofa
<br />_
<br />Central
<br />#3-
<br />;:10°
<br />AP
<br />20°
<br />25°,
<br />30"
<br />85°,
<br />40°
<br />.45°
<br />.30°
<br />850,
<br />Or
<br />65°
<br />70°
<br />Angle
<br />10° r.
<br />03
<br />J .08
<br />!09
<br />.13
<br />15
<br />:10
<br />1.22
<br />: 25
<br />.28
<br />;.a1
<br />.34
<br />.38
<br />.42
<br />.48 .
<br />15° ,:
<br />04
<br />•,:10
<br />.
<br />:14
<br />s 19
<br />;24
<br />:29
<br />.34
<br />:39
<br />!,45
<br />.51
<br />.53
<br />:58
<br />:63
<br />.68
<br />SO°
<br />�:06
<br />6
<br />.00
<br />":26;:32
<br />.01
<br />::39
<br />'.45
<br />.51
<br />:58
<br />.85..72,:79
<br />.01
<br />.05
<br />.84
<br />.90
<br />S5° t ',
<br />OB
<br />,.13
<br />_ .16
<br />,.19
<br />:24
<br />:33
<br />; :40
<br />: i49
<br />.58
<br />j..
<br />.67
<br />.75
<br />.83
<br />.90
<br />.991.06
<br />.08
<br />1.14
<br />80° s,
<br />. 30
<br />.19
<br />.29
<br />.39
<br />; .49
<br />: 59
<br />.03
<br />.79
<br />11. B9
<br />:.99
<br />I.09
<br />1.20
<br />1.29
<br />1.39
<br />,,
<br />85°
<br />.11
<br />,22
<br />:34
<br />:47
<br />:58
<br />.69
<br />_,.69
<br />!.70
<br />.81
<br />'.92
<br />1.04
<br />1.29
<br />1.42
<br />1.54
<br />1.66_
<br />40°
<br />.33
<br />.26
<br />:40
<br />53
<br />; . 57
<br />: 80
<br />i 93
<br />1;06
<br />1.20
<br />1: 34
<br />1.49
<br />1.64
<br />3.79
<br />1-.94
<br />16
<br />, .30
<br />:44
<br />60
<br />.76
<br />:. 91
<br />11. DB
<br />1.21
<br />1.37
<br />1.32
<br />1.70
<br />1.87
<br />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
<br />2.29
<br />2.48
<br />58°
<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 />a
<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 />65°.23
<br />.24
<br />.46
<br />.69
<br />.93
<br />1.16
<br />1:40
<br />1.04
<br />1.88
<br />2,13
<br />2.38
<br />2.63
<br />2.88
<br />3.13
<br />3.39
<br />'
<br />x,.25
<br />t
<br />.51
<br />:78
<br />1.62
<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 />-
<br />3.72
<br />76P y
<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 />3.78
<br />4.09
<br />80°
<br />, . 30
<br />-4.
<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 />659'
<br />4.33
<br />' .66
<br />1.00
<br />1_.33
<br />1.68
<br />2.02
<br />2:38
<br />2.70
<br />3.05
<br />3.40.3.77
<br />197.54
<br />4.14
<br />4,35
<br />4.89
<br />90'
<br />1.38
<br />,72
<br />1:09
<br />1.45
<br />1183
<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 />96°
<br />39
<br />.79
<br />1:19
<br />1.55
<br />2.00
<br />2.40
<br />2. SO
<br />3.20
<br />3.61
<br />4: 02
<br />4.40
<br />4.98
<br />5.38
<br />5.83
<br />100°. - F',
<br />.43',
<br />. 86
<br />1.30
<br />1.74
<br />2.1S
<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 />8.34
<br />282.71
<br />. ,
<br />l,0311.562.082;613.14,3.674.214,765.315.866.437.017.60
<br />88
<br />.18
<br />.36
<br />.51
<br />.62
<br />.70
<br />.71
<br />.66
<br />.53
<br />.31
<br />1.86
<br />26
<br />120° ;R,'
<br />,.62
<br />1.25
<br />1:43
<br />2;:52
<br />3. 16
<br />3.'81
<br />4.45
<br />5.115..77
<br />.77
<br />8.44
<br />7.12
<br />7.80
<br />8.50
<br />9.22
<br />• - -'+. , Fon+EXTEI67A1:S ADD •.:
<br />CEIItral j
<br />t ADEoaEE OF 09nvB
<br />Anile
<br />388.
<br />42
<br />.23.44
<br />.62
<br />.76
<br />.85
<br />:S7.
<br />.81
<br />.65
<br />.38
<br />2.28
<br />90
<br />193.18
<br />273.20
<br />5°'
<br />,10°
<br />15°
<br />20° '25°
<br />.48
<br />'30°
<br />35°
<br />•40°
<br />45°1
<br />50°'
<br />55°
<br />60°
<br />65°
<br />70°
<br />10".001
<br />,
<br />.003
<br />326.08
<br />.004
<br />'.006
<br />.007
<br />.008
<br />.009
<br />,011
<br />.012
<br />.014
<br />.015
<br />.017
<br />.018
<br />AM
<br />1S° ;.003.007
<br />191.26
<br />265.81
<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 />2OP: ;,006.011
<br />86
<br />190. 21261.80
<br />.017
<br />.022
<br />.028
<br />'.034
<br />,038
<br />.045
<br />AS
<br />.057
<br />-.063
<br />.070
<br />.076
<br />.083
<br />l 45°
<br />009.018
<br />38
<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 />W
<br />.013.025
<br />3.52
<br />.038
<br />.051
<br />:085
<br />.078
<br />.090;.103
<br />64
<br />.116
<br />.129
<br />.149
<br />.170
<br />.179
<br />.186
<br />86", :,018.035
<br />1.09
<br />.84
<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 />1.57
<br />023.046
<br />1,17
<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 />46° i
<br />.030 .060
<br />1.57
<br />.099
<br />.119
<br />.153
<br />.184
<br />.216
<br />.254
<br />.289
<br />:325
<br />.351
<br />.378
<br />.411
<br />.445
<br />600
<br />037.075
<br />1.811.68
<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 />55-
<br />,049.093
<br />Dec.LENGTH
<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 />/80°
<br />056:112
<br />.108
<br />.225
<br />.289
<br />.340
<br />.398
<br />.457
<br />.516
<br />.575
<br />.636
<br />.897
<br />.774
<br />.851
<br />` W.
<br />,057
<br />.135
<br />.204
<br />.273
<br />.343
<br />.412
<br />,483
<br />' .554
<br />.625
<br />.697
<br />.711
<br />.845
<br />.022
<br />1.01
<br />70°
<br />080.159
<br />008
<br />•240
<br />.321
<br />.403
<br />.485
<br />.568
<br />.652
<br />.735
<br />.819
<br />.908
<br />.004
<br />1,08
<br />1.17
<br />T6°
<br />.095.182
<br />:017
<br />.286
<br />.383
<br />.486
<br />.578
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18
<br />129.
<br />1.39
<br />80°
<br />.110.220
<br />.026
<br />.332
<br />.445
<br />.55
<br />.671
<br />.787
<br />.9031.02
<br />.190 .1
<br />1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.62
<br />88°
<br />.128.259
<br />.035
<br />.391
<br />.524
<br />.657
<br />.790
<br />.9261.06
<br />.238
<br />1.20
<br />1.34
<br />1.47
<br />1.62
<br />I.76
<br />1.91
<br />SO°
<br />.149.299
<br />.044
<br />.450
<br />.603
<br />.756
<br />.9101.07
<br />.296
<br />1.22
<br />1.38
<br />1.54
<br />1.70
<br />1.87
<br />2.03
<br />2.20
<br />98° ..174
<br />.064
<br />AM
<br />.522
<br />.706
<br />.985
<br />1.06
<br />1.25
<br />1.43
<br />1.82
<br />1.80
<br />1,99
<br />2.18
<br />2.38
<br />2.58
<br />100°
<br />.200
<br />.401
<br />.604
<br />AM
<br />1.01
<br />1.22
<br />1.43
<br />L84
<br />1.85
<br />2,06
<br />2.28
<br />2.50
<br />2.73
<br />2.96
<br />110°
<br />.288.5,41
<br />.8061
<br />.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 />1S0°
<br />.360
<br />,721
<br />1,08
<br />1
<br />1.45
<br />1.82
<br />2.I9
<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 />.125
<br />TABLE VIII, -CORRECTIONS FOR SUB -CHORDS AND I.ON4 CRORDB
<br />FOR SUB -CHORDS ADD '
<br />Excess
<br />LONG CHORDS
<br />of Are
<br />per
<br />D
<br />10
<br />20
<br />30
<br />40
<br />50
<br />60
<br />70
<br />80
<br />90
<br />100 ft,
<br />D
<br />200
<br />300
<br />400
<br />501
<br />4°
<br />.00
<br />.00
<br />.01
<br />.01
<br />.01
<br />..01
<br />.01
<br />.01
<br />.00
<br />.02
<br />1
<br />199.90
<br />299.97
<br />399.92
<br />499.
<br />6
<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
<br />299.88
<br />399.70
<br />499.
<br />8
<br />.01
<br />.02
<br />.02
<br />.03
<br />.03
<br />.03,_03
<br />.02
<br />.01
<br />.08
<br />8
<br />199.93
<br />299.73
<br />399.32
<br />498.
<br />10
<br />.01
<br />.02
<br />.03
<br />.04
<br />.0.5
<br />.05
<br />.05
<br />.04
<br />.02
<br />.13
<br />4
<br />199.88
<br />299.51
<br />398.78
<br />497.
<br />18
<br />.02
<br />.04
<br />.05
<br />.06
<br />.07
<br />.07
<br />, 07
<br />.05
<br />.03
<br />_188199.81
<br />299.24
<br />398.10
<br />496.
<br />1 4
<br />.02
<br />.05
<br />.07
<br />.08
<br />.09
<br />.10
<br />.09
<br />.07.04
<br />.25
<br />6199,
<br />73
<br />298, 90
<br />397.28
<br />494.
<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
<br />298.51
<br />396.28
<br />492.
<br />18
<br />.04
<br />.08
<br />.11
<br />.14
<br />.15
<br />.16
<br />.15
<br />.12
<br />.07
<br />.41
<br />8
<br />199.51
<br />298.05
<br />395.14
<br />490.
<br />80
<br />.05
<br />.10
<br />,14
<br />.17
<br />.19
<br />:20
<br />.18
<br />.15
<br />_00
<br />.51
<br />9
<br />199.38
<br />297.54
<br />393.86
<br />487.
<br />SS
<br />.06
<br />.12
<br />.17
<br />.21
<br />.23
<br />.24
<br />.22
<br />.18
<br />.16
<br />.62
<br />10
<br />199.24
<br />296.96
<br />392.42
<br />484.
<br />94
<br />.07
<br />.14
<br />.20
<br />.25
<br />.2S
<br />.28
<br />.26
<br />.21
<br />.12
<br />.74
<br />1S
<br />198.90
<br />295.63
<br />389.12
<br />478.
<br />26
<br />.09
<br />.17
<br />.24
<br />.29
<br />.32
<br />.33
<br />.31
<br />.25
<br />.15
<br />,86
<br />14
<br />198.51
<br />294.06385M
<br />470.
<br />98
<br />.10
<br />.19
<br />.27
<br />.34'.37
<br />.38
<br />.36
<br />.20
<br />.17
<br />1.00
<br />16
<br />198.05
<br />292.25
<br />380.76
<br />461'
<br />80
<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.
<br />84
<br />.13
<br />.25
<br />.36
<br />.44
<br />..49
<br />.50
<br />.47
<br />.38
<br />_22
<br />1.31
<br />80
<br />196.96
<br />287.94
<br />370.17
<br />441.
<br />84
<br />.15
<br />.28
<br />.40
<br />.50
<br />.55
<br />.57
<br />.58
<br />.43
<br />.25
<br />1.48
<br />SS
<br />196.32
<br />285.44
<br />364.08
<br />429.
<br />86
<br />.17
<br />.32
<br />.45
<br />.56
<br />.62
<br />.64
<br />_59
<br />.48
<br />,28
<br />1.66
<br />84
<br />195.63
<br />282.71
<br />357.43
<br />416-
<br />88
<br />.18
<br />.36
<br />.51
<br />.62
<br />.70
<br />.71
<br />.66
<br />.53
<br />.31
<br />1.86
<br />26
<br />194.87
<br />279.76
<br />350.30
<br />402.
<br />40
<br />.21
<br />.40
<br />sib
<br />-.69
<br />.77
<br />.79
<br />.73
<br />.59
<br />.35
<br />2.08
<br />SB
<br />194.06
<br />276.59
<br />342.60
<br />388.
<br />42
<br />.23.44
<br />.62
<br />.76
<br />.85
<br />:S7.
<br />.81
<br />.65
<br />.38
<br />2.28
<br />90
<br />193.18
<br />273.20
<br />334.61
<br />373.
<br />N
<br />.25
<br />.48
<br />.68
<br />.84
<br />.04
<br />.00
<br />.89
<br />,72
<br />.42
<br />2.50
<br />8S
<br />192.25
<br />269.61
<br />326.08
<br />357.
<br />46
<br />.27
<br />.52
<br />.75
<br />.92
<br />1.02
<br />1.05
<br />.98
<br />.78
<br />.46
<br />2.74
<br />84
<br />191.26
<br />265.81
<br />317. 12
<br />340.
<br />118
<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 />86
<br />190. 21261.80
<br />307.77
<br />323.
<br />50
<br />.32
<br />.62
<br />.89
<br />1.09
<br />1.21
<br />1.21
<br />1.15
<br />, 93
<br />.55
<br />3:24
<br />38
<br />189. 10
<br />257.60
<br />298.03
<br />3M,
<br />68
<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,
<br />64
<br />.38
<br />.73
<br />1.04
<br />1.28
<br />1,42
<br />1.48
<br />1.35
<br />1.09
<br />.84
<br />3.80
<br />42
<br />188.72
<br />248.63
<br />277.51
<br />269.
<br />56
<br />.41
<br />.78
<br />1.12
<br />1.38
<br />1.53
<br />1.57
<br />1.46
<br />1,17
<br />.69
<br />'4. 09
<br />44
<br />185.44
<br />243.87
<br />266.78
<br />250.
<br />58
<br />.44
<br />.84
<br />t . 20
<br />1.48
<br />1.65
<br />1.89
<br />1.57
<br />1.26
<br />.74
<br />4.40
<br />46
<br />184. 10
<br />239.03
<br />255.78
<br />231.
<br />60
<br />.47
<br />.01
<br />1
<br />1.29
<br />1.59
<br />1.76
<br />1.811.68
<br />1, 35
<br />.80
<br />4.72
<br />48
<br />182.71
<br />233:83
<br />244, 51
<br />212.
<br />NOTE. --When a chord of lase than 100 ft. is used the corrections given in the abo
<br />table should be added to the nominal length of chord to get the length which should
<br />used in order that the 100 ft. points will check with these obtained by using the stands
<br />100 ft. chord. Thus in locating a 14° curve by 25 ft. chords measure 25'.08 lox each chin
<br />Long chords are useful in passing obstacles,
<br />t. TAE'LE IX. -MIDDLE ORDINATES FOR RAILS IN FEET
<br />Dec.LENGTH
<br />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 2
<br />19
<br />022
<br />.020.016
<br />.013
<br />.011
<br />. 009
<br />008
<br />16°
<br />.856
<br />.318
<br />. 273
<br />.236
<br />200
<br />.170.1
<br />2
<br />045
<br />,038
<br />.034
<br />.029
<br />.025
<br />.021
<br />:017
<br />17
<br />378
<br />.383
<br />.290
<br />.252
<br />.213
<br />180.1
<br />8
<br />.037
<br />.058
<br />:051
<br />.044
<br />.037
<br />.031
<br />.026
<br />10
<br />.400
<br />.351
<br />. W6
<br />.265
<br />.225
<br />.190 .1
<br />4
<br />.089
<br />.079
<br />.069
<br />.080
<br />.050
<br />.042
<br />.035
<br />19
<br />.423
<br />.371
<br />.324
<br />.280
<br />.238
<br />.2 DI . 1
<br />5
<br />112
<br />.099
<br />.086
<br />.074
<br />.063
<br />.053
<br />.044
<br />20
<br />.445
<br />.392
<br />.341
<br />.296
<br />.250
<br />.212 . 1
<br />6
<br />.134
<br />.117
<br />.102
<br />.088
<br />.076
<br />.064
<br />, 052
<br />91
<br />.466
<br />.410
<br />.357
<br />.309
<br />.262
<br />.222 . 1
<br />7
<br />.156
<br />.137
<br />,120.
<br />104
<br />.088
<br />074.061
<br />99
<br />.487
<br />.430
<br />.375
<br />.325
<br />.275
<br />.233 . 1
<br />8
<br />.179
<br />.158
<br />,137
<br />.119
<br />.100
<br />.085
<br />.070
<br />99
<br />.509
<br />.450
<br />.390
<br />.338
<br />.287
<br />.243 .1'
<br />9
<br />.201
<br />.175
<br />.153
<br />.133
<br />,112
<br />, 095.078
<br />94
<br />5311
<br />469
<br />.408
<br />.354
<br />.299
<br />.253 .2
<br />10
<br />.223
<br />.196
<br />,171
<br />.148
<br />.125
<br />.106
<br />.087
<br />26
<br />.552
<br />.488
<br />.424.367
<br />.311
<br />.263 .2
<br />11
<br />.245
<br />.216
<br />,188
<br />.163
<br />.139
<br />.117.006
<br />26
<br />.573
<br />.5M
<br />.441
<br />.882
<br />.323
<br />.274 .2
<br />12
<br />.268
<br />.236
<br />.206
<br />.179
<br />.151
<br />.128.105
<br />87
<br />.594
<br />.524
<br />.457'
<br />.396
<br />.335
<br />.284 .2'.
<br />18
<br />.290.254
<br />.222.
<br />192
<br />.103
<br />.138
<br />113
<br />28
<br />.618
<br />- 545
<br />.475
<br />.411
<br />.348
<br />.294 .2
<br />14
<br />.312
<br />.275
<br />.239
<br />.207
<br />.175
<br />.148.122
<br />39
<br />.638
<br />.564
<br />.491
<br />.424
<br />.361
<br />.303.2
<br />18
<br />.334
<br />.295.257
<br />.223
<br />.188
<br />.159
<br />.131
<br />30
<br />.660
<br />.583
<br />.508.438
<br />.374
<br />.313 . 2
<br />
|