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/ � 1
<br />+' TA13LE'V — Middle` Ordinate; -for Rails' i i
<br />1)D
<br />of
<br />Curve
<br />' 'r L1;i\OT OF'R�1'L� ` •.
<br />,
<br />- --
<br />r
<br />Deg
<br />of
<br />Cane
<br />. 'q LENGTH'OF
<br />- LENGTH OF RAILS
<br />- - -
<br />92 80J !28-- 26 24 22 '20
<br />82
<br />FO`
<br />�,
<br />i
<br />�4II
<br />22
<br />120
<br />a
<br />AV
<br />*022
<br />'02Q
<br />017
<br />01,
<br />013
<br />011
<br />009
<br />*116°
<br />456
<br />313
<br />'279
<br />236
<br />200
<br />170
<br />139
<br />2
<br />045
<br />.03
<br />0641
<br />030
<br />025
<br />021
<br />017
<br />17
<br />378
<br />333
<br />290'
<br />202
<br />219
<br />'180
<br />148
<br />3
<br />03,4
<br />Q09
<br />031
<br />044
<br />038
<br />032
<br />026
<br />+18
<br />400
<br />Sal
<br />306
<br />26a
<br />225
<br />'190
<br />156
<br />4
<br />1,
<br />@Be
<br />'a
<br />068
<br />059
<br />050
<br />042
<br />095
<br />'044
<br />19
<br />1423
<br />144o
<br />3,1
<br />324
<br />280
<br />238
<br />201
<br />165
<br />5
<br />8 '
<br />112
<br />134
<br />098
<br />11
<br />086
<br />0'
<br />Oat
<br />063
<br />070
<br />051[
<br />'08S
<br />052
<br />1 20
<br />21
<br />466
<br />392
<br />410
<br />1341
<br />35,
<br />296
<br />309
<br />250
<br />262
<br />212
<br />222
<br />174
<br />182
<br />I7 r
<br />l,r
<br />147
<br />1 0'
<br />103
<br />089
<br />074
<br />061
<br />`1 22
<br />`48,
<br />430
<br />375
<br />32o
<br />275
<br />233
<br />101
<br />r 8�
<br />179
<br />15,
<br />71
<br />119
<br />100
<br />084
<br />'070
<br />'21
<br />' 009
<br />40'
<br />390
<br />338
<br />287
<br />243
<br />199
<br />9
<br />201
<br />l i7
<br />1 ,
<br />133
<br />113'
<br />"095
<br />'o,8
<br />' 24
<br />a31
<br />4691
<br />1408
<br />354
<br />299
<br />253
<br />208
<br />10a'
<br />-231
<br />196`
<br />1-11
<br />147
<br />126'
<br />-106
<br />1087
<br />l25
<br />1,a2
<br />466
<br />424
<br />367
<br />311
<br />263
<br />216
<br />lilt
<br />245,
<br />21;
<br />188
<br />162
<br />133
<br />116
<br />090
<br />26
<br />bi3
<br />506
<br />441
<br />382
<br />323
<br />'274
<br />225
<br />12
<br />268,
<br />235
<br />20l
<br />177
<br />151
<br />'127
<br />105
<br />-27
<br />594
<br />524
<br />`457
<br />396
<br />333
<br />1284
<br />233
<br />1 i f
<br />290
<br />2a4
<br />222
<br />192
<br />1f,4
<br />' 138
<br />113
<br />--28
<br />'619
<br />540
<br />14%
<br />411
<br />348
<br />294
<br />242
<br />)14
<br />312;
<br />2,0
<br />'30'
<br />207
<br />17o
<br />148
<br />122
<br />-29
<br />643
<br />564'
<br />491
<br />424
<br />361
<br />303
<br />200-
<br />15
<br />434
<br />'290
<br />207,k223
<br />188
<br />159
<br />131
<br />30
<br />'660
<br />583
<br />608
<br />438
<br />374
<br />313
<br />2a9
<br />TI i
<br />CURVE � FOR11ULrE It .1
<br />T=12 tan I I - a[ , 1,t'
<br />.R=T cot ii Chord def—ehord2 Z
<br />;,Tf 50!tln'4giI' c i�—, r� ! _ N ,. _ i
<br />,
<br />t
<br />bin, 1) ,` - 'R=` ^'50 I di^^s �'is , It
<br />CSin - l ll = 0' i e t,�; t' ' �a nl D- - r2 t,No , chords = $ I ;
<br />hu 1 , a + ,D
<br />'D, )0 tin � ,l �E , R es�sec iIl-
<br />Sin U, -,- , ; " 1
<br />t - i, r ^ T E`= T t"n, r `IT Tan 2def'—, y chord defy
<br />"The square bflany distance, divided by'twice thekradlns, will equal the
<br />distance fromntangent oto curie„ very; ncai ll s: fG ' , t; _ t b „ , :,
<br />Table'I1'l contains Tangents and Exteii141s to a 49cnrve 1 Tan 'and Ext " 1
<br />to"anj, other radius may be-found,,nearly enough; by"dmding the Tan or
<br />Ext 0uposito7tbegii eu centr'al -angle by the ure e
<br />given degree lof c'
<br />To find 'De',, of Curve;' havmg7the'Centfal. Angle andiTangent Divide
<br />Tan opposite the riven Central Aug1(,-by4 the-glien Tangent ;
<br />To find Deg of Cuive? having1the`Cential Angle'and'F,,ternal Divide
<br />Est opposite the given Central Augle,by the gmeu{Evteludl- i
<br />To find Nat Tau and' Nat Ev -See i for in) angle b} Table IV Tan `
<br />or Ext of tivice the, given dnglc divided by'tlle radius -of a 102curve will be r
<br />the, Nat` Tau or Nat Ex 'Sec 1 r , ! t''b26 t f C
<br />`l'u find angle (foi a given distance audcdeflectiou'n
<br />Rule 1' Alultlply the given distance by to1745 (def for 10 for 1' ft), and
<br />divide gri cu deflection by the product a' P r,, I i 1
<br />Rule 2 Multiply givcuTdeflection by, 57 3, and divide the, product by,
<br />the giienidistance
<br />To find,d'efie'cfton for a gneu angle and distance--llultlply the angle
<br />by ' 01745, and tho'product by,the" diisCdnce
<br />Ri6HT ANGLE Tx1ANGLFo Square the' altitude, divide b).tvvlce the base
<br />Add quotient to base for liyf)othcnuserl ; r ' I
<br />Given, Base 100, Alt 10 - 102 -_200= 3,:r 100-}- 5=100 5 hyp ;
<br />' Given Hyp 100, Alt 25 r 259 200=0' 125 100-3 125=96 875=Base l
<br />ii , E1ioi in first"eaample,y 001., 1n last, ,1045
<br />To find Tons of Rail in one mile of track inultiply height per yard
<br />by 11, and divide by 7
<br />WGCa
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