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TA741.} X I--hllddle Ordinates for Rails
<br />lleg
<br />of
<br />CU,N°
<br />LE\(ilii OF RAILIIS''
<br />ljeg
<br />of
<br />Cuirve
<br />1 LENGTH OFRAMSRAILS
<br />92 30
<br />`_'S I 26 ,
<br />1
<br />24,1
<br />22 20
<br />32, 30
<br />� r
<br />28
<br />126-1
<br />24
<br />I
<br />1,1 22
<br />120
<br />10
<br />022' 020
<br />017
<br />Olo
<br />013
<br />"011 '009
<br />16-
<br />356 313'
<br />273
<br />298
<br />200
<br />170
<br />139
<br />; ti ,
<br />045 039
<br />034
<br />(130
<br />025
<br />021 017
<br />' 17,
<br />376 333
<br />290
<br />202
<br />218
<br />1180
<br />148
<br />3
<br />037' 059
<br />0 1
<br />044
<br />OH
<br />032 026
<br />Ib
<br />400 351°
<br />306
<br />265
<br />225
<br />190
<br />156
<br />4
<br />0991 079
<br />063
<br />059
<br />0-)0`042
<br />031
<br />19
<br />X423 3711
<br />'324
<br />280
<br />299
<br />201
<br />165
<br />S
<br />112 098
<br />09-
<br />074
<br />063,
<br />053 1044
<br />- 20
<br />44,) 392
<br />341
<br />296
<br />200
<br />212
<br />174
<br />6
<br />174 118
<br />103,
<br />095
<br />075
<br />Ong 052
<br />21 ,
<br />46b 410
<br />307
<br />309
<br />262
<br />222
<br />182
<br />7,
<br />l+6 137
<br />120,
<br />101
<br />Ob4
<br />U 4 '061
<br />a,2
<br />48, 430
<br />3 a
<br />320
<br />27a
<br />299
<br />191
<br />S ,
<br />179 167
<br />137
<br />116
<br />100
<br />084 '0,0
<br />21
<br />,)09 1-,0
<br />990
<br />318
<br />287
<br />243
<br />199
<br />9
<br />201 177
<br />14,
<br />193
<br />113,
<br />09, 0,8
<br />24
<br />091 469
<br />406
<br />354
<br />299
<br />203
<br />209
<br />10
<br />223 19G
<br />1 1,
<br />147
<br />12p,
<br />105OG,-
<br />25
<br />,)02 436
<br />424
<br />3G7
<br />311
<br />263
<br />216
<br />11
<br />241 216
<br />155
<br />162
<br />131,
<br />116 '0`14
<br />26
<br />,)73 ,)06
<br />14t
<br />942
<br />323
<br />27,
<br />225
<br />113
<br />26b 2 a
<br />20a
<br />177,
<br />lot
<br />l2, '10Y
<br />27
<br />o94 324;
<br />41,7
<br />396
<br />335
<br />1284
<br />233
<br />11
<br />2901 254
<br />222
<br />192
<br />169
<br />119 '113
<br />'S 2S
<br />61b a43
<br />4 ,)
<br />411
<br />348
<br />1294
<br />242
<br />14'
<br />3121 2,i
<br />3'9t
<br />207
<br />1-5
<br />148 '122
<br />29
<br />635 ab4,
<br />49t
<br />IN
<br />961
<br />303
<br />2550
<br />115
<br />334' 2ns
<br />21,)7
<br />223
<br />188
<br />f10 131
<br />30
<br />660 049
<br />508
<br />Y 36,
<br />3-4
<br />313
<br />259
<br />'
<br />1. •• 0 r Cnr
<br />.d ,The square of ;any distance divided by 1twlce�the radius, Hill equal the
<br />distance from, tangent ito'curve,,,icry ncaily ; T
<br />Table IV ,contains Tangcnt� and Estelnals to a 1°curve t Tan aid`Ft {`
<br />I`0 3,n} other -radius may be' found, ,ueailfl enough,' b} dividing thel Tan or U
<br />Yt opposite the', given central angle by the 4grven degree lof curve
<br />I!i 1 fi To find Deg of Curve, liu_vin9 ills -Central An gleiand'TAngent Divide 11
<br />�I'Tan opposite the given. u
<br />Central An le Divide W the, -given Tangent 1 i „
<br />11 To find Deg' of Curve, hang $ie,Central Angle,aud External l
<br />Eat opposite the given Central Angle b} the gii en (Eeternal
<br />To find Nat Tan and' Nat Fv,Sec �foi, any jangle by Table, IN ',Tan
<br />4 or Ext of ,twice the given uigle divided by the radius' of a 10 curve will be
<br />i l+ the -Nat Tau or,' Nat ,RFa aeci a I i E�w l 1.
<br />To find angle for a given distance Ind deflection i , u
<br />1) Ynla 1 117
<br />1t1
<br />ply the gn en' distance by ;01745 (def for' 10 for l ,ft ), and �3
<br />3dlvlde ;u en deflection b} the product
<br />I Rule 2 Miltipl}' given'deticution by 57 3, and divide the product by
<br />'the gii en dlst971ce ,rr I "'' , f '`" '" f + '
<br />qqTo find dpflectiol fol a gii on angle and, distance Multiply the angle
<br />h
<br />i' y 01795, 2nd the product by the dist ince e ' i
<br />i 1 Risiir AvGLE TR14ivGLES ' Square tlyc dtizude, dnlide by toric„ the base
<br />` ` 1 tAdd quotient to base forrhypothenuse-
<br />j' Given, Base 100 Alt 10 102-200= 5 1,„100-}- 5=100 5 b3p
<br />t1J Given Hyp 100 Alt 25,252-200=:,'l25' 100-5 125=96 875=Base A
<br />Ei ror in first ex ample, 002,, m last, � 045
<br />To find Tons of Rail to one mile of'tiac6 multiply weight per lard
<br />kby 11, -ind hide by 7 ' r
<br />J
<br />,I
<br />P. 11) L I
<br />ttau
<br />-+
<br />T
<br />1
<br />I"='1
<br />Chord def `=
<br />1 t'+
<br />chord 2
<br />1
<br />T -
<br />5n ,SII
<br />`1�
<br />hot, ` �1 r
<br />f
<br />;
<br />RS0
<br />'
<br />oD 1,I
<br />4-+'R'
<br />; ti ,
<br />a
<br />N
<br />�Sm
<br />D = 50 ! n`
<br />l,�
<br />1
<br />; Stn ll
<br />p -No chords=
<br />i
<br />V 1
<br />Stn D = 50 tan I z+I
<br />l
<br />j, ,
<br />E =
<br />T t9u
<br />�I fY +
<br />Tan def ='g chord def
<br />1. •• 0 r Cnr
<br />.d ,The square of ;any distance divided by 1twlce�the radius, Hill equal the
<br />distance from, tangent ito'curve,,,icry ncaily ; T
<br />Table IV ,contains Tangcnt� and Estelnals to a 1°curve t Tan aid`Ft {`
<br />I`0 3,n} other -radius may be' found, ,ueailfl enough,' b} dividing thel Tan or U
<br />Yt opposite the', given central angle by the 4grven degree lof curve
<br />I!i 1 fi To find Deg of Curve, liu_vin9 ills -Central An gleiand'TAngent Divide 11
<br />�I'Tan opposite the given. u
<br />Central An le Divide W the, -given Tangent 1 i „
<br />11 To find Deg' of Curve, hang $ie,Central Angle,aud External l
<br />Eat opposite the given Central Angle b} the gii en (Eeternal
<br />To find Nat Tan and' Nat Fv,Sec �foi, any jangle by Table, IN ',Tan
<br />4 or Ext of ,twice the given uigle divided by the radius' of a 10 curve will be
<br />i l+ the -Nat Tau or,' Nat ,RFa aeci a I i E�w l 1.
<br />To find angle for a given distance Ind deflection i , u
<br />1) Ynla 1 117
<br />1t1
<br />ply the gn en' distance by ;01745 (def for' 10 for l ,ft ), and �3
<br />3dlvlde ;u en deflection b} the product
<br />I Rule 2 Miltipl}' given'deticution by 57 3, and divide the product by
<br />'the gii en dlst971ce ,rr I "'' , f '`" '" f + '
<br />qqTo find dpflectiol fol a gii on angle and, distance Multiply the angle
<br />h
<br />i' y 01795, 2nd the product by the dist ince e ' i
<br />i 1 Risiir AvGLE TR14ivGLES ' Square tlyc dtizude, dnlide by toric„ the base
<br />` ` 1 tAdd quotient to base forrhypothenuse-
<br />j' Given, Base 100 Alt 10 102-200= 5 1,„100-}- 5=100 5 b3p
<br />t1J Given Hyp 100 Alt 25,252-200=:,'l25' 100-5 125=96 875=Base A
<br />Ei ror in first ex ample, 002,, m last, � 045
<br />To find Tons of Rail to one mile of'tiac6 multiply weight per lard
<br />kby 11, -ind hide by 7 ' r
<br />a
<br />J
<br />a
<br />
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