. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . , as shov,n in thefigure, from B to Ai- Through B draw the planes B E E^, B A^Ei,and BEiFi, dividing the half-section into three quadrangular pyra-mids, having for their common vertex the point B, and for their basesthe planes A A^ E^E, E E^ F^ F, and A, B, F^ E,. For the areasof these bases we
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . , as shov,n in thefigure, from B to Ai- Through B draw the planes B E E^, B A^Ei,and BEiFi, dividing the half-section into three quadrangular pyra-mids, having for their common vertex the point B, and for their basesthe planes A A^ E^E, E E^ F^ F, and A, B, F^ E,. For the areasof these bases we have Areaof^^i^iJ^; = ^ E E, x{AL-]-A^E,) -|/(c-fc,), ^ =EFxEEi =^l^h » A, B, F, E, = ^ A, E^xdi + k ^i F^Xh, = ^d,c, -\- ibh,, and for the perpendiculars from the vertex B on these bases, producedwhen necessary, plane ; for if it is a plane, the descent from A to B will be to the descent from Ai toBi, as the distance out at the first station is to the distance out at the second sta-tion, that is, c — h:ci — hi = d:di. K we had c = 9, A = 6, fi = 12, «! = 8,d = 24, and di = 27, the formula would give 3 : 4 = 24 : 27 which shows that tholurface is not a plane. CENTRE AND SIDE HEIGHTS GIVEN Perpendicular on A A^^ E^ E — E G = d, E E, F, F =^ BG ^K A,B,F,E, = EE, -/. 10) A I Fig. Then (Tab. X. 52) the solidities of the three pyramids arc B-AA,E,E = :^d X ^-Mc + ci) = |/(c?c + c/c,), B-EE,F,F = I A X ^ ^^ =llbh, B-A,B,F,E, =kl X h{dic, + ^bh,) = U(^iCi+^6A,). Their mm, or tlic solidity of the half-section, is ll{dc-\- d,c^ + dc, + hh + hhK). (1) Next, suppose that the diagonal runs from A to B^. In this case,through B, draw the planes B, E, E, B, A E, and B^EF {not rep-resented in the figure), dividing the half-section again into threequadrangular pyramids, having for their common vertex the pointBi, and for their bases the planes A A, E^ E, EE^ F^ F, and A BFEFor the areas of these bases -vve have Area of ^ ^1, ^, ^ = U^^^: X {A E-{- A^E^) ^ ^l {^ + c^), EE^FiF
Size: 1522px × 1642px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
