. 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 . D E C, andthe altitude a perpendicular let fall from A on D E. Represent thisperpendicular by p, and we have (Tab, X. 52) the solidity of the pyra-mid = ^px BDEC ==\pxDExh{BD^ C E) = ^pXDE X ^ {BD -\- CE) = A X h [BD + CE), since hp X DE= A D E = A. But I {BD -\- CE) is the mean height of the ve
. 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 . D E C, andthe altitude a perpendicular let fall from A on D E. Represent thisperpendicular by p, and we have (Tab, X. 52) the solidity of the pyra-mid = ^px BDEC ==\pxDExh{BD^ C E) = ^pXDE X ^ {BD -\- CE) = A X h [BD + CE), since hp X DE= A D E = A. But I {BD -\- CE) is the mean height of the verti-cal edges of the truncated portion, the height at A being 0. Hencethe formula already found for a prism not truncated, will apply to theportion above the plane ^ Z> £, as well as to that below. The samereasoning would apply, if the lower end also were truncated. Hence,for the solidity of the Avhole prism, whether truncated or not, we have S=AXhih + h,+ h.). 116. Problem. Given the edges h, h^, hn, and A3, to Ji7id tUsolidity S of a vertical prism, ivheiher truncated or not, whose horizoUatsection is a parallelogram, of given area A. BORROW-PITS. 9fi Solution. Let B H (fig. 49) represent such a prism, whether trimcated or not, and let the plane BFHD diviie it into two triangular Fig. 49. prisms AFH and CFH. The horizontal section of each of theseprisms will be ^ A, and if A, h^, h^, and h^ represent the edges to whichthey are attached in the figure, we have for their solidity (§ 115)A FH =^A X k i^i-^ h + h). and CFH = ^A X ^ (^i + h +^g). Therefore, the whole prism will have for its solidity S = ^ A X^ {h + 2/tji + 112 + 2 A3). Let the whole prism be again divided b}the plane AE G C into two triangular prisms BEG and D E GThen we have for these prisms, B E G = hA X ^ {^^ + ^h + h)^and D E G = h A X J (^ + ^2 + ^3)5 and for the whole prism, S —^A X ^ (2 A + /ij + 2 /etter
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
