. 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 . avation ismade, the same subdivisions are laid off from the base line upon theoottom of the excavation, and levels referred to the same bench-markare taken at all the angles. This method divides the excavation into a series of vertical prisms,generally truncated at top and bottom. The vertical e
. 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 . avation ismade, the same subdivisions are laid off from the base line upon theoottom of the excavation, and levels referred to the same bench-markare taken at all the angles. This method divides the excavation into a series of vertical prisms,generally truncated at top and bottom. The vertical edges of theseprisms are known, since they are the differences of the levels at thetop and bottom of the excavation. The horizontal section of theprisms is also knoAvn, because the parallelograms or triangles, intowhich the surface is divided, are always measured horizontally. Problem. Given the edges h, hi, and ho , to find the solidity • If the ground is divided into rectangles, as is generally done, and one side b«made 27 feet, or some multiple of 27 feet, the contents may be obtained at once inrubic yards, by merely omitting the factor 27 in the calculation. 94 EARTH-WORK. S of a veitical prism, whether truncated or not. whose horizontal section tio triangle of given area A. Fig. 48. Solution. Wlicn the prism is not truncated, we have h = h^ = k^The ordinary mle for the solidity of a prism gives, therefore, S = Ah■^ A X b {h + hi -{- hr,). When the prism is truncated, let ABG-F G H{i\g. 48) represent such a prism, truncated at the top. Throughthe lowest point A of the upper face draw a horizontal plane A D Ecutting off a pyramid, of which the base is the trapezoid B 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
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
