. 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 . first radius is taken, the shorter willbe the second radius. Example. Given R — and 7= 45°, to find i?2> if ^i is as-sumed = , and A D and B D> each 100. Here, by Table I.,Dj = 1° 30. Then A, —R = i / = 22° 30 sin. —2D,-= 19° 30 sin.
. 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 . first radius is taken, the shorter willbe the second radius. Example. Given R — and 7= 45°, to find i?2> if ^i is as-sumed = , and A D and B D> each 100. Here, by Table I.,Dj = 1° 30. Then A, —R = i / = 22° 30 sin. —2D,-= 19° 30 sin. Ri — R^ = .-. /?2 = 72i — = 82. Problem. To locate the second brcrch of a compound or re-versed curve from a station on the first branch. Solution. Let J. B (fig 32) be the first branch of a compound curve^and D its deflection angle, and let it be required to locate the secondbranch AB\ whose deflection angle is Z), from some station BunA B. MISCELLANEOUS PROBLEMS. 61 Let n be tfie number of stations from A to B, and n the number of sta-lions from A to any station B on the second branch. Represent by Vtht%ngle A B B, which it is necessary to lay off from the chord B A to strikeB>. Let the correspondinj:; ande A B B on the other curve be repre-. Fig. 32 rented by V. Then we have F+ F = 180° — BAB. But ifTT be the common tangent at A, we have TA B + T A B = nDJ^ n D = 180° — BAB. Therefore, V-{- V = nD -{• in the triangle ABB we have sin. V : sin. V= AB : A B : A B = n :n, nearly, and sin. V : sin. V = V : V, near- n ly. Therefore we have approximately F: F = n : n, or F = -, F. Substituting this value of F in the equation for F+ F, we haver+J V=nD-\-nD. Therefore, nF+n F= ?i(nZ) + nZ)), or n -\- n The same reasoning will apply to reversed curves, the only changebeing that in this case F+ V = nD — nD, and consequently V= ^ i»^ — ^D) n -{• n When in this formula nD becomes greater than n D, V becomesm
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
