. 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 . on -4 C produced n partsequal to those on A C, and the proper deflections will be, as before, amultiplied by the square of the number of parts from A. But an * Since C D is drawn to the middle of the base of the triangle ^ iS C, we have, hjRwmetrj-, C D^ = ^ (A C^ + B C^) — A D-. LOCATING PARABO
. 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 . on -4 C produced n partsequal to those on A C, and the proper deflections will be, as before, amultiplied by the square of the number of parts from A. But an * Since C D is drawn to the middle of the base of the triangle ^ iS C, we have, hjRwmetrj-, C D^ = ^ (A C^ + B C^) — A D-. LOCATING PARABOLIC CURVES. 67 PaMcr way generally of finding points beyond E is to divide the sec-ond tangent B Cinto equal parts, and proceed as in the case of ^ the number of parts on B C be made the same as on A (7, it is obvi-ous that the deflections from both tangents will be of the same lengthfor corresponding points. The angles to be laid off from B C must, Df course, be equal to BCD. The points or stations thus found, though corresponding to equaldistances on the tangents, are not themselves equidistant. The lengthof the curve is obtained by actual measurement. 86. Problem. Given the tangents A C and B C, equal or unequal,[fig. 37,) and the chord A B, to lay out a parabola by middle Solution. Bisect A B in D, draw CD, and its middle point E willoe a point on the curve (§ 84, L). D E is the first middle oi^.nate,and its length may be measured or calculated. To the point E drawt> chords A E and BE, lay off the second middle ordinates G K andHL, each equal to \DE{^ 84, III), and K and L are points on thecurve. Draw the chords A K, K E, E L, and L B, and lay oft thirdmiddle ordinates, each equal to one fourth the second middle ordi-nates, and four additional points on the curve will be this process, until a sufficient number of points is obtained 87. Prol>leiIl. To draiv a tangent to a parabola at any station. Solution. I. If the curve has
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
