. 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 . Fig. 34. Second Method. Lay off ^ C (fig. 34) perpendicular to A B. Meas-ure xi C, and at Clay off CZ) perpendicular to the direction CB, andmeeting the line of /I B in D. Measure A D. Then the trianglesA CD and ABC are similar, and give AD : A C =- A C : AB. Therefore, AB ^ -^ . If from C, dete
. 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 . Fig. 34. Second Method. Lay off ^ C (fig. 34) perpendicular to A B. Meas-ure xi C, and at Clay off CZ) perpendicular to the direction CB, andmeeting the line of /I B in D. Measure A D. Then the trianglesA CD and ABC are similar, and give AD : A C =- A C : AB. Therefore, AB ^ -^ . If from C, determined as before, the angle A C B be laid off equalto yl CB, we have, without calculation, A B = AB. Third Method. Measure a line A D (fig. 35) in an oblique directionfrom the bank, and fix its middle point C From any convenientpoint E in the line of A B, measure the distance E C, and prodiue 64 MISCELLANEOUS PR0BLE3IS. E C until CF= Ea Then, since the triangles A CE and D CFare similar by construction, we see that DF is parallel to E B. Find Fig. 35. now a point G, that shall be at the same time in the line of CB andof D F, and measure G D. Then the triangles ABC and D G C sreequal, and G D is equal to the required distance A B. As the object of drawing E Fis to obtain a line parallel to A B, thisline may be dispensed with, if by any other means a line GFhe drawnthrough D parallel to AB. A point G being found on this parallel inthe line of CB, we have, as before, GD = AB. PARABOLIC CURVES. 65 CHAPTER II. PARABOLIC I. — Locating Parabolic Curves. 84. Let AEB (fig. 36) be a parabola, A Cand B C its tangents,iiid .1 B the chord uniting the tangent points. Bisect A B in D, andoin CD. Then, according to Analytical Geometry, — Fig. 36.
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
