. 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 . 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 m
. 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 . 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. L CD is a diameter of the parabola, and the curve bisects CDinE- II. If from any points T, T, T, &c., on a tangent A F, lines to the curve parallel to the diameter, these lines T M, T M ,1 M &c., called tangent deflections, will be to each other as theBenares of the distances AT, A T>, A T\ &c. from the tangent ptint A. III. A line F D (fig. 37), drawn from the middle of a chord A Biothe curve, and parallel to the diameter, may be called the middle ordinate of that chord ; and if the secondary chords A E and B E he drawn,the middle ordinates of these chords, K G and /. H. are each equal to{ED. In like manner, if the chords A A, KE,EL, and LB hedrawn, their middle ordinates will be equal to \KG or \L H. \V. K tangent to the curve at the extremity of a middle ordinate,is parallel to the chord of that ordinate. Thus MF, tangent to thecur\ e at E, is parallel to A B. rs PARABOLIC CURVES. V. If any two tangents, as yl C and B C, be bisected in M and /ihe line il
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