. 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 . h 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
. 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 . h 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/F, joining the points of bisection, will be a new tangent, itamiddle point E being the point of tangency. 85. I*rol>leill. Given the tangents A C and B C, equal or unequal^{Jig. 36,) and the chord A B, to lay out a parabola hy tangent deflections. Fig. 36. Soluticm. Bisect A B in A and measure CD and the angle A CD^or calculate CD* and A CD from the original data. Divide the tan-gent A C into any number n of equal parts, and call the deflectionJM/for the first point a. Then {§ 84, II.) the deflection for the sec-ond point will be T M = 4 a, for the third point T M = 9 a, and60 on to the nth point or C, where it will be n^a. But the deflectionat this last point \sGE = ^CD{^ 84, I). Therefore, n^ a = C CE a = n* Having thus found a, we have also the succeeding deflections 4 a, 9 a, &c. Then laying ofl^ at T, T, &c. the angles A TM, A T M>,&c. each equal to A CD, and measuring down the proper deflections,just found, the points M,
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
