. 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 . s must be parallel to CD, and the dis-tances on the new tangent must be equal to 7iV or iViV, whichmay be measured. 89. Problem. Giveii the tangents A C and B C, equal or uneqiml,[Jiy 38,) to lay out a parabola by bisecting tangents. Solution. Bisect A C and B C in D and F, join D F, and find £,
. 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 . s must be parallel to CD, and the dis-tances on the new tangent must be equal to 7iV or iViV, whichmay be measured. 89. Problem. Giveii the tangents A C and B C, equal or uneqiml,[Jiy 38,) to lay out a parabola by bisecting tangents. Solution. Bisect A C and B C in D and F, join D F, and find £, themiddle point of D F. E will be a point on the curve (§ 84, V.). Wehave now two pairs of what may be called second tangents, A D andI) E, and E F and F B. Bisect A Din G and D E in H, join G H,and its middle point ilf will be a point on the curve. Bisect £ F andF Bin K and L, join KL, and its middle point iVwill be a point onthe curve. We have now four pairs of third tangents, A G and G M,M H and U E, E K and KN, and NL and L B. Bisect each pair inturn, join the points of bisection, and the middle points of the joininj; LOCATING PARABOLIC CURVES. 69 lines will be four new points, il/, M, iV, and N. The same methcx?may be continued, until a sufficient number of points is obtained. Fig. 90. Problem. Given the tangents A C and B C, equal or unequalHg. 39,) and the chord A B, to lay out a parabola by intersections. Fig. 39
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
