. 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 . 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. Solution. Bisect A B in D, draw CD, and bisect it in E. Dividethe tangents A Cand B C, the half-chords A D and D B, and the lineCE, into the same number of eq
. 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 . 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. Solution. Bisect A B in D, draw CD, and bisect it in E. Dividethe tangents A Cand B C, the half-chords A D and D B, and the lineCE, into the same number of equal parts ; five, for example. Thenthe intersection M of A a and F G will be a point on the curve. ForFM = I Ca, and Ca = i CE. Therefore. FM= 55 CE, which isthe proper deflection from the tangent atFto the curve (§ ). Inlike manner, the intersection N of Ab and IIK may be shown to be apoint on the curve, and the same is true of all the similar intersectionsindicated in the figure. If the line DE were also divided into five equal parts, the line A awould be intersected in il/on the curve by a line drawn from B througha, the line A b would be intersected in iVon the cur\e by a line drawn 70 PARABOLIC CURVES. from B through 6, and in general any two lines, drawn from A and Bthrough two points on CD equally distant from the extremities CandD, will intei-sect on the curve. To show this for any point, as x)/, it issufficient to sh
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
