. 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 . Solution. First Method. Let A B (fig. 33) be the required distanceMeasure a line A C along the bank, and take the angles B A C andACB. Then in the triangle ^1 C Cwe have one side and two angles to nnd A B. 1( A Cis of such a length that an angle A CB = ^D A C can helaid off to a point on the far
. 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 . Solution. First Method. Let A B (fig. 33) be the required distanceMeasure a line A C along the bank, and take the angles B A C andACB. Then in the triangle ^1 C Cwe have one side and two angles to nnd A B. 1( A Cis of such a length that an angle A CB = ^D A C can helaid off to a point on the farther side, we have ABC=^DAC=^ACB. Therefore, without calculation, AB = 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
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectrailroadengineering
