. A manual of the principles and practice of road-making : comprising the location, consruction, and improvement of roads (common, macadam, paved, plank, etc.) and railroads . ut the proper onewould be determined by a similar algebraic condition.* The choice would be indifferent, if BC —AC = BD —AD,orif AD —AC = BD —BC; for then, AD + BC = AC + BD. Two points, A and B, Fig. 72, being found which fulfil thiscondition, other points will be found at the intersection of arcs Fig. 72. C described from C and D as centres, with radii of which the dif-ferences are respectively equal to the given diffe
. A manual of the principles and practice of road-making : comprising the location, consruction, and improvement of roads (common, macadam, paved, plank, etc.) and railroads . ut the proper onewould be determined by a similar algebraic condition.* The choice would be indifferent, if BC —AC = BD —AD,orif AD —AC = BD —BC; for then, AD + BC = AC + BD. Two points, A and B, Fig. 72, being found which fulfil thiscondition, other points will be found at the intersection of arcs Fig. 72. C described from C and D as centres, with radii of which the dif-ferences are respectively equal to the given difference AD—AC,or BD — BC. If a great number of these points were found,the polygonal line ABEFG would become an hyperbola, pos-sessing the remarkable property of so dividing the transporta-tion, that C should receive all the excavation from one side ofit, and D all from the other. Suppose that embankments at C and D, Fig. 73, are to bemade from a mass of earth mnop, just equal to them in minimum of expense will be obtained by finding the curveAG, which shall divide the area rmiop into two parts equal to * Gayffier, p. 134. REMOVAL OF THE EARTH. 153. E D those required at C and D, and which shall also possess theproperties enunciated in the preceding paragraph. If the line EFdrawn perpendicular to CD, from its middle E, does not cut offa sufficient portion of the area to supply D, this shows that thecurve will be concave towards C. Then divide geometricallythe area mnop in the required proportion, by a straight line rs,inclined approximately as the curve would be, and adopt itsmiddle point as a point of the curve. Then will BD — BC bethe constant difference of radii required to find the other pointsof the dividing curve. If the amount of embankment, which might be deposited atC and at D, was indefinite, and the only requirement was itsmost economical removal from mnop, then the perpendicular EFdrawn from the middle of CD, would divide the area into twoport
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Keywords: ., bookcentury1800, bookdecade1850, booksubjectrailroa, bookyear1853
