. Un manuel des principes et de la pratique de la construction de routes : comprenant l'emplacement, la conruction, et l'amélioration des routes (communes, macadam, pavés, planches, etc.) et des chemins de fer . à GH/?W, shouldbe transporté à EFO?z, il s'ensuit que le rembrembmentGHZm doit être obtenu d'une partie de l'excavation au-delà de la ligne, Et que les chemins des deux volumescroisseront l'un l'autre, ce qui est donc une désavantageusement disposition, car il augmente les distances parcourues.toute telle traversée des chemins des volumes trans-ferred, soit horizontalement ou verticalement, peut être généralesévitée par con

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. 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 . to GH/?w, shouldbe transported to EFo?z, it follows that the embankmentGHZm must be obtained from a portion of the excavationbeyond the line ik, and that the paths of the two volumeswill cross each other, which is therefore a disadvantageousdisposition, since it increases the distances passed over.Any such crossing of the paths of the volumes trans-ferred, either horizontally or vertically, may be generallyavoided by conceiving the solids of excavation and em-bankment to be intersected by parallel planes, such asDCHG, ik, Im, &c., and by transferring the partial solidsin the manner indicated by the boundaries marked out bythese planes. In many cases the most economical distribution of the earth, can be determined only bya special construction.Thus in the figure, sup-pose that earth is to betaken from A and B toform embankments at Cand D; it is required toknow which should formthe embankment at C, andwhich that at D, To bringthe case within the ap-plication of the principle Fig. 71.. 152 THE CONSTRUCTION OF ROADS. just enunciated, conceive the triangle ABD to turn around theline AB as on a hinge, so that the point D comes to occupy apoint D, symmetrical with its former position. It is now evident that to avoid the crossing of the paths, theearth from A must be taken to D, {i. e. D) and the earth fromB to C ; AD + BC being less than AC + BD. If the pointD had fallen beyond C the reverse would have been proper.If the point D had fallen within the triangle ABC, there wouldbe no crossing in either mode of transport, but 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

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