22

THE PRINCIPLES OF BRIDGES.

TRACT I.

point k, &c. Let a very fine and thin, but strong line, suchas a fine siJkencord, or abricklayer’s working line, or perhapsa very fine and slender chain of small links, be suspendedfrom the extreme points a and m, and of such a length, thatits middle point may hang at the point d, or a little below it.Divide the given span or width am into a number of equalparts, the more the better, as at the points 1,2, 3, 4, 5, &c;from which draw vertical lines, cutting the festoon chainor cord in the corresponding points 1, 2, 3, 4, 5, &c. Thentake short pieces of another chain, and suspend them bythese points of the festoon 1, 2, 3, &c, as represented by thedotted verticals in the lower part of the figure. This willsomewhat alter the form of the curve. If now the new curveshould correspond with the point d, and all the bottoms ofthe vertical pieces of appended chain also coincide with thegiven line of roadway Ik n, the business is done. But if boththose coincidences do not take place, then alterations mustbe made, by trials and by judgment, in lengthening or short-ening either the festoon A(/m, or the appended vertical piecesof chain, or in both, till such time as those coincidences areaccomplished, namely, the bottom of the arch with the pointd, and the bottom of the appended pieces with the boundaryIk 7i. Then re-invert the whole figure, or otherwise trace outthe upper curve adm exactly like or the same as the lowerone a</m, and there will be obtained an arch sustaining thewall above in perfect equilibrium.

Scholium .—Thus then, as explained by professor Robison,we have an easy and practical way, by which any common in-telligent workman may readily construct for himself the formof a real balanced arch, to any proposed design for a bridge.In this method, the thinner and lighter the festoon line is, soas to bear but a small proportion to the weight of the ap-pended pieces of chain, so much the more exact will theconclusion be obtained, when the superincumbent wall is ofuniform weight of masonry. But as the festoon line repre-sents the line of voussoirs or arcl> stones, in the constructed