SECT. i.

OF THE ARCHES.

67

GENERAL SCHOLIUM.

In the foregoing propositions have been delivered thechief vai-iety of ways for constructing the arches of bridges,so as they may be in equilibrio or balanced in themselves.There are three of these different methods; first; that whichis derived from the consideration of the equilibrium producedby the mutual thrusts, weights and pressures of the archstones, supposing them prevented from sliding on each otherat the oblique joints, either by their roughness and friction,or by the cement, or stone locks, or iron bars let into everyadjacent pair of stones ; which give the arch the effect ofone compacted frame, pressed on vertically by the weightof the superincumbent load of Wall above it: which seemsto be the true and genuine way of considering the action ofthat load on the arcln

The second method; is that in which the balanced arch iscomputed on the supposition that the arch stones have theirbutting sides perfectly smooth, and at free liberty to slide oneach Other. A method which is but little insisted on, as itis founded on a supposition which is neither in nature norart, and-which can never take place in any real constructionof an arch.

The third method, is that which has for its principle thecatenarian or festoon arch, formed by the suspension of aslack chain or cord, by its two ends, and afterwards invert-ed. This idea it seems was first proposed by Dr. Hooke,near the latter part of the 17th century, when the Newtonianmathematics prepared the way to true mechanical science.This is a strictly just and useful principle, and may be mosteasily extended to every case that can happen in practice.At first indeed the idea had nothing more in view than thebalancing of the single or thin arch, formed by the voussoirsonly, as the catenarian curve, formed by a simple chain orcord, can aim at nothing further than the balancing of thatsimple string of arch stones, without any other wall to fill