20

THE PRINCIPLES OF BRIDGES.

TRACT 2.

corollaries to the 3d prop, will equally apply to the festoonor lower figure hanging in equilibrio.

This is a most useful principle in all cases of equilibriums,especially to the mere practical mechanist, and enables himin an experimental way to resolve problems, which the bestmathematicians have found it no easy matter to effect by merecomputation. For thus, in a simple and easy way he ob-tains the shape of an equilibrated arch or bridge; and thusalso he readily obtains the positions of the rafters in the frameof an equilibrated curb or mansard roof; a single instanceof which may serve to show the extent and uses to whichit may be applied. Thus, if it should be required to make acurb frame roof having a given widthae, and consisting of four rafters ab,bc, cd, de, which shall either beequal or in any given proportion toeach other. There can bc no doubtbut that the best form of the roof will be that which- putsall its parts in ,equilibrio, so that there may be no un-balanced parts, which may require the aid of ties or stays,to keep the frame in its position. Here the mechanic hasnothing to do, but to take four like but small pieces, thatare either equal or in the same given proportions as thoseproposed, and connect them loosely together at the jointsA, b, e, d, e, by pins or strings, so as to be freely move-able about them; then suspend this y

from two pins, a, e f fixed ina horizontal line, and the chainof the pieces will arrange itself insuch a festoon or form, abode, thatall its parts will come to rest inequilibrio. Then, by inverting thefigure, it will exhibit the form andframe of a curb roof a£y$e, which will also be in equilibrio,the thrusts of the pieces now balancing each other, in thesame manner as was done by the mutual pulls or tensions