ECT. 2.

OF THE ARCHES.

23

arch, if these only are solid, and the rest of the wall or matterabove them be looser and lighter, then there ought to be anequality of proportion between the weights of the festoon,chain and the string or rib of arch stones, and between thesuperior wall and the appended pieces of chain ; a circum-stance of equality to be obtained by mutual accommodations' and calculations adapted to the real circumstances of thecase.

The chief objection to the curve found in this way is awant of elegance, and perhaps too of convenience and ofeconomy, because it does not spring or rise at right anglesto the horizontal line, but at a much smaller angle; andwhich indeed is the case with all curves of equilibration.However, this is a circumstance which can be very safelyand profitably remedied; for in the part of the flanks nearthe piers, it may be cut away to hollow the arch out to anyform we please, so as, for instance, to resemble the ellipticalarch, which is one of the most graceful of all; because themasonry is so solid and strong in that part. And this will benot only more agreeable to the eye, but will also leave moreroom for water and boats to pass, and will be a saving in theexpence of masonry. To accomplish this end with more re-gularity and method, instead of dividing the horizontal lineinto equal parts at the points 1, 2, 3, &c, if the festoon chainitself be so divided, viz, into equal parts, and the pieces ofchain be appended at these, in the manner before mentioned,then the greater number of these pieces being thus near theextremities, they will draw the arch more down in that part,and thus hollow it out there in a more regular and uniformmanner, making the shape more pleasing and commodious,and yet leaving it sufficiently near a true balance.

The following proposition is here added, to determine thefigure of a balanced arch, on the supposition that the voussoirsare at liberty to slide on each other. A principle indeedhaving no real foundation in fact, though it has been muchinsisted on by some persons.