58

OF RIBBED VAULTS.

knowledge of the Turks, in respect of the scientificconstruction of a cupola, or the builders of themiddle ages of that of arches, it must be admitted,that both the one and the other have been very luckyin their practice.

The advantage peculiar to the different kinds ofvaulting were concentrated in the next efforts ; wherethe form of the vault (Fig. 21.) may be conceived tobe composed of the four quadrants of an invertedfigure generated by the revolution of a curve round atangent to it, by which the curvature of each rib is ofthe same genesis. These ribs are either equal arcs ofthe same curve, and separated by a quadrangle withconcave sides, fitting the convexity of the inver-ted figure (Fig. 21.), the materials of which areposited domewise, or the ribs are protracted until theymeet (Fig. 20.) It will be manifest, after having in-vestigated the generation of groined vaults, andconsidered them analogically to these examples, thatshould the ribs be all of the same curvature, or arcsof the same curve, and protracted until they meet,that the rib over the diagonal of the plan will neces-sarily be longer and higher than the others, and theywould decrease in height according to their proximityto that over the side (Fig. 20.)

In an early investigation of vaulting, it had beenobserved, that the continued key-stone or ridgeof the vaults in some of the Cathedrals rose and fellin a kind of undulation. What then was attributedto error and defective workmanship, has since beenthe cause of solid content and admiration. It is dif-ficult to make judgment wait upon knowledge ; andthis apology will, it is hoped, be recollected and ac-