OF GROINED RIBBED VAULTS.

Dr. Robison, with peculiar felicity, praises, con-demns, and excuses, the artists of the thirteenth andtwo following centuries. Speaking of their knowledgeof vaulting, he observes, “ An art so multifarious,and so much out of the road of ordinary thought,could not but become an object of fond study to thearchitects most eminent for ingenuity and invention ;becoming thus the dupes of their own ingenuity,they were fond of displaying it where not necessary.”The ingenious and promising invention of substitutingribs for the groins of a groined vault required thepractice of increasing the height of the generatingcurve over the sides of the space to be covered.When the arch over the side of the polygon (Fig.5.)is a semi-circle, the arch over the diagonal becomeselliptic, the longer axis horizontal. By making the archover the side a semi-ellipse, the short axis horizontal,the arch over the diagonal becomes proportionallyelevated. If the arch over the diagonal in an octagonplan (Fig. 6.) be semi-circular, that over the side willbecome elevated in proportion to its width, as theradius 1, to .7653, the side of an inscribed octagon.*At the baths of Diocletian the crossing vaults of thegreat hall are elliptic; the short axis horizontal, andof such a curvature, that the groins or arches overthe diagonals of the side groined vaults are semi-circles.

* See Table of the sides of equilateral figures, Bishop of Ro-chester’s Elem. Trea. Prac. Mat. Page 109 .

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