The last case I have named--that of the triangular gore of an apse or circle (Fig. 341)--also solves the difficult case I mentioned at the beginning of this lecture as arising in the groining of a polygon, owing to the excessive lowness of the arch formed by the intersecting angles. These are now raised to the full height of a semicircle, while if half of such a polygonal vault be used for an apse, it agrees in height with the main vault without the use of stilting. It may, however, be mentioned that, as stilting is sometimes most useful in making room for windows, it was not superseded by this invention; the two systems continuing to be used at pleasure, and sometimes a union of the two, which, however, is so arbitrary as to defy definition. The form last described for a vaulted circle is often used as a variety of the dome by raising numerous small arches round its circumference, and giving a sort of fluted or shell-like surface to the dome. I think I have now described the principal varieties of round-arched vaulting with two exceptions. The one is that in which the side vaults of oblong compartments cut the higher and main vault at a level lower than its crown. This is vulgarly known as “Welsh” groining, and though not quite pleasing in effect, it is a very legitimate mode of covering an oblong compartment. It is customary to obviate the unpleasing coal-scuttle shape of the true line of intersection (Fig. 342) (such as may be seen in St. Martin’s Church), by making them take the lines given by vertical planes, and throwing the irregular geometrical curve into the surfaces of the cells where it does not strike the eye, or perhaps generating them by the motion forward of the side arch (Fig. 343). This has been done in the Sistine Chapel, and Mr. Smirke has, I think, done the same in our Great Exhibition Room. In a ceiling to be decorated with painting, this form of vaulting possesses the great advantage of leaving the central range unbroken by diagonal lines. [Illustration: St. Martin’s-in-the-Fields, London. Fig. 342. Fig. 343.] The other form I have omitted is the square or polygonal dome, or that generated by the intersection of vaults running parallel to the sides of the base, instead of, as in the groined vault, running at right angles to them (Figs. 344, 345). [Illustration: Fig. 344.] [Illustration: Fig. 345.]