M. Viollet Le Duc gives a curious instance of sexpartite or septipartite vaulting united with another form (Fig. 368), for which I know no definite name, but which is itself a union of the groined vault with what I have elsewhere called the square dome. [Illustration: Fig. 368.] I will describe the last-named vault by a comparison between those of two corresponding chapels near the west end of Lincoln Cathedral, to the right and left of the nave. [Illustration: Fig. 371. Fig. 369. Fig. 372. Fig. 370.] The two chapels are alike in plan (Figs. 369, 370),--an oblong, each side of which is divided into two arches. They only differ in that one has a central pillar and the other has none. The one is simply divided into four groined vaults on the most customary principle (Fig. 371). The other is similarly vaulted up to the line of the square, the angles of which would be represented by the four bosses of the first-named vaults; but from thence the diagonal ribs, instead of returning downwards on to a central pillar, continue to rise till they meet in the middle point of the chapel (Fig. 372). This upper portion, therefore, is the top of a square dome; and the whole vault may be described as a square dome penetrated on each side by two Welsh groined cross vaults. This combination is common in the vaulting under central towers, as at Lincoln and York; though in these cases the central portion is bounded by a strongly-marked horizontal line defining the boundary of the half-groins below, and the square dome above. In the chapel I have been describing there is no such boundary-line, but the groining compartments continue till they meet in a point at the top. This system may be carried out with any number of bays; and we have in the Chapter-house at York an instance of its application to an octagon. The plan of the vaulting there is identical (or nearly so) with that of Westminster or Salisbury, but the portion enclosed within the inner octagon, instead of turning down to the central pillar, runs up to the point at which all the arched lines would meet in the centre (Fig. 373). [Illustration: Fig. 373.--Chapter-house, York.] The relation between the vaulting of the Chapter-houses of York and Westminster is, in fact, the same as that between the two chapels at Lincoln just described. In each case we see how similar forms may be covered over with vaulting nearly identical in plan--with or without a central pillar at pleasure. There is a parallel case in the crypt of Glasgow Cathedral, in which the compartment is divided on three of its sides into _two_, and on the other into _three_ arches. This crypt is a work in which the architect would appear to have revelled in self-sought perplexities, and to have solved them, one after another, with singular success. [Illustration: Fig. 374.--Glasgow Cathedral. Plan of vaulting of the Crypt under the Choir.]