The portion of the crypt which represents the choir overhead is really one of the most lively and amusing pieces of vaulting I know (Fig. 374). It consists of _ten_ bays; and, as the east end is necessarily divided into _two_ bays for the support of those above, nothing would have been more natural than to have placed an intermediate row of columns down the centre, dividing the whole into two ordinary ranges of vaulting. But no, the architect would have lost his fun by any such commonplace scheme, and _we_ should have lost a very pretty and instructive puzzle. Beginning at the east end, he first cut off a space two bays long, then a second of three bays long, then a single bay, then another space of three bays, and finally a single bay at the west end; while to each of his groups of three bays, he gave a central column, and repeated the threefold division on its east and west sides. These square spaces, then, each of whose sides is divided into three, became the key-notes of his scheme, and most ingeniously and beautifully he vaulted them. The principle followed is really, however, nothing more than an adaptation of the ordinary mode of dividing a square into four smaller squares of groining, to a space whose sides are divided into _three_ instead of _two_ (A). The central square resting on the column remains unaltered, but the sides have each _three_ cells, the transverse ribs from the central column being bifurcated at their apices, and instead of going across to an opposite pillar, spread right and left to the _two_ pillars, while the main diagonal ribs remain unaltered. These are met at their apices by half-diagonals coming obliquely from the same pillars in the sides. The result is a star-like arrangement of an exceedingly pleasing, though at first sight, intricate character. Adjoining one of these beautiful squares comes the compartment first alluded to (B). It is a very parallel case to that last described. On three sides it is the same as the Lincoln chapel, with a portion of a square dome instead of a central column (excepting only that this has the boundary-line), while the fourth side, having _three_ divisions instead of two, is dealt with precisely as has been described in the preceding case. Amongst these intricate compartments are alternated single bays, each divided transversely into three squares of ordinary groining; and the perplexity of the effect of the crypt arises not so much from the difficulty of any of the forms of vaulting, as from the constant change from one form to another, no two adjoining divisions being alike. The whole is carried out with excellent detail, and forms a most beautiful and interesting interior. [Illustration: Fig. 375.--Choir, Lincoln Cathedral.]