To go back, however, to our previous case of the apsidal termination of a vaulted space, it affords a very fair solution of the difficulty by which we were before encountered; for it is clear that the arches on the sides of the octagon may be lifted up till their crowns become level with that of the main vault; and, as the intersecting angles of a polygonal groined vault coincide with its transverse ribs, we have nothing to do but to raise from every angle a transverse rib similar, or very nearly similar, to those of the main vault, and to make the smaller vaults of the octagon to intersect upon them (Fig. 326). There will be a little geometrical inaccuracy in the forms of these cells of vaulting; but, as the angle ribs would assume correct lines, these inaccuracies would not seriously offend the eye. [Illustration: Fig. 326.] There is, however, another method of meeting the difficulty; but before describing it, I will say a few words on the treatment of other difficulties resulting from the irregularities in form of spaces which have to be vaulted. Let us, as an example, suppose an aisle or corridor passing round such a polygonal figure as we have been considering. It is manifest that its compartments will have a form enclosed by unequal sides, or, to say the least, one side will differ greatly in width from that opposite to it. The stilting system before-mentioned is the most obvious method of getting over the difficulty. It may be, that three of the arches surrounding such a compartment may be about equal, and no great difficulty would occur as to _their_ intersection; but the fourth, being far narrower, would have to be stilted to raise its crown to the level of the others, and its lines of intersection will consequently be more or less disturbed. [Illustration: Fig. 327.--St. John’s Chapel, Tower of London.] [Illustration: Fig. 328.--St. Bartholomew’s Church, Smithfield.] The difficulty is, in early specimens, increased through the apse being usually round instead of polygonal; though this does not very materially alter the case. We have in London two excellent examples of this apsidal aisle; that in the chapel of the Tower of London[43] (Fig. 327), and that in St. Bartholomew’s Church in Smithfield (Figs. 328, 329),--the former of an early, and the latter of a later type. [Illustration: Fig. 329.--Plan of Apse, St. Bartholomew’s Church, Smithfield.]