In the square groined space with level ridges there was no alteration excepting in the form of the arch, and in the more finished mouldings made use of. The diagonal ribs often took the form of a round arch, but this depended wholly on the proportions of the surrounding pointed arches. As the diagonals were not formed by elliptical curves, it followed that the vaulting surfaces were not portions of cylinders, and that an error had to be thrown into them. In fact, they were filled in from rib to rib without any view to purely geometrical forms. When the pointed arch is applied to an oblong compartment, or to the sides of a polygonal apse, its advantage becomes more manifest; for the power of making the narrow arches against the walls as high as we please wholly removes the difficulty which we encountered while limited to the round arch, and that without the _necessity_ of stilting, though the convenience which the last-named method offered for the introduction of windows still led to its frequent use. The irregular compartments of an apsidal aisle ceased now to present difficulties, as all their arches could be made of equal height. It is curious that, while we have in London two specimens of such aisles in the round-arched style (those in the Tower of London and St. Bartholomew’s), so have we also two in the pointed arched style, and those very different indeed in their treatment. The aisle round the apse of Westminster Abbey has compartments enormously wider on one side than on the other, and this is met simply by the varied proportions of the arches (Fig. 350); while that surrounding the round portion of the Temple Church[51] has double as many compartments as there are pillars in the arcade, and, consequently, behind every arch of the great arcade is a groined compartment which is nearly square, while behind every pillar is one of a triangular plan, vaulted in a peculiar manner from its corners without any ribs between the transverse ribs. The vaulting of a polygon with a central pillar assumed now a form of exquisite beauty. Its two special types in its simpler form are the Chapter-houses at Salisbury and Westminster,--truly a _par nobile fratrum_,--and claiming special attention as showing the extraordinary beauty attained by the use of ribbed vaulting united with the pointed arch. [Illustration: Fig. 350.--Westminster Abbey. Vaulting of Aisle round Apse.] [Illustration: Fig. 351.] [Illustration: Fig. 352.] I have already mentioned that in this form of vaulting [Illustration: Fig. 353.--Interior of the Chapter-house, Westminster Abbey.] there is a choice between two methods of effecting it: either by supposing the main vault to span from _wall to pillar_ or from _angle to pillar_ (Figs. 351, 352).