In cases where it was preferred to support the adjoining springings of two arches upon a single column, though the arch was sometimes left undivided, the same system of sub-orders was more usual. In this case if the abacus remained square, its angles, being unoccupied, would present a clumsy appearance. This led to the breaking of the capital into orders, though resting upon a single shaft, or the abacus was made round or octagonal. Such a column as this often alternated between two clustered piers, making an extremely agreeable group. The developments I have described--so logical in their motive that one fancies that one might have originated them all by a mere process of inductive reasoning--supply nine-tenths of all the elements of the perfected Romanesque style. Extend, now, the same principles to a vaulted space which we have hitherto applied only to an arcaded wall, and we gain another great instalment of the elements of the style by a simple process of reasoning. [Illustration: Fig. 235. Fig. 236.] The normal form of groined or intersecting vaulting,--the simplest manner in which a large space may be arched over in moderate spans,--is, by the two or more intersecting vaults, springing directly from a square pier (Fig. 235). Now, this is not only inartistic, but is bad in construction. The line of intersection is necessarily weak, and the vault requires aid to make it perfect in construction; and this can only be given it in the form of increased thickness, which is at once obtained by altering the form of the pier from a square to a cross form, and applying to the vault the same principle of divided orders as we have done before to arches (Fig. 236); only that, in this case the upper order is a vault, and the lower one only an arched rib coming in to aid the vault. The groined vault is thus divided into compartments, and beauty and strength at once provided for. This elementary form may be decorated in a multitude of ways. The mere addition of an impost and a base to the pier does much to relieve its plainness. We may, however, as in the case of arches, substitute shafts for the divisions of the pier, or double shafts where the ribs are wide; or we may, instead of amplifying the forms of the pier, concentrate it to a column, from whose capital the ribs spring, as we have already seen in case of the double arch.