A final type of rather primitive vaulting which was subsequent to the introduction of ribbed vaulting but would seem to be prior to the use or at least to the extensive knowledge of the chevet, consisted in the employment of a simple four-part vault over the semicircle of the apse (Plate II-a).[352] The result was an awkward kind of chevet vault which is worthy of consideration as perhaps having a part in the development of the true Gothic form. It might properly be called a four-part cross-ribbed apse vault. [Illustration: PLATE II] THE CHEVET VAULT By the middle of the twelfth century, all the methods of apse vaulting thus far described, were abandoned[353] in favor of the ribbed Gothic chevet[354] which was then developed. In this new vault the masonry courses are no longer horizontal and concentric but run in a generally perpendicular direction from a series of radiating ribs, which have a common keystone, to a wall rib or a curved line of intersection above the heads of a series of apse windows in whole or in part above the level of the impost of the radiants. In other words, the chevet vault consists of a series of triangular severies, each essentially like one quarter of a four-part cross-ribbed vault. The evolution of this developed chevet from the earlier types of apse vaulting already discussed is difficult to trace and in fact it seems most reasonable to imagine that it was a spontaneous transformation which did not require any intermediate steps. It has, for instance, been pointed out that the greatest problem of the apse builder was to place a clerestory of good sized windows above the ambulatory arcade or at least as high as possible in the apse wall and at the same time to keep the pressures and thrusts of his vault at the lowest possible point. Imagine then a builder with this in mind starting to construct a ribbed half dome with windows rising above its impost. Suppose that the radiating ribs were first constructed and the space to be vaulted thus divided into triangular compartments. Now assume that the builder was familiar with the four-part cross-ribbed vault--a reasonable assumption since everything seems to point to an earlier date for such vaults than for the ribbed chevet. Would he not be prompt to see that a series of clerestory windows could be built around the apse precisely like those along the walls of nave or choir and each triangular space thus formed, be covered by one quarter of four-part vault? Is not this especially reasonable in view of the fact that there existed groined vaults of just this type,[355] exactly as there existed groined prototypes out of which sprang the simple four-part cross-ribbed vault? Furthermore, if the peculiar four-part apse vaults described as sometimes employed in transitional churches are any or all of them earlier than the earliest of the true chevets, would it not seem as if the builders were bent upon using quadripartite vaulting of some form, even over the apse, in order