Much larger in number and extent is the second series of churches with rib-vaulted apses, though they are in general of later date than those in Provence. Their radiants have a certain structural character, for they are independent of the vault surface and were doubtless erected in most cases as a permanent centering to aid in the construction of the half dome. They do not, however, aid to any extent in its support, for the courses of masonry in the vaults are still horizontal and concentric with the curve of the apse, and the completed half domes would therefore stand just as well were the ribs removed. It may be that they were introduced in order to make the apse correspond more closely in appearance with the ribbed vault which had in many cases been introduced in the naves of the churches in which the ribbed half domes are found. In any event, they mark a stage in apse vaulting between the simple half dome and the developed chevet, which is worthy of careful consideration. Most of these vaults date from the second quarter of the twelfth century and are to be found within the zone of influence of the Ile-de-France, though occasionally an example is found at a long distance from this center as in the case of Sant’ Abondio at Como,[342] Santa Maria di Castello at Corneto-Tarquinia in Italy,[343] and such churches as that of the Monasterio de la Oliva (Navarra) in Spain,[344] (1198). The number of ribs varies considerably, though two is most common particularly in the smaller churches and chapels.[345] Of these, the church at Morienval (Oise) (Fig. 77) furnishes a good, though recently reconstructed, example, while Saint Georges-de-Boscherville (Fig. 61) may be cited as possessing a large apse of similar character. The important thing in a comparison of these two vaults is the difference in the lighting of the completed apse. At Boscherville, it was a simple matter to pierce the exterior wall with windows, in this case in two stages, and still keep their crowns practically below the level of the impost of the half dome, since the latter rested directly upon the outer walls. But at Morienval there was an ambulatory, and in order to get a clerestory above its arches, the windows had to be cut into the curved surface of the half dome itself, with the result that they were so deep as to prove of only limited usefulness. Other examples could be cited where this same attempt is made to obtain sufficiently large windows by shoving their heads into the half dome,[346] while at Beaulieu (Corrèze)[347] the windows lie entirely above the impost.