Of these vaults with added ribs, perhaps the simplest are those in which the western bay is subdivided by the introduction of a ridge rib running about half way to the crown of the apsidal arch and there met by two tiercerons rising from the imposts of this same arch (Plate II-n). A good example appears in the cathedral of Bayonne (Basses-Pyrénées) (after 1213), and another in that of Saint Quentin (Aisne) (commenced 1257), while the same subdivision of this severy in combination with other subdivided cells is to be seen in the Marien-kirche at Stargarde (Germany) (fourteenth century) (Plate IV-d). A second and unusual division of this severy appears in the cathedral of Saint Jean at Perpignan (Pyrénées-Orientales) (1324-1509),[387] where the customary three-part bay containing the buttressing ribs also contains two diagonals precisely like those in a four-part vault (Plate II-o). A similar arrangement, with the addition of a ridge rib (Plate II-p), may be seen in the church of Saint Jean at Ambert (Puy-de-Dôme) (fifteenth and sixteenth centuries). Such subdivisions as these last two quite evidently had for their object not merely a reduction in the size of the spaces to be vaulted but also an effort to retain the buttressing-ribbed type of chevet and still obtain a window cell which would not have the warped surface characteristic of this form. [Illustration: FIG. 71.--CHALONS-SUR-MARNE (NEAR), NOTRE DAME-DE-L’ÉPINE.] A still more elaborate subdivision of the rectangular vaulting bay appears in the chevet of Notre Dame-de-l’Épine near Chalons-sur-Marne (1419-1459) (Fig. 71), where this bay contains no diagonals at all but is divided by a series of tiercerons and short ridge ribs in a manner best understood from the plan (Plate II-q). But it is the subdivision of the window cells of the apse proper which is of especial interest at l’Épine, for the method here employed was very widely extended in the later Gothic period. It consists in the introduction into each of these cells of a short ridge rib running from the central keystone to a point about half way to the window crowns where it is met by two tiercerons which rise from the impost of the principal ribs of the chevet on either side of the window. The apparent object of the system is to so subdivide the vault surface as to break up its compound or ploughshare curves and substitute smaller panels whose surfaces are simpler to construct exactly as in the similar nave vaults previously described. This purpose does not show to advantage at l’Épine, where the awkward adjustment between the vault panels and the window heads would seem to indicate that the apse was originally designed for a simple form of chevet with no added ribs. Better examples could be cited, among them Saint Severin at Paris. Such an arrangement of window cells as that in these vaults practically converts the chevet into a ribbed half dome pierced with lunettes which do not rise to its crown.