[Illustration: FIG. 83.--REIMS, SAINT REMI.] AMBULATORY VAULTS WHICH INCLUDE THE RADIATING CHAPELS In all the churches thus far discussed, and, in fact, in the majority of those constructed during the Gothic period, the radiating chapels are separated from the rest of the ambulatory by arches directly across their entrances. But quite frequently these chapels, particularly when they were comparatively shallow, as in the cathedral of Chartres (Plate III-g), or [Illustration: FIG. 84.--AUXERRE, CATHEDRAL.] even when comparatively deep as at Saint Denis[439] and Saint Maclou at Pontoise (Plate III-h), were treated as part of the ambulatory and an added rib was introduced in vaulting them exactly in the manner described in connection with the trapezoidal bays of Rouen and Coutances. Furthermore, as the chapels were increased in size, more than one extra rib was added in the severy of the trapezoidal vault which embraced them so that there were, sometimes, two such ribs, as in the cathedral of Tournai (1240-1260) (Fig. 85).[440] Occasionally, also, as in the cathedral of Saint Quentin (after 1230) (Plate III-i), similar bays and vaults occur, with the addition of large radiating chapels opening off of the more shallow curves of the ambulatory bays, suggesting a combination of the Tournai type with that of Auxerre (Plate III-f). In some of the larger and deeper chapels there were even four added ribs as, for example, in the cathedral [Illustration: FIG. 85.--TOURNAI, CATHEDRAL.] [Illustration: FIG. 86.--BAYONNE, CATHEDRAL.] of Bayonne (Fig. 86), where the ambulatory is further noteworthy because the builders, in an attempt to equalize the vaulting severies, have moved the keystones of the diagonals almost out to a point on the line of the outer walls. As a matter of fact, it was moved out to such a point in a number of instances (Plate III-j), as, for example, in Soissons cathedral[441] where it becomes the keystone of an arch directly across the entrance of the chapel as well as being the center for all the ribs both of this chapel and the ambulatory. Each trapezoidal bay is thus divided not into four but into three triangular panels, the chapel itself being covered by a fully developed five-part chevet vault for which the two ribs of the ambulatory bay act as buttresses. A similar but more logical vault appears in the ambulatory and two eastern chapels of Pamplona cathedral (begun 1397) (Plate III-k). This is a church with an axial eastern pier, and its radiating chapels are arranged so as to form perfect hexagons with the bays of the ambulatory. The keystone is then moved out, as at Soissons, to the crown of the chapel arch where it lies in the exact center of each hexagonal bay and thus produces a perfectly symmetrical vault. AMBULATORIES WITH ALTERNATE SQUARE AND TRIANGULAR BAYS