The Cathedral of Sens marks a new phase of development by its suppression of the upper gallery over the side aisles. These are now vaulted and covered by a lean-to roof; a flying buttress of single span receives the thrust of the main vault. The building is perfectly solid; its construction shows research, though it is as illogical as that of Laon or of Paris; for the exterior flying buttresses are all of equal strength, and so fail to proclaim their true functions, the interior thrusts varying considerably. [Illustration: 40. SENS CATHEDRAL. PLAN OF A BAY. VAULT IN SQUARE COMPARTMENTS OF TWO BAYS] [Illustration: 41. SENS CATHEDRAL. SECTION OF A BAY OF THE NAVE] [Illustration: 42. SENS CATHEDRAL. INTERIOR VIEW OF LATERAL BAYS] The arrangement at Bourges, which appears to have been mainly built, if not actually finished, in the first half of the thirteenth century, differs from that of Sens. The structure is one of five aisles, and in plan recalls Notre Dame de Paris, but the details are very dissimilar. The inner side aisles no longer support a gallery, nor are they of equal height with the outer aisles; they are raised so as to afford space for lighting (see Fig. 43). The main vault is sex-partite planned on squares; but the same illogicality exists here which we have already pointed out, and in connection with which we will risk appearing somewhat insistent, in the hope of directing special attention to it. It is more glaring here than elsewhere, the flying buttresses themselves being of exaggerated dimensions and of double span, embracing the two side aisles. [Illustration: 43. BOURGES CATHEDRAL. SECTION OF THE NAVE] Both at Bourges and Sens the space between the summit of the archivolts and the bases of the upper windows, known as the frieze, or, in modern parlance, the triforium, becomes a purely decorative feature. It consists of a narrow arcaded corridor, occupying in the interior of the building that portion of the wall space which in the exterior has been appropriated by the lean-to roof of the side aisles. At Sens there is merely a single gallery; at Bourges it becomes double, through the stepped arrangement of the side aisles (see Fig. 43), a variation in which we may trace an ingenious blending of the systems of Anjou and Poitiers with those of the Ile-de-France. CHAPTER VII THE CATHEDRALS OF THE THIRTEENTH CENTURY The Cathedral of Rheims, which was begun soon after the destruction of the original building by the fire of 1211, is a supreme expression of the fusion of the three systems--those of Aquitaine, of Anjou, and of the Ile-de-France. It may be taken as the most perfect manifestation of persistent efforts to establish a method of construction based on equilibrium--the equilibrium, that is to say, of a building vaulted on intersecting arches, the thrusts of which are received by exterior flying buttresses.