So much for the exteriors of these cathedrals. It is, however, when we compare the interior of Notre Dame with that of Amiens, that we see in what direction French Gothic was travelling. In the case of Amiens, it is as if some power had pulled the older form upward into a slenderer, more elastic fabric; less massive, possibly less stately, but also less inert, infinitely alive in its inspiring growth, with grace of movement as well as dignity. Notre Dame is still, as it were, anchored to the comparative ponderousness of the Romanesque style. The round columns with capitals of the Corinthian type still follow the model, though not the proportions, of the Roman. Their effect of dumpiness is further increased by the projecting half-round pilaster column that supports the main member of the vaulting shaft. On the other hand, the clustered piers at Amiens are slender, loftier in proportion to width; while a simple logic of structural purpose is apparent in the three-quarter attached shafts which carry the arches and aisle-vaults, and the main shaft of the nave vaulting rises uninterruptedly from the ground. The pier, in fact, operates as an abutting support to the members, which actually sustain the arch and vaulting, and their relation to the pier is asserted by the continuous _abacus_ which binds all lightly but firmly together. A corresponding logical simplicity distinguishes the four-part nave vaulting at Amiens, where the pressure is concentrated equally on all the columns in succession without the need of intermediate ones to carry the added transverse rib. Other great examples of the thirteenth century are the cathedrals of =Laon=, =Chartres=, =Rouen=, =Beauvais=, =Auxerre=, =Bourges=, and =Le Mans=--the last especially celebrated for its superb chevêt and flying buttresses--and the =Collegiate Church= of =S. Quentin=. =Sainte Chapelle.=--The problem of concentration of strains was most triumphantly solved in the _Sainte Chapelle_ (1242-1247) or Royal Chapel, in Paris, in which the Gothic system of construction may be said to have reached complete maturity. Here the vaulting is carried on buttress-piers, and the spaces between the latter are entirely filled with windows, 15 feet wide and 50 high. The structure below the vaulting is literally a framework, a lantern for the display of the stained glass; “a great translucent tabernacle merely ribbed and braced with stone.” The influence of Sainte Chapelle affected French construction for half a century and was developed to its furthest possible point in =S. Urban= at =Troyes=, begun in 1260.