and the arch of the main arcade, dc. It is evident that the three arches ad, ab, dc, and ac all have bases of varying length. Consequently, if they were constructed with a semicircular radius, they would all rise to the varying heights shown in the diagram. The impossibility of adjusting a vault surface to all these different altitudes is perfectly evident; it is only necessary to imagine the pitch of the transverse ridge, lp, which is mathematically worked out in the oblique line, ml, to realize how bizarre this construction would be. Still another trouble is to be found in the longitudinal ridge of the vault. This should be concentric with the walls of the ambulatory, and lie in the center of the vault; in other words, in the line, fji. But the crowns (g, h) of the diagonal ribs do not lie in this line. Therefore the ridge of the vault would be forced to run in a straight or broken line, fghi, quite unsymmetrical with the plan of the ambulatory. Enough has been said to show how complicated was the problem which confronted the builders of Morienval. However, they proved equal to the situation, and by the application of that inexorable spirit of logic which was to become the watchword of Gothic progress, they constructed a vault perfect, it is true, - but one that has stood for nearly eight hundred years, and one which provided a solid foundation for the achievements of their successors. far from First of all, by redoubled orders, they built out the responds at a and b (Ill. 165, Fig. 2), and contracted those at d and c, so that the central points, f and i, of the transverse arches fell considerably inside the center of the vault. Then the diagonals, ac and bd, were built on a plan slightly curved (probably as much so as the builders dared to construct them). By this means the ridge passing through f, g, h, and i, was made concentric with the ambulatory, though not placed in its center. The curving in plan of the diagonals brought the point e slightly nearer to the center of the vault. Finally the arches of the various ribs were made to rise to nearly the same height by depressing the wall rib ab, and stilting or pointing the transverse rib and the arch of the main arcade. The vault of Morienval, as completed, is far from elegant, but it is of priceless value in demonstrating the logical and thoughtful, if somewhat groping, manner in which French architecture was feeling its way along untrodden paths. The problems attacked were not simple, and the builders lacked skill and technique. But by dint of systematic experiment and perserverance, not one, but a dozen methods were found for surmounting each obstacle. Morienval marks a distinct epoch in the evolution of French Gothic, and certainly represents the summit of achievement in the first quarter of the XII century. It is now necessary to abandon again for a moment strict chronological sequence, and, before taking up the advance made in other directions by the monuments built directly after Morienval in the second quarter of the XII century, to trace the ultimate solutions found for the problem of the rib-vaulted ambulatory. For at least ten years no other ambulatory seems to have been |