The Rémois architects, while exercised by the problems of equilibrium which their system involved, sought to minimise its dangers, which they recognised no less fully than their predecessors, by prudently avoiding all false bearings. It will be easily seen by a comparison of the two sections (Figs. 45 and 48) that the builders of Amiens were troubled by no such misgivings, or that they were at least more venturesome if not more accomplished. They did not hesitate to base the columns which received the crowns of the flying buttresses on a corbel arrangement which had no solid bearing, as may be seen by following the direction of the dotted line X in Fig. 48. The boldness, or rather the imprudence of such an arrangement is patent, for the failure of anyone of the courses, or the decay of any part of the pier into which the corbels are keyed, would necessarily involve a rupture in the flying buttresses, on which the stability of the main vault depends. The disintegration of the whole building and its total ruin could be the only result. The perils of such combinations, or rather such _tours de force_ of equilibrium, are exemplified at Beauvais. The architects who built the choir, about the year 1225, basing it on that of Amiens, determined to raise a monument which should surpass, both in plan and elevation, all the structures of their epoch. They increased the breadth of the choir and of its bays, raising, in the latter, intermediate piers on the crowns of the lower archivolts, thus dividing the upper bays, and at the same time strengthening the vault by auxiliary transverse arches. They exaggerated the height of the archivolts and of the large windows, and diminished their thickness, in order to give greater elegance and lightness, and the main vault rose to a height of more than 160 feet above the ground level. This tremendous elevation, the exaggeration of which in proportion to the width of the nave is striking, necessitated a complicated system of flying buttresses surpassing in boldness all that had gone before. The section in Fig. 51 will give some idea of what has been justly described as an architectural folly. It is astonishing that the structure should have stood as it has done, taking into account the false bearings of the intermediate piers, here again shown by the dotted line X (Fig. 51). [Illustration: 47. AMIENS CATHEDRAL. PLAN] [Illustration: 48. AMIENS CATHEDRAL. SECTION THROUGH THE NAVE] These rest for half of their thickness on off-sets from the piers, which, proving unequal to the strain, have been temporarily stayed, and must eventually be consolidated.