The temerity, and even the dangers of such a system, are sufficiently demonstrated in the wonderful works of the thirteenth-century architects themselves. For, notwithstanding the skill and beauty of their many admirable combinations, they were unable to reduce their methods to scientific formulæ. The statical power of their structures remained an uncertain quantity, determined by the durability of the material and its exposure or non-exposure to the weather, the interior skeleton being formed of the same material as the exterior. [Illustration: 44. RHEIMS CATHEDRAL. PLAN] The perils inherent in such a system are more apparent at Rheims than elsewhere, because of the colossal proportions of the building. The arrangement of the flying buttresses, however, is more logical than at Laon, Paris, Sens, and Bourges, by reason of the quadripartite arrangement of the main vault. The thrusts being equally distributed among the supporting piers, each flying buttress performs an identical office; their equal strength and solidity is therefore perfectly appropriate and logical. But though theoretically correct in its disposition of flying buttresses of equal strength to meet thrusts of equal strength, the method is vitiated by its inherent weakness as a system of abutment. The fragility of the flying buttress exposed it to two grave dangers, active and passive; active, taking into account the constant strain upon it as an abutment; passive, in regard to the gradual reduction of its solidity by exposure to weather. In support of this statement, it is only necessary to refer to the restorations which it has been found necessary to make within the last few years, to preserve the nave. The flying buttresses have been strengthened from below, a proceeding without which the collapse of the huge building would have been inevitable. But we shall find much to call for unqualified admiration at Rheims in the grandiose conception of the work and in its powerful execution, in the magnificent arrangement of its eastern façade, and in the perfect harmony of the ornamentation, where sculpture, capitals, friezes, crockets, and floriations are so many types of mediæval decorative art at its best. The Cathedral of Amiens, which dates from about 1220, and is one of the largest as well as one of the most admired of Gothic masterpieces, is directly founded upon that of Rheims. The plan is on the same lines, with this exception, that at Amiens the choir is of greater importance relatively to the nave, and that the piers and points of support are weaker and much more lofty. [Illustration: 45. RHEIMS CATHEDRAL. SECTION OF THE NAVE] [Illustration: 46. RHEIMS CATHEDRAL. FLYING BUTTRESSES OF THE CHOIR]