The employment of buttresses was a constructive expedient that followed almost indispensably on the use of vaults for the roofing of churches. It was necessary either to employ enormously thick walls to resist the thrust, or to support them by some more scientific arrangement of the materials. The theory of the buttress will be easily understood from the diagram (Woodcut No. 662), representing seven blocks or masses of masonry, disposed first so as to form a continuous wall, but which evidently affords very little resistance to a thrust or push tending to overturn it from within. The left-hand arrangement is, from the additional breadth of base in the direction of the thrust, much less liable to fall outwards, provided the distance of the blocks from one another is not too great, and the mass of the vault does not press heavily on the intermediate space. This last difficulty was so much felt by the earlier French architects that, as we have seen, in the South of France especially, they used the roof of the side-aisle as a continuous buttress to resist the thrust of their tunnel-vaults. It was surmounted also by the introduction of intersecting vaults, inasmuch as by this expedient all the thrusts were collected together at a point over each pier, and a resisting mass applied on that one point was sufficient to give all the stability required. This, and the desire of raising the lights as high as possible into the roof, were the principal causes that brought this form of vaulting into general use; still it has not yet been shown that the continuous vault is not artistically the more beautiful of the two forms, if not constructively so also. [Illustration: 662. Diagram of Buttresses.] There was yet another difficulty to be mastered, which was that the principal vault to be abutted was that over the nave or central part of the church, and buttresses of the requisite depth would have filled up the side-aisles entirely. The difficulty first presented itself in the building of the basilica of Maxentius (Woodcut No. 203), and was there got over in something like the manner practically adopted in the Middle Ages, except that the arch was there carried inside, whereas the Gothic architects threw the abutting arch across on the outside and above the roof. [Illustration: 663. Flying Buttress of St. Ouen. (From Batissier, ‘Histoire de l’Art.’)] Several of the previous woodcuts[46] show the system of flying buttresses in various stages of advancement. The view of one of those of the choir of St. Ouen (No. 663) exhibits the system in its greatest degree of development. Here there are two vertical and two flying buttresses, forming a system of great lightness, but at the same time of immense constructive strength, and when used sparingly and with elegance, as in this instance, constituting an object of great beauty. The abuse of this expedient, as in the cathedral at Cologne and elsewhere, went very far to mar the proper effect.