(_αα_) We have nothing further to add with respect to walls except the fact that they must be built in a straight and even line and perpendicularly for the reason that walls that rise obliquely to acute and obtuse angles present the threatening aspect of collapse, and possess no direction once and for all securely defined; it can merely appear as a matter of chance that they are reared in whatever more acute or obtuse angle it may happen to be. The demand of scientific rule and purpose alike is here also once more for the right angle. (_ββ_) Owing to the fact that walls act as enclosures no less than as means of support, while we restricted the true function of the column to that of mere support, we approximate to the conception that where we have to satisfy these two distinct needs of support and enclosure columns may be set up and may be united to one another by means of thick walls in such partitions; it is thus that we get _half_ _columns._ In this way, for example, Hirt, following Vitruvius, makes a start in his original type of construction with four corner-posts. If the necessity of an enclosure is to be satisfied no doubt our columns, if we are obliged to include such, must be walled up and it is not difficult to prove that half columns date from remote antiquity. Hirt, for instance[89], affirms that the employment of half columns is as old as the art of building itself, and deduces their origin from the circumstance that columns and piers supported and carried the roofing and other superimposed structures, but at the same time rendered partition walls necessary as a protection against sun and inclement weather. Since, however, the columns already supported the main building in a sufficient manner, it was not necessary to erect partition walls of either so thick or firm a material as the columns, and consequently this latter, as a rule, abutted on the exterior of the building. This theory of their origin may be correct, but for all that half columns are repugnant to a rational view of them; we have, in short, here two ends standing side by side in _opposition_, and essentially _confounding each other_, without any law of necessity being disclosed. It is of course possible to defend half columns, if the point of departure in considering even the column is so strictly that of the structure of wood, that we regard their essential function to be that of an enclosure. Placed in thick walls, however, the column has lost all its significance; it is degraded to the mere post. The true column is in its nature round, essentially complete, and expresses by this very trait of exclusiveness in a visible way that it is antagonistic to an even surface, and, consequently, every inclusion in a wall. If, therefore, we desire to have the support of walls such must be even, not circular columns, but surfaces which can be extended evenly in a wall.