Brick vaults and arches must have been far more numerous in Egypt than might be supposed from the few examples that remain. They must have suggested the use of off-set vaults in the case of stone, which, it must not be forgotten, would seem to the Egyptians to offer all the advantages of a vault without its drawbacks. In other countries the stages of progression were different, and the true arch came very late into use; but in Egypt it certainly seems to have preceded the off-set arch. In the valley of the Nile the latter is an imitative form. The form of elliptic arch which we find in certain funerary chambers at Abydos seems to show this. When the architect of a tomb or temple wished to substitute a concave surface for a flat ceiling he made use of this hollowed-out vault. He thus saved himself from any anxiety as to the stability of his structure, he avoided the necessity of introducing what would seem to him a cause of eventual destruction, while he gave variety of line and, perhaps, additional symbolic meaning to his work. § 5 _The Pier and Column.--The Egyptian Orders._ THEIR ORIGIN. After the wall and the covering which the wall supports, we must study in some detail the pier, and the column which is the perfected form of the pier. Thanks to these latter elements of construction the architect is able to cover large spaces without impeding circulation, to exactly apportion the strength and number of his points of support to the weight to be carried and to the other conditions of the problem. By the form of their bases and capitals, by the proportions of their shafts, by the ornament laid upon them in colour or chiselled in their substance, he is enabled to give an artistic richness and variety which are practically infinite. Their arrangements and the proportions of their spacing are also of the greatest importance in the production of effect. In attempting to define a style of architecture and its individual expression, there is no part to which so much attention should be paid as the column. It should be examined, in the first place, as an isolated individual, with a stature and physiognomy proper to itself. Then in its social state, if we may use such a phrase; in the various groups which go to make porticos, hypostyle halls, and colonnades. We shall begin, therefore, by examining what may be called the Egyptian orders, and afterwards we shall describe the principal combinations in which they were employed by the Theban architects.