Egyptian vaults may be divided into two great categories, according to the method of their construction. 1. _Off-set vaults._ These vaults are composed of courses off-set one from another, and with their faces hollowed to the segment of a circle. (Fig. 74.) [Illustration: FIG. 74.--Element of an off-set arch.] [Illustration: FIG. 75.--Arrangement of the courses in an off-set arch.] [Illustration: FIG. 76.--Off-set semicircular arch.] If the face of those stones which, in the form of inverted steps, are turned to the void which has to be covered, be cut into the line of a continuous curve, the superficial appearance of a segmental arch or barrel vault will be obtained; but this appearance will be no more than superficial, the vault will be in fact a false one, because, in such a construction, all the stones which enframe the void and offer to the eye the form of a vault, are really laid horizontally one upon another, and their lateral joints are vertical. (Fig. 76.) When the units of such vaults are properly proportioned they are stable in themselves, and they have no lateral thrust. 2. _Centred vaults._ These are true vaults. They are composed of voussoirs, whose lateral joints are oblique, and radiate towards one centre or more. (Figs. 77, 78, and 79.) [Illustration: FIG. 77.--Voussoir.] [Illustration: FIG. 78.--Arrangement of voussoirs.] [Illustration: FIG. 79.--Semicircular vault.] This method of construction is very convenient because it enables the builder to utilize constructive units of very small dimensions, such as bricks. But this advantage has a corresponding drawback. These voussoirs thrust one against another and tend towards disintegration. They are not stable in themselves, and in order to give them stability they must be kept in place by surrounding them with opposing forces which will effectually prevent their setting up any movement in the structure of which they form a part. This function is fulfilled by the wall in Egyptian architecture, which is consequently very thick, but the radiating arch never arrived at such a development in Egypt as to lead to the adoption of any contrivance specially charged with the maintenance of vaults in a state of proper rigidity. The Egyptians not only employed the semicircular arch; they made use, in a few instances, of the pointed form, and many of their underground buildings have roofs cut out of the rock in the form of a segmental vault. The fact that these sepulchral chambers affected the aspect of vaulted halls, can only be explained by the supposition that a similar construction was common in the dwellings of the living.[106]