_Arch Forms._--The great arches under the dome have their centres two feet six inches above the springing line. Those in the principal arcade appear to be semicircular. In the adjoining exedras, the porphyry columns not being nearly so long as the green ones, they were set on pedestals, and the arches are “horseshoe” in form, at least towards the nave, for they are built “winding,” so as to approach a square impost on their caps. We say approach, for there is a gradual modification; the caps being an inch or two wider towards the aisles, the impost increases this by a few inches more. The openings from gynaeceum at west end are segmental, some arches to the side windows and the lateral windows of west elevation, Fig. 25, are bluntly pointed. The transverse arching of narthex is semielliptical, or rather three-centred, a segment with the curve at the ends quickened to become tangential to the wall. The pointed arch is used in the great aqueduct near Constantinople and in one of the city cisterns: both appear to be of the age of Justinian.[341] _Vaulting._--The vaulting is executed with the mastery and freedom that comes of confidence in direct methods. Certain portions are cylindrical, and others are formed by cylindrical cross-penetrations. The octagon of the baptistery, and the square compartments of the gynaeceum, are covered by domes which penetrate down into the angles with continuous pendentives. The larger compartments of the vaults of the aisles require some explanation. Where four semicircular arches open about a square or oblong space, and it is desired to make the vault conform exactly to them, this may be accomplished by a semispherical dome, the span of which is equal to the _diagonal_ of the compartment to be covered; such a vault presents an unbroken surface. Or two cylindrical vaults may penetrate at right angles, when the vault is broken by the intersection into four surfaces. At S. Sophia it was evidently desired to keep the springing high for the sake of the monolith columns, and yet to maintain, so far as possible, a domical surface. [Illustration: FIG. 40.--Construction of Vaults.]