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.
Fig. 40.—Construction of Vaults.
Thus in [Fig. 40] the dome springing out of the angle requires the height a, the radius being equal to half the diameter; but it was wished to flatten this to b, and yet for the vault to rise everywhere from the arched line e, c. Now if the vault conforms to the surfaces generated by the revolution of the arc d, f, b, about the axis o, d, intersecting with a similarly generated surface at right angles, we get a mean between the domed and cylindrical forms—a domical vault. The intersections, instead of being everywhere square on plan as at x, x, and rising just to the crown of the vault, as would be the case with cylindrical penetrations, will be obtuse as at i, i, and not rising so high will practically leave a large concave surface unbroken at the crown of the vault. This is the principle of the vaults of S. Sophia; the gradations being gentle and the means less obvious, the forms are more like those found in nature, and the result is extremely beautiful. The forms are further softened by every edge of arch and vault being rounded, so that the mosaic completely envelops the whole like a vast embroidered gold tissue.
There would be no difficulty in construction, for the vault falls everywhere on an arch in the angle e, f, b that is in planes which are radii to the arch. The vaulting of the narthex is made up of a series of compartments, much narrower than the span, divided by plain arched bands. To meet the requirements of such oblong spaces two gauges would be needed. The “winding” of the lines of intersection was not to be feared, as they were so soon lost in the more domical surface of the upper part of the vault.
After the above was written we found the geometrical and practical construction of these vaults explained in L’Art de Bâtir chez les Byzantins, in a manner which differs from that here given. M. Choisy’s method is first of all to design the curve of the intersection over the diagonal of the plan as a segment of a circle: then he considers all sections of each compartment of the vault, taken parallel to its arch, and therefore perpendicular to its axis, to be also segments of circles springing from a series of points on the diagonals, their centres being on the axis of each vault.
We cannot agree with this, for, although theoretically the vault so conceived differs immaterially from the solution we have proposed, yet practically its erection would be full of difficulty. M. Choisy’s method is that proposed by M. Viollet-le-Duc for the later Romanesque vaults, in which, the materials being poor rubble, centring must have been required. In these Viollet-le-Duc thinks that diagonal centres were used, and then planks were placed from them to the generating arches, and the additional height of a domical vault made up by a layer of earth. It is to be noticed that diagonal centres in this case almost immediately produced diagonal stone ribs.
M. Choisy in his most interesting book shows that the chief consideration in the construction of the Byzantine vaults was to avoid wooden centring. With this view we entirely agree, but in the system explained in L’Art de Bâtir, the lines of construction would be arrived at by an elaborate system, which required fixed axes to the vaults and either a diagonal centre or a rod revolving in a vertical plane over the diagonal. Then two rods, forming an angle with its apex touching any given point in the diagonal curve and the ends resting on the axis of the vault as a base, revolved as a trammel for that course of the filling. This had to be repeated for a series of points.