By the method we have suggested nothing was required except a single template to a fixed angle, the upper arm cut to the curve from the crown of the arch to the crown of the vault; we may suppose this to sweep round the generating arches like a trammel, but practically testing the work with it at the crown, as it gradually grew forward, was doubtless found sufficient (see [Fig. 40]). Thus the vault surfaces gave the conditions of the problem and the intersections found themselves.

We did not notice the curious “curve of inflection” of which M. Choisy speaks; certainly it does not generally exist, although according to L’Art de Bâtir “S. Sophia is the most curious example which remains of this singular conception, where the spirit of Greek logic did not hesitate before anomalies of form” (p. 55). We believe this curve is deduced only by the logic with which M. Choisy’s follows up his method of geometrical projection, which certainly generates such an inflected curve. We cannot say this without at the same time expressing our great admiration for L’Art de Bâtir; its freshness of sight, clearness, vitality, and logic are entirely delightful. Strzygowski and Forchheimer[342] follow Choisy’s demonstration; and give an elaborate and analytical explanation of the curve and its points of inflexion. One of the cisterns they say showed the inflected line in the axial sections of the vaults (p. 71).

Now the cistern vaults are roughly built and some of them may have settled down; some indeed may have been designed so that the axial section is horizontal for some distance from the walls before the doming is commenced, especially in the long direction of parallelogramic compartments. The essential points are two. Did these vaults grow forward from the walls and the intersections find themselves, or was the curve of intersection first designed? Are horizontal sections through the intersection of two vault surfaces just above the springing obtuse or acute? The vaults at S. Sophia have the angles of intersection so obtuse that this first drew our attention to the subject.

For a general view of the vaulted system of S. Sophia we would especially refer to Choisy, whose remarks on the construction of these vaults are most interesting. He clearly shows how the large flat bricks made possible the construction of vaults without centring. The extrados of the arches from which the vaults spring being splayed to a skew back, the large surfaces of the thin light bricks allowed them to be stuck up against this skew back, or any part already done, much as if they were square sheets of cardboard (see left side of [Fig. 40]). Indeed the bricks seem sometimes to have been placed quite vertically, but the better plan seems to have been to incline the beds, the vaults were thus built in sections rather than in layers. To take the simplest instance, a cylindrical vault, the arching would begin at one end against the vertical wall, the rings of large thin bricks being placed “on edge” in planes of say 60° right down the vault. In other words, in a longitudinal section of such a vault the joints instead of being horizontal might be vertical, or a mean between the two. This method was known in ancient Egypt and at Khorsabad, and the immense vault at Ctesiphon is built in this way. Although the mosaic covers most of the vaults at S. Sophia, a vast number are exposed in the contemporary cisterns, and Choisy seems to have found a cylindrical vault uncovered in a chamber in one of the buttress masses (Plate ii.), he also shows the construction of the aisle and narthex vaults (Plates ix. and xi.), but he does not say if he had any authority for these. We agree with him that the vaults of S. Sophia owe much of their exceptional beauty to the fact that arches do not break up the curving expanse of the vaulting to any appreciable degree; in the narthex the arches become one with the vault, see [Fig. 41].

Fig. 41.—Section of Narthex and Gallery over showing Royal Doors. Scale twelve and a half feet to an inch (1/125).

Fig. 42.—Dome Construction.

Domes.—In elaborating his theory of Byzantine dome construction Choisy refers to a passage in Eton’s Turkish Empire[343] which describes domes the latter saw built without any kind of centring. The builders put a post in the middle about the height of the walls. To this is fixed a pole reaching to the inside surface of the dome, which is free to move in all directions. Below is attached to the post another pole, which reaches to the outside and describes the outside curvature of the cupola. These give the thickness at the top and bottom and at every intermediate point. “Where they build these cupolas of bricks they use gypsum instead of lime, finishing one layer all round before they begin another. Scaffolding is only required for the workmen to close the opening at the top.” Our diagram A, [Fig. 42], represents this fascinating scheme of building: with such a rod any point in the whole curvature is defined in a moment; it equally gauges the horizontal courses and the rise of the dome. Choisy suggests a second scheme which will be made clear by B. There is no reason, he points out, why the beds of the bricks in a dome should radiate to the centre of the curve: in the Byzantine domes the beds were flattened so that they radiated more or less accurately to the springing of the opposite side of the dome. The thrusts were thus minimised, and the construction was facilitated. If rods forming a triangle revolve about a vertical post as shown, the horizontal curvature is gauged and the top rod will define the slope for the bed. These rods can then be raised to another position as shown in the figure. We should have supposed that little care would be taken with the slope of the beds, as from the thin bricks used the construction practically became homogeneous.

Choisy even thinks that the great dome of S. Sophia may have been built in the air without centring. C, in [Fig. 42], gives his representation of the construction of the semidomes, which he thinks were built out some way entirely without support. The outer arch was then built on a centre and the filling completed “in space” (a straight joint between the arch and the dome filling is shown in the figure in Salzenberg’s text). We think it more likely that in all the larger domes auxiliary support was required “to close the opening at the top,” when the space had been so contracted that a light centring resting on the part already completed was all that would be needed.