§ 4. STRUCTURAL SYSTEM AND VAULTING.
The geometrical scheme of this building, which in its final form must be the result of hundreds of adjustments, modifications, and expedients, to meet newly discovered emergencies, is withal so seemingly simple, that it may be read as a bare mechanical solution of the primary conditions.
The great central area, excepting only the narrow bema, is surrounded by two stories of vaults; the thrust of the dome over the square of about 100 feet is not only resisted by these, but by the four immense buttressing masses (or rather chambers for they are built hollow) which, pierced by arches, pass right across the aisles. East and west the dome is sustained by the semidomes of the great hemicycles, and these in turn by the vaults of the three subdivisions of the hemicycles. The thrusts are thus distributed in a regular pyramid. The external wall, which incloses the whole, being built out to the extremity of the great buttress piers of the north and south sides, and the lesser piers east and west, is thus little more than a screen, inclosing the more active parts of the structure.
One of the most remarkable expedients of this marvellously planned building is that by which the vaults of the side aisles,—which, having large spans, necessarily spring comparatively low down—are received on the secondary order of columns, standing behind the pillars of the great order. This allows of the stately colonnade on either side of the central space and those in the four exedras being only controlled by the height of the upper floor, which is forty-four feet above the area as is explained by Figs. [36], [38]. These secondary pillars also transform the spaces left by the exedras into square compartments.
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.
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.
From the importance attached to wood ties or girdles built into the small domes of Mount Athos, we may be certain that some system of chaining was applied to the great dome of S. Sophia. Choisy gives an example of the former, and also a dome constructed by interlocking semicircular bricks, “two courses of which make a circlet absolutely inextensible.” See B in [Fig. 45]. The dome of S. Vitale at Ravenna is built of layers of earthenware pots or tapering tubes, the end of one fitting into the next and rising in a continuous spiral course, round and round from the bottom to the crown of the dome.
The question of dome construction without centring is of the greatest interest, and much might doubtless be gathered of the traditional methods still followed in modern Greece, Egypt, Persia, and S. Italy. Our [Fig. 43] represents modern domes in Persia, the upper diagram being an ordinary type of exterior from a photograph of Koum. The dome beneath, [Fig. 44], is from a sketch made in a Persian caravanserai by Mr. Wm. Simpson,[344] who describes it as built of burnt brick, square below, round above. “As I was told that centring was never used in Persia I presume this one was constructed without it.” This beautiful form may be considered as four conical squinches penetrating a hemisphere as at A, or as a gradual transition from square to round, B. Ancient Persian domes of substantially the same form, in which a hemisphere penetrates a pyramid, are shown by Dieulafoy.[345]
Figs. 43 and 44.—Modern Domes built without Centring.
Chainage and Walling.—In the East the frequency of severe earthquakes necessitated a manner of construction which should resist disruption. The massive walls of stone of the Classic period are cramped together with metal. The stone Byzantine church at Ezra has a course of interlocking stones forming a chain around the octagon beneath the dome ([Fig. 45] a). At S. Sophia the continuous courses of stone some feet above the floor, mentioned by Salzenberg, are almost certainly converted into a chain by cramps; and the stone course at the springing of the great arches probably has the same function. In brickwork lateral cohesion was usually obtained by a system of continuous wood ties, which is described by Choisy as built into the wall at every five or six feet of height. According to the Greek architect, M. Kouppas, ties of bond timbers were used in this way in the construction of the cisterns, “laid not only along the outside walls but also in parallel rows beneath the lines of pillars and arches;” other rows of timber were built in either as ties or struts in continuous lines at the springing of the vaults.
At S. Sophia there was doubtless a large use made of temporary ties of this kind during the construction. In many places at the springing of the gynaeceum vaults the ends of such provisional ties, which have been sawn away, appear. Besides these there is a series of wood beams which from the first were intended to be permanent, for they are richly carved (C in [Fig. 45]); these are shown by double lines on the right-hand side of Figs. [5] and [6], the single lines showing the iron ties. These carved beams, as Choisy points out, are struts rather than ties. If we take one of the columns standing in an angle in the aisles, an impost of marble connects it with the wall to which it is nearest, and a carved wood beam forms a strut to the other wall. The beam across the central bay of secondary order ([Fig. 5]) forms a rigid strut to the two wider arches (see [Fig. 38], where, however, by oversight the beam has been omitted; it is at the springing of narrow arch high above iron tie). Choisy asserts that “the architect intended to preserve only the struts, all the ties subject to extension were removed, but their suppression was disastrous, and they had hastily to replace them by bars of iron which were fixed with difficulty.” We do not know what reason Choisy had for supposing the system of iron ties to be an afterthought, unless it is because in some cases they appear directly above the ends of the removed wooden ties. Now we believe they occur equally above the carved beams in the openings from the gallery to the nave, and there is no sign of wood ties having been removed from the ground-floor vaults, where the iron bars fulfil such an important function. It is certain that the iron bars to all the nave arches are original, for the marble casing shows no sign of alteration, and they are evidently threaded continuously through the imposts. The important iron ties across the aisles are shown in [Fig. 45]: d is the attachment to the column of great order, e to impost of secondary order behind it, f is a king rod. Across the west gallery the span is lessened by stone corbels beneath the ties g.
With a view of binding the vaults and walls together into a homogeneous mass, the arched vaulting of the interior was carried through the thickness of the walls: in some cases these arches were left open, to be afterwards filled with a screen of windows. The walling of the sides of the church is built independently of the great piers, as straight joints on the exterior show, and Choisy remarks that the independence of masonry unequally charged was a leading idea in Byzantine construction; indeed it is obviously necessary where the quantity of mortar is so great that the brick at times becomes secondary to the joints.
Fig. 45.—Methods of Chainage.
Mortar and Cement.—The mortar used by the Byzantine builders was called Keramotos, from the crushed pottery or tiles which was used in its composition. In an article in the Transactions of the Philological Society of Constantinople M. Kouppas[346] enters fully into the methods which have been traditionally followed in cistern building, and describes this mortar as formed of powdered unslaked lime (asbestos), crushed pottery, coarse sand, and tow or hair, fully a third being lime, another third the crushed pottery, about a fifth the coarse sand, and the rest or 10 per cent. of hair or tow. These were then mixed together in water.
M. Kouppas also describes a hydraulic cement made of “coarse lime (titanos) slaked by water into powder, sifted and laid in layers with cotton shreds. This was thoroughly mixed, and then olive oil was poured in, and the whole gradually brought to a homogeneous mass.” Andreossy[347] describes a mixture (called lukium) made of a hundred “ocques” of lime, freshly slaked in the form of powder, twenty-five “ocques” of linseed oil of the best quality, and twenty drachms of filaments of cotton. This was reduced to a dough, and then before using fresh oil was added. Strzygowski[348] also speaks of a Turkish cement “of six parts by weight linseed oil, eight parts slaked and powdered lime, and one part of cotton.” He refers to a Roman mixture mentioned by Pliny of “oil and quicklime.”
By far the best and earliest account of the methods used for obtaining lime and making cement at Constantinople is contained in Dr. Covel’s MS. in the British Museum (1670-7). The lime was burnt in a pit dug in the ground, the stone, which was hard and black and like “Plymouth stone,” being piled up in and above it like a beehive hut, an opening being contrived in the side for inserting fuel, and a smaller pit dug in the middle for the ashes; it was fired for three days. Then he describes in detail how a cement was made which recalls what the Anonymous says of the joints of the piers at S. Sophia being made of unslaked lime (asbestos) and oil: “To make good lukium (a strong cement as I may call it) they take the above said calx or burnt stone and slake it with water, and so soon as it is moulded and turned into a meal (even while it is warm) they work it with linseed oil and cotton till it is well saturated and brought to the consistency of plaster, and make present use of it, for it will not rest in its perfection above one day or two at most, and if they use it immediately after it is tempered it is certainly the best. In the works of their Bagnos so soon as it is laid on [as a plastering, understood here] they let the water come to it, which, by tempering the heat of the lime, hinders it from cracking. Cotton is better to be mixed amongst it than hair, it being more tenacious and apt to incorporate.” He again describes a similar cement (“lukium, an excellent mortar”) used in some waterworks. “It is made of unslaked lime and beaten brick most finely powdered and sifted, cotton wool very thinly pulled and strewed on, and then all slaked with linseed oil and mixed together: then they use it whilst it is fresh made, otherwise it hardens immediately.”[349] Such a cement must have had the hardening qualities of gesso; the oil cements or mastics used in England some fifty years ago were closely allied in their composition. Modern mortar has lost much by our neglecting the tradition of using crushed brick.
Eastern builders spared neither labour nor time in preparing and testing their materials. Tavernier tells us the waterproof terraces of the Persian houses were formed of “a layer of lime beaten for eight days, which became hard like marble.” The materials used in Byzantine building were tested by long exposure, slaked lime was sealed up in pits for one or two years; and stones, bricks, and tiles they had found should not be used new, for, as Vitruvius says, “the only way of ascertaining their goodness is to try them through a summer and winter.”