Meanwhile what the Byzantine architects developed was a geometrically exact system of converting the square into a circle by means of concave triangular members that are specifically called pendentives.
The character and function of a pendentive may be readily grasped by a practical experiment. Cut an orange into two hemispheres. Lay the flat of one on four reels, placed at the four angles of a square, inscribed within the circle. These reels represent the piers on which the pendentives are to be constructed. Now by four perpendicular incisions of the knife cut off the segments of the hemisphere that project beyond the square. The lateral spaces between the piers will now be spanned by four arches. Finally, a trifle above the top of the arches, make a horizontal cut, removing the upper part of the hemisphere. The rind which remains represents the four pendentives. The flesh inside of it may be likened to the timber centering used in the construction of the pendentives and, now that the latter are completed, may be removed. Remove also the flesh from inside the upper part of the hemisphere. It will then be a hollow cap, which you can replace on the top of the pendentives. You now have an instance of a dome and pendentives included in a single hemisphere. More usually, however, the architect makes the curve of the dome different from that of the pendentives. Frequently, too, to give the dome superior distinction, he constructs a cylindrical wall on the circle of the pendentives, and on this drum, as it is called, elevates his dome.
Scientifically stated: “If a hemisphere be cut by five planes, four perpendicular to its base and bounding a square inscribed therein, and the fifth parallel to the base and tangent to the semi-circular intersection made by the first four, there will remain of the original surface only four triangular spaces bounded by arcs of circles. These are called pendentives.” (Professor Hamlin.)
The first church built by Justinian was SS. Sergius and Bacchus in Constantinople. The part dedicated to the latter saint—a small basilica—was destroyed by the Turks. The remainder presents the plan of a rectangle enclosing an octagon on which rests a dome of a curious, fluted, melon shape.
A few years later was erected the church of S. Vitale in Ravenna, probably as the Court Church. Its plan is an octagon within an octagon; the inner one being surmounted by a dome.
The domical arrangement of both these churches may have been originally derived from the Pantheon, modified by the example in Rome, of what is called the Temple of Minerva Medica, though it was probably a nymphæum. This building is decagonal with niches projecting from nine of the sides, while the tenth provides the entrance. The dome, of concrete ribbed with tiles, is built over an inner decagon of ten piers carrying ten arches. These in turn support a decagonal drum, pierced with windows, the angles at the top being filled in with rudimentary pendentives. The same principle of construction reappears in both S. Sergius and S. Vitale; the dome of the latter being composed, for the sake of lightness, of earthenware, amphora-shaped pots, the bottom of one being fixed in the lip of another. It is sheathed on the outside with a wooden roof.
This Church of S. Vitale became the model on which Charlemagne based his domical church at Aix-la-Chapelle, which was built as a royal tomb, A.D. 796-814, and was afterward used as the crowning-place of the Emperors of the West.
S. Sophia.—Finally, the pendentive system was fully developed in Justinian’s church in Constantinople dedicated to the Holy Wisdom—Hagia Sophia, called, though erroneously, S. Sophia. It marks the highest development of the Byzantine genius for domical construction.
The architects were Anthemius of Tralles and Isidorus of Miletus, who began the work in 532 and finished it in 537. The plan shows four mighty piers, 25 feet square, set at the angles of a square of 107 feet. These support four arches and intermediate pendentives of noble height, the apex of the dome being 175 feet from the pavement. For the original dome, having collapsed in 555, was replaced by a higher one, lighted by the introduction of forty circular-headed windows around the spring of the curve; an arrangement not only excellent in admitting light to the interior, but also as wonderfully impressive in its way as the single eye of the Pantheon. Rows of small circular headed windows are also pierced in the screens which fill in the north and south arches.
Abutting on the east and west arches of this central mass are semi-domes, supported upon the central piers and two others. And from these project, as in S. Sergius and S. Vitale, small semicircular domes, sustained by an upper and lower story of arcades. Thus was created a vast oval-ended hall, 267 feet long by 107, from every part of which the summit of the dome is visible.