In the central area, let us say, of a rectangular building, 235 feet N. and S. by 250 feet E. and W., erect a square structure of four arches. Where arch bends away from arch, there are triangular empty spaces breaking the continuity of the lines of the square summit. Such a base is not round, and it is broken. Can it be made continuous and circular--that is the question? It can. Fill the yawning triangular spaces with masonry to the level of the heads of the arches; only let that masonry be made concave, as though portions of the proposed dome were inserted between the arches, to dovetail with them. And to your surprise, perhaps, but inevitably, the square summit is transformed into a circle, capable of becoming the bed on which a dome may rest as accurately and securely, as though the square of arches was round and solid to the very floor. It is all very simple, after you have seen it done; but the device which introduced into those triangular gaps at the upper corners of the square the pendentives which, when they mounted to the height of the arches, converted a square into a circle was a master-stroke of genius, whoever conceived it first, and an epoch in the history of architecture. But how is this domed square structure to be connected with the walls of the rectangular area within which it is enclosed? How, especially, is it to be held in position, lest it be split open by the thrust of the dome and hurled to the ground? The double-storied aisles to the north and the south furnish the required support in those directions. But it was in the means devised to sustain the dome on the east and the west, that Anthemius and Isidorus displayed all their daring, and secured an effect that has never been matched for grandeur and beauty. They placed two comparatively small piers to the east of the dome-crowned fabric and two to the west of it; arched the piers, and connected them to the right and the left, still with arches, with the great piers to the rear of which they respectively stood. Filling up the triangular void spaces between these arches, they thus gained a semicircular base upon which to rear, at either extremity, a semi-dome, climbing with gentle curve to the feet of the great dome, to support it in its lordly place, and (if the expression may be pardoned) to stretch it from one end of the nave to the other. It is as though the octagon of SS. Sergius and Bacchus had been cut in twain and set east and west of a square surmounted by a dome, converting the central area of the church into an elliptical or oval figure. For elasticity of spring, for the grace and majesty of its upward flight, for amplitude, for the lightness with which it hangs in air, there is no canopy like the arched roof spread over the nave extending from the Royal Gates to the altar of S. Sophia.