To comprehend the pendentive, let us take a circle and inscribe within it a square; at the four angles of the square we will place solid piers of masonry and connect them with semicircular arches. Let us now suppose that a hemispherical dome had been built upon this circle as plan, and we will see that the planes of the arches and the plane passing at the level of the top of the keystones of the arches, in intersecting this dome, would leave but four triangular portions of it. These triangular portions are called pendentives, and are the only portions of the original hemisphere which are actually built. As this hemisphere would have been necessarily constructed of materials the joints of which would have radiated from the centre of the sphere, so also do the joints of the pendentives radiate from this same centre, which is identical with the centre of the original circle. The plane passing at the level of the top of the keystones in intersecting the hemisphere describes another circle, upon which the actual dome is placed. The question has not been established satisfactorily whether the Byzantine architects really understood the pendentive, as in many instances they resorted to less scientific methods of filling in the vacant spaces between the arches and the upper dome, but the only logical method of constructing it is that which has just been described. In building domes, it was not uncommon in the East to replace stonework by light terra-cotta pipes, fitting into each other, giving great lightness and comparative strength. Justinian gave a marked impetus to architectural work and to the building of religious edifices in particular. He commissioned Anthemius of Thralles, and Isidor of Miletus, to execute the plans for the new church of St. Sophia, upon the site of an older building of Constantine, also dedicated to the “Holy Wisdom,” which had been burnt during an emeute soon after it had been repaired by Theodosius. Justinian had already built the church of Sergius and Bacchus in Constantinople, on a plan nearly identical with that of St. Vitale, at Ravenna, with the exception that the whole structure was externally in the form of a square, enclosing the octagon supporting the dome. This served as a stepping-stone to the conception of the larger church, which became the type of all subsequent Byzantine constructions. [Illustration: CHURCH OF SERGIUS AND BACCHUS AT CONSTANTINOPLE.] [Illustration: PLAN OF ST. SOPHIA, CONSTANTINOPLE.] By comparing the plans of the Pantheon, the temple of Minerva Medica, the baptistery of Constantine, St. Vitale, at Ravenna, and the church of Sergius and Bacchus, in the order in which they are enumerated, with that of St. Sophia, the sequence and continuous progress of domical construction is at once apparent, and such comparison explains the successive steps in a more satisfactory manner than a folio of description.