The widest hall vaulted by the Romans was that of the

throne room in the palace 'of Diocletian on the Palatine Hill, and this had the enormous span of ioq ft., its. thrust being counteracted by other halls on, either Iside with buttresses outside. In provincial' towns and in -other parts of the ; Roman Empire, where the material pozzolana was not procurable, the Romans had to trust to their mortar as a cementing medium, but this, though excellent of its kind, was not of sufficient cohesive strength to allow of the erection of vaults of more than about 40 ft. span, which were generally built in rubble masonry; There still, exist in Asia Minor ..and Syria some vaulted halls, generally attached to thermae, which are. carried on walls of grea,t thickness. There were' Bran}* varieties of the Roman vault, whether continuous or intersected, such as those employed oyer the cotridors on the Colosseum and the theatre of Mar- cellus, but in these Cases the springing of the vault was above the summit of the Arches of the main front, so that there was no intersection; on the other hand, over the corridors were either elliptical or semicircular, or over the staircases rising vaults, all of which were more difficult to construct; there were also numerous solutions of vault over circular halls, of which that of the Pantheon was the most important example, having a diameter of 142 ft., and over the hemicycles,: which were sometimes of great size; that known as Canopus in Hadrian's villa atiTivoli had a diameter of 75 ft., and was vaulted over with a series of ribs, between which were alternating rampant flat and semicircular webs and cells; in the same villa and in Rome were octagonal halls with various other combinations of vault. Another type of vault not yet referred to isthat of the Tabularium arcade where the cloister vault was employed. Fig. 3 compared with fig. 2 will show the : difference ; in the former the angles of

intersection are inset* and in the latter they are groins with.- pr6r jecting angles at the base, which die away at the summit.

The vault of the basilica* commenced .by. ' Diocletiah and completed by Constantine, Was the last great work carried out by the Romans, and two centuries pass before the next important development is found in the church of Sta Sophia at Con- stantinople. It is probable that the realization of the great advance in the science of vaulting shown in .this church owed something to the eastern tradition of dome Vaulting seen in the Assyrian domes, which are known to us only^by the repre- sentations in the bas-relief from Nimrud (fig. 1), because in the great water cisterns in Constantinople, known as the'Yeri Batan Serai (the -underground palace) and Bin bir-derek (cistern with a thousand and one columns), both built by Constantine, we find the intersecting groin vaults of the Romans already replaced by small . cupolas or domes. These domes* however, «(re of small dimensions when compared with that projected and carried out! by Justinian in Sta Sophia. Previous to this the greatest dome was that of the Panthe6n at Rome, but this was carried on an immense wall 20 ft. thick, and with the exception of small .niches or recesses in the thickness of the wall could not be extended* so that Justinian apparently instructed his architect to provide an immense hemi cycle or apse at the eastern end, a similar apse at the western end, and great arches Oft, either -side, -the. .walls under which . would be pierced with windows.

The diagram (fig. 4) shows the outlines of the solution of the problem. If a hemispherical dome is eut by four vertical planes, the intersection gives four semicircular arches ; if cut in addition by a horizontal plane tangent to the, top of these arches, it describes a circle; that portion of the : sphere which is below this circle and between the^aircTiesi forming a spherical spandrii; is the rtendentive (fig. 5), and its radius is equal to the diagonal of the squareon which the four arches rest. Having obtained a, circle for the base" of the dome, it is not necessary that the upper portion of the dome should

Fig. 3.

Fig, 4.

Fig. 5.

AA, pendentive. spring from the same level as the arches, or that its domical surface should be a continuation of that of the pendentive. The first and second dome of Sta Sophia apparently fell down, so that Justinian determined to raise it, possibly to give greater lightness to the structure, but mainly in order to obtain increased light for the interior of the church. This was effected by piercing it with forty windows— the effect of which was of an extraordinary nature, as, the light streaming through these windows gave to the dome the appear- ance of.beihg suspended in the air. The pendentive which carried the dome rested on four great arches, the thrust of those crossing the church being counteracted by immense buttresses which tra- versed the aisles, arid the other>tw6 partly by smaller arches in the apse, the thrust being carried to the outer waUVjMid to a certain ex- tent by the side walls which Were built under tW arches. From the description giy#h by Procopius we gather that theicentring employed for the gr^t arches cpusisteci of a wall erected to support them during their erection,; ' The construction of the peridenrives is-not known, but it is surmised that to the top of the pendentives they were built in horizontal courses of brick, projecting one oyer the other, the projecting angles being cut off afterwards and covered with stucco in which the mosaics were embedded ; this, was the method employed in the erection of the Perigprdian denies* to which we shall return; these, however, Were of leS6 diameter thaft. those of Sta Sophia, being only about, 40 to 6b: ft. .instead of: 107 'ft;'. The apotheosis of Byzantine architecture, 4i fact, was reached hi Sta Sophia, for although ft formed the model on which all subsequent; Byzantine churches were based, so far as their plan was cotiotfrntd, no domes approaching' the former in dimensions were eVeft attempted. The principal -difference in some later examples' is that wWcfi took place in the form of the pendentive on which the dome was carried. Instead of the spherical,, spandrii of Sta Sophia, large niches were formed in the angles, 3s: in the .mosque of Parrtascus, which was built by Byzantine workmen for the Shjerif al Walid in a.d. 705; these gave, an -octagonal base on; which* ; the hemispherical dome rested (fig". 6); for again, as in "the S^Sjariian palaces iof- Serbistan and Firuzab^d; of, the 4th 'and 5th century of our: em, TvhenVa eenfes of concentric arch rings, pr6jectin^ ohe m front of the other, were built, giving also an octagonal base; each of these penden- tives is known as a squinch.

There is one other : remarkable vault, also built by Justinian, in the church of S. Sergius and Bacchus in Constantinople. The central area of this' church was octa- gonal on plan,' and the dome is divided into sixteen compartments;, of these eight consist, of broad flat bands rising Fig. 6. — BB, niche or from the centre of each qf the walls, squinch pendentive., and the alternate eight are Concave cells over the angles of the octagon, which externally and internally give to the roof the appearance of an umbrella.

Aithough the dome constitutes the principal characteristic of the Byzantine church, throughout Asia Minor are numerous examples in which the naves are vaulted with the semicircular

barrel vault, and this is the type of vault found throughout 1 the south of France in the nth and 12th centuries, the only change being the occasional substitution of the pointed barrel vault, adopted not only on account of its exerting a less thrust, but because, as pointed out by Fergusson (vol. iL p. 46), the roofing tiles were laid directly on the vault and a less amount of filling in at the top was required. The continuous thrust of the barrel vault in these cases was met either by semicircular or pointed barrel vaults on the aisles; which had only half the span- of the naVe; of this there is an interesting example hi the chapel of St John in the ToWer of London — and sometimes by half-barrel vaults, i The great thickness of the walls, however, required in such constructions would seem to have led to another sdlutiori