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 of the problem of roofing Over churches with incombustible material, viz. that which is found throughout Perigord and La Charente, where a series of domes carried on pendentives covered over the nave, the chief peculiarities of these domes being the fact that the arches, carrying them form part of the pendentives, which are all built in horizontal courses.

The intersecting and groined vault of the Romans. was employed in the early Christian churches in Rome, but only over the aisles, which were comparatively of small span, but in these there was a tendency to raise the centres of these Vaults, which became slightly domical; in all these cases centring was employed.

Reference has been made to the twisting of the groins in Roman work, where the intersecting barrel vaults were not of the same diameter; their construction must at all times have been somewhat difficult, but where the barrel vaulting was carried, round over the choir aisle and was intersected, as in St Bartholomew’s, Smithfield, by semicones, instead of cylinders, it became worse and the groins more complicated; this would seem to have led to a change of system, and to the introduction of a new feature, which completely revolutionized the construction of the vault. Hitherto the intersecting features' were geometrical surfaces, of which the diagonal groins were, the intersections, elliptical in form, generally weak in construction and often twisting (Plate I. fig. 13). The medieval builder reversed the process, and set up the diagonal ribs first, which were utilized as permanent centres, and on these he carried his vault or web, which henceforward took its shape from the ribs. Instead of the elliptical curve which was given by the intersection of two semicircular barrel vaults, or cylinders, he employed the semicircular arch for the diagonal ribs; this, however, raised the centre of the square bay vaulted above the level of the transverse arches and of the wall ribs, and thus gave the appearance of a dome to the vault, such as may be seen in the nave of Sant’ Ambrogio, Milan. To meet this, at first tjie transverse and wall ribs were stilted, or the upper part of their arches was raised, as in the Abbaye-aux-Hommes at Gaen, and the abbey of Lessay, in Normandy. The problem was ultimately solved by the introduction of the pointed arch for the transverse and wall ribs—the pointed arch had long been known and employed, on account of its much greater strength and of the less thrust it exerted on the walls. When employed for the ribs of a vault, however narrow the span might be, by adopting a pointed arch, its summit could be made to range in height with the diagonal rib; and, moreover, when utilized for the ribs of the annular vault, as in the aisle round the apsidal termination of the choir, it was not necessary that the half ribs on the outer side should be in the same plane as those of the inner side; for when the opposite ribs met in the centre of the annular vault, the thrust was equally transmitted from one to the other, and being already a broken arch the change of its direction was not noticeable.

The first introduction of the pointed arch rib would seem to have taken place in the choir aisles of the abbey of St Denis, near Paris, built by the Abbé Suger in 1135, and it was in the church at Vezelay (1140) that it was extended to the square bay of the porch. Before entering into the question of the web or stone shell of the vault carried on the ribs, the earlier development of the great vaults which were thrown over the naves of a cathedral, or church, before the introduction of the pointed arch rib, shall here be noted. As has been pointed out, the aisles had already in the early Christian churches been covered over with groined vaults, the only advance made in the later developments being the introduction of transverse ribs dividing the bays into square compartments; but when in the 12th century the first attempts were made to vault over the naves, another difficulty presented itself, because the latter were twice the width of the aisles, so that it became necessary to include two bays of the aisles to form one square bay in the nave. This was an immense space to vault over, and, moreover, it followed that every alternate pier served no purpose, so far as the support of the nave vault was concerned, and this would seem to have suggested an alternative; viz. to provide a supplementary rib across the church and between the transverse ribs. This resulted in what is known as a sexpartite, or six-celled vault, of which one of the earliest examples is found in the Abbaye-aux-Hommes (S. Étienne) at Caen. This church, built by William the Conqueror, was originally constructed to carry a timber roof only, but nearly a century later the upper part of the nave walls were partly rebuilt, in order that it might be covered with a vault. The immense size, however, of the square vault over the nave necessitated some additional support, so that an intermediate rib was thrown across the church, dividing the square compartment into six cells, and called the sexpartite vault (fig. 7);

Fig. 7.—Sexpartite.

this was adopted in the cathedrals of Sens (1170), Laon (1195), Noyon (1190), Paris (1223–35), and Bourges, (1250). The, intermediate rib, however, had the disadvantage of partially obscuring one side of the clerestory windows, and it threw unequal weights on the alternate piers, so that in the cathedral of Soissons (1205) a quadripartite (fig. 8) or

Fig. 8.—Quadripartite.

four-celled vault was introduced, the width of each bay being half the span of the nave, and corresponding therefore with the aisle piers. To this there are some exceptions, in Sant’ Ambrogio, Milan, and San Michele, Pavia (the original vault), and in the cathedrals of Spires, Mainz and Worms, where the quadripartite vaults are nearly square, the intermediate piers of the aisles being of much smaller dimensions. In England sexpartite vaults exist at Canterbury (1175) (set out by William of Sens), Rochester (1200), Lincoln (1215), Durham (east transept), and St Faith’s chapel, Westminster; Abbey.

In the earlier stage of rib vaulting, the arched ribs consisted of independent or separate Voussoirs down to the springing; the difficulty, however, of working the ribs separately led to two other important changes: (1) the lower part of the transverse diagonal