These differences have been so admirably summed up by Lasteyrie[10] that a translation of his summary with a few additions will perhaps give the best possible account of them. They are grouped under six chief heads which may all be studied by using the cathedral of Saint Front at Périgueux (Figs. 1 and 2) as a model. First, the French pendentives are borne on pointed instead of semicircular arches; second, the surface of the pendentive at Saint Front rises from the intrados rather than from the extrados of the voussoirs; third, the diagonal profile of the French pendentive is a complex curve[11] instead of a quarter circle; fourth, the oldest French pendentives have their masonry in horizontal courses while the Byzantine frequently have their courses more or less normal to the curve; fifth the springing of the domes of Saint Front is some distance back from the circle formed by the pendentives, the diameter of the dome being thus greater than its impost,[12] while in Byzantine models, the two correspond; and sixth and last, the domes of Saint Front are slightly pointed and, for that matter, all the French domes are at least semicircular, while the Byzantine domes are generally of segmental section. The explanation of all these differences lies in the material employed, for the domes of Perigord are of stone, those of Byzantine architecture are of brick or some other light material. The pointed arch having less thrust than that of semicircular section was better suited for stone construction, a fact which explains the pointed section of many French domes whose outward thrusts were thereby greatly reduced. Moreover, while the light Byzantine material made possible a dome without centering constructed after the manner of the Egyptian “voute-par-tranches,”[13] the heavy stone of the French vault made a centering absolutely necessary, a fact which explains the setting back of the dome from the curve of the pendentives so that the ledge thus formed might serve to support the wooden centering employed.[14] It explains also the horizontal courses since these allowed a greater amount of the weight of each course to be borne by the one beneath it, thus reducing the pressure and making possible a centering of comparative lightness. But these were not the only results of the employment of stone. Since the domes of Perigord are much heavier than the Byzantine domes and exert much more outward thrust it was essential for them to have very firm supports. Perhaps it is with this in view that the churches of this school are for the greater part without side aisles, their outer walls with heavy applied and transverse arches providing suitable support for the domes. Even when aisles exist, they are merely deep wall arches forming transverse tunnel vaults rising from the level of the imposts of the transverse arches of the nave and, with them, furnishing the support for the triangular pendentives. This