[Illustration: 1. PLAN OF A CUPOLA OF THE ABBEY CHURCH OF ST. FRONT AT PÉRIGUEUX] [Illustration: 2. PENDENTIVE (MARKED A) OF A CUPOLA OF THE ABBEY CHURCH OF ST. FRONT] [Illustration: 3. SECTION OF A PENDENTIVE ON THE DIAGONAL A TO B IN PLAN, FIG. 1] Fig. 3 is a section through one of the pendentives of St. Front, following the line A B in Fig. 1. It shows that the first six courses are cut so as to make what is called a _tas de chargé_; the upper surfaces are horizontal, the faces curved to the radius of the dome itself. After the sixth course the voussoirs are cut normally to the curve of the arch. The vaulting of religious buildings having long been the crux of mediæval architects, the construction of the St. Front cupolas must have been an event much noised abroad, for towards the close of the eleventh century a large number of churches with cupolas were built in imitation of the mother church at Périgueux. The construction of the churches of Angoulême and Fontevrault in the first years of the twelfth century shows that the architects were attempting to cover spaces of ever-increasing span on the Aquitainian model, while at the same time they set themselves to lighten their vaults, and consequently to reduce their points of support. Fig. 4 gives the plan of one of the cupolas of Angoulême or of Fontevrault, both being built on precisely similar plan, with the exception of the number of bays to the nave. [Illustration: 4. PLAN OF A CUPOLA OF ANGOULÊME OR FONTEVRAULT] Fig. 5 gives the section of a bay in one of these churches, and illustrates the considerable difference already existing between the mother cupola of St. Front and its offspring. The cupola on pendentives begins to show a certain attenuation, and we shall presently note a fresh step forward towards the solution of that problem so persistently grappled with by the mediæval architect--how to reduce the weight of the vault. [Illustration: 5. SECTION OF A BAY OF THE CUPOLAS OF ANGOULÊME] The Church of St. Avit-Sénieur furnishes a most instructive example. The cupola of this building is strengthened by stiffening ribs. It becomes an annular vault, formed of almost horizontal keyed courses, sustained by transverse and diagonal ribs, which act the part of a permanent centering. The Church of St. Pierre at Saumur marks a further step onwards in the construction of vaults derived from the cupola.[5] [5] _L'Architecture Romane_, by Ed. Corroyer. Finally, the architects of Maine and Anjou achieved the long-desired consummation. Under their treatment the pendentives resolved themselves into their actively useful elements, the visible signs of which were diagonal or intersecting arches, salient and independent, set in precisely the same manner as the pendentives of the cupola (Fig. 3), and performing identical functions (Fig. 8). [Illustration: 6. SECTION OF A BAY IN THE CHURCH OF ST. AVIT-SÉNIEUR] [Illustration: 7. PLAN OF VAULT ON INTERSECTING ARCHES]