The arrangement of the belfry stage, with its gable on each face, is very noteworthy, and is, perhaps, one of the earliest examples of a type which was developed afterwards into the well-known arrangement of the belfry of the south-west tower at Chartres, and this, with the influence of the churches of the Rhine,[38] developed in almost all subsequent modifications of the spire with its gabled spire-lights; one of the windows under this pediment is planned in a most ingenious manner, presenting externally a semi-dome pierced by two pointed arches; another window is pierced with a trefoil head, the diameter of which is much larger than that of the light it surmounts. This is a favorite form of cusping throughout this district. I have seen it in Lyon, at Vienne, often at Le Puy, at Brioude, at Notre-Dame-du-Port, Clermont, and in the south porch at Bourges; and there can, I think, be little doubt that it is somewhat Eastern in its origin, and analogous to the horseshoe form of arch.
The cloister on the north side of the church appears to be in part coeval with the earliest,[39] or, perhaps, the second portion of the fabric, and in part with the later additions to it. It consists of a simple arcade of round arches on rather solid piers, with a detached shaft on each face. The capitals are all richly sculptured, some with figures, some with foliage. The spandrels of the arches are filled in with a reticulation of coloured stones; above the arches runs a band of similar ornament, and above this again a carved cornice, which in the later part of the cloister forms a sort of frieze. In this portion the arches have sculptured key-stones, a peculiarity which I hardly remember to have met with before in work of the same date. On the south side there are two fluted shafts and one spiral; all the rest are circular, but noticeable for their very considerable entasis. The groining is all quadripartite without ribs, and executed with rough stones, set in concrete, on a centring of boards. The cloister was surrounded on all sides with buildings. On the south is the cathedral; on the east, and opening to the cloister by an arcade of open arches, is a large hall covered with a pointed barrel-vault. This was originally called the choir of S. André, and in it masses in commemoration of the dead were said, and services held on the feasts of the Invention and Exaltation of the Cross, and on the feasts of S. Andrew and S. Eustachius. It was also called “cæmeterium,” being used for the burial of the clergy, and is now called the chapel _des Morts_. On the wall are still to be seen remains of a painting of the Crucifixion, with many prophets and angels, S. Mary and S. John, the sun and moon, etc. In the northern gable of this building is a fine cylindrical chimney, built in alternate courses of dark and light stone, and rising from a fireplace in a chamber over the hall, and of the same date as the hall. M. Viollet-le-Duc gives a drawing of the fireplace, which is of a not uncommon early type, the head projecting considerably on a semicircular plan. At the north end of the _Salle des Morts_ is a passage leading to the cloister, and along the whole northern boundary once stood a vast range of building called the Maîtrise.[40] Nothing now remains of this save its undercroft, which was spanned by bold pointed arches of stone, on which the wooden floor rested. The Maîtrise was pulled down a few years since, and, not long before, a tower close by it, called the tower of S. Mayol, was also destroyed. It is described as an erection of the eleventh century, battlemented, but without machicoulis.[41] It seems to have served as part of the fortification of the church, which was also attended to in an alteration of the building on the west side of the cloister, in the fourteenth century. This building contained, below, a hall on a level with the church, which was the chapel of the Holy Relics; above was the _Salle des États_ of Velay, with a stone barrel-roof, now both thrown into one room. Above these again was an open space under the roof, protected on the side towards the town by a magnificent overhanging battlement and machicolation of the fourteenth century, and quite open on the side towards the cloister save for the stone piers supporting the roof. The machicoulis are some of the finest I have ever seen, and project from the buttresses as well as from the walls. The only access to this stage of the building seems to have been from the roof of the cathedral.