ence, which is worthy of notice, between these two constructions. In the choir of Noyon, the vaults being quadripartite, the ribs of the compartment adjoining the apse would not naturally have furnished an abutment for those of the apse; for the diagonals of a quadripartite vault intersect in the middle of the compartment. Therefore in order to secure abutment this compartment was made tripartite as we have seen, uniformity being sacrificed, in a truly Gothic spirit, to constructive exigency. But in Paris, and also at Bourges, the vaults of the choir being sexpartite, the plan is so arranged that a half of a double compartment shall adjoin the apse. The transverse rib upon which the apse ribs intersect thus corresponds to the intermediate rib of a sexpartite compartment, and hence this rectangular compartment is naturally tripartite, and forms a natural abutment to the compartment of the apse. For a sexpartite system no better arrangement could be devised.
Even for quadripartite vaulting the arrangement of Noyon, though logical and effectual, is not the best. The marked disparity in form and in the size of the respective cells, which it occasions between the easternmost compartment and the other compartments of the choir, was a defect which the builders were not slow to observe and to correct.
A better arrangement was discovered at Chartres (Fig. 51), and was afterwards more perfectly carried out at Amiens. At Chartres the centre of the arc of the apse is, as at Paris set eastward of the line spanned by the easternmost transverse rib; but instead of lengthening the apse ribs (as they are lengthened at Paris) to meet this transverse rib, they are shortened so as to meet a little eastward of the true centre, while additional ribs, a, are introduced, springing from the easternmost piers of the choir, whence they also converge upon the same point. These additional ribs thus furnish effectual abutment to the others, and the vault of the apse is rendered independent of the vaults of the choir. The choir vaults are now uniformly quadripartite; the awkward expedient adopted at Noyon being no longer necessary. At Chartres, too, the semicircular or segmental form is replaced by that of a polygon. The introduction of the two additional ribs in the vault gives eight instead of five cells to the apse, and the plan thus becomes a polygon of seven sides ex-
