But now another and most important change was to come over the vault. The mediaeval architects were not satisfied with the mere edge left by the Romans in their vaults, and even before the full Gothic period the Roman builders had emphasized their oblique arches in many cases by ponderous courses of moulded or unmoulded stone in the form of vaulting ribs. These, in the case of Norman building, were probably not merely put for the purpose of architectural expression, but also because they afforded an opportunity of concealing behind the lines of a regularly curved groin rib the irregular curves which were really formed by the junction of the vaulting surfaces. But when the vault become more manageable in its curves after the adoption of the pointed arch, the groin rib became adopted in the early pointed vaulting as a means of giving expression and carrying up the lines of the architectural design. On its edge were stones moulded with the deep undercut hollows of early English moulding, defining the curves of the oblique as well as of the cross arches with strongly marked lines, and, moreover, falling on a level with each other in architectural importance; the oblique vault of the arch is no longer a secondary line in the vaulting design; on the contrary, the cross arches are usually omitted, as shown in Figs. 102 and 103 (view and plan of an early Gothic quadripartite vault); so that the cross rib, which, in the early Romanesque wagon vault (Fig. 90), was the one marked line on the vaulting surface, has now been obliterated, and the line of the oblique arch (E F, Figs. 102, 103) has taken its place.

The effect of the strongly marked lines of the groin ribs, radiating from the cap of the shaft which was their architectural support, seems to have been so far attractive to the mediaeval builders that they soon endeavored to improve upon it and carry it further by multiplying the groin ribs. One of the stages of this progress is shown in Figs. 104, 105. Here it will be seen that the cross rib is again shown, and that intermediate ribs have been introduced between it and the oblique rib. The richness of effect of the vault is much heightened thereby; but a very important modification in the mode of constructing it has been introduced. As the groin ribs become multiplied, it came to be seen that it was easier to construct them first, and fill in the spaces afterward; accordingly the groin, instead of being, as it was in the early days of vaulting, merely the line formed by the meeting of two arch surfaces, became a kind of stone scaffolding or frame work, between which the vaulting surfaces were filled in with lighter material.

This arrangement of course made an immense difference in the whole principle of constructing the vault, and rendered it much more ductile in the hands of the builder, more capable of taking any form which he wished to impose on it, than when the vault was regarded and built as an intersection of surfaces. There was still one difficulty, however, one slight failure both practical and theoretical in the vault architecture, which for a long time much exercised the minds of the builders. The ribs of the vaulting being all of unequal length, they had to assume different curves almost immediately on rising from the impost; and as the mouldings of the ribs have to be run into each other ("mitered" is the technical term) on the impost, there not being room to receive them all separately, it was almost impossible to get them to make their divergence from each other in a completely symmetrical manner; the shorter ribs with the quicker curves parted from each other at a lower point than the larger ones, and the "miters" occurred at unequal heights.

The effort to get over this unsatisfactory and irregular junction of the ribs at the springing was made first by setting back the feet of the shorter ribs on the impost capping, somewhat in the rear of the feet of the larger ribs, so as to throw their parting point higher up; but this also was only a makeshift, which it was hoped the eye would pass over; and in fact it is rarely noticeable except to those who know about it and look for it. Still the defect was there, and was not got over until the idea occurred of making all the ribs of the same curvature and the same length, and intercepting them all by a circle at the apex of the vault, as shown in Figs. 106, 107; the space between the circles at the apex of the vault being practically a nearly flat surface or plafond held in its place by the arches surrounding it; though, for effect, it is often treated otherwise in external appearance, being decorated by pendants giving a reversed curve at this point, but which of course are only ornamental features hung from the roof. If we look again at Fig. 104, we shall see that this was a very natural transition after all, for the arrangement of the ribs and vaulting surfaces in that example is manifestly suggestive of a form radiating round the central point of springing, though it only suggests that, and does not completely realize it. But here came a further and very curious change in the method of building the vault, for as the ribs were made more numerous, for richness of effect, in this form of vaulting, it was discovered that it was much easier to build the whole as a solid face of masonry, working the ribs on the face of it. Thus the ribs, which in the intermediate period were the constructive framework of the vault, in the final form of fan vaulting came back to their original use as merely a form of architectural expression, meant to carry on the architectural lines of the design; and they perform, on a larger scale and with a different expression, much the same kind of function which the fluting lines performed in the Greek column.

The fan vault is therefore a kind of inverted dome, built up in courses on much the same principle as a dome, but a convex curve internally, instead of a concave one, the whole forming a series of inverted conoid forms abutting against the wall at the foot and against each other at their upper margins. This form of roof is wonderfully rich in effect, and has the appearance of being a piece of purely artistic work done for the pleasure of seeing it; yet, as we have seen, it is in reality, like almost everything good in architecture, the logical outcome of a contention with structural problems.