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