In the Norman cathedrals the general scheme seems to have been to divide the height into three equal parts, and to allot one to the pier arch, another to the triforium or great gallery, and the third to the clerestory. In all the examples we now have, the upper is the smallest division; but I cannot help fancying that some arrangement of the timbers of the roof gave the additional height required. It is generally supposed that the roof at Peterborough (Woodcut No. 810) was originally flat. This, however, is by no means clear, nor that it started so low; but, be that as it may, the woodcut (No. 820) will explain the usual arrangement, as well as the changes afterwards introduced. At Winchester the two lower divisions are practically equal, the upper somewhat less, and the alternate arrangement of the piers hints at a hexapartite vault, if such should ever come to be executed. When William of Wykeham undertook to remodel the style of the nave, he first threw the two lower compartments into one, as shown on the left-hand side of the cut. He then divided the whole height, as nearly as the masonry would allow him, into two equal parts, allotting one to the pier arches, and apportioning the upper as nearly as he could by giving two-thirds to the clerestory and one-third to the triforium. With pointed arches this was the most pleasing and satisfactory arrangement adopted during the Middle Ages; but when something very like it was attempted in the nave of Gloucester with round arches, the effect was most unpleasing. Before the architects, however, settled down to this proportion, a variety of experiments were tried. One of the most successful was the nave of Lichfield Cathedral (Woodcut No. 812). Here the whole height is divided equally: one half is given to the pier arches, and the other divided equally between the clerestory and triforium. If the latter had been glazed externally, as was the case at Westminster Abbey and elsewhere, and made to look like part of the church, the whole might be considered as satisfactory. As it is, the area of the clerestory is so much less than that of the triforium, that the proportion is not quite agreeable, though the solidity and repose which this arrangement gives to the roof is above all praise. [Illustration: 822. Two Bays of the Nave of Westminster Abbey. Scale 25 ft. to 1 in.] [Illustration: 823. One Bay of Cathedral at Exeter. Scale 25 ft. to 1 in.]