utely pointed, and that
which spanned it the wide way were either semicircular or
flatly-pointed, it became easy to arrange that the startings of both
vaults should be at the same level, and that they should rise to the
same height, which is the condition essential to the production of a
satisfactory intersection.

Scott enumerates not fewer than fourteen varieties of mediaeval
vaults[19] and points out that specimens of thirteen are to be found
at Westminster. Without such minute detail we may select some
well-known varieties:--(1) The plain waggon-head vault, as at the
Chapel of the Tower; (2) in advanced Norman works, cross-vaults formed
by two intersecting semicircular vaults, the diagonal line being
called a groin. (3) The earliest transitional and E. E. vaults,
pointed and with transverse and diagonal ribs, and bosses at the
intersection of ribs, _e.g._, in the aisles and the early part of the
cloisters at Westminster. (4) In the advanced part of the E. E.
period, the addition of a rib at the ridge, as seen in the presbytery
and transepts at Westminster. (5) At the time of the transition to
Dec. (_temp._ Ed. 1.) additional ribs began to be introduced between
the diagonal and the transverse ribs. (6) As the Dec. period advanced
other ribs, called _liernes_, were introduced, running in various
directions over the surface of the vault, making star-like figures on
the vault. (7) The vault of the early Perp., which is similar to the
last, but more complicated and approaching No. 8, _e.g._, Abbot
Islip's chapel. (8) Lastly, the distinctive vault of the advanced or
Tudor Perp., is the fan-tracery vault of which Henry VII.'s Chapel
roof is the climax. The vaulting surfaces in these are portions of
hollow conoids, and are covered by a net-work of fine ribs, connected
together by bands of cusping (Fig. 23).

[Illustration: FIG. 23.--HENRY VII.'S CHAPEL. (1503-1512.)]

In Scott's enumeration the vaults of octagons and irregular
compartments, and such varieties as the one called sexpartite, find a
place; here they have been intentionally excluded. Many of them are
works of the greatest skill and beauty, especially the vaults of
octagonal chapter houses springing from one centre pier (_e.g._,
Chapter Houses at Worcester, Westminster, Wells, and Salisbury).

Externally, the roofs of buildings became very steep in the thirteenth
century; they were not quite so steep in the fourteenth, and in the
fifteenth they were freque