Scott enumerates not fewer than fourteen varieties of mediæval 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 frequently almost flat. They were always relied upon to add to the effectiveness of a building, and were enriched sometimes by variegated tiles or other covering, sometimes by the introduction of small windows, known as dormer windows, each with its own gablet and its little roof, and sometimes by the addition of a steep sided roof in the shape of a lantern or a "flèche" on the ridge, or a pyramidal covering to some projecting octagon or turret. All these have their value in breaking up the sky-line of the building, and adding interest and beauty to it. Still more striking, however, in its effect on the sky-line was the spire, a feature to which great attention was paid in English architecture. _Spires._