Sometimes the tiercerons are used in both the transverse and the longitudinal severies and sometimes only in one of them. Their number also varies greatly, though of course they are always in pairs. Lincoln cathedral presbytery (cir. 1266-1280) (Fig. 36) affords an example of a single pair in each of the large transverse severies with none in the window cells (Plate I-m), while Chester cathedral chapter-house (first half of the thirteenth century), and Worcester cathedral nave (cir. 1350-1377) (Fig. 89) are rare examples of the opposite arrangement (Plate I-n).[230] To support such tiercerons as these at their crown, a transverse ridge rib was added to the construction, sometimes as in Chester chapter-house (Plate I-n), Lincoln nave (before 1233),[231] and Ely presbytery (1235-1252),[232] running out only to the new keystone (Plate I-o) and thus playing a purely structural rôle, but often extending to the window head (Plate I-p) as in Lichfield cathedral south transept (cir. 1220) and choir (fourteenth century). These portions of Lichfield, together with the nave of Lincoln and the presbytery of Ely cathedral, are also important as showing the employment of a single pair of tiercerons in each of the four panels of the vaulting bays (Plate I-p). This system is slightly varied in the naves of Lichfield and Hereford (Plate I-q-r), where the true transverse arch is omitted between the bays, but these vaults like those of Durham are merely variants of the more standard types.[233] [Illustration: FIG. 36.--LINCOLN, CATHEDRAL.] The introduction of a single pair of tiercerons in each major panel was soon followed, especially in the window cells where the surface was warped, by the use of two (Plate I-s) and even of three such pairs (Plate I-t). Two are found in Hereford cathedral south transept (cir. 1400),[234] and in the choir of Saint Mary Redcliffe at Bristol (fifteenth century),[235] while three appear at Exeter (between 1280-1350) (Fig. 37). This last may well be said to mark the highest point in tierceron vaulting,[236] and it must be acknowledged that the decorative effect produced is most pleasing. Placed as they are over comparatively low naves, these vaults harmonize in an admirable manner with the clustered piers, moulded archivolts, and substantial walls provided for their support, and carry to the crown of the vault that wealth of moulding which lends so much of grace and charm to the English Gothic of the Decorated period. Were such vaults used above the lofty naves of Amiens or Beauvais, they would doubtless appear oppressively heavy but the lowness and solidity of English construction entirely dispels such a feeling. Of course, tiercerons are not essential members of the vaulting system and perhaps they were better omitted altogether, but that their usage can be vindicated from an aesthetic standpoint is proved by such vaults as those at Exeter. [Illustration: FIG. 37.--EXETER, CATHEDRAL.] LIERNE VAULTING