I will now describe a form of vaulting which, though it originated during the round-arched period, seems more properly to belong to that now under consideration. We have seen that the arches of churches were frequently arranged in _pairs_; the piers alternating in size and design. Supposing each arch to be about half the width of the nave, each _pair_ of arches would form a square on the plan; and, though such a square space may be, and often was, divided into two oblongs in the vaulting, it is equally natural to vault it as a single square. As, however, this leaves the alternate piers unrepresented in the vaulting, it became frequent to carry across from this intermediate pier a single transverse rib crossing the diagonals at their point of intersection, and between it and those diagonals to introduce oblique vaulting cells, whose ridges strike from the centres of the half-bays to the point of intersection. [Illustration: Fig. 364.] [Illustration: Fig. 365.] [Illustration: Fig. 366.] Dr. Whewell, followed by Professor Willis, has given this the name of “_sexpartite_” vaulting (Fig. 364), ordinary vaulting being _quadri_partite, as having four cells. It is obvious that, in a square building of two bays on each of its sides, this may be carried out on all four sides, and thus become an _octo_partite vault (Fig. 365);[55] or, as in the aisles of Lincoln Cathedral, it may be adopted on one side only, and so be _quinque_partite (Fig. 366). These forms of vaulting were most frequent during the transitional period; that is to say, during the latter part of the twelfth century. Thus it is used in the work of William of Sens at Canterbury, and by Bishop Hugh at Lincoln, and preparations were made for it at St. David’s. It was, however, continued at Lincoln in the great transept, and in the aisles of the nave, which are of later date; and we have an instance of it at Westminster, as late as 1250, in the Chapel of St. Faith.[56] The same principle was applied, in a varied form, at the east end of the Priory Church at Tynemouth, where, though the bays have ordinary vaulting, the eastern wall is divided into three parts, corresponding with the windows, over which cells of vaulting are formed, converging to the intersecting point of the compartment.[57] Curiously enough, we find the same arrangement repeated a century and a quarter later in the crypt of St. Stephen’s Chapel, in the Palace of Westminster. [Illustration: Fig. 367.] In the Lady Chapel at Auxerre the same idea is carried out still farther, the vaulting, square in plan, having two of its sides divided into two cells each, as on the sexpartite principle, and the other two into _three_ each, as those above referred to, making in all a _deca_partite vault (Fig. 367). If _all_ sides had the threefold division, it would have become _dodeca_partite, or a vault of twelve cells.