is slightly pointed, but the sides are nevertheless so much curved in elevation that a structure of this form would not stand without strong cinctures. It is, however, not unlikely that the fresco painter has given it a more bulging shape than Arnolfo intended. But domes of this character were exceptional in the Middle Ages. The builders of that epoch confined their practice for the most part to the safer form in which the vault is made to spring from within the drum, and is thus necessarily, either in part or entirely, hidden from external view. [Illustration: FIG. 3.--Dome of Pisa.] [Illustration: FIG. 4.--Dome of Arnolfo.] [Illustration: FIG. 5.--Section of Baptistery.] A remarkable dome of this latter class is that of the Baptistery of Florence, which, though the building has undergone various superficial transformations since its original construction at an early, though uncertain, epoch, has come down to us in essential integrity. This building on plan is in the form of an octagon, and the dome is of corresponding shape, and sprung from a level far below the top of the enclosing walls. In elevation the dome (Fig. 5) has a pointed outline, and is covered by a pyramidal roof of stone the upper part of which is incorporated with the dome itself, while beneath the lower portion is a void between the dome and the enclosing wall. The structure has an internal anatomy that is both ingenious and admirable. The span is about 25 metres, and the wall at the level of the springing is over 3 metres thick. Above this the wall (_a_, Fig. 5) rises to a height of about 8 metres. The dome at its base is about 1 metre thick, and its extrados rises vertically to a height of about 2½ metres, leaving an open space between it and the wall of the enclosing drum of 1.26 metres in width. Above this vertical portion the extrados is stepped by several courses of masonry, somewhat after the manner of the dome of the Pantheon. From the reëntrant angles of the octagon (_a_, Fig. 6) solid abutments are built up against the salient angles of the vault, and, between these, two secondary abutments (_b_) are carried up against each of its sides. These buttresses are in the form of cross walls dividing the space on each side of the octagon into three compartments, and over each of these compartments a barrel vault, on an axis inclined in conformity with the slope of the roof, is turned. The upper ends of these vaults intersect on the surface of the dome, as shown in Figures 5 and 6. The voids between the crowns of these vaults and the buttresses are filled in with masonry so as to form the sloping planes of the roof below where it is incorporated with the dome, and on these are laid the slabs that form the external covering. With such an effective buttress system as is here provided it is hard to find a reason for the chain of timbers which is inserted at the haunch of the dome. The constructive principle embodied in this