_Abutments._--The system of abutments in the Byzantine churches of the great period has been carefully studied by M. Choisy.[33] In early examples the dome springs directly from the pendentives on the inside, but is thickened externally over the haunches, producing a double curve and an apparent drum. This is seen very clearly in SS. Sergius and Bacchus. In S. Sophia the numerous windows are cut through this drum, so that it resembles rather a series of small abutments. The object was to support the crown of the dome by adding weight over the haunches. In both these churches the thrust of the dome and its supporting arches is taken by the two-storied galleries, which form, in fact, flying buttresses within the buildings, and are adapted to their architectural requirements. The square plan and the enormous size of the dome in S. Sophia demanded the great buttresses on the sides; while in SS. Sergius and Bacchus the eight buttresses show only on the outside of the dome and are not carried over the aisles as they are in S. Sophia. Below the roof the arches and piers of the galleries and aisles are arranged so as to carry the thrust to the external walls, and following the tradition of Roman vaulting all buttressing is internal. In S. Irene, where the true drum dome first appears, the buttresses between the windows of the dome still remain, though much reduced in size. A dome raised on a drum can evidently no longer exercise a thrust against the dome-arches; its thrust must be taken by the drum, and only its weight can rest on the arches. The weight of the drum and dome rests on the pendentives and dome-arches. Their thrust is neutralized by the use of ties and by the barrel vaults of the cross arms, and these in their turn depend on the thickness of the walls. The lower buildings attached to the church in the form of side-chapels and the narthex also helped to stiffen and buttress the cross walls. The system is by no means perfect in these late churches. It was apparently found impossible to construct drum domes of any size, except at the extreme risk of their falling in, and probably it is for this reason that many of the larger domes in late churches, like SS. Peter and Mark, S. Theodosia, the Chora, have fallen. No system of chainage appears to have been used for domes in Constantinople.