ibrary, which has on each side
a large wall arch strongly elliptical in form (p. 270). Two arches of
somewhat similar form and apparently original are found in the south end
of the gynecaeum of the Pantokrator (p. 237). These arches may have been
built in this manner to economise centering. Still, in the library they
are wall arches easily constructed without centering.

Failing the examination of a larger number of buildings in
Constantinople we can hardly judge of the later methods of vault and
arch construction, but one point may be further noticed. The wall
internally is often set back slightly at each spring course, so that
with the projection of the course a considerable ledge or shelf is left.
On this ledge centering could easily be supported and would have
required no further framework to the ground. Centering seems to have
been used for dorm, arches, vaults, and door and window openings. It was
not used in small vaults. But it is difficult to imagine any method of
constructing such groined vaults as those found in the narthexes of the
Pantokrator without a very considerable amount of centering.

_Ties._--As a general rule tie rods or beams were used, either of iron
or wood. In the latter case they were painted with leaf or fret
ornaments, and were evidently considered as natural features. But large
vaults are often found without such ties as in the narthex of the
Pantokrator. Many churches have ties to the dome-arches, and none to the
main vault; but it is difficult to lay down a fixed rule. The enormous
amount of mortar in the walls must have made them yield to a certain
degree when newly built, and some of the larger vaults would have been
the better for rods.

_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 arch