ly above the dome arches are flat, and flush
with the inner face of the octagon, and in each of them is a
semicircular-headed window. They rise perpendicular to a point a little
above the windows, and then curve with a radius to the centre of the
dome.

[Illustration: PLATE XV.
THE BAPTISTERY, S. SOPHIA, FROM THE EAST.
THE BAPTISTERY, S. SOPHIA. THE INTERIOR, LOOKING WEST.
_To face page 76._]

[Illustration: FIG. 21.--VIEW OF THE EXTERIOR OF THE DOME OF SS. SERGIUS
AND BACCHUS.]

On the other hand the eight compartments directly above the angles of
the octagon are narrower than the preceding compartments; they have no
windows, and, what is of special importance to note, they are deeply
concave.[115] Such marked hollowness is found in later domes as a
decorative feature, but here it is primarily and supremely a
constructive device. By its means the concave compartments are set
slightly back from the octagon's inner face, leaving, at the springing
line, portions of the wall-head to appear as little flat ledges on each
side of the angles. This is a most skilful expedient, and compares
favourably with the methods employed elsewhere to apply the dome to the
octagon.[116] In the octagonal church of S. Lorenzo at Milan the octagon
is turned into the circle by the introduction of squinches. In San
Vitale a considerable walling is built between the line of the octagon
and the springing line of the dome, while the bed for the dome is formed
by introducing, in the space over the angles of the octagon, niches
which are worked above to the circle on plan. On the other hand, it is
interesting to compare with these methods the method employed in the
baptistery of S. Sophia, now a Sultan's Turbe, near the southern
entrance to the inner narthex. Although the walls of the building
describe a square on the exterior, they form an octagon on the interior
with semicircular bays at the diagonals, as in SS. Sergius and Bacchus.
But in the application of the dome the true pendentive is used. The
baptistery was erected shortly before S. Sophia, and in view of the
erection of the great church.

The curvature of the dome of SS. Sergius and Bacchus has three zones,
which have respectively a radius of m. 8, (drawn from the centre of the
octagon), m. 3-1/4, and m. 9-1/2, (centre about m. 2, below the
springing of the dome). The first extends to a point a little above the
heads of the dome windows; the second about m. 2 higher; the t