ins, accordingly, lose themselves in the vaulting surface.
This form is found in Greek churches of late date, but does not occur in
the later churches of Constantinople. A full description of the form and
construction is given by Choisy[31] and by Lethaby and Swainson.[32]

The cross-groined vault as found in the Myrelaion and many other
churches of the city is level in the crown, with clearly marked groins.
It is sometimes used with transverse arches resting on pilasters, or
without these adjuncts.

One of the most interesting of the vault forms is the dome-vault, a
shallow dome with continuous pendentives. It is distinguished in
appearance from the groined vault, as found in S. Sophia, by the absence
of any groin line, and is completely different in construction.

The geometrical construction is that of the pendentives of all domes.
The four supporting arches intersect a hemispherical surface whose
diameter is equal to the diagonal of the supporting square. The
pendentives produce at the crown line of the arches a circular plan
which is filled in by a saucer dome of the same radius as the
pendentives, constructed of circular brick rings, the joints of which
radiate to the centre. If the space to be covered is not square the
broader arches intersect at a higher level, while the narrow arches are
not stilted, but kept down so as to receive the dome surface, and in
this case the narrow arches are not semicircular, but segmental. Where
the difference in size between the two sides was not great, the
difficulty presented was easily overcome by the Byzantine builder, who
in the later buildings, at any rate, rarely built anything within four
inches of its geometrical position. Where the difference was too great
it was frankly accepted, and we find segmental arches at the narrow
ends.

[Illustration: FIG. 11.]

The vaulting of the outer narthex of S. Saviour in the Chora illustrates
this fully (Fig. 11). Though some of the bays of that narthex are oblong
and others almost square all are covered with dome vaults. The almost
square bays, although their sides vary considerably, are covered
precisely as if their sides were exactly equal. But in two of the
oblong bays, which are nearly three times as long as they are broad,
such a method could not be applied. Longitudinal arches (AA) were
accordingly thrown between the transverse arches (CC) and made to rest
on their spandrils. The oblong form of the intervening space was th