masonry, working the ribs on the face of it. Thus
the ribs, which in the intermediate period were the constructive
framework of the vault, in the final form of fan vaulting came back to
their original use as merely a form of architectural expression, meant
to carry on the architectural lines of the design; and they perform,
on a larger scale and with a different expression, much the same kind
of function which the fluting lines performed in the Greek column. The
fan vault is therefore a kind of inverted dome, built up in courses on
much the same principle as a dome, but a convex curve internally,
instead of a concave one, the whole forming a series of inverted
conoid forms abutting against the wall at the foot and against each
other at their upper margins. This form of roof is wonderfully rich in
effect, and has the appearance of being a piece of purely artistic
work done for the pleasure of seeing it; yet, as we have seen, it is
in reality, like almost everything good in architecture, the logical
outcome of a contention with structural problems.

We have already noticed the suggestion, in early Gothic or Romanesque,
of the dividing up of a pier into a multiple pier, of which each part
supports a special member of the superstructure, as indicated in Fig.
90. The Gothic pier, in its development in this respect, affords a
striking example of that influence of the superstructure on the plan
which has before been referred to. The peculiar manner of building the
arch in Gothic work led almost inevitably to this breaking up of the
pier into various members. The Roman arch was on its lower surface a
simple flat section, the decorative treatment in the way of mouldings
being round the circumference, and not on the under side or _soffit_
of the arch, and in early Romanesque work this method was still
followed. The mediaeval builders, partly in the first instance because
they built with smaller stones, adopted at an early period the plan of
building an arch in two or more courses or rings, one below and
recessed within the other. As the process of moulding the arch stones
became more elaborated, and a larger number of subarches one within
another were introduced, this characteristic form of subarches became
almost lost to the eye in the multiplicity of the mouldings used. But
up to nearly the latest period of Gothic architecture this form may
still be traced, if looked for, as the basis of the arrangement of the
mouldings, which