the rigid and
unmanageable proportions of the circular arch, and which could not be
even partially solved till the introduction of the pointed arch. The
pointed arch is the other most marked and characteristic feature of
Gothic architecture, and, like the buttress, it will be seen that it
arose entirely out of constructive difficulties.

These difficulties were of two kinds; the first arose from the
tendency of the round arch, when on a large scale and heavily
weighted, to sink at the crown if there is even any very slight
settlement of the abutments. If we turn again to diagram 77, and
observe the nearly vertical line formed there by the joints of the
keystone, and if we suppose the scale of that arch very much increased
without increasing the width of each voussoir, and suppose it built in
two or three rings one over the other (which is really the
constructive method of a Gothic arch), we shall see that these joints
in the uppermost portion of the arch must in that case become still
more nearly vertical; in other words, the voussoirs almost lose the
wedge shape which is necessary to keep them in their places, and a
very slight movement or settlement of the abutments is sufficient to
make the arch stones lose some of their grip on each other and sink
more or less, leaving the arch flat at the crown. There can be no
doubt that it was the observance of this partial failure of the round
arch (partly owing probably to their own careless way of preparing the
foundations for their piers--for the mediaeval builders were very bad
engineers in that respect) which induced the builders of the early
transitional abbeys, such as Furness and Fountains and Kirkstall, to
build the large arches of the nave pointed, though they still retain
the circular-headed form for the smaller arches in the same buildings,
which were not so constructively important. This is one of the
constructive reasons which led to the adoption of the pointed arch in
mediaeval architecture, and one which is easily stated and easily
understood. The other influence is one arising out of the lengthened
conflict with the practical difficulties of vaulting, and is a rather
more complicated matter, which we must now endeavor to follow out.

[Illustration: Figs. 93-107.]

Looking at Fig. 92, it will be seen that in addition to the
perspective sketch of the intersecting arches, there is drawn under it
a plan, which represents the four points of the abutment of the arc