n something like a numerical representation of the
number of possible and beautiful cornices which may be based upon these
four types or roots, and among which the architect has leave to
choose according to the circumstances of his building and the method of
its composition, let him set down a figure 1 to begin with, and write
ciphers after it as fast as he can, without stopping, for an hour.

Sec. V. None of the types are, however, found in perfection of curvature,
except in the best work. Very often cornices are worked with circular
segments (with a noble, massive effect, for instance, in St. Michele of
Lucca), or with rude approximation to finer curvature, especially _a_,
Plate XV., which occurs often so small as to render it useless to take
much pains upon its curve. It occurs perfectly pure in the condition
represented by 1 of the series 1-6, in Plate XV., on many of the
Byzantine and early Gothic buildings of Venice; in more developed form
it becomes the profile of the bell of the capital in the later Venetian
Gothic, and in much of the best Northern Gothic. It also represents the
Corinthian capital, in which the curvature is taken from the bell to be
added in some excess to the nodding leaves. It is the most graceful of
all simple profiles of cornice and capital.

Sec. VI. _b_ is a much rarer and less manageable type: for this evident
reason, that while _a_ is the natural condition of a line rooted and
strong beneath, but bent out by superincumbent weight, or nodding over
in freedom, _b_ is yielding at the base and rigid at the summit. It has,
however, some exquisite uses, especially in combination, as the reader
may see by glancing in advance at the inner line of the profile 14 in
Plate XV.

Sec. VII. _c_ is the leading convex or Doric type, as _a_ is the leading
concave or Corinthian. Its relation to the best Greek Doric is exactly
what the relation of _a_ is to the Corinthian; that is to say, the
curvature must be taken from the straighter limb of the curve and added
to the bolder bend, giving it a sudden turn inwards (as in the
Corinthian a nod outwards), as the reader may see in the capital of the
Parthenon in the British Museum, where the lower limb of the curve is
_all but_ a right line.[84] But these Doric and Corinthian lines are
mere varieties of the great families which are represented by the
central lines _a_ and _c_, including not only the Doric capital, but all
the small cornices formed by a sligh