t increase of the curve of _c_,
which are of so frequent occurrence in Greek ornaments.

Sec. VIII. _d_ is the Christian Doric, which I said (Chap. I., Sec. XX.)
was invented to replace the antique: it is the representative of the great
Byzantine and Norman families of convex cornice and capital, and, next
to the profile _a_, the most important of the four, being the best
profile for the convex capital, as _a_ is for the concave; _a_ being the
best expression of an elastic line inserted vertically in the shaft, and
_d_ of an elastic line inserted horizontally and rising to meet vertical
pressure.

If the reader will glance at the arrangements of boughs of trees, he
will find them commonly dividing into these two families, _a_ and _d_:
they rise out of the trunk and nod from it as _a_, or they spring with
sudden curvature out from it, and rise into sympathy with it, as at _d_;
but they only accidentally display tendencies to the lines _b_ or _c_.
Boughs which fall as they spring from the tree also describe the curve
_d_ in the plurality of instances, but reversed in arrangement; their
junction with the stem being at the top of it, their sprays bending out
into rounder curvature.

Sec. IX. These then being the two primal groups, we have next to note the
combined group, formed by the concave and convex lines joined in various
proportions of curvature, so as to form together the reversed or ogee
curve, represented in one of its most beautiful states by the glacier
line _a_, on Plate VII. I would rather have taken this line than any
other to have formed my third group of cornices by, but as it is too
large, and almost too delicate, we will take instead that of the
Matterhorn side, _e f_, Plate VII. For uniformity's sake I keep the
slope of the dotted line the same as in the primal forms; and applying
this Matterhorn curve in its four relative positions to that line, I
have the types of the four cornices or capitals of the third family,
_e_, _f_, _g_, _h_, on Plate XV.

These are, however, general types only thus far, that their line is
composed of one short and one long curve, and that they represent the
four conditions of treatment of every such line; namely, the longest
curve concave in _e_ and _f_, and convex in _g_ and _h_; and the point
of contrary flexure set high in _e_ and _g_, and low in _f_ and _h_. The
relative depth of the arcs, or nature of their curvature, cannot be
taken into consideration without a comple