xity of system which my space
does not admit.

Of the four types thus constituted, _e_ and _f_ are of great importance;
the other two are rarely used, having an appearance of weakness in
consequence of the shortest curve being concave: the profiles _e_ and
_f_, when used for cornices, have usually a fuller sweep and somewhat
greater equality between the branches of the curve; but those here given
are better representatives of the structure applicable to capitals and
cornices indifferently.

Sec. X. Very often, in the farther treatment of the profiles _e_ or _f_,
another limb is added to their curve in order to join it to the upper or
lower members of the cornice or capital. I do not consider this addition
as forming another family of cornices, because the leading and effective
part of the curve is in these, as in the others, the single ogee; and
the added bend is merely a less abrupt termination of it above or below:
still this group is of so great importance in the richer kinds of
ornamentation that we must have it sufficiently represented. We shall
obtain a type of it by merely continuing the line of the Matterhorn
side, of which before we took only a fragment. The entire line _e_ to
_g_ on Plate VII., is evidently composed of three curves of unequal
lengths, which if we call the shortest 1, the intermediate one 2, and
the longest 3, are there arranged in the order 1, 3, 2, counting
upwards. But evidently we might also have had the arrangements 1, 2, 3,
and 2, 1, 3, giving us three distinct lines, altogether independent of
position, which being applied to one general dotted slope will each give
four cornices, or twelve altogether. Of these the six most important are
those which have the shortest curve convex: they are given in light
relief from _k_ to _p_, Plate XV., and, by turning the page upside down,
the other six will be seen in dark relief, only the little upright bits
of shadow at the bottom are not to be considered as parts of them, being
only admitted in order to give the complete profile of the more
important cornices in light.

Sec. XI. In these types, as in _e_ and _f_, the only general condition is,
that their line shall be composed of three curves of different lengths
and different arrangements (the depth of arcs and radius of curvatures
being unconsidered). They are arranged in three couples, each couple
being two positions of the same entire line; so that numbering the
component curves in order of m