,
or over a small space. Music must rise to its utmost loudness, and fall
from it; color must be gradated to its extreme brightness, and descend
from it; and I believe that absolutely perfect treatment would, in
either case, permit the intensest sound and purest color only for a
point or for a moment.

[Illustration: 42. Leaf Curvature. Magnolia and Laburnum.]

[Illustration: 43. Leaf Curvature. Dead Laurel.]

[Illustration: 44. Leaf Curvature. Young Ivy.]

Curvature is regulated by precisely the same laws. For the most part,
delicate or slight curvature is more agreeable than violent or rapid
curvature; nevertheless, in the best compositions, violent
curvature is permitted, but permitted only over small spaces in the
curve.

Sec. 11. The right line is to the curve what monotony is to melody, and
what unvaried color is to gradated color. And as often the sweetest
music is so low and continuous as to approach a monotone; and as often
the sweetest gradations so delicate and subdued as to approach to
flatness, so the finest curves are apt to hover about the right line,
nearly coinciding with it for a long space of their curve; never
absolutely losing their own curvilinear character, but apparently every
moment on the point of merging into the right line. When this is the
case, the line generally returns into vigorous curvature at some part of
its course, otherwise it is apt to be weak, or slightly rigid;
multitudes of other curves, not approaching the right line so nearly,
remain less vigorously bent in the rest of their course; so that the
quantity[88] of curvature is the same in both, though differently
distributed.

[Illustration: FIG. 95.]

Sec. 12. The modes in which Nature produces variable curves on a large
scale are very numerous, but may generally be resolved into the gradual
increase or diminution of some given force. Thus, if a chain hangs
between two points A and B, Fig. 95, the weight of chain sustained by
any given link increases gradually from the central link at C, which has
only its own weight to sustain, to the link at B, which sustains,
besides its own, the weight of all the links between it and C. This
increased weight is continually pulling the curve of the swinging chain
more nearly straight as it ascends towards B; and hence one of the most
beautifully gradated natural curves--called the catenary--of course
assumed not by chains only, but by all flexible and elongated
substances, suspended