The Law of Curvature

206. Well, as curves are more beautiful than straight lines, it is necessary to a good composition that its continuities of object, mass, or colour should be, if possible, in curves, rather than straight lines or angular ones . . . . Now it is almost always possible, not only to secure such a continuity in the arrangement or boundaries of objects which, like these bridge aches or the corks of the net, are actually connected with each other, but--and this is a still more noble and interesting kind of continuity--among features which appear at first entirely separate . . . . on a larger scale [for example] the reader may easily perceive that there is a subtle cadence and harmony among them [towers]. The reason of this is, that they are all bounded by one grand curve, traced by the dotted line; out of the seven towers, four precisely touch this curve, the others only falling back from it here and there to keep the eye from discovering it too easily.

207. And it is not only always possible to obtain continuities of this kind: it is, in drawing large forest or mountain forms, essential to truth . . . .

Graceful curvature is distinguished from ungraceful by two characters; first in its moderation, that is to say, its close approach to straightness in some part of its course; and secondly, by its variation, that is to say, its never remaining equal in degree at different parts of its course.

208. This variation is itself twofold in all good curves.
A. There is, first, a steady change through the whole line, from less to more curvature, or more to less so that no part of the line is a segment of a circle, or can be drawn by compasses in any way whatever . . . . a) is a bad curve because it is part of a circle, and is therefore monotonous throughout; but b) is a good curve, because it continually changes its direction as it proceeds . . . . observance of this fact . . . . the springiness of character dependent on the changefulness of the curve [in a bough of leaves, for example]. [Variations of curvature in tree boughs--foliage arranged at the extremities instead of the flanks, etc . . . . ]

209.
B. Not only does every good curve vary in general tendency, but it is modulated, as it proceeds, by myriads of subordinate curves. Thus the outlines of a tree trunk . . . . So also in waves, clouds, and all other noble formed masses. Thus another essential difference between good and bad drawing, or good and bad sculpture, depends on the quantity and refinement of minor curvatures carried, by good work, into the great lines. Strictly speaking, however, this is not variation in large curves, but composition of large curves out of small ones; it is an increase in the quantity of the beautiful element, but not a change in its nature.