§ 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.
§ 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 between two points. If the points of suspension be near each other, we have such curves as at D; and if, as in nine cases out of ten will be the case, one point of suspension is lower than the other, a still more varied and beautiful curve is formed, as at E. Such curves constitute nearly the whole beauty of general contour in falling drapery, tendrils and festoons of weeds over rocks, and such other pendent objects.[89]
§ 13. Again. If any object be cast into the air, the force with which it is cast dies gradually away, and its own weight brings it downwards; at first slowly, then faster and faster every moment, in a curve which, as the line of fall necessarily nears the perpendicular, is continually approximating to a straight line. This curve—called the parabola—is that of all projected or bounding objects.
§ 14. Again. If a rod or stick of any kind gradually becomes more slender or more flexible, and is bent by any external force, the force will not only increase in effect as the rod becomes weaker, but the rod itself, once bent, will continually yield more willingly, and be more easily bent farther in the same direction, and will thus show a continual increase of curvature from its thickest or most rigid part to its extremity. This kind of line is that assumed by boughs of trees under wind.
§ 15. Again. Whenever any vital force is impressed on any organic substance, so as to die gradually away as the substance extends, an infinite curve is commonly produced by its outline. Thus, in the budding of the leaf, already examined, the gradual dying away of the exhilaration of the younger ribs produces an infinite curve in the outline of the leaf, which sometimes fades imperceptibly into a right line,—sometimes is terminated sharply, by meeting the opposite curve at the point of the leaf.
§ 16. Nature, however, rarely condescends to use one curve only in any of her finer forms. She almost always unites two infinite ones, so as to form a reversed curve for each main line, and then modulates each of them into myriads of minor ones. In a single elm leaf, such as Fig. 4, Plate 8, she uses three such—one for the stalk, and one for each of the sides,—to regulate their general flow; dividing afterwards each of their broad lateral lines into some twenty less curves by the jags of the leaf, and then again into minor waves. Thus, in any complicated group of leaves whatever, the infinite curves are themselves almost countless. In a single extremity of a magnolia spray, the uppermost figure in [Plate 42], including only sixteen leaves, each leaf having some three to five distinct curves along its edge, the lines for separate study, including those of the stems, would be between sixty and eighty. In a single spring-shoot of laburnum, the lower figure in the same plate, I leave the reader to count them for himself; all these, observe, being seen at one view only, and every change of position bringing into sight another equally numerous set of curves. For instance, in [Plate 43] is a group of four withered leaves, in four positions, giving, each, a beautiful and well composed group of curves, variable gradually into the next group as the branch is turned.
§ 17. The following Plate ([44]), representing a young shoot of independent ivy, just beginning to think it would like to get something to cling to, shows the way in which Nature brings subtle curvature into forms that at first seem rigid. The stems of the young leaves look nearly straight, and the sides of the projecting points, or bastions, of the leaves themselves nearly so; but on examination it will be found that there is not a stem nor a leaf-edge but is a portion of one infinite curve, if not of two or three. The main line of the supporting stem is a very lovely one; and the little half-opened leaves, in their thirteenth-century segmental simplicity (compare Fig. 9, Plate 8 in Vol. III.), singularly spirited and beautiful. It may, perhaps, interest the general reader to know that one of the infinite curves derives its name from its supposed resemblance to the climbing of ivy up a tree.
| Fig. 97. |
§ 18. I spoke just now of "well-composed" curves,—I mean curves so arranged as to oppose and set each other off, and yet united by a common law; for as the beauty of every curve depends on the unity of its several component lines, so the beauty of each group of curves depends on their submission to some general law. In forms which quickly attract the eye, the law which unites the curves is distinctly manifest; but, in the richer compositions of Nature, cunningly concealed by delicate infractions of it;—wilfulnesses they seem, and forgetfulnesses, which, if once the law be perceived, only increase our delight in it by showing that it is one of equity, not of rigor, and allows, within certain limits, a kind of individual liberty. Thus the system of unison which regulates the magnolia shoot, in [Plate 42], is formally expressed in [Fig. 97]. Every line has its origin in the point p, and the curves generally diminish in intensity towards the extremities of the leaves, one or two, however, again increasing their sweep near the points. In vulgar ornamentation, entirely rigid laws of line are always observed; and the common Greek honeysuckle and other such formalisms are attractive to uneducated eyes, owing to their manifest compliance with the first conditions of unity and symmetry, being to really noble ornamentation what the sing-song of a bad reader of poetry, laying regular emphasis on every required syllable of every foot, is to the varied, irregular, unexpected, inimitable cadence of the voice of a person of sense and feeling reciting the same lines,—not incognisant of the rhythm, but delicately bending it to the expression of passion, and the natural sequence of the thought.
§ 19. In mechanically drawn patterns of dress, Alhambra and common Moorish ornament, Greek mouldings, common flamboyant traceries, common Corinthian and Ionic capitals, and such other work, lines of this declared kind (generally to be classed under the head of "doggerel ornamentation") may be seen in rich profusion; and they are necessarily the only kind of lines which can be felt or enjoyed by persons who have been educated without reference to natural forms; their instincts being blunt, and their eyes actually incapable of perceiving the inflexion of noble curves. But the moment the perceptions have been refined by reference to natural form, the eye requires perpetual variation and transgression of the formal law. Take the simplest possible condition of thirteenth-century scroll-work, [Fig. 98]. The law or cadence established is of a circling tendril, terminating in an ivy-leaf. In vulgar design, the curves of the circling tendril would have been similar to each other, and might have been drawn by a machine, or by some mathematical formula. But in good design all imitation by machinery is impossible. No curve is like another for an instant; no branch springs at an expected point. A cadence is observed, as in the returning clauses of a beautiful air in music; but every clause has its own change, its own surprises. The enclosing form is here stiff and (nearly) straight-sided, in order to oppose the circular scroll-work; but on looking close it will be found that each of its sides is a portion of an infinite curve, almost too delicate to be traced; except the short lowest one, which is made quite straight, to oppose the rest.