“The Beauty of Curved Lines.—As from the foregoing analysis of the vision of straight lines in general, it results that they are deficient in the elements of ocular agreeableness, in other words, of beauty; little more need be said of regular and gentle curves, than that the survey of them is not attended with the abovementioned disadvantages. In viewing a regular curve, no muscle of the eyeball acts continuously and uniformly, but enjoys partial relief by remissions, or total relief by intermissions of its action; and the regularity of these remissions and intermissions, as well as the equal distribution of exercise, is promoted by the regularity of the curve. Acting in succession, the muscles afford mutual relief after actions of such short duration and variable intensity, as to afford positive pleasure; and in this muscular pleasure of the eye consists the beauty of configuration.
“The successive and accurate survey of distant points is not, however, invariably requisite to a degree of similar pleasure, in viewing a figure of such small angular extent as to be instantly recognised by one location of its image, as analogous to a larger one whose survey has directly afforded muscular pleasure. Although I thus recognise the influence of association, the facts of this very case afford an interesting confirmation of the physiological theory; for a large circle or ellipse is more beautiful than one of diminutive size. The beauty of the one is original, its influence is direct; the beauty of the other is in part borrowed, and this part is weakened by reflection. Or, to express it more literally, the one excites a pleasurable sensation, the other suggests a similar idea; the one affords a perception, the other a conception, of beauty. Such, even with similar color and brilliancy, would be the difference between the full moon and a circular dot (·) or period; such the difference between a rainbow and a diminutive arc (
) (◠), a short accent inverted. Here the critic might be inclined to charge us with confounding the beautiful with the sublime. But the fact is, that criticism has constructed the sublime—as it has the beautiful—from heterogeneous materials, one of which is identical with one of the elements of beauty, and should, in a physiological arrangement, be referred to the same class. In many instances a magnifying instrument will disclose minute irregularities and blemishes; but in every other case, physiology would show, that, within certain limits, to magnify a beautiful object is to magnify beauty.
“The foregoing statements of general principles preclude the necessity of minute details in relation to particular curves. I shall at present consider those which do not return into themselves, so as to constitute the outlines of figures in the geometrical sense. Let us first select a semi-circumference, for example, that of a rainbow of maximum dimensions. In tracing it once, we employ three out of the four muscles. They are brought into action successively and rapidly, but not abruptly. All these circumstances are favorable to pleasure. Yet they are not conducive to it in the highest possible degree; for each muscle acts only once unless the examination be repeated; and in case of its repetition, the momentum of the eyeball is destroyed in stopping and reversing its motion. The waving line, as Hogarth’s line of beauty, obviates the first difficulty. This ensures not only the successive action of different muscles, but a repetition of action in the same. If the line forms a number of equal waves, these repetitions will be proportional to the number of waves, and will alternately and totally relieve, at least two muscles, and allow, in the action of a third, regular remissions of intensity at equal intervals. We have proved then, that on this physiological theory, a semi-circumference possesses more of the elements of beauty than any straight line, and a regular-waved line more than either. These results are conformable to experience. If there is any difficulty in admitting this, it will vanish on comparing the ocular with other muscles.
“Let us select a joint, which, in its spherical form, and the circular arrangement of its muscles, is analogous to the eye; for example, the shoulder joint. I think it will be uniformly found, that in the use of this joint, the curves most readily traced, are those of gentle and nearly equal curvature, and being such as are most easily traced by the eye, they would appear more beautiful than those drawn by the fingers with the same education. For example, let a man, without bending his wrist or elbow, draw various lines with a light stick or cane on the surface of snow: the lines most easily drawn (or most easily traced if already drawn), will be curves of considerable beauty, and nearly equal curvature; such as waved lines and spirals and looped curves. Circles and ellipses would also be among the figures with most facility and precision traced, and especially in cases of repeated tracing; but we are not at present considering figures in the proper geometrical sense of the term. In writing letters by the above method, a succession of ‘e’s, would be more readily drawn than a succession of ‘i’s, or a zigzag line with acute angles.
“To institute a fair comparison between terminated lines and figures, the component lines of the figures should be as beautiful as the terminated lines with which they are compared. With this precaution, physiology will conduct to the conclusion, that figures are more beautiful than terminated lines. For the survey of any figure requires the successive action of all these ocular muscles, and a repeated survey requires no reversal of the motion.
“We may apply the same principles to figures as compared with each other. Here we shall find the advantage on the side of those which are geometrically regular. We perceive that the circle and ellipse must possess in great perfection the essentials of beauty.
“From figures, the transition is natural and easy to solids or bodies of three dimensions. The form of a body depends on those of all its faces and sections; and these last are plane figures. The elliptical sections of a regular spheroid are all highly beautiful, but its sections are not all elliptical. Unless the spheroid be in certain positions, the sphere possesses still higher beauty, as presenting the same circular and highly beautiful outline in every position; although a variety of positions is not essential to the perception of its peculiar beauty, whenever the observer has learned by different methods, and especially by different degrees of convergence of the two optic axes, to estimate the relative distances of the different points of the visible hemisphere, and thus to recognise the spherical form. I will only add, from the analysis of the beauty of the circle it is evident, that within certain limits, to magnify a sphere is to magnify its beauty.
“The relative beauty of the sphere and spheroid, and of the spheroid as compared with itself in different positions, is modified by symmetry. The principle of symmetry, is in some measure distinct from any other heretofore considered. It may be treated under the heads of 1st, geometrical symmetry, or symmetry of form; 2d, of symmetry of position.