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 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] Sec. 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.