We have already asserted that all curves are more beautiful than right lines. All curves, however, are not equally beautiful, and their differences of beauty depend on the different proportions borne to each other by those infinitely small right lines of which they may be conceived as composed. When these lines are equal and contain equal angles, there can be no connection or unity of sequence in them. The resulting curve, the circle, is therefore the least beautiful of all curves. When the lines bear to each other some certain proportion; or when, the lines remaining equal, the angles vary; or when by any means whatsoever, and in whatever complicated modes, such differences as shall imply connection are established between the infinitely small segments, the resulting curves become beautiful. The simplest of the beautiful curves are the conic, and the various spirals; but it is as rash as it is difficult to endeavor to trace any ground of superiority or inferiority among the infinite numbers of the higher curves. I believe that almost all are beautiful in their own nature, and that their comparative beauty depends on the constant quantities involved in their equations. Of this point I shall speak hereafter at greater length. Sec. 12. How by nature obtained. The universal forces of nature, and the individual energies of the matter submitted to them, are so appointed and balanced, that they are continually bringing out curves of this kind in all visible forms, and that circular lines become nearly impossible under any circumstances. The gradual acceleration, for instance, of velocity, in streams that descend from hill-sides, as it gradually increases their power of erosion increases in the same gradual degree the rate of curvature in the descent of the slope, until at a certain degree of steepness this descent meets, and is concealed by the right line of the detritus. The junction of this right line with the plain is again modified by the farther bounding of the larger blocks, and by the successively diminishing proportion of landslips caused by erosion at the bottom, so that the whole line of the hill is one of curvature, first, gradually increasing in rapidity to the maximum steepness of which the particular rock is capable, and then decreasing in a decreasing ratio, until it arrives at the plain level. This type of form, modified of course more or less by the original boldness of the mountain, and dependent both on its age, its constituent rock, and the circumstances of its exposure, is yet in its general formula applicable to all. So the curves of all things in motion, and of all organic forms, most rudely and simply in the shell spirals, and in their most complicated development in the muscular lines of the higher animals.