appreciates the simplicity of their relations. In selecting the prominent features of a figure, the eye is not seeking to compare their relative distances—it is occupied solely with their relative positions. In tracing the contour, in like manner, it is not left in vague uncertainty as to what is the curve which is presented to it; unconsciously it feels the complete ellipse developed before it; and if that ellipse and its position are both formed by angles of the same simple relative value as those which aided its determination of the positions of the prominent features, it is satisfied, and finds the symmetry perfect. Müller, and other investigators into the archæology of art, refer to the great difficulty which exists in discovering the principles which the ancients followed in regard to the proportions of the human figure, from the different sexes and characters to which they require to be applied. But in the system thus founded upon the harmonic law of nature, no such difficulty is felt, for it is as applicable to the massive proportions which characterise the ancient representations of the Hercules, as to the delicate and perfectly symmetrical beauty of the Venus. This change is effected simply by an increase in the fundamental angle. For instance, in the construction of a figure of the exact proportions of the Venus, the right angle is adopted. But in the construction of a figure of the massive proportions of the Hercules, it is requisite to adopt an angle which bears to the right angle the ratio of 6:5. The adoption of this angle I have shewn in another work[20] to produce in the Hercules those proportions which are so characteristic of physical power. The ellipses which govern the outline, being also formed upon the same larger class of angles, give the contour of the muscles a more massive character. In comparing the male and female forms thus geometrically constructed, it will be found that that of the female is more harmoniously symmetrical, because the right angle is the fundamental angle for the trunk and the limbs as well as for the head and countenance; while in that of the male, the right angle is the fundamental angle for the head only. It may also be observed, that, from the greater proportional width of the pelvis of the female, the centres of that motion which the heads of the thigh bones perform in the cotyloid cavities, and the centres of that still more extensive range of motion which the arm is capable of performing at the shoulder joints, are nearly in the same line which determines the central motion of the vertebral column, while those of the male are not; consequently all the motions of the female are more graceful than those of the male.