| Tonic. | Dominant. | Mediant. | Subtonic. |
|---|---|---|---|
| (¹⁄₂) | (¹⁄₃) | (¹⁄₅) | (¹⁄₇) |
| (¹⁄₄) | (¹⁄₆) |
These angles, and the figures which belong to them, are thus arranged:—
The vertical line A B ([Plate IX.] fig. 2) represents the full length of the head and face. Taking this line as the greater axis of an ellipse of (¹⁄₃), such an ellipse is described around it. Through A the lines A G, A K, A L, A M, and A N, are drawn on each side of the line A B, making, with the vertical, respectively the angles of (¹⁄₃), (¹⁄₄), (¹⁄₅), (¹⁄₆), and (¹⁄₇). Through the points G, K, L, M, and N, where these straight lines meet the curved line of the ellipse, horizontal lines are drawn by which the following isosceles triangles are formed, A G G, A K K, A L L, A M M, and A N N. From the centre X of the equilateral triangle A G G the curvilinear figure of (¹⁄₂), viz., the circle, is described circumscribing that triangle.
The curvilinear plane figures of (¹⁄₂) and (¹⁄₃), respectively, represent the solid bodies of which they are sections, viz., a sphere and a prolate spheroid. These bodies, from the manner in which they are here placed, are partially amalgamated, as shewn in figures 1 and 3 of the same plate, thus representing the form of the human head and countenance, both in their external appearance and osseous structure, more correctly than they could be represented by any other geometrical figures. Thus, the angles of (¹⁄₂) and (¹⁄₃) determine the typical form.
From each of the points u and n, where A M cuts G G on both sides of A B, a circle is described through the points p and q, where A K cuts G G on both sides of A B, and with the same radius a circle is described from the point a, where K K cuts A B.
The circles u and n determine the position and size of the eyeballs, and the circle a the width of the nose, as also the horizontal width of the mouth.
The lines G G and K K also determine the length of the joinings of the ear to the head. The lines L L and M M determine the vertical width of the mouth and lips when at perfect repose, and the line N N the superior edge of the chin. Thus simply are the features arranged and proportioned on the facial surface.
It must, however, be borne in mind, that in treating simply of the æsthetic beauty of the human head and countenance, we have only to do with the external appearance. In this research, therefore, the system of Dr Camper, Dr Owen, and others, whose investigations were more of a physiological than an æsthetic character, can be of little service; because, according to that system, the facial angle is determined by drawing a line tangential to the exterior margin of the sockets of the front teeth of the upper jaw, and the most prominent part of the forehead. Now, as these sockets are, when the skull is naturally clothed, and the features in repose, entirely concealed by the upper lip, we must take the prominent part of it, instead of the sockets under it, in order to determine properly this distinguishing mark of humanity. And I believe it will be found, that when the head is properly poised, the nearer the angle which this line makes with the horizontal approaches 90°, the more symmetrically beautiful will be the general arrangement of the parts (see line y z, figure 3, [Plate IX.]).