Of the work alluded to at page 58 I was favoured with two opinions—the one referring to the theory it propounds, and the other to its anatomical accuracy—both of which I have been kindly permitted to publish. The first is from Sir WILLIAM HAMILTON, Bart., professor of logic and metaphysics in the University of Edinburgh, and is as follows:— “Your very elegant volume is to me extremely interesting, as affording an able contribution to what is the ancient, and, I conceive, the true theory of the Beautiful. But though your doctrine coincides with the one prevalent through all antiquity, it appears to me quite independent and original in you; and I esteem it the more, that it stands opposed to the hundred one-sided and exclusive views prevalent in modern times.—_16 Great King Street, March 5, 1849._” The second is from JOHN GOODSIR, Esq., professor of anatomy in the University of Edinburgh, and is as follows:— “I have examined the plates in your work on the proportions of the human head and countenance, and find the head you have given as typical of human beauty to be anatomically correct in its structure, only differing from ordinary nature in its proportions being more mathematically precise, and consequently more symmetrically beautiful.—_College, Edinburgh, 17th April 1849._” No. IV. I shall here shew, as I have done in a former work, how the curvilinear outline of the figure is traced upon the rectilinear diagrams by portions of the ellipse of (¹⁄₃), (¹⁄₄), (¹⁄₅), and (¹⁄₆). [Sidenote: Plate XIX.]