In the diagram ([Plate XVII.]), I endeavour to exhibit the geometric construction of the upper part of one of the ornamental apices, termed antefixæ, which surmounted the cornice of the Parthenon.
The first ellipse employed is that of (¹⁄₃), whose greater axis a b is in the vertical line; the second is also that of (¹⁄₃), whose greater axis c d makes, with the vertical, an angle of (¹⁄₁₂); the third ellipse is the same with its major axis e f in the vertical line. Through one of the foci of this ellipse at A the line A C is drawn, and upon the part of the circumference C e, the number of parts, 1, 2, 3, 4, 5, 6, 7, of which the surmounting part of this ornament is to consist, are set off. That part of the circumference of the ellipse whose larger axis is c d is divided from g to c into a like number of parts. The third ellipse employed is one of (¹⁄₄).
Take a cut-out ellipse of this kind, whose larger axis is equal in length to the inscribing rectangle. Place it with its vertex upon the same ellipse at g, so that its circumference will pass through C, and trace it; remove its apix first to p, then to q, and proceed in the same way to q, r, s, t, u, and v, so that its circumference will pass through the seven divisions on c g and e C: v o, u n, t m, s i, r k, q j, p l, and g x, are parts of the larger axes of the ellipses from which the curves are traced. The small ellipse of which the ends of the parts are formed is that of (¹⁄₃).
In the diagram ([Plate XVIII.]), I endeavour to exhibit the geometric construction of the ancient Grecian ornament, commonly called the Honeysuckle, from its resemblance to the flower of that name. The first part of the process is similar to that just explained with reference to the antefixæ of the Parthenon, although the angles in some parts differ. The contour is determined by the circumference of an ellipse of (¹⁄₃), whose major axis A B makes an angle of (¹⁄₉) with the vertical, and the leaves or petals are arranged upon a portion of the perimeter of a similar ellipse whose larger axis E F is in the vertical line, and these parts are again arranged upon a similar ellipse whose larger axis C D makes an angle of (¹⁄₁₂) with the vertical. The first series of curved lines proceeding from 1, 2, 3, 4, 5, 6, 7, and 8, are between K E and H C, part of the circumference of an ellipse of (¹⁄₃); and those between C H and A G are parts of the circumference of four ellipses, each of (¹⁄₃), but varying as to the lengths of their larger axes from 5 to 3 inches. The change from the convex to the concave, which produces the ogie forms of which this ornament is composed, takes place upon the line C H, and the lines a b, c d, e f, g h, i k, l m, n o, and p q, are parts of the larger axis of the four ellipses the circumference of which give the upper parts of the petals or leaves.
This peculiar Grecian ornament is often, like the antefixæ of the Parthenon, combined with the curve of the spiral scroll. But the volute is so well understood that I have not rendered my diagrams more complex by adding that figure. Many varieties of this union are to be found in Tatham’s etchings, already referred to. The antefixæ of the Parthenon, and its only other ornament the honeysuckle, as represented on the soffit of the cornice, are to be found in Stewart’s “Athens.”
APPENDIX.
No. I.
In pages [34], [35], and [58], I have reiterated an opinion advanced in several of my former works, viz., that, besides genius, and the study of nature, an additional cause must be assigned for the general excellence which characterises such works of Grecian art as were executed during a period commencing about 500 B.C., and ending about 200 B.C. And that this cause most probably was, that the artists of that period were instructed in a system of fixed principles, based upon the doctrines of Pythagoras and Plato. This opinion has not been objected to by the generality of those critics who have reviewed my works; but has, however, met with an opponent, whose recondite researches and learned observations are worthy of particular attention. These are given in an essay by Mr C. Knight Watson, “On the Classical Authorities for Ancient Art,” which appeared in the Cambridge Journal of Classical and Sacred Philology in June 1854. As this essay is not otherwise likely to meet the eyes of the generality of my readers, and as the objections he raises to my opinion only occupy two out of the sixteen ample paragraphs which constitute the first part of the essay, I shall quote them fully:—