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). [Sidenote: Plate XVIII.] 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.