But I have shewn, in a former work,[13] that the contours of these mouldings are composed of curves of the composite ellipse,—a figure which I so name because it is composed simply of arcs of various ellipses harmonically flowing into each other. The composite ellipse, when drawn systematically upon the isosceles triangle, resembles closely parabolic and hyperbolic curves—only differing from these inasmuch as it possesses the essential quality of circumscribing harmonically one of the elementary rectilinear figures employed in architecture, while those of the parabola and hyperbola, as I have just observed, are merely curves of motion, and, consequently, never can harmonically circumscribe or be resolved into any regular figure. The composite ellipse may be thus described. [Sidenote: Plate VI.] Let A B C (Plate VI.) be a vertical isosceles triangle of (¹⁄₆), bisect A B in D, and through D draw indefinitely D _f_ perpendicular to A B, and through B draw indefinitely B _g_, making the angle D B _g_ (¹⁄₈), D _f_ and B _g_ intersecting each other in M. Take B D and D M as semi-axes of an ellipse, the foci of which will be at _p_ and _q_, in each of these, and in each of the foci _h t_ and _k r_ in the lines A C and B C, fix a pin, and one also in the point M, tie a thread around these pins, withdraw the pin from M, and trace the composite ellipse in the manner already described with respect to the simple ellipse. In some of my earlier works I described this figure by taking the angles of the isosceles triangle as foci; but the above method is much more correct. As the elementary angle of the triangle is (¹⁄₆), and that of the elliptic curve described around it (¹⁄₈), I call it the composite ellipse of (¹⁄₆) and (¹⁄₈), their harmonic ratio being 4:3; and so on of all others, according to the difference that may thus exist between the elementary angles. The visible curves which soften and beautify the melody of the outline of the front of the Parthenon, as given in Mr Penrose’s great work, I have carefully analysed, and have found them in as perfect agreement with this system, as its rectilinear harmony has been shewn to be. This I demonstrated in the work just referred to[14] by a series of twelve plates, shewing that the entasis of the columns (a subject upon which there has been much speculation) is simply an arc of an ellipse of (¹⁄₄₈), whose greater axis makes with the vertical an angle of (¹⁄₆₄); or simply, the form of one of these columns is the frustrum of an elliptic-sided or prolate-spheroidal cone, whose section is a composite ellipse of (¹⁄₄₈) and (¹⁄₆₄), the harmonic ratio of these two angles being 4:3, the same as that of the angles of the composite ellipse just exemplified. [Sidenote: Plate VII.] [Sidenote: Plate VIII.]