In Plate VII. is represented the section of such a cone, of which A B C is the isosceles triangle of (¹⁄₄₈), and B D and D M the semi-axes of an ellipse of (¹⁄₆₄). M N and O P are the entases of the column, and _d e f_ the normal construction of the capital. All these are fully illustrated in the work above referred to,[15] in which I have also shewn that the curve of the neck of the column is that of an ellipse of (¹⁄₆); the curve of the capital or echinus, that of an ellipse of (¹⁄₁₄); the curve of the moulding under the cymatium of the pediment, that of an ellipse of (¹⁄₃); and the curve of the bed-moulding of the cornice of the pediment, that of an ellipse of (¹⁄₃). The curve of the cavetto of the soffit of the corona is composed of ellipses of (¹⁄₆) and (¹⁄₁₄); the curve of the cymatium which surmounts the corona, is that of an ellipse of (¹⁄₃); the curve of the moulding of the capital of the antæ of the posticum, that of an ellipse of (¹⁄₃); the curves of the lower moulding of the same capital are composed of those of an ellipse of (¹⁄₃) and of the circle (¹⁄₂); the curve of the moulding which is placed between the two latter is that of an ellipse of (¹⁄₃); the curve of the upper moulding of the band under the beams of the ceiling of the peristyle, that of an ellipse of (¹⁄₃); the curve of the lower moulding of the same band, that of an ellipse of (¹⁄₄); and the curves of the moulding at the bottom of the small step or podium between the columns, are those of the circle (¹⁄₂) and of an ellipse of (¹⁄₃). I have also shewn the curve of the fluting of the columns to be that of (¹⁄₁₄). The greater axis of each of these ellipses, when not in the vertical or horizontal lines, makes an harmonic angle with one or other of them. In Plate VIII., sections of the two last-named mouldings are represented full size, which will give the reader an idea of the simple manner in which the ellipses are employed in the production of those harmonic curves. Thus we find that the system here adopted for applying this law of nature to the production of beauty in the abstract forms employed in architectural composition, so far from involving us in anything complicated, is characterised by extreme simplicity.