[Sidenote: Plate XX.] In order to exemplify more clearly the manner in which these various curves appear in the outline of the figure, I give in Plate XX. the whole curvilinear figures, complete, to which these portions belong that form the outline of the sides of the head, neck, and trunk, and of the outer surface of the thighs and legs. The various angles which the axes of these ellipses form with the vertical, will be found amongst other details in the works I have just referred to. No. V. At page 85 I have remarked upon the variety that may be introduced into any particular form of vase; and, in order to give the reader an idea of the ease with which this may be done without violating the harmonic law, I shall here give three examples:— [Sidenote: Plate XXI.] The first of these (Plate XXI.) differs from the Portland vase, in the concave curve of the neck flowing more gradually into the convex curve of the body. [Sidenote: Plate XXII.] The second (Plate XXII.) differs from the same vase in the same change of contour, as also in being of a smaller diameter at the top and at the bottom. [Sidenote: Plate XXIII.] The third (Plate XXIII.) is the most simple arrangement of the elliptic curve by which this kind of form may be produced; and it differs from the Portland vase in the relative proportions of height and diameter, and in having a fuller curve of contour. The following comparison of the angles employed in these examples, with the angles employed in the original, will shew that the changes of contour in these forms, arise more from the mode in which the angles are arranged than in a change of the angles themselves:— Line Line Line Line Plate VIII. _A C_ (¹⁄₂) _B C_ (¹⁄₃) _o p_ (H) _v u_ (³⁄₁₀) Plate XXI. (¹⁄₂) (¹⁄₃) (²⁄₉) (¹⁄₄) Plate XXII. (¹⁄₂) (¹⁄₃) (¹⁄₈) (⁴⁄₉) Plate XXIII. (¹⁄₂) (¹⁄₄) (H) (-) Line Line Plate VIII. _m n_ (¹⁄₃) _i k_ (¹⁄₅) ellipse (¹⁄₄) rectangle (²⁄₅) Plate XXI. (²⁄₉) (¹⁄₅) (¹⁄₄) (²⁄₅) Plate XXII. (¹⁄₃) (¹⁄₅) (¹⁄₄) (²⁄₅) Plate XXIII. (¹⁄₅) (¹⁄₅) ellipses {(¹⁄₃)} (¹⁄₃) {(¹⁄₄)} The harmonic elements of each are therefore simply the following parts of the right angle:— Tonic. Dominant. Mediant. Submediant. Plate VIII. (¹⁄₂) (¹⁄₃) (¹⁄₅) (³⁄₁₀) (¹⁄₄) Tonic. Dominant. Mediant. Supertonic. Plate XXI. (¹⁄₂) (¹⁄₃) (¹⁄₅) (²⁄₉) (¹⁄₄) Tonic. Dominant. Mediant. Supertonic. Plate XXII. (¹⁄₂) (¹⁄₃) (¹⁄₅) (⁴⁄₉) (¹⁄₄) (¹⁄₈)