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.
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.
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 | Line | Line | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Plate VIII. | A C | (¹⁄₂) | B C | (¹⁄₃) | o p | (H) | v u | (³⁄₁₀) | m n | (¹⁄₃) | i k | (¹⁄₅) | ellipse | (¹⁄₄) | rectangle | (²⁄₅) |
| Plate XXI. | (¹⁄₂) | (¹⁄₃) | (²⁄₉) | (¹⁄₄) | (²⁄₉) | (¹⁄₅) | (¹⁄₄) | (²⁄₅) | ||||||||
| Plate XXII. | (¹⁄₂) | (¹⁄₃) | (¹⁄₈) | (⁴⁄₉) | (¹⁄₃) | (¹⁄₅) | (¹⁄₄) | (²⁄₅) | ||||||||
| Plate XXIII. | (¹⁄₂) | (¹⁄₄) | (H) | (-) | (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:—