The angles which govern the proportions of this beautiful elevation are the following harmonic parts of the right angle—
| Tonic Angles. | Dominant Angles. | Mediant Angles. | Subtonic Angle. | Supertonic Angles. |
|---|---|---|---|---|
| (¹⁄₂) | (¹⁄₃) | (¹⁄₅) | (¹⁄₇) | (¹⁄₉) |
| (¹⁄₄) | (¹⁄₆) | (¹⁄₁₀) | (¹⁄₁₈) | |
| (¹⁄₈) | ||||
| (¹⁄₁₆) |
In [Plate II.] I give a diagram of its rectilinear orthography, which is simply constructed by lines drawn, either horizontally, vertically, or obliquely, which latter make with either of the former lines one or other of the harmonic angles in the above series. For example, the horizontal line AB represents the length of the base or surface of the upper step of the substructure of the building. The line AE, which makes an angle of (¹⁄₅) with the horizontal, determines the height of the colonnade. The line AD, which makes an angle of (¹⁄₄) with the horizontal, determines the height of the portico, exclusive of the pediment. The line AC, which makes an angle of (¹⁄₃) with the horizontal, determines the height of the portico, including the pediment. The line GD, which makes an angle of (¹⁄₇) with the horizontal, determines the form of the pediment. The lines EZ and LY, which respectively make angles of (¹⁄₁₆) and (¹⁄₁₈) with the horizontal, determine the breadth of the architrave, frieze, and cornice. The line v n u, which makes an angle of (¹⁄₃) with the vertical, determines the breadth of the triglyphs. The line t d, which makes an angle of (¹⁄₂), determines the breadth of the metops. The lines c b r f, and a i, which make each an angle of (¹⁄₆) with the vertical, determine the width of the five centre intercolumniations. The line z k, which makes an angle of (¹⁄₈) with the vertical, determines the width of the two remaining intercolumniations. The lines c s, q x, and y h, each of which makes an angle of (¹⁄₁₀) with the vertical, determine the diameters of the three columns on each side of the centre. The line w l, which makes an angle of (¹⁄₉) with the vertical, determines the diameter of the two remaining or corner columns.
In all this, the length and breadth of the parts are determined by horizontal and vertical lines, which are necessarily at right angles with each other, and the position of which are determined by one or other of the lines making the harmonic angles above enumerated.
Now, the lengths and breadths thus so simply determined by these few angles, have been proved to be correct by their agreement with the most careful measurements which could possibly be made of this exquisite specimen of formative art. These measurements were obtained by the “Society of Dilettanti,” London, who, expressly for that purpose, sent Mr F. C. Penrose, a highly educated architect, to Athens, where he remained for about five months, engaged in the execution of this interesting commission, the results of which are now published in a magnificent volume by the Society.[8] The agreement was so striking, that Mr Penrose has been publicly thanked by an eminent man of science for bearing testimony to the truth of my theory, who in doing so observes, “The dimensions which he (Mr Penrose) gives are to me the surest verification of the theory I could have desired. The minute discrepancies form that very element of practical incertitude, both as to execution and direct measurement, which always prevails in materialising a mathematical calculation made under such conditions.”[9]
Although the measurements taken by Mr Penrose are undeniably correct, as all who examine the great work just referred to must acknowledge, and although they have afforded me the best possible means of testing the accuracy of my theory as applied to the Parthenon, yet the ideas of Mr Penrose as to the principles they evolve are founded upon the fallacious doctrine which has so long prevailed, and still prevails, in the æsthetics of architecture, viz., that harmony may be imparted by ratios between the lengths and breadths of parts.
I have taken for my second example an elevation which, although of smaller dimensions, is no less celebrated for the beauty of its proportions than the Parthenon itself, viz., the front portico of the temple of Theseus, which has also been measured by Mr Penrose.
The angles which govern the proportions of this elevation are the following harmonic parts of the right angle:—