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:— Tonic Dominant Mediant Angles. Angles. Angles. (¹⁄₂) (¹⁄₃) (²⁄₅) (¹⁄₄) (¹⁄₆) (¹⁄₅) (¹⁄₁₂) [Sidenote: Plate III.] A diagram of the rectilinear orthography of this portico is given in Plate III. Its construction is similar to that of the Parthenon in respect to the harmonic parts of the right angle, and I have therefore only to observe, that the line A E makes an angle of (¹⁄₄); the line A D an angle of (¹⁄₃); the line A C an angle of (²⁄₅); the line G D an angle of (¹⁄₆); and the lines E Z and L Y angles of (¹⁄₁₂) with the horizontal.