was the difficulty got over? It was effected by means of this golden rule. This is its great, its ruling application; and if we adopt the notion that the ancients were possessed with the idea of the existence of angular symmetry, we shall have no difficulty in accounting for their appreciation of this problem. Nay, we may even go further, and admit, with Dr Zeising, the interpretation of the passage of Plato,—only with this limitation, that Plato, as a geometer, was carried away by the geometry of æsthetics from the thing itself. It may be asked again—Is it not probable that _some_ proportionality does exist amongst the parts of natural objects? We reply—That, _à priori_, we expect some such system to exist, but that it is inconsistent with the scheme of _least effort_, which pervades and characterises all natural succession in space or in time, that that system should be a complicated one. Whatever it is, its essence must be simplicity. And no system of simple linear proportion is found in nature; quite the contrary. We are, therefore, driven to another hypothesis, viz.—that the simplicity is one of angles, not of lines; that the eye estimates by search round a point, not by ascending and descending, going to the right and to the left,—a theory which we conceive all nature conspires to prove. Beauty was not created for the eye of man, but the eye of man and his mental eye were created for the appreciation of beauty. Examine the forms of animals and plants so minute that nothing short of the most recent improvements in the microscope can succeed in detecting their symmetry; or examine the forms of those little silicious creations which grew thousands of years before Man was placed on the earth, and, with forms of marvellous and varied beauty, they all point to its source in angular symmetry. This is the keystone of formal beauty, alike in the minutest animalcule, and in the noblest of God’s works, his own image—Man.” THE END. BALLANTYNE AND COMPANY, PRINTERS, EDINBURGH. FOOTNOTES [1] Sir David Brewster. [2] No. CLVIII., October 1843. [3] Diogenes Laërtius’s “Lives of the Philosophers,” literally translated. Bohn: London. [4] Ibid. [5] Rose’s “Biographical Dictionary.” [6] Professor Laycock, now of the University of Edinburgh. [7] “The Geometric Beauty of the Human Figure Defined,” &c. [8] Longman and Co., London. [9] See Appendix. [10] “The Orthographic Beauty of the Parthenon,” &c., and “The Harmonic Law of Nature applied to Architectural Design.” [11] For further details, see “Harmonic Law of Nature,” &c. [12] By a very simple machine, which I have lately invented, an ellipse of any given proportions, even to those of (¹⁄₆₄), which is the curve of the entases of the columns of the Parthenon (see Plate VII.), and of any length, from half an inch to fifty feet or upwards, may be easily and correctly described; the length and angle of the required ellipse being all that need be given.