The fact is the theory of “beautiful” rectangles is not new. The classic exponent of it is Fechner, who essayed to base it on actual experiment. He placed a number of rectangular cards of various dimensions before his friends, and asked them to select the one they thought most beautiful. Apparently the “golden section” rectangle got most votes. But “most of the persons began by saying that it all depended on the application to be made of the figure, and on being told to disregard this, showed much hesitation in choosing.” (Bosanquet: “History of Æsthetic,” p. 382.) If they had been Greeks of the best period, they would have all gone with one accord for the “golden section” rectangle. Nor have the geometers of beauty restricted their favours to the rectangle. Some have favoured the circle, some the square, others the ellipse. And what about Hogarth’s “line of beauty”? I last saw it affectionately alluded to in the advertisement of a corset manufacturer. So, evidently, Hogarth’s idea has not been wasted. One sympathizes with Fechner’s friends who said it all depended upon the application to be made of the figure. The “art” in a picture is generally to be looked for inside the frame. The Parthenon may have been planned on the √5/2 rectangle, but you cannot evolve the Parthenon itself out of that vulgar fraction. Fechner proceeded on the assumption that art is a physical fact and that its “secret” could be wrung out of it, as in any other physical inquiry, by observation and experiment, by induction from a sufficient number of facts. But when he came to have a theory of it he found, like anybody else, that introspection was the only way.