Every line of this useful book shews that the author has contrived to intellectualise his subject in a very interesting manner. The principles of harmony in colour as applied to decorative purposes, are explained and enforced in a lucid and practical style, and the relations of the various tints and shades to each other, so as to produce a harmonious result, are descanted upon most satisfactorily and originally. _From the Edinburgh Review._ In so far as we know, Mr Hay is the first and only modern artist who has entered upon the study of these subjects without the trammels of prejudice and authority. Setting aside the ordinances of fashion, as well as the dicta of speculation, he has sought the foundation of his profession in the properties of light, and in the laws of visual sensation, by which these properties are recognised and modified. The truths to which he has appealed are fundamental and irrefragable. _From the Athenæum._ We have regarded, and do still regard, the production of Mr Hay’s works as a remarkable psychological phenomenon—one which is instructive both for the philosopher and the critic to study with care and interest, not unmingled with respect. We see how his mind has been gradually guided by Nature herself out of one track, and into another, and ever and anon leading him to some vein of the beautiful and true, hitherto unworked. VIII. In 4to, 25 Plates, price 36s., ON THE SCIENCE OF THOSE PROPORTIONS BY WHICH THE HUMAN HEAD AND COUNTENANCE, AS REPRESENTED IN ANCIENT GREEK ART, ARE DISTINGUISHED FROM THOSE OF ORDINARY NATURE. (PRINTED BY PERMISSION.) _From a Letter to the Author by Sir William Hamilton, Bart., Professor of Logic and Metaphysics in the Edinburgh University._ Your very elegant volume, “Science of those Proportions,” &c., is to me extremely interesting, as affording an able contribution to what is the ancient, and, I conceive, the true theory of the beautiful. But though your doctrine coincides with the one prevalent through all antiquity, it appears to me quite independent and original in you; and I esteem it the more that it stands opposed to the hundred one-sided and exclusive views prevalent in modern times. _From Chambers’s Edinburgh Journal._ We now come to another, and much more remarkable corroboration, which calls upon us to introduce to our readers one of the most valuable and original contributions that have ever been made to the Philosophy of Art, viz., Mr Hay’s work “On the Science of those Proportions,” &c. Mr Hay’s plan is simply to form a scale composed of the well-known vibrations of the monochord, which are the alphabet of music, and then to draw upon the quadrant of a circle angles _answering to these vibrations_. With the series of triangles thus obtained he combines a circle and an ellipse, the proportions of which are derived from the triangles themselves; and thus he obtains an infallible rule for the composition of the head of ideal beauty. IX.