In other articles, where the matter is of prime importance, I have been anxious faithfully to reproduce the original; nor have I in any such cases allowed a regard for form to interfere with the plain duty of exactly rendering the author’s meaning. E. ATKINSON. PORTESBERY HILL, CAMBERLEY: _Dec. 1880_. CONTENTS. LECTURE PAGE I. GUSTAV MAGNUS. IN MEMORIAM 1 II. ON THE ORIGIN AND SIGNIFICANCE OF GEOMETRICAL AXIOMS 27 III. ON THE RELATION OF OPTICS TO PAINTING 73 I. Form 78 II. Shade 94 III. Colour 110 IV. Harmony of Colour 124 IV. ON THE ORIGIN OF THE PLANETARY SYSTEM 139 V. ON THOUGHT IN MEDICINE 199 VI. ON ACADEMIC FREEDOM IN GERMAN UNIVERSITIES 237 VII. HERMANN VON HELMHOLTZ. AN AUTOBIOGRAPHICAL SKETCH 266 GUSTAV MAGNUS. _In Memoriam._ _Address delivered in the Leibnitz meeting of the Academy of Sciences on July 6, 1871._ The honourable duty has fallen on me of expressing in the name of this Academy what it has lost in Gustav Magnus, who belonged to it for thirty years. As a grateful pupil, as a friend, and finally as his successor, it was a pleasure to me as well as a duty to fulfil such a task. But I find the best part of my work already done by our colleague Hofmann at the request of the German Chemical Society, of which he is the President. He has solved the difficulty of giving a picture of the life and work of Magnus in the most complete and most charming manner. He has not only anticipated me, but he stood in much closer and more intimate personal relation to Magnus than I did; and, on the other hand, he is much better qualified than I to pronounce a competent judgment on the principal side of Magnus’s activity, namely, the chemical. Hence what remains for me to do is greatly restricted. I shall scarcely venture to speak as the biographer of Magnus, but only of what he was to us and to science, to represent which is our allotted task.