friendship. On the evening of the same day that very valuable Institution of the British Association, its conversazione, gave us opportunity for a good hour's talk and discussion over all that either of us knew of thermodynamics. I gained ideas which had never entered my mind before, and I thought I too suggested something worthy of Joule's consideration when I told him of Carnot's theory. Then and there in the Radcliffe Library, Oxford, we parted, both of us, I am sure, feeling that we had much more to say to one another and much matter for reflection in what we had talked over that evening. But what was my surprise a fortnight later when, walking down the valley of Chamounix, I saw in the distance a young man walking up the road towards me and carrying in his hand something which looked like a stick, but which he was using neither as an Alpenstock nor as a walking stick. It was Joule with a long thermometer in his hand, which he would not trust by itself in the char-à-banc coming slowly up the hill behind him lest it should get broken. But there comfortably and safely seated on the char-à-banc was his bride-the sympathetic companion and sharer in his work of after years. He had not told me in Section A or in the Radcliffe Library that he was going to be married in three days, but now in the valley of Chamounix, he introduced me to his young wife. We appointed to meet again a fortnight later at Martigny to make experiments on the heat of a waterfall (Sallanches) with that thermometer: and afterwards we met again and again and again, and from that time indeed remained close friends till the end of Joule's life. I had the great pleasure and satisfaction for many years, beginning just forty years ago, of making experiments along with Joule which led to some important results in respect to the theory of thermodynamics. This is one of the most valuable recollections of my life, and is indeed as valuable a recollection as I can conceive in the possession of any man interested in science. Joule's initial work was the very foundation of our knowledge of the steam engine and steam power. Taken along with Carnot's theory it has given the scientific founda tion on which all the great improvements since the year 1850 have been worked out, not in a haphazard way but on a careful philosophical basis. James Watt had anticipated to some degree in his compound engine and his expansive system the benefits now realised, but he was before his time in that respect and he had not the complete foundation which Joule's mechanical equivalent and Carnot's theory have since given for the improvement of the steam engine. May I be allowed to congratulate the city of Manchester on its proceedings to-day? When the cover was lifted from the statue of Joule I felt deeply touched at the sight of the face of my old friend. To my mind it is a most admirable likeness, and the ideality of the accessory of the little brass model held in the hand, the eidolon of what was in the mind of the powerful thinking face shown in marble, seems to me most interesting and most striking-I think I may say poetical. This little model is not Joule's first apparatus nor his second: it is his third and greatest apparatus for the determination of the mechanical equivalent of heat-that by which he corrected the British Association's standard ohm, which he found to be 17 per cent. wrong. Regarding the ohm a diplomatic correspondence is now going on through our Foreign Office with other Governments for the purpose of arranging the precise terms of the definition of the ohm, of which a correct standard was really first worked out by Joule. May I be allowed to congratulate the sculptor, Mr. Gilbert, on the great beauty, originality, and success of his work. Manchester now possesses two statues, Dalton on the left and Joule on the right of the entrance to its Municipal Buildings; the man who laid the foundation of the atomic theory in chemistry and the man who discovered the mechanical equivalent of heat. If the prosperity of Manchester does not depend on chemistry and on the steam engine and thermodynamics I do not know upon what it does depend, unless it be the energy and industry and honourable character of its inhabitants; but you must ever remember that the material prosperity of this great city has owed more to philosophic thought than to any material appliance whatever. ISOPERIMETRICAL PROBLEMS. [Being a Friday evening Lecture delivered to the Royal Institution, May 12th, 1893.] Dido, B. C. 800 or 900. Horatius Cocles, B.C. 508. Pappus, Book V., A.D. 390. John Bernoulli, A.D. 1700. Euler, A. D. 1744. Maupertuis (Least Action), b. 1698, d. 1759. Lagrange (Calculus of Variations), 1759. Hamilton (Actional Equations of Dynamics), 1834. THE first isoperimetrical problem known in history was practically solved by Dido, a clever Phoenician princess, who left her Tyrian home and emigrated to North Africa, with all her property and a large retinue, because her brother Pygmalion murdered her rich uncle and husband Acerbas, and plotted to defraud her of the money |