Middlesex Hospital-Reports for 1893. 8vo. 1894. New South Wales, The Agent-General for—A Statistical Account of the Seven Colonies of Australasia. By G. A. Boulenger. 8vo. 1894. New York Academy of Sciences-Transactions, Vol. XIII. 1893-94. 8vo. New Zealand, The Registrar-General of-Statistics of the Colony of New Zealand for 1893. 8vo. 1894. North of England Institute of Mining and Mechanical Engineers—Transactions, Numismatic Society-Chronicle and Journal, 1894, Part 4. 8vo. 1894. 8vo. Photographic Society of Great Britain, Royal―Journal and Transactions, Vol. Physical Society of London-Proceedings, Vol. XIII. Part 3. 8vo. 1895. 1894. Roma, Ministero di Agricultura, Industria e Commercio-Statistica delle Biblio- Mathematisch-physische Classe, Band XXI. No. 3. 8vo. 1895. Society of Aniiquaries-Proceedings, 2nd Series, Vol. XV. No. 2. 8vo. 1894. Society of Arts-Journal for February, 1895. 8vo. St. Petersbourg, Académie Impériale des Sciences—Bulletin, Vo Serie, Tome II. No. 1. 8vo. 1895. Tacchini, Prof. P. Hon. Mem. R.I. (the Author)-Memorie della Società degli Spettroscopisti Italiani, Vol. XXIII. Disp. 12. 4to. 1895. United Service Institution, Royal-Journal, No. 204. 8vo. 1895. United States Patent Office-Official Gazette, Vol. LXIX. Nos. 10-12. 8vo. 1894. Vereins zur Beförderung des Gewerbfleisses in Preussen-Verhandlungen, 1895, Heft. 1. 4to. 1895. WEEKLY EVENING MEETING, Friday, March 8, 1895. SIR FREDERICK ABEL, BART. K.C.B. D.C.L. LL.D. F.R.S. PROFESSOR A. W. RÜCKER, M.A. F.R.S. M.R.I. The Physical Work of von Helmholtz. THE career we are to consider this evening was a career of singular distinction. In days when the range of "natural knowledge" is so vast that most workers are compelled to be content if they can add something to one or two of the sub-divisions of one of the main branches of science, von Helmholtz showed that it is not impossible to be at once a great mathematician, a great experimental physicist, and, in the widest sense of the term, a great biologist. It was but eight months yesterday since he delivered his last lecture; it is six months to-day since he died, and the interval is too short for us to attempt to decide on the exact place which will be assigned to him by posterity; but making all allowance for the fact that each age is apt to place its own great among the greatest, making all allowance for the spell which his name cast over many of us in the lecture rooms where we ourselves first gained some knowledge of science, I am sure that I only express the views of all those who know his work best, when I say that we place him in the very front rank of those who have led the great scientific movement of our time. This opinion I have now to justify. I must try to convey to you in some sixty minutes an outline of the work of more than fifty strenuous years, to give you some idea of the wide range of the multifold activities which were crowded into them, of the marvellous insight with which the most diverse problems were attacked and solved, and, if it may be, some image of the man himself. The task is impossible, and I can but attempt some fragments of it. The history of von Helmholtz is in one respect a simple tale. There are no life and death struggles with fate to record. His work was not done with the wolf at the door, or while he himself was wrestling with disease. He passed through no crises in which success or failure, immortality or oblivion, seemed to depend on the casting of a die. He suffered neither from poverty nor riches. He was a hale, strong man on whom external circumstances neither imposed exceptional disabilities, nor conferred exceptional advantages, but who, by sheer force of the genius that was in him, passed on from success to success till he was recognised by all as the admirable Crichton of modern science, the most widely cultivated of all students of nature, the acknowledged leader of German science, and one of the first scientific men in the world. It is the more fitting that this evening should have been set aside for the consideration of the work of Helmholtz, in that England may claim some share in his greatness. Before her marriage his mother bore an English name- -Čaroline Penn; she was, as her name implied, of English descent. His father was a Professor of Literature in the Gymnasium at Potsdam, so that his early days were passed amid that plain living and high thinking which are characteristic of intellectual circles in Germany. The boy did well at school, and when the time came for choosing a profession, his passion for mathematics and physics had already developed itself. The course of his love for these sciences did not run quite smooth. The path of his ambition was crossed by the hard necessity which in some cases checks, in others fosters, but in all chastens the aspirations of youth. He had to make his livelihood. Science must be to him what the Germans happily call a "bread-study." Medicine offered a fair prospect of prosperity. Physics, in those days, was but an intellectual pastime. And so the young man took his father's advice, and became an army doctor. In this, as in so many other cases, "the path of duty was the way to glory." It is possible that if von Helmholtz had been what-with a sad consciousness of the limitations it implies-I may call a mere physicist, he would have played a greater part in the development of some of those subjects, the study of which he initiated or helped to initiate, but did not thereafter pursue. It is possible that had he been a biologist, and nothing more, he would have followed up the early investigation in which he dealt a blow at the theory that putrefaction and fermentation are chemical processes only, clearly indicating, if he did not actually demonstrate, that the decay which follows death is due to an outburst of low forms of life. He might thus under other circumstances have done work for which he showed his competence, but which is now chiefly associated with other names; but it is certain that without the unusual combination of wonderful mathematical power and a professional knowledge of anatomy, he would never have accomplished the special tasks which it is his special glory to have achieved. His first three papers, however, hardly displayed the fusion between his various powers which was afterwards so remarkable a characteristic of his work. The first two were on biological subjects. The third was the famous essay on the 'Conservation of Force.' I have told elsewhere the story of the dramatic circumstances under which it was given to the world, of the interest it excited among the members of the Physical Society of Berlin, the refusal of the editor of Poggendorf's Annalen to publish it, and the final triumph of the author and his views.* Helmholtz was not, and did not claim to be an original author of the doctrine of the conservation of energy; but two young men, Sir William Thomson in England, and Helmholtz in Germany, independently, and within a month of each other, were the first persons who compelled the scientific world to regard it seriously. There is one interesting fact which connects this essay directly with the Royal Institution. Four years after it was published, it was placed by Du Bois Reymond in the hands of one who was lost to science in the same year as von Helmholtz himself-the late Prof. Tyndall. He was much impressed, and has spoken of the incident as bringing him face to face with the great doctrine of the "Conservation of Energy." He translated the essay into English, and for many years made it his habit to place every physical paper published by Helmholtz within the reach of English readers. And now, having brought you to the point at which Helmholtz may be said to have been fairly started on his life's work, let me first describe briefly his official career, before I consider his achievements in greater detail. When his extraordinary abilities became evident, he was permitted to sever his connection with the army. At twenty-seven years of age he became Teacher of Anatomy in the Academy of Arts at Berlin. In the next year he was appointed Professor of Anatomy and Physiology at Königsberg, and he held similar posts in the Universities of Bonn (1855-58) and Heidelberg (1858-71). It was not till 1871 that his early love for physics was finally rewarded. When the chair of Physics was to be filled in the University of the newly-founded German Empire, in Berlin, it was felt that even in Germany-the land of specialists-no better occupant could be found than one who was then in his fiftieth year, and who had been all his life a teacher of anatomy and physiology. The choice was universally approved and completely justified, and von Helmholtz held this post till his death. In this connection I am, by the kindness of Sir Henry Roscoe, enabled to show to you a relic of remarkable interest. It is a photograph of the great teacher and investigator, taken at the very last lecture that he delivered-that, namely, on July 7, 1894. For some years, that is, from the date of its foundation, von Helmholtz was the president of the Physikalisch-Technische ReichsAnstalt in Charlottenburg. This institution, founded partly by the munificence of the late Dr. Werner Siemens, partly by funds supplied by the State, has no precise analogue in this country. It is devoted to the carrying out of systematic researches on questions of fundamental importance to which a long time must be devoted. *Fortnightly Review, November, 1894. + Introduction to Popular Lectures by Helmholtz,' translated by E. Atkinson, 1873. The most characteristic work of Helmholtz was, as I have already hinted, that in which his knowledge of physics and his knowledge of anatomy were both directed to a common end. He dealt in turns with the external physical phenomena, with the mechanism of the organs which the phenomena affect, with the relations between the mechanical effect on the organ and the sensations which it excites, and, lastly, with the connection between the sensations in those simple cases which can alone be investigated in the laboratory, and the complex laws of æsthetics and art. The two books in which these problems were chiefly treated were the 'Physiological Optics,' and the Sensations of Sound.' It is impossible to do more than lay before you a sample which may afford some idea of the intricacy of the problems with which he dealt, and of the pitfalls amongst which he walked so warily. For this purpose I have chosen one branch of his work on Sound.' I have deliberately selected that particular portion which has been most questioned, that on which the verdict of most of those who have sat in judgment on his views has been against him. In discussing this question I must give a general description of the principle phenomena; but if I were to attempt an exhaustive catalogue of all the facts disputed and undisputed, and of all the theories which have been based upon or upset by them, not only would time fail me, but those who have not given special attention to the subject would, I fear, become hopelessly confused amid the chaos of opposing statements and views. Another reason which urges me to be brief, is that a few years ago Prof. Silvanus Thompson explained the whole subject to the members of the Royal Institution, having kindly consented to act as the mouthpiece of the celebrated instrument maker, König, who has played so large a part in these controversies. Among the chief achievements of Helmholtz was an explanation of the physical difference between pairs of notes which we recognise as concords and discords respectively. When two neighbouring notes are sounded, alternate swellings and fallings off of the intensity are heard which are called beats. These produce an unpleasant effect, which depends partly on their number, partly on the relative pitches of the beating notes. When two notes beat badly, they form an intolerable discord. When they become separated by a wider interval, the beats are so rapid that they cease to be unpleasant. The sense of dissonance produced by many of these wider intervals, such as the seventh (47), requires further explanation. In general, the fundamental musical note is only the first and loudest of a series of so-called partials, whose vibration frequencies are 2, 3, 4, &c. times that of the fundamental, and the consonance and dissonance of two notes is shown to depend on the presence or absence of beats between important members of these series. Thus in the case of the seventh the frequencies of the octave of the lower note and that of the upper |