No. 3921, DECEMBER 23, 1944 NATURE 791 The Royal Society elected Barkla to its fellowship in appointed assistant professor of mathematics at 1912, and in the following year he accepted the pro­ Princeton in 1909. It was here that he wrote the fessorship of natural philosophy in the University of memoir on the "General Theory of Linear Difference Edinburgh, which he held until his death. Equations" (Trans. Amer. Math. Soc., 1911) which During the most active period of his life, Barkla's first brought him into prominence; the ".Jahrbuch investigations dealt mainly with X-rays and their iiber die Fortschritte der Mathematik" devoted more absorption by matter, and with the emission of than two pages to a notice of it, a rare honour for a secondary radiation. He was the first to show that young and unknown author. Fundamental solutions the secondary emission is of two kinds, one consisting of linear difference equations with rational coefficients of X-rays scattered unchanged in quality, and the were obtained for the entire plane of the complex other a 'fluorescent radiation', characteristic of the variable by direct matrix methods, and their nature scattering substance and accompanied by selective was studied from the functional point of view. Birk­ absorption of the primary beam. The secondary hoff showed that there exists a purely Riemannian radiation of the first kind Barkla showed to be theory of the equations, and found quantities which polarized, an experimental result of fundamental play a part like that of the monodromic group con­ importance, for it indicated that X-radiation was to stants of an ordinary linear differential equation. be regarded as similar to ordinary light, a point His methods were of wide generality, and the paper which, up to that time, was thought to be doubtful. constituted a striking advance in the subject, to For the discovery of the characteristic radiation which he made further contributions from time to and for the explanation of its origin Barkla was most time, notably in a memoir in Acta Math., 54 (1930). deservedly awarded the Nobel Prize for Physics in A closely related branch of mathematics which the year 1917. His outstanding achievements were also owes much to Birkhoff is the theory of linear also recognized by the Royal Society, which appointed differential equations, on which he published many him Bakerian Lecturer for 1916 and .awarded him memoirs from 1910 onwards (Proc. Amer. Acad. and the Hughes Medal in the following year. Trans. Amer. Math. Soc.); the earlier ones were Barkla was a successful teacher who inspired many particularly concerned with the problem of construct­ of his pupils with an enthusiasm for research. He ing systems of linear differential equations with pre­ was in great request as an examiner in physics, and scribed singular points of given character and with few excelled him at this work. His long experience a given monodromic group. of students in three universities, the wide range of Birkhoff's interests were shared between pure and his knowledge of physics, his judgment and common applied mathematics, and his work in dynamics was sense made him an eminently fair and discriminating of great value. In an extensive memoir-almost a examiner. He would re-read with extreme patience complete treatise--on "Dynamical Systems with Two (not always shared by his co-examiner) any script of Degrees of Freedom" (Trans. Amer. Math. Soc., 18 ; a 'border-line' candidate which he found difficult to 1917), he reduced all problems relating to such assess, and his verdict, when finally delivered, could systems, even in the 'irreversible' case, to the problem be accepted with confidence. of determining the orbits of a particle constrained While a lecturer at Liverpool, Barkla married to move on a smooth surface which rotates about Mary Esther, eldest daughter of the late .John T. a fixed axis with uniform angular velocity and which Cowell, receiver-general of the Isle of Man. He carries with it a conservative field of force ; and he leaves two sons and a daughter. Only in t.he last year showed how the existence of periodic solutions may was his life clouded by indifferent health ; but be directly inferred, and their form determined. This the family had previously suffered a grievous loss by investigation was followed by others, especially on the death at Carthage in August 1943 of the young­ periodic orbits and the problem of three bodies est son, Flight-Lieutenant Michael Barkla, whose (Acta Math., Amer. J. Math. and elsewhere) ; a achievements at school and at the university had connected account of much of his dynamical work given promise of a career no less brilliant than that appeared in 1927 as one of the American Mathematical of his distinguished father. Society's Colloquium volumes, under the title Those who were privileged to know Barkla well "Dynamical Systems". will treasure the memory of his open-hearted friendli­ His two books on relativity, "Relativity and ness and personal charm, of the delights of the Modern Physics" (1923) and "The Origin, Nature, Hermitage of Braid-his earlier home in Edinburgh and Influence of Relativity" (1925) were useful and --and of the almost idyllic happiness of his domestic widely read, and characteristically original in treat­ life there. FRANK HoRTON. ment. In later life, Birkhoff became much occupied with the discovery of mathematical relations in ::esthetics. Prof. G. D. Birkhoff As is well known, more than two thousand years ago THE many friends of Prof. G. D. Birkhoff on the Pythagoras fonnded the scientific theory of music by eastern side of the Atlantic are deeply grieved to showing that simple numerical ratios exist between hear of his death on November 12. For a whole the lengths of the strings the notes of which yield generation he had been a commanding figure among agreeable melodic progressions. Birkhoff's aim was mathematicians and a link between American men to create a theory of similar character for the fine of science and their colleagues ill both western and arts; the results obtained were described in his eastern Europe. book "Aesthetic Measure", published in 1933, George David Birkhoff was born at Overisel, Birkhoff was professor of mathematics in Harvard Michigan, on March 21, 1884; as the name would University from 1919 onwards, president of the indicate, his family was originally Dutch, but it has American Mathematical Society during 1924--26, long been settled in the United States. He studied president of the American Association for the first at Chicago and then at Harvard, returning to Advancement of Science during 1936-37; an Chicago for his doctorate ; and, after a short period honorary doctor of many American universities and as instructor in the University of Wisconsin, was of St. Andrews, Poitiers, Paris, Athens and Sofia; 792 NATURE DECEMBER 23, 1944 VoL. 154 a foreign member of many European academies discovery and application of thiatricarbocyanines. (including the Institut de France, the Lincei and the Later he turned to demonstrating the importance Pontifical Academy) and mathematical societies, and of photography as an indispensable tool in many an Officier de Ia Legion d'honneur. His last years branches of science and industry, and in these lectures were gladdened by the knowledge that his brilliant Bloch referred- always to his convictiop. that photo­ son Garrett was steadily:advancing towards a position graphy is grossly neglected by British universities in the world of mathematics not inferior to his own. as a subject for teaching and research. The founda­ E. T. WHITTAKER. tion of a chair of photographic science at a university in Britain was a cause very dear to him, so that he found particular pleasure in helping academic scien­ tific workers in their photographic problems. Thus Dr. 0. F. Bloch by collaboration with Dr. F. W. Aston he produced OLAF BLOCH was a man of remarkable energy plates especially designed for recording atomic par­ largely applied to the progress of photographic science ticles of low penetration, and these were used in the and in furthering the application of photography as a classical investigation of isotopes. A range of materials tool in many branches of science and technology. He of special characteristics and spectral sensitivities received his earliest scientific training at the Finsbury was prepared for use in astronomy and related Technical Institute under Prof. H. E. Armstrong, sciences. More recently, Bloch eagerly accepted and having spent some years in the Davy Faraday opportunities to collaborate with atomic physicists Laboratory and in chemical manufacture, he joined· to evolve photographic emulsion layers of value in the staff of Ilford, Ltd., in 1910. Little can be written recording tracks produced by penetrating atomic of his very successful work over many years to pro­ particles. duce improved light-sensitive materials, for much of These and other services to scientific investigation it was made known only to his closest associates and were recognized by the University of Aberdeen by publication in this field is rare ; but mention may the award of the honorary degree of LL.D. He be made of important work with F. F. Renwick on received the Progress Medal of the Royal Photographic the optical properties of photographic layers, and Society, and, appropriately, was chosen to preside at early attempts, with Miss F. M. Hamer, to relate the commemoration of the centenary of photography the chemical structure of cyanine dyes with their at the Royal Society of Arts in 1939. sensitizing properties. Away from his work, Bloch had a remarkable As secretary of the Scientific and Technical Group range of interests ; he was deeply appreciative of of the Royal Photographic Society in the years literature and the arts, and was a keen gardener with following the War of 1914-18, Bloch took a leading an encyclopoodic knowledge of garden plants.