MacTutor
Sir James Hopwood Jeans was born at Southport on September 11, 1877.
He was the son of William Tulloch Jeans of Tulse Hill, his father's profession being that of parliamentary journalist. He was educated at Merchant Taylors' School from 1890 to 1896. He went up to Trinity College, Cambridge, as a Scholar in 1896, read mathematics, and was bracketed Second Wrangler in the Mathematical Tripos of 1898 with J. F. Cameron, now Master of Gonville and Caius College. He took a First Class in Part II of the Mathematical Tripos in 1900 and was awarded an Isaac Newton Studentship He won a Smith's Prize in 1900 and was elected to a Fellowship at Trinity in 1901. He was appointed University Lecturer in Mathematics in 1904 but became Professor of Applied Mathematics at Princeton, New Jersey, in 1905, holding the chair there until 1909. It was during this period that he published his well-known textbook "Theoretical Mechanics" (1906). He returned to Cambridge as Stokes Lecturer in 1910 but resigned the post in 1912. Thereafter he held no teaching post for the rest of his life, though he was appointed Professor of Astronomy at the Royal Institution in 1935 and was annually re-elected to the professorship until he resigned from ill-health in 1946.
He was awarded the Adams Prize of the University of Cambridge in 1917 for an essay entitled "Problems of Cosmogony and Stellar Dynamics", which was published in 1919. In 1922 he delivered the Halley Lecture at Oxford on the subject of "The Nebular Hypothesis and Modern Cosmogony". In 1923 he was appointed a Research Associate of Mount Wilson Observatory. In 1925 he delivered the Rouse Ball Lecture at Cambridge under the title "Atomicity and Quanta" and in 1930 the Rede Lecture, under the title, under the title "The Mysterious Universe".
He was awarded the Gold Medal of the Royal Astronomical Society in 1922 and served as President for the two years 1925–1927, delivering three Presidential Addresses on the respective occasions of presenting the Society's Gold Medal to Sir Frank Dyson (June 1925), Einstein (February 1926), and Schlesinger (February 1927). In 1927, the Royal Astronomical Society founded the annual George Darwin Lecture, the endowment for which was presented by Jeans, who thus desired to commemorate the famous mathematical astronomer who had been such an inspiration to him
Jeans was elected a Fellow of the Royal Society in 1906, at the early age of twenty-eight. He gave his Bakerian Lecture in 1917 under the title "The Configurations of Rotating Compressible Masses" (published in Phil. Trans. A, 218). He was awarded the Royal Medal of the Royal Society in 1919, in which year he became one of the Honorary Secretaries of that Society, serving until 1929. During his Secretaryship, he developed the Society's Proceedings A into a leading scientific journal from a status of comparative unimportance
He was created a knight in 1928. In 1934 he was President of the British Association at its Aberdeen meeting. He became an Honorary Fellow of the Institute of Physics in 1929. He was awarded the Franklin Medal in 1931, the Mukerjee Medal of the Indian Association for the Advancement of Science in 1937, and the Calcutta Medal of the Royal Asiatic Society of Bengal in 1938. He received honorary degrees from Oxford, Manchester, Dublin, Aberdeen, St. Andrews, Johns Hopkins, Benares, and Calcutta. He was awarded the supreme distinction of the Order of Merit in 1939
Jeans married Charlotte Tiffany, daughter of Alfred Mitchell, of New London, Connecticut, in 1907. She died in 1934, leaving one daughter. In 1935, he married Susi, daughter of Oskar Hock, of Vienna, by whom he had two sons and a daughter. He died at his home, Cleveland Lodge, Dorking, on September 16, 1946.
Jeans was brisk, matter-of-fact, and business-like in ordinary conversation, not at all suggesting the deep academic thinker and mathematician that he was. In lecturing, this style of his developed into a most attractive persuasiveness. He was also deeply interested in music and possessed and played his own organ. Mention may be made here of his semi-popular and highly successful book, Science and Music, published in 1938, in which his treatment ranged from "Tuning Forks and Pure Tones" through "Harmony and Discord" to the acoustics of the concert room
The Order of Merit was a public recognition of the fact that Jeans attained the highest possible distinction both in scientific research and in the dissemination of the results of scientific research amongst the community at large. Primarily Jeans was a mathematician—an applied mathematician, if we use the term in its sense of natural philosopher—who devoted his gifts to elucidating problems in theoretical physics on the one hand and in astronomy and cosmogony on the other hand.
His earliest and his latest original papers were concerned with the evolution of celestial bodies, especially the stability of masses of fluid with or without rotation. There was a phase when his interests were directed chiefly to statistical mechanics, in relation both to matter (molecules and gas theory) and radiation (quantum theory). After this he returned to his first love and expanded his interests to include stellar dynamics and the motions of and in star clusters, the origin of stellar energy, the equilibrium of gaseous and liquid stars and planetary nebulae, the evolutionary history of star types and spiral nebulae, the origin of stellar variability and the phenomenon of radiative viscosity. He wrote on all these topics with amazing fluency and in a highly readable mathematical style. He was a master of his mathematical techniques, which he never allowed to overwhelm his physical objectives, and it is fair to say that he scarcely wrote a dull page. Indeed it is difficult to describe the undercurrent of thrilling expectation which Jeans's technical papers and treatises convey to the interested reader. The present writer vividly remembers being almost swept off his feet when he first read the passages in Jeans's Dynamical Theory of Gases dealing with systems of N molecules described in 6N-dimensional phase-space (this was in 1919, before he knew Jeans personally); it was an emotional experience seldom equalled in the writer's mathematical experience. Power and generality—those were the features of Jeans's mathematical style at its best. He always led the mathematics, never allowing it to dominate. For sheer beauty of technical exposition, Jeans must rarely have been surpassed.
But, almost suddenly, this phase of scientific creative work gave place to a phase of popularization. His last technical paper, on "liquid stars," in the Monthly Notices, appeared in 1928; his popular The Universe Around Us appeared in 1929, and thereafter, he devoted himself to writing books in which he expounded, for world-wide audiences, the results of his own and others' research in the fields he had made his own These volumes were distinguished by a fertility of simile which made real to his readers both the incredibly small dimensions of atomic physics and the incredibly large dimensions of cosmical physics. He had a happy way of hitting off orders of magnitude so that they could be readily apprehended. This was no mere pose he was possessed of a power of mental arithmetic, of rapidly estimating the sizes of physical quantities, which was amazing; and he could perform as readily in a public lecture or in ordinary conversation as in the privacy of his study. The writer remembers his rapidly estimating the cubic capacity of wood in the giant pines of California, and correcting someone present who disagreed with the answer. It is true that Jeans sometimes bludgeoned the minds of his readers with the vastness of astronomical distances or masses, and had a tendency to over-positiveness in his recapitulations of not fully accepted theories. But his popular writings were as enjoyable, as pellucid, as exciting as his technical papers; and astronomy owes a debt to Jeans for the remarkable public interest in what is sometimes reckoned, in this sadly utilitarian age, a mere academic and economically useless study.
I pass to an account of the substance of his original work. Jeans's earliest memoirs were in the Philosophical Transactions of the Royal Society and closely followed paths trodden by Sir George Darwin. These early results were amalgamated, digested, and extended in his Adams Prize Essay of 1917, which is considered below. Jeans soon turned to physics. It was soon after the turn of the century; Lord Rayleigh had attacked the problem of the partition of radiant energy in an enclosure, on the classical theory, and Planck had enunciated his radiation law. Jeans developed new proofs of the theorem of equipartition of energy amongst the degrees of freedom of a system describable by a large number of coordinates and applied them both to molecules and to radiation. The result was to confirm and render more precise the result enunciated by Lord Rayleigh, which has since been known as the Rayleigh-Jeans law: the classical partition of radiant energy (of wavelength A), per unit volume, in an enclosure at temperature T, is 8 RTX-dd. This was an essential step in the proof of the inadequacy of classical mechanics, for it indicated, in contradiction to observation, that the energy of blackbody radiation should be concentrated in the smallest wavelengths.
Jeans summarized his research and expounded the whole of the kinetic theory of gases in his fine treatise, The Dynamical Theory of Gases (first published in 1904); it has appeared in many later editions and, like its companion volume, The Mathematical Theory of Electricity and Magnetism (first published in 1908), has been used by generations of students. In 1914, Jeans's Report on Radiation and the Quantum Theory appeared, written for the Physical Society of London, which had a marked influence in leading to the general acceptance of the Quantum Theory.
Jeans did not become a Fellow of the Royal Astronomical Society until 1909 and did not publish in its Monthly Notices until 1913. Thereafter, he published some 35 substantial papers and notes in the Monthly Notices, the series ending in 1928. As time went on, his ideas developed and his conclusions were revised His considered conclusions were published in the superb Problems of Cosmogony and Stellar Dynamics (the Adams Prize Essay), published in 1919, and in Astronomy and Cosmogony (1928). In view of these volumes, it is scarcely necessary to describe the individual technical papers in Monthly Notices. It may be mentioned, however, that Jeans's earliest papers in Monthly Notices dealt with star streaming, the motions of star clusters, and the structure of the galaxy. This work was very fine. It has formed a basis for recent developments by Chandrasekhar, Camm, and others. Jeans was a pioneer in the field of modifying the methods of the dynamical theory of gases so as to make them applicable to a collection of stars in which close encounters are rare but the cumulative effect of small deflections is appreciable.
Jeans's research on the stability of rotating masses of fluid was fully expounded in the Problems of Cosmogony and Stellar Dynamics, which is difficult to overpraise When a mass of incompressible liquid is rotating under its own gravitation with constant angular momentum but increasing density, it first passes through a stable series of equilibrium configurations known as Maclaurin's spheroids; these remain secularly stable until reaches the value 0.18712; thereafter, stability passes to a second series, known as Jacobi's ellipsoids; at = 0.14200 a new configuration of equilibrium becomes possible, called by Darwin the "pear-shaped" figure, which is produced by the formation of a furrow around the long axis of the Jacobian ellipsoid. This pear-shaped figure was discovered by Poincaré in 1885. Important cosmogonic questions are involved in the stability or instability of the pear-shaped figure. If it is stable, it might be expected to evolve quasi-statically by deepening the furrow into two separate bodies, forming a stable double-star configuration; but if it is unstable, increasing density along the Jacobian series should result in a cataclysm, and we should have a possible cataclysmic origin for double stars. Poincaré was unable to ascertain definitely the stability of the pear-shaped figure, though it was Poincaré who developed the general principles governing stability in a famous paper in the Acta Mathematica of 1885. In 1902, Sir George Darwin published a lengthy investigation in the Philosophical Transactions of the Royal Society in which he claimed to show that the pear-shaped figure was stable; but in 1905 Liapounoff published at St. Petersburg, in Russian, an investigation claiming to show that the pear-shaped figure was unstable. It was difficult to judge who was right. Jeans re-attacked the question by calculating the gravitational potential of a distorted ellipsoid by a new and powerful method, avoiding the method of ellipsoidal harmonics used by Darwin, and finally showed that the pear-shaped figure was unstable. Moreover, he was able to show how Darwin had gone astray, not so much by an actual error as by an unexpected complexity in the relation of the pear-shaped figures to the Jacobian ellipsoids.
Jeans reproduced the whole of his investigations very elegantly in his Problems of Cosmogony of 1919. But in that volume he did much more than summarize his own investigations. He gave a general account of Poincare's theory of linear series and points of bifurcation, considered separately the pure rotation problem, the tidal problem, and the double-star problem, both for incompressible and compressible matter, treated of Roche's model, reproduced the calculation of Roche's limit for satellites, and fused the whole subject into a monumental unity He then, with this substantial mathematical harvest as a background, applied the results to see what light they shed on the origins of the different types of celestial bodies. He concluded that double stars could be formed by the cataclysmic fission of "liquid" masses consistent with increasing density; that large compressible masses of the type in Roche's model would break up by forming a sharp lenticular ledge, which with increasing contraction of the main mass would eject streams of matter from two antipodal points determined by the residual tidal force arising from the rest of the universe, and that this might be the origin of the spiral nebulae; but that rotation alone could never result in anything resembling the solar system. He accordingly rejected the nebular hypothesis of Kant and Laplace in its original form and favored instead a disruption of the Sun by the tidal effects of a passing star, as suggested in a less precise form by Chamberlin and Moulton. He emphasized the rarity of encounters of the necessary closeness (in the then state of knowledge) and concluded that the solar system might even be unique in the universe.
Many of Jeans's specific applications of his results need or have found revision in the light of our later knowledge, and especially in the light of the expansion of the universe. Nevertheless, Problems of Cosmogony was a magnificent attack on magnificent problems, conducted by a master mathematician. The cores of its investigations remain standard work today. And it must be remembered that Jeans repeatedly emphasized in this book the provisional nature of his applications. Similar reservations, combined with flashes of foresight, occur in many of his papers. Thus, as early as 1916, when he was discussing the density law in star clusters and reducing the problem to an Emden equation, he wrote: "It is as though a rich pattern were being woven, and we had only been able to follow one thread" (M.N., 76, 567, 1916). In 1922, he foresaw the likelihood of the expansion of the universe when he remarked that "many circumstances ... suggest that the stars of our system must have been more closely packed than they are now" (M.N., 82, 139, 1922). And again, in 1927, before the doctrine of the creation of the universe at the natural origin of time had been developed, he remarked that "it would be difficult to deny that all the matter of the universe may have been created at the same instant" (M.N., 87, 709, 1927).
Jeans's later book, Astronomy and Cosmogony, which combined into a single volume much of the Adams Prize Essay along with his own research from 1917 to 1928 on the subject of stellar equilibrium and stability, was perhaps less successful. It exhibits the same grand sweep of investigation, the same breadth and power, but less clarity. And it has to be confessed that many of his results are not accepted today, at any rate in the form in which he put them forward. He dealt with stellar equilibrium in a different manner from Eddington. He claimed to show that the cores of stars would be unstable if they were wholly gaseous, and that, if the equation of the state of stellar matter is taken to be of the form , we must have as a necessary condition of stability. He did this by an actual calculation of the equation for the oscillations of such a star. He described this result by saying that the interiors of stars must be "liquid". (The view of many workers today is that stars have a convective, not radiative, core.) He then claimed to show that the untenanted portions of the Russell-Hertzsprung diagram corresponded to regions of instability due to successive removals of shells of electrons by ionization; thus the giant stars were to correspond to the loss of the M-ring electrons, the main sequence to the loss of L-ring electrons and the white dwarfs to the loss of K-ring electrons, these being stable halting places where the configurations of equilibrium would tend to congregate. He was mistaken in some of his conclusions: for example, he thought that the central temperatures of white dwarfs must be enormously high, whereas today we recognize that it is only in the non-degenerate fringe of a white dwarf that an appreciable temperature gradient can be present. He required further that the atoms forming the interiors of stars should have atomic numbers of the order of 95, that is, above 92 (uranium), the then highest known atomic number. Finally, he attributed Cepheid variation to the rotations of ellipsoidal stars near the verge of instability, as against the current pulsation theory.
Although these conclusions were far from fashionable when they were first announced, it is possible that time will justify Jeans. Certainly there is much less acceptance today of what was in 1928 the "orthodox" theory of stellar equilibrium. But it should be remembered that Jeans made several valuable suggestions in the early days of Eddington's theory of the radiative equilibrium of the stars. In 1917, he pointed out that, at the temperatures deduced by Eddington for stellar interiors, the atoms must be very considerably ionized, and the mean molecular weight much lower than Eddington had originally assumed; and Eddington adopted this suggestion. Years before that, in 1904, Jeans had suggested as a possible source of stellar energy the mutual annihilation of electrons and what are now called protons, with conversion of mass into energy.
Yet it would be improper to minimize the fact that those two Titans, Eddington and Jeans, differed and differed strongly on the theory of stellar structure Eddington's theory had a beauty, the beauty of a rosy dawn, in bringing together in a very simple way the ideas of perfect gases, of radiation pressure and ionization, of opacity, of hydrostatic and radiative equilibrium. And Eddington, the professional astronomer, dealt with the physical properties of matter in a more physical way than Jeans, the physicist, was accustomed to. Nevertheless, in the present writer's opinion, Jeans was fully justified in his criticisms of the early forms of Eddington's theory. Eddington was led to the conclusion that a star was built according to an Emden polytrope of index , and he thus appeared to be able to show, without any consideration of the mechanism of energy generation, that an arbitrary mass of perfect gas, in a steady state, must have a perfectly definite luminosity, whereas, as Jeans pointed out, an arbitrary mass of matter could be in a steady state with any luminosity whatever, depending on the intensity of the energy sources with which it was provided. Eddington never explicitly recognized that his original luminosity formula was merely the mathematical condition that a given mass of gas should be gaseous throughout; it did not predict that a star of this mass should have this particular luminosity. For his model was open to the obvious objection: what happened if its natural sources of energy did not amount to the prescribed luminosity? The answer is now well known: the star ceases to be wholly in the state of a perfect gas and assumes a composite configuration; Emden's equation has other solutions besides that used by Eddington, and it is these other solutions which are relevant to the gaseous part of the star when the total rate of generation of energy does not equal that predicted by the luminosity formula. (The white dwarfs are examples.) Jeans was as much puzzled as the astronomical world in general by the way Eddington appeared to be producing rabbits out of a hat: it was obviously impossible to find out the luminosity of a star without consideration of the mode of generation of stellar energy - But Jeans never clinched his argument in the way I have described above. The answer to Eddington's contentions was to express the different stellar variables central temperature, pressure and density, radius and effective temperature as functions of two independent variables, and M. And this Jeans never did. For example he explicitly stated, on p. 83 of Astronomy and Cosmogony, that a star of given mass can have any luminosity whatever from 0 to ∞ (actually there must be an upper limit, for equilibrium); but yet he was so little able to emancipate himself from Eddington's ideas that on page 88 of the same work he stated that the ratio of gas pressure to radiation pressure for stars of different (small) mass is proportional to , not recognizing that if is arbitrary the ratio in question can take arbitrary values.
In Astronomy and Cosmogony Jeans appears less of a physicist than his admittedly important contributions to physics would have led us to expect. He scarcely formulated the problem of stellar structure with the clarity with which he stated the stability problems in the Adams Prize Essay For example, he used the Saha dissociation formula (as modified by R. H. Fowler) in contexts where he was specifically assuming the material not to be in the form of a perfect gas, but to be akin to a liquid, whereas the derivation of the dissociation formula uses the entropy formula for perfect gases. Nevertheless, the striking series of papers in Monthly Notices, of which Astronomy and Cosmogony was an expansion, includes several topics which were characteristic of Jeans at his best. He studied the equilibrium of the shell of a planetary nebula; he examined the effects of loss of mass on the dynamics of binaries; and he discovered and traced the astronomical consequences of the phenomenon of radiative viscosity. And so Astronomy and Cosmogony, irritating though it is in many parts, was a notable contribution to the theoretical problems of stellar structure. It compels attention throughout. It showed the subject in a state of flux and transition; and it demonstrated Jeans's courage in venturing on conclusions differing in so many ways from those of his brother theorists.
Having made up his mind about the main cosmogonic questions, Jeans set himself to convey his results to the public at large. His principal popular volumes, in addition to the one on music already mentioned, were The Universe Around Us (1929), Eos or the Wider Aspects of Cosmogony (1930), The Stars in Their Courses (1931), The New Background of Science (1933), Through Space and Time (1934), and, in a different vein, The Mysterious Universe (1930), and Physics and Philosophy (1942). In all these, he gave his readers the enjoyment of what he called "the most poetical of the sciences," which he had experienced himself and which he had previously shared with his scientific colleagues
Jeans was always much impressed by the Second Law of Thermodynamics. He had dealt with it in refined detail in his work on gas theory, on Boltzmann's H-theorem, and on statistical mechanics in general; and he preached without reservation the doctrine of the ultimate heat-death of the universe. I think he tended to ignore the facts (a) that the formal thermodynamic proof of the increasing property of entropy is subject to severe limitations; (b) that the phenomenon of the expanding universe, with its indication of a natural origin of time and with the slowing down of time at great distances owing to the recession, causes a substantial revision of the heat-death doctrine. This was an example of Jeans's tendency to take an over-positive, non-critical, non-skeptical view of contemporary physics (The New Background of Science is altogether too complacent), although that was not his attitude to astrophysics. It was also an example of Jeans's tendency to move off into the philosophical implications of science. Like Eddington, he attached importance of a philosophical kind to the principle of indeterminacy, suspecting that many causal laws were actually statistical in their origin; in this he was no doubt influenced by his early research in statistical mechanics. But what impressed him most in Nature was its apparent docility to the sway of mathematical concepts. Emphasizing that mankind had successively rejected the anthropomorphic view of the universe and the engineering view of the universe customary in the 19th century, he considered that the world appeared to be built on what could only be described as a mathematical pattern; In short, the Great Architect of the universe must be a mathematician – that "the universe can best be pictured as consisting of pure thought, the thought of what we must describe as a mathematical thinker". "Primitive cosmologies pictured a creator working in space and time, forging sun, moon and stars out of existent raw material. Modern scientific theory compels us to think of the creator as working outside time and space, which are part of his creation, just as the artist is outside his canvas". And Jeans could quote Plato as holding the same ideas.
Jeans was much criticized by professional philosophers; but in Physics and Philosophy he gave as good as he got, and made some shrewd hits against traditional philosophy, accusing it of omitting all half shades in its picture of reality and attributing its differences from physics to differences of idiom. I think it is a sign of Jeans's greatness that he ended as a philosopher; that he came inevitably to philosophy through the path of mathematics and physics; that he was not content to contemplate the universe merely as a spectacle, but that he had to seek the inner meaning of it all. Jeans died rich in honors; but to him the greatest honor was that in all his activities he deserved well of astronomy. He was elected a Fellow on May 14, 1909.
E. A. Milne
He was the son of William Tulloch Jeans of Tulse Hill, his father's profession being that of parliamentary journalist. He was educated at Merchant Taylors' School from 1890 to 1896. He went up to Trinity College, Cambridge, as a Scholar in 1896, read mathematics, and was bracketed Second Wrangler in the Mathematical Tripos of 1898 with J. F. Cameron, now Master of Gonville and Caius College. He took a First Class in Part II of the Mathematical Tripos in 1900 and was awarded an Isaac Newton Studentship He won a Smith's Prize in 1900 and was elected to a Fellowship at Trinity in 1901. He was appointed University Lecturer in Mathematics in 1904 but became Professor of Applied Mathematics at Princeton, New Jersey, in 1905, holding the chair there until 1909. It was during this period that he published his well-known textbook "Theoretical Mechanics" (1906). He returned to Cambridge as Stokes Lecturer in 1910 but resigned the post in 1912. Thereafter he held no teaching post for the rest of his life, though he was appointed Professor of Astronomy at the Royal Institution in 1935 and was annually re-elected to the professorship until he resigned from ill-health in 1946.
He was awarded the Adams Prize of the University of Cambridge in 1917 for an essay entitled "Problems of Cosmogony and Stellar Dynamics", which was published in 1919. In 1922 he delivered the Halley Lecture at Oxford on the subject of "The Nebular Hypothesis and Modern Cosmogony". In 1923 he was appointed a Research Associate of Mount Wilson Observatory. In 1925 he delivered the Rouse Ball Lecture at Cambridge under the title "Atomicity and Quanta" and in 1930 the Rede Lecture, under the title, under the title "The Mysterious Universe".
He was awarded the Gold Medal of the Royal Astronomical Society in 1922 and served as President for the two years 1925–1927, delivering three Presidential Addresses on the respective occasions of presenting the Society's Gold Medal to Sir Frank Dyson (June 1925), Einstein (February 1926), and Schlesinger (February 1927). In 1927, the Royal Astronomical Society founded the annual George Darwin Lecture, the endowment for which was presented by Jeans, who thus desired to commemorate the famous mathematical astronomer who had been such an inspiration to him
Jeans was elected a Fellow of the Royal Society in 1906, at the early age of twenty-eight. He gave his Bakerian Lecture in 1917 under the title "The Configurations of Rotating Compressible Masses" (published in Phil. Trans. A, 218). He was awarded the Royal Medal of the Royal Society in 1919, in which year he became one of the Honorary Secretaries of that Society, serving until 1929. During his Secretaryship, he developed the Society's Proceedings A into a leading scientific journal from a status of comparative unimportance
He was created a knight in 1928. In 1934 he was President of the British Association at its Aberdeen meeting. He became an Honorary Fellow of the Institute of Physics in 1929. He was awarded the Franklin Medal in 1931, the Mukerjee Medal of the Indian Association for the Advancement of Science in 1937, and the Calcutta Medal of the Royal Asiatic Society of Bengal in 1938. He received honorary degrees from Oxford, Manchester, Dublin, Aberdeen, St. Andrews, Johns Hopkins, Benares, and Calcutta. He was awarded the supreme distinction of the Order of Merit in 1939
Jeans married Charlotte Tiffany, daughter of Alfred Mitchell, of New London, Connecticut, in 1907. She died in 1934, leaving one daughter. In 1935, he married Susi, daughter of Oskar Hock, of Vienna, by whom he had two sons and a daughter. He died at his home, Cleveland Lodge, Dorking, on September 16, 1946.
Jeans was brisk, matter-of-fact, and business-like in ordinary conversation, not at all suggesting the deep academic thinker and mathematician that he was. In lecturing, this style of his developed into a most attractive persuasiveness. He was also deeply interested in music and possessed and played his own organ. Mention may be made here of his semi-popular and highly successful book, Science and Music, published in 1938, in which his treatment ranged from "Tuning Forks and Pure Tones" through "Harmony and Discord" to the acoustics of the concert room
The Order of Merit was a public recognition of the fact that Jeans attained the highest possible distinction both in scientific research and in the dissemination of the results of scientific research amongst the community at large. Primarily Jeans was a mathematician—an applied mathematician, if we use the term in its sense of natural philosopher—who devoted his gifts to elucidating problems in theoretical physics on the one hand and in astronomy and cosmogony on the other hand.
His earliest and his latest original papers were concerned with the evolution of celestial bodies, especially the stability of masses of fluid with or without rotation. There was a phase when his interests were directed chiefly to statistical mechanics, in relation both to matter (molecules and gas theory) and radiation (quantum theory). After this he returned to his first love and expanded his interests to include stellar dynamics and the motions of and in star clusters, the origin of stellar energy, the equilibrium of gaseous and liquid stars and planetary nebulae, the evolutionary history of star types and spiral nebulae, the origin of stellar variability and the phenomenon of radiative viscosity. He wrote on all these topics with amazing fluency and in a highly readable mathematical style. He was a master of his mathematical techniques, which he never allowed to overwhelm his physical objectives, and it is fair to say that he scarcely wrote a dull page. Indeed it is difficult to describe the undercurrent of thrilling expectation which Jeans's technical papers and treatises convey to the interested reader. The present writer vividly remembers being almost swept off his feet when he first read the passages in Jeans's Dynamical Theory of Gases dealing with systems of N molecules described in 6N-dimensional phase-space (this was in 1919, before he knew Jeans personally); it was an emotional experience seldom equalled in the writer's mathematical experience. Power and generality—those were the features of Jeans's mathematical style at its best. He always led the mathematics, never allowing it to dominate. For sheer beauty of technical exposition, Jeans must rarely have been surpassed.
But, almost suddenly, this phase of scientific creative work gave place to a phase of popularization. His last technical paper, on "liquid stars," in the Monthly Notices, appeared in 1928; his popular The Universe Around Us appeared in 1929, and thereafter, he devoted himself to writing books in which he expounded, for world-wide audiences, the results of his own and others' research in the fields he had made his own These volumes were distinguished by a fertility of simile which made real to his readers both the incredibly small dimensions of atomic physics and the incredibly large dimensions of cosmical physics. He had a happy way of hitting off orders of magnitude so that they could be readily apprehended. This was no mere pose he was possessed of a power of mental arithmetic, of rapidly estimating the sizes of physical quantities, which was amazing; and he could perform as readily in a public lecture or in ordinary conversation as in the privacy of his study. The writer remembers his rapidly estimating the cubic capacity of wood in the giant pines of California, and correcting someone present who disagreed with the answer. It is true that Jeans sometimes bludgeoned the minds of his readers with the vastness of astronomical distances or masses, and had a tendency to over-positiveness in his recapitulations of not fully accepted theories. But his popular writings were as enjoyable, as pellucid, as exciting as his technical papers; and astronomy owes a debt to Jeans for the remarkable public interest in what is sometimes reckoned, in this sadly utilitarian age, a mere academic and economically useless study.
I pass to an account of the substance of his original work. Jeans's earliest memoirs were in the Philosophical Transactions of the Royal Society and closely followed paths trodden by Sir George Darwin. These early results were amalgamated, digested, and extended in his Adams Prize Essay of 1917, which is considered below. Jeans soon turned to physics. It was soon after the turn of the century; Lord Rayleigh had attacked the problem of the partition of radiant energy in an enclosure, on the classical theory, and Planck had enunciated his radiation law. Jeans developed new proofs of the theorem of equipartition of energy amongst the degrees of freedom of a system describable by a large number of coordinates and applied them both to molecules and to radiation. The result was to confirm and render more precise the result enunciated by Lord Rayleigh, which has since been known as the Rayleigh-Jeans law: the classical partition of radiant energy (of wavelength A), per unit volume, in an enclosure at temperature T, is 8 RTX-dd. This was an essential step in the proof of the inadequacy of classical mechanics, for it indicated, in contradiction to observation, that the energy of blackbody radiation should be concentrated in the smallest wavelengths.
Jeans summarized his research and expounded the whole of the kinetic theory of gases in his fine treatise, The Dynamical Theory of Gases (first published in 1904); it has appeared in many later editions and, like its companion volume, The Mathematical Theory of Electricity and Magnetism (first published in 1908), has been used by generations of students. In 1914, Jeans's Report on Radiation and the Quantum Theory appeared, written for the Physical Society of London, which had a marked influence in leading to the general acceptance of the Quantum Theory.
Jeans did not become a Fellow of the Royal Astronomical Society until 1909 and did not publish in its Monthly Notices until 1913. Thereafter, he published some 35 substantial papers and notes in the Monthly Notices, the series ending in 1928. As time went on, his ideas developed and his conclusions were revised His considered conclusions were published in the superb Problems of Cosmogony and Stellar Dynamics (the Adams Prize Essay), published in 1919, and in Astronomy and Cosmogony (1928). In view of these volumes, it is scarcely necessary to describe the individual technical papers in Monthly Notices. It may be mentioned, however, that Jeans's earliest papers in Monthly Notices dealt with star streaming, the motions of star clusters, and the structure of the galaxy. This work was very fine. It has formed a basis for recent developments by Chandrasekhar, Camm, and others. Jeans was a pioneer in the field of modifying the methods of the dynamical theory of gases so as to make them applicable to a collection of stars in which close encounters are rare but the cumulative effect of small deflections is appreciable.
Jeans's research on the stability of rotating masses of fluid was fully expounded in the Problems of Cosmogony and Stellar Dynamics, which is difficult to overpraise When a mass of incompressible liquid is rotating under its own gravitation with constant angular momentum but increasing density, it first passes through a stable series of equilibrium configurations known as Maclaurin's spheroids; these remain secularly stable until reaches the value 0.18712; thereafter, stability passes to a second series, known as Jacobi's ellipsoids; at = 0.14200 a new configuration of equilibrium becomes possible, called by Darwin the "pear-shaped" figure, which is produced by the formation of a furrow around the long axis of the Jacobian ellipsoid. This pear-shaped figure was discovered by Poincaré in 1885. Important cosmogonic questions are involved in the stability or instability of the pear-shaped figure. If it is stable, it might be expected to evolve quasi-statically by deepening the furrow into two separate bodies, forming a stable double-star configuration; but if it is unstable, increasing density along the Jacobian series should result in a cataclysm, and we should have a possible cataclysmic origin for double stars. Poincaré was unable to ascertain definitely the stability of the pear-shaped figure, though it was Poincaré who developed the general principles governing stability in a famous paper in the Acta Mathematica of 1885. In 1902, Sir George Darwin published a lengthy investigation in the Philosophical Transactions of the Royal Society in which he claimed to show that the pear-shaped figure was stable; but in 1905 Liapounoff published at St. Petersburg, in Russian, an investigation claiming to show that the pear-shaped figure was unstable. It was difficult to judge who was right. Jeans re-attacked the question by calculating the gravitational potential of a distorted ellipsoid by a new and powerful method, avoiding the method of ellipsoidal harmonics used by Darwin, and finally showed that the pear-shaped figure was unstable. Moreover, he was able to show how Darwin had gone astray, not so much by an actual error as by an unexpected complexity in the relation of the pear-shaped figures to the Jacobian ellipsoids.
Jeans reproduced the whole of his investigations very elegantly in his Problems of Cosmogony of 1919. But in that volume he did much more than summarize his own investigations. He gave a general account of Poincare's theory of linear series and points of bifurcation, considered separately the pure rotation problem, the tidal problem, and the double-star problem, both for incompressible and compressible matter, treated of Roche's model, reproduced the calculation of Roche's limit for satellites, and fused the whole subject into a monumental unity He then, with this substantial mathematical harvest as a background, applied the results to see what light they shed on the origins of the different types of celestial bodies. He concluded that double stars could be formed by the cataclysmic fission of "liquid" masses consistent with increasing density; that large compressible masses of the type in Roche's model would break up by forming a sharp lenticular ledge, which with increasing contraction of the main mass would eject streams of matter from two antipodal points determined by the residual tidal force arising from the rest of the universe, and that this might be the origin of the spiral nebulae; but that rotation alone could never result in anything resembling the solar system. He accordingly rejected the nebular hypothesis of Kant and Laplace in its original form and favored instead a disruption of the Sun by the tidal effects of a passing star, as suggested in a less precise form by Chamberlin and Moulton. He emphasized the rarity of encounters of the necessary closeness (in the then state of knowledge) and concluded that the solar system might even be unique in the universe.
Many of Jeans's specific applications of his results need or have found revision in the light of our later knowledge, and especially in the light of the expansion of the universe. Nevertheless, Problems of Cosmogony was a magnificent attack on magnificent problems, conducted by a master mathematician. The cores of its investigations remain standard work today. And it must be remembered that Jeans repeatedly emphasized in this book the provisional nature of his applications. Similar reservations, combined with flashes of foresight, occur in many of his papers. Thus, as early as 1916, when he was discussing the density law in star clusters and reducing the problem to an Emden equation, he wrote: "It is as though a rich pattern were being woven, and we had only been able to follow one thread" (M.N., 76, 567, 1916). In 1922, he foresaw the likelihood of the expansion of the universe when he remarked that "many circumstances ... suggest that the stars of our system must have been more closely packed than they are now" (M.N., 82, 139, 1922). And again, in 1927, before the doctrine of the creation of the universe at the natural origin of time had been developed, he remarked that "it would be difficult to deny that all the matter of the universe may have been created at the same instant" (M.N., 87, 709, 1927).
Jeans's later book, Astronomy and Cosmogony, which combined into a single volume much of the Adams Prize Essay along with his own research from 1917 to 1928 on the subject of stellar equilibrium and stability, was perhaps less successful. It exhibits the same grand sweep of investigation, the same breadth and power, but less clarity. And it has to be confessed that many of his results are not accepted today, at any rate in the form in which he put them forward. He dealt with stellar equilibrium in a different manner from Eddington. He claimed to show that the cores of stars would be unstable if they were wholly gaseous, and that, if the equation of the state of stellar matter is taken to be of the form , we must have as a necessary condition of stability. He did this by an actual calculation of the equation for the oscillations of such a star. He described this result by saying that the interiors of stars must be "liquid". (The view of many workers today is that stars have a convective, not radiative, core.) He then claimed to show that the untenanted portions of the Russell-Hertzsprung diagram corresponded to regions of instability due to successive removals of shells of electrons by ionization; thus the giant stars were to correspond to the loss of the M-ring electrons, the main sequence to the loss of L-ring electrons and the white dwarfs to the loss of K-ring electrons, these being stable halting places where the configurations of equilibrium would tend to congregate. He was mistaken in some of his conclusions: for example, he thought that the central temperatures of white dwarfs must be enormously high, whereas today we recognize that it is only in the non-degenerate fringe of a white dwarf that an appreciable temperature gradient can be present. He required further that the atoms forming the interiors of stars should have atomic numbers of the order of 95, that is, above 92 (uranium), the then highest known atomic number. Finally, he attributed Cepheid variation to the rotations of ellipsoidal stars near the verge of instability, as against the current pulsation theory.
Although these conclusions were far from fashionable when they were first announced, it is possible that time will justify Jeans. Certainly there is much less acceptance today of what was in 1928 the "orthodox" theory of stellar equilibrium. But it should be remembered that Jeans made several valuable suggestions in the early days of Eddington's theory of the radiative equilibrium of the stars. In 1917, he pointed out that, at the temperatures deduced by Eddington for stellar interiors, the atoms must be very considerably ionized, and the mean molecular weight much lower than Eddington had originally assumed; and Eddington adopted this suggestion. Years before that, in 1904, Jeans had suggested as a possible source of stellar energy the mutual annihilation of electrons and what are now called protons, with conversion of mass into energy.
Yet it would be improper to minimize the fact that those two Titans, Eddington and Jeans, differed and differed strongly on the theory of stellar structure Eddington's theory had a beauty, the beauty of a rosy dawn, in bringing together in a very simple way the ideas of perfect gases, of radiation pressure and ionization, of opacity, of hydrostatic and radiative equilibrium. And Eddington, the professional astronomer, dealt with the physical properties of matter in a more physical way than Jeans, the physicist, was accustomed to. Nevertheless, in the present writer's opinion, Jeans was fully justified in his criticisms of the early forms of Eddington's theory. Eddington was led to the conclusion that a star was built according to an Emden polytrope of index , and he thus appeared to be able to show, without any consideration of the mechanism of energy generation, that an arbitrary mass of perfect gas, in a steady state, must have a perfectly definite luminosity, whereas, as Jeans pointed out, an arbitrary mass of matter could be in a steady state with any luminosity whatever, depending on the intensity of the energy sources with which it was provided. Eddington never explicitly recognized that his original luminosity formula was merely the mathematical condition that a given mass of gas should be gaseous throughout; it did not predict that a star of this mass should have this particular luminosity. For his model was open to the obvious objection: what happened if its natural sources of energy did not amount to the prescribed luminosity? The answer is now well known: the star ceases to be wholly in the state of a perfect gas and assumes a composite configuration; Emden's equation has other solutions besides that used by Eddington, and it is these other solutions which are relevant to the gaseous part of the star when the total rate of generation of energy does not equal that predicted by the luminosity formula. (The white dwarfs are examples.) Jeans was as much puzzled as the astronomical world in general by the way Eddington appeared to be producing rabbits out of a hat: it was obviously impossible to find out the luminosity of a star without consideration of the mode of generation of stellar energy - But Jeans never clinched his argument in the way I have described above. The answer to Eddington's contentions was to express the different stellar variables central temperature, pressure and density, radius and effective temperature as functions of two independent variables, and M. And this Jeans never did. For example he explicitly stated, on p. 83 of Astronomy and Cosmogony, that a star of given mass can have any luminosity whatever from 0 to ∞ (actually there must be an upper limit, for equilibrium); but yet he was so little able to emancipate himself from Eddington's ideas that on page 88 of the same work he stated that the ratio of gas pressure to radiation pressure for stars of different (small) mass is proportional to , not recognizing that if is arbitrary the ratio in question can take arbitrary values.
In Astronomy and Cosmogony Jeans appears less of a physicist than his admittedly important contributions to physics would have led us to expect. He scarcely formulated the problem of stellar structure with the clarity with which he stated the stability problems in the Adams Prize Essay For example, he used the Saha dissociation formula (as modified by R. H. Fowler) in contexts where he was specifically assuming the material not to be in the form of a perfect gas, but to be akin to a liquid, whereas the derivation of the dissociation formula uses the entropy formula for perfect gases. Nevertheless, the striking series of papers in Monthly Notices, of which Astronomy and Cosmogony was an expansion, includes several topics which were characteristic of Jeans at his best. He studied the equilibrium of the shell of a planetary nebula; he examined the effects of loss of mass on the dynamics of binaries; and he discovered and traced the astronomical consequences of the phenomenon of radiative viscosity. And so Astronomy and Cosmogony, irritating though it is in many parts, was a notable contribution to the theoretical problems of stellar structure. It compels attention throughout. It showed the subject in a state of flux and transition; and it demonstrated Jeans's courage in venturing on conclusions differing in so many ways from those of his brother theorists.
Having made up his mind about the main cosmogonic questions, Jeans set himself to convey his results to the public at large. His principal popular volumes, in addition to the one on music already mentioned, were The Universe Around Us (1929), Eos or the Wider Aspects of Cosmogony (1930), The Stars in Their Courses (1931), The New Background of Science (1933), Through Space and Time (1934), and, in a different vein, The Mysterious Universe (1930), and Physics and Philosophy (1942). In all these, he gave his readers the enjoyment of what he called "the most poetical of the sciences," which he had experienced himself and which he had previously shared with his scientific colleagues
Jeans was always much impressed by the Second Law of Thermodynamics. He had dealt with it in refined detail in his work on gas theory, on Boltzmann's H-theorem, and on statistical mechanics in general; and he preached without reservation the doctrine of the ultimate heat-death of the universe. I think he tended to ignore the facts (a) that the formal thermodynamic proof of the increasing property of entropy is subject to severe limitations; (b) that the phenomenon of the expanding universe, with its indication of a natural origin of time and with the slowing down of time at great distances owing to the recession, causes a substantial revision of the heat-death doctrine. This was an example of Jeans's tendency to take an over-positive, non-critical, non-skeptical view of contemporary physics (The New Background of Science is altogether too complacent), although that was not his attitude to astrophysics. It was also an example of Jeans's tendency to move off into the philosophical implications of science. Like Eddington, he attached importance of a philosophical kind to the principle of indeterminacy, suspecting that many causal laws were actually statistical in their origin; in this he was no doubt influenced by his early research in statistical mechanics. But what impressed him most in Nature was its apparent docility to the sway of mathematical concepts. Emphasizing that mankind had successively rejected the anthropomorphic view of the universe and the engineering view of the universe customary in the 19th century, he considered that the world appeared to be built on what could only be described as a mathematical pattern; In short, the Great Architect of the universe must be a mathematician – that "the universe can best be pictured as consisting of pure thought, the thought of what we must describe as a mathematical thinker". "Primitive cosmologies pictured a creator working in space and time, forging sun, moon and stars out of existent raw material. Modern scientific theory compels us to think of the creator as working outside time and space, which are part of his creation, just as the artist is outside his canvas". And Jeans could quote Plato as holding the same ideas.
Jeans was much criticized by professional philosophers; but in Physics and Philosophy he gave as good as he got, and made some shrewd hits against traditional philosophy, accusing it of omitting all half shades in its picture of reality and attributing its differences from physics to differences of idiom. I think it is a sign of Jeans's greatness that he ended as a philosopher; that he came inevitably to philosophy through the path of mathematics and physics; that he was not content to contemplate the universe merely as a spectacle, but that he had to seek the inner meaning of it all. Jeans died rich in honors; but to him the greatest honor was that in all his activities he deserved well of astronomy. He was elected a Fellow on May 14, 1909.
E. A. Milne
James Hopwood Jeans's obituary appeared in Journal of the Royal Astronomical Society 107:1 (1947), 46-53.