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A range of precision farming technologies are used commercially for variable rate applications of nitrogen (N) for cereals, yet these usually adjust N rates from a pre-set value, rather than predicting economically optimal N requirements on an absolute basis. This paper reports chessboard experiments set up to examine variation in N requirements, and to develop and test systems for its prediction, and to assess its predictability. Results showed very substantial variability in fertiliser N requirements within fields, typically >150 kg ha−1, and large variation in optimal yields, typically >2 t ha−1. Despite this, calculated increases in yield and gross margin with N requirements perfectly matched across fields were surprisingly modest (compared to the uniform average rate). Implications are discussed, including the causes of the large remaining variation in grain yield, after N limitations were removed.
The International Federation for Emergency Medicine (IFEM) Ultrasound Special Interest Group (USIG) was tasked with development of a hierarchical consensus approach to the use of point of care ultrasound (PoCUS) in patients with hypotension and cardiac arrest.
The IFEM USIG invited 24 recognized international leaders in PoCUS from emergency medicine and critical care to form an expert panel to develop the sonography in hypotension and cardiac arrest (SHoC) protocol. The panel was provided with reported disease incidence, along with a list of recommended PoCUS views from previously published protocols and guidelines. Using a modified Delphi methodology the panel was tasked with integrating the disease incidence, their clinical experience and their knowledge of the medical literature to evaluate what role each view should play in the proposed SHoC protocol.
Consensus on the SHoC protocols for hypotension and cardiac arrest was reached after three rounds of the modified Delphi process. The final SHoC protocol and operator checklist received over 80% consensus approval. The IFEM-approved final protocol, recommend Core, Supplementary, and Additional PoCUS views. SHoC-hypotension core views consist of cardiac, lung, and inferior vena vaca (IVC) views, with supplementary cardiac views, and additional views when clinically indicated. Subxiphoid or parasternal cardiac views, minimizing pauses in chest compressions, are recommended as core views for SHoC-cardiac arrest; supplementary views are lung and IVC, with additional views when clinically indicated. Both protocols recommend use of the “4 F” approach: fluid, form, function, filling.
An international consensus on sonography in hypotension and cardiac arrest is presented. Future prospective validation is required.
The fertilizer-nitrogen (N) requirement for wheat grown in the UK varies from field to field. Differences in the soil type, climate and cropping history result in differences in (i) the crops’ demands for N, (ii) the supply of N from the soil (SNS) and (iii) the recovery of the fertilizer by the crops. These three components generally form the basis of systems for N recommendation. Three field experiments were set out to investigate the variation of the N requirement for wheat within fields and to explore the importance of variation in the crops’ demands for N, SNS and fertilizer recovery in explaining the differences in the economic optima for N. The N optima were found to vary by >100 kg N/ha at two of the sites. At the other site, the yield response to N was small. Yields at the optimum rate of N varied spatially by c. 4 t/ha at each site. Soil N supply, which was estimated by the unfertilized crops’ harvested N, varied spatially by 120, 75 and 60 kg/ha in the three experiments. Fertilizer recovery varied spatially from 30% to >100% at each of the sites. There were clear relationships between the SNS and the N optima at all the three sites. The expected relationship between the crop's demand for N and N optima was evident at only one of the three sites. There was no consistent relationship between the N recovery and the N optima. A consistent relationship emerged, however, between the optimal yield and SNS; areas with a greater yield potential tending to also supply more N from the soil. This moderated the expected effect of the SNS and the crop's demand for N on the N optima.
Originally published in 1952, this book by E. A. Milne examines the life and work of influential astrophysicist Sir James Jeans. The text includes reproductions of correspondence between Jeans and such luminaries as G. H. Hardy and G. E. Hale, and is introduced by a personal memoir by the publisher S. C. Roberts. This book will be of value to anyone with an interest in Jeans' work and the history of astrophysics.
BEFORE passing to an account of Jeans's technical and scientific achievements, it may be of interest to sketch the background of science in the days of his boyhood, more especially as Jeans himself was to write, at the age of fiftysix, a volume entitled The New Background of Science. And, as Jeans devoted the last eighteen years of his life to popular exposition, the best way of doing this would appear to be to take a brief survey of the state of popular science in the last half of the nineteenth century.
Let us take the lectures and writings of two renowned expositors of physics, Helmholtz in Germany and Tyndall in England.
The Popular Lectures on Scientific Subjects of Hermann von Helmholtz were published in an excellent English translation in two volumes in 1893. They consisted of addresses on sundry formal occasions, delivered to educated but not specialist audiences, and covered ground to which Helmholtz himself had made notable contributions. One group of addresses was concerned with the first law of thermodynamics (as it is now called), namely, the law of conservation of energy or, as Helmholtz termed it, the law of conservation of force. This great generalization appealed strongly to Helmholtz. It was the subject of his Carlsruhe address of 1862, ‘On the Conservation of Force’; he had emphasized it in his Konigsberg address of 1854 ‘On the Interaction of Natural Forces’, and he was to dwell on it again in his Innsbruck address of 1869, ‘On the Aim and Progress of Physical Science’. The possibility that the law of conservation of energy applied to all forms of energy had been outlined by Julius Robert Mayer in 1842; but it was the experiments of James Prescott Joule, published in 1843, which first established the strict equivalence of heat and mechanical energy. Joule's classical paper on this subject was dated 1849. It is evident from Helmholtz's insistence on the importance of this law that its power and generality were not fully realized by the audiences which he was addressing: It was necessary for him to pile example upon example.
IT was shown in 1861 by G. Kirchhoff that in an enclosure at temperature T, the state of the field of radiation depends only on this temperature T, and does not depend on the optical properties of the substances that happen to be present in the enclosure. This state of radiation is called complete or equilibrium radiation, or black-body radiation. It was one of the primary objects of theoretical physics in the nineteenth century to determine this characteristic state of radiation by calculation.
In the preceding paragraph I have stated the broad facts, so that the reader may see the issue. To give these facts their quantitative form, certain refinements of statement are needed. What Kirchhoff actually showed, by means of thermodynamic arguments, is as follows. Let the enclosure contain substances capable of emitting and absorbing radiation of energy frequency v. At any point P in the enclosure, let the specific intensity of radiation for frequency v be Iv; that is to say, in a short time dt through an element of area dS containing P, in a cone of directions of solid angle dω making an angle with θ the normal to dS, the flow of energy is taken to be IvdvdtdS cos θ dω, dv being a small range of frequencies surrounding v. Further, let kv be the absorption coefficient of the material at P, jv the emission coefficient of the same material. These statements mean that a beam of radiation of intensity Iv traversing a thin layer of the material of thickness dl is weakened by the amount dIv = — kvpIv dl, where p is the density; and that the emission of radiant energy from a small element pdv of volume dv in time dt in directions included in dω is jvp dv dt dω.
IN 1942 Jeans published a small volume entitled Physics and Philosophy, which I reviewed in Nature. In 1947 there was published posthumously a more substantial volume, entitled The Growth of Physical Science. (The proofs of this book had been revised by Jeans shortly before his death in September 1946.) The volumes to some extent overlap, since the one specifically dealing with philosophy includes sketches of the history of the progress in physics as the chapter sub-titles indicate: ‘The two voices of science and philosophy’ (Plato to the present); ‘How do we know?’ (Descartes to Kant; Eddington); ‘The passing of the mechanical age’ (Newton to Einstein);’ The new physics’ (Planck, Rutherford, Bohr); and ‘From appearance to reality’ (Bohr, Heisenberg, de Broglie, Schrödinger, Dirac); whilst the volume with the deliberately historical approach has chapters on the remote beginnings of science in Babylonia, Egypt, Phoenicia and Greece; science in Ionia and early Greece (including mathematics, physics, philosophy and astronomy); science in Alexandria, in the Dark Ages, in the Renaissance, in the century of genius (1601—1700), in the two centuries following Newton and in the modern era.
Jeans evidently took great pains over the latter book; it is well illustrated by reproductions of contemporary prints, paintings, etc., and it is indeed a more serious work. Physics and Philosophy is of a rather journalistic character, and has been much criticized by professional philosophers.
In my Nature review of Physics and Philosophy (from which I see no reason to differ today) I quoted Emerson's definition of philosophy as ‘the account which the human mind gives to itself of the constitution of the world’. Jeans in his preface modestly disavowed any acquaintance with philosophy other than that of an intruder, and disclaimed any intention to pose as an authority on questions of pure philosophy. Yet, on Emerson's definition of philosophy, no one had a greater right than Jeans to treat the subject of philosophy. Indeed, many of the great mathematical physicists of our generation, starting as mathematical technicians, have been compelled by their own researches to study the philosophy underlying them—Eddington, Planck, Einstein and Schrödinger.
I PROPOSE in this chapter to sketch in as non-technical language as possible the classical subject of the forms of equilibrium of rotating, gravitating fluid masses and their stability, as it was when Jeans began to make contributions to it, and the nature of Jeans's contributions.
Suppose we consider a mass of incompressible liquid, spinning about an axis and isolated in space. What form will it assume, and how will the form change, if at all, as the mass shrinks? By the theorem of the conservation of angular momentum, as such a mass shrinks, and its moment of inertia consequently decreases, its angular velocity will increase. The problem can therefore be reduced to that of the forms of equilibrium of a rotating homogeneous mass as its angular velocity increases from zero upwards. When the angular velocity is zero, the form is evidently that of a sphere (though this is by no means as easy to prove as it looks). It was shown by Newton, and more particularly by Maclaurin, that as angular velocity sets in, the form is initially that of an ellipsoid of revolution, an oblate spheroid in fact, with the shorter (polar) axis lying along the axis of rotation. As the angular velocity increases, the polar axis shortens and the equatorial axes lengthen. This process goes on until the angular velocity w reaches a certain maximum (given by ω2/2πGρ= 0.2247, corresponding to an eccentricity of meridian section equal to 0.93). For higher values of the angular velocity, no forms of equilibrium of the type of a spheroid are possible. But a second set of spheroidal figures are possible, corresponding to decreasing angular velocity but still increasing eccentricity, until in the limit the form assumed is that of a flat disk of very large radius and zero thickness, rotating very slowly about an axis through its centre normal to its plane.
Not all these configurations of relative equilibrium, however, are stable. The configurations for which ω2/2πGρ has diminished again beyond the value of 0.2247 are all unstable, in the ordinary sense of that word. Thus all the disk-like configurations are unstable. But some of the configurations on the ascending branch of angular velocity are unstable in another sense. This type of instability occurs when dissipative forces are present. It arises in the following way.
MANY honours came to Jeans. The Merchant Taylors' Company admitted him to the Honorary Freedom of the Company—a rare distinction—and he received honorary degrees from many universities, including those of Oxford, Manchester, Dublin, Benares, St Andrews, Aberdeen, Johns Hopkins and Calcutta; but no award gave him greater pleasure than that of the Franklin Medal by the Franklin Institute of Philadelphia in 1931. On 24 February of that year he wrote to G. E. Hale:
At last, to my great pleasure, I find it is possible to visit Mount Wilson, as far as I can tell in the first fortnight in May. I am writing at once to enquire whether there is any prospect of seeing you at that time in Pasadena, or if you will not be there, where you are likely to be. You have probably seen in the newspapers that the Franklin Institute have been good enough to award me their Medal, and I am crossing to receive it on May 20th. I shall leave here as soon as Olivia returns to College, which I think is the 17th April, and shall come almost directly to the Observatory.
I much hope it may be possible to see you somehow or other. My wife joins me in sincerest good wishes to Mrs Hale and yourself. We both hope your health is much better.
Hale, in reply, expressed his delight that the Franklin Institute had voted their highest distinction to Jeans and went on:
Adams and Millikan, who are arranging for the coming meeting of the American Association for the Advancement of Science in Pasadena, have cabled to ask if you can come after instead of before the Franklin Institute presentation, so as to be the principal speaker during the sessions, which extend from June 15 to June 20. Although I still have to avoid all scientific and social functions (thereby missing the many opportunities afforded by Einstein's visit), I sincerely hope you can accept this invitation, as they naturally wish to make this first meeting of the whole Association in the West as successful as possible.
JEANS was knighted in 1928 for his services to science and to the Royal Society, and it is noteworthy that this honour came to him before the publication of any of his popular books. To this phase of Jeans's life we now come.
Astronomy and Cosmogony (1928) concluded with a very moving chapter, in which Jeans summed up, without mathematics but with some vivid diagrams, his life-work of research in the ‘natural history’ of the astronomical formations—galaxies, stellar clusters, nebulae, stars (simple, double and multiple), Cepheids, novae and solar systems—which appear to constitute the material universe. The three concluding paragraphs of this chapter may be quoted in extenso:
The cosmogonist has finished his task when he has described to the best of his ability the inevitable sequence of changes which constitute the history of the material universe. But the picture which he draws opens questions of the widest interest not only to science, but also to humanity. What is the significance of the vast processes it portrays? what is the meaning, if any there be which is intelligible to us, of the vast accumulations of matter which appear, on our present interpretations of space and time, to have been created in order that they may destroy themselves? What is the relation of life to that universe of which, if we are right, it can occupy only so small a corner? What if any is our relation to the remote nebulas, for surely there must be some more direct contact than that light can travel between them and us in a hundred million years? Do their colossal incomprehending masses come nearer to representing the main ultimate reality of the universe, or do we? Are we merely part of the same picture as they, or is it possible that we are part of the artist? Are they perchance only a dream, while we are brain-cells in the mind of the dreamer? Or is our importance measured solely by the fractions of space and time we occupy—space infinitely less than a speck of dust in a vast city, and time less than one tick of a clock which has endured for ages and will tick on for ages yet to come?
BORN on 11 September 1877 at Ormskirk, Lancashire, James Hopwood Jeans came of a family of journalists. Both his grandfather and his great-grandfather had owned newspapers and his father's cousin, Sir Alexander Jeans, had been proprietor of the Liverpool Daily Post and Echo. His father, William Tulloch Jeans, was a parliamentary journalist, representing the Globe in the press gallery of the House of Commons. He had a remarkable knowledge of parliamentary procedure and his Fleet Street colleagues always turned to him in their troubles. He was also a keen student of economics and his published works included The Lives of Electricians and Creators of the Age of Steel.
James's mother, from whom he derived the name Hopwood, came from Stockport and belonged to an evangelical family. Her great-great-great-grandfather had been an Independent minister in Cromwell's time and his small chapel, now used as a school, still stands at Marple, Cheshire. For a time, during James's infancy, his parents lived at Brighton. When he was three years old, they moved to London, living first at Tulse Hill and afterwards at Clapham Park.
James was a precocious child. He could tell the time at the age of three and could read when he was four. He seized upon anything that came his way, even a Times leading article which he would read aloud to his parents. The home atmosphere was strictly Victorian, especially in relation to religious observance, and James, naturally shy, began to develop his own interests. He took long walks in London and bicycled into the surrounding country. Later, he accompanied his father very happily on walking tours and the father never ceased to encourage the boy's intellectual development.
From the beginning James displayed a passion for numbers. He could memorize them with ease and at the age of seven made a practice of factorizing cab-numbers. About the same time he came upon his father's book of logarithm tables. He could not make out their purpose, but seized the opportunity of learning the first twenty logarithms by heart. Again, when his mother once lost her ticket on a railway journey, he was able to satisfy the inspector by quoting its number.
IN 1919, Jeans was awarded one of the Royal Medals of the Royal Society, and in the same year he was elected to the office of Honorary Secretary of the Society. Hale's letter of congratulation to Jeans contains several points of interest:
Pasadena, California May 25, 1920
Mr J. H. JEANS,
Cleveland Lodge, Dorking, England
My dear Mr Jeans,
I meant long since to send you my heartiest congratulations on your election as Secretary of the Royal Society, or rather to offer my congratulations to the Council, as I am sure that the event is of no small significance in its bearing on the future development of the Society. This is unquestionably a very critical period in the progress of science and the policy adopted by such authoritative bodies as the Royal Society may turn the scale in the right direction. In this country, and probably England, the conditions are very complex. On the one hand, the increased cost of living and the high salaries offered by the industries are drawing good research men away from the faculties of educational institutions. On the other hand, there is such a marked advance in the public appreciation of science and research and such an obvious necessity of developing more investigators that the opportunity to interest governments and individual donors is greater than ever before. This is manifested in part by the strong expressions of the value of pure science made by industrial leaders. The pamphlet I am sending you under separate cover (Scientific Discovery and the Wireless Telephone was prepared by the American Telephone and Telegraph Company to accompany their exhibit of the wireless telephone and its scientific development, first shown at the building of the National Research Council in Washington and now at the American Museum of Natural History in New York. You will see what emphasis they lay upon the importance of research in physics without reference to practical return. If we can convince everyone of this, I am sure we can obtain large new funds for pure science.
IN 1928 Jeans published his Astronomy and Cosmogony, which he considered to be in a sense a sequel to his Problems of Cosmogony and Stellar Dynamics of a decade previous. Actually it comprises much that was in the Adams Prize Essay; but it also includes much original work, besides the contents of a long series of papers in the Monthly Notices of the Royal Astronomical Society. Though this book is exciting and interesting from cover to cover, it cannot be regarded as a masterpiece of the quality of the Adams Prize Essay, for reasons stated earlier. Nevertheless, the ideas on stellar structure contained in this book are well worth recapitulating.
He begins with a survey of the facts of observational astronomy, with an account of the distances of the principal types of astronomical objects, and catalogues in turn the properties of binary stars, variable stars, triple and multiple systems, moving clusters of stars, globular clusters, planetary nebulae, irregular nebulae and extra-galactic nebulae. This leads him to ask the fundamental questions:
What, in ultimate fact, are the stars? What causes them to shine, and for how long can they continue thus to shine? Why are binary and multiple stars such frequent objects in the sky, and how have they come into being? What is the significance of the characteristic flattened shape of the galactic system, and why do some of its stars move in clusters, like shoals of fish, while others pursue independent courses? What is the significance of the extra-galactic nebulae, which appear at a first glance to be other universes outside our own galactic universe comparable in size with it, although different in general quality? and behind all looms the fundamental question: What changes are taking place in this complex system of astronomical bodies, how did they start and how will they end?
Many of these questions were answered in the Adams Prize Essay, and Astronomy and Cosmogony does not carry this part of the story much further. But here we shall try to give an account of Jeans's ideas ‘of the object which occurs most frequently of all in nature's astronomical museum, the simple star’.
IN December, 1913, Jeans wrote an important paper in what was to him a new, though at the same time familiar, field. It was entitled ‘The kinetic theory of star clusters'. It was his first paper in the Monthly Notices of the Royal Astronomical Society. The field was familiar, because it made a calculation similar to those Jeans had been frequently making in his work on the kinetic theory of gases; it was new, because it was the first occasion on which Jeans ventured into the theory of star clusters. Its object was to determine the deviation of direction in the motion of stars due to close approaches by other stars.
The formula I need not quote. But some of Jeans's applications of it are of interest. Assuming 109 stars within a distance of 1000 parsecs, assuming each star to be on the average five times as massive as the sun, and assuming a typical relative velocity between members of a pair of stars ‘in collision’ to be 60km. sec.-1, he calculated that a gross deflexion of 1° would be acquired after a distance of 4 x 1023 cm., or, with an individual star velocity of 40 km. sec.-1, after an interval of 3200 million years, which is the present estimate of the age of the universe. This is the result of the accumulation of small deflexions, excluding ‘violent’ deviations. A sudden deviation of, say, 5° would occur once in 5 million million years; and one of 2°, once in 8 x 1011 years.
He further summarized what might be deduced from his formula in the following vivid passage:
… let us take a definite instance of a star stream in which the stars all start with equal and parallel velocities of 40 km. sec.-1. Let us suppose that a star is still considered to belong to the main stream as long as its direction of motion makes an angle not greater than 2° with the main stream. After 100 million years, the stream will have lost only one in 8000 of its original members, and the remainder will make angles with the main stream of which the average amount is only 10′.
SHORTLY after his return to England, Jeans was appointed Stokes Lecturer in Applied Mathematics in the University of Cambridge (1910). He retained this appointment till 1912, when he retired and went to live at Guildford, there devoting himself to mathematical research.
In 1914 Jeans published his justly famous Report on Radiation and the Quantum Theory for the Physical Society of London. As a result of the outbreak of war, it did not at first reach a large circle of readers, but it was eagerly read when students of mathematics and physics returned from the war in 1919; and it did much to establish confidence in the quantum theory and in Bohr's then entirely unorthodox theory of the atom and atomic spectra. Together with Eddington's Report on the Relativity Theory of Gravitation (1918), also made for the Physical Society of London, it decisively influenced the acceptance by responsible scientists of a new theory.
Jeans's Report consisted of seven chapters, of which the first was entitled ‘ Introductory: On the Need for a Quantum Theory’, and the last ‘On the Physical Basis of the Quantum Theory’. Of the other five chapters the first two summarized the substantial parts of Jeans's own researches in radiation according to the classical mechanics and the revolutionary modifications of that theory at the hands of Planck, and the remaining three dealt with Bohr's theory of the hydrogen and hydrogen-like atoms and their spectra, Einstein's theory of the photo-electric effect, and the theory of the specific heats of solids, due to Einstein, Debye and Lindemann. The whole Report amounts to ninety pages.
This was of course well before the days of quantum mechanics, and the theory was a collection of dynamical contradictions. At the end of his Report Jeans wrote:
…It may be asserted with confidence that until some kind of reconciliation can be effected between the demands of the quantum theory and those of the undulatory theory of light, the physical interpretation of the quantum theory is likely to remain in a very unsatisfactory state… the explanation of the black-body spectrum demands the quantum theory and nothing but the quantum theory, all the discontinuities of the theory and their surprising physical consequences included.