SOPHIA RARE BOOKS

First edition, journal issue in never-bound sheets, of the first and most important of Edgeworth's papers on the application of the statistical methods of the theory of errors to the social sciences and economics. "Of all the great economists in this book, he [Edgeworth] is (apart from Bernoulli and Slutsky) the only one to have made original contributions to mathematical statistics" (Blaug, Great Economists before Keynes (1986), pp. 69-71). "Francis Ysidro Edgeworth (1845-1926) was perhaps the statistician with the greatest mathematical abilities at the end of the 19th century" (Fischer, p. 122). "In 1883 began the series of papers that were to make [Edgeworth] the leading theorist of mathematical statistics of the latter half of the 19th century" (Stigler, The History of Statistics, p. 98). "He set himself to do at last what had been talked about and assumed possible for over a century but had never been accomplished: adapt the statistical methods of the theory of errors to the quantification of uncertainty in the social, particularly economic, sciences. In this he succeeded brilliantly" (ODNB). "Edgeworth's 1885 articles, particularly 'Observations and statistics' and 'Methods of Statistics', were widely noticed, both in England and on the continent, and until the end of the century when texts such as Bowley's Elements of Statistics began to appear, they served as basic references for the theory and application of statistical techniques to social and economic data" (Stigler, p. 297). RBH lists no copy of this paper (in any form). "The type of questions Edgeworth sought to treat and the difficulties he saw in their treatment were described in an 1884 review of a posthumously published collection of Jevons's papers, Investigations in Currency and Finance. Edgeworth commented upon the beautiful diagrams in the book, which he thought would assist the reader to estimate the probability that the differences in the averages for different weeks and months are not accidental: 'The question which has been just indicated, one of the most delicate in statistics - namely, under what circumstances does a difference in figures correspond to a difference of fact - comes up often in these pages. Thus Mr. Jevons, comparing the amount of bills created in the different quarters of the year, speaks of a variation to the extent of about six percent. as 'no great difference.' On the other hand, he regards it as noteworthy that, 'out of 79,794 bankruptcies which were gazetted from the beginning of 1806 to the end of 1860, 28,391 occurred in the second month of the quarter, 26,427 in the third month, and only 24,976 in the first month.' No doubt a similar disparity between 'heads' and 'tails' in the result of so many throws of a coin would prove a cause, a want of symmetry in the coin. But our knowledge of the behaviour of tossed coins rests at bottom upon observation and experiments such as those which Mr. Jevons once performed. That what is true of games of chance is true of bankruptcies is not to be assumed without examination.' "Edgeworth was to provide this examination. "Edgeworth's key work on this topic was contained in a series of four papers read in the year 1885. The first of these, 'Observations and statistics: An essay on the theory of errors of observation and the first principles of statistics,' was read on 25 May 1885 to the Cambridge Philosophical Society. It concentrated on statistical theory and summarized and extended his work of the previous two years. The second paper, 'Methods of statistics,' was read a month later, on June 23, to the international gathering to celebrate the jubilee of the [Royal] Statistical Society. It was concerned with methodology and presented, through an extensive series of examples taken from all manner of fields, an exposition of the application and interpretation of significance tests for the comparison of means. Much of the material in these two papers was presented at least in outline in Edgeworth's evening classes in logic starting in April 1885. The third and fourth papers, 'On methods of ascertaining variations in the rate of births, deaths, and marriages' and 'Progressive means,' were read at meetings of the British Association in September and October. The third presented a remarkable analysis for two-way classifications that anticipated many ideas of the analysis of variance. The fourth article, 'Progressive means,' was a brief discussion of the use of linear least squares for detrending time series, including the estimation of the coefficients' variabilities to permit significance tests for trend or comparisons of different series. "For Edgeworth the distinction between observations and statistics was an important one: 'Observations and statistics agree in being quantities grouped about a Mean; they differ, in that the Mean of observations is real, of statistics is fictitious. The mean of observations is a cause, as it were the source from which diverging errors emanate. The mean of statistics is a description, a representative quantity put for a whole group, the best representative of the group, that quantity which, if we must in practice put one quantity for many, minimizes the error unavoidably attending such practice. Thus measurements by the reduction of which we ascertain a real time, number, distance are observations. Returns of prices, exports and imports, legitimate and illegitimate marriages or births and so forth, the averages of which constitute the premises of practical reasoning, are statistics. In short observations are different copies of one original; statistics are different originals affording one 'generic portrait.' Different measurements of the same man are observations; but measurements of different men, grouped round l'homme moyen, are primâ facie at least statistics' (pp. 139-140) "Edgeworth's aim was to apply the tools developed in the previous century for observations in astronomy and geodesy, where a more or less objectively d.

First edition. BABBAGE'S 'CALCULUS OF NOTATION'. First edition, journal issue in never-bound sheets, of Babbage's first and most important paper on mathematical notation, which was essential for his major mathematical invention, the calculus of functions. Babbage's preoccupation with systems of notation found its most important expression in the development of his symbolic notation for the action of the Difference and Analytical Engines, the invention of which has earned him the title 'father of the computer'. "Throughout his career he emphasised the vital importance of a good working symbolism. At Cambridge he crusaded successfully for the reformation of notation in the differential calculus. Later he published his views at greater length, not only devising a set of rules that all mathematical notations were to follow but even constructing a kind of notational calculus. We can see continuity from the mathematical to the less mathematical part of his life, when he later devised, as an essential feature of his drawings for the engines, a workable convention which he described as the 'mechanical notation'" (Dubbey, p. 9). In the calculus of functions, Babbage "took a branch of mathematics barely considered by his predecessors and transformed it into a systematic calculus, the analysis containing some very original stratagems and devices" (ibid., p. 8). "Babbage believed that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation, and it is possible to see here a hint of the inspiration for his concept of the Analytical Engine. While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was the area he often yearned to continue. In fact the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find the most fascinating" (Dubbey, in The Works of Charles Babbage, Vol. 1 (2014), p. 21). Many years later, in his Passages from the Life of a Philosopher, Babbage referred to the calculus of functions as his 'earliest step' and 'one to which I would willingly recur if other demands on my time permitted.' RBH lists one copy of the offprint, no copy of the journal issue. "Babbage was very much involved in notational reform in his early career. Later, he wrote three long and interesting papers on the subject of notation, the first of which was 'Observations on the notation employed in the calculus of functions.' "This is quite a remarkable paper, for the writer not only demonstrates conclusively the excellence of his notation introduced for his own invented subject, the calculus of functions, but even performs a series of calculations to prove the conciseness of the symbolism. One might almost describe the paper as another branch of mathematics invented by Babbage, the 'calculus of notations'. "Before considering any of the calculations, I will quote Babbage's introduction at length: 'Amongst the various causes which combine in enabling us by the use of analytical reasoning to connect through a long succession of intermediate steps the data of a question with its solution, no one exerts a more powerful influence than the brevity and compactness which is so peculiar to the language employed. The progress of improvement in leading us from the simpler up to the most complex relations has gradually produced new codes of shortening the ancient paths, and the symbols which have thus been invented in many instances from a partial view, or for very limited purposes, have themselves given rise to questions far beyond the expectations of their authors, and which have materially contributed to the progress of the science. Few indeed have been so fortunate as at once to perceive all the bearings and foresee all the consequences which result either necessarily, or analogically even from some of the simplest improvements. 'The first analyst who employed the very natural abbreviation of a2 instead of aa little contemplated the existence of fractional negative and imaginary exponents, at the moment when he adopted this apparently insignificant mode of abridging his labor, so great however is the connection that subsists between all branches of pure analysis, that we cannot employ a new symbol or make a new definition, without at once introducing a whole train of consequences, and in defiance of ourselves, the very sign we have created, and on which we have bestowed a meaning, itself almost prescribes the path our future investigations are to follow' (pp. 63-4). "The symbolism introduced in the first place for convenience, opens up totally new possibilities for the branch of reasoning being considered. This is admirably illustrated by Babbage's example of the use of a2, a3, a4 for aa, aaa, aaaa, . suggesting the possibility of quantities with negative or fractional indices. One could cite the case of the differential notation in the calculus similarly suggesting possibilities that would be hidden forever in the fluxionary notation. "Babbage now applies this principle to the construction of a suitable notation for the calculus of functions. "He uses the letter f to denote the general functional operation and suggests that a repetition of the operation involving f should be written as f2(x) rather than ffx. Similarly f3(x) will be written for fffx . "From this he produces the obvious, but important, identity (A) that fn+m(x) = fnfm(x), where n and m are whole numbers . The equation (A), which can be proved inductively whenever the indices are positive integers, can now be used to assign meanings to the function raised to a fractional, surd or negative index. All we have to do is to use the equation (A) as a definition as far as these quantities are concerned, and a whole range of new functions are introduced in a way logically continuous with those already known. 'The ind.

First edition. HILBERT'S INAUGURAL DISSERTATION. First edition, very rare, of Hilbert's inaugural dissertation at the University of Königsberg, 'On the invariant properties of special binary forms, in particular the spherical functions,' in which he began his study of invariant theory. This subject was at the forefront of mathematics in the second half of the 19th century, and Hilbert's work in this area made his name in the mathematical world. Hilbert (1862-1943) "studied at the University of Königsberg from 1880 to 1884 . Königsberg, the university where Immanuel Kant had studied and taught, became a center of mathematical learning through Jacobi's activity (1827-1842). When Hilbert began his studies there, the algebraist Heinrich Weber, Dedekind's collaborator on the theory of algebraic functions, was a professor at Königsberg. In 1883 Weber left. His successor was Lindemann, a famous but muddle-headed mathematician who the year before had had the good luck to prove the transcendence of ? . Under his influence Hilbert became interested in the theory of invariants, his first area of research" (DSB). Hilbert himself was the first to assess the historical significance of his own work on invariant theory. In a review article read in his name at the International Congress of Mathematicians held in Chicago in 1893, Hilbert mentioned three clearly separated stages, that in his view mathematical theories usually undergo in their development: the naive, the formal and the critical. In the case of invariant theory, Hilbert saw the works of Cayley and Sylvester as representing the naive stage and the work of Gordan and of Clebsch representing the formal stage. In Hilbert's assessment, his own work was the only representative of the critical stage in the theory of invariants. Ultimately Emmy Noether and others enlarged on Hilbert's ideas to found modern algebra. OCLC lists four copies in US. No copies in auction records. Invariant theory dates back at least to Gauss' study of binary quadratic forms in his Disquisitiones Arithmeticae (1801). A 'binary quadratic form' is an expression ax2 + bxy + cy2 in the 'variables' x, y, the 'coefficients' a, b, c being numbers. If we make a change of variables x = ?X + ?Y, y = ?X + ?Y, the original quadratic form becomes AX2 + BXY + CY2, where A, B, C can be expressed in terms of a, b, c and the coefficients of the change of variables ?, ?, ?, ? One finds that B2 - 4AC = D2(b2 - 4ac), where D = ?? - ?? is the 'determinant' of the change of variables. In general, an 'invariant' of the binary quadratic form is any expression in the coefficients of the form that is altered by a change of variables only by a power of the determinant D. This can be generalized to forms involving more than two variables, and to forms of higher degree (i.e., involving higher powers of the variables). There are also the 'covariants', which are similarly defined functions involving both the coefficients and the variables of the form. Even before Gauss, Lagrange in his Méchanique analitique (1788) had studied the transformation properties of forms under changes of variables. Lagrange's work was taken up by Boole in his paper 'Researches on the theory of analytical transformations' (1839), which must be considered the foundation work in invariant theory and the birth of the British/Irish school of invariant theory. "Formally, invariant theory began with Cayley and Sylvester in the late 1840s. Cayley used it to bring to light the deeper connections between metric and projective geometry. Although important connections with geometry were maintained throughout the nineteenth and early twentieth centuries, invariant theory soon became an area of investigation independent of its relations to geometry. In fact, it became an important branch of algebra in the second half of the 19th century . Many of the major mathematicians of the second half of the nineteenth century worked on the computation of invariants of specific forms. This led to the major problem of invariant theory, namely to determine a complete system of invariants-a basis-for a given form. That is, to find invariants of the form-it was conjectured that finitely many would do-such that every other invariant could be expressed as a combination of these. Cayley showed in 1856 that the finitely many invariants he had found earlier for binary quartic forms (i.e., forms of degree four in two variables) are a complete system. About ten years later Gordan proved that every binary form, of any degree, has a finite basis. Gordan's proof of this important result was computational-he exhibited a complete system of invariants" (Kleiner, pp. 92-93). This was the situation in invariant theory when Hilbert arrived in Königsberg. "Having completed the eight university semesters required for a doctor's degree, Hilbert began to consider possible subjects for his dissertation. In this work he would be expected to make some sort of original contribution to mathematics. At first he thought he might like to investigate a generalization of continued fractions; and he went to Lindemann, who was his 'Doctor-Father', with this proposal. Lindemann informed him that unfortunately such a generalization had already been given by Jacobi. Why not, Lindemann suggested, take instead a problem in the theory of invariants . "The problem which Lindemann suggested to Hilbert for his doctoral dissertation was the question of the invariant properties for certain algebraic forms. This was an appropriately difficult problem for a doctoral candidate, but not so difficult that he could not be expected to solve it. Hilbert showed his originality by following a different path from the one generally believed to lead to a solution. It was a very nice piece of work, and Lindemann was satisfied. "A copy of the dissertation was dispatched to Minkowski, who after his father's recent death had gone to Wiesbaden with his mother. 'I studied your work with great interest,' Minkowski wrote to Hilbert,

First edition. FIRST PROOF THAT ELECTROMAGNETIC EFFECTS PROPAGATE AT THE SPEED OF LIGHT. First edition, complete journal issue in original printed wrappers, of one of the two most important papers of Hertz's on electromagnetic waves, in which he demonstrates for the first time that electromagnetic effects propagate at the speed of light (it was only a month later that he first produced and detected electric waves). "In his Treatise on Electricity and Magnetism (1873) [Maxwell] gave no theory of oscillatory circuits or of the connection between currents and electromagnetic waves. The possibility of producing electromagnetic waves in air was inherent in his theory, but it was by no means obvious and was nowhere spelled out. Hertz's proof of such waves was in part owing to his theoretical penetration into Maxwell's thought" (DSB). "Experimental proof by Hertz of the Faraday-Maxwell hypothesis that electrical waves can be projected through space was begun in 1887, eight years after Maxwell's death . The experiments were reported periodically from 1887 onward in Annalen der Physik und Chemie" (PMM). "This discovery [of electromagnetic waves] and its demonstration led directly to radio communication, television and radar" (Dibner). "In the early 1890s the young inventor Guglielmo Marconi read of Hertz's electric wave experiments in an Italian electrical journal and began considering the possibility of communication by wireless waves. Hertz's work initiated a technological development as momentous as its physical counterpart" (DSB). This paper was first published in the Sitzungsberichte (offered here) and then three months later in Annalen der Physik (Bd. 270, Heft 7, pp. 551-569). ABPC/RBH list one copy of the offprint (Swann 1994) and none of the journal issue. Hertz's work on electric waves began with Helmholtz's proposal in 1879 of a prize problem connected with the behaviour of unclosed circuits in Maxwell's theory. "Central to Maxwell's theory was the assumption that changes in dielectric polarization yield electromagnetic effects in precisely the same manner as conduction currents do. Helmholtz wanted an experimental test of the existence of these effects or, conversely, of the electromagnetic production of dielectric polarization. Although at the time Hertz declined to try the Berlin Academy problem because the oscillations of Leyden jars and open induction coils which he was familiar with did not seem capable of producing observable effects, he kept the problem constantly in mind; and in 1886 shortly after arriving in Karlsruhe, he found that the Riess or Knochenhauer induction coils he was using in lecture demonstrations were precisely the means he needed for undertaking Helmholtz' test of Maxwell's theory . "He produced electric waves with an unclosed circuit connected to an induction coil, and he detected them with a simple unclosed loop of wire. He regarded his detection device as his most original stroke, since no amount of theory could have predicted that it would work. Across the darkened Karlsruhe lecture hall he could see faint sparks in the air gap of the detector. By moving it to different parts of the hall he measured the length of the electric waves; with this value and the calculated frequency of the oscillator he calculated the velocity of the waves. For Hertz his determination at the end of 1887 of the velocity - equal to the enormous velocity of light - was the most exciting moment in the entire sequence of experiments. He and others saw its significance as the first demonstration of the finite propagation of a supposed action at a distance" (DSB). Hertz himself gives an account of the present paper in the introduction to Electric Waves (pp. 7-8), which contains English translations of his most important papers on the subject. "A scheme was conceived which was carried out as described in the research 'On the finite velocity of propagation of electromagnetic actions.' The first step that had to be taken was easy. In straight stretched wires surprisingly distinct stationary waves were produced with nodes and anti-nodes, and by means of these it was possible to determine the wavelength and the change of phase along the wire. Nor was there any greater difficulty in producing interference between the action which had travelled along the wire and that which had travelled through the air, and thus in comparing their phases. Now if both actions were propagated, as I expected, with one and the same finite velocity, they must at all distances interfere with the same phase. A simple qualitative experiment which, with the experience I had now gained, could be finished within an hour, must decide this question and lead at once to the goal. But when I had carefully set up the apparatus and carried out the experiment, I found that the phase of the interference was obviously different at different distances, and that the alternation was such as would correspond to an infinite rate of propagation in air. Disheartened, I gave up experimenting. Some weeks passed before I began again. I reflected that it would be quite as important to find out that electric force was propagated with an infinite velocity, and that Maxwell's theory was false, as it would be, on the other hand, to prove that this theory was correct, provided only that the result arrived that should be definite and certain. I therefore confirmed with the greatest care, and without heeding what the outcome might be, the phenomena observed: the conclusions are given in the paper. When I then proceeded to consider more closely these results, I saw that the sequence of the interferences could not be harmonised with the assumption of an infinite rate of propagation; that it was necessary to assume that the velocity [in air] was finite but greater than that in the wire. As shown in the paper, I endeavoured to bring into harmony the various possibilities; and although the differences in the velocities appeared to me to be somewhat improbable, I co.

First edition. SCIENTIFIC FRAUD: THE EINSTEIN-RUPP EXPERIMENTS. First edition, extremely rare author's presentation offprint (not to be confused with the much more common trade separate - see below), from the library of the great German physicist Arnold Sommerfeld, of the notorious Einstein/Rupp experiments. "In the fall of 1926, Albert Einstein published the outline of two experiments in the Proceedings of the Berlin Academy. They addressed one of the most urgent questions in physics at the time: the experiments were to show if the emission of light was a process that was extended in time, or if instead light emission occurred in an instantaneous act. Of course, the first possibility would confirm a traditional oscillator-and-wave-like view, whereas the second possibility would cohere well with Einstein's own ideas on light quanta. It is quite surprising that these experiments are so unfamiliar today. Apart from addressing a central question and being proposed by no lesser figure than Einstein, they also circulated at a crucial moment in the history of quantum theory. Still, the experiments are not mentioned in any of the standard Einstein biographies and there is no substantial treatment of them in histories of the quantum theory . The likely cause for this lack of attention is at least as surprising: the experiments were-supposedly-conducted by Emil Rupp, yet a decade later Rupp was exposed as a scientific fraudster; the results, obtained by Rupp in close consultation with Einstein and published back-to-back with the latter's theoretical paper, were in the end generally believed to have been fabrications" (Van Dongen). As Walter Gerlach (of Stern-Gerlach fame) said (in an interview with Thomas Kuhn in 1963), "Rupp, in the late twenties, early thirties, was regarded as the most important and most competent physicist. He did incredible things. . Later, it turned out that everything that he had ever published, everything, was forged. This had gone on for ten years, ten years!" Nevertheless, "these experiments played a substantial role in developments in 1926. Most importantly, they confirmed a wave picture of light, when many, including Einstein himself, initially expected a particle-like, instantaneous picture of light emission to be confirmed. After all, only a few years before Compton scattering had been shown, and as little as a year before the Einstein-Rupp experiments Walther Bothe and Hans Geiger had done the experiments that dismissed the BKS theory. But the experiments of Einstein and Rupp also influenced events in other ways. For instance, their initial interpretation was most likely of direct importance for Max Born, when he proposed the probabilistic interpretation of the wave function. The experiments further played a role in the thinking of Werner Heisenberg, as he formulated his uncertainty relations . these experiments deserve renewed attention, and their current obscure status is not warranted by their historical importance" (Van Dongen). OCLC locates only three copies, two in Switzerland, one in Germany, but it is unclear which of these (if any) are author's presentation offprints. The presentation offprint was not present in the collection of Einstein's son Hans Albert (Christie's 2006), but it was in Einstein's own collection of his offprints (Christie's 2008). Provenance: Arnold Sommerfeld (1868-1951) (his characteristic numbering ('46') in red pencil on front cover). "The son of a physician, Sommerfeld was educated at the University of Königsberg. After teaching briefly at the universities of Göttingen, Clausthal, and Aachen he was appointed professor of physics at the University of Münich in 1906. Sommerfeld should have retired in 1936 in favour of his pupil, Werner Heisenberg. Opposition from the Nazi party to Heisenberg's appointment prolonged Sommerfeld's tenure and it was not in fact until late 1939 that he finally retired, to be succeeded not by Heisenberg but by Wilhelm Müller, a Nazi aerodynamicist without a single publication in physics to his credit. Although Sommerfeld and Heisenberg were not Jewish, they were regarded by the Nazis as Jewish sympathizers. Sommerfeld, however, survived the war and returned to his Münich chair in 1945, continuing to work at physics until he died in a car accident in 1951" (Oxford Reference). "Arnold Sommerfeld was one of the most distinguished representatives of the transition period between classical and modern theoretical physics. The work of his youth was still firmly anchored in the conceptions of the nineteenth century; but when in the first decennium of the century the flood of new discoveries, experimental and theoretical, broke the dams of tradition, he became a leader of the new movement, and in combining the two ways of thinking he exerted a powerful influence on the younger generation. This combination of a classical mind, to whom clarity of conception and mathematical rigour are essential, with the adventurous spirit of a pioneer, are the roots of his scientific success, while his exceptional gift of communicating his ideas by spoken and written word made him a great teacher" (Max Born, p. 275). "Born in 1898, Rupp began his career in the 1920s studying canal rays, beams of positive ions and atoms formed between an anode and cathode, the latter punctured with holes (or "canals"), in a gas discharge tube. When these rays shoot through the canals and into a vacuum chamber, the ions rapidly lose and gain charge, emitting visible light that becomes less intense at the other end of the canal. "In his first experiments in the mid-1920s, Rupp measured the coherence length of light - the distance over which the light maintains a consistent phase - emitted by hydrogen and mercury atoms in the canal rays. He measured these lengths as 62 centimeters for hydrogen and 15.2 centimeters for mercury. These were blockbuster results: A moving hydrogen atom was expected to stay coherent over a much smaller distance. "What's more, Rupp's extra-lo.

THE INSPIRATION FOR THE MICHELSON-MORLEY EXPERIMENT. First edition, in the very rare original printed wrappers, of Maxwell's last paper, "published posthumously in the Proceedings of the Royal Society, [which] concerned a means of measuring the speed of the Earth through the hypothetical aether, and was the inspiration for Michelson and Morley's famous experiment. The null result of that experiment was to lead to the Special Theory of Relativity" (Longair, Maxwell's Enduring Legacy, p. 71). "Maxwell's words had stimulated Michelson to carry out one of the great experiments of physics" (Longair, CavMag, p. 13). "The paper was in fact by George Stokes, reporting a letter which Maxwell sent to Mr. D[avid] P[eck] Todd of the Nautical Almanac Office in Washington dated 19 March 1879. The main body of the letter concerns the use of accurate timing of the eclipses of Jupiter's satellites as a means of measuring the speed of light plus the Earth's motion through the ether. This required an accurate knowledge of the orbits of Jupiter's satellites. Maxwell writes, 'I have therefore taken the liberty of writing to you, as the matter is beyond the reach of anyone who has not made a special study of the satellites.' But, more germane is the remark in an earlier paragraph. '. in the terrestrial methods of determining the velocity of light, the light comes back along the same path again, so that the velocity of the earth with respect to the ether would alter the time of the double passage by a quantity depending on the square of the ratio of the earth's velocity to that of light, and this is quite too small to be observed' . Albert Michelson recognised that, contrary to Maxwell's assertion, very small path differences could be detected by optical interferometry. In his paper on the first version of the experiment of 1881 ['The Relative Motion of the Earth and the Luminiferous Ether,' American Journal of Science, 22, 120-129], Michelson states explicitly that: 'The following is intended to show that, with a wave-length of yellow light as a standard, the quantity [the path difference between the light rays] ? if it exists ? is easily measurable" (ibid., p. 12). But Michelson made an error in his calculations in 1881 and realised that an improved version of the experiment was necessary; this he carried out with Morley in 1887 ('On the Relative Motion of the Earth and the Luminiferous Ether,' American Journal of Science, 34, 333-345). The offered paper was published simultaneously in the Royal Society's Proceedings and in the journal Nature (Vol. 21, p. 315). "Maxwell's (1831-79) influence in suggesting the Michelson-Morley ether-drift experiment is widely acknowledged, but the story is a curiously tangled one. It originates in the problem of the aberration of starlight. During the course of a year the apparent positions of stars, as fixed by transit measurements, vary by ±20.5 arc-seconds. This effect was discovered in 1728 by [James] Bradley (1693-1762). He attributed it to the lateral motion of the telescope traveling at velocity v with the earth about the sun. On the corpuscular theory of light the motion causes a displacement of the image, while the particles travel from the objective to the focus, through an angular range v/c just equal to the observed displacement [c is the velocity of light]. An explanation of aberration on the wave theory of light is harder to come by. If the ether were a gas like the Earth's atmosphere (as was first supposed), it would be carried along with the telescope and one scarcely would expect any displacement. [Thomas] Young (1773-1829) in 1804 therefore proposed the ether must pass between the atoms in the telescope wall "as freely perhaps as the wind passes through a grove of trees." The idea had promise, but in working it out other phenomena needed to be considered, many of which further illustrate the difficulties of classical ethers . "In 1859 [Hippolyte] Fizeau (1819-96) proved experimentally that the velocity of light in a moving column of water is greater downstream than upstream. A natural supposition is that the water drags the ether along with it. This contradicts Young's hypothesis in its most primitive form; however, the modified velocity was not c + w but c + w(1 - 1/?2), where ? is the refractive index of water [and w is the velocity of the water], and that tallied with a more sophisticated theory of aberration due to [Augustin-Jean] Fresnel (1788-1827). Fresnel held the conviction (not actually verified until 1871) that the aberration coefficient in a telescope full of water must remain unchanged, which on Young's theory it does not. He was able to satisfy that requirement by combining Young's hypothesis with the further assumption that refraction is due to condensation of the ether in ordinary matter, the ether density in a medium of refractive index ? being ?2 times its value in free space. With the excess ether carried along by matter one obtains the quoted formula, which in consequence is still known as the "Fresnel drag" term, though it stands on broader foundations, as [Joseph] Larmor (1857-1942) afterwards proved. Indeed Fresnel's condensation hypothesis is logically inconsistent with another principle that became accepted in the 1820s, namely, that the ether, to convey transverse but not longitudinal waves, must be an incompressible solid. A dissatisfaction with Fresnel's "startling assumptions" made [George] Stokes (1819-1903) in 1846 propose a radically new theory of aberration, treating the ether as a viscoelastic substance, like pitch or glass. For the rapid vibrations of light the ether acts as a solid, but for the slow motions of the solar system it resembles a viscous liquid, a portion of which is dragged along with each planetary body. A plausible circuital condition on the motion gives a deflection v/c for a beam of light approaching the earth, identical with the displacement that occurs inside the telescope in the other theories. "Some ti.

First edition. FEYNMAN'S LECTURES ON PHYSICS- EXTREMELY RARE PRE-PUBLICATION ISSUE. Extremely rare pre-publication issue of a section of Feynman's legendary lectures on physics, namely that devoted to electromagnetism, from Maxwell's equations to the optical and magnetic properties of materials, and concluding with four lectures on elasticity and fluid flow. According to the curators of Caltech's Feynman Lectures website (), this preliminary edition was produced by Caltech's graphics department between the end of the 1962-1963 academic year and the beginning of the 1963-64 academic year. It is copyrighted 1963, one year before the first published edition of the Feynman lectures, produced by Addison-Wesley. No more than 300 copies of this pre-publication edition were printed. This section of the Feynman Lectures is a record of part of the second year's lectures, which were given to the sophomore class during the 1962-1963 academic year (all Caltech sophomores were required to take the class, regardless of their majors). The printed lectures were not a verbatim transcript of what Feynman said, but were edited by Leighton and Sands. "We hoped to make the written version as clear an exposition as possible of the ideas on which the original lectures were based. For some of the lectures this could be done by making only minor adjustments of the wording in the original transcript. For others of the lectures a major reworking and rearrangement of the material was required. Sometimes we felt we should add some new material to improve the clarity or balance of the presentation. Throughout the process we benefitted from the continual help and advice of Professor Feynman" (Sands). "Feynman's lectures are as powerful today as when first published, thanks to Feynman's unique physics insights and pedagogy. They have been studied worldwide by novices and mature physicists alike; they have been translated into at least a dozen languages with more than 1.5 millions copies printed in the English language alone. Perhaps no other set of physics books has had such wide impact, for so long" (Kip Thorne). "Mark Kac, the eminent Polish-American mathematician, wrote: 'In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the 'ordinary' and the 'magicians'. An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with magicians . the working of their minds is for all intents and purposes incomprehensible . Richard Feynman [was] a magician of the highest caliber'" (Biographical Memoirs of Fellows of the Royal Society of London 48 (2002), p. 99). Widely regarded as the most brilliant, influential, and iconoclastic figure in theoretical physics in the post-World War II era, Feynman shared the Nobel Prize in Physics 1965 with Sin-Itiro Tomonaga and Julian Schwinger "for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles." We are not aware of any other copy of this preliminary version of Feynman's lectures having appeared on the market, and we have located no institutional holdings other than Caltech. Matthew Sands joined the physics department at Caltech in 1950, at the same time as did Richard Feynman. They had known each other at Los Alamos and at Cornell, but at Caltech their acquaintance matured. In the 1950s, Sands served on the Commission on College Physics, which had been established to work on the improvement of physics teaching. "Until that time he had been teaching graduate courses and, with Feynman's help, had restructured the graduate curriculum at Caltech. Stimulated by his work on the Commission on College Physics, he took a close look at the undergraduate physics curriculum at Caltech and didn't like what he saw . in the first two years, when students took chemistry, physics, and engineering, no mention was made of atomic physics, quantum theory, and relativity . [Sands] felt very strongly that they should revise the undergraduate introductory courses in physics. At first, he got only a negative response from Robert Bacher, who was then head of the division of physics, mathematics, and astronomy [but Sands] ultimately convinced Bacher that it would be good to modernize the program . [Bacher] thought that Matt Sands himself was too radical, so he asked Robert Leighton, a quiet conservative, and Victor Neher - an old collaborator of Millikan's and an excellent designer of pedagogical experiments - all three to work on revising the introductory physics curriculum . 'About half way through the year [1960] I [Sands] became very frustrated because Leighton kept coming back with a very traditional outline, and we could not seem to converge on a solution which would meet my requirements and his. One day I had the brilliant inspiration of saying, "Look, why don't we get Feynman to give the lectures and let him make the final decision on the contents?"' "So Sand went to see Feynman at his house and said, 'Look, Richard, you have spent forty years trying to understand physics. Now here is your chance to distil it down to the essence at the level of a freshman.' Feynman thought about it and said, 'Hmm! That might be interesting! But, you know, I have never taught freshman physics before.' Sands had seen Feynman lecture in graduate courses and seminars and was convinced that his style and thought would be very good for what he had in mind. From their discussion, Feynman obtained a good feeling for what might be possible, 'So he said he would think about it for a day or two and I saw him later on and he asked: "Do you know if there has ever been a great physicist who lectured on freshman physics?" I said, "I don't know, but I don't think so!" And he said, "I'll do it!" (Mehra, pp. 483-484). Bacher initially opposed the idea, par.

First edition. "THE WORLD'S FIRST LOGIC MACHINE" (MARTIN GARDNER). First edition, extremely rare separately-paginated offprint, inscribed by the author, of the first published description of "the world's first logic machine" (Martin Gardner), designed by Charles Stanhope, third Earl Stanhope, in the 1770s. "His system consisted essentially in the reduction of both positive and negative propositions to a single form, that of the identity of two things or classes of things, and in the employment of symbols to represent the quantities of things involved in such propositions. In his general use of logical symbols and his manipulation of them he introduced a new rigour into the science and looked ahead towards Boole's virtual reduction of logic to a branch of pure mathematics" (Beatty, p. 206). Stanhope "succeed[s] in demonstrating that the consequences of two logical statements are capable of solution by mechanical means. Although earlier logicians had proposed mechanical contrivances (e.g., Euler's circles), Stanhope was the first to construct an instrument to deal with this kind of problem" (ibid., p. 208). "The first model was constructed in 1775. It consisted of two slides coloured red and gray mounted in a square brass frame. This could be used to demonstrate the solution to a syllogistic type of problem in which objects might have two different properties and the question was how many would have both properties. Scales marked zero to ten were used to set the numbers or proportions of objects with the two properties. This form of inference anticipated the numerically definite syllogism which Augustus De Morgan laid out in his book, Formal Logic, in 1847 . At least four of the devices with this square style were built. In 1879, Robert Harley wrote that he had one which he had been given by Stanhope's great-grandson, Arthur, who had kept one. The other two were owned by General Babbage - the son of Charles Babbage, who continued his work on the Analytical Engine. One of the devices was donated to the Science Museum, London by the last Earl in 1953. Other styles, such as circular models, were constructed, but these were less convenient" (Wikipedia). "Stanhope's speculations on logic covered a period of some thirty years, but he published nothing about his logical views beyond printing on his own hand press several early chapters of an unfinished work, titled The Science of Reasoning Clearly Explained upon New Principles. These chapters were circulated only among a few acquaintances. In a letter written shortly before his death, he advises a friend not to discuss his logical methods with others lest 'some bastard imitation' of his views appear before the publication of his projected work [which was, in fact, never completed or published]. It was not until 60 years later that one of the earl's contrivances, together with relevant letters and notes, came into the hands of Rev. Robert Harley, who then published an account of the demonstrator and the logic on which it was based" (Gardner, pp. 80-81). Harley notes that "Earl Stanhope's Demonstrator is much less powerful as a logical instrument than Professor Jevons' machine, but the former is undoubtedly a distinct anticipation of the latter. It is probably the first attempt ever made to solve logical problems by mechanical methods." OCLC lists 5 copies worldwide (Trinity College, Cambridge; National Library of Wales; Glasgow; Chicago; Huntington); not in BL. Not on RBH. Provenance: Inscribed on upper wrapper, 'George Wooding Esqre. / With the Writer's kind regards.' "Although Ramon Llull made use of rotating discs to facilitate the working of his eccentric system of reasoning, his devices are not logic machines in the sense that they can be used to solving problems in formal logic. The inventor of the world's first logic machine in the strict sense of the term was a colorful eighteenth-century British statesman and scientist, Charles Stanhope, third Earl Stanhope (1753-1816). His curious device, which he called a 'demonstrator,' is interesting in more ways than one. Not only could it be used for solving traditional syllogisms by a method closely linked to the Venn circles; it also took care of numerical syllogisms (anticipating De Morgan's analysis of such forms) as well as elementary problems of probability. In addition, it was based on a system of logical notation which clearly foreshadowed Hamilton's technique of reducing syllogisms to statements of identity by making use of negative terms and quantify products . "In his day, Stanhope was better known throughout England for his fiery political opinions and confused domestic affairs than for his many scientific inventions. His first wife was the sister of England's young and controversial prime minister, William Pitt. For a time the earl was a supporter of Pitt, but he later broke with the ministry to become a vigorous opponent of most of its measures. As a member of the Revolution Society, formed to honor the revolution of 1688, his political views were strongly liberal and democratic. His impetuous proposals in the House of Lords were so often and so soundly defeated that he was widely known as 'the minority of one', and his thin figure was prominent in the political cartoons of the period. He was an ardent supporter of the French republicans in the early days of the French Revolution. It is said that even went so far as to discard all the external trappings of his peerage. "At the early age of 19 he was elected a fellow of the Royal Society and for the rest of his life he devoted a large segment of his time and income to scientific pursuits . In addition to his logic machine, he also devised an arithmetical calculating machine employing geared wheels" (Gardner, pp. 80-81). "Stanhope's Demonstrator was designed as a device able to solve mechanically traditional syllogisms, numerical syllogisms, and elementary probability problems. The rectangular version of the device consists of a brass plate (size 10 x.

First edition. PARITY AND TIME-REVERSAL IN QUANTUM MECHANICS. First edition, very rare offprints, of these two fundamental papers in quantum mechanics, the "invention of spatial parity as a quantum mechanical conserved quantity [I] [and the] introduction of the time inversion transformation in quantum mechanics [II]" (). "Wigner was invited to Göttingen in 1927 to become Hilbert's assistant. Hilbert, already interested in quantum mechanics, felt that he needed a physicist as an assistant to complement his own expertise. This was an important time for Wigner who produced papers of great depth and significance, introducing in his paper 'On the conservation laws of quantum mechanics' (1927) [I] the new concept of parity" (). "Wigner performed pioneering work by studying such symmetries in the laws of motion for the electrons and had made important discoveries by investigating e.g., those symmetries which express the fact that the laws mentioned make no difference between left and right and that backward in time according to them is equivalent to forward in time. These investigations were extended by Wigner to the atomic nuclei at the end of the 1930s and he explored then also the newly discovered symmetry property of the force between two nucleons to be the same whether either of the nucleons is a proton or a neutron. This work by Wigner and his other investigations of the symmetry principles in physics are important far beyond nuclear physics proper. His methods and results have become an indispensable guide for the interpretation of the rich and complicated picture which has emerged from recent years' experimental research on elementary particles" Presentation speech for Wigner's Nobel Prize). "Wigner was a member of the race of giants that reformulated the laws of nature after the quantum mechanics revolution of 1924-25. In a series of papers on atomic and molecular structure, written between 1926 and 1928, Wigner laid the foundations for both the application of group theory to quantum mechanics and for the role of symmetry in quantum mechanics" (David J. Gross, 'Symmetry in Physics: Wigner's legacy,' Physics Today, December 1995, pp. 46-50). Wigner was awarded the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles." "Nearly a decade after he was awarded the Nobel Prize, Wigner's early group theory research was described as so farsighted that it was not immediately recognized for its importance as a pioneering advance in mathematical physics . The parity law states that particles emitted during a physical process should emanate from the left and right in equal numbers or equivalently that a nuclear process should be indistinguishable from its mirror image. The parity concept was not challenged until 1956 when it was disproved in certain so-called 'weak decay' interactions in experiments by Tsung-Dao Lee of Columbia and Chen-Ning Yang of Princeton. Lee and Yang were awarded the Nobel Prize in 1957 for their empirical refutation of Wigner's parity theory in this special case. The theory however remained substantially intact and along with other of Wigner's discoveries useful as a further guide in nuclear research" (DSB). "It is scarcely possible to overemphasize the role played by symmetry principles in quantum mechanics" (C. N. Yang, Nobel Lecture, p. 394). No copies on OCLC or RBH. Provenance: I. Felix Bloch (1905-83), Swiss-American physicist who shared the 1952 Nobel Prize for Physics with Edward Purcell for "their development of new ways and methods for nuclear magnetic precision measurements" ('Bloch' written in ink on front wrapper). II. Ralph Kronig (1904-95), German physicist who first put forward the concept of electron spin ('Kronig' written in pencil on front wrapper). The concept of parity refers to the behavior of classical and quantum systems under the 'inversion' operation, which takes a point in three dimensions with Cartesian coordinates x, y, z to the point with coordinates -x, -y, -z (more generally, this can be any 'linear transformation' that is not a rotation, for example the 'mirror reflection' that takes x, y, z to -x, y, z). Symmetry under inversion, or reflection, was used in classical physics, but was not of any great practical importance there. One reason for this derives from the fact that right-left symmetry is a discrete symmetry, unlike rotational symmetry which is continuous. In a famous paper in 1918, Emmy Noether showed that continuous symmetries always lead to conservation laws in classical physics - but a discrete symmetry does not. With the introduction of quantum mechanics, however, this difference between discrete and continuous symmetries disappears. Wigner was led to his study of parity by work of Otto Laporte in 1924. Laporte studied the structure of the spectrum of iron and found that there are two kinds of energy levels, which he called 'stroked' ('gestrichene') and 'unstroked' ('ungestrichene'). He discovered a selection rule (later called Laporte's rule) that the transitions occurred always from stroked to unstroked levels or vice versa, and never between stroked or between unstroked levels. A few months later similar observations on the spectrum of titanium were made by Henry Norris Russell. No convincing explanation of the existence of two types of levels was found within the framework of the old quantum theory. In 1927, Wigner analysed Laporte's finding and showed that the two types of levels and the selection rule followed from the invariance of the electromagnetic forces in the atom under the operation of inversion of coordinates. This led him quickly to the idea of parity conservation in quantum mechanics. He wrote, 'But that was very easy. I knew the spectroscopic rules, and Laporte's rule was similar to the theory of inversion'. Wigner introduced the parity operator, and parity conservation, forma.

First edition. HEISENBERG'S FIRST PUBLISHED PAPER. First edition of Heisenberg's first published paper, journal issue in original printed wrappers, describing his 'core model' of the atom and its application to solve the problems of the multiplet structure in atomic spectra and the anomalous Zeeman effect, which had defeated all previous attempts. "Just a year after entering Sommerfeld's program, Heisenberg amazed his teacher by presenting a model of atoms that seemed to resolve every spectroscopic riddle at a stroke. But the model succeeded only because its daring inventor failed to follow the requirements of an acceptable quantum theory" (Cassidy, Beyond Uncertainty, p. 95). "Werner Heisenberg had just celebrated his twentieth birthday when he presented his first paper for publication in 1921. This paper, a long and complex study entitled 'On the Quantum Theory of Line Structure and of the Anomalous Zeeman Effects,' immediately placed its young author on the forefront of theoretical spectroscopy. 'He understands everything,' Niels Bohr remarked. But, as often happens with brilliant first papers, its unique proposals were as controversial and perplexing as the phenomena they purported to explain" (Cassidy, 'Heisenberg's first paper,' Physics Today 31 (1978), p. 23). "In 1922 he publicly displayed his audacity-and his intuition-in his first published paper, which offered a model for the Zeeman effect [the splitting of atomic spectral lines when a magnetic field is applied] that described all of the known data in terms of the couplings between valence electrons and the remaining atomic 'core' electrons. The model, however, violated many of the basic principles of quantum theory and classical mechanics. It thus served both as the basis for most of the subsequent work on the Zeeman effect until the advent of electron spin and as the first indication of the radical changes required for solving the quantum riddle. The core model brought its author to the attention of established theoreticians. Sommerfeld had already written to his colleagues about Heisenberg's work when, in June 1922, he brought his student to Göttingen for a series of lectures on quantum atomic physics presented by Bohr. Heisenberg's audacious criticism of one of Bohr's assertions and a subsequent confrontation between the two over the core model resulted in a mutual admiration and the beginning of a lifelong collaboration that was as important for Heisenberg as his collaboration with Pauli" (DSB). Sommerfeld's own attempt to solve the same problems precedes Heisenberg's paper in the same issue. "The Bohr theory of atoms and molecules, Sommerfeld's "quantum theory of spectral lines," and the correspondence principle of 1918. formed the foundations of the Bohr quantum theory. This theory provided in turn the basis for model interpretations of most, but not all, existing phenomena of empirical spectroscopy. Two phenomena, multiplet line spectra and the anomalous Zeeman effect, continually resisted explanation by quantized mechanical models" (Cassidy, pp. 191-192). The eighteen-year-old Heisenberg entered Sommerfeld's institute in the winter semester of 1920-21, and Sommerfeld immediately introduced him to the Bohr theory. In June 1921 Alfred Landé gave a phenomenological explanation of the splittings observed in the anomalous Zeeman effect, but he did not propose any physical interpretation of his theory, writing to Bohr: "With regard to the complicated types of the Zeeman effect, I have found a few empirical rules which. permit one to make predictions regarding the neon spectrum. But what these rules signify is entirely incomprehensible to me." Sommerfeld suggested that Heisenberg should try to find a model to explain Landé's rules. The result was the present paper, submitted in his third semester, when he was just twenty years old. "In it he claimed that he was presenting the essential details of a complete quantum-theoretical "model interpretation" of the empirical regularities of optical multiplet lines in spectroscopy and the anomalous Zeeman effect of these lines in a magnetic field. All previous attempts to explain these lines by mechanical models had failed. The model was nevertheless riddled with what Max Born called "conscious deviations" from accepted principles and procedures. "Heisenberg, Sommerfeld's "vastly gifted pupil," had reduced the previously inexplicable line structure to internal magnetic interactions between the valence electrons and the rest of the atom. The inner orbits and nucleus acted as a solid core. possessing on the average a half-unit of angular momentum. Half-integral quantum numbers and magnetic interactions between orbital interactions between orbital electrons had already appeared in the work of Landé and others, but half-integral momenta and a magnetic core had not. They could not be justified in either classical or quantum theory, despite Sommerfeld's blessing. "Although the model was theoretically untenable, with it Heisenberg could quantitatively account for doublet and triplet term energies. By attributing half-integral angular momenta to the valence electrons, he could also derive the semi-empirical Landé g-factors for the anomalous Zeeman effect and their continuous transition to unity in the Paschen-Back effect. "Heisenberg's accomplishments were unique, but Bohr judged his "interesting paper" to be "hardly agreeable with the general assumptions" of quantum theory. Not only had Heisenberg introduced real non-integral momenta, but he had also violated the Sommerfeld quantum conditions, classical radiation theory, the Larmor precession theorem, and the semi-classical criterion of perceptual clarity (Anschaulichkeit) in model interpretations. The impact of these violations upon the rational advance of quantum theory spurred Bohr and others to try to derive Heisenberg's results without straying too far from current principles and procedures" (ibid. pp. 190-191). Cassidy sees in this paper the formatio.

First edition. THE FIRST TEST OF QUANTUM MECHANICS. First edition, journal issue in original printed wrappers, of Pauli's important derivation of the hydrogen spectrum from the new quantum mechanics, providing the first validation of Heisenberg's theory. As Pauli explains in the abstract: "It is shown that the Balmer terms of an atom with a single electron are yielded correctly by the new quantum mechanics and that the difficulties which arose in the old theory. disappear in the new theory." Heisenberg's epochal 'Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,' the invention of quantum mechanics, had appeared just a few months earlier, in September 1925. "The first nontrivial and physically important application of quantum mechanics was made soon afterwards by Wolfgang Pauli [in the present paper], who calculated the stationary energy values of the hydrogen atom by the matrix method and found complete agreement with Bohr's 1913 formulas. From this moment, there was no longer any doubt about the correctness of the theory among physicists" (Max Born, Physics in My Generation (1956), p. 181). "The Heisenberg formulation of quantum mechanics is exceedingly easy to apply to problems with linear equations of motion, such as that of the harmonic oscillator, but the presence of the inverse square law in the attractive force of the hydrogen problem leads to mathematical problems of considerable complexity. This paper therefor added important support to the new mechanics. In his discussion of the hydrogen atom, he of course included the new degree of freedom to which he had previously drawn attention and referred to the new hypothesis of Uhlenbeck and Goudsmit, which identified this degree of freedom with an internal rotation or 'spin' of the electron, a hypothesis which by this time, after some initial controversy, was beginning to find acceptance" (Peierls, p. 179). "Now the time had come to test the new formalism on the hydrogen atom. Dirac. had solved a two-dimensional hydrogen model ['Quantum mechanics and a preliminary investigation of the hydrogen atom,' Proc. Roy. Soc.,Vol. 110 (1926)]. But the real thing apparently was too difficult even for Born. Heisenberg wrote in his contribution to the Memorial Volume for Pauli: 'At that time I myself was somewhat unhappy that I did not succeed in deriving even the simple hydrogen atom.' Liberated from his work on the 'Quantentheorie' [Handbuch der Physik, Vol. 23, pp. 1-278] Pauli had gone into this problem at full pelt, and on 17 January 1926 he submitted for publication his paper 'On the hydrogen spectrum from the standpoint of the new quantum mechanics.' Already on 3 November 1925 Heisenberg had written to Pauli: 'I probably don't have to tell you how much I rejoiced at your new theory of hydrogen and how much I admire that you have made out this theory so far,' and he closed the letter with 'hearty congratulations for your theory'" (Enz, No Time to be Brief (2002), pp. 134-5). "Besides Heisenberg, it was Niels Bohr who first learned about the results of Pauli's hydrogen calculation. Hendrik Kramers, who spent a few days in Hamburg in early November, had informed Bohr about it. Bohr immediately wrote to Pauli: 'To my great joy I heard from Kramers that you have succeeded in deriving the Balmer formula' (Bohr to Pauli, 13 November 1925). In the same letter Bohr asked for further details of the calculation and Pauli obliged without delay. Bohr and the theoreticians close to him found Pauli's success striking. Convinced that it was indeed true, Bohr wrote to Pauli: 'Kramers, Kronig and I, who have just gone once again with the greatest pleasure through your beautiful calculation on the hydrogen spectrum, send you many friendly greetings from Tisvilde (Bohr to Pauli, 5 December 1925). "The great satisfaction which Heisenberg and Bohr expressed on Pauli's achievement arose for a reason which could be appreciated nowhere better than in Gottingen and Copenhagen. At these places the conclusion had been reached during the past three years that Bohr's apparently-so-successful theory of atomic systems, including his celebrated derivation of the Balmer formula, possessed no rational theoretical foundation whatsoever. However, Paulis admirable calculation of the hydrogen spectrum, performed on the basis of the matrix mechanics, which could be regarded as the complete logical and mathematical formulation of the quantum concepts developed in Copenhagen and Gottingen since 1923, now provided the necessary justification of the fundamental formula of Bohr's theory" (Mehra & Rechenberg, p. 181). Van der Waerden, Sources of Quantum Mechanics, no. 16. Mehra & Rechenberg, The Historical Development of Quantum Theory, vol. III, 1982. Peierls, 'Wolfgang Ernst Pauli. 1900-1958,' Biographical Memoirs of Fellows of the Royal Society 5 (1960), pp. 174-192. 8vo (229 x 157 mm), pp. 325-400. Original printed wrappers. Very fine. / Hardcover. First edition. ?The first nontrivial and physically important application of quantum mechanics was made soon afterwards by Wolfgang Pauli [in the present paper], who calculated the stationary energy values of the hydrogen atom by the matrix method and found complete agreement with Bohr?s 1913 formulas. From this moment, there was no longer any doubt about the correctness of the theory among physicists? (Max Born).

First edition. THE CORIOLIS FORCE. First edition, complete journal issue ('cahier') in original printed wrappers, of the first formulation of the 'Coriolis force'. "On a rotating earth the Coriolis force acts to change the direction of a moving body to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This deflection is not only instrumental in the large-scale atmospheric circulation, the development of storms, and the sea-breeze circulation, it can even affect the outcome of baseball tournaments: a ball thrown horizontally 100m in 4s in the United States will, due to the Coriolis force, deviate 1.5cm to the right" (Persson, p. 1373). In 1829 Coriolis published Calcul de l'Effet des Machines, which for the first time gave the correct expression for kinetic energy, mv2/2, and its relation to mechanical work. "During the following years Coriolis worked to extend the notion of kinetic energy and work to rotating systems. The first of his papers, 'Sur le principe des forces vives dans les mouvements relatifs des machines', was read to the Académie des Sciences in 1832. Three years later came the paper that would make his name famous, 'Sur les équations du mouvement relatif des systèmes de corps'. Coriolis's papers do not deal with the atmosphere or even the rotation of the earth, but with the transfer of energy in rotating systems like waterwheels. The 1832 paper established that the relation between potential and kinetic energy for a body affected by a force is the same in a rotating system as in a non-rotating one .Three years later, in 1835, Coriolis went back to analyze the relative motion associated with the system, in particular the centrifugal force. It is directed perpendicular to the moving body's trajectory (seen from a fixed frame of reference), which for a stationary body is radially out from the center of rotation. For a moving body this is not the case; it will point off from the center of rotation. The centrifugal force can therefore be decomposed into one radial centrifugal force, and another, the 'Coriolis force.' It is worth noting that Coriolis called the two components 'forces centrifuges composées' and was interested in 'his' force only in combination with the radial centrifugal force to be able to compute the total centrifugal force" (ibid., p. 1378). No copies listed on ABPC/RBH. "The first ideas concerning the influence of the Earth's diurnal rotation on terrestrial objects came with the debate on the very existence of that rotation. This was inevitable, for Aristotelian physics offered a seemingly weighty argument against it: everything lifted into the sky, such as birds or clouds, would no longer share the Earth's rotational movement and hence should drift away to the west at a gigantic speed. Since this is not what we observe, the conclusion had to be that the Earth does not rotate. To move beyond this Aristotelian argument, a different notion of inertia was needed. It was provided by Galilei who put forward the idea that objects persist in their horizontal movement, by which he meant that they would continue their circular trajectory; thus, a stone thrown up in the air does not suddenly lose its rotational motion but keeps on moving along with the Earth. "In 1668, Giovanni Borelli, a member of the Accademia del Cimento in Florence, examined what this principle of inertia implies for objects that are dropped from a tower. On the rotating Earth, the top of a tower describes a larger zonal circle than its foot, and thus must have a higher (circular) velocity to the east. Borelli supposed that an object falling from the top must retain this excess in eastward velocity and hence land slightly to the east of the tower's foot . he found the right direction and the right order of magnitude [but] concluded that the effect was too small to be measured, as the deflection is easily dwarfed by other perturbing effects. More than a century would pass before significant progress was made on this problem. In 1803, Laplace and Gauss independently derived an expression for the eastward deflection of freely falling objects . "A related but more complicated problem is that of the deflection of bodies launched in an arbitrary direction. Riccioli in his Almagestum Novum (1651) argued that, if the Earth rotates, a projectile fired northward should deflect to the east: the projectile comes from a latitude whose zonal circle is larger than the one to which it goes; the accompanying excess in eastward velocity would be retained by the projectile, amounting to a deflection to the east. By contrast, Riccioli (incorrectly) expected no deflection for eastwardly fired objects. His reasoning implies that a systematic difference between northwardly and eastwardly fired objects should have been detected; he took the absence of any such evidence as an argument against the Earth's rotation. Once again, it was Laplace who put the problem on a solid mathematical footing; in the fourth volume of his Mécanique Céleste he derived the equations governing the deflection of projectiles. He showed, in particular, that a body launched vertically upward would land slightly westward. "Laplace's work on the deflection of projectiles was a spin-off of his earlier treatise on tides, which was published in its definitive form in the first volume of his Mécanique Céleste. For a hypothetical ocean covering the entire planet, he examined their modes of propagation. To do this, he first had to derive the equations of motion including the effects of the Earth's rotation. Adopting the usual geographical coordinates, he demonstrated that these equations contain four terms that represent a deflecting force due to the Earth's rotation; moving bodies are subject to a deflecting force in a direction perpendicular to - and in magnitude proportional to - their velocity . "In 1835, Coriolis derived 'his' force in a theoretical treatise on the forces acting in rotating devices [in the offered paper]. He called it.

First edition. EXPLANATION OF THE ANOMALOUS ZEEMAN EFFECT. First edition of the explanation of the anomalous Zeeman effect on the basis of matrix mechanics. "By including the spin property of the electron, Heisenberg and Jordan obtained perhaps the greatest triumph of matrix mechanics: they were able to derive all observed phenomena connected with the anomalous Zeeman effect" (Rechenberg, p. 211). When an atom is placed in a magnetic field, its spectral lines split into a series of equidistant lines - always an odd number - whose separation is proportional to the field strength. This, the normal Zeeman effect, was explained in 1916 by Debye and Sommerfeld in terms of the 'old' quantum theory: the splitting was due to the interaction between the magnetic field and the orbital magnetic moment of the electrons in the atom. However, there is also an anomalous Zeeman effect, observed particularly in atoms with odd atomic number, in which the lines split in a more complex fashion. "During 1920-24, many physicists attacked the problem [of the anomalous Zeeman effect], including Landé, who was able to give a phenomenological explanation of the observed splitting of spectral lines. However, neither Landé, Sommerfeld, Pauli, Heisenberg nor other physicists occupied with the problem could justify their results in terms of quantum theory. "It's a great misery with the theory of anomalous Zeeman effect," Pauli wrote to Sommerfeld on July 19, 1923" (Kragh, p. 158). This paper was of crucial importance in the early history of quantum mechanics because its success in explaining the hitherto mysterious anomalous Zeeman effect validated not only the new quantum mechanics itself but also the highly controversial concept of electron spin, discovered by Uhlenbeck and Goudsmit in the previous year. After Heisenberg's introduction of matrix (quantum) mechanics in 1925, one of the first problems he wanted to address using his new theory was the anomalous Zeeman effect. The crucial ingredient was electron spin, which Uhlenbeck and Goudsmit had discovered by studying the regularities in the anomalous Zeeman effect documented by Landé. "Although based originally upon the classical concept of a rotating electron, electron spin is a purely quantum mechanical property intrinsic to the electron. Opinions were strongly divided about the validity of the concept, Pauli taking a strongly negative position, while Bohr, Heisenberg and Jordan took a more positive view. The challenge taken up by Heisenberg was to find a quantum mechanical solution for the anomalous Zeeman effect using the concept of a spin-½ particle within the context of their recently completed matrix formalism. "Despite the less than encouraging views of Pauli, in November 1925 Heisenberg set about [finding] the stationary states and line splittings associated with the anomalous Zeeman effect. Disappointingly, he almost reproduced Landé's formula for the anomalous Zeeman effect, but the crucial spin-orbit coupling term resulted in a factor of 2 discrepancy from Landé's expression, a result which cast doubt on the whole scheme. "The solution was, however, at hand thanks to the insight of Llewellyn Thomas who had arrived recently at Bohr's Institute in Copenhagen as a visiting graduate student . Thomas was aware of the fact that there is an additional kinematic effect associated with the orbital motion of a vector, such as the spin vector of the electron, according to the special theory of relativity. This purely kinematic effect results in an additional contribution to the precession, and hence interaction energy of the electron. and can account completely for the discrepant factor of 2. After considerable debate, even Pauli was convinced and the paper on the quantum mechanical explanation for the anomalous Zeeman effect was published by Heisenberg and Jordan in June 1926. Rechenberg has written in his summary of the history of quanta and quantum mechanics that the explanation of the anomalous Zeeman effect was one of the greatest triumphs of matrix mechanics" (Longair, pp. 312-5). Heisenberg and Jordan described their results in the abstract of the paper as follows: "For explaining the anomalous Zeeman effect, Uhlenbeck and Goudsmit have applied Compton's hypothesis of the rotating electron. In the present paper [we] investigate the quantum mechanical behaviour of the atomic model characterized by this hypothesis. The result is that the Zeeman effect and the fine structure of the doublet spectra can be explained completely by the said hypothesis" (Mehra & Rechenberg, p. 273). Helge Kragh, Quantum Generations, 1999; Malcolm Longair, Quantum Concepts in Physics, 2013; Helmut Rechenberg, Ch. 3, 'Quanta and Quantum Mechanics,' in Twentieth Century Physics, Vol. 1, L. Brown, B. Pippard & A. Pais (eds.), 1995. For a detailed analysis of the paper, see Jagdish Mehra & Helmut Rechenberg, The Historical Development of Quantum Theory, Vol. 3, 1982, pp. 272-281. 8vo (229 x 156 mm), pp. 235-394. Original printed wrappers. / Hardcover. First edition. ?By including the spin property of the electron, Heisenberg and Jordan obtained perhaps the greatest triumph of matrix mechanics: they were able to derive all observed phenomena connected with the anomalous Zeeman effect? (Rechenberg). This success validated not only the new quantum mechanics but also the highly controversial concept of electron spin, discovered by Uhlenbeck and Goudsmit in the previous year.

First edition. RARE OFFPRINT OF GAUSS ON THE CALCULUS OF VARIATIONS. First edition, the rare separately-paginated offprint, and a fine copy in original state, of this early contribution of Gauss (1777-1855) to mathematical physics, which contains a fundamental and groundbreaking contribution to the calculus of variations. "Gauss ranks, together with Archimedes and Newton, as one of the greatest geniuses in the history of mathematics" (Printing & the Mind of Man, p. 155). He is best known today for giving the first satisfactory proof of the fundamental theorem of algebra (1799), for Disquisitiones arithmeticae (1801), which revolutionized number theory, and for Disquisitiones generales circa superficies curvas (1828), which laid the foundations of differential geometry. The present work deals with the theory of capillary action, the rise or fall of liquids in narrow tubes, the foundations of which were laid by Thomas Young in 1805, who provided a qualitative theory for surface tension, and by Pierre-Simon Laplace, who mathematically formalized the relationship described by Young a year later. Gauss wrote that Laplace's "investigations, which have found their confirmation in striking agreement with careful experiments, are among the most beautiful enrichments of natural science that we owe to the great mathematician" (translation from p. 2). However, Laplace's theory depended on hypotheses about molecular forces, which were little known at the time, and so open to criticism, by Young among others. "The principle which [Gauss] adopted is that of virtual velocities, a principle which under his hands was gradually transforming itself into what is now known as the principle of the conservation of energy. Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbouring particles, he formed a single expression which is the aggregate of all the potentials arising from the mutual action between pairs of particles . With its sign reversed it is now called the potential energy of the system . The condition of equilibrium is that this expression shall be a minimum. This condition when worked out gives not only the equation of the free surface in the form already established by Laplace, but the conditions of the angle of contact of this surface with the surface of a solid. Gauss thus supplied the principal defect in the great work of Laplace" (Britannica). To find the conditions under which the potential energy is a minimum, Gauss used the calculus of variations and his own generalization of d'Alembert's 'principle of virtual work'.In the process he created the method for varying double integrals with variable limits, a problem that both Euler and Jacobi had failed to solve. "In 1830 appeared Principia generalia theoriae figurae fluidorum in statu aequilibrii, his one contribution to capillarity and an important paper in the calculus of variations, since it was the first solution of a variational problem involving double integrals, boundary conditions, and variable limits" (DSB). "Gauss had always been interested in physics .[This] is a theoretical paper, not connected to any experiment . one of Gauss's objectives appeared to be to show how much mathematics could contribute to the elucidation and explanation of nature . Principia generalia should be counted among Gauss's work in the calculus of variations. It also contains interesting results in potential theory . it is closely connected to Gauss's other work in this area" (Bühler, pp. 121-3). This is an offprint from Commentationes Societatis Regiae Scientiarum Göttingensis. It was published in Vol. VII (1832), pp. 39-88 of the Commentationes Classis Mathematicae. As was often the case with the Commentationes, articles appeared in offprint form before the publication of the journal, in this case two years before. Gauss offprints are rarely found in original state as here. ABPC/RBH list only two other copies, both in modern bindings (one with library stamps). "Capillary phenomena and their explanation have undergone a considerable change of status in the physical sciences. Whereas the rise or fall of liquids in tubes or the apparent attraction or repulsion of small floating bodies figure only in subordinate chapters in 20th-century textbooks or in specialized monographs, these phenomena claimed a prominent place in general physics from the early 18th well into the late 19th century. An account of capillarity phenomena formed part of Newton's programme, contained in the last Query in the second English edition of his Opticks (1718), to explain chemical, optical and other phenomena related to cohesion in terms of strong, short-range forces between the microscopic constituents of bodies. For James Clark Maxwell in 1870, the study of capillary action helped to smooth 'the path which leads to the development of molecular physics.' The theory of capillarty was indeed, after the kinetic theory of gases, the most intensively cultivated field of 19th-century molecular physics" (Rüger, p. 1202). At the end of the 18th century, "Laplace developed his programme of reducing 'the phenomena of nature . ultimately to action ad distans between molecules'. Optical refraction and capillary action figured as the first applications of 'Laplacian physics'; elasticity, heat, electricity, magnetism and chemical affinities were to follow. "In the first supplement to book 10 of his Mécanique céleste (1806), Laplace calculated the pressure that a curved surface exerts on the column of liquid in a capillary tube. This capillary pressure is proportional to the mean curvature of the meniscus. According to whether the curvature is negative (concave) or positive (convex), the pressure will be smaller or greater than the pressure under a plane liquid surface, and this pressure difference will cause the liquid in the tube to rise above or sink below the level of the plane surface. Laplace's main result was the differential equation fo.

KINETIC ENERGY AND INERTIAL FORCES. First edition, complete journal volume in original printed wrappers, of this important work on the theory of machines, a follow-up to his Du calcul de l'effet des machines, published in 1829 (but begun a decade earlier) in which he studied dynamical problems associated with rotating machinery. "His approach differs substantially from the usual Newtonian mechanics method used in the eighteenth century and is also quite different from the general mechanics of the nineteenth century" (Oliveira, p. 2). This paper introduced the new notion at that time of 'inertial forces' (forces d'entraînement), and also contains the calculational basis for a sequel published in 1835 in which Coriolis introduced the famous 'Coriolis force' ('Sur les Équations du Mouvement Relatif des Systèmes des Corps', Journal de l'École Polytechnique 15, pp. 142-154). But the main object of the paper is to relate the kinetic energy (forces vives) of a machine when viewed from two different inertial reference frames. He describes his result as follows: "The equation of the live forces can be applied by entering the relative speeds, and the amounts of action or of work that also relate to relative motions. But in these amounts of action, also, forces that are immediately given and that contribute at the absolute moment, others must be considered whose nature is easy to indicate: they are opposite the forces that ought to be applied to the material points of the system if they were free, to force them to conserve compared to the moving planes the relative positions that they have at some given point . it would be a mistake if the proposal was regarded as obvious, even in this fairly simple example. It is so unobvious that these forces must be introduced that we would arrive at false results if we were to proceed with issues other than that of the live forces" (translation from ). One copy (offprint) listed on ABPC/RBH. "In 1829 Coriolis published his first book, Du calcul de l'effet des machines, begun ten years earlier and inspired by the writings of Lazare Carnot . While many scientists seemed to favor a radical separation of theory from technology, Coriolis voiced the belief that rational mechanics should be developed as a discipline for the enunciation of general principles applicable to the operation of motors and analysis of the functioning of machinery. The changes in terminology that he proposed, largely as a result of his teaching experience, were in fact conformable to this clearly conceived policy, as they were to the requirements of the theory itself. "The first of these changes consisted in abandoning for the term 'force-displacement' the ambiguous designations of mechanical power, quantity of action, and dynamic effect, in all of which was subsumed the consideration that processes occurred in time. The word 'work' was in the air following the publication in 1821 of the treatise in which Coulomb had attempted with reference to the limited capacity for activity in men and animals to characterize the notion of the consumption of something in overcoming resistance. The French word-travail-conveys the idea particularly well, and it was certainly Coriolis' contribution to assign it a technical meaning and thereby clarify a notion as old as mechanics itself . "The second important innovation made by Coriolis was to apply the term force vive (kinetic energy) to one-half the product mV2. This was a simple matter of coefficient but convenient in the formulation of the general equations of dynamics. Coriolis thus expressed the principle of vis viva as the 'principle of the transmission of work.' By development of the applications inherent in this change of viewpoint, Coriolis' 'small contribution' marked an important step in the realization of his comprehensive theory. "Coriolis did not delay in producing more. Indeed, he had been led to study the work of internal forces in a material system in order to determine under what conditions this work is nil; he thus discovered the very remarkable characteristic that the value of the work done by a system of forces of which the resultant is equal to zero is independent of the frame of reference with respect to which the changes of position are considered. Wishing to evaluate the work done by fluids in hydraulic machines and steam engines, he found simple expressions that apply to the fixed framework of the machine with respect to which the moving parts are in motion. It was therefore natural that the question of relative motions in machines should occur to Coriolis and that it should entail study of the effects of changes in the system of reference on the fundamental equations of analytical mechanics. But he confined himself at first to the simple problem of comparing two systems of reference in rectilinear translation moving uniformly in respect to each other, for which the work done by inertial forces is identical. On 6 June 1831 Coriolis submitted a memoir to the Academy on the problem of the general case [the offered paper]. He envisaged it in a highly characteristic fashion; to the extent that consideration of relative motion in machines was unavoidable either to eliminate or to simplify the work of linking forces, theory has necessarily to deal with the question of inertial forces when the system of reference is changed. "Thus for the first time Coriolis entered into the study of acceleration in composite motions, and the various phases of this study's formalization deserve attention. "In his 1831 paper, Coriolis had limited himself to exhibiting the existence of a term complementary to relative acceleration and to acceleration of the drive. Since his explicit aim was to enrich rational mechanics with a new statement concerning the transmission of work in relative motion, he was satisfied to demonstrate by computation-without interpreting the analytical expressions for complementary acceleration-that the work of connecting inertial forc.

First edition. THE FIRST PAPER ON FRACTALS "FAMOUS IN THE HISTORY OF MATHEMATICS". First edition, journal issue in original printed wrappers, of Mandelbrot's first paper on fractals (a term he coined in 1975). "Today Mandelbrot's paper on the coast of Britain is famous in the history of mathematics" (). "Mandelbrot had come across the coastline question in an obscure posthumous article by an English scientist, Lewis F. Richardson, who groped with a surprising number of the issues that later became part of chaos [theory] . Wondering about coastlines, Richardson checked encyclopaedias in Spain and Portugal, Belgium and the Netherlands, and discovered discrepancies of 20% in the estimated lengths of their common frontiers . [Mandelbrot] argued [that] . the answer depends on the length of your ruler. Consider one plausible method of measuring. A surveyor takes a set of dividers, opens them to a length of one yard, and walks them along the coastline. The resulting number of yards is just an approximation of the true length, because the dividers skip over twists and turns smaller than one yard, but the surveyor writes the number down anyway. Then he sets the dividers to a smaller length - say, one foot - and repeats the process. He arrives at a somewhat greater length, because the dividers will capture more of the detail and it will take more than three one-foot steps to cover the distance previously covered by a one-yard step. He writes this new number down, sets the dividers at four inches, and starts again . Common sense suggests that, although these estimates will continue to get larger, they will approach some particular final value, the true length of the coastline . if a coastline were some Euclidean shape, such as a circle, this method of summing finer and finer straight-line distances would indeed converge. But Mandelbrot found that as the scale of measurement becomes smaller, the measured length of a coastline rises without limit" (Gleick, pp. 94-96). A copy of Richardson's 'obscure' article, posthumously published in 1961 although written in the 1920s, accompanies Mandelbrot's article here. Richardson proposed, in section 7 ('Lengths of land frontiers or seacoasts') of his article, that the measured length of the coastline should be proportional to G1 - D, where G is the length of the ruler and D is a number, possibly fractional, greater than or equal to 1. On p. 636 of his article, Mandelbrot notes that: "Such a formula, of an entirely empirical character, was proposed by Lewis F. Richardson [in the offered paper] but unfortunately it attracted no attention." Mandelbrot suggests that D should be regarded as the dimension of the coastline - it is now known as the 'fractal dimension'. "Although the key concepts associated with fractals had been studied for years by mathematicians, and many examples, such as the Koch 'snowflake' curve were long known, Mandelbrot was the first to point out that fractals could be an ideal tool in applied mathematics for modeling a variety of phenomena from physical objects to the behavior of the stock market. Since its introduction in 1975, the concept of the fractal has given rise to a new system of geometry that has had a significant impact on such diverse fields as physical chemistry, physiology, and fluid mechanics. Many fractals possess the property of self-similarity, at least approximately, if not exactly. A self-similar object is one whose component parts resemble the whole. This reiteration of details or patterns occurs at progressively smaller scales and can, in the case of purely abstract entities, continue indefinitely, so that each part of each part, when magnified, will look basically like a fixed part of the whole object . This fractal phenomenon can often be detected in such objects as snowflakes and tree barks. All natural fractals of this kind, as well as some mathematical self-similar ones, are stochastic, or random; they thus scale in a statistical sense" (Britannica). "The paper examines the coastline paradox: the property that the measured length of a stretch of coastline depends on the scale of measurement . Th[e] discussion implies that it is meaningless to talk about the length of a coastline; some other means of quantifying coastlines are needed. Mandelbrot discusses an empirical law discovered by Lewis Fry Richardson (1881-1953), who observed that the measured length L(G) of various geographic borders was a of the measurement scale G. Collecting data from several different examples, Richardson conjectured that L(G) could be closely approximated by a function of the form L(G) = MG1 - D where M is a positive constant and D is a constant, called the dimension, greater than or equal to 1 [now known as the 'fractal dimension']. Intuitively, if a coastline looks smooth it should have dimension close to 1; and the more irregular the coastline looks the closer its dimension should be to 2. The examples in Richardson's research have dimensions ranging from 1.02 for the coastline of South Africa to 1.25 for the West coast of Britain. "Mandelbrot then describes various mathematical curves, related to the 'Koch snowflake,' which are defined in such a way that they are strictly self-similar. Mandelbrot shows how to calculate the Hausdorff dimension of each of these curves, each of which has a dimension D between 1 and 2 (he also mentions but does not give a construction for the space-filling 'Peano curve,' which has a dimension exactly 2). He notes that the approximation of these curves with segments of length G have lengths of the form G1 - D. The The resemblance with Richardson's law is striking. The paper does not claim that any coastline or geographic border actually has fractional dimension. Instead, it notes that Richardson's empirical law is compatible with the idea that geographic curves, such as coastlines, can be modelled by random self-similar figures of fractional dimension. "Near the end of the paper Mandelbrot briefly discusses how one migh.

First edition. QUINE'S 'NEW FOUNDATIONS'. First edition, the rare offprint issue, of the paper in which Quine first presented his axiom system for set theory (now usually known as 'NF'). "Although [Quine] is best known to a wider public for his philosophical writings, his most enduring and most concrete legacy for the next 50 years may well turn out to be his most mathematical: he gave us NF" (Forster, p. 838). NF was intended to address the 'crisis of foundations' that mathematicians have attempted to resolve since the early 20th century. "This 'crisis' had many causes and - despite the disappearance of the expression from contemporary speech - has never really been resolved. One of its many causes was the increasing formalisation of mathematics, which brought with it the realisation that the paradox of the liar could infect even mathematics itself. This appears most simply in the form of 'Russell's paradox', appropriately in the heart of set theory. At first blush one might think that where sets are concerned any intension has an extension: this is the axiom of naïve set existence. For any property of sets there exists a set containing precisely the sets with that property, all of those and no others. This leads rapidly to Russell's paradox, the paradox of the class of all sets that are not members of themselves. This is the Russell class. Is it a member of itself? Well, if it is, it isn't, and if it isn't, it is. This is Russell's paradox. The aperçu that leapt to mind was that the problem has something to do with the possibility of sets being members of themselves, or to do with defining sets in terms of membership of themselves. Although these two might sound like formulations of the same insight, they nevertheless lead to radically different resolutions, and to two traditions in set theory represented by Zermelo-Fraenkel set theory (often just called 'set theory' by its votaries, and in any case universally abbreviated to 'ZF') and Quine's NF" (ibid., pp. 838-9). No copies of this offprint listed on ABPC/RBH. The first attempt to resolve Russell's and other similar paradoxes was made by Russell himself (1908) in his theory of types. In this theory, every set is assigned a type (a positive whole number); the bottom type is a type of atoms and sets of type n+1 are sets of things of type n. Every variable of the theory is constrained to range over one level only. This means that Russell's paradox cannot even be formulated within type theory. However, the theory was found to have many drawbacks, as it prevented not only the formulation of the troublesome paradoxes, but also other apparently sensible statements. In addition, it necessarily introduces infinite multiplicities: for example, there has to be one empty set of each possible type, as well as a set of natural numbers of each type, etc. NF is similar to Russell's theory in that it involves types, but rather than assign a type to each set once and for all, it assigns a type to each variable in a given formula. If a variable x in a given formula is assigned type n, and if 'x ? y' appears in the formula, then y must be assigned type n+1. In addition, if 'x = y' appears in the formula, then x and y must have the same type. A formula is 'stratified' if there is an assignment of types to variables in the formula that meets these constraints. The axioms of NF are now simply stated: extensionality, together with a scheme that says that the extension of a stratified formula is a stratified formula. NF avoids the paradoxes of naive set theory because the formulas necessary to formulate the paradoxes are not stratified (for example, a set cannot be a member of itself because x ? x is obviously not a stratified formula). But it also avoids the multiplicities and other difficulties inherent in Russell's type theory. The approach taken in ZF is to restrict what objects can be called sets, rather than to impose restrictions on how sets are defined, as is done in NF. In ZF the empty set is a set, and any collection of sets is a set (and there are no other sets). ZF appears to resolve Russell's paradox because the 'set' of all sets that are not members of themselves is not in fact a set. Although ZF appears to be able to accommodate the whole of mathematics, many mathematicians believe ZF fails to capture the informal concept of a set: in ZF there is no universal set ('the set of all sets'), and the universe of sets is not closed under the elementary operations of the algebra of sets. NF is less restrictive: for example, in NF there is a universal set ('the set of all sets'). On the other hand, it was proved by Specker that the Axiom of Choice is false in NF, which some mathematicians believe restricts its usefulness for mathematics. The debate NF vs. ZF is ongoing. T. Forster, 'Quine's NF - 60 years on,' The American Mathematical Monthly 104 (1997), pp. 838-845. 8vo (255 x 182 mm, pp. 70-80. Original grey printed wrappers. A fine copy. / Hardcover. First edition, the rare offprint issue, Quine?s first presentation of his axiom system for set theory, ?NF? This was intended to address the ?crisis of foundations? that mathematicians had attempted to resolve since the early 20th century, resulting from the paradoxes that afflict ?naïve? set theory.

'A FUNDAMENTAL THEORY OF NEUTRON-INDUCED NUCLEAR REACTIONS' (DSB). First edition, very rare offprint, of this sequel to the paper of Bohr & Kalckar, 'On the Transmutation of Atomic Nuclei by Impact of Material Particles', which had introduced the 'liquid-drop model' of the nucleus. "Bohr's 'droplet model' of nuclear reactions, refined in various ways since it was proposed in 1936, still holds as the adequate mode of description of one of the most important types of nuclear processes" (DSB). "In 1938 [Bohr] began a collaboration with Rudolph Peierls and George Placzek on an improved general treatment of nuclear reactions at higher energies (denser levels). Preliminary results were published in 1939 [in the offered paper]. Plans for a longer paper, interrupted by the war and taken up again thereafter, were never executed. 'Copies of some drafts circulated during [the war years] and as a result the paper was cited repeatedly in the literature, making it one of the most cited unpublished papers'" (Pais, Niels Bohr's Times, p. 341). In the present paper, the authors study the impact of neutrons of sufficiently high energy on medium and heavy nuclei, and the probability (or 'cross-section') for the temporary capture of a neutron by a nucleus. One of its most important contributions was to establish a quantum mechanical version of the 'optical theorem,' a general law relating the forward scattering amplitude to the cross section of the scatterer. "Using the optical theorem and Bohr's liquid-drop model of the nucleus, Placzek, Bohr, and Peierls offered a fundamental theory of neutron-induced nuclear reactions. These works proved essential to the subsequent development of nuclear theory and to development of nuclear reactor design" (DSB, under Placzek). Bohr, Peierls, and Placzek drafted and redrafted a detailed paper many times. In June 1939 Bohr wrote to Peierls that "'Placzek suggested it would be nice if a short account of the result could appear in Nature in the near future, and I shall bring with me a draft Placzek and I have written' . This draft, after minimal polishing, was published in the July 29, 1939 issue of Nature" (George Placzek: A Nuclear Physicist's Odyssey, p. 31). It carries the following footnote: "The details of this and of the other arguments of this note will be published in the Proceedings of the Copenhagen Academy." But in fact no detailed version of this paper ever appeared. No other copy listed on ABPC/RBH. Not on OCLC. In the present paper, the authors study the impact of neutrons of sufficiently high energy on medium and heavy nuclei, and the probability (or 'cross-section') for the temporary capture of a neutron by a nucleus. One of its most important contributions was to establish a quantum mechanical version of the 'optical theorem,' a general law relating the forward scattering amplitude to the cross section of the scatterer. In classical physics, the optical theorem was first derived by Lord Rayleigh in the context of scattering and absorption of light (he used it to explain why the sky is blue). In the present case it applies to the scattering of neutrons by heavy nuclei. It is of very general applicability as it depends only on conservation of energy (in the classical case) or conservation of probability (in the quantum mechanical case). The optical theorem is still often called the Bohr-Peierls-Placzek relation. The emergence of the optical theorem in the problem of quantum scattering came as an unexpected surprise. The optical theorem now appears in all advanced textbooks of quantum mechanics, although its authors, Bohr, Peierls, and Placzek, are rarely mentioned. In addition to the optical theorem, this paper also addresses a fundamental difficulty that occurs when one is concerned with the region of continuous energy. "The general theory of resonance processes [those which occur preferentially at or near particular impact energies], first derived by Breit and Wigner for the case of a single resonance level, was at first applied also to the case in which the width of the resonance levels is greater than their spacing, so that at any energy a number of levels contribute. On the other hand one can derive the cross section for the formation of a compound nucleus by the capture of a particle from the general theorem of detailed balancing in terms of the decay constant, i.e., the probability of escape of the same particle from the compound nucleus. As long as the levels do not overlap, the two methods give the same answer, but in the case of overlapping levels, they differ. This discrepancy had already been noticed by Kalckar, Oppenheimer and Serber, who concluded that the result obtained from the extension of the Breit-Wigner formula was the correct one . The conclusion of Bohr, Peierls and Placzek, summarized in [the present letter], was that, in fact, the answer from the detailed balancing argument was the right one. The failure of the other result was due to the fact that, in the case of overlapping levels, the state of the compound nucleus is not uniquely defined by its energy . "Bohr read a paper to the [Copenhagen] Academy on 21 October 1938, of which only an abstract is available, which describes this talk as "in connexion with the communication of a paper, written in collaboration with G. Placzek and R. Peierls". No such joint paper was available at the time, but perhaps Bohr reported in his talk the stage which the discussions and partial drafting of a paper had reached. The published abstract is not sufficiently detailed to indicate this. "The drafting of a paper, which was meant to be a sequel to the Bohr-Kalckar paper, had in fact been underway since the spring of 1938. The difficulties in trying to arrive at an agreed draft were mostly concerned with presentation, rather than substance. Peierls and Placzek were anxious to base the arguments on a complete theoretical foundation . Bohr found these calculations rather complicated and formal. He tried.

First edition. A seminal treatise on paediatrics. First edition in book form, rare, of this seminal treatise on paediatrics. "Sir Frederic Still considered this work 'the most progressive which had yet been written;' it gave an impetus to research which influenced the future course of paediatrics. Rosen was particularly interested in infant feeding. The Underrattelser were originally published in the calendars of the Academy and were later collected and issued in book form in 1764" (Garrison-Morton). "In 1764 a very important work on the diseases of children and their treatment was published in Stockholm by a physician who had already become famous" (Still). The book contained chapters on such topics as smallpox and smallpox inoculation, teething, and measles. Also included were suggestions on the frequency of breastfeeding and information on how breastfeeding affects an infant's health. He was ahead of his time when he recommended feeding young children with diluted cow's milk by means of a bottle for sucking. He also advised that children's foods be covered to avoid contact with insects, along with other hygienic precautions. He accurately described and prescribed care for scarlet fever, whooping cough, diarrhoea, and other illnesses. "Nils Rosén lived and worked in a time when Sweden was a poor country with a low average life span and a child mortality rate exceeding fifty per cent . In 1753, when the Gregorian calendar was introduced and Sweden got a new chronology, Nils Rosén started to publish articles in small almanacs published by the Royal Academy of Sciences. The articles dealt with children ?s diseases, breast-feeding, nursing and preventive medical treatment, e.g., what then constituted fresh and new results of his empirical research work. Later, the articles were collected, re-edited and published in a book, Underrättelser om Barn-Sjukdomar och deras Bote-Medel (1764). It was the first veritable textbook of paediatrics. In 1771 it appeared in a new, improved and enlarged edition. The book was soon translated into many other European languages and became the Swedish textbook - all categories - that has been the most spread throughout the world. It was published in twenty-six editions and in ten different languages within the eighteen and nineteenth centuries. One of Linné's 'apostles', Anders Sparrman, translated it into English during a round-the-world sailing tour with the legendary captain James Cook on board The Resolution (1772-75). This book, The Diseases of Children and their Remedies, was printed in London in 1776" (Sjögren). RBH lists three copies. OCLC lists, in the US: Yale, New York Academy of Medicine, NLM, Minnesota, Indiana, Austin, Harvard. "Nils Rosen was born in Westgothland in 1706. In his youth he studied theology at Lund, but later deserted this subject for medicine. He was a pupil of Stobaeus at Upsala, and later of Friedrich Hoffmann at Halle. After a short period of study in Paris he returned to Sweden and took his M.D. at Harderwijk in I73I. For a time he taught anatomy and practical medicine at Upsala, and published a Compendium Anatomicum (Stockholm, 1738). He was early marked out for distinction, for in 1735, at the age of twenty-nine years, he became physician to the King of Sweden. The Swedish Academy of Sciences was founded in 1739 and Rosen became one of its original members. In 1740 he was appointed Professor of Natural History at Upsala, and Carl von Linné was Professor of Medicine. To the good fortune of posterity these two agreed to exchange appointments, so that the great naturalist and botanist occupied his proper position whilst Rosen became Professor of Medicine. With two such distinguished occupants of chairs, the University of Upsala became renowned as a seat of learning. Honours were poured upon Rosen. He was appointed 'Archiater' - Physician-in-Chief - at Upsala, and in 1762 was ennobled under the title of Rosen von Rosenstein. Upon his death in 1773 the Swedish Academy of Sciences had a medal struck in his memory, and another medal in his honour was struck as late as 1814. "He contributed important papers to the Academy of Sciences, one, in 1744, describing for the first time an epidemic of scarlet fever in Sweden, a rather late successor to Sydenham's description of an epidemic of scarlet fever in 1675, and in the same year also he described a case of hyoscyamus poisoning in a boy and drew attention to the mydriatic effect of certain drugs. But by far the most important of his writings was his book on diseases of children, Underrattelser om barnasjuk- domar och deras botemedel (Stockholm, 1765). It was at once recognized as a work of great value . "Rosenstein's outlook is evident from the authorities he quotes. Only once, I think, does he mention the name of any of the ancient writers, and that only to give a synonym for epilepsy used by Hippocrates. His references are to the latest writers, and to recent contributions to scientific societies, and to his own personal observations. Now and again the influence of tradition shows itself, and one realizes how strong is the hold of error when it has been inculcated for centuries. Of the mother's milk he says 'it frees the child from many disorders and makes it acquire her own temper and disposition. Therefore we see that young lions who have sucked a cow or a goat have by this means been as it were tamed; and dogs, on the contrary, who have sucked a she-wolf have become beasts of prey' [quotations are from the English edition of 1776]. In the testing of the breast-milk he has gone little further than Soranus. It is to be tested 'By its consistence because when thin it is always better than when thick: therefore a drop of it on your nail ought easily to run off on inclining it, even on shaking the finger hastily there ought not to remain the least white streak on your nail: By the touch, because not any pain ought to be felt on letting a drop of it fall into the eye: With rennet, for if the milk gives.

First edition. "ONE OF THE MOST IMPORTANT PIECES OF ANALYSIS IN THIS CENTURY" (JOHN CONWAY). First edition of Nash's most famous work in pure mathematics, his solution of "a deep philosophical problem concerning geometry", first posed by Bernhard Riemann, "one of the most important pieces of mathematical analysis in this century" which "has completely changed the perspective on partial differential equations" (see below). Nash, "the most remarkable mathematician of the second half of the century" (Mikhail Gromov), is best known for his work in game theory, for which he was awarded the 1994 Nobel Prize in Economics. However, even before completing his thesis on game theory, he had become interested in the geometric objects called manifolds, which play a role in many physical problems, including cosmology. The problem Nash solved asked whether every Riemannian manifold can be isometrically embedded in Euclidean space ('isometrically' means bending without stretching). The Harvard mathematician Shlomo Sternberg calls the embedding problem "a deep philosophical problem concerning the foundations of geometry that virtually every mathematician - from Riemann and Hilbert to Élie Cartan and Hermann Weyl - working in the field of differential geometry has asked himself" (quoted in A Beautiful Mind, p. 157). "In 1955, Nash unveiled a stunning result to a disbelieving audience at the University of Chicago. "I did this because of a bet," he announced. "One of his colleagues at MIT [Warren Ambrose] had, two years earlier, challenged him. "If you're so good, why don't you solve the embedding problem . . . ?" When Nash took up the challenge and announced that "he had solved it, modulo details," the consensus around Cambridge was that "he is getting nowhere." The precise question that Nash was posing-"Is it possible to embed any Riemannian manifold in a Euclidean space?"-was a challenge that had frustrated the efforts of eminent mathematicians for three-quarters of a century. "By the early 1950s, interest had shifted to geometric objects in higher dimensions, partly because of the large role played by distorted-time and space relationships in Einstein's theory of relativity. Embedding means presenting a given geometric object as a subset of a space of possibly higher dimension, while preserving its essential topological properties. Take, for instance, the surface of a balloon, which is two-dimensional. You cannot put it on a blackboard, which is two-dimensional, but you can make it a subset of a space of three or more dimensions. "John Conway, the Princeton mathematician who discovered surreal numbers, calls Nash's result "one of the most important pieces of mathematical analysis in this century." Nash's theorem stated that any kind of surface that embodied a special notion of smoothness could actually be embedded in a Euclidean space. He showed, essentially, that you could fold a manifold like a handkerchief without distorting it. Nobody would have expected Nash's theorem to be true. In fact, most people who heard the result for the first time couldn't believe it. "It took enormous courage to attack these problems," said Paul Cohen, a mathematician who knew Nash at MIT. "After the publication of "The Imbedding Problem for Riemannian Manifolds" in the Annals of Mathematics, the earlier perspective on partial differential equations was completely altered. "Many of us have the power to develop existing ideas," said Mikhail Gromov, a geometer whose work was influenced by Nash. "We follow paths prepared by others. But most of us could never produce anything comparable to what Nash produced. It's like lightening striking. Psychologically the barrier he broke is absolutely fantastic. He has completely changed the perspective on partial differential equations. There has been some tendency in recent decades to move from harmony to chaos. Nash said that chaos was just around the corner" (Sylvia Nasar, Introduction to The Essential John Nash, 2001). The present paper is actually the second of Nash's papers on the embedding problem. It was preceded two years earlier by 'C1-isometric imbeddings,' pp. 383-396 in Annals of Mathematics, Vol. 60, No. 3. This paper treats the same embedding problem but only asks for a 'continuously differentiable' embedding rather than an 'infinitely differentiable' one. Although the proof in the C1 case is easier, some of the consequences are highly surprising and counter-intuitive. A copy of this paper, also in original printed wrappers, accompanies the 1956 paper. Nash's solution of the embedding problem in the 'smooth' case was extended by Jürgen Moser to give the 'Nash-Moser implicit function theorem,' which is now a standard technique in the study of non-linear partial differential equations and has been used by Moser to solve problems connected to the existence of periodic orbits in celestial mechanics. For a detailed account, see Sylvia Nasar, A Beautiful Mind (1998), Ch. 20. 8vo (256 x 173 mm), pp. 190, [1]. Original printed wrappers, mint condition. / Hardcover. First edition of Nash?s most famous work in pure mathematics, his solution of ?a deep philosophical problem concerning geometry?, first posed by Bernhard Riemann, ?one of the most important pieces of mathematical analysis in this century? which ?has completely changed the perspective on partial differential equations? (Gromov).

First edition. THE BIRTH OF MODERN NUMERICAL ANALYSIS. First edition, journal issues in the original printed wrappers, of two of von Neumann's major papers. "The 1947 paper by John von Neumann and Herman Goldstine, 'Numerical Inverting of Matrices of High Order' (Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous" (Bultheel & Cools). "Just when modern computers were being invented (those digital, electronic, and programmable), John von Neumann and Herman Goldstine wrote a paper to illustrate the mathematical analyses that they believed would be needed to use the new machines effectively and to guide the development of still faster computers. Their foresight and the congruence of historical events made their work the first modern paper in numerical analysis. Von Neumann once remarked that to found a mathematical theory one had to prove the first theorem, which he and Goldstine did concerning the accuracy of mechanized Gaussian elimination - but their paper was about more than that. Von Neumann and Goldstine described what they surmised would be the significant questions once computers became available for computational science, and they suggested enduring ways to answer them" (Grcar, p. 607). "In sum, von Neumann's paper contains much that is unappreciated or at least unattributed to him. The contents are so familiar, it is easy to forget von Neumann is not repeating what everyone knows. He anticipated many of the developments in the field he originated, and his theorems on the accuracy of Gaussian elimination have not been encompassed in half a century. The paper is among von Neumann's many firsts in computer science. It is the first paper in modern numerical analysis, and the most recent by a person of von Neumann's genius" (Vuik). Von Neumann & Goldstine's 1947 paper is here accompanied by its sequel (the 1947 paper comprises Chapters I-VII, the sequel Chapters VIII-IX), in which the authors reassess the error estimates proved in the first part from a probabilistic point of view. The only other copy of either paper listed on ABPC/RBH is the OOC copy of part I (both journal issue and offprint). "Before computers, numerical analysis consisted of stopgap measures for the physical problems that could not be analytically reduced. The resulting hand computations were increasingly aided by mechanical tools which are comparatively well documented, but little was written about numerical algorithms because computing was not considered an archival contribution. "The state of numerical mathematics stayed pretty much the same as Gauss left it until World War II" [Goldstine, The Computer from Pascal to Von Neumann (1972), p. 287]. "Some astronomers and statisticians did computing as part of their research, but few other scientists were numerically oriented. Among mathematicians, numerical analysis had a poor reputation and attracted few specialists" [Aspray, John von Neumann and the Origins of Modern Computing (1999), pp. 49-50]. "As a branch of mathematics, it probably ranked the lowest, even below statistics, in terms of what most university mathematicians found interesting" [Hodges, Alan Turing: the Enigma (1983), p. 316]. "In this environment John von Neumann and Herman Goldstine wrote the first modern paper on numerical analysis, 'Numerical Inverting of Matrices of High Order', and they audaciously published the paper in the journal of record for the American Mathematical Society. The inversion paper was part of von Neumann's efforts to create a mathematical discipline around the new computing machines. Gaussian elimination was chosen to focus the paper, but matrices were not its only subject. The paper was the first to distinguish between the stability of a mathematical problem and of its numerical approximation, to explain the significance in this context of the 'Courant criterium' (later CFL condition), to point out the advantages of computerized mixed precision arithmetic, to use a matrix decomposition to prove the accuracy of a calculation, to describe a 'figure of merit' for calculations that became the matrix condition number, and to explain the concept of inverse, or backward, error. The inversion paper thus marked the first appearance in print of many basic concepts in numerical analysis. "The inversion paper may not be the source from which most people learn of von Neumann's ideas, because he disseminated his work on computing almost exclusively outside refereed journals. Such communication occurred in meetings with the many researchers who visited him at Princeton and with the staff of the numerous industrial and government laboratories whom he advised, in the extemporaneous lectures that he gave during his almost continual travels around the country, and through his many research reports which were widely circulated, although they remained unpublished. As von Neumann's only archival publication about computers, the inversion paper offers an integrated summary of his ideas about a rapidly developing field at a time when the field had no publication venues of its own. "The inversion paper was a seminal work whose ideas became so fully accepted that today they may appear to lack novelty or to have originated with later authors who elaborated on them more fully. It is possible to trace many provenances to the paper by noting the sequence of events, similarities of presentation, and the context of von Neumann's activities" (Grcar, pp. 609-610). We are fortunate to have an account of the genesis and content of these two important papers in Goldstine's own words. In the years immediately following the end of World War II, Von Neumann, Goldstine and others instituted the 'electronic computer project' at the Institute for Advanced Study at Princeton, NJ. One of the first topics discussed "was the solution of large systems of linear equations, since they arise almost everywhere in numerical work.

First editions, first printings. THE FOUNDATIONS OF QUANTUM ELECTRODYNAMICS. First edition, journal issues in original printed wrappers, of this two-part paper which represents the "formal invention of quantum electrodynamics [QED]" (Miller, p. xiii). "Three years before the discovery of the positron Heisenberg and Pauli - in two papers 'Zur Quantenmechanik der Wellenfelder' and 'Zur Quantenmechanik der Wellenfelder II' of 29 March and 7 September 1929, respectively - took a decisive step forward to develop a consistent theory of quantum electrodynamics" (Mehra & Milton, p. 186). "This extremely technical and mathematical branch of quantum physics, the foundations of which were laid by Heisenberg, Dirac, Pauli, Jordan, and their colleagues during the late 1920s and early 1930s, continues to this day with much the same program and approach . . . [Heisenberg was] a leading member of the small band of abstract theorists who established the program and laid the foundations of relativistic quantum field theory as it has been pursued ever since" (Cassidy, p. 276). This paper - the only one that Heisenberg and Pauli co-authored - attempted to establish "a consistent extension of the quantum formalism that would yield a satisfactory unification of quantum mechanics and relativity theory . . . In 1929, drawing upon the work of Dirac, Jordan, Oskar Klein, and others, Heisenberg and Pauli succeeded in formulating a general gauge-invariant relativistic quantum field theory by treating particles and fields as separate entities interacting through the intermediaries of field quanta. The formalism led to the creation of a relativistic quantum electrodynamics, equivalent to that developed by Dirac, which, despite its puzzling negative energy states, seemed satisfactory at low energies and small orders of interaction. But at high energies, where particles approach closer than their radii, the interaction energy diverges to infinity. Even at rest, a lone electron interacting with its own field seemed to possess an infinite self-energy" (DSB, under Heisenberg). "Heisenberg and Pauli were well aware of the shortcomings of their theory: the divergence difficulties and the problem of negative energies for the electron. However, the importance of the Heisenberg-Pauli theory cannot be exaggerated; it opened the road to a general theory of quantized fields and thereby prepared the tools, albeit not perfect ones, for the Pauli-Fermi theory of beta-decay and for the meson theories" (Mehra & Milton, p. 188). The divergence problems were not resolved until the late 1940s, with the advent of the renormalization techniques of Feynman, Schwinger and Tomonaga. "Soon after reading the manuscript of Dirac's QED paper ['The quantum theory of the emission and absorption of radiation,' Proceedings of the Royal Society A114 (1927), pp. 243-265], Pauli embarked on a program to construct his own version of quantum electrodynamics, one in which [unlike in Dirac's theory] the relativistic-invariance-covariance would be apparent and the relation to Maxwell theory manifest. He evidently outlined his proposal in a letter to Heisenberg that is no longer extant. In February 1927 Heisenberg countered: 'I agree very much with your program concerning electrodynamics, but not quite concerning the analogy, quantum wave-mechanics: classical mechanics = quantum electrodynamics : classical Maxwell theory. That one must quantize the Maxwell equations to get light quanta and so on à la Dirac, I believe already; but perhaps the de Broglie waves will later also have to be quantized in order to obtain charge and mass and statistics (!!) of electrons and nuclei.' Pauli and Heisenberg evidently disagreed about what had to be quantized. Heisenberg accepted [Pascual] Jordan's viewpoint and was prepared to quantize all wave fields - including matter waves. Pauli, on the other hand, was ready to quantize only the electromagnetic field. With that in mind he studied the mathematics of functionals that Vito Volterra had elaborated. On March 12, 1927, Pauli wrote Jordan: 'I believe that I now have the essential understanding of the Hamilton-Jacobi theory of Maxwell's equations. My principal source is a (French) book by P. Levy, Leçons d'analyse fonctionelle, Paris, 1922. We will thus see whether I can erect a quantum electrodynamics. For the present I am in good spirits.' In late March 1927 Pauli sent Bohr a note to inform him that 'at the moment I am much occupied with quantum electrodynamics . I have written briefly to Heisenberg about my general foundational standpoint about quantum electrodynamics and would very much like to hear from him . (I dare not ask you what your opinion is).' A few days later Pauli received a letter from Heisenberg asking him a couple of things about his 'Program': 'I am in full agreement with the foundations of your program that [the electromagnetic field variables] are not c[ommuting] fields, but are q fields, and that they must satisfy commutation rules that express this fact. But .' "And so began the collaboration between Heisenberg and Pauli that eventually resulted in two important papers, 'On the quantum dynamics of wave fields,' that were published in February and September 1929 [sic]. In them a general method for quantizing any field is presented . "Pauli outlined the scheme in a letter to [Oskar] Klein in mid-February 1929 and included in his letter some of the conclusions Heisenberg and he had reached: The theory contains divergences stemming from the self-energy of the charged particles; The matter field can seemingly be quantized so as to obey either Fermi or Bose statistics; The theory introduces three kinds of fields: the electromagnetic field, the matter field describing electrons, and the matter field describing protons. "The first of the two lengthy papers Heisenberg and Pauli wrote on the quantum theory of wave fields was received by Zeitschrift für Physik on March 19, 1929. Although their correspondence reflects a pessimistic assessment of t.

First edition. THE FAMOUS 'ERLANGEN PROGRAM': THE UNIFICATION OF GEOMETRY. First edition, rare in the original printed wrappers, of Klein's 'Erlangen Program,' his most famous and influential work. 'Klein's most important achievements in geometry, however, were the projective foundation of the non-Euclidean geometries and the creation of the 'Erlangen Progamm'" (DSB). After lecturing at Göttingen for a year, Klein joined the faculty at the University of Erlangen in 1872. "As was the custom, Klein had to present an Inaugural Address . It is commonly confused with the Erlangen Program, but that was not the Address. Rather, the Erlangen Program was a pamphlet printed by Deichert in Erlangen and distributed to those who came to the Inauguration. A few copies were doubtless distributed to friends and colleagues abroad, and to some libraries, because that was customary at the time; but the informal nature of the publication partially accounts for the negligible response to the Erlangen Program in 1872" (Gray in Landmark Writings, p. 546). It "comprised a proposal for the unification of Euclidean geometry with the geometries that had been devised during the nineteenth century by mathematicians such as Karl Gauss, Nicolai Lobachevsky, Janos Bolyai and Bernhard Riemann. He showed that the different geometries are each associated with a separate 'collection' or 'group' of transformations. Seen in this way, the geometries could all be treated as individual members of one overall family, and from this very connection conclusions and inferences could be drawn. Klein . demonstrated that every individual geometry could be constructed purely projectively; he produced projective models for Euclidean, elliptic, and hyperbolic geometries. Much later in his life, Klein returned to the Erlangen progamme to apply it to problems in theoretical physics, with special relevance to the theory of relativity" (Hutchinson DSB, p. 393). "For Klein, his Erlangen Program was an attempt to create an underlying unity for what had become the fragmented discipline of geometry. He did this through his innovative use of the group concept, which was not then widely known . Mathematicians were accustomed to using transformations of figures, say to replace a figure with an equivalent but simpler one, or to choose more convenient coordinate axes. Klein shifted attention from the figures to the transformations, and argued that henceforth geometry should be about groups as well as the properties of shapes. So a geometric property was one that was invariant under all the operations of the group associated to that geometry. He specifically employed the idea of one group being a subgroup of another. This enabled him to fix a space but vary the group, either to introduce a new geometry or to recognise a known one in an unexpected setting . Klein recognised that by selecting a figure in a space and considering the subgroup that maps that figure to itself was a fundamental way to inter-relate geometries and so to find a unifying principle that would encompass all of geometry . Klein ended his Erlangen Program with a series of seven notes of varying length and significance. One is worth picking out. Note 5 referred to what Klein cautiously continued to call the 'so-called non-Euclidean geometry' in order to avoid debates with non-mathematicians. Non-Euclidean geometry was the subject of two important memoirs by Klein written on either side of the Erlangen Program which probably did more to convey the message of the Program than did his obscurely published pamphlet" (Gray, Worlds Out of Nothing (2011), pp. 235-6). RBH lists two copies, neither in the original printed wrappers. "Klein chose the title to his essay carefully: he intended first to review, and then to compare, a number of recent researches in different areas of geometry. He claimed no novelty for the way he treated specific topics; what was original was the unified viewpoint he offered and its suggestions for the direction of future work. This viewpoint centred on the group-theoretic classification of the different geometrical methods then in use, and this emphasis owes a lot to Lie's influence. The Program was written while Klein was in daily contact with Lie, and reviewing its origins as he did when it was reprinted in his Collected Works he wrote that Lie was very much persuaded of the merits of the idea. "It is easiest to understand this idea in its paradigm example: the way non-Euclidean geometry appears as a sub-geometry of projective geometry, done in an Appendix to the Erlangen Program. Klein had learned of non-Euclidean geometry from Otto Stolz when in Berlin, but initially had had a hard time understanding it, and then in persuading Weierstrass of the value of his new point of view. "Inspired by a serendipitous reading of a paper by the English mathematician Arthur Cayley, who had had a glimmer of the same idea, Klein argued as follows. The model of non-Euclidean geometry developed by Eugenio Beltrami draws the entire non-Euclidean plane inside a circle, and it draws straight lines in non-Euclidean geometry as straight lines inside the circle. This suggested to Klein that the allowable transformations of figures in non-Euclidean geometry ought to be those which are projective transformations mapping the circle to itself, because they will automatically map each straight line to a straight line. Now, a non-Euclidean transformation is one that maps a line segment in non-Euclidean geometry to another line segment of equal non-Euclidean length. Projective geometry, on the other hand, can map any two points to any two points; the most important property of projective transformations is that they map four points on a line to four points on a line if and only if the four points have the same cross-ratio. For Klein's idea to work, he had to find a way of expressing non-Euclidean distance, which only involves two points, in terms of the four-point projective invariant, cross-ratio. He did th.

First edition. THE INVENTION OF THE TRANSISTOR. First edition, journal issue in original printed wrappers, of the first comprehensive report on the transistor, one of the most important inventions of the 20th Century. "In the 1930s, Bell Labs scientists were trying to use ultrahigh frequency waves for telephone communications, and needed a more reliable detection method than the vacuum tube, which proved incapable of picking up rapid vibrations . John Bardeen, Walter Brattain and William Shockley spearheaded the Bell Labs effort to develop a new means of amplification," developing, by 1948, a novel device that would effectively amplify and control electric signals. "At roughly half an inch high, the first transistor was huge by today's standards, when 7 million transistors can fit onto a single silicon chip. But it was the very first solid state device capable of doing the amplification work of a vacuum tube, earning Bardeen, Brattain and Shockley the Nobel Prize in Physics in 1956. More significantly, it spawned an entire industry and ushered in the Information Age, revolutionizing global society" (The American Physical Society). The invention of the transistor was first announced in three short letters by Bardeen, Brattain, Shockley, and Pearson, in The Physical Review (July 1948). The following year Bardeen and Brattain published the more comprehensive report 'Physical Principles Involved in Transistor Action'. This paper was simultaneously published, the same month, in The Physical Review and The Bell System Technical Journal. Offered here is the Bell printing [no priority established]. In 1956 Bardeen and Brattain shared the Nobel Prize in Physics with William Shockley "for their researches on semiconductors and their discovery of the transistor effect". In 1972 Bardeen again received the Nobel Prize in Physics for his part in the development of the theory of superconductivity (BCS-theory), and thus became the only person, until this day, to receive the Nobel Prize more than once in the same field. Provenance: Regnar Holfrid Svensson (1910-90), Swedish engineer and inventor (signature to front wrapper). "The first patent for the field-effect transistor principle was filed in Canada by Austrian-Hungarian physicist Julius Edgar Lilienfeld on October 22, 1925, but Lilienfeld published no research articles about his devices, and his work was ignored by industry. In 1934 German physicist Dr. Oskar Heil patented another field-effect transistor. There is no direct evidence that these devices were built, but later work in the 1990s show that one of Lilienfeld's designs worked as described and gave substantial gain. Legal papers from the Bell Labs patent show that William Shockley and a co-worker at Bell Labs, Gerald Pearson, had built operational versions from Lilienfeld's patents, yet they never referenced this work in any of their later research papers or historical articles. "The Bell Labs work on the transistor emerged from war-time efforts to produce extremely pure germanium 'crystal' mixer diodes, used in radar units as a frequency mixer element in microwave radar receivers. UK researchers had produced models using a tungsten filament on a germanium disk, but these were difficult to manufacture and not particularly robust. Bell's version was a single-crystal design that was both smaller and completely solid. A parallel project on germanium diodes at Purdue University succeeded in producing the good-quality germanium semiconducting crystals that were used at Bell Labs. Early tube-based circuits did not switch fast enough for this role, leading the Bell team to use solid-state diodes instead. After the war, Shockley decided to attempt the building of a triode-like semiconductor device. He secured funding and lab space, and went to work on the problem with Bardeen and Brattain. John Bardeen eventually developed a new branch of quantum mechanics known as surface physics to account for the 'odd' behavior they saw, and Bardeen and Walter Brattain eventually succeeded in building a working device. "The key to the development of the transistor was the further understanding of the process of the electron mobility in a semiconductor. It was realized that if there was some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode (discovered 1874; patented 1906), one could build an amplifier. For instance, if one placed contacts on either side of a single type of crystal, the current would not flow through it. However, if a third contact could then 'inject' electrons or holes into the material, the current would flow. "Actually doing this appeared to be very difficult. If the crystal were of any reasonable size, the number of electrons (or holes) required to be injected would have to be very large, making it less useful as an amplifier because it would require a large injection current to start with. That said, the whole idea of the crystal diode was that the crystal itself could provide the electrons over a very small distance, the depletion region. The key appeared to be to place the input and output contacts very close together on the surface of the crystal on either side of this region. "Brattain started working on building such a device, and tantalizing hints of amplification continued to appear as the team worked on the problem. Sometimes the system would work, but then stop working unexpectedly. In one instance a non-working system started working when placed in water. The electrons in any one piece of the crystal would migrate about due to nearby charges. Electrons in the emitters, or the 'holes' in the collectors, would cluster at the surface of the crystal, where they could find their opposite charge 'floating around' in the air (or water). Yet they could be pushed away from the surface with the application of a small amount of charge from any other location on the crystal. Instead of needing a large supply of injected electrons, a very small number in.

First edition. ONE OF THE MOST IMPORTANT 17TH CENTURY CHEMISTRY TEXTBOOKS. First edition, rare, of this very important chemistry text, which went through some thirteen editions between 1663 and 1710. "The Traité is Glaser's only publication. Printed in a small number at the author's expense, the first edition was sold from his house. Rapidly becoming a best seller, many editions in French appeared, with translations into German and English. A milestone in the development of the chemical text, it is stripped of alchemical mysticism and gives clear descriptions of chemical preparations" (The Roy G. Neville Historical Chemical Library, p. 528). "The work is divided into two books: book I briefly describes the utility, definitions, principles, operations, and apparatus of chemistry: book II is devoted to a description of medicinal preparations drawn from the mineral, vegetable, and animal kingdoms. The section devoted to mineral remedies is by far the largest. Little is novel in these preparations, although Glaser displays individual refinements of technique. His recipe for a sel antifebrile (potassium sulfate made by heating saltpeter and sulfur and recrystallizing from water) became uniquely identified with him and was later known as sel polychrestum Glaseri. The naturally occurring mixed sulfate of sodium and potassium (3K2SO4:Na2SO4) was named glaserite in his honor. Due to his influence on Lemery, Glaser's importance for the development of chemistry was greater than the contents of his book at first indicate. Although Fontenelle in his éloge of Lemery states that Lemery, finding Glaser obscure and secretive, abandoned studies with him after two months in 1666, the early editions of Lemery's highly successful Cours de chymie bear a remarkable resemblance both in organization and content to Glaser's textbook. There seems little doubt that Glaser's modest work served as a model for at least the practical part of the most popular chemical textbook of the late seventeenth century" (DSB). No other copy listed on ABPC/RBH in the last 40 years. Christopher Glaser was born in 1615 in Basel, Switzerland. "Little is known about Glaser's early life, but he seems to have been trained as a pharmacist in his native city, and references in his published work indicate that he traveled in eastern Europe to observe mining practice. Sometime prior to 1662 he settled in Paris, where he opened an apothecary's shop in the Faubourg Saint-Germain. Here he prospered, becoming apothecary in ordinary to Louis XIV and to the king's brother, the duke of Orleans. He also enjoyed the patronage of Nicolas Fouquet, the ill-fated superintendent of finances. In 1662 he was appointed demonstrator in chemistry at the Jardin du Roi in Paris in succession to Nicolas Le Fèvre. His most noted pupil in Paris was Nicolas Lemery. "The events of Glaser's later life are likewise elusive. In 1672 he was implicated in the famous Brinvilliers poison case when evidence came to light that the marquise de Brinvilliers and her accomplice Gaudin de Sainte-Croix had used a recipe of Glaser's to prepare the poison with which they disposed of the marquise's father (1666) and two brothers (1669-1670). At this point Glaser disappeared from public life in France. If the preface by the printer to the 1673 edition of Glaser's Traité is to be believed, Glaser died before completing the revisions for this new edition, which received the approbation of the Paris Faculty of Medicine on 15 October 1672. At her interrogation in 1676 the marquise de Brinvilliers alleged that Glaser had indeed prepared poison for Sainte-Croix but that he had been dead for a long time. One source maintains, however, that Glaser returned to Basel, where he died in 1678. "In the series of French chemical manuals of the seventeenth century, that of Glaser appeared between the more famous works of Le Fèvre and Lemery. Whereas Le Fèvre's textbook drew on the Paracelsian-Helmontian tradition for its theoretical content and Lemery attempted a corpuscularian interpretation of the processes he described, Glaser largely eschewed theory and was content with a straightforward, concise recital of chemical operations and recipes" (DSB). The Traité "gives definitions of chemical operations in alphabetical order, from 'alkooliser' (powdering finely) to 'vitrifier', describes and illustrates vessels and furnaces and lutes, and the seven degrees of fire. The second book deals wiith preparations, minerals (including metals, coral and amber) occupying a large part of the whole. Vegetables take less space and the short section on animals deals with the distillation of human skull and blood, vipers, urine, wax, manna, honey, and May dew. In describing diaphoretic gold, made by burning linen rags soaked in a solution of gold in aqua regia mixed with saltpetre, Glaser says that a silver vessel rubbed with the moistened powder is gilded. He describes the casting of fused silver nitrate (pierre infernale, caustique perpetuel) in iron moulds; its corrosive effects are due to the nitric acid. He says 1 lb. of lead increases in weight by more than 2 oz. on calcination 'à cause des corpuscules du feu qui s'incorporent avec luy', and tin and other imperfect metals similarly increase in weight. "In his description of salts, Glaser mentions sel prunel made by throwing sulphur on fused saltpetre, and sel antifebrile (afterwards called sal polychrestum Glaseri, from [the Greek] 'very useful') by heating saltpetre and sulphur and crystallising the potassium sulphate from water. Oil of arsenic (arsenic trichloride) is made by distilling regulus of arsenic (the element) with corrosive sublimate, the residual mercury passing over at a higher temperature; magistery of bismuth (the oxynitrate) by pouring a solution of 'bismuth ou estain de glace' in nitric acid into water (before Lemery). He mentions 'zinck', which 'approaches very close to the nature of bismuth but contains a purer sulphur'; although the metal was known to Le F.

First edition. DISCOVERY OF THE COMPTON EFFECT. First edition, journal issue in original printed wrappers, of the 'Compton effect,' which demonstrated the existence of quanta of electromagnetic radiation, later called photons. "This discovery 'created a sensation among the physicists of the time.' There were the inevitable controversies surrounding a discovery of such major proportions. Nevertheless, the photon idea was rapidly accepted. Sommerfeld incorporated the Compton effect in his new edition of Atombau und Spektrallinien with the comment, 'It is probably the most important discovery which could have been made in the current state of physics'" (Pais, Subtle is the Lord, p. 414). "Arthur Holly Compton will always be remembered as one of the world's great physicists. His discovery of the Compton effect, so vital in the development of quantum physics, has ensured him a secure place among the great scientists" (DSB). The explanation and measurement of the Compton effect earned Compton a share of the Nobel Prize in physics in 1927. Compton (1892-1962) received his PhD from Princeton in 1916 for research on the intensity distribution of X-rays reflected from crystals. After a period working for the Westinghouse Company he returned to fundamental research in 1919, when he obtained one of the first National Research Council Fellowships (established by Millikan). He used it to spend a year at the Cavendish Laboratory in Cambridge, where he continued his experiments on the scattering of radiation. In 1920 Compton moved to Washington University in St. Louis, where he continued his work on X-ray scattering, using a Bragg spectrometer he had brought from Cambridge. By this time it had become apparent that the scattered radiation had a wavelength longer than that of the primary radiation, and that the shift of wavelength varied with the scattering angle: this became known as the Compton effect. "It was only late in 1922, when considering all data available to him, that Compton saw the necessity for a light quantum with energy and momentum to explain the scattering of X-rays. Compton read a paper entitled 'A quantum theory of the scattering of X-rays by light elements' at a meeting of the American Physical Society in Chicago, which took place on 1 and 2 December 1922. Its abstract begins as follows: 'The hypothesis is suggested that when an X-ray quantum is scattered it spends all its energy and momentum upon some particular electron. The electron in turn scatters the ray to some definite direction. The change in momentum of the X-ray quantum due to the change in direction of its propagation results in a recoil of the scattering electron. The energy in the scattered quantum is thus less than the energy of the primary quantum by the kinetic energy of recoil of the scattering electron.' "The full paper was published a little later [the offered paper]. It contains . the calculation of the shift in wavelength between primary and secondary radiation as a function of scattering angle. Compton had data for only one scattering angle, 90 degrees, for which he had measured the spectrum. It was obtained with a primary radiation which was the K? radiation of molybdenum produced by an X-ray tube with a molybdenum anticathode" (Brandt, The Harvest of a Century, Chapter 31). "The Compton effect, aptly characterized by Karl K. Darrow as one of the most superbly lucid processes in nature, is now part of the fabric of physics; and it is of interest to recall its influence on the development of the quantum theory during the years 1923-1930. "In the first place, it provided conclusive proof that Einstein's concept of a photon as having both energy and directed momentum was essentially correct. Einstein himself brought considerable attention to Compton's discovery by his discussions at the Berlin seminars. Interest was also high at Gottingen, Munich, Zurich, Copenhagen, and other Continental centers where theoretical physics was rapidly developing. "However, the quantitative proof of the photon character of radiation had been established by Compton's use of a Bragg crystal spectrometer, the function of which depended directly on the wave nature of X-rays. Thus a more general synthesis was clearly required, in which both the corpuscular photon and the electromagnetic wave would be included and would continue to play the roles demanded by experiment. "The final great synthesis of quantum mechanics and quantum electrodynamics was forced upon physics by the crucial experiments of the Compton effect, electron diffraction, space quantization, and the existence of sharp spectral lines, which could not be brought into line with classical theory. It required the final relativistic form of quantum mechanics, developed by Paul Dirac, to give a completely quantitative explanation of Compton scattering in regard to both intensity and state of polarization by the formula derived by O. Klein and Nishina from the Dirac relativistic theory of the electron" (DSB). For a detailed account of Compton's work, see the Introduction to Scientific Papers of Arthur Holly Compton: X-ray and other studies, University of Chicago Press, 1974. 8vo, pp. 8, 483-584, 9-12. Original printed wrappers. Rare in this condition. / Hardcover. First edition of this landmark paper in modern physics, which demonstrated the existence of quanta of electromagnetic radiation, later called photons. ?This discovery created a sensation among the physicists of the time. It is probably the most important discovery which could have been made in the current state of physics? (Pais). The explanation and measurement of the Compton effect earned Compton a share of the Nobel Prize in physics in 1927.

First edition. THE FIRST TEXTBOOK OF OPHTHALMOLOGY IN ITALIAN. First edition of the first textbook on the diseases of the eye to be published in Italian. "The author has been called the father of Italian ophthalmology" (Garrison-Morton). "In this work Scarpa first described the operation of iridodialysis. The chapters on diseases of the vessels in the eye, on cataract, and on staphyloma are particularly noteworthy. Scarpa's books were all superbly illustrated with his own drawings and the plates in this work, engraved by Faustino Anderloni, bear witness to Scarpa's artistic talent. Duke-Elder considered this the greatest work on ophthalmology that had appeared up to its time." Becker Garrison considered Scarpa's illustrations to be the "crown and flower of achievement in anatomic pen-drawing." Scarpa "himself trained the famous Faustino Anderloni (who become the engraver of his illustrations). The latter's brother, Pietro Anderloni, assisted Faustino in the beginning. His anatomic prints are therefore models of anatomic representation as regards faithful differentiation of the tissues, correctness of form, and the utmost perfection of engraving. They rank with Soemmerring's illustrations and even surpass them in respect of the vigor of the engravings" (Choulant, p. 298). "This classic work on ophthalmology remained the standard text for several decades, going through several editions and translations. It established Scarpa's reputation as a leading ophthalmologist and is especially notable for its copperplate engravings of the anatomy of the eye, drawn by the anatomist" (Heirs of Hippocrates). Antonio Scarpa studied at the University of Padua, where he served as assistant and personal secretary to Morgagni, the master of pathological anatomy. After ten years as professor of anatomy and clinical surgery at the University of Modena, Scarpa joined the medical faculty at Pavia and served as chair of anatomy for the rest of his professional life. Scarpa wrote important works in otolaryngology, orthopedics, ophthalmology, neuroanatomy, and general surgery. He was the first to demonstrate cardiac innervation and to accurately describe the pathological anatomy of congenital club-foot. He also introduced the concept of arteriosclerosis, identified 'Scarpa's triangle' of the thigh, and provided the first detailed description of sliding hernia of the large bowel. Provenance: Gaetano Tamanti (?) (signature on title). "Antonio Scarpa (1747-1832) was not an ophthalmologist, yet he wrote a hugely influential textbook on ophthalmology. He studied under a professor who gave his name to a type of cataract, yet he severely retarded the progress of cataract surgery throughout Europe. And despite his interest in ocular disease, he was scathing about the idea that eye surgery should exist as a distinct surgical speciality. He was famous in his time and gave his name to several anatomical features, yet was shunned and alone at the time of his death. Who was this contrary doctor and why was his influence on ophthalmology so great? "Scarpa was born into a poor family in the northern Italian town of Motta di Livenzo in 1752. His early education was heavily influenced by his uncle, a priest. And, having become as a result of this tuition an excellent Latinist, he was able to pass the entrance examinations of the University of Padua at just 15 years of age. There he came under the tutelage of the renowned anatomist Giovanni Baptista Morgagni (he of the morgagnic cataract) who became so impressed with Scarpa's Latin and anatomical skills that he appointed him as his personal assistant and secretary. Scarpa received his medical degree when still only 19 years old from Morgagni himself, only a short time before the great man's death. "With the first of some notable acts of patronage in his favour Morgagni, before his death, had eased the way for Scarpa to obtain the post of Professor of Anatomy and Clinical Surgery at Modena, a mere year later - a post he was to keep for a decade. His star rising, Scarpa published important work on the inner ear in which its membranous labyrinth was elucidated for the first time. But his work on the second tympanic membrane partly mirrored work on the subject by Galvani, who became convinced that he was being plagiarised. Perhaps not coincidentally, Scarpa managed now to obtain funding from the Duke of Modena for a study tour of Europe, thus keeping him away from the worst of the controversy. "The two-year tour of France, Austria and England (where he worked with the famous surgeons John and William Hunter) was a success on its own terms. But probably the most useful outcome of the trip was the friendship he made with Alessandro Brambilla, chief surgeon to Emperor Joseph II of Austria. Soon after his return to Modena he learned that Brambilla had procured an invitation for Scarpa to take up the chair of anatomy at the University of Pavia. The city of Pavia was then under the rule of the Austrian Emperor, and its university one of Italy's oldest and most prestigious. Somehow Scarpa managed to extricate himself from Modena and his previous patron on amicable terms. "Scarpa's first lecture at Pavia, on November 25 1783, was to prove a watershed in medical education. Instead of a lecture in the classic style, Scarpa gave an anatomical demonstration showing the relationship between structures and organs while paying due attention to the physiology of those structures. The students were required to repeat his exercises in dissection so as to gain knowledge by experience, a standard technique in medical schools today. "Emperor Joseph II's patronage was important in Pavia becoming the world's premier centre of anatomical study. Scarpa's innovative teaching and research were pivotal too and resulted in him being given an additional post after four years there, the chair of clinical surgery. At Scarpa's suggestion, the emperor decreed that all the bodies of the deceased from the state hospital were to be tran.

First edition. INSCRIBED PRESENTATION OFFPRINT. Presentation offprint, inscribed in Bohr's hand to the chemist Einar Biilmann, of the 'Second Royal Society Paper' - what Bohr "learned by working in this field may have been a help to him when, more than a quarter of a century later, he showed that some of the properties of atomic nuclei can be understood by comparing them to liquid drops [i.e., Bohr's liquid-drop model]." (J. Rud Nielsen). In February 1905 the Royal Danish Academy of Sciences and Letters announced a prize concerning Lord Rayleigh's 1879 theory that the surface tension of liquids could be determined from the surface vibrations of liquid jets. The problem proposed by the Academy was to perform quantitative experiments to implement Rayleigh's method. Bohr faced formidable difficulties, not least the fact that, since the university had no physics laboratory, Bohr had to perform the experiments at night (to avoid perturbations due to passing traffic) in his father's physiology laboratory. Bohr's paper was submitted on the deadline of 30 October 1906, and on 23 February 1907 the Academy notified Bohr that he had won its gold medal. "After receiving the gold medal, Bohr carried out additional measurements of the surface tension of water. At the same time he was occupied with the considerable task of preparing his work for publication. In the latter part of 1908 he submitted a paper entitled 'Determination of the Surface-Tension of Water by the Method of Jet Vibration' to the Royal Society of London. This paper is not a simple translation of the prize essay but deviates from the latter at a number of points. "In 1910, while Bohr was working on his doctor's dissertation, a paper was published by P. Lenard, in which he claimed that a recently formed water surface has a high surface tension which rapidly decreases. Lenard stated that this was in agreement with Bohr's results. This led Bohr to re-examine the matter and, in particular, to test by new calculations the claim made by Lenard that a variation of the velocity over the different concentric parts of a jet will prolong the periods of vibration and increase the wavelengths of surface waves on the jet. He made a direct calculation of the wavelength when the velocity in the jet varies with the distance from the axis and concluded that his experiments do not support the claims made by Lenard. In August, 1910, he submitted to the Royal Society a paper entitled 'On the Determination of the Tension in a recently formed Water- Surface [i.e, the offered paper], which was published in its Proceedings. This was Bohr's last work on surface tension. The results of this paper, and the merit of the experimental method described, have apparently been appreciated by most later workers in the field. Thus, N. K. Adam writes in his book The physics and chemistry of surfaces. 'Bohr's work on oscillating jets is probably the best of any dynamic methods.' "What he learned by working in this field may have been a help to him when, more than a quarter of a century later, he showed that some of the properties of atomic nuclei can be understood by comparing them to liquid drops [i.e., Bohr's liquid-drop model]." (J. Rud Nielsen, Collected Works, pp. 8-12). Large 8vo (254 x 176 mm), offprint from the Proceedings of the Royal Society, A, Vol. 84, 1910, pp. [395] 396-403 [404:blank], original light brown printed wrappers, inscribed in Bohr's hand to the upper right corner of front wrapper: 'Hr Professor E. Biilmann / ærbødisgst fra Forf.' (i.e., Mr. Professor E. Biilmann / respectfully from the author), Prof. Einar Biilmann (1873-1946) was a Danish chemist and early friend of Bohr, number in blue pencil to upper right corner of front wrapper (probably a library numbering from Biilmann). / Hardcover. First edition, offprint inscribed by Bohr, of his last work on surface tension. ?What he learned by working in this field may have been a help to him when, more than a quarter of a century later, he showed that some of the properties of atomic nuclei can be understood by comparing them to liquid drops [i.e., Bohr?s liquid-drop model]? (Collected Works).

First edition. ANTICIPATING DIRAC ON QUANTUM FIELD THEORY AND FERMI AND DIRAC ON THEIR STATISTICS . First edition, extremely rare offprint, of this important paper, in which Jordan introduces his approach to quantum field theory, independent of Dirac's, and also gives his formulation of Fermi-Dirac statistics, which he had developed earlier than both Fermi and Dirac. "Pascual Jordan is the unsung hero among the creators of quantum mechanics. Major portions of the two papers he co-authored with Born and Heisenberg that elaborated matrix mechanics, following Heisenberg's initial insight, were Jordan's contribution. Similarly, he was responsible for laying the foundations of quantum field theory" (Schweber, pp. 5-6). "Before the end of the year [1925] Jordan had submitted a single author paper. This papercontained what is nowadays known as the Fermi-Dirac statistics; however it encountered an extremely unfortunate fate after its submission because it landed on the bottom of one of Max Born's (in his role as the editor of the Zeitschrift für Physik) suitcases on the eve of an extended lecture tour to the US, where it remained for about half a year. When Born discovered this mishap, the papers of Dirac and Fermi were already in the process of being published. This paper by Jordan was never published, but he further developed its contents and this extended piece of work, Zur Quantenmechanik der Gasentartung ['On the quantum mechanics of gas degeneracy'], was published by Jordan in 1927" (Mactutor). "Jordan was the earliest and most ambitious visionary of the quantum field theory program: long before this became commonly accepted in the second half of the twentieth century, he saw in quantum field theory a unified basis for all of modern physics" (Lehner, p. 272). The present paper "already defines Jordan's program: a unified quantum field theory for matter and radiation. Particles and waves are only two different aspects of the same underlying quantum field both in the case of light and in the case of matter" (ibid., pp. 280-281). No copies in auction records. Not on OCLC. "The year 1925 was a bright start for the 22-year-old Jordan. After the submission of the joint work with Max Born on Matrix Mechanics, in which the p-q commutation relation appeared for the first time, there came the famous 'Dreimännerarbeit' with Born and Heisenberg in November of the same year, only to conclude the year's harvest with a paper by him alone on the 'Pauli statistics'. Jordan's manuscript contained what is nowadays known as the Fermi-Dirac statistics; however it encountered an extremely unfortunate fate after its submission . In the words of Max Born a quarter of a century later: 'I hate Jordan's politics, but I can never undo what I did to him . When I returned to Germany half a year later I found the paper on the bottom of my suitcase. It contained what one calls nowadays the Fermi-Dirac statistics. In the meantime it was independently discovered by Enrico Fermi and Paul Dirac. But Jordan was the first'" (Schroer, pp. 2-3). "The year 1927 was the most fruitful in Jordan's career . The second paper submitted in July 1927 [offered here] was inspired by Dirac's field-theoretic transcription of the quantum mechanical multi-particle configuration space for Schrödinger's formalism ('high dimensional abstract space') to the quantization of Schrödinger waves in ordinary space. Jordan sets out to do something analog[ous] for 'Fermi's instead of Einstein's gas'. He develops what he refers to as the 'Pauli-statistics' (probably using material from his ill-fated 1925 manuscript which ended in Born's suitcase) and uses the quantized spacetime field formulation to compute the density fluctuations in a Fermi gas" (ibid., p. 4). "As he claimed in [the present paper, p. 480] and in a letter to Schrödinger, his occupation with the quantum theory of the ideal gas had suggested this further application of the theory of quantized waves. Jordan writes in the letter: 'Then your hydrogen paper [i.e., 'Quantisierung als Eigenwertproblem (Zweite Mitteilung)'] gave hope that by following up this correspondence also the non-ideal gas could be represented by quantized waves - that therefore a complete theory of light and matter could be derived in which, as an essential ingredient, this wave field itself operates in a quantum, non-classical way'. "Jordan saw Schrödinger's wave-functions as a generalization of the simple plane waves that he had quantized in the 'Dreimännerarbeit' and interpreted as the quantum mechanical representation of the Bose-Einstein ideal gas; he was convinced that the quantization of these wave-functions was the method necessary to apply quantum mechanics to the case of several interacting particles. In the letter to Schrödinger, Jordan gives two reasons why he did not pursue this program immediately: The problem to account for Fermi-Dirac statistics, since it seemed that the wave picture would always lead to Bose-Einstein statistics, and the reservations of his colleagues Heisenberg, Pauli, and Born" (Lehner, p. 276). Although Jordan had introduced the idea of a quantized field at the end of the 'Dreimännerarbeit', it "only came to the attention of a wider group of physicists through Paul Dirac's 'The quantum theory of emission and absorption of radiation.' Paradoxically, the notion of quantizing a field appears nowhere in the paper . Dirac explicitly denied that the 'wave function of the light quanta' is the same as the electromagnetic field. He also argued that while an ensemble of light quanta can be associated with a light wave, there is no such physical wave associated with an ensemble of matter particles such as electrons. Therefore, he did not see the quantization procedure as an explanation of the quantum nature of radiation. It was to him only an elegant way to take into account the Bose statistics of light quanta. Since electrons do not obey Bose statistics, the procedure is not applicable to them. Dirac maintained.

First edition. COMMENTARY ON ARCHIMEDES' ON THE SPHERE AND CYLINDER . First edition of this rare Galileianum, an explication and extension of the two books of Archimedes' On the sphere and the cylinder, which gave the first exact determination of the area and volume of a curved figure. They "are, of course, exceptional masterpieces. According to a testimony by Cicero, whom there is no reason to doubt, Archimedes' tomb had inscribed a sphere circumscribed inside a cylinder, recalling the major measurement of volume obtained in [the first book]: if so, either Archimedes or those close to him considered [this book] to be somehow the peak of his achievement. The reason is not difficult to find. Archimedes' works are almost all motivated by the problem of measuring curvilinear figures, all of course indirectly related to the problem of measuring the circle . Measuring the sphere is the closest Archimedes, or mathematics in general, has ever got to measuring the circle. The sphere is measured by being reduced to other curvilinear figures. Still, the main results obtained - that the sphere as a solid is two thirds the cylinder circumscribing it, its surface four times its great circle - are remarkable in simplifying curvilinear, three-dimensional objects, that arise very naturally" (Netz, p. 19). Archimedes' proof is extraordinarily ingenious. "A circle with a polygon inscribed within it is imagined rotated in space, yielding a sphere with a figure inscribed within it. The inscribed figure is made of truncated cones . Furthermore, with the same idea extended to a circumscribed polygon yielding a circumscribed figure made of truncated cones, proportion inequalities come about involving the circumscribed and inscribed figures . such proportion inequalities can be manipulated to combine with the measurements of the inscribed and circumscribed figures, reaching, indirectly, a measurement of the sphere itself" (ibid., pp. 20-21). In this, probably White's only published work, he uses Archimedes' techniques to study other solids that can be inscribed in, and circumscribed about, a hemisphere. He also studies the relation between the areas and volumes of parts of a hemisphere and corresponding parts of a cylinder or a cone. White was personally acquainted with Galileo and he and his younger brother Thomas were instrumental in bringing Galileo's discoveries and opinions to the attention of British scientists, notably Francis Bacon. In the preface White praises Galileo as the outstanding investigator of the heavens above, the waves below (a reference to the tidal theories of the Dialogo - see below), and mechanics on Earth, "though it was published in Rome under license during a period in which many Italian writers found it prudent to forgo any favourable reference to Galileo in their published works. White also conducted some elaborate experiments concerning specific gravities and made accurate observations of Halley's comet" (Drake, p. 245). Richard White was elected a fellow of the Royal Society in 1661. OCLC lists Columbia, Harvard, Huntington and Linda Hall in US. RBH lists four copies since 1931. Richard White (1590-1682) was born to a prominent Catholic family in Essex; his mother was the daughter of the celebrated jurist Edmund Plowden. In his preface, White explains how the urge 'to cross the furious ramparts of the ocean which surround Britain' led him through France to Florence in the company of one James Clayton (probably a member of another Recusant family). He lived for most of his life in Italy: he tells us that he first studied Aristotle in Florence (beginning with the Organon and thence to the Physics), where he came into contact with Galileo and his circle, especially Benedetto Castelli, who taught him Euclid, and Bonaventura Cavalieri, famous for his Geometria indivisibilibus (1635), which introduced the method of indivisibles, an important precursor of calculus. Richard was joined by his brother Thomas in Italy who encouraged him to study Archimedes' writings on the sphere and cylinder, resulting in the present work. Its publication, some years later, was partly at the urging of Michelangelo Ricci. Thomas White, a Jesuit, was a prolific writer. He was acquainted with prominent British intellectuals, including Thomas Hobbes and Sir Kenelm Digby, and belonged to the Mersenne circle in Paris in the 1640s. Richard White was instrumental in correcting a statement made by Galileo in his theory of the tides, 'Discorso sul flusso e it reflusso del mare,' which he submitted in the form of a private letter to Cardinal Orsini in 1616. Galileo believed that the tides were the result of the differential motions of different regions of the Earth, according to whether in a particular region the diurnal rotation of the Earth around its axis was in the same or the opposite direction as its annual rotation around the Sun; he used the analogy of a vase containing water - when the vase undergoes irregular motion the water itself acquires a motion relative to the vase. In the 1616 letter Galileo stated that the tides at Lisbon were half as frequent as those on the Mediterranean, which he explained from the fact that the Atlantic Ocean is twice as wide as the Mediterranean. These statements were omitted from the printed version in the Fourth Day of the Dialogo (1632), because in 1619 Richard White had informed Galileo that his data on the Lisbon tides were incorrect. In the same year White brought to England copies of Galileo's books and manuscripts, leaving them with Francis Bacon. This probably led to Bacon omitting from his Instauratio magna (1620) his essay on tides, 'On the ebb and flow of the seas,' written about 1611 and sent to Galileo in 1618. Bacon's essay had explained the tides as the effect on the oceans of the daily east-west motion of the Earth relative to the heavens, in opposition to Galileo's conclusion in the Orsini letter. According to some sources (e.g., Encyclopaedia Britannica, Vol. 20 (1842), p.