Bound volume of 25 offprints, including the four papers in which Born introduced the probability (or Copenhagen) interpretation of quantum mechanics (1926), two giving Heisenberg’s explanation of the anomalous Zeeman effect on the basis of the Bohr-Sommerfeld quantum theory (1924/5), and two more by Heisenberg giving his solution of the Helium problem by means of his new quantum mechanics (1926/7).

[Vp: Vp, 1924-1927].

An extraordinary sammelband of offprints from the period 1924-27, during which Heisenberg’s new quantum mechanics (1925) revolutionized the study of atomic phenomena. The most important are the four papers by Max Born in which he introduced the statistical interpretation of quantum mechanics (nos. 10, 14, 15 and 25 in the list below). “On 20 June 1926 Born’s first paper on wave mechanics was received [no. 14] … It is the first paper to contain the quantum mechanical probability concept” (Pais 1991, p. 286 – his italics). “The introduction of probability in the sense of quantum mechanics, that is, probability as an inherent feature of fundamental physical law, may well be the most drastic scientific change yet effected in the twentieth century” (Pais 1982). “Max Born was one of the founding fathers of quantum mechanics – indeed, he coined its name even before his assistant, Werner Heisenberg, gave birth to the theory with a breakthrough paper in the summer of 1925” (Gottfried). Born won the Nobel Prize in Physics 1954 “for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wave-function.” “The prize recognized, at long last, Born’s discovery of the statistical interpretation of the wave function. He was the first to recognize the profound departure from classical concepts of causality that quantum mechanics implies. In particular, he recognized that although the Schrödinger equation describes a continuous and causal evolution, it nevertheless makes only statistical predictions about observable events. This was before Heisenberg's discovery of the uncertainty principle and Bohr's formulation of complementarity, the essential ingredients in the Copenhagen interpretation” (Gottfried). Two of the Heisenberg papers in this volume relate to the Bohr-Sommerfeld quantum theory (pre-quantum mechanics), and two to quantum mechanics. Nos. 9 & 11, treat the ‘anomalous Zeeman effect,’ on the basis of the Bohr-Sommerfeld theory. “Heisenberg’s real talents emerged in his work on the anomalous Zeeman effect, in which atomic spectral lines are split into multiple components under the influence of a magnetic field. Heisenberg developed a model that accounted for this phenomenon, though at the cost of introducing half-integer quantum numbers, a notion at odds with Bohr’s theory as understood to date” (Brittanica). Nos. 17 & 18 present Heisenberg’s solution of the ‘Helium problem’ “that had haunted the theoreticians since 1913 and had contributed primarily in 1923 to the recognition of the failure of the Bohr-Sommerfeld quantum theory” (Mehra & Rechenberg, vol. 6, p. 128). “His helium calculation constituted a major triumph in quantum mechanics … Heisenberg’s successors would improve the approximation methods … but the basic ideas did not have to be altered. In this respect, Heisenberg’s helium calculation became a classic in atomic theory” (Mehra & Rechenberg, vol. 5, p. 745). Heisenberg achieved this breakthrough by incorporating for the first time the Pauli exclusion principle into quantum mechanics: he discovered that the Pauli principle requires the two-electron wave function to be antisymmetric. This was the first step towards Fermi-Dirac statistics.

Provenance: Douglas Rayner Hartree FRS (1897-1958), English mathematician, physicist and computer pioneer.

“Until the spring of 1926, quantum mechanics, whether in its matrix or its wave formulation, was high mathematical technology of a new kind, manifestly important because of the answers it produced, but without clearly stated underlying physical principles … The break with the past came in a paper by Born received on June 25, 1926 [no. 14]. In order to make his decisive new step, ‘It is necessary, (Born wrote half a year thereafter) [in no. 25] to drop completely the physical pictures of Schrödinger which aim at a revitalization of the classical continuum theory, to retain only the formalism and to fill that with new physical content.’ In his June paper, entitled ‘Quantum mechanics of collision phenomena’, Born considers (among other things) the elastic scattering of a steady beam of particles … [Born showed that the number of particles scattered into the element of solid angle is given by N|Ψ|2dω, where N is the number of particles in the incident beam crossing unit area per unit time and Ψ is the wave function.] Then, Born declares: Ψ determines the probability for the scattering of the electron from the z-direction into [a given other] direction … Born added a footnote in proof to his evidently hastily written paper: ‘A more precise consideration shows that the probability is proportional to the square of Ψ. He should have said ‘absolute square.’ But he clearly bad got the point, and so the correct expression for the transition probability concept entered physics via a footnote …

“If Born’s paper lacked formal precision, causality was brought sharply into focus as the central issue: ‘One obtains the answer to the question, not ‘what is the state after the collision’ but ‘how probable is a given effect of the collision’ … Here the whole problem of determinism arises. From the point of view of our quantum mechanics there exists no quantity which in an individual case causally determines the effect of a collision I myself tend to give up determinism in the atomic world.’ …

“One month after the June paper, Born completed a sequel with the same title [no. 15]. His formalism is firm now and he makes a major new point. He considers a normalized stationary wave function Ψ referring to a system with discrete, non-degenerate eigenstates Ψn and notes that in the expansion

Ψ = Σ cnΨn,

|cn|2 is the probability for the system to be in the state n. In June he had discussed probabilities of transition, a concept which, at least phenomenologically, had been part of physics since 1916 when Einstein had introduced his A- and B-coefficients in the theory of radiative transitions – and at once had begun to worry about causality. Now Born introduced the probability of a state. That had never been done before. He also expressed beautifully the essence of wave mechanics: ‘The motion of particles follows probability laws but the probability itself propagates according to the law of causality’” (Pais 1982).

“The results from the theory agreed, as Born noted happily, with experimental observation … Hence, Born concluded that his collision theory, involving the probability interpretation as an integral part, indeed solved the problem of quantum-mechanical scattering completely within the wave-mechanical formulation. He further declared that, if one so wished, the usual concepts of space and time might be retained but not the causal determination of single events …

“In the next two investigations of his program, … [Born dealt with the problems] of adiabatic invariance and an exact evaluation of the collision of an atomic particle (electron or alpha particle) with a neutral hydrogen atom. He submitted the result of the latter calculation to the Göttingen Academy in late fall 1928 [no. 25]. In it, Born proved the Rutherford scattering formula for large values of the incident momentum of the alpha particle” (Mehra & Rechenberg, vol. 6, p. 48). The method introduced in this paper is now known to every student of quantum mechanics as the ‘Born approximation’.

The paper on adiabatic invariance is notable particularly for Born’s discussion of ‘quantum jumps.’ “Early in October 1926 Born completed a paper [no. 10] on the adiabatic principle in quantum mechanics in which he generalised his probabilistic interpretation for arbitrary quantum transitions. Accepting Schrödinger’s formalism, but not his interpretation of it as a ‘casual continuum theory in the classical sense,’ Born pointed out that the wave mechanical formulation, rather than necessarily implying a continuum interpretation, may well be ‘amalgamated’ with the description of atomic processes in terms of discrete quantum transitions (quantum jumps) … ‘The individual process, the ‘quantum jump’, continued Born, ‘is therefore not causally determined in contrast to the a priori probability of its occurrence; this probability is ascertainable by the integration of Schrödinger’s differential equation which is completely analogous to the corresponding equation in classical mechanics, putting into relation two stationary states separated by a finite temporal interval. The jump thus passes over a considerable abyss: whatever occurs during the transition can hardly be described within the conceptual framework of Bohr’s theory, nay, probably in no language which lends itself to visualizability’” (Jammer, pp. 41-42).

According to the ‘adiabatic principle’ of the Bohr-Sommerfeld theory, since an atomic system can exchange energy only in discrete elements (Planck quanta), a very slowly changing force (with only small frequency components) can produce no ‘quantum jump’ between stationary states, but only a continuous modification of the properties of these states. This principle was used to determine the quantities which were characteristic for the stationary states (adiabatic invariants). In no. 10 Born showed how to derive this adiabatic property from quantum mechanics. He concluded that quantum-mechanical transition processes are reversible like the classical ones, except that the reversibility is now expressed as a property of the transition probabilities, and that for infinitely slow perturbations the probability of a quantum jump is zero.

The Heisenberg papers in the present volume relate to the anomalous Zeeman effect and the spectrum of the Helium atom. 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 Bohr-Sommerfeld 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] … [but no one] 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).

Heisenberg’s treatment of the anomalous Zeeman effect in nos. 9 & 11 is based on his ‘core model’ of atomic structure, which he introduced in 1922 in his first published paper. “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. “In [the resulting paper] 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).

“It was well known that the Bohr-Sommerfeld quantum theory had insuperable problems in dealing with atoms with more than one electron and Heisenberg was well aware of these, having already worked on the theory of the helium atom on the basis of the Bohr-Sommerfeld theory of atomic structure. By 1926, however, the problem was ripe for a renewed attack. The discoveries of electron spin by Uhlenbeck and Goudsmit and Pauli’s exclusion principle [both in 1925] as well as the success with which Heisenberg and Jordan had accounted for the anomalous Zeeman effect suggested a new approach to the helium problem. At the same time, Heisenberg rapidly assimilated Schrödinger’s wave mechanics which provided a simpler means of determining the relevant matrix elements” (Longair, p. 316).

In no. 17, Heisenberg reformulated the two-electron problem in the language of wave mechanics, and used it to calculate the energy levels of the helium atom. “This language appeared to be more appropriate for calculating the energy states of the real two-electron system in the Coulomb field of the helium nucleus. After all … a one-to-one relationship existed among the crucial elements of the interaction-Hamiltonian matrix and the corresponding integrals of the Schrödinger method, which could be obtained in some approximation by taking the overlap of two one-electron wave functions, the so-called ‘exchange integral.’ Although the results – including also the magnetic electron-spin interaction, which again introduced two separated term systems – came out indeed quite crudely, ‘there followed a satisfactory description of the most essential properties of these spectra’ (p. 499)” (Mehra & Rechenberg 6, 128). “Thus the helium calculation – in spite of the fact that wave mechanical methods entered into it only as a tool for evaluating complicated matrix elements – also represented a major triumph of Schrödinger’s theory, perhaps one of the greatest in view of the many unsuccessful efforts during the first half of the 1920s” (Mehra & Rechenberg, vol. 5, pp. 745-6).

“In December, [Heisenberg] completed his extended memoir on the quantum-mechanical many-body problem, so to say, the extension and completion (in the mathematical sense and the physical interpretation) of his previous work on the two-electron atoms [no. 18]. Although the wave-mechanical language might have been most suitable in formulating the rather complicated fundamental equations, Heisenberg again avoided in his Section I on ‘General principles’ all references to the ‘hostile’ scheme [wave mechanics], using only matrix and operator expressions. Just for practical purposes – in Section II, ‘Atomic systems with two electrons,’ and Section III, ‘Resonance effect in the theory of band spectra’ – did he permit himself to speak about wave functions” (Mehra & Rechenberg, vol. 6, p. 129).

“These calculations were also to lead to the development of the concept of exchange forces, the quantum mechanical force associated with the fact that two identical electrons cannot occupy the same quantum state” (Longair, p. 318). Freeman Dyson showed that it is these exchange forces that are responsible for the imperviousness of solid matter (rather than electrostatic repulsion as had been previously assumed); they are also responsible for the formation of white dwarf stars.

One further paper in the collection which is of great historical significance is no. 6, which treats the phenomenon of ‘Thomas precession.’ By 1925, several discrepancies had been found between experimental measurements of the splitting of atomic energy levels and the predictions of the Bohr-Sommerfeld theory. To explain them, Pauli had found it necessary to postulate a ‘particular two-valuedness of the quantum-theoretic properties of the electron, which cannot be described from the classical point of view,’ later recognized as the electron spin which was proposed, independently, by Kronig and by Goudsmit and Uhlenbeck (and initially opposed by Pauli!). A problem quickly arose, however: Heisenberg calculated the splitting of the energy levels based on Uhlenbeck and Goudsmit’s idea and found that it was twice as large as the experimentally observed value. “The missing factor of two was found by [the British physicist Llewellyn] Thomas early in 1926, then working in Bohr’s institute. The transformation between the two reference systems (orbiting electron and electron at rest) is, of course, a Lorentz transformation. After all, in his first paper on special relativity Einstein had used it to connect the electric field of a charge at rest with the magnetic field of a moving charge. But a Lorentz transformation can be applied only if the two reference systems are in uniform (unaccelerated) motion with respect to each other. The circular motion appearing here, however, is accelerated. By taking this fact properly into account Thomas was able to explain the mysterious factor of two, later called the Thomas factor” (Brandt, p. 151). Pauli initially rejected Thomas’s work but later, following Bohr’s intervention, he conceded that it was correct. It was this historical episode which led to spin being accepted as a central concept in quantum physics.

Hartree attended St John's College, Cambridge but World War I interrupted his studies. He joined a group working on anti-aircraft ballistics, gaining considerable skill and an abiding interest in numerical methods for the solution of differential equations. After the end of the war Hartree returned to Cambridge. In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr’s theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger’s equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. He derived the ‘Hartree equations’ for the distribution of electrons in an atom and proposed the ‘self-consistent field method’ for their solution. The Soviet physicist Vladimir Fock modified the Hartree equations so as to be consistent with the Pauli exclusion principle. The resulting ‘Hartree-Fock equations’ are of great importance to the field of computational chemistry. Hartree held the chair of applied mathematics at the University of Manchester from 1929 to 1946, when he returned to Cambridge as professor of theoretical physics. In the 1930s, Hartree became interested in electronic computers, constructing his own version of the Bush differential analyzer and later advising on the use of the ENIAC.

Brandt, Harvest of a Century, 2009. Cassidy, ‘Heisenberg’s first core model of the atom: the formation of a professional style,’ Historical Studies in the Physical Sciences 10 (1979), pp. 187-224. Gottfried, ‘Born to greatness?’ Nature 435 (2005), pp. 739-740. Jammer, The Philosophy of Quantum Mechanics, 1974. Kragh, Quantum Generations, 1999. Longair, Quantum Concepts in Physics, 2013. Mehra & Rechenberg, The Historical Development of Quantum Theory. Pais, ‘Max Born’s statistical interpretation of quantum mechanics,’ Science 218 (1982), pp. 1193-1198. Pais, Niels Bohr’s Times, 1991.

CONTENTS

  1. Darwin, Charles G. The Electron as a Vector Wave. Nature, Vol. 119, No. 2990, 19 February 1927, pp. [1], 2-8 [journal pagination 282-284]. Self-wrappers. [See Mehra & Rechenberg, vol. 6, pp. 281-4]
  2. Stoner, Edmund C. X-Ray Term Values, Absorption Limits, and Critical Potentials. Philosophical Magazine, Series 7, Vol. 2, No. 7, July 1926, pp. [97], 98-113. Original printed wrappers.
  3. Dirac, Paul. The Adiabatic Hypothesis for Magnetic Fields. Proceedings of theCambridge Philosophical Society, Vol. XXIII, No. 1, February 1926, pp. [69], 70-72. Self-wrappers.
  4. Hönl, Helmut. Zum Intensitätsproblem der Spektrallinien. Annalen der Physik, Folge 4, Bd. 79, Heft 4, 13 March 1926, pp. [273], 274--323. Inscribed by author. Self-wrappers.
  5. Fowler, Ralph H. A Note on the Summation Rules for the Intensities of Spectral Lines. Philosophical Magazine, Series 6, Vol. 50, No. 299, November 1925, pp. [1079], 1080-1083. Original printed wrappers.
  6. Thomas, Llewellyn H. The Kinematics of an Electron with an Axis. Philosophical Magazine, Series 7, Vol. 3, No. 13, January 1927, pp. [1], 2-22. Original plain wrappers.
  1. Ornstein, Leonard S. & Burger, Herman C. Nachschrift zu der Arbeit Intensität der Komponenten im Zeemaneffekt. Zeitschrift für Physik, Bd. 29, Heft 3/4, 28 October 1924, pp. 241-242. Original printed wrappers (‘Dup’ written on front wrapper – presumably ‘Duplikat’).
  1. Takamine, Toshio. Intensitāt der verbotenen Quecksilberlinie (l 2270Å). Zeitschrift für Physik, Bd. 37, Heft 1/2, 1 January 1926, pp. [1, blank], 72-79. Original printed wrappers. Inscribed by author (‘Dr. D. R. Hartree / With Compliments’) on front wrapper.
  1. Heisenberg, Werner. Zur Quantentheorie der Multiplettstruktur und der anomalen Zeemaneffekte. Zeitschrift für Physik, Bd. 32, Heft 12, 18 September 1925, pp. 841-860. Original printed wrappers (pencil annotations by Hartree to front wrapper and margins of text).
  1. BORN, Max. Das Adiabatenprinzip in der Quantenmechanik. Zeitschrift für Physik, Bd. 40, Heft 3/4, 6 December 1926, pp. 167-192. Original printed wrappers.
  1. Heisenberg, Werner. Über eine Abänderung der formalen Regeln der Quantentheorie beim Problem der anomalen Zeemaneffekte. Zeitschrift für Physik, Bd. 26, Heft 4/5, 14 August 1924, pp. 291-307. Original printed wrappers.
  1. Sommerfeld, Arnold & UnsÖld, Albrecht. Über das Spektrum des Wasserstoffs. Zeitschrift für Physik, Bd. 36, Heft 4, 22 March 1926, pp. 259-275. Original printed wrappers. Inscribed and signed by Sommerfeld on front wrapper. [See Mehra & Rechenberg, vol. 5, p. 538]
  1. Hönl, Helmut & London, Fritz. Über die Intensitaten der Bandenlinien. Zeitschrift für Physik, Bd. 33, Heft 10/11, 31 August 1925, pp. 803-809. Original printed wrappers.
  1. BORN, Max. Zur Quantenmechanik der Stobvorgange. Zeitschrift für Physik, Bd. 37, Heft 12, 10 July 1926, pp. 863-867. Original printed wrappers.
  1. BORN, Max. Quantenmechanik der Stobvorgange. Zeitschrift für Physik, Bd. 38, Heft 11/12, 14 September 1926, pp. 803-827. Original printed wrappers.
  1. Waller, Ivar. Der Starkeffekt zweiter Ordnung bei Wasserstoff und die Rydbergkorrektion der Spektra von He und Li+. Zeitschrift für Physik, Bd. 38, Heft 8, 1 August 1926, pp. 635-646. Original printed wrappers. Inscribed and signed by author on front wrapper.
  2. Heisenberg, Werner. Über die Spektra von Atomsystemen mit zwei Elektronen. Zeitschrift für Physik, Bd. 39, Heft 7/8, 26 October 1926, pp. 499-518. Original printed wrappers.
  3. Heisenberg, Werner. Mehrkörperprobleme und Resonanz in der Quantenmechanik II. Zeitschrift für Physik, Bd. 41, Heft 4/5, 14 February 1927, pp. 239-267. Original printed wrappers.
  1. Hund, Friedrich. Zur Deutung der Molekülspektren I. Zeitschrift für Physik, Bd. 40, Heft 10, 8 January 1927, pp. [1, blank], 742-764. Original printed wrappers. [Hund introduced here the concept of ‘molecular orbitals’.]
  1. Ditchburn, Robert W. The Quenching of Resonance Radiation and the Breadth of Absorption-Lines. Proceedings of theCambridge Philosophical Society, Vol. XXIII, No.1, February 1926, pp. [1], 78-84. Original printed wrappers.
  1. Lindsay, Robert B. On the Atomic Models of the Alkali Metals [Doctoral thesis]. Publications of the Massachusetts Institute of Technology, Series II, No. 20, May 1924, pp. [191], 192-236. Original printed wrappers. Inscribed by author on front wrapper (‘Compliments of the author’). (“In 1927, a year after the publication of the Schrödinger equation, Hartree formulated what are now known as the Hartree equations for atoms, using the concept of self-consistency that Lindsay had introduced [in this paper] in his study of many electron systems in the context of Bohr Theory” (Wikipedia).)
  1. Urey, Harold C. On the Effect of Perturbing Electric Fields on the Zeeman Effect of the Hydrogen Spectrum. Det Kongelige Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser, Vol. VI, No. 2, 1924, pp. [1-3], 4-19. Original printed wrappers. Marginal annotations in pencil in Hartree’s hand.
  1. Sugiura, Yoshikatsu & Urey, Harold C. On the Quantum Theory Explanation of the Anomalies in the 6th and 7th Periods of the Periodic Table. Det Kongelige Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser. Vol. VII, No. 13, 1926, pp. [1-3], 4-18. Original printed wrappers. Inscribed on front wrapper (‘Dr. D. R. Hartree / With the authors’ compliments’) (inscription slightly cropped).
  1. Burrau, Øyvind. Berechnung des Energiewertes des Wasserstoffmolekül-Ions (H2+) im Normalzustand. Det Kongelige Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser, Vol. VII, No. 14, 1927, pp. [1-3], 4-18. Original printed wrappers.
  1. BORN, Max. Zur Wellenmechanik der Stobvorgange. Nachrichten der Gesellschaft der Wissenschaften zu Göttingen, 1926, pp. [1], [146], 147-160. Original printed wrappers.


Twenty-five offprints bound in one vol., 8vo. Contemporary dark blue cloth (rear joint cracked but firm, extremities rubbed), binder’s ticket on rear paste-down.

Item #5363

Price: $25,000.00