1. G. P. THOMSON, The Wave Mechanics of Free Electrons, 1930, McGraw-Hill Book Company, Inc., New York, p. 179.
2. E. RUPP, Experimentelle Untersuchungen zur Elektronenbeugung, Ergebn. der exakten Naturw. Vol. 9, 1930, Julius Springer, Berlin.

3. H. MARK und R. Wierl, Die experimentellen und theoretischen Grundlagen der Elektronenbeugung, 1931, Gebr. Borntraeger, Berlin, p. 126, price RM 13.60.

4. G. P. THOMSON, Wave Mechanics of Free Electrons.

5. E. RUPP, Experimental Studies of Electron Diffraction.
6. H. MARK and R. WIERL, Experimental and Theoretical Foundations of Electron Diffraction.

The development of wave mechanics almost from the very beginning called into being a new field of experimental physics—the field of studying phenomena in which the wave nature of matter is directly manifested. From the beginning of 1927 the study of diffraction, interference, and reflection of electron waves, and subsequently also of the waves of other material particles (atoms, ions), became the subject of work in a number of laboratories in all civilized countries. Results of enormous fundamental importance were obtained above all by Davisson in America, Thomson in England, Rup-

in Germany. After the basic features of the new phenomena had been clarified and the correctness of the fundamental propositions of the de Broglie–Schrödinger theory had been proved, it became possible to apply the diffraction of electron waves to the study of structures that do not lend themselves, or lend themselves poorly, to analysis by X-rays (the structure of molecules, adsorption of gases by surface layers of metals, etc.). At present the number of works in this field is already considerably greater than one hundred.

In such a state of affairs it is quite natural to take stock of the work and to give a consolidated exposition of the question, intended both for specialists and for wider circles interested in the achievements of physics. Almost from the very beginning of “electron optics,” review articles, both popular and specialized in character, began to appear in a number of journals abroad and in the USSR*.

The books under review are the first fairly large monographs in this field, written, moreover, by prominent specialists whose works constitute an important contribution to science.

The principal content of all three monographs is to a considerable extent common. All the main, most important investigations are analyzed in them. There are, however, substantial differences in the tone of exposition; in addition, for such a rapidly developing field of research, the difference is already determined by the date of publication of the book: the book by Mark and Wierl, published in 1931, is the newest and contains a survey of investigations from 1930 and 1931.

Rupp’s small review (44 pages, together with the table of contents and bibliography) is almost exclusively experimental in character.

The theory of the question, just like a deeper comparison of the experimental results with theoretical conceptions, is almost entirely absent. After brief preliminary remarks and a consideration of the question of the diffraction of electrons by an artificial grating, the central chapter of the review (IV) considers diffraction by crystals, with separate treatment given to phenomena with fast electrons, determination of the atomic factor, phenomena with slow electrons, the question of the refractive index, and several others. The remaining very brief chapters consider some other phenomena and applications of electron diffraction to the study of surface structures. The list

* Davisson, Electrons and Quanta, Bell Syst. Techn. Journ. 8, 217, 1929. Are electrons waves? (Waves or electrons?) See Uspekhi Fiz. Nauk, 1928; Debye, Elektroneninterferenzen, Leipziger Vortr. 1930 (collection of articles); Kikuchi, Beugung der Materiestrahlen, Phys. ZS. 31, 777, 1930. In Russian, besides Davisson’s article: P. Tartakovsky, Wave views on the nature of matter and experiment, Uspekhi Fiz. Nauk, 1928; Granovsky, Uspekhi Fiz. Nauk; Mark and Wierl, The latest data on electron diffraction, Uspekhi Fiz. Nauk, and others.

BIBLIOGRAPHY

The literature contains 62 citations (48 experimental, 14 theoretical).

The exposition, as in most articles in Ergebnisse der exakten Naturwissenschaften, is very compressed, in places almost in outline form. The review, in our opinion, is not successful: for persons working in the given field it provides almost no new material, while for the rest it offers too few general indications and is almost a bare enumeration of facts. The experimental methodology is scarcely illuminated.

The most interesting is Thomson’s book, which represents a series of lectures delivered by the author in America. The introductory chapters allow even those with little preparation in this field to understand the subsequent exposition. A very considerable place is allotted to theory, as is already evident from the table of contents of the book, which we reproduce in full: introductory lecture—waves and particles, I—general theory of waves, II—de Broglie wave mechanics, III—theory of the diffraction of waves in crystals, IV—experimental data, V—influence on waves of a continuous medium, VI—interaction between electrons and atoms, VII—theoretical interpretation, VIII—physical theory, IX—magnetic properties of the electron, X—application of electron diffraction. Theoretical ideas throughout the book are the main core of the exposition. In the introduction and in the first three chapters the basic ideas and formulae of wave mechanics are set out briefly, but quite clearly and with emphasis, and the diffraction of waves in crystals is considered. The latter is by no means superfluous for those readers who have not dealt with X-ray analysis. Chapter IV is central. In the presentation of the experiments the principal results and their analysis are successfully singled out (in separate paragraphs), followed by paragraphs describing the details and methodology of the experiment. Thus, in addition to general acquaintance with the subject, the book also provides guidance for those who will undertake independent work in this field. After presenting the work of Davisson and Germer, the author dwells in detail on his own investigations and on those of his school. This is perhaps the most interesting part of the book. In the following chapter the question of the refractive index of electron waves is considered in detail, and the connection of this question with Sommerfeld’s theory of metals is given. There is less direct numerical material here than in Rupp’s article, which set out his investigations on this subject in detail. Chapter VI analyzes the question of the atomic factor, while Chapter VII dwells on the general theory of non-stationary phenomena in wave mechanics. In Chapter IX the question of the polarization of electron waves is considered in the light of Dirac’s theory of the electron (taking account of the magnetic moment). Finally, in the last chapter the author treats applications of electron diffraction to the study of surface layers and of gases adsorbed by metals, dwelling mainly on his work with fast electrons.

The whole book is written interestingly and vividly and gives much both to the reader,

only to someone becoming acquainted with the field of research, but also to someone who has a sufficiently good command of it. The successful arrangement of the material facilitates the use of the book.

The book by Mark and Wierl likewise begins with a chapter devoted to theory and containing, in addition to a brief introduction to wave mechanics, an analysis of electron diffraction in the case of various objects (individual atoms, molecules, crystal lattices). The question of the atomic factor and the fundamentals of calculating the diffraction pattern from molecules are treated in rather great detail. Chapter II is devoted to an analysis of the experimental material. After a brief historical survey (1927–1931), the principal methods for studying the diffraction of fast and slow electrons are examined—the method of Laue (single crystals), Debye (polycrystals), and Bragg* (constant angle). In the following paragraph a summary is given of works connected with the verification of the basic de Broglie relation \(\left(\lambda=\frac{h}{mv}\right)\), and the principal types of electron diffraction patterns studied up to the present are also analyzed.

Next comes a paragraph devoted to questions of intensity and to the determination of the atomic factor for electrons. In this paragraph the theoretical considerations of Chapter I are used, and the exposition is based on the authors’ own investigations. One of the following paragraphs is devoted to the authors’ results in the study of the diffraction of fast electrons within molecules. The authors investigated 20 different types of molecules and determined their structures; in many cases the experimental results confirm propositions long since expressed in organic chemistry. In considering the diffraction of slow electrons, sufficient attention is given to the question of the refractive index and the inner potential. In the remaining paragraphs of this chapter the usual series of phenomena is analyzed: Davisson’s experiments, polarization of electron waves, adsorption of gases by surfaces, and so forth. The question of intra-atomic diffraction deserves special attention. These works were carried out in 1931, chiefly by Arnot, and yielded a number of “intra-atomic” maxima fully consistent with the requirements of the theory; this new field of investigation is closely connected with the Ramsauer effect.

The last chapter of the book contains a bibliography comprising 101 citations of experimental works and 41 of theoretical ones. The list of literature is brought almost up to the time of publication of the book (autumn 1931).

The whole exposition is much more concise than in Thomson’s book. There are fewer experimental details; however, the basic methods of the experiments are described with sufficient clarity. Interesting illustrative material has been selected. The most interesting paragraphs are those devoted to the atomic factor and to electron diffraction in molecules. The book should be regarded as successful.

* Unfortunately, many errors have crept into this part in the formulas, making reading difficult.

All three reviews concern only electron diffraction. It is a pity that they do not touch upon the quite interesting experiments on the diffraction of atoms and ions. This would have completed the picture of diffraction phenomena with matter waves.

P. Tartakovsky