H. A. Lorentz. The Theory of Electrons. Leipzig, B. Teubner. Second edition, 1919.

Lorentz’s book, in the twelve years that have elapsed since the appearance of its first edition, has become a classic and may rightly be placed alongside Newton’s Principia and Maxwell’s Treatise on Electricity and Magnetism as a milestone marking a new stage in the physical worldview. The book is a brilliant development of all the numerous consequences flowing from the fundamental differential equations of the electron formulated by Lorentz, and at the same time it sums up an entire period of theoretical physics, the end of which approximately coincides with the appearance of quantum theory and the principle of relativity. We have already passed into a new stage in the history of physics, but the outlines of the new worldview are not yet clear; Lorentz’s book is a monument to the preceding classical epoch.

The second edition of The Theory of Electrons has remained essentially unchanged, preserving its classical completeness. The original text has not been touched at all. The book has increased by 10 pages, and the additions (placed in the notes to the second part of the book) concern a few new experimental data; for the most part they are devoted to the principle of relativity as applied to the motion of the electron. One small addition, purely methodological in character, concerns quantum theory.

C. Vavilov.

A. Sommerfeld. Atombau und Spektrallinien. 2nd ed. Braunschweig, 1921, pp. XIV + 583.

The discovery of radioactivity and the related theory of atomic structure proposed by Rutherford and further developed by Bohr has now led Rutherford, as is well known, to the decomposition of the positive nuclei of elements into their constituent parts, which is undoubtedly an event in the field of physicochemical doctrines. On the other hand, the Rutherford–Bohr theory of the atom has also yielded remarkable results in the theory of the structure of spectral lines, so that it now seems absolutely necessary to bring together everything obtained so far and to provide guiding threads for future work. All this is splendidly accomplished by the excellent, clearly written book of A. Sommerfeld, the author of a number of major works in the field of the doctrine of atomic structure in connection with its spectrum. The book first appeared in 1919 and was issued in 1921 in a second edition—proof that both its content and its mode of presentation may count on educated readers in physics and chemistry. In Russia a translation is being prepared (organized by Prof. D. A. Goldhammer), and one can only wish that this translation may see the light as soon as possible and exert on Russian science the influence it is capable of exerting.

P. Lazarev.