R. TOLMAN. Statistical Mechanics with Applications to Physiks and Chemistry. American Chemical Society Monograph Series. The Mechanical Catalog Company. New-York, 1927. T. p. 334.

R. Tolman. Statistical mechanics and its applications to physics and chemistry.

Despite the fact that the range of application of statistical mechanics is growing wider and wider with each passing day, and that at the present time many major physicists are close to the view that, in general, all physical laws recognized by us have a statistical character, the literature devoted to statistical mechanics and its applications is very small—especially if one compares it with the literature treating such questions as the principle of relativity or the structure of the atom. It is particularly difficult to point to books that not only set forth the foundations of statistical mechanics, but also show, through concrete examples, the methods of applying it to the solution of various problems of physics and chemistry. Gibbs’s classical book and P. Hertz’s extensive survey in the “Repertorium” on the physics of Gans and Weber are too abstract and difficult to be recommended to a reader becoming acquainted with statistical mechanics for the first time; Lorentz’s book “Statistical Theories in Thermodynamics” is devoted chiefly to the exposition of general questions. Therefore there remain only chapters devoted to statistical mechanics in various Handbücher and books similar to Jeans’s well-known book, which are not always complete

and not always successful. For chemists, who at the present time are becoming more and more interested in the methods of statistical mechanics, this literature is of little use. Tolman’s book fills precisely this gap; it may with full justification be called statistical mechanics for chemists. In it the center of gravity of the exposition is shifted from general questions to applications of statistical mechanics to the solution of a wide variety of physical and physicochemical problems. Although the author does not dwell on questions of a purely mathematical character, he nevertheless carefully elucidates all the hypotheses underlying the methods under consideration (for example, the famous ergodic hypothesis) and the physical meaning of the mathematical approximations. Therefore the attentive reader obtains not only an idea of statistical mechanics as a working tool of scientific investigation, but also of the limits within which this tool can be used.

The book begins with an explanation of the essence of the statistical method, after which follows the derivation of Hamilton’s equations and an exposition of the general foundations of Gibbs’s method. These chapters are written so clearly that they cannot cause special difficulties even for the non-physicist reader. After this the author gives the definition of the canonical distribution and, without investigating its general properties—which he touches on only slightly in the next chapter—proceeds directly to the consideration of the microcanonical distribution, which he uses throughout almost the entire book. This excessive attachment to the microcanonical distribution is undoubtedly a shortcoming of the book, since because of it the author gives little attention to questions concerning statistical methods for calculating thermodynamic potentials, the most convenient of which are connected, as is known, with the use of the canonical ensemble. This is all the more regrettable because, as we have already said, Tolman’s book may be called statistical mechanics for chemists, and it is precisely for chemists that the method of thermodynamic potentials is the most familiar; hence the desire to become acquainted with its statistical interpretation is quite natural. On the other hand, chemists will find a sufficiently complete and thorough exposition of the question of the application of statistical mechanics to the consideration of the kinetics of chemical reactions. The chapters preceding this part of the book, devoted to the exposition of Einstein’s theory of absorption and the role of collisions of the second kind, serve, as it were, as an introduction to it and allow the author, in presenting questions of kinetics, to touch upon all the latest (though, alas, contributing little clarification to the matter) theories of activation. Indeed, in general it must be said that the whole book is very up to date and almost always acquaints the reader with the most recent works in the given field. The only, perhaps, exception in this respect is the author’s ignoring of the works of Bose–Einstein and Fermi, which had already appeared while the book was being written; these are not only not expounded, but not even mentioned. This is all the more strange since quantum theory is used very widely in the book.

In presenting many questions, Tolman uses the method and terminology introduced by Ehrenfest and Trkal in their work on the calculation of the chemical constant. This method is indeed very convenient, and one can only wish it still wider dissemination.

The book contains quite a bit of material connected with Tolman’s own work—for example, the derivation of the energy distribution law for the case when the energy is not a quadratic function of the coordinates; the generalization of the H-theorem to the case of molecules that absorb the incident radiation and emit radiation; and, based on this generalization, the simultaneous derivation of the laws of Maxwell-Boltzmann and Planck. Of interest is the symbolic method that Tolman uses in deriving the H-theorem in its classical form, based on the more precise classification of collisions that he gives.

The clarity and simplicity of the exposition, the large number of questions touched upon, and the freshness of the material make Tolman’s book very valuable. In the scant literature on statistical mechanics, this is perhaps the only book that can be unreservedly recommended to all physical chemists wishing to become acquainted with statistical mechanics and its methods. Apparently the author himself intended his book chiefly for chemists, stressing at the very beginning the necessity for them to master the methods of statistical mechanics for the further development of theoretical chemistry, which until recently had made almost exclusive use of the methods of classical thermodynamics. Many pages devoted to quantum theory may also prove useful and will save some chemists from lofty contempt for this, as they call it, “mathematical fiction,” and others from a superstitious reverence based on faith in the boundless power of this theory.

Vl. Semenchenko.