Bibliography

D. Reiss. Statistical Physics. Translated from the English by B. N. Finkelstein. State Scientific-Technical Publishing House of Ukraine, 1934, 283 pp., price 4 rubles 50 kopecks.

In a book of modest size, Reiss attempts to give the reader an account of the basic statistical methods of classical and modern physics. He begins by considering the very essence of the statistical method by means of simple examples: the tossing of a coin and games of chance (Ch. I), after which he proceeds to the statistics of the simplest molecular systems (Chs. II and III). In Chapter IV the equation of state of an ideal gas is derived in an elementary way, and the physical meaning of the distribution modulus is determined. In the same chapter the concept of pressure is analyzed, which is very useful, since it is sometimes, unfortunately, the question of why internal (for example, osmotic) pressure does not burst a vessel containing liquid that causes difficulties not only for students. Chapter V is devoted to the law of equipartition, Chapter VI to clarifying analogies between statistical and thermodynamic functions. The author then proceeds to calculating the entropy constant of an ideal gas (Ch. VII) and to applying the results obtained to gaseous equilibrium (Ch. VIII). Chapter IX is devoted to the consideration of the influence of molecular forces and to the derivation of the van der Waals equation. In Chapter X the question of density fluctuations is considered, and both methods of solution are presented (those of Smoluchowski and Einstein). In Chapter XI the author shows that the presence of molecular forces does not change the conclusions obtained earlier for an ideal system in connection with changes in entropy and probability. Further (Ch. XII) a statistical derivation of the vapor-pressure equation of a liquid is given. In Chapter XIII the author turns to the theory of the solid state, showing that classical ideas lead to the Dulong–Petit law. Chapter XIV, devoted to quantum theory, begins with a historical survey of the three main stages of its development, after which the author derives Planck’s formula and gives an account of the geometrical interpretation of quantum states in phase space. The concept of zero-point energy is introduced there as well. Chapter XV acquaints the reader with the foundations of Bohr’s theory of the atom. Chapter XVI considers the question of the distribution of systems by energy. Then follow applications of quantum theory to questions of the heat capacity of gases (Ch. XVII) and of the solid body (Ch. XX). Chapters XVIII and XIX contain necessary auxiliary information. Chapters XXI and XXII are devoted to methods for calculating the entropy constant of a monatomic gas. In Chapters XXIII and XXIV the author sets forth the foundations of Gibbs’s method. Appendix A presents the foundations of the new statistical methods developed by Bose–Einstein, Fermi–Dirac, and Darwin–Fowler; Appendix B presents the foundations of chemical kinetics.

From this brief review of the book’s contents it is clear that the fundamental questions of statistical mechanics are presented by the author rather fully. Unfortunately, the same cannot be said of the applications, despite the fact that the author at the beginning of the book (p. 31) states that “his readers are most eager to see the results,” without being overly concerned with the necessary—

...ness and logical substantiation of the postulates. The latter, if they possess even some sign of plausibility, will obviously be accepted without objection, especially if they lead to results that agree with experiment and with experimental facts.” There we read: “The benefit that the inexperienced mind will derive from excessive immersion in ‘foundations’ is very doubtful.” From this it would seem to follow that later on we should expect the author to solve a large number of physical and physico-chemical problems, to show the enormous role that statistical methods play in modern physics, and to conclude this book by evoking in most readers a desire to gain a deeper acquaintance with the fundamental foundations of methods that yield such great results. In fact, however, everything is quite otherwise: almost the whole book is devoted to an exposition of statistical methods precisely without “excessive immersion in foundations,” since, apparently, the author intended his book for “inexperienced minds.” The author’s slight concern for “immature minds” was also expressed in the fact that he almost completely does not make use of drawings, which often greatly facilitate the understanding of the geometrical images of statistical mechanics, and several times asks the reader independently to carry out calculations that are comparatively difficult for a beginner. Such calculations contribute far more to scattering the reader’s attention than to developing independence in him; and it is not in vain that in such impeccable books from a pedagogical point of view as Sommerfeld’s Atomic Structure and Brillouin’s Quantum Statistics, all calculations are carried through to the end.

Despite these shortcomings, Rice’s book represents a valuable contribution to the not especially rich literature on statistical mechanics. It reflects all the most important directions of statistical mechanics. A reader with good mathematical preparation can form from it a clear and sufficiently complete conception of the statistical methods of modern physics. Perhaps only in Rice’s book is there a successful exposition of the foundations of the Darwin–Fowler method, which, although it has contributed nothing new in applications, nevertheless represents a significant step forward in the development of the mathematical apparatus of statistical mechanics, quite apart from its fundamental significance.

The book may be fully recommended to mathematicians and physicists for an initial acquaintance with statistical mechanics. For experimental physicists and physical chemists, as it seems to us, it is not entirely suitable either in material or in method of exposition.

The translation, made by B. N. Finkelstein, is irreproachable both in accuracy and in style. The only possible objection would be to the introduction of the term “complexion,” which sometimes produces extremely curious word combinations.

The list of books on statistical mechanics given at the end of the book is incomplete. It seems to us that their number is so small that all of them could have been listed.

Vl. Selezhnenko