Bibliography

R. H. FOWLER. Statistical Mechanics. The Theory of the Properties of Matter in Equilibrium. Cambridge, at the University Press, 1929. Pp. 570.

R. Fowler. Statistical Mechanics.

The outstanding role of Fowler’s large treatise on statistical mechanics—not only as the most complete and modern handbook, but also as a very significant stage in the substantiation of this scientific discipline itself—has been recognized by the entire scientific criticism of the world.

It is well known what difficulties are involved in the striving to create a unified and coherent theory in statistical mechanics. Alongside difficulties of a fundamental nature, revealed with exhaustive clarity and completeness in Ehrenfest’s well-known encyclopedic article and still not overcome even at the present time, one must also deal here with specific difficulties of mathematical analysis. The last decade, in connection with the development of the new mechanics of the atom, has set before physical statistics a series of new problems, whose inclusion in the general scheme has made the creation of a theoretically integral conception of statistical mechanics still more difficult. Fowler’s book, overcoming these difficulties to a considerable degree, differs from other modern expositions of the subject in three very essential respects.

First, the author, in principle and systematically, instead of considering the most probable values of quantities, studies and takes as characterizing the physical state of matter their mean values, thereby overcoming the tradition that goes back to Boltzmann. It is known that, because of the special character of the problems of physical statistics, this substitution cannot in any significant way change the result of the investigation; however, the formal method of the science gains much from this, chiefly in the sense of unity and mathematical rigor, which in the earlier treatment left much to be desired.

Second, Fowler’s book gives a unified theory embracing the statistics of both “classical” and “quantum” mechani-

ical systems. The exposition is constructed in such a way that the theory of quantum systems serves as the foundation, while classical theory appears as its limiting case.

Finally, thirdly, Fowler’s book, in a very organic form, also includes those new types of physical statistics which have developed so fruitfully in recent years in connection with the new mechanics of atoms, electrons, and light quanta. The statistical concepts of Boltzmann, Bose—Einstein, and Fermi—Dirac here appear as natural varieties of a single general statistical scheme, which the author substantiates very deeply and elegantly in connection with Heisenberg’s theoretical investigations, which have solved the riddle of the existence of separate spectra that do not combine with one another in helium and other elements.

Having thus achieved a theoretical wholeness unprecedented for statistical mechanics, Fowler at the same time carries out, with extraordinary detail, a statistical analysis of the concrete physical problems, touched upon in enormous number in his book. Not being a physicist, the reviewer must leave it to specialists to judge these aspects of the book. We shall cite only the table of contents of the book, which testifies to the breadth and variety of its contents.

Table of commonly used physical constants. Introduction. Rules for determining weights and theorems of statistical mechanics for collections of unchanged systems. Specific heat of monatomic gases. Distribution functions for thermal radiation and for crystals. The simplest properties of crystals. Theory of arbitrary collections. Dissociation and vapor formation. The relationship between the theory of equilibrium and classical thermodynamics. Nernst’s theorem and chemical constants. Theory of imperfect gases. Intra-atomic forces. Application of the theory of equilibrium to thermionics. Dielectric and magnetic constants of gases. Application to liquids. Properties of weak solutions. Collections of atoms, ions, and electrons. Problems of the atmosphere. Application to the study of the internal structure of stars. Mechanisms of interactions. Radiation processes. Fluctuations. New statistical mechanics. Index.

A. Khinchin.