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The investigations on the few typical organogels have revealed the r81e, in the disappearance of the hysteresis loop in sorption, of the elasticity of organogels which swell on the imbibition of water. The author is grateful t o Prof. B. Sanjiva Rao for his keen interest in this work. REFERESCES (1) (2) (3) (4) (5) (6) (7) (8)
McBaxs: J. Am. Chem. Soc. 67, 699 (1935). Rho, B. S.: Current Sci. 6, 446 (1938). RAO,K. S.: Current Sci. 8, 256 (1939). R.40, K. S.: Current Sci. 9, 19 (1950). Rao, K . S.: Current Sci. 9, 68 (1940). Rho, K. S.: J . Phys. Chem. 46, 517 (1941); Paper IV. SHEPPARD AXD S E W S O J.~Phys. I E : Chem. 33, 1817 (1929). U R Q U H . 4 R T : J. Textile Inst. 20, T125 (1929).
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Statistical Mechanics. By J. E. JIAYERA X D M. G. MAYER. xi 495 pp. S e w York: John M’iley and Sons, Inc., 1910. Price: $5.50. Within the last few years, a wealth of books has appeared which are devoted essentially t o the modern or quantum-mechanical version of statistical mechanics, and applications thereof. The bookshelf on this subject now includes the second edition of Fowler’s Statistical Mechanics (1936),Tolman’s T h e Principles ofStatistical Mechanics (1938), Fowler and Guggenheim’s Statistical Thermodynamics (1939), and most recently the volume written by the hlayers. As regards the level on which the presentation is pitched, their book may be classified as less advanced than the tomes by Fowler and by Tolman, and a little more elementary than the contribution by Fowler and Guggenheim. I t is, on the other hand, more advanced than Slater’s text-book, Introduction to Chemical Physics, and is about on a level with Brillouin’s Les Statistipues Quantipues et Leurs Applications, though more comprehensive than the latter. As t o subject matter, the Tolman volume is devoted mainly t o questions of principle, whereas the Fowler or Fowler and Guggenheim treatises deal almost exclusively with applications. The >layers’ monograph steers more or less a middle ground, most of the emphasis being on applications, but still with some attention t o the logical foundations of the statistical theory. No use is made of the FonlerDarwin method of contour integration and steepest descents. Instead, factorials are approximated in the conventional manner by means of Sterling’s theorem, and in consequence the presentation, though perhaps somewhat less elegant, is certainly easier for those not mathematically inclined than if the Fowler procedure were used. The table of contents may be roughly summarized as follows: About the first third of the book is devoted t o kinetic theory, classical and quantum-mechanical preliminaries, and the derivation of the laws of thermodynamics. The general method of approach is somewhat similar t o t h a t in Jordan’s Statistische Mechanik auf Quanten Theoretischer Grundlage. A discussion is given of the rather timely subject of the entropy of isotope mixing. Only one chapter is devoted t o the dynamics of crystal gratings, although one of the Mayers has made notable contributions on this subject.
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The chapters on imperfect gases and on condensation and the critical region, on the other hand, are developed in more detail proportionately than the rest of the volume, and constitute probably the most difficult reading of any part of the book. However, i t is proper that emphasis should thus have been placed on this involved but interesting subject; namely, that one can actually show by statistical mechanics that, under certain conditions, a gas should condense if sufficiently compressed. Indeed, any book should carry some flavor of the author’s speciality, and J. E. Mayer’s original contributions t o this subject are well known. There is a nicely written but brief chapter on electric and magnetic fields, and a final chapter on degenerate gases, ending with the up-to-the-minute topic of liquid helium 11, the “superfluid,” regarded as a degenerate Einstein-Bose gas. It is t o be regretted t h a t the volume could not have been at least 50 per cent longer. For one thing, this increase would have permitted inclusion of frequent comparisons with experiment, which always add variety and spice t o a purely theoretical treatment. -4180, i t would have allowed certain topics t o be presented in a less sketchy fashion. Although the groundwork, and certain subjects,-for instance, the partition function of a diatomic gas,-are treated in considerable detail, there are other items which are dismissed rather briefly because of limitations of space. For instance, i t is doubtful whether the chapter on polyatomic molecules is detailed enough t o give the reader a real feeling for this difficult subject, although the treatment does emphasize the interesting r6les of symmetry number and nuclear spin, and although the development of a really adequate background mould require practically making the reader into t h a t TUTU uvis, the polyatomic spectroscopist. On the whole, the book gives the impression of being carefully written, rather than superficially and in a hurry. The standard of clarity is usually high, and the presentation factually correct. The reviewer believes that the reader is a p t t o be misled by the statement on page 61 that “The Liouville theorem is essential for the complete understanding of the uncertainty principle. . . If a t one time the coordinate of a particle is known with an accuracy A q , the momentum within a range A p , in agreement with the uncertainty principle, the predictions that can be made for the future are neither more nor less than the initial uncertainty, namely A p A q 2 h / 2 ~ . ” Actually, the uncertainty is invariant of time only if the coordinates and momenta are chosen in a particular fashion, not that employed in the conventional discussions of the uncertainty principle, nor of most direct operational significance. A detailed discussion of this point is being published by the reviewer elsewhere (Philosophy of Science Journal, in press). Throughout the volume, quantum-mechanical systems are viewed mainly from the standpoint of stationary states, wherein an atomic system is considered t o pass suddenly from one configuration t o another, rather than from the more general formalism in which the state of a system is described by a statistical matrix. The latter viewpoint, however, is essential for certain problems which involve questions of interference of phases and which are therefore not treated in the book. Because of phase questions, the proof of the validity of the principle of detailed balancing may not always be as immediate as is implied on page 56. There is precedent for husband and wife t o write a book together on statistical mechanics, as one recalls the monograph of P. and T. Ehrenfest. The two Mayers have proved themselves worthy of the tradition, although their contribution is of an entirely different type, being essentially a text-book rather than a critique of the foundations of statistical mechanics. Those readers will particularly welcome the Mayers’ volume who desire an up-to-date, quantum-mechanical, and reasonably rigorous treatment of statistical mechanics, developed with a minimum of mathematical machinery and with some stress on applications. J. H. VAN VLECK.
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