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ists.” He writes in his preface, “This book alone is not necessarily sufficient t o s u p p l i the detailed instruction which would permit the reader to use quantum mechanics and statistical mechanics as tools for himself. I t s primary object is t o help him understand clearly how they have been employed by others t o obtain results of chemical significance.” The chapter headings are : “Quantum Numbers”; “Quantum Mechanics”; “Quantum Theory of Valence”; “Molecular Spectra: Diatomic Molecules”; “Molecular Spectra: Polyatoniic Molecules” ; “The Electronic Configurations of Diatomic Molecules” ; “Statistical Mechanics”; “Statistical Thermodynamics and Intermolecular Forces.” The book has the virtues and the faults familiar t o readers of the author’s earlier books. The topics are presented in readable style; and the mathematical derivations are in general clearly traced through, with a minimum of those sudden leaps which are bewildering t o a student even though obvious t o a n author. (It is questionable whether the student t o whom this volume is addressed would be familiar with Lagrange’s equation (page 204) or with the Euler-Maclaurin summation formula (page 374) ; but these are exceptions.) Thus the book will be of use t o the student or instructor who wishes t o refer t o a reasonably detailed exposition of a standard topic, such as the quantum-mechanical treatment of t h e hydrogen molecule, or the elements of normal coordinates. Unfortunately, the book does not give a n integrated critical exposition of fundamentals; in our opinion, a studcnt would not gain from this text a real insight into the basic physical meanings of quantum and statistical mechanics, or a real feeling for these disciplines. There are some surprising omissions. Thus, we found no discussion of simultaneous eigen values, or of the properties of angular momentum. The energy levels of the symmetric top are not derived. K O derivacions of selection rules are given-though this topic is certainly no more difficult than the evaluation of integrals in the hydrogen-molecule problem, which is given in rather complete detail. The Born-Oppenheimer theorem is not even alluded to. We feel t h a t the book would have been more useful had the author included some of t h e valuable empirical correlations such as Badger’s rule, bond radii, etc.; but this means only t h a t we should like t o take the adjective “theoretical” less strictly than the author. We also feel t h a t i t would have been helpful to include some problems, on which t h e student might test his comfortable feeling of understanding. There are a few misstatements which we noticed: e.g., the dimensions of the polarizability ellipsoid (page 195) are not given by the components of the polarizability, but by their reciprocal square-roots. Nor can a power series be expressed in general by a simple exponential function (page 181). But these slips are not serious. BRYCEL. CRAWFORD, JR. T h e Theory of X - r a y Diffraction i n Crystals. By W. H. ZACHARIASEN. 255 pp. John Wiley and Sons, Inc., 1944. Price: $4.00. In this new book the distinguished President of t h e recently formed American Society for X-ray and Electron Diffraction has given a resume of two important branches of the field of crystal analysis: (i) the theory of symmetry groups and lattices, and (ii)the theory of diffraction in perfect and imperfect crystals. The discussion is based on lecture notes given t o students i n this field a t the University of Chicago, and forms a worthy companion volume to the book on X - r a y Crystallography by Buerger, recently issued by the same publishers. For use as a textbook for students not already familiar with x-ray theory and technique it will require amplification of a n illustrative nature such as can be found in the book of Compton and Allison. The treatment of the symmetry groups of lattice structures occupies about one-third of the book, inclusive of t w o appendices on dyadics and group theory. This condensation of the theory of space groups into some seventy-five pages is made possible only by a purely algebraic treatment, which is based on the dyadic notation of Gibbs. To many readers this may seem like a severe dehydration of a n already dry subject. However, the discussion is clearly written, and i n view of the peculiar poverty of the literature in English on this
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subject i t should be welcomed as a treatment which can be mastered without extensive excursions into group theory. References t o the more geometrical treafment in the older book of Hilton, and the tensor treatment of Seits will be helpful in livening up the study. The reviewer cannot refrain from two small technical criticisms: (h) the use of bold-face type for dyadics has forced the employment of a barred notation for vectors which is unpleasant, and could well be reversed i n future editions, and ( b ) the convention on the ordering of operations (page 26) is the reverse of t h a t now customary i n mathematical physics. The reader will probably be glad t o know t h a t he can, if he wishes, proceed t o the chapters on diffraction without mastering the theory of symmetry groups. The reviewer has found Chapter I11 on ideal crystals, and Chapter I V on real crystals t o give a n excellent review of the mathematical theory of x-ray diffraction. The treatment is based on semiclassical formulas of electromagnetic theory, but brief indications of the alterations due t o quantum-mechanical studies have been inserted. The sections on the effect of lattice disorders due t o thermal agitations, and t o substitutions, are particularly welcome, since much of this work is of recent date and shows all promise of becoming of increasing importance in the general study of the solid state. The author and the publishers are t o be congratulated on the appearance of this book of relatively advanced character, all too rare i n American scientific literature as yet, and i t i s to be hoped t h a t the demand for i t will permit them t o issue revised and expanded editions in this important field at reasonable intervals. E. L. HILL.
