BOOK REVIEWS the mathematical analysis. This seems to be the correct way to proceed in teachine science students. It allows them to participate in the process of abstraction that leads to making a. mathematical model for the physicd system. This book would also he suitable for independent study. I n a. way it is a sort of "mathematical physics without tears!' A student who had mastered it would be well prepared for a subsequent rigorous course in theoretical physics. There are extensive problems, hut unfortunately they are mostly routine exercises in 2'8 and y's which provide the student no opportunity to apply hi newly learned mathematics to the analysis of physical situations. So far as this author is concerned, "Physical Sciences" in the title appears to be synonymous with "classical physics" and scant mention is made of chemistry, astronomy, geology, or modern physics. The book might have been considerably enlivened by inclusion of more recent physical science drawn from a wider variety of fields. It is doubtful that one would turn to Boas for reference purposes with more comprehensive sources available. Despite its rather grand title, the book by Anderson covers only a few topics. The author states that "this book attempts to lay down a central core of physiod and mathematical background for quantum chemistry in general, but for moleculm spectroscopy in particular." This ambitious program is wisely no1 attempted in the 149 pagesavailable. What we actually get is an excellent 41-page summary of orthogonal functions, which is always clear, concise, and to the point [except for serious misprints in eq. (2-102)l. This is followed by 56 pages on abstract linear algebra. The final section of the hook attempts to discuss the classical merhal~ic.;of vibration, and n,tations in 30 1,nge.i 2nd predirtnldy) f s i l i t u preient the nlawrixi ndrountelv. I'ntii this frrlal chapter ~ndersan.mttin'tainsa.rigid wall of separation between mathematics and science. Does he expect the science student to study all the mathematics first before being shown any of the applications? The important place of this book will be as a valuable supplement to a c o m e in molecular structure or quantum chemistry. These three books left me with the feeling that the task outlined by Professor Pillow has not yet been seriously begun. For example, none of these books makes reference to the existence of giant computers which have already produced a revolutionary expansion in the theoretical treatment of chemical problems. (It is as if a physician wrote a treatise on bacterial diseases without reference to antibiotics.) We are far from havinu solved
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chemistry teaching. The authors of these books deserve our thanks for attacking some aspects of an important problem in a practical way. We may hope that many more books will be written in this field so that we may
A352
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Journal o f Chemical Education
learn through experiment how best to present to university students a coherent understanding of mathematics as applied in the chemical sciences. It seems that we might seriously consider a solution in which we would withdraw our chemistry students from the pure mathematicians and arrange for them to be taught by specialists in applied mathematics, by theoretical chemists, or both. WALTERJ. MOORE Indiana University Bloominglon
Molecular Aspects of Symmetry Robin M . Hochstrasser, University of Pennsylvania, Philadelphia. W. A. Benjamin, Inc., New York, 1966. 355 pp. Figs. and tables. xiii 16 X 23.5 em. $14.75.
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In recent yesrs a number of books or parts of books have appeared in which some results of group theory are presented in an elementary way for application to systems of physical and chemical interest. This trend is not fallowed by Professor Hochstrasser; the present volume would be undertaken most profitably Bfter a good introductory course in quantum mechanics. The level of presentation is similar to that found in the books by Tinkham and by Heine, in which group theory and its applications in physics are considered. More than 40 percent of the text is devoted to mathematical background, group thwry itself, including representations, and a discussion of the various point groups. In the remainder of the book numerous applications are discussed, including angular momenta of atoms and molecules, MO states and symmetry, selection rules for electric and magnetic dipole transitions, vibrrttiond and vibronic states, spin-orbit coupling, singlettriplet transitions, spin-vibronic interactions, and the symmetry and spectra of organic molecular crystals. The author adopts a. fundamental viewpoint; he derives theorems, beginning at the basic principles. The style is brief though precise, and it is inevitable that numerous mathematical expressions appear. For these reasons a student would find it very difficultto work systematically through the book by himself; an instructor and course atmosphere would be invaluhble. However, in the sections covering applications numerous detailed examples are given; it should be possible for a student to follow these and obtain useful Unforresults for similar systems. tunately, few problems or exercises are provided. The typography and proofreading seem of high caliber; only rare ermm were noted, and they were minor. This book should be exceedingly useful to those working in electronic spectroscopy; it could do much to broaden the outlook of those in related areas. I believe the price is too high; a volume of this nature should
be owned by the user, ratner than by the institution or library. D. F. EGGERS,JR. Uniwersily of Washinglm SeatU..
The Principles of Chemical Equilibrium
Kenneth Denbigh, University of London. Cambridge, a t the University Press, 494 pp. Figs. 1966. 2nd ed. xxi and tables. 14.5 X 22 cm. Paperbound, $3.95; clothbound, $9.50.
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My high opinion of this book has not changed since its first publication in 1955 (J. CHEM.EDUC.,33 305 [1956]), but I would not c d the present volume a. revision. The only change in the Table of Contents is the addition of two pages to Chapter 1. The rest of the changes are decidedly minor, and represent a tidying up, an updating of the references, m d a use of mare contemporary terminology. But, after all, if you do an excellent jab the first time, there is not much that can be added to a basic treatment of thermcdynamics-the subject having been around for some time now. This is still a fine book, and should be carefully examined before anyone chooses another volume from which to teach classical and statistical thermodynamics.
J. A. CAMPBELL Harvey Mudd College Claremoni, California
Thermoanalytical Methods of Investigation Paul D. Garn, University of Akron, Akron, Ohio. Academic Press, Inc., 606 pp. New York, 1965. xvi Figs. and tables. 16 X 23.5 em. $19.50.
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In the ten-year period preceding the publication of Dr. Garn's book, thermoanalytical methods grew from a few scab tered experiments with rocks and homemade DTA units or quartz spring McBain type balances, to a sophisticated multimillion dollar industry which has placed complex electronic thermal boxes in many laboratories. The growth parallels that of gas chromatography, but unlike that field, there are few useful books to which a new investigator can turn for a comprehensive assessment of the field. Dr. Gam hss attempted to fill part of that void with his extensive treatise. In its 17 chapters, hediscusses thevarious types of apparatus, methods of sample preparation and a ~ e r s t i n econditions for makine differ-
the qualitative and quantitative interpretations of DTA curves. He also reports attempts to extract kinetic dats from such curves. His review of thermogravimetric apparatus, procedures, and associated techniques is similarly detailed. Through(Continued ma page AAS64)
