DECEMBER. 1949
685
There are indeed no half tone cuts a t all in the book but only line drawings of such simplicity as to be readily comprehended by the student. The errors, both typographical and factual, are fewer than in manv books coverine the same subiects. The ~roblemsare well chosen, and varied, with an avers& of about i 0 for each of the ~
26 .. . rhnntem. .
Tllc majority of rmclrrrs of bryirrning chcmiirry will rwr.tinly find it worth their a.l.il~t o Iouk o w r thi; volumr fur it voraraiqe. mueh of the n.rm rwcnt contributioni of arrudural rlwmi-trv without breaking sharply with the most common order and content in elementary chemistry courses. J. A. CAMPBELL O ~ ~ n m Com,Eaa s O B E R ~ NOar0 ,
MATHEMATICAL FOUNDATIONS OF STATISTICAL MECHANICS
A. I. Khinchin. Translated from the Russian by G. Gamow, Proflesor at George Washington University. First American Edition. Dover Publications. Inc., 1780 Broadway. New York 19, 1949. viii 179 pp. 12.75 X 18.75 cm. $2.95.
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ACCORDING t o the publisher's circular the author "has been prominently identified with the remarkable researoh devclopments in mathematied analysis a t the First Moscow University." The translator is a well-known physicist and author. It is difficult to sppraise what a book like the present one will contribute toward helping the efforts of physical chemists engaged in applying statistical mechanics to their many problc~m. Fundamental and laudable as they are, the preoccupations of this hook are more of the type of those of the mathematician and of the theoretical physicist. As explicitly stated in the Preface, "the hook is written, above all, for the msthematician, and its purpose is to introduce him t o the problems of statistical mechanics in an atmosphere of logical preoision, outside of which ho cannot assimilate and work, and which, unfortunately, is lacking in the existing physical expositions." The titles of the eight chapters will give B more ooncrete idea, of the author's purpose and scope: Introduction, Geometry and kinematics of the phase space (not "phas3 rule" as is hopefully stated on the jacket), Ergodic problem, Reduction to the problem of the theory of probability, Application of the central limit theorem, Ideal monatomic gas, The Foundation of thermodynamics, Dispersion and the distributions of sum functions. There is an Appendix entitled "The proof of the oentral limit theorem of the theory of probability," a. table of Notations and a short Index. The physical chemist may accept, no doubt with a mild shock, that the mathcmaticrtl level of the Maxwell-Boltammn invcstigations is "quite low" and that of Gibbs' Elementary Principles of Statistical Mechanics "not high" and he may go along with the author toward the summits of Birkhoff's theorem with its implications concerning the ergodic hypothesis. The esthetic and logicd reward may be great but the new outlook cannot be very different from that so aptly stated by Tolman ("The Principles . .it is of Statistical Mechanics, Oxford Press, 1938, p. 70): evident that such studies can neither contradict the mechanical possibility for some paths, which would exhibit time averages quite different from the ensemble averages, nor eliminate the ultimate necessity for recourse to a postulate as to a priori probabilities." To t,hose students of statistical mechanics who have made the effort of mastering the Fowler-Darwin method of steepest descents as well as to the more numerous ones who have remained eatisfied with the Stirling approximation type of derive
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will prove of intenst. According to the author"'thi only essentially new material in this book consists of the systematic use of limit theorems of the theory of probability for rigorous proofs
of asymptotic formulas'' (i. e., formulas "which approach the precise ones when the number of pa~ticlesconstituting the system increases beyond any limit"). The avoidance of quantum st* tistics greatly but purposely limits the scope of the book from bath the theoretical and applied standpoints. In times like the present, when statistical mechanics enthusiastically attacks one new problem after another (as evidenced, for instance, by the colloquium recently held in Florence by the International Union of Physics), it is usoful and even essential to have available the cautious stability of books acutely concerned with fundamentals like the one under review. Should this translation do no more than succeed in obtaining the active interest of a few mathematicians as well as the studious curiosity of a few physical chemists its publication will he well justified. To some readers i t will perhaps be a matter for slight d i e appointment that the translator's customary humor and artistic akill could not be called in to relieve somewhat the arduousness of the mathematical arguments. PIERRE VAN RYSSELBERGHE T~NIYEASITY
01.OREGON
E V G E NO ~ .S ~ G O N
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CHEMISTRY OF SPECIFIC, SELECTIVE AND SENSI. TIVE REACTIONS
Fritz Feigl, Engineer, Laboratory of Mineral Products, Ministry of Agriculture, Rio d e Janeiro, Brazil; formerly Professor of Analytical and Inorganic Chemistry at the University of Vienna. Translated by Ralph E. Oesper. Professor of Chemistry, University of Cincinnati, Ohio. Academic Press, Inc., New York City, 1949. xiv i-740 pp. 29 tables. 15 X 23 cm. $13.50. THE author states in the first sentence in the preface that "during the past twenty-five yeam andytieal methods based on the properties and reactions of the substances to be detected or identified have been improved to a greater extent than in all the preceding years." Older methods have been improved, new methods developed and rtnalytical procedures placed on a scientific basis. During this same period rapid progress has been made in the development of analytical instruments that often simplify the making of quantitative measurements and gotttly extend the accuracy and sensitivity of the methods. Tho present book is "an attempt to summarize our knowledge of the soientifio background of the specificity, selectivity, and analytical procedures." No other person is better qualified to do a job of this magnitude and scope than Dr. Feigl who has contrihuted so mueh through his researches in the field of spot test analysis for mare than a quarter of a oentury. Throughout the hook the experimental side has been stressed and the author has drawn on all fields of chemistry-inorganic, organic, physical, colloid, photochemistry, etc.-in his study of specificity, selectivity, and sensitivity. There are hundreds of references to the original literature, as well as many citations to work done in Dr. Feigl'a laboratory and published here for the first time. The book is replete with critical remarks pertinent to the subject. These not only enhance the value of the book but also should stimulate research in the field of specific, selective, and sensitive reaotions. These "critical remarks" arc frequently to be found in footnotes in smell print. A hasty count by the reviewer gave no less than 190 pages having one footnote and more than 40 pages with two or three. I t would have made reading easier had these footnotes been placed in the main body of the text (in the samo small type, perhaps, to emnomiae with space). Most of these would have required little or no change in their wording. This is only a suggestion which the author may wish to consider in a future
treated are: General oomments on the analytical usefulness oi chemical reactions (Chapter I, 5 pages); characterization of chemical tests by sensitivity, selectivity, specificity, and limiting
