APRIL. 1952
209
they do not. Something simple and direct seems to be conveyed by words such as 'resonance' and 'activity,' which is not legitimately conveyed a t all. By certain descriptions, whioh it is easy t o give, one is reminded of Alice: 'Somehow it seems to fill my head with idezm-only I don't exactly know what they are.' Many of the mathematical equations whioh serve important technical purphses in the modern forms of theoretical chemistry are of a highly abstract kind, but they have acquired a dangerous seductiveness in that they clothe themselves rather readily in metsphars." There is little development of the concepts or the mathematics to the point of use. The reader of this book will be little abler to apply the concepts in obtaining numerical answers to concrete problems than he was before reading it. This characteristic of the baok ia a limitation, not a defect. The development of such ability is not part of the purpose of the book and could not have been added in a book of this ske. There remains the question how far the author has succeeded in realizing his objective. The material presented is unified fairly well-perhaps as well as can ever be donein a subject that is still alive and growing. Part of this unity has been attained, however, by subordinating those concepts that do not fit into the pattern that Professor Hiushelwood has used. Thermodynamics is treated, for example, as an outgrowth of the ideas that are involved in the world of moleoulsr chaos, and 22 pages, less than five per cent of the book, are given to thedevelopment and discussion of the principles of this subject. This treatment does not seem to accord with thestill considerableimportance and independence of phenomenological thermodynamics in current thinking in physical chemistry. The justification that isgiven for this treatment oansists merely of statine - some of the armunents against it in phraseology chosen to be unconvincing. Whether such a treatment as this book presents is desirable would seem to depend in part on whether unity in science is or is not something to be sought for its own sake. If the task of a science is to describe part of the red world, rather than to fit the real world into an existing pattern, it would seem that unity should arise, if it exists, from the observations and their interpretation. The assumptions that unity does, or that it does not, exist in such a science as physical chemistry seem equally gratuitous. This book is impressive and successful, on the other hand, if it is viewed as an effort to see how much of physical chemistry can be brought together under the domination of one single set of ideas. Furthermore, the allocation of space, and the viewpoint, reflect fairly well current thinking among those who are advancing the subject. This baok compares reasonably well with "Annual Reviews of Physical Chemistry" in these respects, . . for. .example, . . and both contrast strikingly with most textboob of thesubject. This book is recommended for all those who me concerned with physical chemistry per se, and who already have gome knowledge of the subject.
technology are listed under subject headings substantially the same as those of the sections of Chemice2 Abstracts. Textbooks and ~pecialworks of reference are described under the following headings: historical; analytical; inorganic and physical; mineral and metallurgical; biochemical; organic; annual reviews and similss volumes. One chapter describes the technique of making a searoh of the literature, and one section of the appendix describes in more detail an example of an organic chemical search ("The nitration of hexane"). Other sections of the appendix list information ahont some old and obselete journals, and give tables listing the year and volume numbers of the main chemical publications. Dr. Dyson writes succinctly and has produced a very readable and instructive volume. The binding and typography leave something to be desired. The author emphasizes that this book is intended to be a beginner's introduction to the literature of chemistry. He states further that the book ". . .has been made 'non-exhaustive' with the express purpose of keeping its price within the reach of all students of the subject." These objectives are amply fulfilled. ROBERT 8. CASEY
W.A. S a ~ a ~ s e n PCOILPWT m Fom M~orsoli.IOWA
0
LINEAR COMPUTATIONS
Paul S. Dwyer, Professor of Mathematics, University of Michigan. John Wiley & Sons, Inc., New York, 1951. xi 344 pp. A p proximately 160 tables. 15 X 23 cm. $6.50.
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LINEAR algebraic equations appear in so many different fields that it is not surprising that there are several literatures on their solution: e. g., those ofptatisticians, theoretical physicists, geodetists, numerical analysts, engineers, psychologists, etc. As the problems vary considerably among these fields, the methods show corresponding variations, and there is surprisingly little cross,communication. The present author is a. statistician, and the bookshows this in numerous ways: preference for elimination methods, highly developed technique on desk mnchimery, knowledge of statistical literature above all other, and perhaps also the lack of mathematical sophistication asked of the reader. By "linear computations" the author means the solution of systems of linear algebraic equations, the inversion of matrices, the evaluetion of determinants and subdeterminants, and closely related topics. The principal purpose of the book is to present effioient techniques of carrying out linear computations on desk calculators. The author dismisses iterative methods (page 252), and devotes the book to mesentine numerous variations of Gaussian pivotal eliminatidn. ~ h i s l i sbasically the method taught in high school, but few casual computers realiee the great efficiencies possible in the arrangements which have been developed by Doolittle, Cholesky, Banachiewicz, Crout, Dwyer, and others. These efficient methods take full advantage of the BTEFFENB ability of the desk oalculator to accumulate products, and minimiae the slow and inaccurate operations of recording. Professor Dwyer is an authority on these efficient techniques and presents them in a carefully prepared order. Each is accompilnied by a table illustrating the arrangement of the computing sheet and A SHORT GUIDE TO CHEMICAL LITERATURE 0 one or more tables illustrating the computation for systems of G. Malcolm Dyson, Longmans, Green and Co., New York, 1951. orders 3 to 5. There are sections on such related topics as solving systems viii 144 pp. 4 tables. 13 X 19.5 ern. $2. with certain variables and equations suppressed, evaluating linear T m bookis divided into five main sections: general dictionaries forms, and calculating the characteristic polynomial of a matrix and encyclopedias; chemical journals and periodicals; abstract (for the latter problem the most efficient techniques are omitted). journals; textbooks and special works of reference; and reference The subject of errors is treated unusually completely. There is works on medicinal chemicals. The latter section is used as an an early chapter on the representation of approximate numbers. example of the literatwe of a subject on the border line between This material is amlied to the evaluation of determinants chemistry and another science. whose elements are approximate numbers, and to bounding the In the above sections the author lids reoresentative exrun~les errors in the solutions of linear systems resulting from nncertainof book3 and jouruuls and desrril,e~each to the lrature of its ties - - in -~ t,he ~roeffinients~ .-.-. contrntc, roverage, rtr. In rhr rection on jourrla1.e tllr variuus The present book has several chapters which constitute a tmrionnl and ~perializedjournals arc dewibed, and jounoala of textbook on using the desk calculatar. The author stresses the
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JOURNAL OF CHEMICAL EDUCATION
210 importance of choosing a machine with "complete carry-over" and with an extra digit in the products register. Principles of oompntational design are set forth, to wntrol blunders and round-off errors, to provide checks, and to minimize the recording effort. A chapter is devoted to the reduction of error accumulation in the evaluation of various statistical formulas. The notation is literally that of easy high-school algebra. In the middle af the book determinants and matrices are defined, and thereafter their mast elementary properties are used. But all the methods of elimination are given in earlier chapters in expanded notation. The hook has over 160 carefully prepared tables and numerous exercises for the readen There are extensive references for each section, strong in the English language, weaker in European material, and devoid of Russian references. The book will surely be a standard reference on elimination methods, and may be consulted profitably by computers a t all levels of mathematical education. There is nothing comparable in the literature. It is unusually free of misprints and has good indexes. Because of its emphssis on techniques as opposed to the development of mathematical tools, it is not recommended as a textbook for wllege students or others who wish to gain a deep insight into the nature of linear computations. Tbese people should begin elsewhere by acquiring a thorough knowledge of matrix theory. GEORGE E. FORSYTHE NATIONAL BOREADor STANDARDS Los ANDELBB. CILIFOB~A
0
STATISTICAL METHODS FOR CHEMISTS
W. I. Youden, National Bureau of Standards, Washington, D. C. 126 pp. 3 figs. John Wiley & Sons, Inc., New York, 1951. x 6 6 tables. 15.5 X 24 om. $3.
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T m s little book is for readers experienced in chemical and physical measurements but untrained in statistical methods, and who are perhaps even unaware of the aid thst the statistical viewpoint can give in the interpretation of experimental dsta. The attentive reader should gain a good idea of what is meant by some important statistical terms, how the precision of a set of measurements is probably best rated, whether the difference between the averages of two sets of data is significant, how constant errors are detected, bow best values are found for the slope and intercept of a straight line thst represents experimental data. Beyond that, concluding chapters tell how to pool or combine data from different sources, how to improve precision and recogniee that it has been improved, how interact ing or independent factors contributing to experimental multa m v be identified. Most of the many short tables are worked numerical examples. This easy introduction to stastistical methods deserves readers in other fields than chemistry, since the ideas it presents are equally valid in other experimental sciences. On the other hand, there might well have been some mention of the ways in which statistical methods have aided chemistry, beyond the range of this book. To mention only three: there is the statistical evidence that cellobiose, rather than a triose or tetrose, is the repeated unit in the cellulose chain-molecule; the statistical treatment of the variation of viscosity with different types of scission of complex molecules; the statistical treatment of fractional distillation and precipitstion. The book is "chsracterised by the complete absence of statistioal theory and proofs." Nevertheless, only thoughtful and persistent readers will be able t o make good use of it, and these might have found a few simple proofs to be stimulating and clarifying. Nothing is said about the origins of our faith in a normal distribution of errors. It is not really based on mere experience nor demonstrable by mathematical proof. On the contrary, it is a sort of philosophy, which inoidentdly points out when a normal distribution is not to be expected. For example, are teachers justified in adjusting student grades to s probability curve?
General references are given to a few hooks covering the subject matter of the present book. More specific references to individual topics would have been helpful, and especially to applications not treated. Many of the "chemists" to which this book is addressed will be teachers of chemistry. Tbese ,will at once conclude thst the practice of obtaining s. semester grade by averaging a set of examination grades is not statistically justified. Rut wheremay one turn tolearnmore? HORACE G. DEMING
Uxrvrasmr or A ~ w m Hoaofinm. HAWAII
X-RAY ANALYSIS OF CRYSTALS
0
1. M. Bijvoet, Professor of Physical Chemistry, University of Utrecht, the late N. H. Kolkmeyer, and Cornline H. MocGillovry, Professor of Crystallography, University of Amsterdam. Based on a translation by H. Littmon Furfh. Butterwortha Scientific Publications, London; Interscience Publishers, Inc., New York, 1951. xii 304 pp. 226 figs. 19 tables. 15.5 X 25.5 cm. 56.50.
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THE Dutch and German editions of this book have been well and favorably known, especially in Europe, for some time. It is now a pleasure to welcome an English version. The authors have had long experience in crystal structure analysis. Professor Bijvoet's standing among his fellow workers in this field is attested by his recent election to the presidency of the International Union of Crystallography. It is not surprising, therefore, to find this book exhibiting a high degree of scientific accuracy. The authors have also shown goad judgment in their choice of topics covered and the allotment of space to each. The presentation is lucid. A reader would not guess that the book was originally written ins. language other than English. All X-ray diffraction workers will surely want this excellent book, for it is full of useful reference material. I t can also be recommended for exsminstion and study by others who wish to become acquainted with themethods of X-ray crystallographyand the results obtained thereby. It would be suitable for s course for graduate students in chemistry. The chapters dealing with typical and significant crystal structures are especially commendable. Teachers. advanced students. and manv other chemists will h d them interesting,instructive and up to date. The publishers, like the authors and the translator, have done their jab well. MAURICE L. HUGGINB K o o u Resmmos L * ~ O R A T O R I'~ . Rocmema. Nan Yonx
0
TREATISE ON ORES AND ASSAYING
Lozorus Ercker. Translated from the German edition of 1580 by Annelieae Grijnholdt Sisco and Cyril Stonley Smith. The University of Chicago Press, Chicago, 1951. miii 360 pp. 59 figs. 17.5 X 27 cm. 510.
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WITHthe publication of this book, the modern reader has access to all the lesding works on metallurgy of the sixteenth century. The little "Bergwerk und Probierbiichlein" and the "De la Pirotechnis" of Biringuccio have been translated by Smith and his associates, and the Hoover translation of Agricola's "De Re Metallica" has recently been reissued. These, together with Ercker's "Treatise," were the standard textbooks of the mining engineer for several centuries. Many of the methods they describe are still in use. Thus, they me fundamental to an understanding of the development of metallurgy and metallurgical chemistry.
Ercker's hook is not inferior to any of the others. Ercker was a ~racticalmetallurgist, Superintendent of Mines to the Emperor Rudolf I1 in Bohemia. He wrote his book for the instruction of young miners and assayers, and so be gives complete details for
