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
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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
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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
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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
