molecules with internal degrees of freedom, and ( c ) cooperative phenomena and its application to nonelectrolyte solution theory. On the other hand Professor Kittel has made the much needed step of introducing many current topics or research interest (in particular transport theory) into a textbook suitable for first or second year graduate tettudonta.
Analysis of Straight-Line Data Forman S. Acton, Associate Professor of Electrical Engineering, Princeton University. John Wiley & Sous, Inc., New York, 1959. xiii + 267 pp. 46 figs. Tables. 15.5 X 23.5 em. $9.
The straight line occupies a central ZEvr \1'. SALSBURG position in the presentation and interpreThe Rice Inslilule tation of experimental results. FreHouston, Texas quently experimenters devote considerable time and ingenuity to the dcvelopment of reasonable (and sometimes unreasonable) procedures for linearizing their data. I t is the objective of this hook to guide the experimenter-analyst through Elementary Matrix Algebra the maze of regression techniques, each with its o m set of assumptions, that. has Franz E. Hohn, Associate Professor of accumulated over the past eighty years. Mathematics, University of Illinois. The author gets off to an excellent The Maemillan Co., New Yo'ork, 1958. start with a hrief discussion of the choice xi 305 pp. 16 X 24 em. $7.50. of a statistied model on which to base the anal.vsis. Most experimenters should pale This hook is the product of several considerably when, after a listing of seven years' experience with a course in linear hypothetical experiments, the author transformations and matrices, which was states ". . . it u-auld he sheer folly to apply primarily for students in a variety of fields cleaaical least-squares fitting to most of including science, engineering, economthese data." Thia phrase should frighten ics, sociology, etc. Specific applicamost people into reading the remainder of tions, however, are omitted for the sake the hook. of brevity. The text is elementary in the Well over a third of this hook deals with sense that an effort has been made to have the so-called classical model in which the it useful a t the junior or senior level. independent variable (z) is considered The book is excellent. The well-orknown (essentially) without error and ganized and clear style of presentation (almost) all of the experimental variation makes i t easy to follow and the select,ion is assumed t o b e associated with the deof topics is most appropriate for a course pendent, variable (y). Considerable emone might wish every graduate student phasisis placed on confidence intervals, in physical chemistry could have. Some and several non-pitramctrie methods are of the principles are included only in prob. discussed and exemplified. lems, a device frequently used in mathoA short chapter is devoted to samples matics. This may make it more difficult from the hivariste normal distribution. as a basis for self-education than as a The middle fifth of the book deals with course textbook. On the other hand, the the knotty problem of what to do when text and examples provide a continuity of both the independent and the dependent development adequate for one to undervariables contain error. Here the author stand the later material without working does well with his opportunity to draw d l the problems. The author, however, together the diverse work on this subject specifically recommends working most of extending over many years and several the problems to get the most out of the countries. Following this is a hrief erbook. position of how the analysis of variance The chapter topics include the introcan be applied to the simultaneous duction to matrix algebra; determinants; examination of several lines. Then comes the inverse of a matrix; rank and eqoivaa chapter on orthogonal polynomials lenee; linear equations and linear depenwhich provides detailed examples for bath dence; vector spaces and linear transforequally and unequally spaced pointe. mations; unitary and orthogonal transThe last three chapters of the book, formations; the characteristic equation of extending over only a dozen pages, coneist a matrix; and bilinear, quadratic, and of a few brief observations on transforHermitian forms. Appendixes cover the mations, the rejection of data, and models summation and product notations; the with cumulative error. An appendix is algebra of complex numbers; and the provided which gives nineteen tables general concept of isomorphism. There including several for "quick and denormais also a bibliography containing referlized" methods of analysis. ences not only to more advanced matheThe line dranings, which are used very matical treatments of the subjects but effectively, are extremely well done. also to books in which applications in the Tho reader will, nevertheless, find that various fields are discussed. the going is not easy. The style of writing The hook is reeommended as a valuahle ranges from heavy (maximum likelihood three-hundred-page collection of mathederivations) to light ("What isn't worth matical concepts and techniques useful to doing a t all isn't worth doing well!"). the modern chemist, especially if he is Sometimes the introduction to a section interested in following recent theoretical is found in the concluding paragraph of developments involving applications of the preceding section. This gives the quantum mechanics. impression that the chapters were written in one breath and makes it difficult to Uniriersity of Washington eonsider an isolated part. Seattle This reviewer feels that the author
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A532 / Journal o f Chemical Education
might well have included examples of the weighting which is sometimes requited to maintain homogeneous variance when a linearizing transiormation is made, and the recent work of Ergun on fitting families of straight lines. The treatment of cnmulative data. (Chapter 10) is much too brief considering the general lack of ~mdcrsbmdingand uhiquity of such systems. And, contrary t o t h e author's advice, the analysis of variance can present serious prohloms because of the high degree of corrclittion among the residrdr in cumulative data. Very few numerical mistakes were noted and none would mislead the reader. I n the discnsaion of rejection o i data, i t is implied that rangieod tests arc applicable when the assumption of normality is in doubt. Unfortunately range tests are also hound by the assumpt,ion of normality. I n his example of testing a value for pomible rejection, the author carries out a one-sided test, whereas a two-sided test would seem more natural. The Referenrea (38) and Additional Bibliography (39) list a wide variety of hooks end nrticlen but overlok a few important cont,rihotions such as that of Msndel and Linnig (.4nal. Chem., 29, 743-9 (1957)). The usefulness of this hook t o chemists is shown by thc fact that nine of t,he thirteen e ~ n m p l s considered s by the author are chemical. The readcr is warned.
LLOYD S. NELSON Cmernl Electric Lamp l>it,ision Cleisland, Ohm
Semiconductor Abstracts. Issue
Volume 4
-1956
Edited h y E. Paskell. Compiled h y Batt,elle Memorial Institute. Sponsore-i h y the Electrochemical Society, Inc. John Wiley Rr Sons, Ine., New York, 1959. 456 pp. 22 X 28.5 em. $12. The literabure for the year 1956 has been reviewed, including papers read s t meeti ings of. the American Physical and Electrochemical Society. 1462 papers are nhstraeted; author and snhject indexes are provided.
W. F. K.
Crystal Structures.
Supplement 4.
W. C. Wyckoff. Interscience Publishers, Inc., New York, 1959. 20 X 25 X 4 cm. $22. This material completes Chapters 9, 10, 13, 14, and 15 of the work first issucd in 1949 (see THIS JOURNAL, 26, 289 (1949) 1. The most recent supplement was issued in 1957 (35, A620 (1958) ). W3.K Volume 36, Number
9,
September
1959
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A533
