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fragment of a lattice and D is the unit of pattern, the composite distribution is that of a small crystal. The transforms of small cubic crystals bounded by various forms are discussed in Chapter i . The possibility of the use of the Fourier transform is mentioned as an aid in the determinafion of the structures of megamolecular crystals in which the structures and even to some extent the compositions of the molecules are unknown. However, for the present we may expect the principal applications to continue to be in determinations of crystal structures containing molecules whose geometry is known a t least approximately. The best information obtained so far concerning the detailed principles upon which the structures of megamolecular crystals are based has come from the relatively few complete structural investigations of simple molecules related to the large molecules. Mathematically, Dr. Wrinch’s book is well preeented. The text is expressed in a compact style, which however is not always clear grammatically (e.g., parts of pages 19, 23, 63, 65, i o ) . T h e printing, binding, and paper are quite good. This excellent book can be recommended highly to anyone interested in the \r.iiys in which the Fourier transform can be used in structural analysis. WILLIAXS . LIIT.COMB. Fundamentals of Semi-micro Qualitative Analysis. By CARLJ. ENGELDER.54 x 8g in.; vi+ 385 pp. New York: ,John Wiley and Sons, Inc., 1947. Price: $3.50. This book differs markedly from the earlier conventional book on Semi-microQualitative A n a l y s i s by Engelder, Dunkelberger, and Schiller in that the theoretical material and laboratory directions are not separated. Each of the first five chapters comprising P a r t I, The Cations, begins with a discussion of some phase of the theory of qualitative analysis, which is followed by a brief discussion of the chemical properties of the ions, preliminary experiments that aid in carrying out the analysis, and a procedure for the analysis of the group. In each chapter, exercises are interposed a t suitable points. Advantage is taken of the simpler chemistry of the ions usually placed in Groups IV and V to pass rapidly into the theories fundamental to the proper understanding of qualitative analysis. Discussions of the ions of Groups 111, 11, and I then follow in t h a t order. Each of the three chapters comprising P a r t 11, The hnions, contains a discussion of the anions, procedure for the analysis of the ions, and some theory. As in Part I, exercises are placed to enable the student to determine whether he has grasped the subject or not -such as the p H of solutions, the theory of neutralization and hydrolysis, and the electrochemical theory of oxidation. I n Part 111, the systematic analysis of liquid and solid samples is discussed for both cations and anions. I n the Appendix is a discussion of colloids; the mathematics involved in qualitative analysis; suggestions to the instructor, including a weekly schedule; lists of apparatus and reagents; tables of the concentrations of reagents; logarithms; etc. The reviewer thinks that the mixing of theory and laboratory directions is a p t to confuse the student. Furthermore, if the anions are not studied, the theory i n this part will have to be worked into that given with the cations. Some of the statements in the theoretical part are questionable; for example, on page 37 the ionization of sodium chloride is said t o be “actually 85.2 per cent,” and on page 152 ff. “the per cent of ionization of 0.1-M sodium hydroxide, hydrochloric, and nitric acids is 91-92%, while that of uni-univalent salts is 8&85%, uni-bivalent salts is 65-75%, and that of bi-bivalent salts is 35-45%.” The use of single and double arrows is confusing. On page 62, a single arrow is used in the equation for the precipitation of a difficultly soluble substance, and on page 64 double arrows are used. Similarly, single arrows are found i n equations used t o write expressions for the appropriate equilibrium constants on pages 68, 135, and 189, and double arrows on pages 184 and 261. The expression for calculating the concentration of a n ion, “Molarity x per cent of ionization” on page 157 is only partly correct. The procedures in general are conventional and are undoubtedly satisfactory. G. B. HEISIG.