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companion series to the previously established M~morial des Sciences Math~matiques devoted exclusively to mathematical subjects of a most advanced type. These volumes are not original memoirs but rather a critical exposition of the latest progress and present state of the subject under discussion. The two volumes above noted are the first of the series to appear. Doctor de Broglie's contribution deals with the abstract concepts of t h e wave-motion mechanics according to modern ideas of space and time. He shows how it has given new meaning to dynamic phenomena, the service it has rendered in the physics of the atom and how it constitutes a new mode of a t t a c k upon those profound problems already approachable by the theory of relativity. The volume constitutes a profound analysis and development of the ultra-modern concepts of mechanics which are applicable to the new atomic theory. Doctor de Gramont's subject is of a more tangible character. Telemeters or range-finders are an indispensable part of the equipment of modern warfare which have assumed a variety of forms in the course of the development of a practical and accurate instrument adapted to the exacting service of field conditions. The work in general is devoted to the description of the optical system and its functioning of the short-base telemeter now widely used in all branches of artillery service. Several forms of these telemeters are described with an explanation of their optical systems, methods of calibration and practical data, L. E. P. A TEXTBOOK OF ORGANIC CHEMISTRY. By Joseph Scudder Chamberlain, Ph.D., Massachusetts Agricultural College. Second Edition Revised, 9Ol pages, illustrations, 8vo. Philadelphia, P. Blakiston's Son and Company, 1928. Price, $4The author who attempts to include in one moderate sized volume a comprehensive summary of organic chemistry has no easy task. He suffers really from the embarrassment of riches, for the amount of information now available concerning both the natural and artificial substances included under the term " o r g a n i c " is enormous and is increasing with accumulating rapidity. The present volume contains a very large amount of information on all the important departments of organic chemistry. Of recent years the extensive development of bio-chemistry, as it has been called, especially in its applications to physiology and pathology has compelled a separation from the general chemical literature into specialized manuals for use more particularly in medical schools. Incidentally it may be mentioned, though it has no great relevancy to the present criticism, t h a t a strong tendency has been developed to assign the teaching of bio-chemistry and the writings of its textbooks to those having degrees not in medicine b u t in science or philosophy. We find as a result of this t h a t a considerable proportion of the faculties of our leading medical schools contain teachers t h a t have not been trained in medical science. It is not appropriate to discuss here the advisability of this method. It is being carried out, and until some definite result, favorable or unfavorable, is manifested it will be unwise to give a positive opinion. Turning to the work in hand which, being a second edition, has thus given evidence of its suitability, the descriptive matter begins as might be expected with t h a t well-known typical molecule, methane, " t h e baby figure of the giant
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[J. F. I.
mass of things to come." Practical information is scattered liberally through the volume in connection with the descriptions of compounds and the development proceeds as usual in textbooks of this character. A noticeable point of difference which will probably be noted more and more in manuals of this type is the treatment of the proteins in connection with the amino-acids following immediately after the starches and sugars. Heretofore we have always had these complex compounds treated at the end of the volume, often somewhat superficially because the great majority of chemists are only superficially familiar with them. Research has brought these proteins much more into the light as regards composition and we may expect much greater information from the active research now being pursued. The volume presents therefore a very satisfactory account of all the basic phases of organic chemistry and will serve well for the student in t h a t field. It is excellently printed with extensive presentation of structural formulas, a detailed table of contents and a good index. HENRY LEFFMANN. LEMONS SUR LES S~RIES DIVERGENTES. Par t~mile Borel, Membre de l'Institut, Professeur ~ ]a Sorbonne, Directeur honoraire de l'I~cole normale sup6rieure, avec le concours de George Bouligand, Professeur & la Facult6 des Sciences de Poitiers. Second edition, 260 pages, 25 x I6 cm., paper. Paris, G a u t h i e r Villars & Cie., I928. Price, 4 ° francs. The influence of Professor Borel's "Lemons" which first appeared in I9OI has done much to stimulate activity in the study of divergent series and their application. In preparing this second edition, M. Bouligand has adhered to the general plan of the original work, yet including an account of recent progress in setting forth the origin of the processes of summation, their general characteristics and the conditions for their concordance. Stress has been laid on applications which reveal the relation of the subject to other theories of analysis. For example in the third chapter a consideration of trigonometric series brings into view two ideas which are essential to the foundation of summation processes, namely, mean value and factors of convergence. The work is addressed to the pure mathematician rather t h a n to the reader who seeks directly applicable mathematical data. Beginning with a historic general review, the chapter headings are: I. Asymptotic series. II. Continued fractions and the theory of Stieltjes. III. The theory of summable series. IV. Summable series and analytical expansion. V. Expansion in series of polynomials. VI. (Appendix) Modern Development of the theory of divergent series. L.E.P. THE A. C. COMMUTATOR MOTOR. By C. W. Olliver, B.Sc., E.S.E. (Paris). xi28I pages, illustrations, plates, 8vo. New York, D. Van Nostrand Company, I927. Price, $7.5o. The alternating-current system as a method of power-supply with its intercommunicating net-work which now include wide areas of service is gradually eliminating the direct-current motor from the field of quantity-supply and with it, the sometimes inevitable but often avoidable commutator trouble. The one important exception is in railway engineering where the direct-current motor still prevails, but part of this condition, the author suggests, may be chargeable to "bureaucratic engineering," not uncommon in public utility organizations.