6 7 8 SCIENCE PROGRESS 



MATHEMATICS 



An Elementary Course of Infinitesimal Calculus. By Horace Lamb, M.A., 

 LL.D., F.R.S , Professor of Mathematics in the Victoria University of 

 Manchester. Third Edition. [Pp. xiv + 530.] (Cambridge : at the 

 University Press, 1919. Price 20s. net.) 



The new edition of Prof. Lamb's Treatise is extremely welcome. This 

 work has for a long time past been regarded, by the majority of teachers 

 of Mathematics, as the best account in our language of the Calculus as 

 designed for students whose aim is less the study of its logical principles 

 than the cultivation of a facility for applying its methods to problems which 

 arise in the application of mathematics to other branches of Science. In 

 this regard the book has never had a serious rival. "We do not wish to 

 imply that logical proofs have been neglected. For Prof. Lamb's treatise, 

 embracing as it does the Differential and Integral Calculus and the more 

 important types of Differential Equations, is quite unusually logical in its 

 procedure, avoiding, at the same time, the repellent atmosphere suggested 

 too often to a physicist or an engineer, by the attempt to give really rigorous 

 statements of the underlying assumptions in theorems which he would 

 often prefer to take for granted. We regard it as the only work on this 

 subject which has as yet succeeded in striking the proper note, and the 

 call for a new edition is a sign of the fact that those whose work involves 

 applications of mathematics are beginning to a greater extent to be really 

 interested in the subject itself, and to appreciate some of its beauty and 

 generality without too close a study. 



The work is too well known for it to be necessary to indicate its main 

 outlines, and we may confine our attention to the main respects in which 

 it differs from previous editions. At the outset, we may say that all the 

 changes made are to the advantage of the book, having regard to its special 

 purpose. The earlier treatment of the more algebraic questions, such as 

 the properties of series and their convergence, has now been restricted almost 

 exclusively to power-series. This is an advantage in that these are the 

 only series with which the physicist or engineer is ordinarily concerned. 

 This modification is of the greatest value, and is the most important difference 

 introduced. Some of the more physical applications of integration, such as 

 the determination of mass centres, have been deleted, being contained 

 in other treatises on the special subjects since published by the author. 

 But we are pleased to observe that the character of the illustrative examples, 

 and of the problems proposed at the end of each chapter, has been preserved, 

 for experience has shown that they constitute, for the elementary student, 

 one of the fundamental merits of the book in a sense surpassed by no other 

 work yet brought to our notice. 



The new edition is, like those preceding it, in every way worthy of the 

 best traditions of the Cambridge University Press. 



Dorothy Wrinch. 



Unified Mathematics. By L. C. Karpinski, Ph.D., Associate Professor 

 of Mathematics, University of Michigan; H. Y. Benedict, Ph.D., 

 Professor of Applied Mathematics, University of Texas ; and J. W. 

 Calhoun, M.A., Associate Professor of Pure Mathematics, University 

 of Texas. [Pp. viii + 522, with numerous diagrams.] (Boston : 

 D. E. Heath & Co. ; London : George G. Harrap & Co., 1919. Price 

 10s. 6d. net.) 



In this little book, the authors present a course of mathematics covering 

 the elementary parts of algebra, trigonometry, and analytical geometry. 

 The book is interesting as an attempt to weld together those portions of 



