Notices respecting New Books. 445> 



thermal relations, together with their other physical and mecha- 

 nical properties (200 pp.). In the second part (230 pp.) a study is. 

 made of particular alloys. In spite of the very modest preface, 

 we have not come across any other text-book in which so much 

 information of such varied kinds is given. Whether the reader 

 wishes for a description of experimental methods or of the modern 

 data in regard to coexistent phases, or data in regard to com- 

 mercial applications (including relative cost of materials), all is set 

 forth clearly here. There are numerous diagrams representing 

 the physico-chemical properties of the alloys selected for description.. 

 We think that this book will be found to be a most useful one. 



Vectors and Vector Diagrams applied to the Alternating Current 

 Circuit. By Q. Ckamp andC. P. Smith. London : Longmans, 

 Green, & Co. 1909. 



This should prove a valuable book to the student of electrical 

 engineering. With a slightly modified notation the authors 

 discuss clearly and systematically the methods of vectorial graphics 

 which have been developed during the last twenty years. These 

 methods have grown naturally out of Maxwell's theory of the 

 sinusoidal current and the geometrical representation of the 

 complex variable. The first three chapters contain a presentation 

 of the foundations of the method, after which follow important 

 chapters on self and mutual induction, the transformer, motors 

 of the induction type, and alternating current commutator motors.. 

 There is, then, a mathematical chapter on the product of two 

 vectors leading up to the two concluding chapters, which deal at 

 considerable length with locus diagrams and examples of the appli- 

 cation of locus diagrams. The book is well illustrated by numerous 

 vectorial diagrams, which are all-important in work of this kind. 



The Elements of Non-Euclidean Geometry. By Julian Lowell 

 Coolidge.' Oxford : at the Clarendon Press. 1909. 



The Harvard Professor has in this book given a well-planned 

 exposition of non-Euclidian geometry of three dimensions. As 

 explained in the Preface, he approaches the subject from three 

 different points of view, namely : (1) The elementary geometry of 

 point, line, and distance ; (2) Projective geometry and the theory 

 of transformation groups ; (.3) Differential geometry with the 

 concepts of distance-element, extremal, and space constant. 

 Chapters XVI II. and XIX. treat respectively of the two last 

 methods. The other sixteen chapters contain an instructive de- 

 velopment of the first method. Professor Coolidge builds the 

 system on XIX Axioms, whose consistency is discussed in 

 Chapter VI. for the three types of geometry — the Euclidean, the 

 hyperbolic, and the elliptic. Thereafter follows the geometrical 

 superstructure of which the foundations have been laid in the 



