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X. Notices respecting New Books, 



Functions of a Complex Variable. Professor James Pierpont. 

 G-imi & Co. 20s. net. 



HPHIS volume deals with the elementary parts of the theory of 

 . functions of a complex variable, and is the outcome of lectures 

 given over a considerable number of years to students of Yale 

 University. 



The opening chapters give an account of the exponential, 

 circular, hyberbolic, and other functions, followed by the consi- 

 deration of differentiation and integration, the general properties 

 of analytic functions, infinite products, and asymptotic series, in 

 the latter case with reference to Gamma and Bessel functions. 



To illustrate the general principles of the theory, a brief 

 treatment is given of the elliptic functions, more particularly 

 from the standpoint of their most characteristic property of 

 double periodicity. The final chapters, devoted to linear differ- 

 ential equations, the functions of Legendre, Laplace, Bessel, and 

 Lame, with their more important properties, will appeal especially 

 to the student of mathematical physics. 



Professor Pierpont's style is clear and simple and his treatment 

 sound and thorough. The book can be heartily recommended to 

 students who need a work in which the principles of the function 

 theory are carefully presented. It will serve as a useful intro- 

 duction to the subject, and will, no doubt, arouse the interest of 

 students and induce them to read the more advanced treatises and 

 original memoirs mentioned in the text. Even the private student, 

 who has not the advantage of a teacher's assistance in overcoming 

 his difficulties, should find the book particularly helpful. 



XI. Intelligence and Miscellaneous Articles. 



ON THE STRUCTURE OF THE SPINEL GROUP OF CRYSTALS. 

 To the Editors of the Philosophical Magazine. 



GENTLEMEN, — 



T HAVE recently received from Mr. S. Nishikawa a copy of a 

 -*- paper which he contributed last December to the Proceedings 

 of the " Tokyo Mathematico-Physieal Society." It deals with the 

 structure of the spinel group of crystals. In August last you 

 were good enough to publish an account of some experiments of 

 my own on the same subject. I need hardly say that if I had 

 known of Mr. Xishikawa's work I shouhl not have written my 

 paper without referring to it. 



I am very glad to find that though our methods were eutirelv 

 different there is no disagreement between our results. 



Tours &c. 



Dec. 15, 1915. W, H. Bragg, 



