Notices respecting New Books. 351 



After a concluding chapter, there occurs a valuable bibliography 

 of over a hundred references, general and special. 



To mathematical treatment this work makes no pretence, scarcely 

 a couple of pages of equations occurring throughout the text. Its 

 strength lies in its experimental and graphical treatment, and in 

 the photographic records giving analyses of sounds from the 

 simplest vibrations of forks up to vowels and the vibrato notes of 

 operatic artists. 



Both for showing what has been accomplished up to date and 

 for the stimulation of further research on this subject, this work 

 may be heartily recommended. 



A Course of Modern Analysis: an Introduction to tlie General 

 Theory of Infinite Series and of Analytic Functions ; with an 

 account of the Principal Transcendental Functions. By E. T. 

 "Whittakee, F.R.S., and Gr. N. Watson, M.A. Cambridge : 

 At the University Press. 1915. Second Edition, completely 

 revised. 

 The first edition of this well-known work was reviewed in these 

 pages in 1904 (Phil. Mag. vii. p. 605). In the preparation of the 

 new edition Professor Whittaker has had the assistance of his 

 friend and former pupil, Mr. G. N. Watson, to whom are due 

 the new chapters on Eiemann Integration, on Integral Equations, 

 and on the Riemann Zeta-Eunction. In addition to these, however, 

 important changes have been made throughout the work. New 

 paragraphs have been added, certain discussions formerly included 

 in one chapter are now rearranged and distributed in two, and in 

 many cases the demonstrations have been altered so as to be in 

 line with the growing demands for greater rigour. The main 

 character of the treatise remains the same, Part I. treating of the 

 Processes of Analysis, and Part II. of the Transcendental Functions. 

 In the Second Part there are introduced, in addition to the Zeta 

 Eunction already named, special discussions of the Mathieu 

 Function and the Theta Functions. There is no doubt that all 

 these changes are of the nature of improvements, and have led 

 naturally to a marked increase in the size of the volume. Nor is 

 this increase merely to be measured by the greater number of 

 pages, practically one half more than the number in the first 

 edition. An important feature of the new work is the use of 

 large and small type to distinguish what might be termed the 

 main stream of discussion from what is more subsidiary ; and 

 by this means more matter is packed into the page. Numerous 

 examples are appended to the chapters, and many of these are 

 quite as important as the illustrations given in the text. By such 

 methods the volume is kept within reasonable dimensions, and yet 

 the ground covered is amazingly extensive. The work abounds in 

 historic references and indications to the student for more extended 

 reading in both original memoirs and treatises on special branches. 

 It is interesting to note that recent work done in Professor 



