298 Scientific Intelligence. 



two parts which deal respectively with the processes of analysis 

 (223 pages) and with the transcendental functions (312 pages). 

 In order to give a general idea of the scope of the course and to 

 suggest the kinds of theorems which are discussed, the titles of 

 the chapters will now be quoted. 



"Part I. I Complex Numbers. II The Theory of Conver- 

 gence. Ill Continuous Functions and Uniform Convergence. 

 IV The Theory of Riemann Integration. V The fundamental 

 properties of Analytic Functions ; Taylor's, Laurent's, and Liou- 

 ville's Theorems. VI The Theory of Residues ; application to 

 the evaluation of Definite Integrals. VII The expansion of 

 functions in Infinite Series. VIII Asymptotic Expansions and 

 Summable Series. IX Fourier Series. X Linear Differential 

 Equations. XI Integral Equations." 



"Part II. XII The Gamma Function. XIII The Zeta Func- 

 tion of Riemann. XIV The Hypergeometric Function. XV 

 Legendre Functions. XVI The Confluent Hypergeometric Func- 

 tion. XVII Bessel Functions. XVIII The Equations of Mathe- 

 matical Physics. XIX Mathieu Functions. XX Elliptic Func- 

 tions. General theorems and the Weierstrassian Functions. 

 XXI The Theta Functions. XXII The Jacobian Elliptic Func- 

 tions." 



As may be inferred from the above titles, the book is of a rela- 

 tively advanced character. The analysis in chapter X is mainly 

 theoretical and consists, for the most part, in existence theorems. 

 Physicists will be especially interested in chapter XVIII. Numer- 

 ous illustrative examples for solution by the reader are scattered 

 through the text and lists of miscellaneous problems are appended 

 to the chapters. At the ends of the chapters bibliographical 

 references may also be found. The volume closes with author 

 and subject indexes. The decimal system of paragraphing is 

 used throughout and every precaution seems to have been taken 

 to minimize the number of typographical errors. h. s. tj. 



10. Edinburgh Mathematical Tracts; edited by E. T. Whit- 

 taker. London, 1915 (G. Bell and Sons). — No. 1. Descriptive 

 Geometry and Photogrammetry y by E. Lindsay Ince. Pp. viii, 

 79. No. 2. Interpolation and Numerical Integration; by David 

 Gibb. Pp. viii, 90. No. 3. Relativity ; by A. W. Conway. 

 Pp. 43. No. 4. Fourier's Analysis and Periodogram Analysis ; 

 by G. A. Caese and G. Shearer. Pp. viii, 66. No. 5. Spheri- 

 cal Triangles ; by Herbert Bell. Pp. viii, 66. No. 6. Auto- 

 morphic Functions ; by Lester R. Ford. Pp. viii, 96. 



The first, second, fourth, and fifth Tracts present short courses 

 for the mathematical laboratory, the chief object of which is to 

 give the non-technical student much needed practice in graphical 

 construction and numerical computation. Tract No. 3 contains 

 the material of four lectures delivered before the Edinburgh 

 Mathematical Colloquium. The subject is developed in the his- 

 torical order and is brought down to the stage in which it was 

 left by Minkowski. The point of view is primarily mathematical, 



