520 SCIENCE PROGRESS 



Four Lectures on Mathematics delivered at Columbia University in 1911. 



By J. Hadamard, Member of the Institute, Professor in the College de 

 France and in the Ecole Polytechnique, Lecturer in Mathematics and 

 Mathematical Physics in Columbia University for 1911. [Pp. vi + 52.] 

 (New York : Columbia University Press, 191 5. Price 75 cents.) 



The titles of these four lectures are : (1) "The Definition of Solutions of Linear 

 Partial Differential Equations by Boundary Conditions " ; (2) " Contemporary 

 Researches in Differential Equations, Integral Equations, and Integro-Differential 

 Equations"; (3) "Analysis Situs in Connection with Correspondences and 

 Differential Equations"; and (4) "Elementary Solutions of Partial Differential 

 Equations and Green's Functions." 



In the first lecture M. Hadamard treats of linear partial differential equations 

 of the second order, and considers only the results which correspond to non- 

 analytic data chiefly because there is a remarkable accordance between them and 

 the results to which physical applications brings us. The second and third lectures 

 are precisely described in their titles. In the fourth lecture the "elementary 

 solutions " referred to are a necessary base of the treatment of every linear partial 

 differential equation, such as those which arise in physical problems ; and Green's 

 functions are related to all the chief topics discussed in these lectures. There are 

 very interesting references to method and the mutual relations of geometry, 

 analysis, and physics ; and, as we should expect, the subjects are treated in a 

 thoroughly masterly fashion. 



Philip E. B. Jourdain. 



STATISTICS 



The Elements of Finite Differences. Also Solutions to Questions set for Part I. 

 of the Examinations of the Institute of Actuaries. Second Edition. By 

 J. Burn, F.I. A., and E. H. Brown, F.I. A. [Pp. iii + 289.] (London: 

 Charles & Edwin Layton, 191 5. Price 10s. 6d. net.) 



The Mathematical Theory of Probabilities and its Application to Frequency 

 Curves and Statistical Methods. By Arne FlSHER, F.S.S. Translated and 

 Edited from the Author's Original Danish Notes with the Assistance of 

 William PONYNGE, B.A. With an Introductory Note by F. W. FRANK- 

 land, F.I.A., F.A.S., F.S.S. Volume I. Mathematical Probabilities and 

 Homograde Statistics. [Pp. xx + 171.] (New York: The Macmillan 

 Company, 1915. Price Ss. bd. net.) 



The Construction of Mortality and Sickness Tables. A Primer by W. PalinJ 

 Elderton and Richard C. Fippard. [Pp. vi + 120.] (London : Adam 

 & Charles Black, 1914. Price .) 



Vital Statistics Explained. Some Practical Suggestions by Joseph Burn, 

 F.I.A., F.S.I. [Pp. x + 140.] (London : Constable & Co. Price4j.net.) 



The study of statistics has become so important for almost every science that 

 t is high time for men of science to be in possession of a single text-book on the 

 subject which will enable any well-educated person to apply statistical methods 

 to his particular branch of knowledge. Unfortunately at present we have to do 

 as best we can with a number of small primers dealing only with special facets, 

 eked out by articles in Biometrika and other journals, none of which supply 

 the need. 



The second edition of the well-known book by Messrs. Burn and Brown will 



