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 RECENT ADVANCES IN SCIENCE 521 



slightly, where it has seemed possible and necessary. It may 

 be added that the London agent for the Revue is now D. J. 

 Bryce, of 149, Strand, W.C.2. 



There is an account of the contents of several new volumes 

 of the Encyklopddie der mathematischen Wissenschaften on 

 pp. 68-9 of the above part of the Revue : the volumes referring 

 to pure mathematics which were published in 1914 and 191 5 

 are concerned with elliptic, automorphic, and modular func- 

 tions ; parts of the theories of ordinary and partial differential 

 equations and of algebraic analysis ; projective, descriptive, 

 and elementary geometry ; systems of co-ordinates ; algebraic 

 curves and surfaces ; contact transformations ; and geometrical 

 theory of differential equations. 



G. A. Miller (Amer. Math. Monthly, 1918, 25, 383-7; cf. 

 428) discusses, with an example, how a mathematical encyclo- 

 paedic dictionary should be written. A contribution to this 

 discussion is made in another article in the present number of 

 Science Progress. 



Among the papers read at the annual meeting of the 

 Mathematical Association on January 1 and 2, 19 19, were 

 T. P. Nurin's Presidential Address on " Astronomy as a School 

 Subject," W. P. Milne's account of the work of the Association 

 in the application of mathematics to industry, B. A. Howard's 

 discussion of the teaching of elementary geometry, and S. 

 Brodetsky's graphical treatment of differential equations 

 (Nature, 1919, 102, 395-6). 



Further detailed suggestions for programmes of under- 

 graduate mathematical clubs (cf. Science Progress, 1919, 

 13, 345) are given (Amer. Math. Monthly, 1918, 25, 316-20, 

 358-60, 41 1-4) respectively on geometry of four dimensions 

 (by H. P. Manning), constructions with a double-edged ruler, 

 and the cattle-problem of Archimedes. 



J. Nyberg (ibid. 337-40) shows how, in conformity with 

 his papers of 191 6 and 191 7, he would introduce exponential 

 and logarithmic functions. G. A. Miller (ibid. 287-90) gives 

 a useful exhibition of various contradictory definitions current 

 of a " discriminant." 



History. — L. M. Klinkenberg (51, 52) gives an account of 

 the origin and history of geometry in Egypt, and with Thales, 

 Pythagoras, and Plato and his contemporaries. H. B. Fine 

 (10) gives a commentary on part of the fifth, sixth, seventh, 



