RECENT ADVANCES IN SCIENCE 



MATHEMATICS. By Philip E. B. Jourdain, M.A., Cambridge. 



It is curious to read in the list of new publications in the 

 Bulletin of the American Mathematical Society (1915, 22, 155) 

 that another part of the French Encyclopedic des sciences mathe- 

 matiques was published by Teubner at Leipzig in 191 5. It is 

 to be hoped that this is an indication that the truth that 

 science is not merely a national question is by no means 

 always denied. 



Among the mathematicians who have died during the year 

 191 5 are to be mentioned, besides Morgan William Crofton (see 

 Science Progress, 191 5, 10, 276), the American George 

 William Hill (1 838—191 5), whose name is associated with dyna- 

 mical astronomy and in particular the theory of the moon's 

 motion, in which infinite determinants were introduced ; 

 William Grylls Adams (1 836-191 5), whose mathematical work 

 was mainly in applications to physics ; and Henry William 

 Lloyd Tanner (1851-1915), whose original work was mainly on 

 the theory of differential equations, the theory of numbers, 

 cyclotomy and group-theory. Notices of all these men appear 

 in Proc. Lond. Math. Soc. 191 5, 14, xxix. 



History. — Prof. Gino Loria (Scientia, 191 5, 18, 357) gives a 

 sketch of the conceptions of infinity and infinitesimal among 

 the mathematicians of antiquity. It is remarkable that Zeno 

 should be said to come, in history, after Democritus, and that 

 Zeno's two last arguments, which are by far the most inter- 

 esting, should not be mentioned, especially as neither the 

 mistake nor the omission is made in Loria 's Le Scienze esatte 

 nelV antica Grecia of 19 14. The second part of the article 

 (ibid. 1916, 19, 1), which deals with the conceptions from the 

 middle ages to the end of the seventeenth century, is of great 

 interest and contains some things which are new to most of 

 us. Loria puts in a strong plea for the publication of all the 

 manuscripts both of Newton and Leibniz. In connection with 

 the subject of the first part of Loria 's article, it should be men- 



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