RECENT ADVANCES IN SCIENCE 91 



the logic of relations (of De Morgan, C. S. Peirce, and Schroder) 

 which is necessary for founding arithmetic, and occupies an 

 important place in the writings of Frege and Russell. English 

 translations of both of these Essays have been published, and 

 they hold an important place in that series of writings which 

 is associated with the names of Weierstrass, Dedekind, Cantor, 

 Frege, Peano, and Russell. Prof. G. B. Mathews (Nature, 191 6, 

 97, 103) gives a short and good account of the mathematical 

 work of Dedekind. 



A biography of Benjamin Williamson (1827 — 191 6) is given 

 in Nature (191 6, 96, 541) ; and biographies and lists of the 

 works of Luciano Orlando (1 877-191 5) and Ruggiero Torelli 

 (1 884-191 5) are given in the Bollettino di bibliografia e storia 

 delle scienze matematiche (191 6, 18, 1 and 11). 



March 16, 191 6, was the seventieth birthday of the great 

 Swedish mathematician, Prof. G. Mittag-Leffler, and he and 

 his wife celebrated the occasion by bequeathing their entire 

 fortune to the foundation of a new international institute for 

 pure mathematics. 



History. — The work of Isaac Barrow is, it has become in- 

 creasingly recognised of late years, very important for the early 

 history of the infinitesimal calculus. J. M. Child (Monist, 191 6, 

 26, 251) gives a short account of the Lectiones Geometrical of 

 1670, and his translation of the work will before very long be 

 published by the Open Court Publishing Company of Chicago 

 and London. 



We must here notice some very able and learned reviews 

 by Prof. R. C. Archibald of books dealing with Napier's 

 Descriptio and Constructio (Bull. Amer. Math. Soc. 191 6, 22, 

 182), mathematical quotation books (ibid. 188), and the history 

 of the construction of the regular polygon of seventeen sides 

 (ibid. 239). 



J. H. Graf (Boll, di bibl. e st. delle sci. mat. 1916, 18, 21) 

 gives the first part of an article on the correspondence between 

 Ludwig Schlafli and the Italian mathematicians. This part 

 contains some letters of Casorati. 



The influence of mathematical conceptions on Berkeley's 

 philosophy, as shown by his attempts to apply mathematical 

 conceptions and methods to problems of nature and morality, is 

 dealt with by G. A. Johnston (Mind, 191 6, 25, 177). Berkeley's 

 pwn important contributions to the logic of the infinitesimal 



