u6 SCIENCE PROGRESS 



given at Oxford ; and its position, like that of this book, was the 

 showing the possibility and importance of applying to philo- 

 sophical problems certain broad principles of method which 

 have been found successful in the study of scientific questions. 

 Other subjects closely connected with Russell's logical doctrines 

 are discussed in many articles of his in the Mo n is t for 1914 and 

 191 5; that in the number for January 1914 is of particular 

 interest to mathematicians. 



Vol. xvii. of the international journal of scientific sjmthesis 

 Scientia, published in Italy, contains an article by Eugenio 

 Rignano in which mathematical symbolism is studied from 

 a psychological point of view. In the third and last part of this 

 article, mathematics and mathematical logic are compared from 

 this point of view, and, as we should expect if we remember 

 that the aims of symbolism in the two cases are almost exactly 

 opposite and that psychologists hardly ever show any sympathy 

 with or knowledge of the aims of logic, the comparison is not 

 favourable to mathematical logic. 



On the subject of Zeno's exceedingly subtle puzzles about 

 motion, which concern the most vital conceptions of pure 

 mathematics, the American Mathematical Monthly for the present 

 year contains a very thorough study of the history of them 

 through all times. This valuable piece of work is by Prof. 

 Florian Cajori, and is the first detailed paper on the subject that 

 has appeared. 



We will now notice shortly some other work dealing chiefly 

 with the history of mathematics and mathematical physics. The 

 numbers of the Mathematical Gazette which have appeared during 

 191 5 contain the final part of a translation of Prof. Gino Loria's 

 address on " The Achievements of Great Britain in the Realm 

 of Mathematics" ; accounts by W. W. Rouse Ball of the work of 

 (1) Pythagoras, (2) De Morgan ; and the Presidential Address to 

 the Mathematical Association by Sir George Greenhill on 

 " Mathematics in Artillery Science." There are numerous short 

 mathematical notes in this periodical, and the reviews of books 

 are a special source of the Gazette's pride : they are nearly 

 always good. Prof. E. W. Hobson published a series of short 

 lectures on the history of investigations on w in Squaring the 

 Circle (Cambridge University Press, 191 3, 35. net). An interest- 

 ing History of Japanese Mathematics by D. E. Smith and 

 Y. Mikami (Chicago and London, Open Court Publishing 



