RECENT ADVANCES IN SCIENCE 617 



a general biography, a list of all the manuscripts that Gauss 

 left behind him, a history of the publication of the Werke, 

 and an index. 



The latest set of letters from Casorati to Schlafli which 

 J. H. Graf has published (Boll, di bibl. e st. delle sci. mat. 1916, 

 18, 1 13 -21) is of greater mathematical interest than most 

 of the preceding ones. In one letter, Gauss's measure of 

 curvature of surfaces is discussed. 



Emil Lampe communicates (Archiv der Math. (3), 1916,24, 

 193-220, 289-310) some letters written by Charles Hermite 

 to Paul du Bois-Reymond during the years 1875-88. 



The fifth volume of Weierstrass's Mathematische Werke, con- 

 taining his lectures on the theory of elliptic functions, was 

 published at Berlin in 191 5 under the editorship of Johannes 

 Knoblauch. In that year, which was the centenary of Weier- 

 strass's birth (see an address by Lampe in Jahresber. der Deutschen 

 Math.-Ver. 24, 416-38) occurred the death of Johannes 

 Knoblauch (see R. Rothe, ibid. 443-57). Rothe also gives 

 a report (ibid. 439-42) on the present state of the editing of 

 Weierstrass's Werke. 



Logic and Principles of Mathematics. — Henri Dufumier 

 (Rev. de Metaphys. et de Morale, 1916, 23, 623) examines how 

 the calculus of classes in logic has been built up, and attempts 

 to show that it only takes a systematic form if we consider it 

 as a generalisation of the theory of aggregates in mathematics. 

 Dufumier 's object is to show how excellent a thing it is for 

 logic and mathematics, which have developed quite separately, 

 to be inseparable. 



In 191 5 Hugo Dingier, whose name was brought promi- 

 nently before many people by the very laudatory reference to 

 him in the preface of the last edition of Mach's Mechanik, 

 published at Munich a book entitled Das Prinzip der logischen 

 Unabhangigkeit in der Mathematik. References to some reviews 

 of it are given in the Rev. semest. (1916, 24 [2], 79). 



It is now possible to give a more accurate description of 

 the paper of K. G. Hagstrom which was mentioned in the last 

 number of Science Progress (191 7, 11, 453), for the author 

 has kindly sent a copy of it to the present writer. Hagstrom 

 points out that Burali-Forti's antinomy was originally stated 

 for " perfectly ordered classes " which at first he thought were 

 always well-ordered but afterwards recognised were not 



