i 9 2 SCIENCE PROGRESS 



published at Paris in 191 6 under the editorship of C. Jordan, 

 H. Poincar6, E. Picard, and E. Vessiot. The volume contains 

 three biographical or bibliographical notices and thirty-nine 

 memoirs of dates 1864 to 1876 {Rev. Sem. 191 7, 25 [1], 82. A 

 full account of the volume appears in Bull, des set. math. 191 6, 

 40, 297-8). 



The third volume of the Opere Mathematiche of Luigi 

 Cremona was published at Milano in 191 6. This volume 

 contains a notice of Cremona's life and works. 



An account of the life and work of Ernst Mach, who lived 

 from 1838 to 1916, was given by G. Bavink in the Unterrichts- 

 bldtter fiir Math, und Naturwiss. (191 6, 22, 41-5). We may 

 refer to the short notice given in Science Progress (191 7, 

 11, 616). 



Logic, Principles, and Theory of Aggregates. — Raphael 

 Demos (Mind, 191 7, 26, 188-196) applies to particular negative 

 propositions the treatment which Russell has applied to simple 

 descriptive phrases or incomplete symbols and of which an 

 account is given in the first volume (1910) of Principia Mathe- 

 matica. 



E. V. Huntington (Bull. Amer. Math. Soc. 191 7, 23, 276-80) 

 establishes the " complete independence " — in the sense of 

 E. H. Moore — of each of three different sets of postulates for 

 serial order, due respectively to Vailati (1892), Huntington 

 (1905), and Huntington (a new and convenient set). Hunting- 

 ton also (ibid. 280-2) gives three sets of independent postulates 

 for well-ordered systems, each of these three sets being again 

 " completely independent." 



Huntington (Amer. Math. Monthly, 191 7, 24, 1-16) outlines 

 in a compact form the logical structure of elementary dynamics. 

 The fundamental concepts include " forces, as suggested by the 

 tension and compression of our own muscles," and not mass. 

 In fact, Huntington gives a system of derived units based on 

 force, length, and time, instead of on mass, length, and 

 time, and maintains the practical superiority of his system 

 (cf. ibid. 296-300). 



A. Natucci (Periodico di Mat. 191 6, 13, 220-34) has a paper 

 on mathematical definitions and the concept of equality in 

 logic, philosophy, and mathematics. Besides discussing such 

 subjects as the homogeneity of definitions and definition by 

 abstraction, the logical postulate of Burali-Forti, which comes 



