Miscellaneous Intelligence. 267 



and the symbolic notation and Aronholdt's operator are not even 

 mentioned. A short chapter later in the book considers some of 

 the simplest rational invariants. 



It is a pleasure to find Sylvester's dialytic method of elimina- 

 tion developed in a careful manner. There is no doubt that this 

 is the simplest and the most effective method to determine the 

 existence of common roots of equations, but apart from the treat- 

 ment in Mansion's Theorie des Determinants, one does not find' 

 the method given the place in the treatises that it deserves. 



The most suggestive and important chapters of the book are 

 the last three, in which the theory of elementary divisors is for 

 the first time made completely accessible to students of geome- 

 try. The fundamental memoirs of Weierstrass, Kronecker and 

 Frobenius are not adapted for a rapid acquisition of the theory 

 and the book of Muth on Elementarteiler can scarcely be called 

 a successful exposition. The only other development of the sub- 

 ject is found in a little tract of Bromwich which is hardly ade- 

 quate algebraically. Professor Bocher's treatment contains all 

 the virtues that the other writers lack. His development follows 

 that of Frobenius though his reduction of a matrix to a normal 

 form in which the elementary divisors are displayed is that of 

 Kronecker. Not enough special cases are included to obscure 

 for a moment the aim of the discussion, which is appropriately 

 closed by an actual enumeration of all classes of collineations and 

 families of quadratic forms. 



An important feature of the book is the large number of exer- 

 cises, the solution of which will ensure a thorough comprehension 

 of the subject. The students of algebra and higher geometry are 

 to be congratulated on the appearance of a work, that to such a 

 marked degree clarifies and simplifies what has hitherto been one 

 of the most difficult subjects in which to obtain a satisfactory 

 perspective. h. e. hawkhs. 



2. Observations simultanees de la Surface de Jupiter • 

 reunis par M. Jean Mascart. Pp. 70. Paris, Societe Astronomique 

 de France. — At the suggestion of M. Jean Mascart of the Paris 

 Observatory, and with the sanction of Flammarion, thirty-six 

 observers residing in Eastern Europe, England and Northern 

 Africa undertook to make a telescopic study of the planet 

 Jupiter dm - ing the month of January 1906, subject to certain 

 rules of procedure drawn up by Mascart — those of prime 

 importance being that the observations should be taken simul- 

 taneously and that each observer should record his results as 

 soon as possible and according to a prescribed form. 



The days were from Jan 2 to 20 and the time, 8 p. m. Paris. 

 172 observations were obtained, each accompanied by a draw- 

 ing, — the least number on any night being 5, the greatest 17 and 

 the average 9. 



The report forms a pamphlet of 70 pages with plates showing 

 separately for each night all the drawings made on that night. 

 The results are analyzed by Mascart for each night — separately, 

 with a resume of all the nights, which is the essentially valuable 



