Notices respecting New Books. 401 



with sodium, the effect in the latter case being evident only 

 at high temperature and increased density. The effect is 

 probably analogous to the similar one which occurs in the 

 case of the iodine vapour in a tube containing helium, 

 excited by the green line of the mercury arc. If the iodine 

 is in a high vacuum the emission spectrum consists of a 

 ssries of 28 members of close doublets. In helium the 

 doublets are weakened and the band spectrum is strongly 

 developed. 



XL. Notices respecting New Books. 



Matrices and Determinoids. By Dr. C. E. Cuxlis. Vol. II. 

 Pp. xxiv + 555. Cambridge: University Press, 1918. 



r PHE first volume of these Readership Lectures at the Uni- 

 -*- versity of Calcutta was published in 1912, and a third 

 volume, " completing the theory of matrices and clearing the 

 way for the applications" (p. xi), is in prospect of publication. 

 This volume is full of elaborate detail, and what may seem to 

 the unsympathetic the monotony of systematic deduction is not 

 relieved for the benefit of lesser mortals by interesting geo- 

 metrical and physical applications or references to th j work of 

 others. Indeed, other persons are not mentioned in this volume 

 with the exception of those — such as Sylvester and Rodrigues — 

 whose names are attached to theorems, and in a short acknow- 

 ledgment on pp. vii-viii of certain books on higher algebra and 

 geometry by Bocher, Heffter and Koehler, Muth, Netto, Veronese, 

 and Whitehead, and papers by Schlafli (1866) and Haripada 

 Datta. 



The absence of applications is at first sight somewhat sur- 

 prising: the author was in the habit of using matrices freely in 

 the solution of problems in algebra, geometry, and applied mathe- 

 matics, and the chief aim of his book is to give a systematic 

 account of certain applications of matrices (p. v). The first 

 volume contained the foundations of a calculus of matrices; an 

 account of the properties of the " determinoid " of a matrix, which 

 becomes the determinant of the matrix when the matrix is square ; 

 an account of the solution of matrix equations of the first degree ; 

 and some other features. This second volume contains those parts 

 of the theory which naturally precede any investigation of the 

 special properties of those (" functional ") matrices whose ele- 

 ments are rational integral functions of a finite number of 

 variables (p. vi). Thus we see that, with regard to that part 

 of Dr. Cullis's w r ork which deals with the applications, the con- 

 stant increase of the theoretical portion has resulted in the 

 applications being driven further back, "though they still remain 

 the ultimate object of the book" (p. v). 



