Notices respecting New Boohs. 429 



Ihe Theory of Determinants in the Historical Order of Development. 

 By Thomas Mum, C.M.G., LL.D., F.R.S. Vol. II. The 

 Period 1841 to 1860. Macmillaii & Co. Limited ; London, 1911. 



The care and thoroughness which characterized the earlier volume 

 of this important history of Determinants is evidenced also in the 

 second volume, which brings the history down to the year 1860. 

 Of the many writers whose works are discussed, Cayley, Sylvester, 

 and Brioschi are the most frequently cited; and of these Cayley 

 Mas the one who gave the great impetus to the study of deter- 

 minants, due, as Dr. Muir expresses it, to " the choice of an 

 exceedingly apt notation and the masterly manner in which he put 

 the functions to use." The method adopted in the first volume of 

 treating special kinds of determinants in appropriate chapters is 

 followed also here, there being fifteen chapters devoted to General 

 Determinants, Axisymmetric Determinants, Alternants, Eecur- 

 rents, Wronskians, Jacobians, Skew Determinants, Hessians, 

 Circulants, and so on ; while in chapter xvi. some less common 

 special forms are considered. Apart from the value of the book 

 as indicating the historic lines along which the subject developed, 

 Dr. Muir's own critical and explanatory remarks are always most 

 interesting and elucidating. The book should be in every mathe- 

 matical library, and students should be encouraged to read it along 

 with their more systematic studies of the method. They will 

 learn a great deal else besides. 



High Temperature Gas Thermometry. By Arthur L. Day and 

 B. B. SosmaN ; with an investigation of the metals, by E. T. 

 Allex. Carnegie Institution of Washington. 



This is a valuable summary of a series of investigations intended 

 to extend the absolute determinations of temperatures above 1200°, 

 using a constant volume nitrogen thermometer with a platinum- 

 rhodium bulb. The conditions of the success of the investigation 

 are very thoroughly detailed. The book should be in the hands 

 of all those engaged in high temperature work. 



Tables Annuelles de Constantes et Donnees numeriques de Chimie, de 

 Physique et de Technologic. Published by the International 

 Committee nominated by the Vllth Congress of Applied 

 Chemistry held in London. Vol. I. ; pp. xxix + 727. Paris : 

 Gauthier-Villars, 1912. 



This fine volume of data comprises those only which were pub- 

 lished during the year 1910. It is intended to issue a volume 

 yearly, each volume to contain only one year's data. To carry out 

 this great scheme it has been necessary to enrol a large number 

 of compilers, who have reduced to order the data obtained for 

 them by a still larger number of abstractors. The general editor 

 is Dr. Charles Marie of Paris ; we must congratulate him on the 

 successful way in which the first fruits of his labours, as presented 

 here, have been reached. 



The issue of such a work as this is bound to facilitate the search 



Phil. Mag. S. 6. Vol. 25. No. 147. March 1913. 2 G 



