140 Notices respecting New Books. 



A Treatise on the Theory of Determinants, with graduated Sets of 

 Exercises for use in Colleges and Schools. By Thomas Muir, 

 M.A. Macmillan : London, 1882. (Pp. vi + 240.) 



The subject of Determinants is every day coming more and more 

 to the front. As evidence of this we may instance the recent 

 works of Mr. Scott and Mr. ~VV. Thomson, and the chapters in 

 Messrs. Burnside and Panton's 'Theory of Equations.' Students are 

 no longer shut up to the advanced works of the masters in the 

 science nor restricted to the small morsels dealt out in two or 

 three of our algebraical textbooks. 



In Prance M. Dostor has recently brought out his Elements 

 de la Theorie des Determinants avec application a VAlgebre, la 

 Trigonometric et la Geometric analytique dans le plan et dans 

 Vespace ; and in this country Mr. Muir, who has done so much 

 good original work, now puts forth the excellent text-book under 

 notice. "Without going into any lengthened detail, we may say 

 that the Author does not touch upon the Geometrical applications 

 of Determinants ; perhaps he considers that these have been dwelt 

 upon with sufficient fulness elsewhere, and is only anxious to 

 provide his readers with a full Algebraical introductory treatise. 

 The first two chapters dwell at considerable length upon Deter- 

 minants in general ; but the third chapter treats much more 

 concisely of the various forms known as Continuants, Alternants, 

 Symmetric and Skew Determinants, Pfaffians and other Deter- 

 minants. Much of this chapter is the Author's own work ; and 

 the whole of it is very suggestive in its treatment. There is 

 apparently much of discovery still in store for the careful worker 

 in this corner of the mathematical field. Ample practice is 

 furnished for the reader in a capital collection of Exercises, to which 

 answers are appended at the end of the book. The fourth chapter 

 contains a slight historical sketch : this is interesting ; but we are 

 inclined to regret that regard to space prevented Mr. Muir from 

 extending it. However, he has made some amends by the publication 

 in the ' Quarterly Journal of Mathematics ' (Oct. 1881) of a " List 

 of Writings on Determinants " (1693 to 1880), which was originally 

 drawn up for the present work. We have noticed only a few errata 

 and a few obscurities of expression. These can be removed in a 

 second edition, which will no doubt be soon called for. Could not 

 the work then be printed in a form better adapted for the 

 numerous lengthy formulas ? 



