Notices respecting New Boohs. 



367 



DL 



CQ 



BR 



AQRL +2BCD 



CP 



DM 



AR 



BRPM + 2CAD 



BP 



AQ 



DN 



CPQN +2ABD 



AL 



£M 



CN 



DLMN + 2ABC 



1 



1 



1 



k 



=o, 



and is at once verified by multiplying columns 1, 2, 3 by 

 ^{ghyz' + g'h'y'z), \{hfzal +h> 'fz'x), \(fgxy> '+f'g'x'y) , and 

 subtracting from the last column. 



Thus in the case of any determinant of the fourth order we 

 have, first, a relation involving the coaxials (a), (ab), (abc), 

 &c. symmetrically ; and, second, four different formulas each 

 expressing the determinant in terms of the coaxials. 



Melbourne, July 23, 1897. 



XLVII. Notices respecting New Books. 



Introductory Course in Differential Equations for Students in Classical 

 and Engineering Colleges. By D. A, Murray, Ph.D. (Long- 

 mans, 1897, pp. xv-f 234.) 

 ^HE title sufficiently indicates the aim of the book. Students 

 -*- -who wish for a thorough discussion of the various points which 

 turn up must go to such treatises as those of Boole, Forsyth, and 

 Johnson. To these classics Dr. Murray gives ample references, as 

 well as to numerous other works and original memoirs. The work, 

 which we have read with considerable interest, assumes in the 

 reader little more than a knowledge of the fundamental formula? 

 of integration, and brings iu many practical applications well 

 adapted for the class of students for whom it is intended. The 

 rigorous proofs of many of the theorems are relegated to an 

 appendix to be read when some familiarity with the subject has 

 been acquired. An interesting feature are the numerous historical 

 and biographical notes scattered throughout the text, and there 

 are full indexes of Names and of Subjects which add to its utility. 

 There is a fair number of well selected examples, many of which 

 are worked out. We have not tested these exercises, but in the 

 text we have come across some sixteen only of clerical errors, 

 easily seen to be such : a remarkable result for a first edition of a 

 work of this kind. 



The elementary part of a treatise on the Dynamics of a System of 



Rigid Bodies, being Part I. of a treatise on the whole subject, with 



numerous examples. By E. J. Bouxh, Sc.D.. F.R.S. (London, 



Macmillan, pp. xiv + 424.) 



The sixth edition of a work by Dr. Bouth on a subject which he 



has made so essentially his own needs no recommendation. It is 



sure to be up to date. We are only called upon to note any new 



