Notices respecting New Books. 395 



peculiar power and symmetry to the dynamics of elliptic space ; but 

 that it did not seem so well suited to the dynamics of Euclidean space. 

 Professor McAulay, in developing a closely allied system applicable 

 to Euclidean space, has found himself obliged to introduce some 

 of the definitions and methods of Grrassmann's Ausdelinungslehre. 

 He confesses that the quaternion analogy was, in his hands at all 

 events, " insufficient to furnish methods for answering various 

 interesting questions that Octonions present." Before proceeding 

 to introduce Grrassmann's notions, the author gives, however, a 

 chapter on physical applications, in which no doubt the power of 

 the octonion method is demonstrated ; but this seems to be at the 

 expense of much of the symmetry of quaternions. At all events, 

 any one familiar with quaternions who tries to work by octonions 

 will have to be constantly on his guard; for although there is 

 a broad analogy between the two, there are important points of 

 departure in the rules of operations. It does not appear what 

 insight octonions (as distinct from quaternions) may bring to the 

 worker in electric and magnetic theory, which bids fair to be in 

 the near future the most fruitful of dynamic studies : but for 

 the study of the general dynamics of a rigid body and of the 

 relations of stress and strain Professor McAulay has provided us 

 with a powerful though not easily handled weapon. 



C. G. Knott. 



Abhandlung uberDynamilc, vohD'Alembert. (Ostwald's Klassiker 



der exakten Wissenschaften, Nr. 106.) Translated and edited by 



Arthur Korn. Leipsic : Engelmann, 1899. 

 Science students in general, and those of Germany in particular, 

 owe a debt of gratitude to Professor Ostwald and his co-workers 

 for the series of classics of which this is the latest volume. 



It is usually difficult, and frequently impossible, for a student to 

 obtain access to the original publications which have in the past 

 directed the course of scientific thought. Our knowledge of them 

 is derived from text-book information, which is itself sometimes 

 indirect ; it is, therefore, always interesting and suggestive to read 

 these classical memoirs. In cases where translation is made into a 

 foreign language some of the freshness of the original is necessarily 

 lost ; this is true of all translations, but more especially in the 

 case of papers written before scientific terminology acquired its 

 present exactness. The modern translated expression may easily in- 

 troduce an idea which was not contemplated by the original author ; 

 or just as easily, by its present restriction of meaning, may fail to 

 convey his thought completely. The translator's task is under 

 these circumstances a Yery difficult one, and Herr Korn is to be 

 congratulated on the successful result of his labour in translating 

 and editing the work of D'Alembert. 



Concerning the memoir itself little need be said, since every 

 student of mechanics is aware that the so-called " D'Alembert's 

 Principle," the discovery of which forms the subject of the treatise, 

 is the foundation-stone of rigid dynamics. J. L. H. 



