ELEMENTS OF NATURAL PHILOSOPHY. 325 



familiarity with the facts of nature, without taking advantage of the opportunity 

 of awakening those powers of thought which each fresh revelation of nature is 

 fitted to call forth. 



There is, however, a third method of cultivating physical science, in which 

 each department in turn is regarded, not merely as a collection of facts to be 

 co-ordinated by means of the formulae laid up in store by the pure mathe- 

 maticians, but as itself a new mathesis by which new ideas may be developed. 



Every science must have its fundamental ideas modes of thought by which 

 the process of our minds is brought into the most complete harmony with the 

 process of nature and these ideas have not attained their most perfect form 

 as long as they are clothed with the imagery, not of the phenomena of the 

 science itself, but of the machinery with which mathematicians have been 

 accustomed to work problems about pure quantities. 



Poinsot has pointed out several of his dynamical investigations as instances 

 of the advantage of keeping before the mind the things themselves rather than 

 arbitrary symbols of them ; and the mastery which Gauss displayed over every 

 subject which he handled is, as he said himself, due to the fact that he never 

 allowed himself to make a single step, without forming a distinct idea of the 

 result of that step. 



The book before us shews that the Professors of Natural Philosophy at 

 Glasgow and Edinburgh have adopted this third method of diffusing physical 

 science. It appears from their preface that it has been since 1863 a text-book 

 in then: classes, and that it is designed for use in schools and in the junior 

 classes ha Universities. The book is therefore primarily intended for students 

 whose mathematical training has not been carried beyond the most elementary 

 stage. 



The matter of the book however bears but small resemblance to that of 

 the treatises usually put into the hands of such students. We are very soon 

 introduced to the combination of harmonic motions, to irrotational strains, to 

 Hamilton's characteristic function, &c., and in every case the reasoning is con- 

 ducted by means of dynamical ideas, and not by making use of the analysis 

 of pure quantity. 



The student, if he has the opportunity of continuing his mathematical 

 studies, may do so with greater relish when he is able to see in the mathe- 

 matical equations the symbols of ideas which have been already presented to 

 his mind in the more vivid colouring of dynamical phenomena. The differential 



