Memoir of Mr Gregory. 225 



dence in Cambridge, of course in eubordinntion to that which 

 was the end principally in view in his becoming a member of 

 the University, namely, the study of mathematics and natural 

 philosophy. 



He became a bachelor of arts in 1837, having taken high 

 mathematical honours ; more, however, might, we may believe, 

 have been effected in this respect, had his activity of mind 

 permitted him to devote himself more exclusively to the pre- 

 scribed course of study. 



From henceforth he felt himself more at liberty to follow 

 original speculations, and, not many months after taking his 

 degree, turned his attention to the general theory of the com- 

 bination of symbols. 



It may be well to say a few words of the history of this 

 part of mathematics. 



One of the first results of the differential notation of Leib- 

 nitz, was the recognition of the analogy of differentials and 

 powers. For instance, it was readily perceived that 



or supposing the y to be understood^ that 



ta \ m+n^ fd \^ rd V 



Kdi) ~ \dx) \dx) 



just as in ordinary algebra we have a being any quantity, 



This, and one or two other remarks of the same kind, were 



sufficient to establish an analogy between --- the symbol of 



differentiation and the ordinary symbols of algebra. And it 

 was not long afterwards remarked that a corresponding ana- 

 logy existed between the latter class of symbols and that 

 which is peculiar to the calculus of finite differences. It was 

 inferred from hence that theorems proved to be true of com- 

 binations of ordinary symbols of quantity, might be applied by 

 analogy to the differential calculus and to that of finite dif- 

 ferences. The meaning and interpretation of such theorems 

 would of course be wholly changed by this kind of transfer 

 from one part of mathematics to another, but their form 



