Memoir of Mr Gregory. 227 



the analogy, as it was called, of powers, differentials, &;c., 

 might be made available in the solution of differential equa- 

 tions, and of equations in finite differences. 



This idea, however, probably from some degree of doubt as 

 to the legitimacy of the methods which it suggested, had not 

 been fully or dearly developed: it seems to have been chiefly 

 employed as affording a convenient way of expressing solutions 

 already obtained by more familiar considerations. 



To this branch of the subject Mr Gregory directed his at- 

 tention, and from the general views of the laws of combina- 

 tion of symbols already noticed, deduced in. a regular and sys- 

 tematic form, methods of solution of a large and important 

 class of differential equations (linear equations with constant 

 coefficients, whether ordinary or partial) of systems of such 

 equations existing simultaneously, of the corresponding classes 

 of equations in finite and mixed differences; and lastly, of 

 many functional equations. The steady and unwavering ap- 

 prehension of the fundamental principle which pervades all 

 these applications of it, gives them a value, quite independent 

 of that whixjh arises from the facility of the methods of solu- 

 tion which they suggest. 



The investigations of which I have endeavoured to illustrate 

 the character and tendency, appeared from time to time in 

 the Cambridge Mathematiaal Journal. 



In this periodical publication Mr Gregory took much inter- 

 est. He had been active in establishing it, and continued to 

 be its editor, except for a short interval, from the time of its 

 first appearance in the autumn of 1837, until a few months 

 before his death. For this occupation he was for many rea- 

 sons well qualified ; iiis acquaintance with mathemati<jal hter- 

 ature was very extensive, .while his interest in all subjects con- 

 nected with it was not only very strong, but also singularly 

 free from the least tinge of jealous or personal feeling. That 

 which another had done or was about to do, seemed to give 

 him as much pleasure as if he himself had been the author of 

 it, and this even when it related to some subject which his 

 own researches miglit seem to have appropriated. 



This trait, as the recollections of those who knew him best 

 will bear me witness, was intimately connected with his whole 



