MEMOIR OF MR GREGORY. 197 



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

 tion of symbols already noticed, deduced in a regular and 

 systematic 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 apprehension 

 of the fundamental principle which pervades all these applica- 

 tions of it, gives them a value quite independent of that which 

 arises from the facility of the methods of solution which they 

 suggest. 



The investigations of which I have endeavoured to illustrate 

 the character and tendency, appeared from time to time in the 

 Cambridge Mathematical Journal. 



In this periodical publication Mr Gregory took much interest. 

 He had been active in establishing it, and continued to be its 

 editor, except for a short interval, from the time of its first ap- 

 pearance in the autumn of 1837, until a few months before his 

 death. For this occupation he was for many reasons well 

 qualified; his acquaintance with mathematical literature was 

 very extensive, while his interest in all subjects connected 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 

 might 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 

 character, which was in truth an illustration of the remark of 

 a French writer, that to be free from envy is the surest indi- 

 cation of a fine nature. 



To the Cambridge Mathematical Journal, Mr Gregory con- 

 tributed many papers beside those which relate to the researches 

 already noticed. In some of these he developed certain parti- 

 cular applications of the principles he had laid down in an Essay 

 on the Foundations of Algebra, presented to the Eoyal Society 

 of Edinburgh in 1838, and printed in the fourteenth volume of 

 their Transactions. I may particularly mention a paper on the 



