228 Memoir of Mr Gregory, 



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 re- 

 searches already noticed. In some of these he developed cer- 

 tain particular applications of the principles he had laid down 

 in an Essay on the Foundations of Algebra, presented to the 

 Royal Society of Edinburgh in 1838, and printed in the four- 

 teenth volume of their Transactions. I may particularly 

 mention a paper on the curious question of the logarithms of 

 negative quantities, a question which, it is well known, has 

 often been discussed among mathematicians, and which even 

 now does not appear to be entirely settled. 



In 1840, Mr Gregory was elected fellow of Trinity College ; 

 in the following year he became master of arts, and was ap- 

 pointed to the office of moderator, that is, of principal mathe- 

 matical examiner. His discharge of the duties of this office 

 (which is looked upon as one of the most honourable of those 

 which are accessible to the younger members of the Univer- 

 sity) was distinguished by great good sense and discretion. 



In the close of the year 1841, Mr Gregory produced his 

 " Collection of Examples of the Processes of the Differential 

 and Integral Calculus;" a work which required, and which 

 manifests much research, and an extensive acquaintance with 

 mathematical writings. He had at first only wished to super- 

 intend the publication of a second edition of the work with a 

 similar title, which appeared more than twenty-five years 

 since, and of which Messrs Herschel, Peacock, and Babbage, 

 were the authors. Difficulties, however, arose, which pre- 

 vented the fulfilment of this wish, and it is not perhaps to be 

 regretted that Mr Gregory was thus led to undertake a more 

 original design. It is well known that the earlier work exer- 

 cised a great and beneficial influence on the studies of the 

 University, nor was it in any way unworthy of the reputation 

 of its authors. The original matter contributed by Sir John 

 Herschel is especially valuable. Nevertheless, the progress 

 which mathematical science has since made, rendered it desir- 

 able that another work of the same kind should be produced, 



