198 MEMOIR OF MR GREGORY. 



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 University) 

 was distinguished by great good sense and discretion. 



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

 1 '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 prevented 

 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 exercised 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 desirable that another work of the 

 same kind should be produced, in which the more recent im- 

 provements of the calculus might be embodied. 



Since the beginning of the century, the general aspect of 

 mathematics has greatly changed. A different class of problems 

 from that which chiefly engaged the attention of the great writers 

 of the last age has arisen, and the new requirements of natural 

 philosophy have greatly influenced the progress of pure analysis. 

 The mathematical theories of heat, light, electricity, and magnet- 

 ism, may be fairly regarded as the achievement of the last fifty 

 years. And in this class of researches an idea is prominent, 

 which comparatively occurs but seldom in purely dynamical 

 enquiries. This is the idea of discontinuity. Thus, for instance, 



