MEMOIR OF MR GREGORY. 199 



in the theory of heat, the conditions relating to the surface of 

 the body whose variations of temperature we are considering, 

 form an essential and peculiar element of the problem; their 

 peculiarity arises from the discontinuity of the transition from 

 the temperature of the body to that of the space in which it is 

 placed. Similarly, in the undulatory theory of light, there is 

 much difficulty in determining the conditions which belong to 

 the bounding surfaces of any portion of ether; and although 

 this difficulty has, in the ordinary applications of the theory, 

 been avoided by the introduction of proximate principles, it 

 cannot be said to have been got rid of. 



The power, therefore, of symbolizing discontinuity, if such 

 an expression may be permitted, is essential to the progress of 

 the more recent applications of mathematics to natural philosophy, 

 and it is well known that this power is intimately connected 

 with the theory of definite integrals. Hence the principal im- 

 portance of this theory, which was altogether passed over in the 

 earlier collection of examples. 



Mr Gregory devoted to it a chapter of his work, and noticed 

 particularly some of the more remarkable applications of definite 

 integrals to the expression of the solutions of partial differential 

 equations. It is not improbable that in another edition he 

 would have developed this subject at somewhat greater length. 

 He had long been an admirer of Fourier's great work on heat, 

 to which this part of mathematics owes so much; and once, 

 while turning over its pages, remarked to the writer, " All 

 these things seem to me to be a kind of mathematical paradise." 



In 1841, the mathematical Professorship at Toronto was 

 offered to Mr Gregory: this, however, circumstances induced 

 him to decline. Some years previously he had been a candidate 

 for the Mathematical Chair at Edinburgh. 



His year of office as moderator ended in October 1842. In 

 the University Examination for Mathematical Honours in the 

 following January, he, however, in accordance with the usual 

 routine, took a share, with the title of examiner, a position 

 little less important, and very nearly as laborious, as that of 

 moderator. Besides these engagements in the University, he 

 had been for two or three years actively employed in lecturing 

 and examining in the College of which he was a Fellow. In 

 the fulfilment of these duties, he shewed an earnest and constant 



