Notices respecting New Books. 77 



quite completed his thirty-first year. Previously to entering at 

 Trinity College, Cambridge, he had attended classes at the Univer- 

 sity of Edinburgh, where he was a favourite pupil of Professor Wal- 

 lace. He passed the examination for the degree of B. A. at Cambridge 

 in 1 837, and was elected Fellow of Trinity College in 1840. In con- 

 sequence of illness he left Cambridge in the spring of 1843, and never 

 returned. In the brief interval between the first and last of these dates 

 he was actively employed in promoting the mathematical studies of 

 the University of Cambridge. This he did in many ways — partly by 

 lecturing and examining, but chiefly by his writings. He was 

 mainly instrumental in establishing the Cambridge Mathematical 

 Journal, and, excepting a short interval, was its editor from the time 

 of its first appearance till a few months before his death. He con- 

 tributed largely to the Journal ; in fact nearly half the first volume 

 came from his pen, as also did a considerable part of both the second 

 and third volumes. These contributions, in addition to a paper read 

 before the Royal Society of Edinburgh, compose the present volume. 

 The most important are those in which he works out the relations 

 existing between the symbols of operation and those of quantity, and 

 applies his results to the solution of large classes of differential 

 equations. These papers are undoubtedly of very great value, and 

 will be read with pleasure by those who take an historical interest in 

 mathematics. Another class of papers relates to the interpretation 

 of results in symbolical algebra, such as that " On the Impossible 

 Logarithms of Quantities," " On the existence of Branches of Curves 

 in several Planes," &c. Other papers are on detached subjects — 

 "Demonstrations of certain properties of Triangles," " Solutions of 

 some Problems in Transversals," &c. The volume contains thirty- 

 seven papers in all : of these but three have any reference to physics ; 

 viz. one, " On the Sympathy of Pendulums," and another " On the 

 Motion of a Pendulum whose point of Suspension is disturbed," and 

 a " Note on a Problem in Dynamics." The two former Mr. Gre- 

 gory wrote in conjunction with Mr. Archibald Smith. 



It is well known that, besides these articles, Mr. Gregory wrote 

 a collection of " Examples of the Processes of the Differential and 

 Integral Calculus." It maybe added that in this work he embodies 

 the results of his most important papers. At the time of his death 

 he left an unfinished MS. Treatise on Geometry of Three dimen- 

 sions, which was completed and published by Mr. Walton in 1845. 



The present volume is in some sort a companion volume to the 

 * Mathematical and other writings of Robert Leslie Ellis,' published 

 about two years ago, and which we noticed at the time. As in the 

 case of that volume, so of this, Mr. Walton has shown himself a 

 faithful editor. The printing and the general appearance of the 

 volume leave nothing to be desired. Mr. Ellis was an intimate 

 friend of Mr. Gregory, and succeeded him as editor of the Mathe- 

 matical Journal. On his death Mr. Ellis wrote a brief life of 

 him, which appeared in the Mathematical Journal, and is reprinted 

 here. Perhaps, as we are noticing a memorial volume, we may be 

 allowed to make from it the following extract. Mr. Gregory had 

 been aware for a short time before his death " that the end was at 



