XIV 



Iii America he appears to have been at war with his surroundings 

 from the first. He found nothing sympathetic or inspiring, and the 

 cause of his exit from the country after six months arose from an 

 unfortunate incident with two students in his own class. 



For two or three years after his return from Virginia he appears 

 to have done little work. As remarked by Dr. Halsted there were dis- 

 tinct periods of his life during which he felt much discouraged, and 

 seemed to have no heart for mathematical research. 



In 1844 activity recommenced. He was elected to the post of 

 Actuary to the Legal and Equitable Life Assurance Company. This 

 was a responsible post, particularly at that time when, through mis- 

 management, one of the principal establishments in England had 

 been brought to the brink of ruin. He made constant valuations and 

 acted as check officer and scientific adviser to the directors of this 

 and some other companies for many years, residing for the greater 

 part of the time at 28, Lincoln's Inn Fields. He also accomplished 

 an extraordinary amount of mathematical research. A few titles of the 

 papers now published during this time will give a general idea of the 

 subjects which principally occupied his mind : " On the Dialytic 

 Method of Elimination," " Elementary Researches on the Analysis of 

 Combinatorial Aggregation," " On a discovery in the Theory of 

 Numbers relative to the Equation Ax 3 + By 3 + Cz 3 = Vxyz," "On the 

 Rotation of a Body about a Fixed Point," " Sketch of a Memoir on 

 Elimination, Transformation, and Canonical Forms," " On the 

 Principles of the Calculus of Forms," " On the Expressions for 

 the Quotients which appear in the Applications of Sturm's 

 Method to the discovery of the real Roots of an Equation." A 

 number of these papers refer to the subject now known as the 

 theory of invariants. It rose from its foundations, which had been 

 partially laid by Boole in 1844, under the strong hands of Cayley 

 and Sylvester. The conception of the problem and much of its 

 orderly development may be ascribed to the former, whilst nearly 

 the whole of the nomenclature and a great deal that is now recog- 

 nised as being of capital importance, both as regards initiation and 

 brilliant extension, is due to the latter. During the decade from 

 1845 he established his position as one of the foremost mathema- 

 ticians of Europe. He had the friendship and esteem of such men 

 on the continent of Europe as Lejeune-Dirichlet, Poncelet, 

 Borchardt, Duhamel, Bertrand, Serret, Hermite, Otto Hesse, Peters, 

 Kummer, Richelot, Joachimsthal, Chasles, with many of whom his 

 correspondence was frequent and voluminous. The contemporaries 

 in his own country William Rowan Hamilton, Ivory, De Morgan, 

 Graves, MacCullagh, John Herschel, Babbage, Donkin, Challis, 

 Kelland, Salmon, William Thomson, and others also testified on 

 occasions that they were aware a great mathematical genius had 





