Vlll 



liis papers of these fourteen years extend is not more remarkable 

 than the vigour of his contributions to knowledge ; and a reference to 

 them will show that he frequently recurs to some given problem, 

 always adding something to the development. 



In judging of this persistent and unflagging activity, some account 

 ought to be taken of his surroundings. It can hardly be that 

 2, Stone Court, from which many of his papers are dated, proved an 

 inspiration to mathematical research. For part of the time, his 

 friend Sylvester was in London then as an actuary '; and I have 

 heard Cayley describe how Sylvester and he walked round the 

 Courts of Lincoln's Inn discussing the theory of invariants and 

 covariants which occupied (and occasionally absorbed) the attention 

 of both of them during the fifties. And on matters which related to 

 analytical geometry he was in frequent (but formal) correspondence 

 with Salmon ; indeed, the relation that existed between the two men 

 developed ultimately into one of warm friendship and deep mutual 

 regard : its sincerity can be gathered from the spirit animating 

 Salmon's notice of Cayley, published in. ' Nature ' in 1883, at the 

 time when the latter was President of the British Association. But, 

 with special exceptions of the types indicated, his work was so largely 

 of the kind that is called path-breaking that he was bound to do it 

 alone : he did it with a simple unconscious courage and with unfailing 

 resolution. 



It may easily be imagined that his links with life at Cambridge 

 had now become slight. During the earliest of the years spent at 

 the bar, he had returned on a few occasions. In 1848, the year before 

 his call, he was the junior mathematical examiner in the regular 

 annual examinations of Trinity ; in 1849, and also in 1850, he was 

 the senior mathematical examiner in the same examinations. In 

 1851 he was Senior Moderator for the Mathematical Tripos ; one of 

 the wranglers, Lightfoot, becoming subsequently his friend, and his 

 colleague in the University, before going to his great work in the 

 diocese of Durham as Bishop. In 1852 he was Senior Examiner for 

 the Tripos, the senior wrangler of the year being Tait (also after- 

 wards one of his intimate friends), now Professor of Natural 

 Philosophy at Edinburgh. These seem to have been the only occa- 

 sions when he was recalled to Cambridge ; and they did not require 

 any permanent connection with the College or the University. He was 

 settled in London, his allegiance divided between law and mathematics. 



A change, however, in the statutes of the University offered an 

 opportunity for his return to Cambridge ; a professorship of pure- 

 mathematics was established upon an old foundation. Lady Mary 

 Sadleir (who endowed the Croonian Lecture Fund of the Royal 

 College of Physicians of London, and also that of the Royal Society, in 

 memory of her first husband, Dr. William Crooue, a physician and 



