482 



NATURE 



{Sept. 20, 1883 



however, not to have been until 1852 that he addressed a 

 memoir to the Royal Society, of which he was elected a 

 Fellow in the same year. 



His mathematical activity during this period was the 

 more surprising, as he was able to devote to these studies 

 only a limited portion of his time. He had been elected 

 a Fellow of Trinity College in 1842; but as he was not 

 willing to take Holy Orders, this was but a temporary 

 provision, for he could only hold his Fellowship for seven 

 years after his Master's degree. It became necessary for 

 him therefore to look out for some profession more re- 

 munerative than mathematics, and very soon after taking 

 his Master's degree he became a pupil of the eminent 

 conveyancer, Mr. Christie. It is said that when offering 

 himself as a pupil he modestly suppressed all mention of 

 his antecedents, and that Mr. Christie was much surprised 

 to find out on cross-examining him that he had to do with 

 a Senior Wrangler and Fellow of Trinity. However this 

 may be, he soon became Mr. Christie's favourite pupil, as 

 indeed was not wonderful in the case of one who possessed 

 a very clear head, immense capacity for work, and the 

 power of throwing his whole mind into the work on which 

 he was at the time engaged. After he was called to the 

 bar he never had occasion to look elsewhere for business, 

 for Mr. Christie was always glad to supply him with as 

 much conveyancing work as he was willing to undertake. 

 I have been told that some of his drafts were made to 

 serve as models for students. But nothing that her 

 wealthy rival had to offer could seduce Cayley into un- 

 faithfulness to his first love, Mathematics. For Mathe- 

 matics he always jealously reserved a due portion of time 

 free from the encroachments of his business relations with 

 Law, and it was during the time of his legal practice that 

 some of his most brilliant mathematical discoveries were 

 made. At last he obtained release from the embarrass- 

 ment of a divided allegiance. By placing Lady Sad- 

 ler's trusts on a new footing and founding the Sadlerian 

 Professorship, his LIniversity was able to invite him 

 to return, and he gladly accepted what was at the time 

 a very modest provision, but which would enable him 

 to give his whole time to the pursuits most congenial 

 to him. Some time after his return to Cambridge his 

 pecuniary position was improved. His College, which 

 on his return had speedily made him an honorary Fellow, 

 after a time reelected him to a foundation Fellowship, 

 necessarily a very rare distinction, since the reelection 

 of an ex-Fellow involves the exclusion of the claims of a 

 younger candidate. Later still, in the course of University 

 legislation about Professorships, the position of the Sad- 

 lerian Professorship was improved. But these things 

 could not have been foreseen at the time that Cayley 

 accepted the office. 



It was in 1863 that, after fourteen years of chamber life 

 in Lincoln's Inn, he married and settled permanently in 

 Cambridge. He never would own to any regret when 

 his friends spoke to him of the prospects of professional 

 advancement which he sacrificed by not remaining at the 

 bar. He knew what mode of life would best promote his 

 own happiness, and he had strength of mind to follow it 

 without troubling his head about the riches or honours a 

 different course might bring. His mathematical work 

 gave him pleasure which he never found in law ; and in 

 his hatred of unnecessary words he was once wicked enough 



to say that the object of law was to say a thing in the greatest 

 number of words, and of mathematics to say it in the 

 fewest. But, jesting apart, the University had no reason 

 to regret the legal training and knowledge which he had 

 acquired during his absence from it. It has much added 

 to his usefulness as a member of the Council of the 

 Senate, where his opinion has carried the greatest weight, 

 and it has enabled him to be particularly useful both to 

 his College and to the University in the drafting of new 

 statutes and in the necessary preliminary deliberations. 

 At the last contested Parliamentary election Cayley pre- 

 sided at one of the three polling places, and gave universal 

 satisfaction, hearing patiently the arguments on both 

 sides on all disputed points, and then promptly making 

 a decision in a few words in such a way as to inspire 

 general confidence. 



But after all it is as a mathematical professor that 

 Cayley is eminently "the right man in the right place." 

 No one could be better fitted to discharge the duties pre- 

 scribed for the Sidlerian Professor, "to explain and teach 

 the principles of pure mathematics, and to apply himself 

 to the advancement of the science." It is seldom that 

 one man so well combines the two qualifications here 

 indicated, viz. power to teach what is known already, and 

 ability to extend the boundaries of knowledge. It con. 

 stantly happens that men of great originality of genius 

 find it irksome to study what has been done by others. 

 And now every department of science has so enlarged its 

 borders that it has not only become impossible for one 

 man to master the whole circle of the sciences ; but even 

 a single department, such as pure mathematics, includes 

 under it so great a variety of subjects that most men are 

 content to be specialists, and, devoting themselves to their 

 favourite topic, are satisfied with a very superficial know- 

 ledge of other branches. Cayley is quite as distinguished 

 for the amount and universality of his reading as for his 

 power of original work, and may fairly count as the most 

 learned mathematician of the present day. I suppose 

 that, if all European mathematicians could be subjected 

 to a tripos competition, no matter who might come out 

 first on the "problem" papers, Cayley would be far 

 ahead in the " book work." And his tastes are so catholic 

 that no form of mathematics comes amiss to him. I re- 

 member how we in Dublin were struck by his proficiency 

 in pure geometry, a subject then much cultivated with us, 

 but which we had been accustomed to look on as too 

 little esteemed at Cambridge. 



This wideness of knowledge has made Cayley invaluable 

 as a mathematical referee. To several scientific societies 

 (the Royal Society, the Mathematical Society, the Royal 

 Astronomical Society, the Cambridge Philosophical So- 

 ciety) he has long been a principal adviser as to the merits 

 of mathematical papers presented for publication, no one 

 being more willing to take the trouble of examining such 

 papers, or being better able to pronounce how much of 

 their contents is new or important. And no one could te 

 more ready and obliging with his advice to private 

 students who have desired to interest him in their inves- 

 tigations, and to be assured by him that no unscrupulous 

 predecessor has plagiarised their discoveries. Repeatedly 

 have foreign mathematicians expressed their surprise at 

 the rapidity with which he has dealt with such inquiries, 

 an answer commonly coming by return of post, probably 



