BIOGRAPHICAL NOTICE OF ARTHUR CAYLEY. 
XV 
and this impression 
t, who says :— 
the Senior Wrangler 
; but they were not 
,ty of his disposition 
I won at Cambridge, 
er known ; jokes, and 
novelties to him, and 
without taking much 
e assiduously to work 
Lonours, he could not 
lost intuitive grasp of 
ity for work and his 
called to the Bar on 
business. Mr. Christie 
jicing work as he was 
ng however favourable, 
i subside into a large 
, and he limited the 
ig work that came to 
3 the Bar and devoted 
ation and a substantial 
serve as models. But 
an irresistible impulse 
his chief desire. To 
1 of his time; and he 
livelihood. 
d three hundred papers 
,de some of the most 
ad the majority of his 
which he develops his 
le entirely descriptive), 
of symmetric functions 
with the development 
id his valuable reports 
tapers of these fourteen 
uributions to knowledge; 
¡o some given problem, 
), voi. in. Part II. p. 1067, 
. in [a] settlement, the work 
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 afterwards one of his 
intimate friends), now Professor of Natural Philosophy at Edinburgh. These seem to 
have been the only occasions when he was recalled to Cambridge; and they did not 
require any permanent connexion 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 ■ Croone, a physician and one of the earliest Fellows 
of the Royal Society) had, by her will, dated 25th September, 1701, and proved 6th 
November, 1706, given to the University an estate, which was to be used as an 
endowment of lectureships in algebra at nine of the colleges in Cambridge. These posts 
were duly established. The great developments of analysis, which took place at the end 
of the last century and during the first half of the present century, gradually proved 
that the restriction to algebra prevented the lectureships from being as adequate an 
encouragement to the advancement of mathematics as they were designed to be at the 
time of their establishment. Moreover, the lecturers had ceased to attract undergraduates 
to their lectures: so that the purpose of the foundation was not being fulfilled. Con 
sequently, in 1857, a proposal was made by the Council of the Senate of the 
University that a new direction should be given to the endowment by the establishment 
C. VIII. C