BIOGRAPHICAL NOTICE OF ARTHUR CAYLEY. 
xiii 
3 Masaccio, Giovanni 
hey proved a delight 
bile he remained in 
d no formal lecturing 
>ils. The leisure that 
pleasant, of uses, in 
'graduate that Cayley 
more than fifty years 
pure mathematics as 
ical activity. By the 
d been set free from 
had proved effective 
)f analytical methods 
l was the foundation 
'ory and Leslie Ellis, 
bion open to mathe- 
I; and young writers, 
it well have hesitated 
rrd. The new journal 
pportunity, previously 
oved a great stimulus 
Only four volumes of 
ne of the Cambridge 
! present time, under 
Though the oppor- 
both in England and 
y ago, the undoubted 
e of the two young 
earliest paper, written 
late—it was the year 
the results are not 
p estigations are worthy 
1 care the Mécanique 
il memoirs in the two 
These achievements of 
plished now and were 
.es, il faut étudier les 
It was as certainly one of the characteristics of Cayley to find a stimulus to new 
developments in the main ideas of other writers as it was one of his characteristics 
to be able to follow out his own ideas with the insistent unwearying patience of an 
investigator creating a new work complete. And it is interesting to see how this 
faculty of receiving inspiration reveals itself from the beginning of his career. 
Once free from the necessity of preparing for his Tripos and his Fellowship 
examination, he was able to throw himself into the work of production. His activity 
may be estimated from the fact that he produced three papers in 1842, eight in 
1843, four in 1844, and thirteen in 1845. Moreover, these papers deal with a great 
variety of subjects. Thus he makes his first investigations in the numerative calculus 
of plane curves : he initiates his discussions about geometry of n dimensions : he 
founds the theory of invariants and covariants : and he elucidates the connexion between 
doubly-infinite products and elliptic functions. Some of these early papers are now 
classical ; and the briefest inspection of them is sufficient to reveal the suggestiveness 
and the easy strength of the young mathematician who was not yet in his twenty-fifth 
year. 
Even by this date the opportunities of publication in England had become 
inadequate to his needs. Curiously enough, he does not appear to have sent any paper 
to the Royal Society until the year 1852, when Sylvester communicated the “Analytical 
Researches connected with Steiner’s Extension of Malfatti’s Problem* ” to that Society. 
Later in the same year, Cayley was elected a Fellow of the Society, and thereafter many 
of his papers appear in its Philosophical Transactions. Before 1852, there were few 
journals either at home or abroad which did not receive communications from him : and 
even in the quite early years of his researches, several of his papers, written in French, 
appeared in Liouville’s journal and in Crelle’s journal. As societies and journals grew 
in number, so the area over which his papers spread became ever wider. 
At first, after winning his Trinity Fellowship, he remained at Cambridge, and his 
time must then have been largely at his own disposal. This freedom, in his circum 
stances, could last for only a limited time because, unless he either entered holy 
orders or devoted himself to teaching in some permanent post (if obtainable) in the 
College, the Fellowship could be held for not more than seven years after his M.A. 
degree—a period that would expire in 1852. He was unwilling to take holy orders— 
not that there was any religious obstacle in his way, for he was not harassed either 
by philosophical doubts or critical difficulties. His simple reason for remaining a 
layman was that, though devout in spirit and an active Churchman, he felt no 
vocation for the sacred office. 
In consequence, it became necessary to choose some profession. Cayley selected 
the law, left Cambridge in 1846, entered at Lincoln’s Inn, and became a pupil of 
the famous conveyancer, Mr. Christie. A story of their first interview, that Mr. Christie 
used to tell in after years, is an illustration of the modesty and the lack of self- 
* Cayley’s Collected Mathematical Papers, vol. ii. No. 114. Subsequent references to this series will be 
made in the form C. M. P.