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BIOGRAPHICAL NOTICE OF ARTHUR CAYLEY.
astronomers, notably by Pontecoulant, and, in consequence, some hesitation about accept
ance was felt by some English astronomers, perhaps not unnaturally in view of the
severe criticisms expressed. Cayley made an independent investigation of the necessary
approximations, and devised a new method for introducing the variation of the eccen
tricity in question—a method effective perhaps chiefly owing to the instinct and power
with which he carried out the laborious analysis required. The memoir, in which he
embodied his results and which was entitled “ On the secular acceleration of the moon’s
mean motion*,” completely confirmed the value obtained by Adams, and was of substantial
help in settling the controversy.
And, in the last place, the preceding sketch of Cayley’s contributions to mathe
matical science seems to refer, for the most part, only to long memoirs. Yet it must
not therefore be supposed that his shorter papers (which are very numerous) can safely
be neglected. Sometimes he wrote a simple note not so much to convey new results
as to set out his view of some particular theorem; these notes were always fresh and
often suggestive. He was specially gratified when he had obtained a brief solution of
some question, and his quite short papers frequently contain most important results.
For instance, in the brief paperf, “On the theory of the singular solutions of differential
equations of the first order,” he was the first to give a clear exposition of the theory
which in Boole’s book had been left in an imperfect state. He there obtained the
broad essential results of the theory, and it is particularly on his work, and on the
work of Darboux published very soon after Cayley’s, that ulterior researches are based.
What has been said may be sufficient to point out Cayley’s place among the
mathematicians of his time, and to indicate the services he rendered to the science
which he loved so well. But he was more than a mathematician. With a singleness
of aim, which Wordsworth could have chosen for his “ Happy Warrior,” he persevered to
the last in his nobly lived ideal. His life had a significant influence on those who
knew him: they admired his character as much as they respected his genius: and they
felt that, at his death, a great man had passed from the world.
A. R. F.
1 June, 1895.
* C. M. P. voi. m. No. 221 ; Monthly Not. R. A. S. voi. xxn. (1862), pp. 171—231.
t G. M. P. vol. vin. No. 545 ; Messenger of Math. voi. n. (1873), pp. 6—12.
