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Special reference should be made to one of Cay ley's astronomical 

 papers. In 1853 Adams had made a new investigation of the value 

 of the secular acceleration of the moon's mean motion, and, taking 

 account of the variation in the eccentricity of the earth's orbit, had 

 obtained a value which differed from that given by Laplace. Unfor- 

 tunately, Adams's result was disputed by some of the great school of 

 French physical astronomers, notably by Pontecoulant, and, in con- 

 sequence, some hesitation about acceptance was felt by some English 

 astronomers, perhaps not unnaturally in view of the severe criticisms 

 expressed. Cayley made an independent investigation of the neces- 

 sary approximations, and devised a new method for introducing 

 the variation of the eccentricity in question a method effective per- 

 haps chiefly owing to the instinct and ppwer with which he carried 

 out the laborious analysis required. The memoir, in which he em- 

 bodied his results and which was entitled ' On the secular acceleration 

 of the moon's mean motion,'* completely confirmed the value obtained 

 by Adaine, and was of substantial help in settling the controversy. 



And, in the last place, the preceding sketch of Cayley's contribu- 

 tions to mathematical 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 questiou, and his quite 

 short papers frequently contain most important results. For 

 instance, in the brief paperf ' On the theory of the singular solu- 

 tions of differential equations of the first order,' he was the first 

 to give a clear exposition of the theory which in Boole's book bad 

 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 Words- 

 worth could have chosen for his ' Happy Warrior,' he persevered to 

 the last iu 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. 



1st June, 1895. 



* ' C. M. P.,' vol. 3, No. 221 ; ' Monthly Not. R.A.S ,' vol. 22 (1862), pp. 171231. 

 t ' C. M. P.,' vol. 8, No. 515; ' Messenger of Math.,' vol. 2 (1873), pp. 612. 

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