XXI 



priority of his results : it is partly owing to his nature. Salmon says 



of him: 



" His motto has always been ' esse quam videri,' and I do not 

 know any one to whom it would be more repulsive to engage in 

 a personal contest by claiming for himself a particle of honour 

 or of money more than was spontaneously conceded. He would 

 be apt to take for his model the patriarch Isaac, who, when the 

 Philistines claimed a well which he had dug, went on and dug 

 another, and when they claimed that, too, went on and dug a 

 third ": 



an exceedingly happy description of the man the tide of whose geniut 



was 



" Too full for sound or foam." 



Some account of his work, some estimate of its character, some 

 indication of the original contributions made by him to his science, 

 may not improperly be given here. It is, of course, impossible to 

 predict what his permanent influence will be upon mathematics, or 

 what opinion coming generations of workers will hold of him : 

 certainly, by his own contemporaries, he was deemed one of the 

 greatest mathematicians the world has seen. Bertrand, Darboux, and 

 Glaisher have compared him to Euler, alike for his range, his 

 analytical power, and, not least, for his prolific production of new 

 views and fertile theories. There is hardly a subject in the whole of 

 pure mathematics at which he has not worked. Some new subjects 

 owe their existence to him ; to others he has made very definite 

 contributions, so that their boundaries have been enlarged often to an 

 enormous extent; there are few upon which he has not left the mark 

 of his genius. 



In several of the notices that appeared at his death he was 

 described as a great explorer. Such he undoubtedly was, but he 

 was more. He not merely discovered new countries but he also 

 opened them up, so that others were able to enter into some possession 

 of those regions without undergoing the difficulties that he had over- 

 come. And if the metaphor may be carried further, he had the 

 restlessness of the explorer : he could not long remain satisfied with 

 an achievement concluded, but must try his fortune again and else- 

 where. 



Varying opinions have been expressed as to Cayley's style ; the 

 variations are largely due to preconceived views of what a mathe- 

 matical paper should be. It certainly is not easy to skim one of his 

 papers ; any attempt to do so leads to an inadequate estimate of 

 what it usually establishes. It is not difficult to read one of his papers, 

 oven to grasp the contents well, provided proper care be devoted to it, 

 because difficulties that occur are completely solved, and nothing lies 



