XVI 



in the same way as the names of many scientific men, engaged in 

 other lines of inquiry, are known. Once, however, in his life cir- 

 cumstances brought him prominently into notice. In 1883, he was 

 President of the British Association for the Advancement of Science, 

 the meeting being held at Southporfc ; and, in that capacity at the 

 opening of the meeting, he had to deliver a formal address, an 

 abstract of which appeared as usual in the leading newspapers of the 

 country. 



In the early days of the Association, the President's address 

 frequently reviewed the whole field of science ; but as knowledge has 

 developed, a tendency has set in, according to which each later 

 President has confined himself more particularly to those matters 

 within whose range he is an authority. And, subject to this restric- 

 tion, it is hoped that the address may be legitimately popular. 

 There have been critics of presidential addresses prepared to assert 

 that science was sacrificed to popularity; there have been immense 

 audiences convinced that popularity was sacrificed to science. Taken 

 together, the presidential addresses, some severe and others popular, 

 form an interesting series of reviews of the successive stages in 

 scientific achievements. 



Cayley's address belonged to the severely scientific class. From 

 the nature of his subject the progress of mathematics, more particu- 

 larly of pure mathematics it was bound to have this character. 

 Few of the members of a regular Association audience have more 

 than a slight acquaintance with pure mathematics ; and, conse- 

 quently, it is impossible to deliver to such a gathering an address 

 which, in a reasonable time, can give them any real idea of the con- 

 dition or the progress of the science. Cayley felt this and confessed 

 to the feeling in a passage which is perhaps the best known in the 

 address : 



" It is difficult to give an idea of the vast extent of modern 

 mathematics. The word ' extent ' is not the right one : I mean 

 extent crowded with beautiful detail not an extent of mere 

 uniformity such as an objectless plain, but of a tract of beautiful 

 country seen at first in the distance, but which will bear to be 

 rambled through and studied in every detail of hillside and 

 valley, stream, rock, wood, and flower. But, as for everything 

 else, so for a mathematical theory beauty can be perceived but 

 not explained." 



But he also felt that the respect due to the Association requires its 

 President to deal with that branch of science about which, as he 

 knows it best, he is best fitted to tell them, so that different subjects 

 may thus in turn be brought before successive meetings. 



